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GATE Exam 2023 Humanities & Social Sciences (XH) Question Paper With Answer Key

August 9, 2023August 9, 2023 by suresh84

GATE-2023

XH : Humanities & Social Sciences

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

3. Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll of the dice and a ‘4’ on the second roll?

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that suprisingly none of the students from the Department of Human Sciences had completed the registration process.

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

We tend to think of cancer as a ‘modern’ illness because its metaphors are so modern. It is a disease of overproduction, of sudden growth, a growth that is unstoppable, tipped into the abyss of no control. Modern cell biology encourages us to imagine the cell as a molecular machine. Cancer is that machine unable to quench its intial command (to grow) and thus transform into an indestructible, self-propelled automaton.

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is ________.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

Reasoning and Comprehension (XH-B1)

XH-B1: Q.11 – Q.17 Carry ONE mark Each

11. Which word below best describes the idea of being both Spineless and Cowardly?

(A) Pusillanimous

(B) Unctuous

(D) Reticent

Answer: (A)

12. Choose the right preposition to fill up the blank:

The whole family got together ___ Diwali

(A) of

(B) at

(D) till

Answer: (B)

13. Select the correct option to fill in all the blanks to complete the passage:

The (i) _______ factor amid this turbulence has been the (ii) ________ of high-octane, action-oriented films such as RRR, K.G.F: Chapter 2 and Pushpa from film industries in the south of the country. Traditionally, films made in the south have done well in their own (iii) _________. But increasingly, their dubbed versions have performed well in the Hindi heartland, with collections (iv) ________ those of their Bollywood counterparts.

(A) (i) disheartening (ii) failure (iii) channels (iv) matching

(B) (i) redeeming (ii) outperformance (iii) geographies (iv) eclipsing

(D) (i) humbling (ii) bombing (iii) theatres (iv) falling behind

Answer: (B)

14. The following passage consists of 6 sentences. The first and sixth sentences of the passage are at their correct positions, while the middle four sentences (represented by 2, 3, 4, and 5) are jumbled up.

Choose the correct sequence of the sentences so that they form a coherent paragraph:

(1) Most obviously, mobility is taken to be a geographical as well as a social phenomenon.

(2) Much of the social mobility literature regarded society as a uniform surface and failed to register the geographical intersections of region, city and place, with the social categories of class, gender and ethnicity.

(3) The existing sociology of migration is incidentally far too limited in its concerns to be very useful here.

(4) Further, I am concerned with the flows of people within, but especially beyond, the territory of each society, and how these flows may relate to many different desires, for work, housing, leisure, religion, family relationships, criminal gain, asylum seeking and so on.

(5) Moreover, not only people are mobile but so too are many ‘objects’.

(6) I show that sociology’s recent development of a ‘sociology of objects’ needs to be taken further and that the diverse flows of objects across societal borders and their intersections with the multiple flows of people are hugely significant.

(A) 3, 2, 5, 4

(B) 2, 3, 4, 5

(D) 4, 2, 5, 3

Answer: (B)

15. The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

(A) -0.25%

(B) 0%

(D) 10.25%

Answer: (A)

16. The words Thin: Slim: Slender are related in some way. Identify the correct option(s) that reflect(s) the same relationship:

(A) Fat: Plump: Voluptuous

(B) Short: Small: Petite

(D) Fair: Dark: Wheatish

Answer: (A, B)

17. A pandemic like situation hit the country last year, resulting in loss of human life and economic depression. To improve the condition of its citizens, the government made a series of emergency medical interventions and increased spending to revive the economy. In both these efforts, district administration authorities were actively involved.

Which of the following action(s) are plausible?

(A) In future, the government can make district administration authorities responsible for protecting health of citizens and reviving the economy.

(B) The government may set up a task force to review the post pandemic situation and ascertain the effectiveness of the measures taken.

(C) The government may set up a committee to formulate a pandemic management program to minimize losses to life and economy in future.

(D) The government may take population control measures to minimize pandemic related losses in future.

Answer: (B, C)

XH-B1: Q.18 – Q.26 Carry TWO marks Each

18. Six students, Arif, Balwinder, Chintu, David, Emon and Fulmoni appeared in the GATE-XH exam in 2022. Balwinder scores less than Chintu in XH-B1, but more than Arif in XH-C1. David scores more than Balwinder in XH-C1, and more than Chintu in XH-B1. Emon scores less than David, but more than Fulmoni in XH-B1. Fulmoni scores more than David in XH-C1. Arif scores less than Emon, but more than Fulmoni in XH-B1. Who scores highest in XH-B1?

(A) Fulmoni

(B) Emon

(D) Chintu

Answer: (C)

19. Select the correct relation between E and F.

(A) E > F

(B) E < F

(D) E < -F

Answer: (B)

20. A code language is formulated thus:

Vowels in the original word are replaced by the next vowel from the list of vowels, A-E-I-O-U (For example, E is replaced by I and U is replaced by A). Consonants in the original word are replaced by previous consonant (For example, T is replaced by S and V is replaced by T).

Then how does the word, GOODMORNING appear in the coded language?

(A) HUUFNUSPOPH

(B) FIICLIQMEMF

(D) HEEDATTACRH

Answer: (C)

21. The stranger is by nature no “owner of soil” — soil not only in the physical, but also in the figurative sense of a life-substance, which is fixed, if not in a point in space, at least in an ideal point of the social environment. Although in more intimate relations, he may develop all kinds of charm and significance, as long as he is considered a stranger in the eyes of the other, he is not an “owner of soil.” Restriction to intermediary trade, and often (as though sublimated from it) to pure finance, gives him the specific character of mobility. If mobility takes place within a closed group, it embodies that synthesis of nearness and distance which constitutes the formal position of the stranger. For, the fundamentally mobile person comes in contact, at one time or another, with every individual, but is not organically connected, through established ties of kinship, locality, and occupation, with any single one.

What assumptions can be made about the stranger from the passage above?

(A) The stranger can become an owner of soil through developing all kinds of charm in more intimate relations.

(B) The stranger cannot become an owner of soil either in the physical or psychological sense.

(D) The stranger might become an owner of soil in the physical sense but not in the psychological

Answer: (B)

22. L is the only son of A and S. S has one sibling, B, who is married to L’s aunt, K. B is the only son of D. How are L and D related?

Select the possible option(s):

(A) Grandchild and Paternal Grandfather

(B) Grandchild and Maternal Grandfather

(D) Grandchild and Maternal Grandmother

Answer: (B, D)

23. Five segments of a sentence are given below. The first and fifth segments are at their correct positions, while the middle three segments (represented by 2, 3, and 4) are jumbled up. Choose the correct order of the segments so that they form a coherent sentence:

(1) Consumed multitudes are jostling and shoving inside me

(2) and guided only by the memory of a large white bedsheet with a roughly circular hole some seven inches in diameter cut into the center,

(3) clutching at the dream of that holey, mutilated square of linen, which is my talisman, my open-sesame,

(4) I must commence the business of remaking my life from the point at which it really began,

(5) some thirty-two years before anything as obvious, as present, as my clock-ridden, crime-stained birth.

(A) 2 – 3 – 4

(B) 3 – 2– 4

(D) 4 – 3 – 2

Answer: (A)

24. “I told you the truth,” I say yet again, “Memory’s truth, because memory has its own special kind. It selects, eliminates, alters, exaggerates, minimizes, glorifies, and vilifies also; but in the end it creates its own reality, its heterogeneous but usually coherent versions of events; and no sane human being ever trusts someone else’s version more than his own.”

What are the different ways in which ‘truth’ can be understood from the passage?

(A) Truth is what can be verified by hard empirical evidence.

(B) Truth is based on what can be perceived by the senses.

(D) Truth is contingent on the observer and can only be partial.

Answer: (C, D)

25. A firm needs both skilled labour and unskilled labour for the production of cloth. The wage of skilled labour is Rs. 40,000 per month, and that of unskilled labour is Rs. 15,000 per month. The total wage bill of the firm for the production of cloth is Rs. 23,75,000 in a month for 100 labour. How many skilled labour are employed by the firm (in Integer)?

Answer: (35 to 35)

26. Select the odd word and write the option number as answer:

(1) Lek (2) Zloty (3) Diner (4) Drachma (5) Real

Answer: (3 to 3)

Economics – C1

XH-C1: Q.27 – Q.44 Carry ONE mark Each

27. An individual is endowed with income of Rs. 142 and has the utility function U(x₁, x₂) = x₂(x₁ + 1), where x₁ ≥ 0, x₂ ≥ 0. The unit price of x₁ is Rs. 2 and the unit price of x₂ is Rs. 3. The utility maximizing bundle is

(A) x₁ = 35, x₂ = 20

(B) x₁ = 30, x₂ = 24

(D) x₁ = 30, x₂ = 20

Answer: (C)

28. The International Monetary Fund (IMF) began operations in the year

(A) 1942

(B) 1947

(D) 1940

Answer: (MTA)

29. According to the Working Group on Money Supply: Analytics and Methodology of Compilation (1998) constituted by the Reserve Bank of India (RBI), which of the following is NOT a component of the new monetary aggregate NM1 ?

(A) Currency with the public

(B) Demand deposits with the banking system

(D) ‘Other’ deposits with the RBI

Answer: (C)

30. Stagflation is a situation when

(A) both unemployment and inflation are low

(B) both unemployment and inflation are high

(D) unemployment is low but inflation is high

Answer: (B)

31. Consider the Keynesian consumption function C = α + βY, where C is the aggregate consumption, Y is the aggregate income, α is a constant (α > 0), and β is the marginal propensity to consume (0 < β < 1). Then, the average propensity to consume is

(A) α

(B)

(D)

Answer: (B)

32. An analyst regressed Y on X₁ and X₂. If she later noticed that X₁ = 5X₂, then which of the following assumptions of the classical linear regression model was violated?

(A) Homoscedasticity

(B) No Perfect Multicollinearity

(D) Linearity in parameters

Answer: (B)

33. Which of the following is NOT an example of non-tariff barriers?

(A) Voluntary export restraint

(B) A procurement law directing a government to buy domestically made products unless comparable foreign made products are substantially cheaper.

(D) An antidumping law

Answer: (D)

34. Among the following, who first proposed that internal government debt does not create a burden for the future generation?

(A) N. Gregory Mankiw

(B) Martin Feldstein

(D) A. P. Lerner

Answer: (D)

35. Which of the following is an example of direct tax?

(A) Sales tax

(B) Customs duty

(D) Excise tax

Answer: (C)

36. In the context of endogenous growth theory, the Nobel laureate Paul Romer emphasized that “ideas” are

(A) non-rival

(B) rival with medium degree of excludability

(D) rival with low degree of excludability

Answer: (A)

37. In the Human Development Index (HDI), the longevity is measured by

(A) child survival rate

(B) healthy life expectancy

(D) life expectancy at birth

Answer: (D)

38. Which of the following statements is correct about the Fourteenth Finance Commission?

(A) The Commission was chaired by Dr. C. Rangarajan.

(B) The Commission recommended achieving 90 percent metering of electricity by the end of the year 2012.

(D) The Commission was mandated to make recommendations for the period 2010-2015.

Answer: (C)

39. Many scholars consider the study conducted by Dandekar and Rath in the 1960s as the first systematic assessment of poverty in independent India. Which option from the following is NOT correct about the study?

(A) The study used the data on monthly per capita consumption expenditure (MPCE) from the 1960-61 round of the National Sample Surveys.

(B) The study used the identical calorie norm for rural and urban areas.

(D) The study used the same poverty line for all states.

Answer: (C)

40. Which of the following statements is/are correct about the Pradhan Mantri Kaushal Vikas Yojana (PMKVY)?

(A) It has been a flagship scheme of the Ministry of Education.

(B) It was launched in the year 2010.

(D) One of the objectives of PMKVY has been to enable a large number of Indian youth to take up industry-relevant skill training.

Answer: (C, D)

41. Which of the following is/are used for testing the assumption of normality?

(A) Shapiro-Wilk test

(B) Breusch-Godfrey test

(D) Park test

Answer: (A, C)

42. Suppose Amar borrows Rs. 1000 from Ujala. After one year, Ujala wants Rs. 1100 back from Amar. The yield to maturity in percent (%) on this borrowing is _______ (round off to one decimal place).

Answer: (10.0 to 10.0)

43. A 250 ml bottle of mango juice costs USD 4 in the United States. If the exchange rate is 0.02 USD per Rupee, then the cost of the same bottle of mango juice in Rupees would be _______ (in integer).

Answer: (200 to 200)

44. The following table provides population information for different age groups in 2010 and 2017.

The percentage change in old-age dependency ratio from 2010 to 2017 is _______ (round off to two decimal places).

Answer: (15.00 to 17.00)

XH-C1: Q.45– Q.65 Carry TWO marks Each

45. A firm in a market with perfect competition has the following total cost (TC) function: TC(Q) = a + b(Q)

where Q is the quantity produced by the firm, 𝑎 is the fixed cost and b(Q) is the variable cost. What will happen if the fixed cost increases?

(A) In the short-run, the firm’s Average Variable Cost (AVC) curve will shift upwards.

(B) In the short-run, the firm’s Average Total Cost (ATC) curve will shift upwards.

(D) In the short-run, the firm’s Marginal Cost (MC) curve will shift upwards.

Answer: (B)

46. The emission of greenhouse gases is an example of “bads” that are

(A) rival and excludable

(B) non-rival and excludable

(D) non-rival and non-excludable

Answer: (D)

47. Consider a closed-economy IS-LM model. The IS and LM equations are

where Y is the output, C is the consumption (C′ > 0), I is the investment (I′ < 0), z ≡ i – π^e, i is the nominal interest rate, π^e is the expected inflation, is the government purchases, is the fixed real money balances, and k and l are positive constants.

Suppose everyone in the economy suddenly expects the inflation to rise in the future. Assuming that the LM curve remains unchanged, what will happen in the short-run?

(A) Equilibrium Y increases.

(B) Aggregate demand remains unchanged.

(D) Aggregate demand shifts down.

Answer: (A)

48. Consider the following simultaneous equations model:

Y_t = β₁ + β₂X_t + β₃X_{t – 1}+ β₄Z_t + μ₁t (1)

Z_t = δ₁ + δ₂Y_t + δ₃W_t + μ_2t (2)

Before estimating the above model, a researcher performed the test of identification using order and rank conditions, and found that equation (2) is over identified. Then, which of the following methods is appropriate to estimate equation (2) ?

(A) Two-Stage Least Squares

(B) Indirect Least Squares

(D) Ordinary Least Squares

Answer: (A)

49. An income tax system is considered as progressive if the average tax rate rises with income. Consider an income tax schedule: T = p + t Y, where T denotes the tax liability, p is a constant, 𝑡 is the constant marginal tax rate, and Y is the income. For this tax schedule to be progressive, the value of p

(A) must be positive

(B) must be negative

(D) can be any value except zero

Answer: (B)

50. Match the following:

(A) I → P ; II → Q ; III → R ; IV → S

(B) I → P ; II → S ; III → Q ; IV → R

(D) I → S ; II → P ; III → R ; IV → Q

Answer: (B)

51. Consider two countries, India and Bangladesh, and two goods, Glass Bottle and Ceramic Plate, with labour requirements of production for a unit of each good given below:

Which of the following options is/are correct?

(A) India has an absolute advantage in Glass Bottle production and a comparative disadvantage in Glass Bottle production.

(B) India has an absolute advantage in Ceramic Plate production and a comparative disadvantage in Ceramic Plate production.

(C) India has an absolute advantage in Ceramic Plate production and a comparative disadvantage in Glass Bottle production.

(D) India has an absolute advantage in Glass Bottle production and a comparative disadvantage in Ceramic Plate production.

Answer: (A, C)

52. Suppose the own price elasticity of demand and income elasticity of demand are given by e_p and e_I, respectively. The subscript p represents own price of a good and the subscript I represents the income of the consumer. Identify the correct statement(s) from the following.

(A) If 1 < e_p < ∞, the demand is price inelastic.

(B) Luxury goods are more price inelastic and the necessities are price elastic.

(D) If 0 < e_p < 1, the demand is price elastic.

Answer: (C)

53. Let π^e be the expected inflation rate, 𝑖 be the nominal interest rate and r be the real interest rate. Which of the following statements is/are correct?

(A) For small values of r and π^e, r ≈ i – π^e

(B) When real interest rate is low, there are greater incentives to borrow and fewer incentives to lend.

(D) If i = 8% and π^e = 10%, then r is approximately (+) 2%.

Answer: (A, B, C)

54. Which of the following models explain(s) the upward-sloping aggregate supply curve in the short-run?

(A) Sticky-wage model

(B) Worker-misperception model

(D) Solow model

Answer: (A, B, C)

55. Consider a Mundell-Fleming model for a small open economy with perfect capital mobility. The goods market equation is

Y = C(Y) + I(r*) + G + NX(e)

where 𝑌 is the output, 𝐶 is the consumption (C′ > 0), I is the investment (I′ < 0), G is the government purchases, and NX is the net exports (NX′ < 0), r∗ is the fixed world interest rate, and e is the exchange rate.

The money market equation is

where M is the money supply, is the fixed price level, and k and l are positive constants.

Which of the following policies is/are ineffective (i.e., have no impact on income) in the short-run?

(A) Expansionary fiscal policy under floating exchange rate

(B) Expansionary monetary policy under floating exchange rate

(D) Expansionary monetary policy under fixed exchange rate

Answer: (A, D)

56. In the context of Balance of Payments accounting, which of the following transactions is/are NOT recorded under the Current Account?

(A) Merchandise trade

(B) Unilateral transfer payments

(D) Purchase of foreign currency by the central bank

Answer: (C, D)

57. The demand and supply functions for a commodity are given by:

D(p) = 10 – 2p and S(p) = −2 + p

where D(p) and S(p) are the quantity demanded and supplied, respectively, and p (in USD) is the unit price of the good.

If the government sets a price ceiling of USD 3 per unit, then the increase in consumer surplus (in USD) is _______ (round off to two decimal places).

Answer: (0.71 to 0.79)

58. A duopoly faces the inverse market demand function p = 120 − Q, where p is the unit price (in Rs.) of the good being sold by firms A and B, and Q is the total output. Firm A has a constant marginal cost of Rs. 20, which is exactly half of firm B’s constant marginal cost. There is no fixed cost for both the firms. If there exists a Cournot-Nash equilibrium, Q is _______ (in integer).

Answer: (60 to 60)

59. Consider the following short-run cost function:

C(q) = 10q³ – 80q² + 300q + 50

At the minimum average variable cost (AVC), the value of marginal cost (MC) is ______ (in integer).

Answer: (140 to 140)

60. Consider the Keynesian Cross Model with a linear consumption function and a zero tax, where the government purchase is Rs. 100 and the equilibrium income is Rs. 1300. If the government purchase is increased to Rs. 125, the equilibrium income increases to Rs. 1400. Using the given information, the marginal propensity to consume is _______ (round off to two decimal places).

Answer: (0.71 to 0.79)

61. Using the Ordinary Least Squares (OLS) method, a researcher estimated the relationship between initial salary (S) of MBA graduates and their cumulative grade point average (CGPA) as

where The standard errors of are 921.79 and 70.01, respectively.

The t-statistic for testing the null hypothesis β₁ = 0 is ______ (round off to two decimal places).

Answer: (9.20 to 9.24)

62. Let X be a random variable with the probability density function f(x) such that

Then, the variance of X is _______ (in integer).

Answer: (1 to 1)

63. Suppose from the estimation of a linear regression model

Y_i = β₀ + β₁X_i + e_i

the residual sum of squares and the total sum of squares are obtained as 44 and 80, respectively. The value of coefficient of determination is _______ (round off to two decimal places).

Answer: (0.43 to 0.47)

64. A labour-augmenting production function is

Y = K^0.33(AL)^0.67

where Y = output, K = capital, L = labour, and A = technology.

Assume that the growth rate of L is 1.2 percent per annum, the growth rate of K is 3 percent per annum, and the growth rate of A is 1.5 percent per annum. Using the growth-accounting approach, the growth rate of Y in percent per annum is _______ (round off to two decimal places).

Answer: (2.70 to 2.90)

65. A monopolist is facing the demand function where Q is the quantity demanded and P is the price per unit of the good (P > 1). The average variable cost for the monopolist is 4/√Q and the fixed cost is 10. The profit maximizing price is _______ (in integer).

Answer: (26 to 26)

XH : Humanities & Social Sciences

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is ________.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

Reasoning and Comprehension (XH-B1)

XH-B1: Q.11 – Q.17 Carry ONE mark Each

11. Which word below best describes the idea of being both Spineless and Cowardly?

(A) Pusillanimous

(B) Unctuous

(D) Reticent

Answer: (A)

12. Choose the right preposition to fill up the blank:

The whole family got together ___ Diwali

(A) of

(B) at

(D) till

Answer: (B)

13. Select the correct option to fill in all the blanks to complete the passage:

(A) (i) disheartening (ii) failure (iii) channels (iv) matching

(B) (i) redeeming (ii) outperformance (iii) geographies (iv) eclipsing

(D) (i) humbling (ii) bombing (iii) theatres (iv) falling behind

Answer: (B)

Choose the correct sequence of the sentences so that they form a coherent paragraph:

(1) Most obviously, mobility is taken to be a geographical as well as a social phenomenon.

(3) The existing sociology of migration is incidentally far too limited in its concerns to be very useful here.

(5) Moreover, not only people are mobile but so too are many ‘objects’.

(A) 3, 2, 5, 4

(B) 2, 3, 4, 5

(D) 4, 2, 5, 3

Answer: (B)

15. The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

(A) -0.25%

(B) 0%

(D) 10.25%

Answer: (A)

16. The words Thin: Slim: Slender are related in some way. Identify the correct option(s) that reflect(s) the same relationship:

(A) Fat: Plump: Voluptuous

(B) Short: Small: Petite

(D) Fair: Dark: Wheatish

Answer: (A, B)

Which of the following action(s) are plausible?

(A) In future, the government can make district administration authorities responsible for protecting health of citizens and reviving the economy.

(B) The government may set up a task force to review the post pandemic situation and ascertain the effectiveness of the measures taken.

(C) The government may set up a committee to formulate a pandemic management program to minimize losses to life and economy in future.

(D) The government may take population control measures to minimize pandemic related losses in future.

Answer: (B, C)

XH-B1: Q.18 – Q.26 Carry TWO marks Each

(A) Fulmoni

(B) Emon

(D) Chintu

Answer: (C)

19. Select the correct relation between E and F.

(A) E > F

(B) E < F

(D) E < -F

Answer: (B)

20. A code language is formulated thus:

Then how does the word, GOODMORNING appear in the coded language?

(A) HUUFNUSPOPH

(B) FIICLIQMEMF

(D) HEEDATTACRH

Answer: (C)

What assumptions can be made about the stranger from the passage above?

(A) The stranger can become an owner of soil through developing all kinds of charm in more intimate relations.

(B) The stranger cannot become an owner of soil either in the physical or psychological sense.

(D) The stranger might become an owner of soil in the physical sense but not in the psychological

Answer: (B)

22. L is the only son of A and S. S has one sibling, B, who is married to L’s aunt, K. B is the only son of D. How are L and D related?

Select the possible option(s):

(A) Grandchild and Paternal Grandfather

(B) Grandchild and Maternal Grandfather

(D) Grandchild and Maternal Grandmother

Answer: (B, D)

(1) Consumed multitudes are jostling and shoving inside me

(2) and guided only by the memory of a large white bedsheet with a roughly circular hole some seven inches in diameter cut into the center,

(3) clutching at the dream of that holey, mutilated square of linen, which is my talisman, my open-sesame,

(4) I must commence the business of remaking my life from the point at which it really began,

(5) some thirty-two years before anything as obvious, as present, as my clock-ridden, crime-stained birth.

(A) 2 – 3 – 4

(B) 3 – 2– 4

(D) 4 – 3 – 2

Answer: (A)

What are the different ways in which ‘truth’ can be understood from the passage?

(A) Truth is what can be verified by hard empirical evidence.

(B) Truth is based on what can be perceived by the senses.

(D) Truth is contingent on the observer and can only be partial.

Answer: (C, D)

Answer: (35 to 35)

26. Select the odd word and write the option number as answer:

(1) Lek (2) Zloty (3) Diner (4) Drachma (5) Real

Answer: (3 to 3)

English – C2

XH-C2: Q.27 – Q.44 Carry ONE mark Each

27. Who published the novel The Bell Jar under the pseudonym Victoria Lucas?

(A) Dorothy Richardson

(B) Virginia Woolf

(D) Alice Walker

Answer: (C)

28. In which collection did Walt Whitman’s poem “Song of Myself” first appear?

(A) Two Rivulets

(B) November Boughs

(D) Leaves of Grass

Answer: (D)

29. Who wrote the introduction to Rabindranath Tagore’s Gitanjali?

(A) T. S. Eliot

(B) Ezra Pound

(D) W. B. Yeats

Answer: (D)

30. Identify the title of the poem in which the following lines appear:

“He was found by the Bureau of Statistics to be

One against whom there was no official complaint,

And all the reports on his conduct agree

That, in the modern sense of an old-fashioned word, he was a saint

For in everything he did he served the greater community.”

(A) “In Memory of W. B. Yeats”

(B) “The Unknown Citizen”

(D) “On this Island”

Answer: (B)

31. Identify the point of view used in the following passage:

“You are not the kind of guy who would be at a place like this at this time of the morning. But here you are, and you cannot say that the terrain is entirely unfamiliar, though the details are fuzzy.”

(A) Third-person point of view

(B) The limited point of view

(D) First-person point of view

Answer: (C)

32. Which of the following is a novel by Charles Dickens?

(A) The Old Curiosity Shop

(B) The Old Wives’ Tale

(D) One Hundred Years of Solitude

Answer: (A)

33. Which linguistic process can be seen in the formation of the following words?

(i) smog, (ii) brunch, (iii) motel (iv) telecast

(A) Borrowing

(B) Compounding

(D) Backformation

Answer: (C)

34. Which writer is credited with the ‘chutneyfication’ of Indian English?

(A) Raja Rao

(B) Salman Rushdie

(D) Arundhati Roy

Answer: (B)

35. Whom would you associate the term ‘simulacra’ with?

(A) Noam Chomsky

(B) Jean Baudrillard

(D) Michel Foucault

Answer: (B)

36. In Plato’s idea of the Republic there is no place for the ___________.

(A) Lawyer

(B) Magistrate

(D) Poet

Answer: (D)

37. What was Aristotle’s definition of hubris?

(A) Tragic flaw in a character

(B) A false sense of pride which eventually causes the character’s downfall

(D) A humble, ascetic quality

Answer: (B)

38. Stephen Dedalus is a recurring character in the works of _________.

(A) James Joyce

(B) H. G. Wells

(D) D. H. Lawrence

Answer: (A)

39. Which of the following novels opens with the sentence, “It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife.”?

(A) Sense and Sensibility

(B) Pride and Prejudice

(D) Emma

Answer: (B)

40. Which of the following novels by Chinua Achebe derives its title from W. B. Yeats’s poem “The Second Coming”?

(A) Arrow of God

(B) No Longer at Ease

(D) Things Fall Apart

Answer: (D)

41. Identify the novels that deal with the trauma of Partition:

(A) Shauna Singh Baldwin’s What the Body Remembers

(B) Amitav Ghosh’s The Shadow Lines

(D) Kamala Markandaya’s Nectar in a Sieve

Answer: (A, B)

42. Which of the following writers are associated with the Theatre of the Absurd?

(A) Harold Pinter

(B) Edward Albee

(D) Eugene O’Neill

Answer: (A, B)

43. Identify the writers who are referred to as ‘metaphysical poets’:

(A) John Donne

(B) Andrew Marvell

(D) T. S. Eliot

Answer: (A, B)

44. What are the sources of Girish Karnad’s Hayavadana?

(A) Thomas Mann’s The Transported Heads

(B) Valmiki’s Ramayana

(D) Franz Kafka’s The Metamorphosis

Answer: (A, C)

XH-C2: Q.45– Q.65 Carry TWO marks Each

45. Which of the following terms are used by Samuel Taylor Coleridge in his theory of imagination?

(A) Primary imagination, secondary imagination, and fancy

(B) Negative capability, Hellenism, and impersonality

(D) Unacknowledged legislation, atheism, and anarchy

Answer: (A)

46. Which of the following is the forerunner of the autobiography?

(A) St. Augustine’s Confessions

(B) James Joyce’s Portrait of the Artist as a Young Man

(D) Izaak Walton’s Lives

Answer: (A)

47. Which of the following poems did Robert Browning intend to write as a play?

(A) “Men and Women”

(B) “Dramatis Personae”

(D) “The Ring and the Book”

Answer: (C)

48. The ‘Age of Reason’ in English literary history is popularly known as:

(A) The Medieval Period

(B) The Neo-classical Age

(D) The Victorian Age

Answer: (B)

49. Who first translated Jacques Derrida’s work into English?

(A) Gayatri C. Spivak

(B) Edward Said

(D) Paul de Man

Answer: (A)

50. Identify the ‘Lake Poets’:

(A) Byron, Shelley, Keats

(B) Wordsworth, Coleridge, Byron

(D) Wordsworth, Coleridge, Southey

Answer: (D)

51. Choose from the following options the type of drama that is intended by the author to be read rather than to be performed:

(A) Kitchen Sink Drama

(B) Closet Drama

(D) Folk Drama

Answer: (B)

52. Identify the commonality shared by the authors of Mansfield Park and Middle March:

(A) Both the novels were authored by men who were sent on exile.

(B) Both the novels were authored by political prisoners.

(D) Both the novels were written by women who wrote under pseudonyms.

Answer: (D)

53. Who said, “Poetry makes nothing happen”?

(A) Marianne Moore

(B) Ezra Pound

(D) W. H. Auden

Answer: (D)

54. Which literary device does the following line employ?

“A timorous foe, and a suspicious friend.”

(A) Antithesis

(B) Antistrophe

(D) Apostrophe

Answer: (A)

55. Match the following excerpts with their authors:

(A) (P)-(iii), (Q)-(iv), (R)-(i), (S)-(ii)

(B) (P)-(iv), (Q)-(iii), (R)-(ii), (S)-(i)

(D) (P)-(i), (Q)-(iv), (R)-(ii), (S)-(iii)

Answer: (A)

56. The 1667 edition of Paradise Lost had 10 books. How many more were added to the 1674 edition?

(A) 2

(B) 4

(D) 12

Answer: (A)

57. Read the following poem and identify the appropriate options:

And search

for certain thin –

stemmed, bubble-eyed water bugs.

See them perch

on dry capillary legs

weightless

on the ripple skin

of a stream.

No, not only prophets

walk on water. This bug sits

on a landslide of lights

and drowns eye –

deep

into its tiny strip

of sky.

(A) It uses free verse form.

(B) It employs imagery.

(D) It juxtaposes the non-human with the human.

Answer: (A, B, D)

58. Which of the following employ ‘Interior Monologue’?

(A) Alfred Lord Tennyson’s “In Memoriam”

(B) The final chapter of James Joyce’s Ulysses

(D) Robert Browning’s “My Last Duchess”

Answer: (B, C)

59. Which of the following works may be described as novels in verse?

(A) Aurora Leigh by Elizabeth Barrett Browning

(B) The Golden Gate by Vikram Seth

(D) Old Possum’s Book of Practical Cats by T. S. Eliot

Answer: (A, B)

60. Which of the following critics belong to the deconstructionist school?

(A) Jacques Derrida

(B) Paul de Man

(D) Kate Soper

Answer: (A, B, C)

61. Cleanth Brooks’s definition of ‘paradox’ in poetry foregrounds the following qualities:

(A) Wonder and irony

(B) Contradiction and qualification

(D) Omniscience and death of the author

Answer: (A, B)

62. Two examples of magic realist fiction include:

(A) Midnight’s Children

(B) The Tin Drum

(D) Tom Jones

Answer: (A, B)

63. Ferdinand de Saussure differentiates language in terms of:

(A) langue

(B) metaphor

(D) parole

Answer: (A, D)

64. Which of the following are considered to be typical postmodern narratives?

(A) Italo Calvino’s If on a Winter’s Night a Traveller

(B) John Barth’s Lost in the Funhouse

(D) Iris Murdoch’s The Bell

Answer: (A, B, C)

65. What does a green reading of a text aim at?

(A) Analyzing the implications of a text for environmental concerns

(B) Deconstructing human exceptionalism

(D) Marginalizing differently abled people

Answer: (A, B, C)

XH : Humanities & Social Sciences

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is ________.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

Reasoning and Comprehension (XH-B1)

XH-B1: Q.11 – Q.17 Carry ONE mark Each

11. Which word below best describes the idea of being both Spineless and Cowardly?

(A) Pusillanimous

(B) Unctuous

(D) Reticent

Answer: (A)

12. Choose the right preposition to fill up the blank:

The whole family got together ___ Diwali

(A) of

(B) at

(D) till

Answer: (B)

13. Select the correct option to fill in all the blanks to complete the passage:

(A) (i) disheartening (ii) failure (iii) channels (iv) matching

(B) (i) redeeming (ii) outperformance (iii) geographies (iv) eclipsing

(D) (i) humbling (ii) bombing (iii) theatres (iv) falling behind

Answer: (B)

Choose the correct sequence of the sentences so that they form a coherent paragraph:

(1) Most obviously, mobility is taken to be a geographical as well as a social phenomenon.

(3) The existing sociology of migration is incidentally far too limited in its concerns to be very useful here.

(5) Moreover, not only people are mobile but so too are many ‘objects’.

(A) 3, 2, 5, 4

(B) 2, 3, 4, 5

(D) 4, 2, 5, 3

Answer: (B)

15. The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

(A) -0.25%

(B) 0%

(D) 10.25%

Answer: (A)

16. The words Thin: Slim: Slender are related in some way. Identify the correct option(s) that reflect(s) the same relationship:

(A) Fat: Plump: Voluptuous

(B) Short: Small: Petite

(D) Fair: Dark: Wheatish

Answer: (A, B)

Which of the following action(s) are plausible?

(A) In future, the government can make district administration authorities responsible for protecting health of citizens and reviving the economy.

(B) The government may set up a task force to review the post pandemic situation and ascertain the effectiveness of the measures taken.

(C) The government may set up a committee to formulate a pandemic management program to minimize losses to life and economy in future.

(D) The government may take population control measures to minimize pandemic related losses in future.

Answer: (B, C)

XH-B1: Q.18 – Q.26 Carry TWO marks Each

(A) Fulmoni

(B) Emon

(D) Chintu

Answer: (C)

19. Select the correct relation between E and F.

(A) E > F

(B) E < F

(D) E < -F

Answer: (B)

20. A code language is formulated thus:

Then how does the word, GOODMORNING appear in the coded language?

(A) HUUFNUSPOPH

(B) FIICLIQMEMF

(D) HEEDATTACRH

Answer: (C)

What assumptions can be made about the stranger from the passage above?

(A) The stranger can become an owner of soil through developing all kinds of charm in more intimate relations.

(B) The stranger cannot become an owner of soil either in the physical or psychological sense.

(D) The stranger might become an owner of soil in the physical sense but not in the psychological

Answer: (B)

22. L is the only son of A and S. S has one sibling, B, who is married to L’s aunt, K. B is the only son of D. How are L and D related?

Select the possible option(s):

(A) Grandchild and Paternal Grandfather

(B) Grandchild and Maternal Grandfather

(D) Grandchild and Maternal Grandmother

Answer: (B, D)

(1) Consumed multitudes are jostling and shoving inside me

(2) and guided only by the memory of a large white bedsheet with a roughly circular hole some seven inches in diameter cut into the center,

(3) clutching at the dream of that holey, mutilated square of linen, which is my talisman, my open-sesame,

(4) I must commence the business of remaking my life from the point at which it really began,

(5) some thirty-two years before anything as obvious, as present, as my clock-ridden, crime-stained birth.

(A) 2 – 3 – 4

(B) 3 – 2– 4

(D) 4 – 3 – 2

Answer: (A)

What are the different ways in which ‘truth’ can be understood from the passage?

(A) Truth is what can be verified by hard empirical evidence.

(B) Truth is based on what can be perceived by the senses.

(D) Truth is contingent on the observer and can only be partial.

Answer: (C, D)

Answer: (35 to 35)

26. Select the odd word and write the option number as answer:

(1) Lek (2) Zloty (3) Diner (4) Drachma (5) Real

Answer: (3 to 3)

Linguistics – C3

XH-C3: Q.27 – Q.44 Carry ONE mark Each

27. In a writing system, if each unique grapheme represents a unique morpheme/word, the writing system is known as _____________.

(A) Logographic

(B) Syllabic

(D) Moraic

Answer: (A)

28. If an SOV language allows movement to OSV and VSO word orders, the resulting word order will be known as:

(A) Unmarked

(B) Marked

(D) Default

Answer: (B)

29. The phenomenon where ‘missed hotel’ is pronounced as ‘hissed motel’ is known as _____________.

(A) Agrammatism

(B) Wernicke’s aphasia

(D) Malapropism

Answer: (C)

30. When new information is introduced in a communication, such information is classified as __________.

(A) Focus

(B) Topic

(D) Theme

Answer: (A)

31. What type of morphological process is involved in the expression ‘English-vinglish’

(A) Complete reduplication

(B) Partial reduplication

(D) Suffixation

Answer: (B)

32. Which one of the following is a language isolate?

(A) Burushashki

(B) Mundari

(D) Kalasha

Answer: (A)

33. Which of the following Dravidian language is spoken in Pakistan?

(A) Konda

(B) Kuvi

(D) Brahui

Answer: (D)

34. Which word-order pair is the most common in world’s languages?

(A) SVO-SOV

(B) SOV-VSO

(D) SOV-VOS

Answer: (A)

35. Which type of morphological process is involved in creating catty from cat?

(A) Inflection

(B) Derivation

(D) Reduplication

Answer: (B)

36. Devanagari organizes the consonant graphemes as shown in the image. What is the parameter by which the following two rows differ?

(A) Voicing

(B) Manner of articulation

(D) Aspiration

Answer: (C)

37. Which option is related to Neo-Whorfism?

(A) Language, thought, worldview

(B) Innateness, deep-structure, surface-structure

(D) Signifier, signified, sign

Answer: (A)

38. Which of the following is/are involved in the comparative method for establishing language families and genetic relationship among languages?

(A) Reconstruction of the proto language

(B) Assembling a list of cognates

(D) Setting up sound correspondences

Answer: (A, B, D)

39. Aphasia can be caused by

(A) Open or closed head trauma

(B) Attention deficit

(D) Lack of motivation

Answer: (A, C)

40. In sociolinguistics, the term ‘anti-language’ refers to the language used for

(A) Academic purposes by professional criminologists

(B) Legal proceedings in the court of law

(D) Communication between caregivers and infants

Answer: (C)

41. In language policy making, which of the following steps is/are necessary for an erstwhile minority language, spoken by a sizeable population, to be introduced as a medium of instruction in schools?

(A) Language revival

(B) Corpus planning

(D) Language preservation

Answer: (B, C)

42. Which of the following research methods involve Reaction Time?

(A) Behavioral methods

(B) Experimental methods

(D) Qualitative methods

Answer: (A, B)

43. If [p] and [p^h] are allophones of the same phoneme /p/, which of the following statements is/are true?

(A) [p] and [p^h] are in contrastive distribution

(B) [p] and [p^h] are in complementary distribution

(D) [p] and [p^h] can be used interchangeably

Answer: (B, C)

44. Which of the following show(s) dissociation between cognitive disorder and language abilities?

(A) Autism spectrum disorder

(B) Williams syndrome

(D) Specific Language Impairment (SLI)

Answer: (B, C, D)

XH-C3: Q.45 – Q.65 Carry TWO mark Each

45. Which of the following sound pairs differ from each other in exactly two articulatory parameters?

(A) [p] vs. [b]

(B) [t] vs. [s]

(D) [n] vs. [d]

Answer: (C)

46. The cover term determiner refers to:

(A) Articles, demonstratives, and possessors

(B) Possessors, prepositions, and demonstratives

(D) Articles, prepositions, and possessors

Answer: (A)

47. In ‘John seems to have left’, the subject John has undergone:

(A) Subject-to-Subject lowering

(B) Object-to-Subject raising

(D) Object-to-Object lowering

Answer: (C)

48. The comparative and superlative forms of the adjective ‘good’ are examples of:

(A) Alternation

(B) Syncope

(D) Suppletion

Answer: (D)

49. Consider the following question and determine where was is moved finally, in accordance with the minimalist assumptions:

Was John, who wrote the book, angry?

(A) T to C

(B) C to T

(D) T to V

Answer: (A)

50. Match the following historical sound changes in Column X with the processes in Column Y

(A) P-2, Q-4, R-1, S-3

(B) P-4, Q-2, R-1, S-3

(D) P-2, Q-4, R-3, S-1

Answer: (A)

51. Consider the following morphological break-up of pfeifing produced by a simultaneous bilingual child. What phenomenon does this example indicate?

(A) Code-mixing arising out of social bilingualism

(B) Code-switching based on context of the conversation

(D) Mixed language arising out of pedagogical preferences

Answer: (C)

52. Which one of the following is compounding of compounded words?

(A) Lighthouse tower

(B) Skating board

(D) Walkman

Answer: (A)

53. What sociolinguistic phenomenon does the following sentence exemplify?

(A) Code switching

(B) Bilingualism

(D) Mixed language

Answer: (D)

54. Identify the labels for X and Y in the following tree.

(A) X: Verb, Y: Adjective

(B) X: Adjective, Y: Adjective

(D) X: Verb, Y: Verb

Answer: (A)

55. From the following, which is the correct order of animacy hierarchy?

(A) 1st/2nd Person > 3rd Person > Proper Name > Human Noun

(B) 3rd Person > 1st/2nd Person > Proper Name > Human Noun

(D) 1st/2nd Person > 3rd Person > Human Noun > Proper Name

Answer: (A)

56. Look at the adjectives in Column X and match with the types of adjectives in Column Y. Choose the correct option.

(A) P-2, Q-3, R-1

(B) P-2, Q-1, R-3

(D) P-1, Q-3, R-2

Answer: (A)

57. In a given constraint ranking of *COMPLEX, DEP-IO >> MAX-IO for the input /spun/, which of the following candidates is/are optimal?

(A) [su.pun]

(B) [pun]

(D) [is.pun]

Answer: (B, C)

58. Consider the pattern of stress assignment shown below. Which of the given statements is/are true?

(A) Stress assignment is from left to right

(B) There are/is extrametrical syllable(s)

(D) Stress system is iambic

Answer: (A, B, C)

59. In word processing studies, visual word recognition is affected by:

(A) Proficiency, word length, neighborhood effect

(B) Frequency, age of acquisition (AoA), familiarity

(D) Language family, areal features, phoneme inventory size

Answer: (A, B)

60. Identify the language(s) that belong(s) to the Balkan Sprachbund.

(A) Romanian

(B) Bulgarian

(D) Swedish

Answer: (A, B)

61. Consider the following tree structure, where A and C are co-referential. Similarly, E and H are co-referential. Identify the incorrect statement(s).

(A) A binds C

(B) C binds E

(D) A binds H

Answer: (B, C, D)

62. Which of the following statements is/are true for the pair – bird : cuckoo

(A) Cuckoo is the hyponym of bird

(B) Bird is the hypernym of cuckoo

(D) Bird is the hyponym of cuckoo

Answer: (A, B)

63. In the sentences 1 through 4, in which one(s) a) entails b)?

(A) 1 a) entails 1 b)

(B) 2 a) entails 2 b)

(D) 4 a) entails 4 b)

Answer: (C, D)

64. The following figure depicts a spectrum of a vowel (dashed line), where F0 = 150 Hz and F0 = H1. The harmonics are indicated from H1 to H11. From the figure, the frequency (in Hz) of the second formant (F2) of this vowel is _______.

Answer: (1350 to 1350)

65. The number of core arguments associated with the ditransitive verb ‘give’ is _______.

Answer: (3 to 3)

XH : Humanities & Social Sciences

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is ________.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

Reasoning and Comprehension (XH-B1)

XH-B1: Q.11 – Q.17 Carry ONE mark Each

11. Which word below best describes the idea of being both Spineless and Cowardly?

(A) Pusillanimous

(B) Unctuous

(D) Reticent

Answer: (A)

12. Choose the right preposition to fill up the blank:

The whole family got together ___ Diwali

(A) of

(B) at

(D) till

Answer: (B)

13. Select the correct option to fill in all the blanks to complete the passage:

(A) (i) disheartening (ii) failure (iii) channels (iv) matching

(B) (i) redeeming (ii) outperformance (iii) geographies (iv) eclipsing

(D) (i) humbling (ii) bombing (iii) theatres (iv) falling behind

Answer: (B)

Choose the correct sequence of the sentences so that they form a coherent paragraph:

(1) Most obviously, mobility is taken to be a geographical as well as a social phenomenon.

(3) The existing sociology of migration is incidentally far too limited in its concerns to be very useful here.

(5) Moreover, not only people are mobile but so too are many ‘objects’.

(A) 3, 2, 5, 4

(B) 2, 3, 4, 5

(D) 4, 2, 5, 3

Answer: (B)

15. The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

(A) -0.25%

(B) 0%

(D) 10.25%

Answer: (A)

16. The words Thin: Slim: Slender are related in some way. Identify the correct option(s) that reflect(s) the same relationship:

(A) Fat: Plump: Voluptuous

(B) Short: Small: Petite

(D) Fair: Dark: Wheatish

Answer: (A, B)

Which of the following action(s) are plausible?

(A) In future, the government can make district administration authorities responsible for protecting health of citizens and reviving the economy.

(B) The government may set up a task force to review the post pandemic situation and ascertain the effectiveness of the measures taken.

(C) The government may set up a committee to formulate a pandemic management program to minimize losses to life and economy in future.

(D) The government may take population control measures to minimize pandemic related losses in future.

Answer: (B, C)

XH-B1: Q.18 – Q.26 Carry TWO marks Each

(A) Fulmoni

(B) Emon

(D) Chintu

Answer: (C)

19. Select the correct relation between E and F.

(A) E > F

(B) E < F

(D) E < -F

Answer: (B)

20. A code language is formulated thus:

Then how does the word, GOODMORNING appear in the coded language?

(A) HUUFNUSPOPH

(B) FIICLIQMEMF

(D) HEEDATTACRH

Answer: (C)

What assumptions can be made about the stranger from the passage above?

(A) The stranger can become an owner of soil through developing all kinds of charm in more intimate relations.

(B) The stranger cannot become an owner of soil either in the physical or psychological sense.

(D) The stranger might become an owner of soil in the physical sense but not in the psychological

Answer: (B)

22. L is the only son of A and S. S has one sibling, B, who is married to L’s aunt, K. B is the only son of D. How are L and D related?

Select the possible option(s):

(A) Grandchild and Paternal Grandfather

(B) Grandchild and Maternal Grandfather

(D) Grandchild and Maternal Grandmother

Answer: (B, D)

(1) Consumed multitudes are jostling and shoving inside me

(2) and guided only by the memory of a large white bedsheet with a roughly circular hole some seven inches in diameter cut into the center,

(3) clutching at the dream of that holey, mutilated square of linen, which is my talisman, my open-sesame,

(4) I must commence the business of remaking my life from the point at which it really began,

(5) some thirty-two years before anything as obvious, as present, as my clock-ridden, crime-stained birth.

(A) 2 – 3 – 4

(B) 3 – 2– 4

(D) 4 – 3 – 2

Answer: (A)

What are the different ways in which ‘truth’ can be understood from the passage?

(A) Truth is what can be verified by hard empirical evidence.

(B) Truth is based on what can be perceived by the senses.

(D) Truth is contingent on the observer and can only be partial.

Answer: (C, D)

Answer: (35 to 35)

26. Select the odd word and write the option number as answer:

(1) Lek (2) Zloty (3) Diner (4) Drachma (5) Real

Answer: (3 to 3)

Philosophy – C4

XH-C4: Q.27 – Q.44 Carry ONE mark Each

27. In Sāṅkhya philosophy ‘mind’ (manas) is an evolute of ______.

(A) Prakṛti

(B) Puruṣa

(D) Puruṣa and Prakṛti

Answer: (A)

28. Which one of the following is the manifestation of the Absolute Spirit in Hegel’s Phenomenology of Spirit?

(A) The devotion of a church congregation

(B) The knowledge of a natural scientist

(D) The mystical insight of an enlightened sage

Answer: (C)

29. The Cārvāka system accepts the following puruṣārthas:

(A) Artha and Kāma

(B) Dharma, Kāma and Mokṣa

(D) Artha, Kāma and Mokṣa

Answer: (A)

30. In Taittirīya Upaniṣad there is a discussion of five sheaths (pañca-koṣa) in which the individual self is encased. Which one of the following is the sheath (koṣa) of knowledge and intelligence?

(A) Vijñānamaya-koṣa

(B) Prāṇamaya-koṣa

(D) Ᾱnandamaya-koṣa

Answer: (A)

31. According to Swami Vivekananda, ‘Universal Religion’ would consist in recognising that there are different ways of approaching the religious object. The watch-word for universal religion is ___________.

(A) Tolerance

(B) Acceptance

(D) Adoration

Answer: (B)

32. In his ‘The Concept of the Absolute and Its Alternative Forms’, K. C. Bhattacharyya says, “… consciousness is of three kinds – knowing, feeling and willing…” Which one of the following is the ‘absolute’ of ‘knowing’?

(A) Truth

(B) Beauty

(D) Bliss

Answer: (A)

33. Which one of the following is NOT considered a pramāṇa by the Prābhākara Mīmāṃsaka?

(A) Anupalabdhi (Non-apprehension)

(B) Anumāna (Inference)

(D) Upamāna (Comparison/ Analogy)

Answer: (A)

34. Marx introduces the concept of ‘commodity fetishism’ in Capital. Which one of the following is a correct description of the concept?

(A) The reflection of human spiritual capacities in the material product

(B) The reflection of human needs in the material product

(D) The reflection of the dignity of human labour in the material product

Answer: (C)

35. W.V. O. Quine famously writes in ‘Two Dogmas of Empiricism’:

(A) No statement is immune to revision

(B) Only analytic statements are immune to revision

(D) Only the statements of empirical sciences are immune to revision

Answer: (A)

36. Comparing the thoughts of Heraclitus and Parmenides, we can say that:

(A) Both assert that only the soul (psuche) truly exists

(B) Heraclitus asserts the unity underlying the plurality of things, whereas Parmenides denies the plurality of things altogether

(D) Heraclitus asserts the incomprehensibility of the plurality of nature, while Parmenides asserts the fundamental comprehensibility of the plurality of nature

Answer: (B)

37. According to Heidegger’s Being and Time, the ontological difference is:

(A) The distinction between Being (Sein) and beings (Seiende)

(B) The distinction between Being (Sein) and Being-there (Dasein)

(D) The difference between Being (Sein) and Non-Being (Nichtsein)

Answer: (A)

38. In Plato’s Republic, the virtue of moderation is present:

(A) Only in the guardians

(B) In the auxiliaries and guardians

(D) Throughout the republic

Answer: (D)

39. In Kāśmīra Śaivism, Śiva is the only reality, the one without a second. Which among the following is/are the other name[s] for Kāśmīra Śaivism?

(A) Pratyabhijñā

(B) Trika

(D) Vīra-śaivism

Answer: (A, B, C)

40. In ‘Democracy’, B. R. Ambedkar lays out certain fundamental assumptions about his conception of democracy. They include:

(A) Adult suffrage and frequent elections are no bar against the governing class reaching places of power and authority

(B) Servile classes volunteering to elect members of the governing class as their rulers is a sign of a thriving democracy

(C) Servile classes in some countries may need other safeguards beside adult suffrage to oust the governing class from the seat of authority

(D) Existence of the governing class is consistent with democracy and self-government

Answer: (A, C)

41. Read the following passage carefully and answer the question:

My uniform experience has convinced me that there is no other God than Truth…That is why my devotion to Truth has drawn me into the field of politics; and I can say without the slightest hesitation, yet in all humility, that those who say that religion has nothing to do with politics do not know what religion means. Identification with everything that lives is impossible without self-purification; without self-purification the observance of the law of Ahimsa must remain an empty dream; God can never be realized by one who is not pure of heart.

– M. K. Gandhi, An Autobiography or the Story of my Experiments with Truth, p. 615

Which among the following are NOT in conformity with the above passage?

(A) God is Truth

(B) Devotion to God, which is Truth, prompted Gandhi to enter politics

(D) Ahimsa and politics do not go hand in hand

Answer: (C, D)

42. Soli likes either logic or biology. If Soli likes logic, then he is not a happy person. Neither Soli nor Rupinder likes biology.

Which among the following can be concluded from the premises given here?

(A) Soli is not a happy person.

(B) Rupinder is not a happy person.

(D) Soli likes logic.

Answer: (A, D)

43. On the basis of Aristotle’s Nicomachean Ethics, we can say the following about virtue:

(A) We can know the virtue of something only if we understand the function (ergon) of that thing

(B) Virtue entails deliberation

(D) Virtue has the nature of a mean between two extremes in most cases

Answer: (A, B, D)

44. According to Hume’s An Inquiry Concerning Human Understanding, the following is/are the principle[s] governing the connection of ideas:

(A) Resemblance

(B) Contiguity in space and time

(D) Cause and Effect

Answer: (A, B, D)

XH-C4: Q.45– Q.65 Carry TWO marks Each

45. In his Yogasūtra, Patañjali mentions five kinds of afflictions (kleśas). Which one of the following is NOT among the five afflictions?

(A) Mātsarya (competition/ rivalry)

(B) Avidyā (false knowledge)

(D) Asmitā (egoism)

Answer: (A)

46. According to Jaina philosophy, all substances (dravya) but one have extension in space (astikāya). That one substance which has no extension in space (anastikāya) is ___.

(A) Time (kāla)

(B) Space (ākāśa)

(D) Motion (dharma)

Answer: (A)

47. Husserl’s fifth Cartesian Meditation is founded upon the realization that the reduction to my transcendental sphere of ownness:

(A) Does not fundamentally cut me off from the other

(B) Fatefully cuts me off from the other

(D) Is not necessary to understand the constitution of the objective world

Answer: (A)

48. According to the Nyāya system, the argument “A sparrow is a bird, since it has wings” would have an inferential defect (hetvābhāsa) called _______.

(A) Svarūpāsiddhi (unestablished in respect of itself)

(B) Āśrayāsiddhi (unestablished in respect of abode)

(D) Asādhāraṇa-anaikāntika (uncommon strayer)

Answer: (C)

49. Consider the following sentence: ‘Dhavala is a white cow.’ For the Vaiśeṣika, the meaning (artha) of the sentence consists of the following padārthas:

(A) Action (karma), Substance (dravya) and Unique particular (viśeṣa) only

(B) Substance (dravya), Universal (sāmānya) and Quality (guṇa) only

(D) Action (karma), Substance (dravya), Unique particular (viśeṣa) and Absence (abhāva) only

Answer: (C)

50. According to the theory advocated by G. Frege in his ‘On Sense and Reference’, the expression ‘the largest prime number’ would have ___________.

(A) Both a sense and a reference

(B) Only sense, and no reference

(D) Neither sense, nor reference

Answer: (B)

51. In the Phaedo, Plato’s Socrates develops a novel way of understanding the beauty of things. He tells us:

(A) The beauty of things is caused by nothing other than a combination of the colour, the shape and the size of a thing

(B) The beauty of things is simply the effect of that thing on the eyes of the observer

(D) The beauty of things is simply an illusion; only the beautiful exists in itself by itself (auto kath’ auto)

Answer: (C)

52. Descartes postulates the evil genius in his Meditations to deny the certainty of which statements?

(I) There is a table lamp to the left of the desk at which I am sitting.

(II) The sum of the angles of a triangle is 180 degrees.

(III) Sodium has only one electron in its outermost shell.

(IV) Plants absorb nourishment from the soil by means of their roots.

(V) I wish you were here.

(VI) I can see my friend in the 10th floor window of that building from where I stand on the road here below.

(VII) I am thinking of my dear mother.

(VIII) 2+2=4.

(A) IV, III and V

(B) I, II and III

(D) II and VIII

Answer: (D)

53. Which of the following statement[s] is/are NOT true in relation to Kant’s concept of the will?

(A) Every will, even the divine will is subject to imperatives

(B) Only the human will is subject to imperatives

(C) The human will is subject to the hypothetical imperative, whereas the divine will is subject to the categorical imperative

(D) The human will is subject to the categorical imperative which comes from God

Answer: (A, C, D)

54. We see a bronze statue of Poseidon in the National Archaeological Museum of Athens. Which of the following would be [a] cause[s] of the statue for Aristotle if we read his Physics?

(A) Bronze

(B) The sculptor who produced it

(D) The space in the temple in which the statue is installed

Answer: (A, B, C)

55. In the Buddhist theory of elements (dharmas), dharmas are the ultimate momentary elements of existence. The number of elements varies in different schools of Buddhism. Of the following alternatives, which pair[s] does/do NOT give us the respective number of dharmas accepted in Sautrāntika and Sarvāstivāda (Vaibhāṣika) schools?

(A) 75 and 43

(B) 43 and 75

(D) 0 and 43

Answer: (A, C, D)

56. According to the Advaita of Śaṅkara, the individual self (jīva) is:

(A) Not ontologically different from Brahman

(B) Empirically different from Brahman due to the limiting adjuncts of body, mind, senses etc.

(D) A part of Brahman

Answer: (A, B, C)

57. Mohammad Iqbal’s views on the nature of ‘intuition’ would state:

(A) Intuition is immediate knowledge of the Reality (God)

(B) Intuitive experience is not only subjective but also objective

(D) Intuition is the property of the mind and the intellect

Answer: (A, B, C)

58. Sandra Harding’s Standpoint Epistemology involves:

(A) Adopting a feminist empiricist point of view that critiques the masculine underpinnings of western sciences

(B) Recognizing that science is value free

(D) Grounding distinctive feminist science in strongly objective accounts of the world

Answer: (D)

59. In J. S. Mill’s articulation of utilitarianism which of the following statements about justice are valid?

(A) Standards of justice stand higher in the scale of social utility

(B) The just and the expedient are divided by an imaginary distinction

(D) Utilitarianism prioritises expediency over justice

Answer: (A, C)

60. According to Russell’s ‘On Denoting’, the proposition, ‘The prime number between 7 and 11 is NOT larger than 12’ would be true, if _______.

(A) The proposition, ‘The prime number between 7 and 11 is larger than 12’ is false

(B) The expression ‘the prime number between 7 and 11’ has a primary occurrence in the proposition

(D) There were only one prime number between 7 and 11

Answer: (C, D)

61. (i) p ⊃ (q ∙ r)

(ii) ~(p ⊃ s)

Taking (i) and (ii) as premises, which of the following can be deduced?

(A) q

(B) r

(D) ~p

Answer: (A, B)

62. ~q can be deduced from ~(p ⊃ (q ∨ r)) by using rules of propositional logic in the following sequence[s]:

(A) Material Implication> De Morgan’s Theorem> Commutation> Simplification> De Morgan’s Theorem> Simplification

(B) Conjunction> Addition> Modus Ponens> De Morgan’s Theorem

(C) Transposition> Material Implication> Double Negation> De Morgan’s Theorem> Simplification> De Morgan’s Theorem> Simplification

(D) Modus Tollens> Conjunction> Hypothetical Syllogism> Simplification

Answer: (A, C)

63. Read the passage below from Wittgenstein’s Philosophical Investigations carefully and answer the question.

I can think of no better expression to characterize these similarities than “family resemblances”; for the various resemblances between members of a family – build, features, colour of eyes, gait, temperament, and so on and so forth – overlap and crisscross in the same way. – And I shall say: ‘games’ form a family.

And likewise the kinds of number, for example, form a family. Why do we call something a “number”? Well, perhaps because it has a – direct – affinity with several things that have hitherto been called “number”; and this can be said to give it an indirect affinity with other things that we also call “numbers.” And we extend our concept of number, as in spinning a thread we twist fibre on fibre. And the strength of the thread resides not in the fact that some one fibre runs through its whole length but in the overlapping of many fibres.

But if someone wanted to say, “So there is something common to all these constructions – namely, the disjunction of all their common properties” – I’d reply: Now you are only playing with a word. One might as well say, “There is a Something that runs through the whole thread – namely, the continuous overlapping of these “fibres.”

– Ludwig Wittgenstein, Philosophical Investigations, Investigation No. 67

Which of the following statement[s] does Wittgenstein imply in the above passage?

(A) The one fibre supposed to run through the length of the thread corresponds to what is supposed to be common to all numbers

(B) The overlapping of the fibres corresponds to the family resemblance Wittgenstein is trying to explicate

(D) To describe a family resemblance is another way to describe the common property shared by all the family members

Answer: (A, B, C)

64. In Kant’s Critique of Pure Reason, the equation 7 + 5 = 12 is synthetic a priori and not simply analytic for the following reason[s].

(A) A simple analysis of the concept of 5, the concept of 7 and the concept of addition does not give us the sum 12

(B) With 7 as the starting point, we require an intuition such as 5 fingers or 5 marks on a page to reach upto 12

(D) We arrive at the knowledge of 7 + 5 = 12 by imitating others adding 7 and 5

Answer: (A, B, C)

65. According to Sartre’s Being and Nothingness, which of following statement[s] is/ are true?

(A) Bad faith is human beings’ denial of their own freedom

(B) To assert the existence of nothingness is to deny the existence of human freedom

(D) Being and nothingness self-evidently exclude each other

Answer: (A, C)

XH : Humanities & Social Sciences

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is ________.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

Reasoning and Comprehension (XH-B1)

XH-B1: Q.11 – Q.17 Carry ONE mark Each

11. Which word below best describes the idea of being both Spineless and Cowardly?

(A) Pusillanimous

(B) Unctuous

(D) Reticent

Answer: (A)

12. Choose the right preposition to fill up the blank:

The whole family got together ___ Diwali

(A) of

(B) at

(D) till

Answer: (B)

13. Select the correct option to fill in all the blanks to complete the passage:

(A) (i) disheartening (ii) failure (iii) channels (iv) matching

(B) (i) redeeming (ii) outperformance (iii) geographies (iv) eclipsing

(D) (i) humbling (ii) bombing (iii) theatres (iv) falling behind

Answer: (B)

Choose the correct sequence of the sentences so that they form a coherent paragraph:

(1) Most obviously, mobility is taken to be a geographical as well as a social phenomenon.

(3) The existing sociology of migration is incidentally far too limited in its concerns to be very useful here.

(5) Moreover, not only people are mobile but so too are many ‘objects’.

(A) 3, 2, 5, 4

(B) 2, 3, 4, 5

(D) 4, 2, 5, 3

Answer: (B)

15. The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

(A) -0.25%

(B) 0%

(D) 10.25%

Answer: (A)

16. The words Thin: Slim: Slender are related in some way. Identify the correct option(s) that reflect(s) the same relationship:

(A) Fat: Plump: Voluptuous

(B) Short: Small: Petite

(D) Fair: Dark: Wheatish

Answer: (A, B)

Which of the following action(s) are plausible?

(A) In future, the government can make district administration authorities responsible for protecting health of citizens and reviving the economy.

(B) The government may set up a task force to review the post pandemic situation and ascertain the effectiveness of the measures taken.

(C) The government may set up a committee to formulate a pandemic management program to minimize losses to life and economy in future.

(D) The government may take population control measures to minimize pandemic related losses in future.

Answer: (B, C)

XH-B1: Q.18 – Q.26 Carry TWO marks Each

(A) Fulmoni

(B) Emon

(D) Chintu

Answer: (C)

19. Select the correct relation between E and F.

(A) E > F

(B) E < F

(D) E < -F

Answer: (B)

20. A code language is formulated thus:

Then how does the word, GOODMORNING appear in the coded language?

(A) HUUFNUSPOPH

(B) FIICLIQMEMF

(D) HEEDATTACRH

Answer: (C)

What assumptions can be made about the stranger from the passage above?

(A) The stranger can become an owner of soil through developing all kinds of charm in more intimate relations.

(B) The stranger cannot become an owner of soil either in the physical or psychological sense.

(D) The stranger might become an owner of soil in the physical sense but not in the psychological

Answer: (B)

22. L is the only son of A and S. S has one sibling, B, who is married to L’s aunt, K. B is the only son of D. How are L and D related?

Select the possible option(s):

(A) Grandchild and Paternal Grandfather

(B) Grandchild and Maternal Grandfather

(D) Grandchild and Maternal Grandmother

Answer: (B, D)

(1) Consumed multitudes are jostling and shoving inside me

(2) and guided only by the memory of a large white bedsheet with a roughly circular hole some seven inches in diameter cut into the center,

(3) clutching at the dream of that holey, mutilated square of linen, which is my talisman, my open-sesame,

(4) I must commence the business of remaking my life from the point at which it really began,

(5) some thirty-two years before anything as obvious, as present, as my clock-ridden, crime-stained birth.

(A) 2 – 3 – 4

(B) 3 – 2– 4

(D) 4 – 3 – 2

Answer: (A)

What are the different ways in which ‘truth’ can be understood from the passage?

(A) Truth is what can be verified by hard empirical evidence.

(B) Truth is based on what can be perceived by the senses.

(D) Truth is contingent on the observer and can only be partial.

Answer: (C, D)

Answer: (35 to 35)

26. Select the odd word and write the option number as answer:

(1) Lek (2) Zloty (3) Diner (4) Drachma (5) Real

Answer: (3 to 3)

Psychology – C5

XH-C5: Q.27 – Q.44 Carry ONE mark Each

27. Blind spot in the retina contains _________.

(A) only rod cells

(B) only cone cells

(D) neither rod nor cone cells

Answer: (D)

28. Taking painkillers eliminates pain, increasing the likelihood that the person will take painkillers again. This is an example of __________.

(A) negative punishment

(B) positive reinforcement

(D) positive punishment

Answer: (C)

29. When learning something new impairs the ability to retrieve information learnt earlier, it is known as ____________.

(A) retroactive interference

(B) proactive interference

(D) recency effect

Answer: (A)

30. Iconic memory is a type of _________.

(A) short term memory

(B) sensory memory

(D) working memory

Answer: (B)

31. Which one of the following components of language has to do with the practical or social aspects of communication with others?

(A) Phonemes

(B) Morphemes

(D) Syntax

Answer: (C)

32. The Yerkes-Dodson law states that _____________.

(A) performance is affected by the level of arousal

(B) frustration leads to aggression

(D) changes in behaviour are a result of experiences that have happened frequently or recently

Answer: (A)

33. Transduction of mechanical energy into nerve impulses in the auditory system takes place in reponse to bending of the ____________.

(A) pinna

(B) hair cells

(D) malleus

Answer: (B)

34. Which one of the following theories states that emotion occurs as a result of physical arousal and labeling of the arousal based on cues from the surrounding environment?

(A) Ekman-Friesen theory

(B) Schachter-Singer theory

(D) Cannon-Bard theory

Answer: (B)

35. Which one of the following is TRUE for the Pain-Gate control theory?

(A) Gate is a physical structure

(B) Activity of gate cannot be closed by non-pain signals

(D) Pain signals must pass through a gate located in the spinal cord

Answer: (D)

36. Being treated with warmth and consideration by others only when one behaves as expected, is called as ___________.

(A) openness to experience

(B) conditional positive regard

(D) zone of proximal development

Answer: (B)

37. Which of the following is/are NOT the factor(s) of the Big Five Personality model?

(A) Conscientiousness

(B) Optimism

(D) Extraversion

Answer: (B, C)

38. Which of the following is/are TRUE for creative individuals?

(A) They are not very good at mental imagery

(B) They are not afraid to be different

(D) They are unconventional in their work

Answer: (B, D)

39. Which of the following is/are included under behavioural genetics studies in humans?

(A) Selective breeding studies

(B) Family studies

(D) Adoption studies

Answer: (B, C, D)

40. Which of the following statements regarding locus of control is/are CORRECT?

(A) It can be internal and/or external

(B) It is associated with self-esteem

(D) Regret has no association with locus of control

Answer: (A, B, C)

41. Which of the following is/are TRUE for nonparametric statistics?

(A) It is often called distribution free statitstics

(B) It is used to analyze interval data

(D) It compares groups in terms of means

Answer: (A, C)

42. According to the review of research on stress and immune system, which of the following statement(s) has/have substantial evidence?

(A) There is a negative relationship between stress and functional immune measures

(B) There is no measurable impact of stress on functional immune measures

(D) There is a positive relationship between long term stressors and functional immune measures

Answer: (A, C)

43. Which of the following influence(s) gender dysphoria?

(A) Prenatal factors

(B) Early childhood experiences

(D) Attention Deficit Hyperactivity Disorder

Answer: (A, B, C)

44. If the variance of a set of scores is 100, the standard deviation is ________ (in integer).

Answer: (10 to 10)

XH-C5: Q.45– Q.65 Carry TWO marks Each

45. Match the structures of the brain in the first column with their respective functions in the second column of the table given below.

(A) P-(iii), Q-(i), R-(iv), S-(ii)

(B) P-(i), Q-(iv), R-(ii), S-(iii)

(D) P-(iii), Q-(iv), R-(i), S-(ii)

Answer: (D)

46. Which one of the following is established by the replication of research studies?

(A) Validity of the results

(B) Reliability of the results

(D) Mediation effect

Answer: (B)

47. Match the theory/law in the first column with the corresponding explanation in the second column of the table given below.

(A) P-(ii), Q-(iv), R-(i), S-(iii)

(B) P-(iv), Q-(iii), R-(ii), S-(i)

(D) P-(iii), Q-(ii), R-(iv), S-(i)

Answer: (C)

48. Match the sleep disorders in the first column with the symptoms in the second column of the table given below.

(A) P-(ii), Q-(iv), R-(i), S-(iii)

(B) P-(ii), Q-(i), R-(iv), S-(iii)

(D) P-(iii), Q-(iv), R-(i), S-(ii)

Answer: (B)

49. __________ explains aging as a process of mutual withdrawal of individual and society, whereas _________ assumes positive correlation between activity and successful aging.

(A) Decay theory, Engagement theory

(B) Balance theory, Engagement theory

(D) Withdrawal theory, Activity theory

Answer: (C)

50. Match the biases/effects in the first column with the descriptions in the second column of the table given below.

(A) P-(i), Q-(iii), R-(ii), S-(iv)

(B) P-(iv), Q-(iii), R-(i), S-(ii)

(D) P-(iv), Q-(i), R-(ii), S-(iii)

Answer: (B)

51. Match the theories in the first column with the central themes in the second column of the table given below.

(A) P-(iv), Q-(i), R-(ii), S-(iii)

(B) P-(iv), Q-(i), R-(iii), S-(ii)

(D) P-(ii), Q-(iii), R-(i), S-(iv)

Answer: (A)

52. Which one of the following would resolve the basic dilemma of the social psychologist?

(A) Conducting carefully designed experiments with high internal validity

(B) By replicating experiments and conducting some new experiments that have internal validity and others that have external validity

(D) Conducting applied rather than basic research

Answer: (B)

53. Match the research methods in the first column with their purposes in the second column of the table given below.

(A) P-(i), Q-(iii), R-(ii), S-(iv)

(B) P-(ii), Q-(iii), R-(iv), S-(i)

(D) P-(ii), Q-(iv), R-(i), S-(iii)

Answer: (D)

54. Which one of the following statements is TRUE according to Brehm’s reactance theory?

(A) A mild sign prohibitting spitting would be more effective in preventing spitting than a strong sign

(B) A strong sign would be more effective in preventing spitting than a mild one

(D) Signs are irrelevant to spitting behaviour

Answer: (A)

55. According to the overjustifcation effect, which one of the following consequences would be TRUE for students who freely choose to study psychology, if marks are given for attendance?

(A) Increased interest of students in the subject

(B) Decreased interest of students in the subject

(D) Increased interest in other social science subjects

Answer: (B)

56. Large rewards and severe punishments are examples of __________ justification for behaviour and result in _________ changes in attitude.

(A) internal; big

(B) external; big

(D) external; small

Answer: (D)

57. Which of the following therapies is/are based on classical conditioning?

(A) Systematic desensitization

(B) Aversion therapy

(D) Rational emotive behaviour therapy

Answer: (A, B)

58. Which of the following characterize(s) Wernicke’s aphasia?

(A) Inability to comprehend spoken words

(B) Inability to understand the meaning of words

(D) Inability to write and understand the symbols that represent speech sounds

Answer: (A, B, C, D)

59. Which of the following is/are the component(s) of Theory of Mind?

(A) Understanding that people can have false beliefs

(B) Distinguishing faces and smells

(D) Having a vast vocabulary to express one’s thoughts

Answer: (A, C)

60. Which of the following would NOT be effective in minimizing groupthink?

(A) The leader being impartial to all ideas no matter what they are

(B) The leader reminding the team that everyone will be held responsible for the decision of the group

(D) The leader arriving at a consensus quickly

Answer: (C, D)

61. Which of the following describe(s) the standard error of the mean?

(A) It is the standard deviation of the sampling distribution of the mean

(B) It reflects the accuracy with which sample means estimate the population mean

(D) It is the standard deviation of a stratified sample

Answer: (A, B)

62. Which of the following describe(s) organizational commitment?

(A) A strong desire to remain a member of the organization

(B) Willingness to exert high level of effort on behalf of the organization

(D) High turnover intention of the employees of the organization

Answer: (A, B, C)

63. Prejudice is supported by the human tendency to categorize into in-groups and out-groups. Prejudice is supported by which of the following processes?

(A) The way we think about others

(B) The way we assign meaning to others behaviour

(D) By working towards a common goal

Answer: (A, B)

64. Which of the following is/are feature(s) of clinical phobia?

(A) The fear must be persistent

(B) The fear must be a source of significant distress

(D) The fear is usually perceived as unwarranted

Answer: (A, B, D)

65. The value of F calculated from the data given in the table below is ________ (rounded off to one decimal place).

Answer: (3.6 to 3.6)

XH : Humanities & Social Sciences

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is ________.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

Reasoning and Comprehension (XH-B1)

XH-B1: Q.11 – Q.17 Carry ONE mark Each

11. Which word below best describes the idea of being both Spineless and Cowardly?

(A) Pusillanimous

(B) Unctuous

(D) Reticent

Answer: (A)

12. Choose the right preposition to fill up the blank:

The whole family got together ___ Diwali

(A) of

(B) at

(D) till

Answer: (B)

13. Select the correct option to fill in all the blanks to complete the passage:

(A) (i) disheartening (ii) failure (iii) channels (iv) matching

(B) (i) redeeming (ii) outperformance (iii) geographies (iv) eclipsing

(D) (i) humbling (ii) bombing (iii) theatres (iv) falling behind

Answer: (B)

Choose the correct sequence of the sentences so that they form a coherent paragraph:

(1) Most obviously, mobility is taken to be a geographical as well as a social phenomenon.

(3) The existing sociology of migration is incidentally far too limited in its concerns to be very useful here.

(5) Moreover, not only people are mobile but so too are many ‘objects’.

(A) 3, 2, 5, 4

(B) 2, 3, 4, 5

(D) 4, 2, 5, 3

Answer: (B)

15. The population of a country increased by 5% from 2020 to 2021. Then, the population decreased by 5% from 2021 to 2022. By what percentage did the population change from 2020 to 2022?

(A) -0.25%

(B) 0%

(D) 10.25%

Answer: (A)

16. The words Thin: Slim: Slender are related in some way. Identify the correct option(s) that reflect(s) the same relationship:

(A) Fat: Plump: Voluptuous

(B) Short: Small: Petite

(D) Fair: Dark: Wheatish

Answer: (A, B)

Which of the following action(s) are plausible?

(A) In future, the government can make district administration authorities responsible for protecting health of citizens and reviving the economy.

(B) The government may set up a task force to review the post pandemic situation and ascertain the effectiveness of the measures taken.

(C) The government may set up a committee to formulate a pandemic management program to minimize losses to life and economy in future.

(D) The government may take population control measures to minimize pandemic related losses in future.

Answer: (B, C)

XH-B1: Q.18 – Q.26 Carry TWO marks Each

(A) Fulmoni

(B) Emon

(D) Chintu

Answer: (C)

19. Select the correct relation between E and F.

(A) E > F

(B) E < F

(D) E < -F

Answer: (B)

20. A code language is formulated thus:

Then how does the word, GOODMORNING appear in the coded language?

(A) HUUFNUSPOPH

(B) FIICLIQMEMF

(D) HEEDATTACRH

Answer: (C)

What assumptions can be made about the stranger from the passage above?

(A) The stranger can become an owner of soil through developing all kinds of charm in more intimate relations.

(B) The stranger cannot become an owner of soil either in the physical or psychological sense.

(D) The stranger might become an owner of soil in the physical sense but not in the psychological

Answer: (B)

22. L is the only son of A and S. S has one sibling, B, who is married to L’s aunt, K. B is the only son of D. How are L and D related?

Select the possible option(s):

(A) Grandchild and Paternal Grandfather

(B) Grandchild and Maternal Grandfather

(D) Grandchild and Maternal Grandmother

Answer: (B, D)

(1) Consumed multitudes are jostling and shoving inside me

(2) and guided only by the memory of a large white bedsheet with a roughly circular hole some seven inches in diameter cut into the center,

(3) clutching at the dream of that holey, mutilated square of linen, which is my talisman, my open-sesame,

(4) I must commence the business of remaking my life from the point at which it really began,

(5) some thirty-two years before anything as obvious, as present, as my clock-ridden, crime-stained birth.

(A) 2 – 3 – 4

(B) 3 – 2– 4

(D) 4 – 3 – 2

Answer: (A)

What are the different ways in which ‘truth’ can be understood from the passage?

(A) Truth is what can be verified by hard empirical evidence.

(B) Truth is based on what can be perceived by the senses.

(D) Truth is contingent on the observer and can only be partial.

Answer: (C, D)

Answer: (35 to 35)

26. Select the odd word and write the option number as answer:

(1) Lek (2) Zloty (3) Diner (4) Drachma (5) Real

Answer: (3 to 3)

Sociology – C6

XH-C6: Q.27 – Q.44 Carry ONE mark Each

27. ___________ has given the concept of ‘thick description’.

(A) Emile Durkheim

(B) Clifford Geertz

(D) Talcott Parsons

Answer: (B)

28. Objectivity in social science research as a matter of transpersonal replicability entails ____________.

(A) Merciless elimination of personal biases

(B) Allocation of costs and benefits to parties be made on normative standards

(D) Reproducibility of findings of research under similar conditions and methods

Answer: (D)

29. Which of the following is NOT a characteristic of hypothesis?

(A) A shrewd hunch suggestive of a possible solution to a problem

(B) A causal relationship between two/more variables

(D) A theoretically derived statement that denies refutability

Answer: (D)

30. ___________ theory most appropriately describes a hierarchy of wealthy ‘core’ nations, poor ‘periphery’ nations, and a middle group of ‘semi-periphery’ nations.

(A) Globalization

(B) Stages of growth

(D) Limits to growth

Answer: (C)

31. In Hindu society, marriage of a widow to the husband’s brother is referred to as __________.

(A) Polygyny

(B) Endogamy

(D) Polyandry

Answer: (C)

32. Because of Covid-19 lockdown, a large number of working-class people lost their jobs. Rising price of commodities has also worsened their economic conditions. ___________ concept of Karl Marx most appropriately describes this ‘increasing impoverishment’ of the poor in contemporary times.

(A) Alienation

(B) Commodity fetishism

(D) Embourgeoisement

Answer: (C)

33. ___________ coined the term, ‘ethnocentrism’.

(A) A.R. Radcliffe-Brown

(B) Bronislaw Malinowski

(D) Harold Garfinkel

Answer: (C)

34. Supremacy of science over non-sciences is attributed to ___________.

(A) Postcolonialism

(B) Neo-Kantianism

(D) Verstehen

Answer: (C)

35. Communism, universalism, disinterestedness and ______________ constitute Mertonian ethos of science.

(A) Organized skepticism

(B) Organized dogmatism

(D) Neutrality

Answer: (A)

36. ____________theory postulates that developing economies would eventually catch up with the developed economies if they follow the social and economic models of Western capitalism.

(A) Postmodern

(B) Subaltern

(D) Modernization

Answer: (D)

37. ____________ approach was NOT propounded by B.S. Cohn as one of the approaches to study Indian civilization.

(A) Administrative

(B) Missionary

(D) Historiographical

Answer: (D)

38. If standard deviation is 0.3, then its corresponding variance would be _________.

(A) 0.9

(B) 0.03

(D) 0.3

Answer: (C)

39. Under __________ land tenurial system during the British rule in India, the individual cultivator/peasant had some ownership right over land holding.

(A) Zamindari

(B) Ryotwari

(D) Talukdari

Answer: (B)

40. ____________ introduced the concept of ‘reconstructive science’.

(A) J. Habermas

(B) A. Giddens

(D) M. Foucault

Answer: (A)

41. _____________ theory lies between minor working hypotheses and master conceptual schemes.

(A) Middle-range

(B) Social action

(D) Symbolic interactionist

Answer: (A)

42. __________ is NOT a characteristic feature of M.N. Srinivas’s concept of ‘dominant caste’.

(A) Numerical strength

(B) Economic power through possession of land

(D) Membership in militant organizations

Answer: (D)

43. Max Weber’s instrumental rationality refers to ___________.

(A) Traditional action

(B) Emotive action

(D) Value-rational action

Answer: (C)

44. The stable pattern of ‘modern men’ formulated by Alex Inkeles does not include __________.

(A) Openness to new experiences

(B) Freedom from traditional authority

(D) Belief in science and technology

Answer: (C)

XH-C6: Q.45 – Q.65 Carry TWO marks Each

45. _____________ refers to the careful consideration of the ways in which researchers’ past experiences, points of view, and roles impact these same researchers’ interactions with, and interpretations of, the research scene.

(A) Self-reflexivity

(B) Social interactionism

(D) Participant action research

Answer: (A)

46. __________ introduced the concept of __________ to refer to situations in which people accept, consent to, internalize, and are complicit in reproducing values and norms that are not in their own best interests.

(A) K. Marx, alienation

(B) M. Foucault, governmentality

(D) R. Putnam, social capital

Answer: (C)

47. ___________ is the process by which researchers begin by identifying several participants who fit the study’s criteria and then ask these people to suggest a colleague, a friend, or a family member who also fits the study’s criteria.

(A) Random sampling

(B) Stratified random sampling

(D) Snowball sampling

Answer: (D)

48. Match the following sociologists as given in Column P with their views on religion as given in Column Q.

(A) A-I, B-II, C-V, D-III

(B) A-I, B-III, C-V, D-II

(D) A-I, B-III, C-IV, D-II

Answer: (D)

49. There are four forms of triangulation, namely data triangulation, __________, theory triangulation and _____________.

(A) Field triangulation, methodological triangulation

(B) Investigator triangulation, methodological triangulation

(D) Investigator triangulation, epistemological triangulation

Answer: (B)

50. ____________ is the process by which groups seek to preserve some advantage by monopolizing resources and restricting access to the group.

(A) Social action

(B) Social construction

(D) Social conflict

Answer: (C)

51. Correlation coefficient lies between __________ and __________, and probability lies between _________ and __________.

(A) – 1 and 1, 0 and 1

(B) 0 and 1, – 1 and 1

(D) – 1 and 1, – 0.5 and 1.5

Answer: (A)

52. Match the following concepts as given in Column P with the Sociologists as given in Column Q:

(A) A-III, B-IV, C-I, D-II

(B) A-III, B-I, C-IV, D-II

(D) A-IV, B-III, C-II, D-I

Answer: (A)

53. Match the following approaches and village study as given in Column P with Sociologists as given in Column Q:

(A) A-III, B-IV, C-I, D-II

(B) A-II, B-IV, C-III D-I

(D) A-IV, B-III, C-II, D-I

Answer: (B)

54. According to the World Commission on Environment and Development, ‘sustainable development’ refers to ______________.

(A) Development that meets the needs of the present

(B) Development that meets the needs of the future

(C) Development that meets the needs of the present without compromising the ability of future generations to meet their own needs

(D) Development that meets the needs of the past

Answer: (C)

55. According to David Pocock, the Indian Jajmani system reflects ___________.

(A) Hierarchical collectivity

(B) Regulated individuality

(D) Anarchic individuality

Answer: (B, C)

56. Which of the following is/are NOT characteristic(s) of class system?

(A) Class systems are fluid and the boundaries between classes are never clear-cut.

(B) Class is a form of stratification in which one’s social position is given for a lifetime.

(D) Class divisions are organized around the purity and pollution.

Answer: (B, D)

57. Which of the following concept(s) is/are NOT propounded by Emile Durkheim?

(A) Collective bargaining

(B) Collective effervescence

(D) Charismatic authority

Answer: (A, D)

58. The example(s) of relations of production is/are ___________.

(A) Labour

(B) Division of labour

(D) Capitalism

Answer: (B, C)

59. While __________ emerges around a charismatic figure, idea or vision, __________ emerges as a breakaway group from a preexisting body of belief, rituals, or believers.

(A) Cult, Sect

(B) Sect, Cult

(D) Religion, Sect

Answer: (A)

60. Which of the following statement(s) is/are true for the Forest Rights Act (2006) of India?

(A) Forest dwellers’ right of conserving and protecting community forest resources

(B) Forest dwellers’ right to rehabilitation

(D) Forest dwellers’ absolute right over all the natural resources within the given forest area

Answer: (A, B, C)

61. The Ethnographic Survey of India as part of the Census 1901 was conducted to __________.

(A) Mitigate the racial and cultural issues faced by the British

(B) Make suitable legislations for Indian subjects

(D) Take executive action (welfare and development)

Answer: (A)

62. ____________ and ___________ propounded conflict theory.

(A) Talcott Parsons

(B) Ralf Dahrendorf

(D) Jeffrey C. Alexander

Answer: (B, C)

63. Which of the following is/are NOT aspect(s) of secularization process?

(A) Privatization of religion

(B) Rising level of membership of religious organizations

(D) Belief in magic and supernatural forces

Answer: (B, D)

64. Which of the following pair(s) is/are correct?

M1: Michel Foucault M2: Pierre Bourdieu M3: John Urry

X1: Archaeology of Knowledge X2: Sociological Imagination X3: Practice Theory

(A) M1 – X1

(B) M2 – X2

(D) M2 – X3

Answer: (A, D)

65. Which of the following statement(s) is/are INCORRECT?

(A) Hypergamy is a form of marriage where bride’s family is of superior status to the groom’s family

(B) Hypogamy is a form of marriage where groom’s family is of superior status to the bride’s family

(D) Polygynandry refers to marriage of several men to several women at the same time

Answer: (A, B)

GATE Exam 2023 Engineering Sciences (XE) Question Paper With Answer Key

August 7, 2023 by suresh84

GATE-2023

XE: Engineering Science

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(D) between

Answer: (D)

2. Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(D) Refute

Answer: (C)

3. A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

(A) 125

(B) 720

(D) 80

Answer: (D)

4. Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(D) At most half the candidates have a score that is larger than the mean.

Answer: (C)

5. In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(D) S

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

6. Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books.

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

Answer: (MTA)

7. Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

(1) At any stage, Ankita can move either one or two stairs up.

(2) At any stage, Ankita cannot move to a lower step.

Let F(N) denote the number of possible ways in which Ankita can reach the 𝑁𝑡ℎ stair. For example, F(1) = 1, F(2) = 2, F(3) = 3.

The value of F(5) is _______.

(A) 8

(B) 7

(D) 5

Answer: (A)

8. The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). The information contained in DNA can then be thought of as a sequence of these four nucleotides: A, T, C, and G. DNA has coding and non-coding regions. Coding regions—where the sequence of these nucleotides are read in groups of three to produce individual amino acids—constitute only about 2% of human DNA. For example, the triplet of nucleotides CCG codes for the amino acid glycine, while the triplet GGA codes for the amino acid proline. Multiple amino acids are then assembled to form a protein.

Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.

(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(D) neither (i) nor (ii)

Answer: (D)

9. Which one of the given figures P, Q, R and S represents the graph of the following function?

f(x) = | |x + 2| − |x – 1| |

(A) P

(B) Q

(D) S

Answer: (A)

10. An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

(A) P

(B) Q

(D) S

Answer: (D)

XE: Engineering Science

Engineering Mathematics: XE-A (Compulsory)

XE-A: Q.11 – Q.17 Carry ONE mark Each

11. Let A be a 3 × 3 real matrix having eigenvalues 1,2, and 3. If B = A² + 2A + I, where I is the 3 × 3 identity matrix, then the eigenvalues of B are

(A) 4, 9, 16

(B) 1, 2, 3

(D) 4, 16, 25

Answer: (A)

12. Let f : ℝ² → ℝ be a function defined by

Then which one of the following statement is TRUE?

(A) f is NOT continuous at (0, 0)

(B)

(C)

(D)

Answer: (A)

13. If the quadrature formula

is exact for all polynomials of degree less than or equal to 2, then

Answer: (A)

14. The second smallest eigenvalue of the eigenvalue problem y(0) = y(π) = 0, is

(A) 4

(B) 3

(D) 9

Answer: (C)

15. Which one of the following functions is differentiable at 𝑧=0 but NOT differentiable at any other point in the complex plane ℂ?

(A) f(z) = z|z|, z ∈ ℂ

(B) f(z) = sin(z), z ∈ ℂ

(D)

Answer: (A)

16. If the polynomial

P(x) = a₀ + a₁x + a₂x(x – 1) + a₃x(x – 1) (x – 2)

interpolates the points (0, 2), (1, 3), (2, 2), and (3,5), then the value of P(5/2) is ______ (round off to 2 decimal places).

Answer: (2.60 to 2.65)

17. The value of m for which the vector field

is a conservative vector field, is ___________ (in integer).

Answer: (3 to 3)

XE-A: Q.18 – Q.21 Carry TWO marks Each

18. Let and

The eigenvalues of both P and Q are 1,1, and 2. Which one of the following statements is TRUE?

(A) Both P and Q are diagonalizable

(B) P is diagonalizable but Q is NOT diagonalizable

(D) Both P and Q are NOT diagonalizable

Answer: (B)

19. The surface area of the portion of the paraboloid

z = x² + y²

that lies between the planes z = 0 and z = 1/4 is

Answer: (A)

20. The probability of a person telling the truth is 4/6. An unbiased die is thrown by the same person twice and the person reports that the numbers appeared in both the throws are same. Then the probability that actually the numbers appeared in both the throws are same is __________ (round off to 2 decimal places).

Answer: (0.26 to 0.30)

21. Let u (x, t) be the solution of the initial boundary value problem

u(x, 0) = sin (πx), x ∈ (0, 2)

u(0, t) = u(2, t) = 0.

Then the value of is ________ (in integer).

Answer: (2 to 2)

Fluid Mechanics (XE-B)

XE-B: Q.22 – Q.30 Carry ONE mark Each

22. Match the following measuring instruments with the appropriate figures.

I – Pitot probe

II – Pitot-static probe

III – Piezometer

(A) I – P; II – Q; III – R

(B) I – R; II – Q; III – P

(D) I – Q; II – P; III – R

Answer: (B)

23. Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?

(A) Froude number

(B) Strouhal number

(D) Lewis number

Answer: (B)

24. For an incompressible boundary layer flow over a flat plate shown in the figure, the momentum thickness is expressed as

Answer: (C)

25. Among the shear stress versus shear strain rate curves shown in the figure, which one corresponds to a shear thinning fluid?

(A) P

(B) Q

(D) S

Answer: (C)

26. Consider steady incompressible flow over a flat plate, where the dashed line represents the edge of the boundary layer, as shown in the figure. Which one among the following statements is true?

(A) Bernoulli’s equation can be applied in Region I between any two arbitrary points.

(B) Bernoulli’s equation can be applied in Region I only along a streamline.

(D) Bernoulli’s equation cannot be applied in Region I.

Answer: (D)

27. An inviscid steady incompressible flow is formed by combining a uniform flow with velocity U_∞ and a clockwise vortex of strength K at the origin, as shown in the figure. Velocity potential (ϕ) for the combined flow in polar coordinate (r, θ) is

(A)

(B)

(D) ϕ = −K ln r + U_∞r sin θ

Answer: (A)

28. Which of the following statements are true?

(i) Conservation of mass for an unsteady incompressible flow can be represented as denotes velocity vector.

(ii) Circulation is defined as the line integral of vorticity about a closed curve.

(iii) For some fluids, shear stress can be a nonlinear function of the shear strain rate.

(iv) Integration of the Bernoulli’s equation along a streamline under steady-state leads to the Euler’s equation.

(A) (i), (ii) and (iv) only

(B) (i), (ii) and (iii) only

(D) (ii) and (iv) only

Answer: (C)

29. For a two-dimensional flow field given as a streamline passes through points (2, 1) and (5, p). The value of p is

(A) 5

(B) 5/2

(D) 2

Answer: (C)

30. A stationary object is fully submerged in a static fluid, as shown in the figure. Here, CG and CB stand for center of gravity and center of buoyancy, respectively. Which one(s) among the following statements is/are true?

(A) The object is in stable equilibrium if y_CG > y_CB.

(B) The object is in stable equilibrium if y_CG < y_CB.

(D) The object is in unstable equilibrium if y_CG > y_CB.

Answer: (A, C)

XE-B: Q.31 – Q.43 Carry TWO marks Each

31. Consider steady fully-developed incompressible flow of a Newtonian fluid between two infinite parallel flat plates. The plates move in the opposite directions, as shown in the figure. In the absence of body force and pressure gradient, the ratio of shear stress at the top surface (y = H) to that at the bottom surface (y = 0) is

(A) 1

(B) U₁/U₂

(D) U₁ + U₂/U₂

Answer: (A)

32. A two-dimensional incompressible flow field is defined as,

where, A and B are constants. The dynamic viscosity of the Newtonian fluid is μ. In the absence of body force, which among the following expressions represents the pressure gradient at the location (5, 0) in the concerned flow field?

Answer: (C)

33. For a potential flow, the fluid velocity is given by The slope of t he potential line at (x, y) is

(A) u/v

(B) v/u

(D) −v/u

Answer: (C)

34. Consider steady incompressible flow of a Newtonian fluid over a horizontal flat plate, as shown in the figure. The boundary layer thickness is proportional to

(A) x^1/4

(B) x^1/2

(D) x²

Answer: (B)

35. In a steady two-dimensional compressible flow, u and v are the x- and y-components of flow velocity, respectively and ρ is the fluid density. Among the following pairs of relations, which one(s) perfectly satisfies/satisfy the definition of stream function, ψ, for this flow?

Answer: (C, D)

36. A water jet (density = 1000 kg/m³) is approaching a vertical plate, having an orifice at the center, as shown in the figure. While a part of the jet passes through the orifice, remainder flows along the plate. Neglect friction and assume both the inlet and exit jets to have circular cross-sections. If V = 5 m/s, 𝐷 = 100 mm and d = 25 mm, magnitude of the horizontal force (in N, rounded off to one decimal place) required to hold the plate in its position is ___________.

Answer: (183.0 to 185.0)

37. Water (density =1000 kg/m³) and alcohol (specific gravity = 0.7) enter a Y-shaped channel at flow rates of 0.2 m³/s and 0.3 m³/s, respectively. Their mixture leaves through the other end of the channel, as shown in the figure. The average density (in kg/m³) of the mixture is _______.

Answer: (820 to 820)

38. The velocity and acceleration of a fluid particle are given as and The magnitude of the component of acceleration (in m/s², rounded off to two decimal places) of the fluid particle along the streamline is _______.

Answer: (2.60 to 2.75)

39. A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed of 1500 rpm. Consider both turbines to operate with the same fluid (identical density and viscosity), and neglect any gravitational effect. Then the power (in W, rounded off to nearest integer) produced by the second turbine is ___________.

Answer: (430 to 460)

40. Water (density = 1000 kg/m³) flows steadily with a flow rate of 0.05 m³/s through a venturimeter having throat diameter of 100 mm. If the pipe diameter is 200 mm and losses are negligible, the pressure drop (in kPa, rounded off to one decimal place) between an upstream location in the pipe and the throat (both at the same elevation) is _______.

Answer: (18.5 to 19.5)

41. Water flows around a thin flat plate (0.25 m long, 2 m wide) with a free stream velocity (U_∞) of 1 m/s, as shown in the figure. Consider linear velocity profile for which the laminar boundary layer thickness is expressed as For water, density = 1000 kg/m³ and dynamic viscosity = 0.001 kg/m.s. Net drag force (in N, rounded off to two decimal places) acting on the plate, neglecting the end effects, is ________.

Answer: (1.10 to 1.20)

42. Axial velocity profile u(r) for an axisymmetric flow through a circular tube of radius R is given as,

where U is the centerline velocity. If V refers to the area-averaged velocity (volume flow rate per unit area), then the ratio V/U for n = 1 (rounded off to two decimal places) is ___________.

Answer: (0.32 to 0.34)

43. A stationary circular pipe of radius R = 0.5 m is half filled with water (density =1000 kg/m3), whereas the upper half is filled with air at atmospheric pressure, as shown in the figure. Acceleration due to gravity is g = 9.81 m/s². The magnitude of the force per unit length (in kN/m, rounded off to one decimal place) applied by water on the pipe section AB is _______.

Answer: (2.2 to 2.4)

Material Science (XE-C)

XE-C: Q.44 – Q.52 Carry ONE mark Each

44. In age-hardening of an aluminium alloy, the purpose of solution treatment followed by quenching is to

(A) form martensitic structure

(B) increase the size of the precipitates

(D) form precipitates at the grain boundaries

Answer: (C)

45. The magnetization (M) – magnetic field (H) curves for four different materials are given below. Which one of these materials is most suitable for use as a permanent magnet?

Answer: (C)

46. The band gap of a semiconducting material is ~ 2 eV. Which one of the following absorption (A) vs. energy (in eV) curves is correct?

Answer: (D)

47. Figures (i) and (ii) show a binary phase diagram and the corresponding Gibbs free energy (G) vs. composition (X_B) diagram, respectively. Figure (ii) corresponds to which one of the temperatures shown in Figure (i)?

(A) T1

(B) T2

(D) T4

Answer: (C)

48. Aliovalent doping of MgCl₂ in NaCl leads to the formation of defects. Which one of the following is the correct defect reaction?

Answer: (B)

49. A screw dislocation in a FCC crystal has Burgers vector of where a is the lattice constant. The possible slip plane(s) is/are:

Answer: (C, D)

50. The tensile true stress (σ) – true strain (ϵ) curve follows the Hollomon equation:

σ = 500ϵ^0.15 MPa

At the maximum load, the work-hardening rate (dσ/dϵ) is (in MPa): _________ (rounded off to nearest integer)

Answer: (350 to 400)

51. A metal has a certain vacancy fraction at a temperature of 600 K. On increasing the temperature to 900 K, the vacancy fraction increases by a factor of ____________ (rounded off to one decimal place)

Given: Gas constant, R=8.31 J mol⁻¹K⁻¹ and activation energy for vacancy formation, Q =68 kJ mol⁻¹

Answer: (90.0 to 105.0)

52. In a semiconductor, the ratio of electronic mobility to hole mobility is 10. The density of electrons and holes are 1015 m⁻³ and 1016 m⁻³, respectively. If the conductivity of the material is 1.6 Ω⁻¹ m⁻¹, then the mobility of holes is (in m2V⁻¹s⁻¹) : ____________ (rounded off to nearest integer)

Given: Charge of an electron: 1.6 × 10⁻¹⁹ C

Answer: (490 to 510)

XH-C: Q.53 – Q.65 Carry TWO marks Each

53. A student performed X-ray diffraction experiment on a FCC polycrystalline pure metal. The following sin²θ values were calculated from the diffraction peaks.

sin² θ = 0.136, 0.185, 0.504, 0.544

However, the student was negligent and missed noting one of the peaks. Which one of the following Miller indices corresponds to the missing peak?

(A) (200)

(B) (220)

(D) (222)

Answer: (B)

54. Match the lattice planes and directions (in Column I) with the corresponding Miller indices (in Column II):

(A) P-2, Q-4, R-1, S-3

(B) P-3, Q-1, R-4, S-2

(D) P-3, Q-4, R-2, S-1

Answer: (A)

55. Match the hardness test (in Column I) with its indenter type (in Column II).

(A) P-2, Q-4, R-1

(B) P-4, Q-2, R-3

(D) P-4, Q-2, R-1

Answer: (D)

56. TTT diagram of a eutectoid steel is shown below. Match the heat treatment cycle (in Column I) with its microstructure (in Column II).

(A) P-1, Q-2, R-4

(B) P-2, Q-3, R-2

(D) P-2, Q-3, R-1

Answer: (C)

57. Which of the following statement(s) is/are true for an optical microscope?

(A) Increasing the aperture of the objective lens deteriorates the resolution

(B) Reducing the wavelength of illuminating light improves the resolution

(D) Reducing the wavelength of illuminating light decreases the depth of field

Answer: (B, C, D)

58. Among the 14 Bravais lattices, there is no base centred cubic unit cell. Which of the following statement(s) is/are true?

(A) The base-centred cubic unit cell is same as the simple tetragonal unit cell

(B) The base-centred cubic unit cell is same as the body centred tetragonal unit cell

(D) The base-centred cubic unit cell does not have any 3-fold rotation axis

Answer: (A, D)

59. Specific heat (C_v) of a material was found to depend on temperature as shown below. Which of the following statement(s) is/are true?

(A) The material is metallic

(B) The material is insulating

(D) The material is one dimensional

Answer: (A, C)

60. A pure Silicon wafer is doped with Boron by exposing it to B₂O₃ vapour at an elevated temperature. It takes 1000 seconds to reach a Boron concentration of 1020 atoms m⁻³ at a depth of 1 μm. The time taken to reach the same concentration of Boron at a depth of 2 μm is (in seconds): _________ (rounded off to nearest integer)

Given: Boron concentration on the wafer surface remains constant.

Answer: (3840 to 4100)

61. The Young’s modulus of a quartz piezoelectric crystal is 100 GPa. The uniaxial stress required to change its polarization by 1% is (give absolute value in GPa) _________ (rounded off to nearest integer)

Answer: (1 to 1)

62. A one-dimensional nanowire has a linear electron density of 10⁸ electrons cm⁻¹. The Fermi energy of the system is (in eV) ______ (rounded off to two decimal places)

Given : where ‘m’ is the mass of an electron

Answer: (9.20 to 9.60)

63. Two moles of a monoatomic ideal gas at 10 atm and 300 K is expanded isothermally and reversibly to a pressure of 2 atm. The absolute value of work done by the system is (in kJ) ____________ (rounded off to two decimal places)

Given: R=8.31 J mol⁻¹K⁻¹, 1 atm = 101 kPa

Answer: (7.90 to 8.05)

64. An electrochemical cell consists of pure Zn electrode (anode) and a hydrogen electrode (cathode) in a dilute Zn⁺² The overall reaction is:

Zn(s) + 2H⁺ = H₂ + Zn⁺²

If the overall cell potential is +0.690 V, then the value of is _______ (rounded off to two decimal places)

Given: Pressure of hydrogen gas = 1 atm; Temperature = 298 K;

RT/F = 0.0256 V, where R is gas constant and F is Faraday constant

The standard reduction potential of :

Zn⁺² + 2e = Zn(E° = −0.762 V) versus Standard Hydrogen Electrode 2H⁺ + 2e = H₂(E° = 0 V)

Answer: (5.25 to 7.00)

65. In a Raman spectroscopy experiment done at 300 K, a Raman line is observed at 200 cm⁻¹ (~25 meV). The ratio of the intensity of the Stokes line to that of the Anti-Stokes line is ____________ (rounded off to two decimal places)

Given: Boltzmann constant, k = 8.62 × 10⁻⁵ eV K⁻¹

Answer: (2.45 to 2.80)

Solid Mechanics (XE-D)

XE-D: Q.66 – Q.74 Carry ONE mark Each

66. A plane truss is simply supported at P and R as shown. A downward force F is applied at hinge Q. The axial force developed in member PS is

(A)

(B)

(D) √5 F Compressive

Answer: (B)

67. A massless rigid rod OP of length L is hinged frictionlessly at O. A concentrated mass m is attached to end P of the rod. Initially, the rod OP is horizontal. Then, it is released from rest. There is gravity as shown. The rod acquires an angular velocity as it swings. The clockwise angular velocity of the rod, when it first reaches the vertical position as shown, is

Answer: (B)

68. Two equivalent descriptions of the state of stress at a point are shown in the figure. The normal stresses σ₁ and σ₂ as shown on the right must be, respectively,

(A) τ_o and –τ_o

(B) –τ_o and τ_o

(D) –τ_o/√2 and τ_o/√2

Answer: (A)

69. The state of strain at a point in a machine component is given as ε_xx = 2.5 × 10⁻⁴, ε_yy = 2.0 × 10⁻⁴, ε_zz = −5 × 10⁻⁴, ε_xy = 2.5 × 10⁻⁴, ε_yz = −0.5 × 10⁻⁴, ε_zx = −1.0 × 10⁻⁴. The volumetric strain at this point is

(A) 4 × 10⁻⁴

(B) 3 × 10⁻⁴

(D) −3 × 10⁻⁴

Answer: (B)

70. A thin walled, closed cylindrical vessel of inside diameter 𝑑 and wall thickness t contains a fluid under pressure p. The figure below shows a part of the cylindrical vessel; end caps are not shown. Consider the small element shown with sides parallel and perpendicular to the axis of the cylinder. The stresses σ₁ and σ₂ are

Answer: (A)

71. A spring mass system is shown in the figure below. Take the acceleration due to gravity as g = 9.81 m/s². The static deflection due to weight and the time period of oscillations, respectively, are

(A) 0.392 m and 1.26 s

(B) 0.392 m and 3.52 s

(D) 0.626 m and 3.52 s

Answer: (A)

72. A rod is subjected to three forces as shown in the figure on the left. An equivalent force system with forces F₁, F₂ and moment M is shown in the figure on the right. The value of M (in N-m) is______(rounded off to one decimal place).

Answer: (117.0 to 118.0)

73. A simply supported beam of length 3 m is loaded as shown in the figure. The magnitude of the shear force (in kN) at the mid-point of the beam is ______ (rounded off to one decimal place).

Answer: (4.9 to 5.1)

74. For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The magnitude of maximum shear stress (in MPa) in the material is ______ (rounded off to one decimal place).

Answer: (49.5 to 50.5)

XE-D: Q.75 – Q.87 Carry TWO marks Each

75. A solid uniform rigid disk of mass 𝑚 and radius R rolls without slipping along a horizontal surface PQ. The speed of the center of the disk is 𝑣. The disk then strikes a hurdle of height 3R/20 at point S. During the impact, there is no rebound or slip at S and no impulse from the surface PQ. The magnitude of the velocity of the center of the disk immediately after the impact is

(A) 0.1v

(B) 0.3v

(D) 0.9v

Answer: (D)

76. A cylinder made of rubber (length = L and diameter = d) is inserted in a rigid container as shown in the figure. The rubber cylinder fits snugly in the rigid container. There is no wall friction. The modulus of elasticity of the rubber is E and its Poisson’s ratio is v. The cylinder is subjected to a small uniform pressure p as shown in the figure. The resulting axial strain (ε_zz) is

Answer: (C)

77. The state of stress at the critical location in a structure is σ_xx = 420 MPa, σ_yy = 100 MPa, σ_zz= σ_xy = σ_yz= σ_zx= 0. The yield stress of the material in uniaxial tension is 400 MPa. Select the correct statement among the following.

(A) The structure is safe by both Tresca (maximum shear stress) theory and von-Mises (distortion energy) theory.

(B) The structure is safe by Tresca (maximum shear stress) theory and unsafe by von-Mises (distortion energy) theory.

(D) The structure is unsafe by both Tresca (maximum shear stress) theory and von-Mises (distortion energy) theory.

Answer: (C)

78. The figure shows a column of rectangular cross section 100 mm × 80 mm. It carries a load of 60 kN at a point 30 mm from the edge PQ. The values of stress component σ_zz on surfaces PQQ′P′ and SRR′S′, at points far away from both ends of the column, are respectively

(A) 18.75 N/mm² (Compressive) and 3.75 N/mm² (Tensile)

(B) 18.75 N/mm² (Compressive) and 3.75 N/mm² (Compressive)

(D) 13.13 N/mm² (Compressive) and 1.88 N/mm² (Compressive)

Answer: (D)

79. Consider an electric pole with dimensions as shown in the figure. Let the end R be subjected to a vertical force F. The flexural rigidity of both vertical and horizontal bars is EI. Neglect the axial deflection of the vertical bar, and all effects of self-weight. The vertical deflection at end R is

(A) 7FL³/3EI

(B) 10FL³/3EI

(D) 8FL³/3EI

Answer: (A)

80. A uniform cantilever beam has flexural rigidity EI and length L. It is subjected to a concentrated force F and moment M = 2FL at the free end as shown. The deflection (δ) at the free end is

(A) 11FL³/12EI

(B) 8FL³/9EI

(D) 7FL³/6EI

Answer: (C)

81. A steel ball of mass m = 10 kg is suspended from the ceiling of a moving carriage by two inextensible strings making 60° with the horizontal as shown. The carriage has an acceleration a such that the tension in the string on the right is double the tension in the string on the left. Take the acceleration due to gravity (g) as 10 m/s². The acceleration a (in m/s²) is ______ (rounded off to one decimal place).

Answer: (1.8 to 2.0)

82. A block of mass m = 10 kg is lying on an inclined plane PQ. The mass is restrained from sliding down the inclined plane by a force F. The coefficient of friction between the block and the inclined plane is 0.3. Take the acceleration due to gravity as 10 m/s². The smallest force F (in N) required to prevent the block from sliding down is______(rounded off to one decimal place).

Answer: (23.0 to 25.0)

83. A spherical rigid ball of mass 10 kg is moving with a speed of 2 m/s in the direction shown. The ball collides with a rigid frictionless wall and rebounds at an angle α with a speed of v, as shown. The coefficient of restitution is 0.9. The angle α (in degrees) is______(rounded off to one decimal place).

Answer: (57.0 to 58.0)

84. A thin steel plate is loaded in the x-y plane as shown in the figure. Take the Poisson’s ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200 GPa. The strain along the 𝑧-direction is ε_zz = −3 × 10⁻⁴. The value of σ_yy (in MPa) is ______ (rounded off to one decimal place).

Answer: (79.5 to 80.5)

85. A composite rod made of steel and copper is fixed immovably at its ends as shown in the figure. The length of each portion of the rod is 1 m as shown. The cross-sections of both portions are the same. The moduli of elasticity of steel and copper are 200 GPa and 100 GPa, respectively. The coefficients of thermal expansion of steel and copper are 12 × 10⁻⁶/℃ and 18 × 10⁻⁶/℃, respectively. The composite rod is initially stress free. Then, the temperature of the composite rod is increased by 100℃. The magnitude of axial stress (in MPa) developed in the steel rod is ______ (rounded off to one decimal place).

Answer: (199.0 to 201.0)

86. A slender uniform elastic rod of length 1 m and of solid circular cross-section of diameter 50 mm is originally straight. It is then loaded by equal and opposite end moments as indicated in the figure. The resulting lateral displacement of the mid-point of the rod is 10 mm (displacements are exaggerated in the figure). The maximum longitudinal strain in the rod is p × 10⁻³, where p is ______ (rounded off to one decimal place).

Answer: (1.9 to 2.1)

87. Consider a solid cylindrical shaft and a hollow cylindrical shaft. Both shafts are axisymmetric and elastic, and have the same cross-sectional area. The hollow shaft has an outside diameter of 150 mm and an inside diameter of 120 mm. When both the shafts are twisted by the same twisting moment, the ratio of maximum shear stress developed in the hollow shaft (τ_h) to maximum shear stress developed in the solid shaft (τ_s) will be ______ (rounded off to three decimal places).

Answer: (0.350 to 0.380)

Thermodynamics (XE-E)

Q.88 – Q.96 Carry ONE mark Each

88. A : The number of properties required to fix the state of a system is given by ‘state postulate’.

R : The state of a simple compressible system is completely specified by two independent, intensive properties.

About the statements A and R applied to a single-phase system,

(A) A is correct and R is incorrect.

(B) A is incorrect and R is correct.

(D) Both A and R are correct.

Answer: (D)

89. Which of the following is an extensive property of a system?

(A) Density

(B) Pressure

(D) Total mass

Answer: (D)

90. A tank of volume V contains homogeneous mixture of two ideal gases, A and B at a temperature T and a pressure P. The mixture contains n_A moles of gas A and n_B moles of gas B. If P_A and P_B are the partial pressures of gas A and gas B, respectively, then

Answer: (A)

91. If an ideal air-standard Otto cycle and an ideal air-standard Diesel cycle operate on the same compression ratio, then the relation between the thermal efficiencies (ηth) of the cycles is

(A) η_{th, Otto} = η_{th, Diesel} and η_{th, Otto} < 1

(B) η_{th, Otto} > η_{th, DIesel}

(D) η_{th, Otto} = η_{th, Diesel} = 1

Answer: (B)

92. The following statements are given:

(i) The third law of thermodynamics deals with the entropy of a substance at the absolute zero temperature.

(ii) Entropy of any non-crystalline structure is zero at absolute zero temperature.

(iii) At the absolute zero temperature, the crystal structure has maximum degree of order.

(iv) The thermal energy of the substance at absolute zero temperature is maximum.

The correct option describing these statements is

(A) Only (i) is correct

(B) Only (ii) is correct

(D) Both (i) and (iv) are correct

Answer: (C)

93. Adiabatic bulk modulus of a substance is defined as

Answer: (D)

94. An insulated rigid closed tank of 2 m³ internal volume contains saturated liquid-vapor mixture of water at 200 ℃. The quality of the mixture is 0.75. The mass of the mixture in the tank is ____________ kg (rounded off to one decimal place).

Use the following data for water:

At 200 ℃: v_f = 0.001156 m³/kg, v_fg = 0.12620 m³/kg, v_g = 0.12736 m³/kg

Answer: (20.5 to 21.5)

95. A rigid closed tank contains 2 kg of an ideal gas at 500 kPa and 350 K. A valve is opened, and half of the mass of the gas is allowed to escape. Then the valve is closed. If the final pressure in the tank is 300 kPa, the final temperature in the tank is _________ K (in integer).

Answer: (420 to 420)

96. Air at 400 K and 200 kPa is heated at constant pressure to 600 K. Assuming that the internal energy is a function of temperature only, the magnitude of change in internal energy during this process is __________ kJ/kmol (rounded off to one decimal place).

Use the following data:

Molar specific heat of air at constant volume : where T is temperature in K, a = 19.686 kJ/kmol-K, b = 0.002 kJ/kmol-K² and c = 0.5 × 10⁻⁵ kJ/kmol-K³.

Answer: (4389 to 4392)

XE-XE: Q.97 – Q.109 Carry TWO marks Each

97. A rigid closed tank having a volume of 2 m³ contains 0.1 m³ of saturated liquid water and 1.9 m³ of saturated water vapor at 100 kPa. Heat is transferred to the tank until the final tank pressure reaches 2 MPa.

Following data for water is given:

At 100 kPa: v_f = 0.001043 m³/kg, v_g = 1.694 m³/kg

u_f = 417.33 kJ/kg, u_g = 2506.06 kJ/kg

At 2 MPa: v_f = 0.001177 m³/kg, v_g = 0.09963 m³/kg,

u_f = 906.42 kJ/kg, u_g = 2600.26 kJ/kg

The magnitude of heat transfer in this process is

(A) 34670 kJ

(B) 55842 kJ

(D) 77470 kJ

Answer: (D)

98. An ideal Diesel cycle has a compression ratio of 20 and cut-off ratio of 1.5. At the beginning of the compression stroke, air is at 100 kPa, 300 K. Use the cold-air-standard assumptions with property value c_p = 1.005 kJ/kg-K. Assume c_p/c_v = 1.4. For this cycle, the net work output per unit mass is

(A) 335 kJ/kg

(B) 395 kJ/kg

(D) 165 kJ/kg

Answer: (A)

99. A 5 kg metal block (c_p = 0.5 kJ/kg-K) at 373 K is submerged into 10 kg of water (c_p = 4.2 kJ/kg-K) at 293 K in an insulated rigid container without spilling. Assuming thermal equilibrium is reached, the approximate entropy change of the universe is

(A) −0.565 kJ/K

(B) 0.073 kJ/K

(D) 0.963 kJ/K

Answer: (B)

100. Match the following:

(A) A1→B2, A2→B4, A3→B1, A4→B3

(B) A1→B4, A2→B2, A3→B1, A4→B3

(D) A1→B4, A2→B2, A3→B3, A4→B1

Answer: (C)

101. A piston-cylinder device initially contains 1 m³ of air at 200 kPa and 25 ℃. Air expands at constant pressure while a heater of 250 W is switched on for 10 minutes. There is a heat loss of 4 kJ during this process. Assuming air as an ideal gas, the final temperature of air is ____________ ℃ (rounded off to one decimal place).

Use the following data for air: R = 0.287 kJ/kg-K, c_p = 1.005 kJ/kg-K

Answer: (85.0 to 88.0)

102. Steam at 2 MPa and 300 ℃ steadily enters a nozzle of inlet diameter of 20 cm. Steam leaves the nozzle with a velocity of 300 m/s. The mass flow rate of steam through the nozzle is 10 kg/s. Assume no work interaction and no change in potential energy. If the heat loss from the nozzle per kg of steam is 3 kJ, the exit enthalpy per kg of steam is ____________ kJ (rounded off to nearest integer).

Use the following data for steam:

At 2 MPa and 300 ℃: v = 0.12551 m³/kg, h = 3024.2 kJ/kg

Answer: (2975 to 2980)

103. A rigid tank of 2 m³ internal volume contains 5 kg of water as a saturated liquid-vapor mixture at 400 kPa. Half of the mass of the saturated liquid in the tank is drained-off while maintaining constant pressure of 400 kPa in the tank. The final quality of the mixture remaining in the tank is ____________ (rounded off to two decimal places).

Use the following data for water:

At 400 kPa: v_f = 0.001084 m³/kg, v_fg = 0.46138 m³/kg, v_g = 0.46246 m³/kg

Answer: (0.90 to 0.95)

104. Consider a spark ignition engine which operates on an ideal air-standard Otto cycle. It uses a fuel which produces 44 MJ/kg of heat in the engine. If the engine requires 40 mg of fuel to produce 1 kJ of work output, then the compression ratio of the Otto cycle is ____________ (rounded off to two decimal places).

For the entire cycle, use c_p/c_v = 1.4

Answer: (8.00 to 8.30)

105. A refrigerator operates on an ideal vapor compression cycle between the pressure limits of 140 kPa and 800 kPa. The working fluid is the refrigerant R-134a. The refrigerant enters the compressor as saturated vapor at 140 kPa and exits at 800 kPa and 60℃. It leaves the condenser as a saturated liquid at 800 kPa. The coefficient of performance (COP) of the refrigerator is ____________ (rounded off to two decimal places).

Use the following property data for R-134a:

At 140 kPa: h_f = 27.06 kJ/kg, h_g = 239.19 kJ/kg

At 800 kPa: h_f = 95.48 kJ/kg, h_g = 267.34 kJ/kg

At 800 kPa and 60 ℃: h = 296.82 kJ/kg

Answer: (2.45 to 2.55)

106. A steam power plant operates on a simple ideal Rankine cycle. The condenser pressure is 10 kPa and the boiler pressure is 5 MPa. The steam enters the turbine at 600 ℃. Mass flow rate of the steam is 50 kg/s. Neglecting the pump work, the net power output of the plant is ____________ MW (rounded off to one decimal place).

Use the following property data for water:

At 10 kPa:

h_f = 191.81 kJ/kg, h_fg = 2392.82 kJ/kg, h_g = 2584.63 kJ/kg

s_f = 0.6492 kJ/kg-K, s_fg = 7.5010 kJ/kg-K, s_g = 8.1502 kJ/kg-K

At 5 MPa and 600℃: h = 3666.47 kJ/kg, s = 7.2588 kJ/kg-K

Answer: (67.3 to 69.3)

107. In an air-conditioning system, air enters at 20 ℃ and 30% relative humidity at a steady rate of 30 m³/min in a humidifier and it is conditioned to 25℃ and 60% relative humidity. Assuming entire process takes place at pressure of 100 kPa, the mass flow rate of the steam added to air in the humidifier is ____________ kg/min (rounded off to three decimal places).

Use the following property data:

At 20℃ and 25℃, saturation pressures of water are 2.3392 kPa and 3.1698 kPa, respectively.

For air, R = 0.287 kJ/kg-K

Answer: (0.262 to 0.290)

108. An office uses a heat pump to receive 500 kJ/day heat in winter to maintain its temperature at 300 K. The ambient temperature is 280 K. If the COP of the heat pump is 60% of its theoretical maximum value, the ratio of actual work input to the minimum theoretical work input to the heat pump is _________ (rounded off to one decimal place).

Answer: (1.6 to 1.8)

109. In a liquid-vapour phase change process, (dP/dT)_sat at 100°C for saturated water is 3750 Pa/K. If the resulting change in specific volume (v_g – v_f) is 1.672 m³/kg, the enthalpy of vaporization (h_fg) will be ______ kJ/kg (in integer).

Answer: (2337 to 2341)

Polymer Science and Engineering (XE-F)

XE-F: Q.110 – Q.118 Carry ONE mark Each

110. Which one of the monomers given is used in the synthesis of cellulose?

(A) Fructose

(B) Lactic acid

(D) Glucose

Answer: (D)

111. A copper wire upon loading instantaneously increases in length to l, and then continues to elongate gradually. Upon unloading, the wire retracts to length l. According to the Maxwell model, which one of the options given correctly relates the total strain E, the applied stress S, the modulus G, the material’s resistance to flow ƞ, and the elapsed time t between loading and unloading?

(A) E = (S/G) – (S/n)t

(B) E = (S/G) × (S/n)t

(D) E = (S/G)/(S/n)t

Answer: (C)

112. Consider the structure of a crosslinked polymer shown in the figure. From the options given, identify the monomers that are used in the synthesis of the polymer.

(A) Melamine and Benzaldehyde

(B) Melamine and Acetone

(D) Melamine and Ethanol

Answer: (C)

113. Among the options given, choose the most suitable compatibilizer for blending Polyvinylidene fluoride (PVDF) and Acrylonitrile butadiene styrene (ABS).

(A) Styrene-acrylonitrile (SAN)

(B) Polybutadiene (PB)

(D) Nylon 6

Answer: (C)

114. A high molecular weight polymer passes through different zones from the hopper to the die in an extruder. Among the options given, identify the correct match between the zones and their key functions.

(A) P-4; Q-3; R-2; S-1

(B) P-3; Q-4; R-1; S-2

(D) P-3; Q-1; R-2; S-4

Answer: (A)

115. Polymer wetting is improved by the addition of fillers with functional groups. In a typical case-study, natural-clay was modified with hydroxyl groups and compounded with Nylon 6 along with an antioxidant. The resulting composite exhibited poor mechanical properties. Which one among the options given explains this observation?

(A) The surface functional groups of the filler reacted with Nylon 6

(B) The antioxidant degraded during the processing

(D) The antioxidant reacted with Nylon 6

Answer: (C)

116. Among the options given, identify the correct match between the polymers and their glass transition temperatures (T_g).

(A) P-2; Q-4; R-3; S-1

(B) P-3; Q-1; R-4; S-2

(D) P-4, Q-2; R-1; S-3

Answer: (B)

117. What is the correct order of decreasing crystallinity of the given polymers?

(A) P > R > S > Q

(B) S > Q > P > R

(D) S > R > Q > P

Answer: (D)

118. Choose the correct option that best correlates the graphs with the polymerization methods.

(A) P – living polymerization; Q – chain growth; R – step growth

(B) P – chain growth; Q – living polymerization; R – step growth

(D) P – living polymerization; Q – step growth; R – chain growth

Answer: (B)

XE-F: Q.119 – Q.131 Carry TWO marks Each

119. From the options given, identify the correct match(es) between the polymer products with the most appropriate processing technique.

(A) P-3; Q-4; R-1; S-2

(B) P-3; Q-2; R-1; S-4

(D) P-3; Q-4; R-1; S-1

Answer: (A, D)

120. Among the options given, which agents are used to vulcanize or cure rubbers?

(A) Dicumyl peroxide

(B) Zinc stearate

(D) Dinitrobenzene

Answer: (A, D)

121. Lipase is a natural enzyme, which cleaves carboxylic ester bonds. Among the options given, identify the polymer(s) degraded by lipase.

(A) Polypropylene (PP)

(B) Polycaprolactone (PCL)

(D) Polyethylene terephthalate (PET)

Answer: (B, D)

122. Among the options given, identify the correct pair(s) of catalyst and co-catalyst that form a Ziegler-Natta catalyst.

(A) TiCl₃ and Al(CH₃CH₂)₂Cl

(B) ZnCl₂ and Al(CH₃)₃

(D) VCl₄ and Al(CH₃CH₂)₂Cl

Answer: (A, D)

123. Mechanical stress is applied on a polymer. Identify the correct match(es) between the statements (1, 2, 3, 4, 5) that describe the deformations and the regimes (P, Q, R).

(A) P-2; Q-5; R-1

(B) P-1; Q-5; R-1

(D) P-4; Q-3; R-1

Answer: (A, D)

124. Stress versus elongation profiles for different polymeric materials are shown in the figure. Choose the combination that best describes these profiles.

(A) 1-Nylon fibers; 2-Polyethylene; 3-Vulcanized rubber; 4-Polystyrene

(B) 1-Polyethylene; 2-Vulcanized rubber; 3-Polystyrene; 4-Nylon fibers

(D) 1-Vulcanized rubber; 2-Polyethylene; 3-Nylon fibers; 4-Polystyrene

Answer: (C)

125. Among the options given, which method(s) is/are used for the synthesis of atactic polystyrene?

(A) Free radical polymerization

(B) Ring opening polymerization

(D) Ionic polymerization

Answer: (A, D)

126. A nylon sample of 0.03 m² cross-sectional area is subjected to a creep load of 10 kN. The load is removed after a duration of 60 s. Young’s modulus and the viscosity for nylon are 1 GPa and 300 Giga Poise. The compliance of the specimen is ________×10⁻⁹ m²/N. (Answer in integer)

Answer: (0.8 to 1.0 OR 3.0 to 3.0)

127. Polyvinylidine fluoride (PVDF) was quenched from the melt in one case and in the other case, it was slowly cooled from the melt at 10 °C/min. The percentage crystallinity of the slowly cooled PVDF is 60%. The heat of fusion for the quenched PVDF is 0.5ΔH_m (ΔH_m is the heat of fusion for the slowly cooled PVDF), and the heat of fusion for 100% crystalline PVDF is 100 J/g. The percentage crystallinity of the quenched PVDF is ______%. (Answer in integer)

Answer: (30 to 30)

128. A polymeric material of density 0.9 g/cc and melt volume of 10 cc in an extruder has a residence time of 100 s. The output of the extruder is _____ kg/h. (Rounded off to two decimal places)

Answer: (0.31 to 0.33)

129. A polymer weighing 0.2 g is dissolved in 100 ml of benzene and has a relative viscosity of 1.5. The polymer obeys Mark-Houwink equation with constants a = 0.5 and K = 0.001. The molecular weight of the polymer is _____ × 10¹⁰ g/mol. (Rounded off to two decimal places)

Answer: (6.24 to 6.26)

130. A continuous and aligned glass-fiber reinforced composite consists of 40 vol% of glass-fiber having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin, which when hardened, displays a modulus of 3.4 GPa. The modulus of elasticity of this composite in the longitudinal direction is _________ GPa. (Rounded off to two decimal places)

Answer: (29.60 to 30.01)

131. The molar mass distribution of a polymer is

The resulting weight average molecular weight of the polymer is _______ g/mol. (Answer in integer)

Answer: (6875 to 6875)

Food Technology (XE-G)

XE-G: Q.132 – Q.140 Carry ONE mark Each

132. Choose the correct group of fat soluble vitamins

(A) Cholecalciferol, α-Tocopherol, Menadione

(B) Thiamine, Cholecalciferol, α-Tocopherol

(D) Biotin, Thiamin, Niacin

Answer: (A)

133. The synthesis of thyroxine T4 in human body requires

(A) Selenium

(B) Iodine

(D) Zinc

Answer: (B)

134. Which among the followings is NOT an essential amino acid?

(A) L-Phenylalanine

(B) L-Valine

(D) L-Arginine

Answer: (D)

135. The time required for stipulated destruction of a microbial population at a given temperature is

(A) D-value

(B) F-value

(D) Q₁₀ value

Answer: (B)

136. Which among the following statements is NOT correct?

(A) Cod fish is a major source of ω-3 fatty acids.

(B) Beetroot is a good source of β-carotene.

(D) Fresh sugarcane juice is a good source of polyphenol oxidase.

Answer: (C)

137. Which of the following statements is NOT correct?

(A) As the shear rate increases, the apparent viscosity decreases for a pseudoplastic fluid.

(B) As the shear rate increases, the apparent viscosity increases for a dilatant fluid.

(D) Rheopectic and thixotropic are two time independent fluids.

Answer: (D)

138. Calculate the efficiency in percent (rounded off to 1 decimal place) of an oil expeller which yields 37 kg oil containing 5% solid impurities from 100 kg mustard seeds. The oil content of the mustard seed is 38%.

Answer: (92.0 to 93.0)

139. Orange juice is packaged aseptically and stored under ambient conditions. The degradation of vitamin C in the juice occurs during storage and it follows first order reaction kinetics. The degradation rate constant is 5.2 × 10⁻³ day⁻¹. The half-life of vitamin C in days is ____________ (in integer).

Answer: (132 to 134)

140. The weight of 10 kg dried cauliflower containing 5% moisture (wet basis) after rehydration is 60 kg. If the fresh cauliflower contained 87% moisture (wet basis), calculate the coefficient of rehydration _____ (rounded off to 2 decimal places).

Answer: (0.75 to 0.90)

XE-G: Q.141 – Q.153 Carry TWO marks Each

141. Match the industrial product in Column I with fermentative organism in Column II.

(A) P-3, Q-4, R-2, S-1

(B) P-1, Q-3, R-2, S-4

(D) P-2, Q-1, R-3, S-4

Answer: (A)

142. Match the enzyme in Column I with its application in food processing/reaction given in Column II.

(A) P-4, Q-3, R-2, S-1

(B) P-3, Q-1, R-2, S-4

(D) P-1, Q-4, R-2, S-3

Answer: (A)

143. Identify the Gram +ve bacteria responsible for causing food borne diseases among the followings

(A) Campylobacter jejuni

(B) Clostridium botulinum

(D) Salmonella typhi

Answer: (B)

144. Extrusion cooking is accomplished in four different stages, which are indicated as I, II, III and IV in the figure given below. Choose the correct option representing the name of each stage.

(A) I – Feeding, II – Cooking, III – Kneading, IV – Expansion

(B) I – Kneading, II – Feeding, III – Cooking, IV – Expansion

(D) I – Cooking, II – Kneading, III – Feeding, IV – Expansion

Answer: (C)

145. Match the method/ value used for measuring lipid characteristics in Column I with the corresponding properties indicated by them, in Column II.

(A) P-3, Q-1, R-4, S-2

(B) P-1, Q-3, R-4, S-2

(D) P-3, Q-4, R-1, S-2

Answer: (A)

146. Match the peeling technique in Column I with the vegetable, for which it is used in industry, given in Column II.

(A) P-3, Q-4, R-1, S-2

(B) P-4, Q-1, R-3, S-2

(D) P-4, Q-3, R-1, S-2

Answer: (D)

147. Match the process in Column I with the related food component in Column II.

(A) P-2, Q-4, R-1, S-3

(B) P-2, Q-1, R-4, S-3

(D) P-2, Q-1, R-3, S-4

Answer: (A)

148. Identify the correct statement(s) related to grain polysaccharides among the followings.

(A) Dextrin are a group of low molecular weight polysaccharides produced by dry hydrolysis of starch.

(B) Amylose is a linear polymer of D-glucose units joined by α (1→6) glycoside linkages.

(D) Retrogradation is a process of reassociation of amylose and formation of crystalline structure by gelatinized starch upon cooling.

Answer: (A, D)

149. Identify the correct pair(s) of governing law with respective process operation.

(A) Stoke’s law – Mass transfer

(B) Kirchhoff’s law – Radiation heat transfer

(D) Fick’s law – Molecular diffusion

Answer: (B, C, D)

150. A hammer mill is used to grind blackgram. The size distribution of the blackgram is such that 80% passes through a 6-mesh (particle size = 3.36 mm) screen. The power requirement to produce a powder, 80% of which passes through a 45-mesh (particle size = 0.354 mm) screen is 4.5 kW. The power in kW required to produce a finer powder 80% of which passes through a 60-mesh (particle size = 0.25 mm) will be ____________ (rounded off to 2 decimal places). Assume the feed rate to the mill is constant in both the cases. Use Bond’s law of size reduction.

Answer: (5.20 to 6.20)

151. If D₁₀ for Salmonella in egg yolk is 0.75 kGy, calculate the radiation dose in kGy (rounded off to 2 decimal places) required for reducing the Salmonella count in egg yolk by 8 log cycles.

Answer: (13.00 to 14.50)

152. The average moisture binding energy of a plant protein based snack at 8% moisture content (dry basis) is 3200 cal.mol-1. If the water activity of the snack at the above moisture content is 0.30 at 30 ℃, the water activity of the sample at 45 ℃ is _________ (rounded off to 2 decimal places). The value of Gas constant R = 1.987 cal.mol⁻¹.K⁻¹.

Answer: (0.32 to 0.41)

153. Cow milk is pasteurized at a flow rate of 1 kg.s-1 in a counter-current heat exchanger using hot water as the heating medium. The milk enters the heat exchanger at 15℃ and exits at 50 ℃. The specific heat of cow milk is 3.5 kJ.kg⁻¹.℃⁻¹ and remains constant at the inlet and exit of the heat exchanger. The inlet and exit temperatures of the hot water are 75℃ and 60 ℃ respectively. If the overall heat transfer coefficient is 1800 W.m⁻².℃⁻¹, the heat transfer surface area in m2 is ______ (rounded off to 2 decimal places). Assume steady state conditions.

Answer: (1.80 to 2.20)

Atmospheric and Ocean Science (XE-H)

XE-H: Q.154 – Q.162 Carry ONE mark Each

154. The net water level elevation near the coast arising due to a tropical-cyclone-induced storm is a combination of the following factors _________.

(A) astronomical tides, and distant cyclonic storm

(B) wind-induced waves, astronomical tides, and distant cyclonic storm

(D) riverine flow, astronomical tides, and distant cyclonic storm

Answer: (B)

155. The typical speeds of a tsunami wave in water depths of 10 m, 100 m, and 1000 m, respectively, are ________.

(A) approximately 100 m s⁻¹, 31 m s⁻¹ and 10 m s⁻¹

(B) approximately 50 m s⁻¹, 75 m s⁻¹ and 100 m s⁻¹

(D) approximately 100 m s⁻¹, 10 m s⁻¹ and 31 m s⁻¹

Answer: (C)

156. Which classification of tides best represents the west coast of India?

(A) Diurnal and Mixed

(B) Semidiurnal and Mixed

(D) only Mixed

Answer: (B)

157. The variation in geostrophic winds with height, in particular, at the atmospheric boundary layer, considering the variation in pressure gradient as a function of height, is referred to as __________.

(A) Isallobaric winds

(B) Gradient winds

(D) Cyclostrophic winds

Answer: (C)

158. Consider the following options and pick out the right choice. The solubility of a gas in sea water increases with ________.

(A) the increase of temperature, salinity and pressure

(B) the decrease of temperature, salinity and pressure

(D) the decrease of temperature and salinity, and the increase of pressure

Answer: (D)

159. From the list given below, identify the organism type in the biological pump that takes up carbon dioxide from the atmosphere into the ocean.

(A) Zooplankton

(B) Fish

(D) Radiolarians

Answer: (C)

160. The amount of CO₂ that can be absorbed _______ when the temperature of seawater decreases.

(A) Remains the same

(B) Increases

(D) Can either increase or decrease

Answer: (B)

161. Which among the following gases has the highest global warming potential?

(A) CO₂

(B) Water vapor

(D) N₂O

Answer: (D)

162. What will happen to the speed of a balanced flow as one moves across the isobar along a particular latitude?

(A) The speed changes for a geostrophic flow and remains constant for a cyclostrophic flow

(B) The speed remains constant for a geostrophic flow and changes for a cyclostrophic flow

(D) The speed changes for both (geostrophic and cyclostrophic) types of flow

Answer: (B)

XE-H: Q.163 – Q.175 Carry TWO marks Each

163. The following illustration depicts the circulation pattern in the North Indian Ocean during the southwest (June-August) monsoon. Identify the markers numbered from 1-5 in the illustration and pick out the right choice.

(A) 1. Great Whirl, 2. East India Coastal Current, 3. East African Coastal Current, 4. Summer (Southwest) Monsoon Current, and 5. West India Coastal Current.

(B) 1. East African Coastal Current, 2. Summer (Southwest) Monsoon Current, 3. Great Whirl, 4. South Equatorial Counter Current, and 5. East India Coastal Current.

(C) 1. Great Whirl, 2. Summer (Southwest) Monsoon Current, 3. West India Coastal Current, 4. Somali Current, and 5. East India Coastal Current.

(D) 1. East African Coastal Current, 2. West India Coastal Current, 3. Somali Current, 4. East India Coastal Current, and 5. South Equatorial Counter Current.

Answer: (A)

164. From the following list identify the region that has low chlorophyll and low nutrients.

(A) Upwelling, anticyclonic eddy

(B) Upwelling, cyclonic eddy

(D) Downwelling, cyclonic eddy

Answer: (C)

165. Match the following physical phenomena from the perspective of monsoonal circulation:

(A) a-i, b-iii, c-ii, d-iv

(B) a-iii, b-i, c-iv, d-ii

(D) a-ii, b-i, c-ii, d-iv

Answer: (B)

166. Choose the correct statement(s) in context to Ekman spiral from the following:

(A) The balance of Coriolis force and pressure

(B) The balance of Coriolis force, wind shear, and frictional force

(D) The increase of current velocity with depth

Answer: (B, C)

167. Which of the following is/are associated with winter rainfall over India?

(A) Northeast monsoon

(B) Southwest monsoon

(D) Agulhas Current

Answer: (A, C)

168. If the global albedo is increased from 0.3 to 0.4, the global radiative equilibrium temperature (in K) would decrease by ________.

(consider no greenhouse effect, solar constant = 1360 W m⁻² and Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W m⁻² K⁻⁴, rounded off to one decimal place).

Answer: (9.5 to 9.7)

169. When a parcel of dry air rises at a rate of 2 cm s⁻¹ vertically, what should be the rate of heating per unit mass in J s⁻¹ kg⁻¹ (due to the radiation, conduction, etc.) in order to maintain the air parcel at a constant temperature?

(consider the acceleration due to gravity as 9.8 m s⁻², rounded off to three decimal places).

Answer: (0.195 to 0.197)

170. Two balls each of 5 cm in diameter are placed 200 m apart on a horizontal frictionless plane at 45º N. The balls are impulsively propelled directly at each other with equal speeds. What must be the speed in m s⁻¹ so that the two balls just miss each other?

(consider the value of Ω as 7.29 × 10⁻⁵ rad s⁻¹, rounded off to two decimal places).

Answer: (20.6 to 20.9)

171. A parcel of dry air having an initial temperature of 30 ºC at 1000 hPa level is lifted adiabatically. At what pressure (in hPa) its density reduces by half?

(consider the ratio of the specific heat of dry air at a constant pressure to the specific heat of dry air at a constant volume, C_p/C_v = 0.71, rounded off to two decimal places).

Answer: (611.30 to 611.35)

172. A cylindrical tank containing water is rotating about the z-axis at a constant angular velocity of 10 rad s⁻¹. The schematic of the isobaric surface is shown in the following illustration, where ‘A’ and ‘B’ are two points on the isobaric surface at heights ‘z₁’ and ‘z₂’, respectively. Assuming the atmospheric pressure to be negligible and no transient flow, estimate the elevation difference in m between ‘z₁’ and ‘z₂’.

(consider r₁ = 0.5 m, r₂ = 1.0 m and gravitational acceleration g = 9.8 m s⁻², rounded off to two decimal places)

Answer: (3.82 to 3.83)

173. Consider that there are 295 million vehicles across India and they drive about 12000 km yr⁻¹. Each vehicle consumes about 25 km lit⁻¹ of petrol and the amount of carbon released per litre is 5.5 gm. What is the amount of carbon emitted into the atmosphere in mega ton per year (rounded off to two decimal places)?

Answer: (0.78 to 0.78)

174. Consider the two parallel isobars separated by a spacing of 250 km at 30ºN (air density = 0.70 kg m⁻³, 2Ω = 14.6 × 10⁻⁵ rad s⁻¹) with a pressure gradient of 5 hPa. Calculate the geostrophic velocity in m s⁻¹ (rounded off to two decimal places).

Answer: (39.06 to 39.37)

175. Considering a gyre system in the following illustration (where ‘L’ and ‘H’ represent low- and high-pressure regions along 45º N), the average slope between the points ‘A’ and ‘B’ is 2.1 cm km⁻¹ under no wind condition. For a steady southerly wind of 10 m s⁻¹ over these regions, find out the magnitude of the current velocity in m s⁻¹ (rounded off to two decimal places).

Answer: (2.10 to 2.11)

GATE Exam 2023 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

August 7, 2023 by suresh84

GATE-2023

TF: Textile Engineering and Fibre Science

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

8. The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sri Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households.

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x − 1)³(x − 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

10. Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

TF: Textile Engineering and Fibre Science

Q.11 – Q.35 Carry ONE mark Each

11. The value of x for which the inverse of the following matrix does not exist is

(A) 0

(B) 1

(D) 12

Answer: (D)

12. The value of y for which the following limit exists is

(A) 2

(B) 3

(D) 5

Answer: (C)

13. The probability of the standard normal variable taking values between 0 and 1 is 0.3413, between 0 and 2 is 0.4772, and between 0 and 3 is 0.4987. The average of marks in an examination is 68 and the standard deviation is 10. The percentage of examinees getting less than 48 marks is

(A) 2.28

(B) 10.31

(D) 52.78

Answer: (A)

14. The amide linkage is NOT present in

(A) Wool

(B) Aramid

(D) Nylon 66

Answer: (C)

15. In the amorphous phase, polymer chains prefer to be in a random coil conformation to

(A) Maximize entropy

(B) Maximize enthalpy

(D) Minimize enthalpy

Answer: (A)

16. The spinning system that inserts false twist is

(A) Ring spinning

(B) Compact spinning

(D) Air-vortex spinning

Answer: (C)

17. In a bobbin leading roving frame, the correct relationship between spindle speed and bobbin speed is

Answer: (C)

18. The bonding process followed for production of highloft nonwoven is

(A) Needle punching

(B) Hydroentanglement

(D) Through-air bonding

Answer: (D)

19. A drum-driven winder is fitted with a 3-diamond drum. The number of revolutions of the drum for single traverse is

(A) 1.5

(B) 3

(D) 9

Answer: (B)

20. The cut length of a staple polyester fibre is approximately equal to the effective length of a specific variety of long staple cotton fibre. When these two types of fibres are blended in nearly equal proportion, the typical comb sorter diagram of the blended fibre-tuft is

Answer: (B)

21. During the measurement of cotton fibre fineness (micronaire) by air flow method, a higher quantity of cotton fibre is taken by mistake than specified. The reading of micronaire value from the instrument will be

(A) Higher for any fibre fineness

(B) Lower for any fibre fineness

(D) Lower for only finer fibres

Answer: (B)

22. Amongst the following, hydrolytic desizing agents attack starch at

(A) α-1, 4 glucosidic linkage

(B) Six membered ring

(D) Carboxyl group

Answer: (A)

23. In resist style of printing, the preferred arrangement for dyeing is

(A) Kiss roll applicator

(B) Nip padding

(D) Immersion padding with horizontal roller arrangement

Answer: (B)

24. If twist factor is same for a set of cotton yarns, then the yarns have same

(A) Linear density

(B) Turns per metre

(D) Angle of twist of surface fibres

Answer: (C, D)

25. Copolymers are present in

(A) Nylon 6 fibre

(B) Nylon 66 fibre

(D) PET fibre

Answer: (C)

26. Amongst the following weft knitted structures, double jersey structure(s) is/are

(A) Rib

(B) Interlock

(D) Eight lock

Answer: (A, B, D)

27. For the same turns per unit length, as the yarn becomes coarser

(A) Twist angle decreases

(B) Twist angle increases

(D) Twist multiplier increases

Answer: (B, D)

28. In flame retardant finishing of cotton fabric, the correct statement(s) is/are

(A) The finishing material forms an insulating layer around the fibre at a temperature above the fibre pyrolysis temperature

(B) The finishing material forms an insulating layer around the fibre at a temperature below the fibre pyrolysis temperature

(D) The finishing material dehydrates the cellulose

Answer: (B, C, D)

29. The Newton-Raphson method is being used for two iterations to find an approximate solution of the equation e^x – 1 = 0 with an initial guess of 1. The difference between the actual and approximate solutions (rounded off to 2 decimal places) is ______________.

Answer: (0.05 to 0.07 OR -0.07 to -0.05)

30. The area under the curve y = x² + 2x between x = 0 and x = 4, using the trapezoidal rule with a step size of one, (in integer) is _______________.

Answer: (38 to 38)

31. A PET sample with 40 % crystallinity shows only a melting endotherm in the first heating cycle of DSC with a melting enthalpy of 50 J/g. The degree of crystallinity (%) of another PET sample which also shows only a melting endotherm but with a melting enthalpy of 80 J/g is (in integer) _____________.

Answer: (64 to 64)

32. If the twist multiplier in the indirect system is 4.8 tpi/Ne⁵, then the twist factor in the direct system (tpm tex^0.5) (rounded off to 2 decimal places) is _____________.

Answer: (4590.00 to 4594.00)

33. A plain woven fabric with 20 ends per cm and 30 picks per cm is prepared with 30 tex warp yarns and 25 tex weft yarns. Neglecting yarn crimp, the areal density (g/m2) of the fabric (in integer) is __________.

Answer: (134 to 136)

34. A ring spun yarn with mean linear density of 32 tex is produced from 2 denier polyester staple fibre. If the standard deviation of the yarn linear density is 3.2 tex, then the index of irregularity of the yarn (up to 1 decimal place) is ___________.

Answer: (1.1 to 1.3)

35. A cotton fabric is to be dyed with 2 % shade (on the weight of fabric). If dye concentration is 0.4 g/L, then the material-to-liquor ratio is 1 : X. The value of X (in integer) is _____________.

Answer: (50 to 50)

Q.36 – Q.65 Carry TWO marks Each

36. Two eigenvalues of the following matrix are 3 and 6. The third eigenvalue is

(A) −5

(B) −1

(D) 4

Answer: (A)

37. Two vertical poles of height 6 m and 18 m are 10 m apart on a flat ground. A string needs to be connected from the top of one pole to a peg on the ground and then on to the top of the other pole. The minimum length (m) of the string is

(A) 25

(B) 26

(D) 28

Answer: (B)

38. Consider the following statements regarding Nylon 6 production from caprolactam using water as a catalyst.

(P) The first reaction involving ring-opening of caprolactam with water is an endothermic reaction

(Q) Increase in water concentration during the polycondensation results in a higher molecular weight polymer

(R) The polycondensation is an irreversible reaction

(S) Increase in temperature during the polycondensation results in a lower molecular weight polymer

The correct combination of TRUE statements is

(A) P and Q

(B) Q and R

(D) S and P

Answer: (D)

39. Determine the correctness or otherwise of the following Assertion [a] and Reason [r].

[a]: In boiling water, polyester POY shows higher shrinkage than polyester FDY

[r]: Molecular chain orientation is higher in polyester FDY than in polyester POY

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(D) [a] is true but [r] is false

Answer: (B)

40. Consider the following activities on a carding machine

(P) Lowering surface speed of feed roller

(Q) Increasing rotational speed of taker-in

(R) Increasing linear density of feed material

(S) Use of shorter and finer fibres

The correct combination of the above activities to obtain more number of taker-in teeth acting per fibre is

(A) P and Q

(B) Q and R

(D) S and P

Answer: (A)

41. Consider the following statements with regard to the timing diagram of a cotton combing machine.

(P) In forward feed system, feeding mostly takes place when nippers are closing

(Q) Cylinder comb starts combing after feeding ends

(R) Detaching rollers move backward during forward movement of nipper assembly

(S) Top comb is not combing when detaching rollers move forward

The correct combination of TRUE statements is

(A) P and Q

(B) Q and R

(D) S and P

Answer: (B)

42. Consider the following reasons of shuttle loom stoppage.

(P) Breakage of warp yarns

(Q) Entrapment of shuttle inside the shed

(R) Flying of shuttle out of the shed

(S) Slackening of a warp yarn

The correct combination that triggers the warp protector motion is

(A) P and Q

(B) Q and R

(D) S and P

Answer: (B)

43. In warp knitting, the lapping movement having only under-lap is

(A) Closed lap

(B) Open lap

(D) Miss-lapping

Answer: (C)

44. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: MgCl₂ is used in the formulation of anti-crease finishing of cotton fabric with DMDHEU

[r]: MgCl₂ is an acidic salt and acts as a catalyst

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not correct reason for [a]

(D) [a] is true but [r] is false

Answer: (A)

45. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: A partially scoured cotton fabric bleached with H2O2 exhibits higher water absorbancy than that bleached with NaClO₂

[r]: Bleaching with H₂O₂ also facilitates scouring

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not correct reason for [a]

(D) [a] is true but [r] is false

Answer: (A)

46. In wet spinning of acrylic fibres

(A) Two-way mass transfer is involved

(B) One-way mass transfer is involved

(D) Coagulation bath having spinneret contains both solvent and non-solvent

Answer: (A, D)

47. Drafting force in drawframe, when fibres are sliding, reduces with higher

(A) Draft

(B) Roller setting

(D) Number of fibres in feed sliver

Answer: (A, B)

48. The force exerted by the reed on the cloth-fell at the instant of beat-up (weaving resistance) depends on

(A) Free length of warp yarn

(B) Elastic modulus of loom-state fabric

(D) Elastic modulus of weft yarn

Answer: (A, B, C)

49. With reference to KES-FB and FAST systems, the same low stress mechanical property is measured by

(A) KES-FB1 and FAST 1

(B) KES-FB2 and FAST 2

(D) KES-FB2 and FAST 3

Answer: (B, C)

50. With reference to the work factor (WF) and work of rupture (WR) of two yarns with same breaking load and same breaking elongation, the correct statement(s) is/are

(A) The WR of yarn with WF = 0.3 is more than that with WF = 0.5

(B) The WR of yarn with WF = 0.3 is less than that with WF = 0.5

(D) If breakage takes place within the Hooke’s region, then the WF is equal to 0.5

Answer: (B, D)

51. Amongst the Classimat faults A2, B1, D4, H2 and I1, the correct statement(s) is/are

(A) D4 and A2 are the thickest fault and the shortest fault, respectively

(B) I1 and H2 are the longest fault and the thinnest fault, respectively

(D) B1 and H2 are the most objectionable fault and the longest fault, respectively

Answer: (A, B)

52. A sample of cotton fabric is dyed with vat dye at 60°C till equilibrium dye uptake is reached. Another sample of the same cotton fabric is dyed with the same dye at 90°C till equilibrium, keeping all other parameters same. Amongst the following, the correct statement(s) is/are

(A) Dye exhaustion will be higher at 90°C as compared to that at 60°C

(B) Dye exhaustion will be lower at 90°C as compared to that at 60°C

(D) Levelness achieved at 90°C will be lower as compared to that at 60°C

Answer: (B, C)

53. In pigment printing of cotton fabric, the pigment (along with binder) can be fixed by using

(A) Saturated steam at 102°C for 4 min

(B) Dry heat at 140°C for 4 min

(D) Super-heated steam at 180°C for 4 min

Answer: (B)

54. If and y(2) = 1, then 1/y(0) (in integer) is _______.

Answer: (33 to 33)

55. If the values of x are 1, 2 and 3 and the corresponding values of y are 9, 8 and 10, respectively, then the slope of the line of regression equation of y on x is (up to 1 decimal place) _________.

Answer: (0.5 to 0.5)

56. Three monodisperse Nylon 6 samples with molar masses 10000 g/mol, 30000 g/mol and 60000 g/mol are mixed in a proportion of 1:1:2 by number of chains. The polydispersity index of the resulting sample (rounded off to 2 decimal places) is ________.

Answer: (1.27 to 1.29)

57. In melt spinning of a monofilament, a polymer is being extruded at a volumetric flow rate of 5 × 10⁻⁵ m³/s through a spinneret of circular cross-section. If the take up velocity of the first winder is 100 m/s with a draw ratio of 50, then the diameter (mm) of the spinneret orifice (rounded off to 2 decimal places) is ____________.

Answer: (5.60 to 5.70)

58. In a roving frame, the ratio of the diameter of the top (driver) cone-drum to the diameter of the bottom (driven) cone-drum is inversely proportional to bobbin diameter.

At an instant,

Top cone-drum diameter = 212 mm

Bottom cone-drum diameter = 108 mm

Bobbin diameter = 54 mm

When the bobbin diameter becomes 100 mm, the ratio of the top cone-drum diameter to the bottom cone-drum diameter (up to 2 decimal places) is ___________.

Answer: (1.04 to 1.08)

59. In a ring frame, the speeds of traveller at 50 mm bobbin diameter (near the base of the cop) and at 25 mm bobbin diameter (near the tip of the cop) are 13500 rpm and 13400 rpm, respectively. The nominal twist (tpm) (rounded off to 2 decimal places) is __________.

Answer: (863.00 to 867.00)

60. A circular knitting machine of 26 inch diameter and 20 gauge with 120 feeders is running at 30 rpm to produce a plain knitted fabric by using 30 tex yarn. If the loop length is 3 mm, then the rate of production (kg/h) of the machine (rounded off to 1 decimal place) is _________.

Answer: (29.0 to 33.0)

61. A square jammed plain cotton woven fabric is produced from 10 Ne yarn of circular cross-section. Assuming density of yarn as 0.91 g/cm³, the number of threads per inch in the fabric (rounded off to the nearest integer) is ___________.

Answer: (49 to 53)

62. In a guarded hot plate, the dimension of the square test plate is 15 cm × 15 cm. Keeping the temperatures of the test plate and the air at 35°C and 20°C, respectively, the power losses from the test plate with and without fabric specimen are 16 W and 40 W, respectively. The intrinsic transmittance [W/(m² K)] of the fabric (rounded off to 2 decimal places) is ___________.

Answer: (77.00 to 81.00)

63. A 36 Ne ring spun yarn is produced from 1.2 Ne roving. The total draft and the break draft of the roving frame are 12 and 1.2, respectively. The diameters of back bottom roller, middle bottom roller and front bottom roller of the roving frame are 28 mm, 25 mm and 28 mm, respectively. If the middle bottom roller of the roving frame is eccentric, then the wavelength (m) of the periodic fault in the yarn, neglecting twist contraction, (rounded off to 2 decimal places) is ____________.

Answer: (23.00 to 24.00)

64. A 30 tex cotton yarn is made into a lea of 120 yards for determining CSP. If the lea strength is 500 N, then the CSP of the yarn (rounded off to the nearest integer) is ___________.

Answer: (2190 to 2230)

65. In a continuous scouring operation, a desized fabric (with 40 % wet expression) is dipped into a saturator (alkali bath) before it enters a J-box for scouring. After saturation in the alkali bath, the wet expression increases to 100 %. The required alkali concentration (w/v) of the liquor present in the fabric exiting the saturator is 6 %. Considering no liquor interchange in the saturator, the alkali concentration (w/v) in percentage in the saturator (in integer) is __________.

Answer: (10 to 10)

GATE Exam 2023 Stastics (ST) Question Paper With Answer Key

August 7, 2023August 5, 2023 by suresh84

GATE-2023

ST: Statistics

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “I have not yet decided what I will do this evening; I ______ visit a friend.”

(A) mite

(B) would

(D) didn’t

Answer: (C)

2. Eject : Insert : : Advance : _______

(By word meaning)

(A) Advent

(B) Progress

(D) Loan

Answer: (C)

3. In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm²) of the shaded region? (The diagram is representative)

(A) 25π/3

(B) 20π/3

(D) 7π

Answer: (A)

4. A duck named Donald Duck says “All ducks always lie.”

Based only on the information above, which one of the following statements can be logically inferred with certainty?

(A) Donald Duck always lies.

(B) Donald Duck always tells the truth.

(D) Donald Duck’s statement is false.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, upto 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)

(A) d

(B) c, d, i

(D) c, d, i, f, g

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

6. Based only on the truth of the statement ‘Some humans are intelligent’, which one of the following options can be logically inferred with certainty?

(A) No human is intelligent.

(B) All humans are intelligent.

(D) Some intelligent beings are humans.

Answer: (D)

7. Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), P(x), of a variable x?

(A) mean = median ≠ mode

(B) mean = median = mode

(D) mean ≠ mode = median

Answer: (A)

8. The James Webb telescope, recently launched in space, is giving humankind unprecedented access to the depths of time by imaging very old stars formed almost 13 billion years ago. Astrophysicists and cosmologists believe that this odyssey in space may even shed light on the existence of dark matter. Dark matter is supposed to interact only via the gravitational interaction and not through the electromagnetic-, the weak- or the strong-interaction. This may justify the epithet “dark” in dark matter.

Based on the above paragraph, which one of the following statements is FALSE?

(A) No other telescope has captured images of stars older than those captured by the James Webb telescope.

(B) People other than astrophysicists and cosmologists may also believe in the existence of dark matter.

(D) If dark matter was known to interact via the strong-interaction, then the epithet “dark” would be justified.

Answer: (D)

9. Let a = 30! , b = 50! , and c = 100! . Consider the following numbers:

log_ac, log_ca, log_ba, log_ab

Which one of the following inequalities is CORRECT?

(A) log_c a > log_b a < log_a b < log_a c

(B) log_c a < log_a b < log_b a < log_b c

(D) log_b a < log_c a < log_a b < log_a c

Answer: (A)

10. A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown.

The area of the shaded region is _______ cm².

(A) 8

(B) 4

(D) 10

Answer: (A)

ST: Statistics

Q.11 – Q.35 Carry ONE mark Each

11. The area of the region bounded by the parabola x = −y² and the line y = x + 2 equals

(A) 3/2

(B) 7/2

(D) 9

Answer: (C)

12. Let A be a 3 × 3 real matrix having eigenvalues 1,0, and −1. If B = A² + 2A + I₃ , where I₃ is the 3 × 3 identity matrix, then which one of the following statements is true?

(A) B³ – 5B² + 4B = 0

(B) B³ – 5B² – 4B = 0

(D) B³ + 5B² + 4B = 0

Answer: (A)

13. Consider the following statements.

(I) Let A and B be two n × n real matrices. If B is invertible, then rank(BA) = rank(A).

(II) Let A be an n × n real matrix. If A²x = b has a solution for every b ∈ ℝⁿ, then Ax = b also has a solution for every b ∈ ℝⁿ.

Which of the above statements is/are true?

(A) Only (I)

(B) Only (II)

(D) Neither (I) nor (II)

Answer: (C)

14. Consider the probability space (Ω, G, P), where Ω = [0, 2] and G = {ϕ, Ω, [0, 1], (1, 2]}. Let X and Y be two functions on Ω defined as

and

Then which one of the following statements is true?

(A) X is a random variable with respect to G, but Y is not a random variable with respect to G

(B) Y is a random variable with respect to G, but X is not a random variable with respect to G

(D) Both X and Y are random variables with respect to G

Answer: (A)

15. Let Φ(∙)denote the cumulative distribution function of a standard normal random variable. If the random variable X has the cumulative distribution function

then which one of the following statements is true?

(A) P(X ≤ −1) = 1/2

(B) P(X = −1) = 1/2

(D) P(X ≤ 0) = 1/2

Answer: (A)

16. Let X be a random variable with probability density function

where α > 0 and λ > 0. If the median of X is 1 and the third quantile is 2, then (α, λ) equals

(A) (1, log_e 2)

(B) (1, 1)

(D) (1, log_e 3)

Answer: (A)

17. Let X be a random variable having Poisson distribution with mean λ > 0. Then equals

Answer: (A)

18. Suppose that X has the probability density function

where α > 0 and λ > 0. Which one of the following statements is NOT true?

(A) E(X) exists for all α > 0 and λ > 0

(B) Variance of X exists for all α > 0 and λ > 0

(D) E(log_e(1 + X)) exists for all α > 0 and λ > 0

Answer: (C)

19. Let (X, Y) have joint probability density function

If E(X|Y = y₀) = 1/2, then y₀ equals

(A) 3/4

(B) 1/2

(D) 2/3

Answer: (A)

20. Suppose that there are 5 boxes, each containing 3 blue pens, 1 red pen and 2 black pens. One pen is drawn at random from each of these 5 boxes. If the random variable X₁ denotes the total number of blue pens drawn and the random variable X₂ denotes the total number of red pens drawn, then P(X₁ = 2, X₂ = 1) equals

(A) 5/36

(B) 5/18

(D) 5/9

Answer: (A)

21. Let {X_n}_n_{≥ 1} and {Y_n}_n_{≥ 1} be two sequences of random variables and X and Y be two random variables, all of them defined on the same probability space. Which one of the following statements is true?

(A) If {X_n}_n_{≥ 1} converges in distribution to a real constant c, then {X_n}_n_{≥ 1} converges in probability to c

(B) If {X_n}_n_{≥ 1} converges in probability to X, then {X_n}_n_{≥ 1} converges in 3^rd mean to X

(C) If {X_n}_n_{≥ 1} converges in distributions to X and {Y_n}_n_{≥ 1} converges in distribution to Y, then {X_n + Y_n}_n_≥₁ converges in distribution X + Y

(D) If {E{X_n}_n_{≥ 1}} converges to E(X), then {X_n}_n_{≥ 1} converges in 1^st mean to X

Answer: (A)

22. Let X be a random variable with probability density function

where λ > 0 is an unknown parameter. Let Y₁, Y₂, …, Y_n be a random sample of size n from a population having the same distribution as X².

If then which one of the following statements is true?

(A) is a method of moments estimator of λ

(B) is a method of moments estimator of λ

(D) is a method of moments estimator of λ

Answer: (A)

23. Let X₁, X₂, …, X_n be a random sample of size n (≥ 2) from a population having probability density function

where θ > 0 is a n unknown parameter. Then which one of the following statements is true?

(A) is the maximum likelihood estimator of θ

(B) is the maximum likelihood estimator of θ

(D) is the maximum likelihood estimator of θ

Answer: (A)

24. Let X₁, X₂, …, X_n be a random sample of size n from a population having uniform distribution over the interval (1/3, θ), where θ > 1/3 is an unknown parameter. If Y = max{X₁, X₂, …, X_n}, then which one of the following statements is true?

(A) is an unbiased estimator of θ

(B) is an unbiased estimator of θ

(D) Y is an unbiased estimator of θ

Answer: (A)

25. Suppose that X₁, X₂, …, X_n, Y₁, Y₂, …, Y_n are independent and identically distributed random vectors each having N_p(μ, ∑) distribution, where ∑ is non-singular, p > 1 and n > 1. If then which one of the following statements is true?

(A) There exists c > 0 such that has χ²-distribution with p degrees of freedom

(B) There exists c > 0 such that has χ²-distribution with (p – 1) degrees of freedom

(D) There exists c > 0 such that has χ²-distribution with p degrees of freedom

Answer: (A)

26. Consider the following regression model

y_k = α₀ + α₁log_ek + ϵ_k, k = 1, 2, …

where ϵ_k’s are independent and identically distributed random variables each having probability density function Then which one of the following statements is true?

(A) The maximum likelihood estimator of α₀ does not exist

(B) The maximum likelihood estimator of α₁ does not exist

(D) The least squares estimator of α₁ exists, but it is not unique

Answer: (C)

27. Suppose that X₁, X₂, …, X_n are independent and identically distributed random variables each having probability density function f(⋅) and median θ. We want to test

H₀ : θ = θ₀ against H₁ : θ > θ₀.

Consider a test that rejects H₀ if S > c for some 𝑐 depending on the size of the test, where 𝑆 is the cardinality of the set {i: X_i > θ₀, 1 ≤ i ≤ n}. Then which one of the following statements is true?

(A) Under H₀, the distribution of S depends on f(⋅)

(B) Under H₁, the distribution of S does not depend on f(⋅)

(D) The power function does not depend on θ

Answer: (C)

28. Suppose that x is an observed sample of size 1 from a population with probability density function f(⋅). Based on x, consider testing

against

Then which one of the following statements is true?

(A) The most powerful test rejects H₀ if |x| > c for some c > 0

(B) The most powerful test rejects H₀ if |x| < c for some c > 0

(D) The most powerful test rejects H₀ if ||x| − 1| < c for some c > 0

Answer: (C)

29. Let f : ℝ² → ℝ be defined by f(x, y) = xy. Then the maximum value (rounded off to two decimal places) of f on the ellipse x² + 2y² = 1 equals __________

Answer: (0.32 to 0.38)

30. Let A be a 2 × 2 real matrix such that AB = BA for all 2 × 2 real matrices B. If trace of 𝐴 equals 5, then determinant of A (rounded off to two decimal places) equals ___________

Answer: (6.10 to 6.40)

31. Two defective bulbs are present in a set of five bulbs. To remove the two defective bulbs, the bulbs are chosen randomly one by one and tested. If X denotes the minimum number of bulbs that must be tested to find out the two defective bulbs, then P(X = 3) (rounded off to two decimal places) equals ___________

Answer: (0.28 to 0.32)

32. Let {X_n}_n_≥₁ be a sequence of independent and identically distributed random variables each having mean 4 and variance 9. If then (in integer) equals ________

Answer: (0 to 0)

33. Let {W_t}_t_≥₀ be a standard Brownian motion. Then (in integer) equals ________

Answer: (6 to 6)

34. Let {X_n}_n_≥1 be a Markov chain with state space {1, 2, 3} and transition probability matrix

Then P(X₂ = 1 | X₁ = 1, X₃ = 2) (rounded off to two decimal places) equals ________.

Answer: (0.36 to 0.39)

35. Suppose that (X₁, X₂, X₃) has N₃(μ, Σ) distribution with

Given that Φ(−0.5) = 0.3085, where Φ(⋅) denotes the cumulative distribution function of a standard normal random variable, P(X₁ – 2X₂ + 2X₃)² < 7/2) (rounded off to two decimal places) equals _________

Answer: (0.35 to 0.40)

Q.36 – Q.65 Carry TWO marks Each

36. Let A be an n × n real matrix. Consider the following statements.

(I) If A is symmetric, then there exists c ≥ 0 such that A + cI_n is symmetric and positive definite, where I_n is the n × n identity matrix.

(II) If A is symmetric and positive definite, then there exists a symmetric and positive definite matrix B such that A = B².

Which of the above statements is/are true?

(A) Only (I)

(B) Only (II)

(D) Neither (I) nor (II)

Answer: (C)

37. Let X be a random variable with probability density function

If Y = log_e X, then P(Y < 1 | Y < 2) equals

Answer: (A)

38. Let {N(t)}_t_≥₀ be a Poisson process with rate 1. Consider the following statements.

(I) P(N(3) = 3|N(5) = 5) =

(II) If S₅ denotes the time of occurrence of the 5^th event for the above Poisson process, then E(S₅|N(5) = 3) = 7.

Which of the above statements is/are true?

(A) Only (I)

(B) Only (II)

(D) Neither (I) nor (II)

Answer: (C)

39. Let X₁, X₂, …, X_n be a random sample of size n from a population having probability density function

where μ ∈ ℝ is an unknown parameter. If is the maximum likelihood estimator of the median of X₁, then which one of the following statements is true?

Answer: (A)

40. Let X₁, X₂, …, X₁₀ be a random sample of size 10 from a population having N(0, θ²) distribution, where θ > 0 is an unknown parameter.

Let If the mean square error of cT (c > 0), as an estimator of θ², is minimized at c = c₀, then the value of c₀ equals

(A) 5/6

(B) 2/3

(D) 1/2

Answer: (A)

41. Suppose that X₁, X₂, …, X₁₀ are independent and identically distributed random vectors each having N₂(μ, ∑) distribution, where ∑ is non-singular. If where then the value of equals

(A) −5

(B) −10

(D) −1

Answer: (A)

42. Suppose that (X, Y) has joint probability mass function

P(X = 0, Y = 0) = P(X = 1, Y = 1) = θ,

P(X = 1, Y = 0) = P(X = 0, Y = 1)

Where 0 ≤ θ 1/2 is an unknown parameter. Consider testing H₀ : θ = 1/4 against H₁ : θ = 1/3, based on a random sample {(X₁, Y₁), (X₂, Y₂), …, (X_n, Y_n)} from the above probability mass function. Let M be the cardinality of the set {i : X_i = Y_i, 1 ≤ i ≤ n}. If m is the observed value of M, then which one of the following statements is true?

(A) The likelihood ratio test rejects H₀ if m > c for some c

(B) The likelihood ratio test rejects H₀ if m < c for some c

(D) The likelihood ratio test rejects H₀ if m < c₁ or m > c₂ for some c₁ and c₂

Answer: (A)

43. Let g(x) = f(x) + f(2 − x) for all x ∈ [0, 2] , where f : [0, 2] → ℝ is continuous on [0, 2] and twice differentiable on (0, 2). If g′ denotes the derivative of g and f′′ denotes the second derivative of f, then which one of the following statements is NOT true?

(A) There exists c ∈ (0, 2) such that g′(c) = 0

(B) If f′′ > 0 on (0, 2), then g is strictly decreasing on (0, 1)

(D) If f′′ = 0 on (0, 2), then g is a constant function

Answer: (C)

44. For any subset 𝒰 of ℝⁿ, let L(𝒰) denote the span of 𝒰. For any two subsets 𝒯 and 𝒮 of ℝⁿ, which one of the following statements is NOT true?

(A) If 𝒯 is a proper subset of 𝒮, then (𝒯) is a proper subset of 𝐿(𝒮)

(B) L(L(𝒮)) = L(𝒮)

(D) If 𝛼, 𝛽 and 𝛾 are three vectors in ℝ𝑛 such that α + 2β + 3𝛾 = 0, then L({α, β}) = L({β, γ})

Answer: (A)

45. Let f be a continuous function from [0,1] to the set of all real numbers. Then which one of the following statements is NOT true?

(A) For any sequence {x_n}_n_≥₁ in [0, 1], is absolutely convergent

(B) If |f(x)| = 1 for all x ∈ [0, 1], then

(D) If f is also monotonically increasing, then the image of f is given by [f(0), f(1)]

Answer: (C)

46. Let X be a random variable with cumulative distribution function

Which one of the following statements is true?

Answer: (B)

47. Let (X, Y) have joint probability mass function

Then which one of the following statements is true?

(A) c = 1/2

(B) c = 1/4

(D) X and Y are independent

Answer: (C)

48. Let X₁, X₂, …, X₁₀ be a random sample of size 10 from a N₃(μ, ∑) distribution, where μ and non-singular ∑ are unknown parameters. If

then which one of the following statements is NOT true?

(A) follows a F-distribution with 3 and 2 degrees of freedom

(B) follows a 𝐹-distribution with 2 and 3 degrees of freedom

(D) 5(S₁ + S₂) follows a Wishart distribution of order 3 with 10 degrees of freedom

Answer: (D)

49. Which of the following sets is/are countable?

(A) The set of all functions from {1,2,3,…,10} to the set of all rational numbers

(B) The set of all functions from the set of all natural numbers to {0,1}

(D) The set of all integer valued sequences converging to 1

Answer: (A, C, D)

50. For a given real number a, let a⁺ = max{a, 0} and a⁻ = max{−a, 0}. If {x_n}_n_≥₁ is a sequence of real numbers, then which of the following statements is/are true?

(A) If {x_n}_n_≥₁ converges, then both {x_n⁺}_n_≥₁ and {x_n⁻}_n_≥₁converge

(B) If {x_n}_n_≥₁ converges to 0, then both {x_n⁺}_n_≥₁ converge to 0

(D) If {x_n²}_n_≥₁ converges, then both {x_n⁺}_n_≥₁ and {x_n⁻}_n_≥₁ converge

Answer: (A, B, C)

51. Let A be a 3 × 3 real matrix such that and Then which of the following statements is/are true?

Answer: (B, D)

52. Let X be a positive valued continuous random variable with finite mean. If Y = [X], the largest integer less than or equal to X, then which of the following statements is/are true?

(A) P(Y ≤ u) ≤ P(x ≤ u) for all u ≥ 0

(B) P(Y ≥ u) ≤ P(X ≥ u) for all u ≥ 0

(D) E(X) > E(Y)

Answer: (B, D)

53. Let X be a random variable with probability density function

For a < 𝑏, if U(a, b) denotes the uniform distribution over the interval (a, b), then which of the following statements is/are true?

(A) e⁻^X follows U(−1, 0) distribution

(B) 1 – e⁻^X follows U(0, 2) distribution

(D) The probability mass function of Y = [X] is P(Y = k) = (1 – e⁻¹)e⁻^k for k = 0, 1, 2, …, where [x] denotes the largest integer not exceeding x

Answer: (C, D)

54. Suppose that X is a discrete random variable with the following probability mass function

Which of the following statements is/are true?

(A) E(X) = 1

(B) E(X) < 1

(D) E(X|X > 0) > 1/2

Answer: (B, D)

55. Suppose that U and V are two independent and identically distributed random variables each having probability density function

where λ > 0. Which of the following statements is/are true?

(A) The distribution of U−V is symmetric about 0

(B) The distribution of 𝑈𝑉 does not depend on λ

(D) The distribution of U/V is symmetric about 1

Answer: (A, C)

56. Let (X, Y) have joint probability mass function

Then which of the following statements is/are true?

(A) E(X|Y = 4) = 2

(B) The moment generating function of Y is for all v ∈ ℝ

(D) The joint moment generating function of (X, Y) is for all (u, v) ∈ ℝ²

Answer: (A, B, D)

57. Let {X_n}_n_≥₁ be a sequence of independent and identically distributed random variables with mean 0 and variance 1, all of them defined on the same probability space. For n =1, 2, 3, …, let

Then which of the following statements is/are true?

(A) {√nY_n}_n_≥₁ converges in distribution to a standard normal random variable

(B) {Y_n}_n_≥₁ converges in 2^nd mean to 0

(D) {X_n}_n_≥₁ converges almost surely to 0

Answer: (A, B, C)

58. Consider the following regression model

y_t = α₀ + α₁t + α₂t² + ϵ_t, t = 1, 2, …, 100,

where α₀, α₁ and α₂ are unknown parameters and ϵ_t’s are independent and identically distributed random variables each having N(μ,1) distribution with μ ∈ ℝ unknown. Then which of the following statements is/are true?

(A) There exists an unbiased estimator of α₁

(B) There exists an unbiased estimator of α₂

(D) There exists an unbiased estimator of μ

Answer: (A, B)

59. Consider the orthonormal set

with respect to the standard inner product on ℝ³. If is the vector such that inner products of u with v₁, v₂ and v₃ are 1, 2 and 3, respectively, then a² + b² + c² (in integer) equals ____________

Answer: (14 to 14)

60. Consider the probability space (Ω, G, P), where Ω = {1, 2, 3, 4}, G = {ϕ, Ω, {1}, {4}, {2, 3}, {1, 4}, {1, 2, 3}, {2, 3, 4}}, and P({1}) = 1/4. Let X be the random variable defined on the above probability space as X(1) = 1, X(2) = X(3) = 2 and X(4) = 3. If P (X ≤ 2) = 3/4, then P({1, 4}) (rounded off to two decimal places) equals ________

Answer: (0.49 to 0.51)

61. Let {X_n}_n_≥₁ be a sequence of independent and identically distributed random variables each having probability density function

For n ≥ 1, let Y_n = |X_2n − X_{2n – 1}|. for n ≥ 1 and converges in distribution to a normal random variable with mean 0 and variance σ², then σ² (rounded off to two decimal places) equals ______________

Answer: (0.12 to 0.16)

62. Consider a birth-death process on the state space {0, 1, 2, 3}. The birth rates are given by λ₀ = 1, λ₁ = 1, λ₂ = 2 and λ₃ = 0. The death rates are given by μ₀ = 0, μ₁ = 1, μ₂ = 1 and μ₃ = 1. If [π₀ + π₁ + π₂ + π₃] is the unique stationary distribution, then π₀ + 2π₁ + 3π₂ + 4π₃ (rounded off to two decimal places) equals _________

Answer: (2.70 to 2.90)

63. Let {−1, −1/2, 1, 5/2, 3} be a realization of a random sample of size 5 from a population having N(1/2, σ²) distribution, where σ > 0 is an unknown parameter. Let T be an unbiased estimator of σ² whose variance attains the Cramer-Rao lower bound. Then based on the above data, the realized value of T (rounded off to two decimal places) equals _______

Answer: (2.60 to 2.90)

64. Let C be a random sample of size 1 from a population with cumulative distribution function

where θ > 0 is an unknown parameter. To test H₀ : θ = 1 against H₁: θ = 2, consider using the critical region {x ∈ ℝ : x < 0.5}. If α and β denote the level and power of the test, respectively, then α + β (rounded off to two decimal places) equals ____________

Answer: (1.20 to 1.30)

65. Let {0.13, 0.12, 0.78, 0.51} be a realization of a random sample of size 4 from a population with cumulative distribution function F(⋅). Consider testing

Let D denote the Kolmogorov-Smirnov test statistic. If P(D > 0.669) = 0.01 under H₀ and

then based on the given data, the observed value of D + ψ (rounded off to two decimal places) equals ___________

Answer: (1.35 to 1.40)

GATE Exam 2023 Production and Industrial Engineering (PI) Question Paper With Answer Key

August 5, 2023 by suresh84

GATE-2023

PI: Production and Industrial Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x − 1)³(x − 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

PI: Production and Industrial Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Given matrices

and

B is skew-symmetric matrix of A. B₁₃ is

(A) −3

(B) −2

(D) 3

Answer: (MTA)

12. The non-linear differential equation from the following options is

Answer: (B)

13. The power series expansion of a function is given as

for 0 < x ≤ 1.

The values of constants b and c, respectively, are

(A) −1/2 and 1/3

(B) 1/2 and −1/3

(D) 1 and −1/2

Answer: (A)

14. Three unbiased coins are tossed. Provided that at least two outcomes are tails, the probability of having all three outcomes as tails is

(A) 1/8

(B) 1/4

(D) 1/2

Answer: (B)

15. Two plane parallel surfaces exchange heat by thermal radiation. A radiation shield is placed in between at equal distance from the two surfaces to reduce heat transfer. All surfaces are black with infinite length and width. The ratio of heat transfer rate between surfaces with and without radiation shield is

(A) 1/2

(B) 1/4

(D) 1/8

Answer: (A)

16. As per the ANSI marking system, a grinding wheel with alumina as abrasive is designated as

51 A 36 K 5 V 23

Here, K indicates that

(A) abrasive used in the wheel is aluminum oxide

(B) hardness of the wheel is medium

(D) structure of the wheel is dense

Answer: (B)

17. The combination of Directrix and Generatrix in a machining operation is shown in figure. The surface produced is

(A) cylindrical

(B) planar

(D) parabolic

Answer: (A)

18. In NC machine, the function of interpolator is to

(A) compute and maintain the tool feed rate

(B) compute and maintain the velocity of the slide

(D) generate reference signals prescribing the shape of the produced part

Answer: (D)

19. Vacuum in the machining zone is an essential requirement for

(A) Electric Discharge Machining

(B) Chemical Machining

(D) Electron Beam Machining

Answer: (D)

20. The qualitative method of forecasting amongst the given options is

(A) Linear Regression

(B) Weighted Moving Average

(D) Exponential Smoothing

Answer: (C)

21. Transformation matrix to translate a point P from (10, 15) to (15, 25) is

Answer: (A)

22. A copper rod of 200 mm diameter and 400 mm length is extruded to the final diameter of 100 mm. The extrusion ratio is

(A) 1

(B) 2

(D) 8

Answer: (C)

23. A symbol for surface texture parameters is shown in figure. The difference between maximum and minimum values of surface roughness (R_a) is

(A) 0.499 μm

(B) 0.508 μm

(D) 1.524 μm

Answer: (C)

24. A thin cylinder has length L, diameter d, and thickness t. It is made of a material with modulus of elasticity E and Poisson’s ratio μ. When the cylinder is subjected to an internal pressure P, the change in length is

Answer: (A)

25. Creep of mild steel at elevated temperature involves

(A) elastic deformation under constant load

(B) elastic deformation under dynamic load

(D) plastic deformation under dynamic load

Answer: (C)

26. Number of minimum control points required to generate a quadratic B-Spline curve is

(A) 2

(B) 4

(D) 16

Answer: (B)

27. The Euler’s method is used to solve

The step size is 0.1. The approximate value of y(0, 1) is _____ (round off to 2 decimal places).

Answer: (0.50 to 0.70)

28. A solid circular disk of 0.025 m thickness is used as flywheel. The density of the disk material is 7800 kg/m³ and the mass moment of inertia of the disk about its center is 4.36 kg-m². The radius, in m, of the disk is _____ (round off to 2 decimal places).

Answer: (0.32 to 0.36)

29. The standard time for completing a job on a machine is 10 minutes. Number of machines available is 5, each machine is available for 300 hours/month, and average machine utilization is 80 %. The maximum number of jobs that can be produced in a month is _____ (in integer).

Answer: (7200 to 7200)

30. Travel details of two persons P and Q travelling from city X to city Y are given as

The positive difference in value of travel between the two modes is _____ (in integer).

Answer: (1 to 1)

31. A wooden cubical block of side 0.1 m has specific gravity (SG) of 0.75. It is held submerged in a pool of oil and water by a massless rigid wire as shown in figure. The density of water is 1000 kg/m³ and acceleration due to gravity is 9.8 m/s². The tension, in N, in the wire is _____ (round off to 2 decimal places).

Answer: (2.30 to 2.60)

32. Under steady state conditions, superheated steam enters the turbine with enthalpy, h₁ = 3200 kJ/kg and wet steam leaves the turbine at pressure p₂= 0.1 bar. The heat loss is 100 kJ/kg and work output is 1000 kJ/kg. Kinetic and potential energies for inflow and outflow are neglected. At pressure 0.1 bar, the enthalpy of saturated liquid is 200 kJ/kg and the enthalpy of vaporization is 2400 kJ/kg. The dryness fraction of the steam at the exit of the turbine is _____ (round off to 2 decimal places).

Answer: (0.75 to 0.85)

33. The total number of nonconformities is 420 from 30 samples. The size of each sample is 100. The lower control limit for the control chart for number of nonconformities is _____ (round off to 2 decimal places).

Answer: (2.60 to 2.95)

34. Two metal sheets are joined using resistance spot welding. A welding current of 4500 A is applied for 0.2 s. The effective contact resistance at the sheet interface is 400 × 10⁻⁶ Ω. The thermal efficiency of the welding process is 50 %. The amount of heat, in J, used for producing a spot weld is _____ (in integer).

Answer: (810 to 810)

35. A metal rod of diameter 14 mm is subjected to a tensile test. After the test, its cross-sectional diameter at the fractured end is 12 mm. The ductility, in %, is _____ (round off to 2 decimal places).

Answer: (25.00 to 28.00)

Q.36 – Q.65 Carry TWO marks Each

36. Given, z(x, y) = e^{x – 2y}, where x(t) = e^t and y(t) = e⁻^t. All the variables are real. The total differential dz/dt is

(A) −z(x + 2y)

(B) −z(x – 2y)

(D) z(x – 2y)

Answer: (C)

37. Two cards are drawn one after the other from a regular deck of 52 playing cards without replacement. The probability that the drawn cards are of different suits is

(A) 39/51

(B) 13/52

(D) 2/51

Answer: (A)

38. Match the machine elements with their functions.

(A) P – 3, Q – 2, R – 1

(B) P – 3, Q – 1, R – 2

(D) P – 1, Q – 3, R – 2

Answer: (B)

39. A massless beam is fixed at one end and supported on a roller at other end. A point force P is applied at the midpoint of the beam as shown in figure. The reaction at the roller support is

(A) 5P/16

(B) 2P/3

(D) 9P/25

Answer: (A)

40. Six jobs (1, 2, 3, 4, 5, 6) undergo drilling, followed by reaming operation. The time required for each operation is given as

The sequence of processing the jobs, using the Johnson’s rule, is

(A) 4 – 1 – 6 – 3 – 5 – 2

(B) 4 – 6 – 1 – 5 – 3 – 2

(D) 2 – 1 – 3 – 6 – 5 – 4

Answer: (A)

41. Match the engineering materials at room temperature with the given crystal structures.

(A) P – 3, Q – 4, R – 1, S – 2

(B) P – 2, Q – 1, R – 4, S – 3

(D) P – 3, Q – 1, R – 4, S – 2

Answer: (A)

42. Match the recording techniques used in method study with the most appropriate application areas.

(A) P – 3, Q – 4, R – 2, S – 1

(B) P – 3, Q – 1, R – 2, S – 4

(D) P – 2, Q – 1, R – 3, S – 4

Answer: (B)

43. Match the products to be manufactured with the given metal working processes.

(A) P – 3, Q – 4, R – 1, S – 2

(B) P – 2, Q – 4, R – 1, S – 3

(D) P – 4, Q – 3, R – 1, S – 2

Answer: (D)

44. The dual of a LPP is

Minimize w = 4w₁ + 6w₂ + 5w₃ – w₄

subject to,

and w_i ≥ 0 for i = 1, 2, 3, 4

The objective function of the primal is

(A) Maximize z = −3x₁ + 2x₂

(B) Maximize z = x₁ + x₃

(D) Maximize z = 3x₁ – 2x₂

Answer: (D)

45. There are four locations (P, Q, R, S) and four factors to be considered for setting up a facility. The scores (on a scale of 0 to 10, with 10 being the maximum) for the given locations and the weight assigned to each factor are given as

The best location for setting up the facility is

(A) P

(B) Q

(D) S

Answer: (C)

46. As per the Fe-C phase diagram, the microstructure of plain carbon steel with 0.4 wt.% carbon at room temperature contains

(A) proeutectoid ferrite and pearlite

(B) proeutectoid cementite and pearlite

(D) austenite and cementite

Answer: (A)

47. The most appropriate process for manufacturing of plastic chair is

(A) injection molding

(B) extrusion

(D) blow molding

Answer: (A)

48. The following equation is solved using Newton-Raphson method

x⁵ – 15 = 0

with initial value x₀ = 1.0.

The value of first approximation x₁ is ________ (round off to 2 decimal places).

Answer: (3.75 to 3.85)

49. For the matrix eigenvalue corresponding to the eigenvector is _____ (in integer).

Answer: (1 to 1)

50. The work sampling study, with 100 observations, revealed 25 % idle time of a worker. The number of observations required for ±10 % accuracy and 95.45 % confidence level is _____ (in integer).

Answer: (71 to 76 OR 1150 to 1210)

51. The information of two products P and Q is given as

The value of is _______ (round off to 2 decimal places).

Answer: (0.82 to 0.84)

52. A system shown in figure has seven components with reliabilities R_A = 0.96, R_B = 0.92, R_C = 0.94, R_D = 0.89, R_E = 0.95, R_F = 0.88, and R_G = 0.90. The reliability of the system is _____ (round off to 2 decimal places).

Answer: (0.80 to 0.84)

53. Details of activities of a project are given as

The time required, in days, to complete the project along the critical path is _____ (in integer).

Answer: (43 to 43)

54. A system has 10 essential components. Each component has an exponential time-to-failure distribution with constant failure rate of 0.04 per 4000 hours. The mean-time-to-failure, in hours, of the system is _____ (in integer).

Answer: (10000 to 10000)

55. A CNC water jet cutting machine is used to cut a straight slot between the points (2, 1) and (10, 10) on the XY plane (dimensions are in mm). If the feed rate is 1.5 mm/s, the time, in s, required to machine the slot following the shortest path, is _____ (round off to 2 decimal places).

Answer: (8.00 to 8.10)

56. In an orthogonal cutting with a tool of rake angle 0°, the value of the cutting force is two times of the thrust force. The coefficient of friction is _____ (round off to 1 decimal place).

Answer: (0.5 to 0.5)

57. The solidification of a cubical casting of side 100 mm takes place with volumetric solidification shrinkage and solid contraction of 10 % each. The shape of the casting is retained on cooling to room temperature. The side of the cubical cast, in mm, at room temperature is _____ (round off to 2 decimal places).

Answer: (88 to 95)

58. A straight turning operation is carried out at the feed rate of 100 mm/min using a single point cutting tool with signature 8 – 8 – 5 – 5 – 7 – 25 – 0 (ASA). The spindle speed is 1600 rpm. The roughness, in μm, of the machined surface in terms of peak-to-valley height is _____ (round off to 2 decimal places).

Answer: (7.10 to 7.40)

59. An arc welding operation is performed at 25 V and 200 A at welding speed of 2 mm/s. The heat used for melting is 80 % of the total heat generated. The unit melting energy of the metal to be joined is 10 J/mm³. The volume of the weld metal produced per unit time, in mm3/s, is _____ (in integer).

Answer: (200 to 200)

60. Water flows through a pipe of diameter 0.02 m. The Reynolds number of the flow is 1000. The pipe is heated from outside with a uniform heat flux. The flow and heat transfer in the pipe are steady and fully developed. The thermal conductivity of water is 0.66 W/(m-K). The convective heat transfer coefficient, in W/(m²-K), is _____ (round off to 2 decimal places).

Answer: (142.00 to 146.00)

61. In an ideal air-standard Brayton cycle, air enters the compressor at 100 kPa and 300 K. Thermal efficiency of the cycle is 50 %. The heat added to air is 1000 kJ/kg. Air has constant specific heat c_p =1.0 kJ/(kg-K) and γ =1.4. Air temperature, in K, at the turbine inlet is ______ (round off to 2 decimal places).

Answer: (1595.00 to 1605.00)

62. A key of width and height of 6 mm each is used to fix a gear on a shaft of 20 mm diameter. The shaft is used to transmit 10 kW power at 600 rpm to the gear. Permissible shear stress in the key is 80 N/mm², while compressive stress in the key is neglected. The minimum length of the key, in mm, is _____ (round off to 2 decimal places).

Answer: (32.00 to 34.00)

63. A cylindrical casting has 10 cm diameter and a mass of 12.56 kg. The material density is 7.85 × 10⁻³ kg/cm³. The value of exponent ‘n’ is 2 and solidification time is 12 min. The Chvorinov’s constant, in min/cm², is ______ (round off to 2 decimal places).

Answer: (2.80 to 3.10)

64. A pair of spur gears is designed to transmit 20 kW power at a pitch line velocity of 10 m/s. Diameter of the driving gear is 0.5 m. The tangential force, in N, between the driver and the driven gear is _____ (in integer).

Answer: (1998 to 2002)

65. Two products, P and Q , are sold in the ratio of 10:1. The fixed cost is Rs. 1,40,000. The selling price of P is Rs. 10/unit and Q is Rs. 40/unit. The variable costs of P and Q are Rs. 5/unit and Rs. 20/unit, respectively. The break-even point in terms of revenue, in Rs., is _____ (in integer).

Answer: (280000 to 28000)

GATE Exam 2023 Physics (PH) Question Paper With Answer Key

August 5, 2023 by suresh84

GATE-2023

PH: Physics

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x − 1)³(x − 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

PH: Physics

Q.11 – Q.25 Carry ONE mark Each

11. Which one of the following entropy (S) – temperature (T) diagrams CORRECTLY represents the Carnot cycle 𝑎𝑏𝑐𝑑𝑎 shown in the P-V diagram?

Answer: (MTA)

12. Which one of the following is a dimensionless constant?

(A) Permittivity of free space

(B) Permeability of free space

(D) Fine structure constant

Answer: (D)

13. Choose the most appropriate matching of the items in Column 1 with those in Column 2.

(A) (i) – Q; (ii) – S; (iii) – P; (iv) – R

(B) (i) – R; (ii) – Q; (iii) – P; (iv) – S

(D) (i) – P; (ii) – Q; (iii) – R; (iv) – S

Answer: (A)

14. The atomic number of an atom is 6. What is the spectroscopic notation of its ground state, according to Hund’s rules?

(A) ³P₀

(B) ³P₁

(D) ³S₁

Answer: (A)

15. H is the Hamiltonian, the orbital angular momentum and L_z is the z-component of .The 1 s state of hydrogen atom in the non-relativistic formalism is an eigen function of which one of the following sets of operators?

(A) H, L² and L_z

(B) H, , L² and Lz

(D) H and L_z only

Answer: (MTA)

16. The Hall experiment is carried out with a non-magnetic semiconductor. The current I is along the x-axis and the magnetic field 𝐵 is along the 𝑧-axis. Which one of the following is the CORRECT representation of the variation of the magnitude of the Hall resistivity ρ_xy as a function of the magnetic field?

Answer: (B)

17. Consider a two dimensional Cartesian coordinate system in which a rank 2 contravariant tensor is represented by the matrix The coordinate system is rotated anticlockwise by an acute angle θ with the origin fixed. Which one of the following matrices represents the tensor in the new coordinate system?

Answer: (B)

18. A compound consists of three ions X, Y and Z. The Z ions are arranged in an FCC arrangement. The X ions occupy 1/6 of the tetrahedral voids and the Y ions occupy 1/3 of the octahedral voids. Which one of the following is the CORRECT chemical formula of the compound?

(A) XY₂Z₄

(B) XYZ₃

(D) XYZ₄

Answer: (B)

19. For a non-magnetic metal, which one of the following graphs best represents the behaviour of C/T vs. T², where C is the heat capacity and T is the temperature?

Answer: (B)

20. For nonrelativistic electrons in a solid, different energy dispersion relations (with effective masses m_a*, m_b*, and m_c*) are schematically shown in the plots. Which one of the following options is CORRECT?

(A) m_a* = m_b* = m_c*

(B) m_b* > m_c* > m_a*

(D) m_a* > m_b* > m_c*

Answer: (D)

21. The figure schematically shows the M (magnetization) – H (magnetic field) plots for certain types of materials. Here M and H are plotted in the same scale and units. Which one of the following is the most appropriate combination?

(A) (Q) – Paramagnet; (R) – Type-I Superconductor; (S) – Antiferromagnet

(B) (P) – Paramagnet; (Q) – Diamagnet; (R) – Type-I Superconductor

(D) (P) – Diamagnet; (R) – Paramagnet; (S) – Type-I Superconductor

Answer: (B)

22. Graphene is a two dimensional material, in which carbon atoms are arranged in a honeycomb lattice with lattice constant a. As shown in the figure, are two lattice vectors. Which one of the following is the area of the first Brillouin zone for this lattice?

Answer: (A)

23. A ⁶⁰Co nucleus emits a β-particle and is converted to ⁶⁰Ni* with J^P = 4⁺, which in turn decays to the ⁶⁰Ni ground state with J^P = 0⁺ be emitting two photons in succession, as shown in the figure. Which one of the following statements is CORRECT?

(A) 4⁺ → 2⁺ is an electric octupole transition

(B) 4⁺ → 2⁺ is a magnetic quadrupole transition

(D) 2⁺ → 0⁺ is a magnetic quadrupole transition

Answer: (C)

24. Which one of the following options is CORRECT for the given logic circuit?

(A) P = 1, Q = 1; X = 0

(B) P = 1, Q = 0; X = 1

(D) P = 0, Q = 0; X = 1

Answer: (D)

25. An atom with non-zero magnetic moment has an angular momentum of magnitude √12 h. When a beam of such atoms is passed through a Stern-Gerlach apparatus, how many beams does it split into?

(A) 3

(B) 7

(D) 25

Answer: (B)

26. A 4 × 4 matrix M has the property M⁺ = −M and M⁴ = 1, where 1 is the 4 × 4 identity matrix. Which one of the following is the CORRECT set of eigenvalues of the matrix M?

(A) (1, 1, −1, −1)

(B) (i, i, −i, −i)

(D) (1, 1, −i, −i)

Answer: (B)

27. The Ξ⁰* particle is a member of the Baryon decuplet with isospin state and strangeness quantum number − In the quark model, which one of the following is the flavour part of the Ξ⁰* wave function?

Answer: (B)

28. Which of the following is(are) the CORRECT option(s) for the Joule-Thomson effect?

(A) It is an isentropic process

(B) It is an isenthalpic process

(D) For an ideal gas it always results in cooling

Answer: (B, C)

29. The deuteron is a bound state of a neutron and a proton. Which of the following statements is(are) CORRECT?

(A) The deuteron has a finite value of electric quadrupole moment due to non-spherical electronic charge distribution

(B) The magnetic moment of the deuteron is equal to the sum of the magnetic moments of the neutron and the proton

(D) The deuteron state is an admixture of ³S₁ and ³P₁ states

Answer: (A, C)

30. The Geiger-Muller counter is a device to detect α, β and γ It is a cylindrical tube filled with monatomic gases like argon, and polyatomic gases such as ethyl alcohol. The inner electrode is along the axis of the cylindrical tube and the outer electrode is the tube. Which of the following statements is(are) CORRECT?

(A) Argon is used so that ambient light coming from the surroundings do not produce any signal in the detector

(B) Ethyl alcohol is used as a quenching gas

(C) The electric field strength decreases from the axis to the edge of the tube and the direction of the field is radially outward

(D) The electric field increases from the axis to the edge of the tube and the field direction is radially inward

Answer: (A, B, C)

31. Consider an isolated magnetized sphere of radius R with a uniform magnetization along the positive z direction, with the north and south poles of the sphere lying on the z axis. It is given that the magnetic field inside the sphere is where μ₀ is the permeability of vacuum. Which of the following statements is(are) CORRECT?

(A) The bound volume current density is zero

(B) The bound surface current density has maximum magnitude at the equator, where this magnitude equals

(D) Far from the sphere, the magnetic field is due to a dipole of moment

Answer: (A, B, D)

32. Which of the following options represent(s) linearly independent pair(s) of functions of a real variable x ?

(A) e^ix and e⁻^ix

(B) x and e^x

(D) e^ix and sin x

Answer: (A, B, D)

33. In the vector model of angular momentum applied to atoms, what is the minimum angle in degrees (in integer) made by the orbital angular momentum vector and the positive z axis for a 2p electron?

Answer: (45 to 45)

34. For a transistor amplifier, the frequency response is such that the mid band voltage gain is 200. The cutoff frequencies are 20 Hz and 20 kHz. What is the ratio (rounded off to two decimal places) of the voltage gain at 10 Hz to that at 100 kHz?

Answer: (2.20 to 2.36)

35. An electric field as a function of radial coordinate r has the form where α is a constant. Assume that dimensions are appropriately taken care of. The electric flux through a sphere of radius √2, centered at the origin, is Φ. What is the value of Φ/2πα (rounded off to two decimal palces)?

Answer: (0.36 to 0.40)

Q.36 – Q.65 Carry TWO marks Each

36. It is given that the electronic ground state of a diatomic molecule X₂ has even parity and the nuclear spin of X is 0. Which one of the following is the CORRECT statement with regard to the rotational Raman spectrum (J is the rotational quantum number) of this molecule?

(A) Lines of all J values are present

(B) Lines have alternating intensity in the ratio of 3 : 1

(D) Lines of only odd J values are present

Answer: (C)

37. An input voltage in the form of a square wave of frequency 1 kHz is given to a circuit, which results in the output shown schematically below. Which one of the following options is the CORRECT representation of the circuit?

Answer: (A)

38. A simple harmonic oscillator with an angular frequency ω is in thermal equilibrium with a reservoir at absolute temperature T, with Which one of the following is the partition function of the system?

Answer: (A)

39. Which one of the following options is the most appropriate match between the items given in Column 1 and Column 2?

(A) (i) – T; (ii) – P,S,T; (iii) – Q,R; (iv) – S

(B) (i) – P,T; (ii) – S; (iii) – R,S; (iv) – S,T

(D) (i) – S,T; (ii) – P,S; (iii) – R,T; (iv) – S

Answer: (A)

40. A rod PQ of proper length L lies along the x-axis and moves towards the positive x direction with speed v = 3c/5 with respect to the ground (see figure), where c is the speed of light in vacuum. An observer on the ground measures the positions of P and Q at different times t_P and t_Q respectively in the ground frame, and finds the difference between them to be 9L/10. What is the value of t_Q – t_P?

(A) L/3c

(B) L/5c

(D) 2L/3c

Answer: (C)

41. A symmetric top has principal moments of inertia I₃ = 2α about a set of principal axes 1, 2, 3 respectively, passing through its center of mass, where 𝛼 is a positive constant. There is no force acting on the body and the angular speed of the body about the 3-axis is ω₃ = 1/8 rad/s. With what angular frequency in rad/s does the angular velocity vector precess about the 3-axis?

(A) 2

(B) 3

(D) 7

Answer: (MTA)

42. A particle of mass m is free to move on a frictionless horizontal two dimensional (r, θ) plane, and is acted upon b y a force with k being a positive constant. If p_r and p_θ are the generalized momenta corresponding to r and θ respectively, then what is the value of dpr/dt?

Answer: (D)

43. Consider two real functions

U(x, y) = xy(x² – y²),

V(x, y) = αx⁴ + by⁴ + cx²y² + k,

where k is a real constant and a, b, c are real coefficients. If U(x, y) + iV(x, y) is analytic, then what is the value of a × b × c ?

(A) 1/8

(B) 3/28

(D) 3/32

Answer: (D)

44. Young’s double slit experiment is performed using a beam of C₆₀ (fullerene) molecules, each molecule being made up of 60 carbon atoms. When the slit separation is 50 nm, fringes are formed on a screen kept at a distance of 1 m from the slits. Now, the experiment is repeated with C₇₀ molecules with a slit separation of 92.5 nm. The kinetic energies of both the beams are the same. The position of the 4th bright fringe for C₆₀ will correspond to the nth bright fringe for C₇₀. What is the value of 𝑛 (rounded off to the nearest integer) ?

(A) 5

(B) 6

(D) 8

Answer: (D)

45. A neutron beam with a wave vector and an energy 20.4 meV diffracts from a crystal with an outgoing wave vector . One of the diffraction peaks is observed for the reciprocal lattice vector of magnitude 3.14 Å⁻¹. What is the diffraction angle in degrees (rounded off to the nearest integer) that makes with the plane? (Use mass of neutron = 1.67 × 10⁻²⁷ Kg)

(A) 15

(B) 30

(D) 60

Answer: (B)

46. In the first Brillouin zone of a rectangular lattice (lattice constants a = 6Å and b = 4 Å), three incoming phonons with the same wave vector 〈2 Å⁻¹, 0.6 Å⁻¹〉 interact to give one phonon. Which one of the following is the CORRECT wave vector of the resulting phonon?

(A) 〈2.56 Å⁻¹, 0.23 Å⁻¹〉

(B) 〈3.60 Å⁻¹, 1.80 Å⁻¹〉

(D) 〈3.60 Å⁻¹, −0.80 Å⁻¹〉

Answer: (C)

47. For a covalently bonded solid consisting of ions of mass m, the binding potential can be assumed to be given by

where ϵ and r₀ are positive constants. What is the Einstein frequency of the solid in Hz?

Answer: (B)

48. In a hadronic interaction, π⁰’s are produced with different momenta, and they immediately decay into two photons with an opening angle 𝜃 between them. Assuming that all these decays occur in one plane, which one of the following figures depicts the behaviour of θ as a function of the π⁰ momentum p?

Answer: (A)

49. A particle has wave function

where N is a normalization constant and α is a positive constant. In this state, which one of the following options represents the eigenvalues of L² and L_z respectively?

Some values of Y_ℓ^𝓂 are :

(A) 0 and 0

(B) ℏ² and −ℏ

(D) ℏ² and ℏ

Answer: (C)

50. The wave function of a particle in one dimension is given by

Here M and a are positive constants. If φ(p) is the corresponding momentum space wave function, which one of the following plots best represents |φ(p)|² ?

Answer: (C)

51. Consider a particle in a two dimensional infinite square well potential of side L, with 0 ≤ x ≤ L and 0 ≤ y ≤ The wave function of the particle is zero only along the line y = L/2, apart from the boundaries of the well. If the energy of the particle in this state is E, what is the energy of the ground state?

Answer: (B)

52. Consider two non-identical spin 1/2 particles labelled 1 and 2 in the spin product state The Hamiltonian of the system is

where are the spin operators of particles 1 and 2, respectively, and λ is a constant with appropriate dimensions. What is the expectation value of H in the above state?

(A) −λ

(B) −2λ

(D) 2λ

Answer: (A)

53. A spin 1/2 particle is in a spin up state along the x-axis (with unit vector ) and is denoted as What is the probability of finding the particle to be in a spin up state along the direction which lies in the xy-plane and makes an angle θ with respect to the positive x-axis, if such a measurement is made?

Answer: (D)

54. Different spectral lines of the Balmer series (transitions n → 2, with n being the principal quantum number) fall one at a time on a Young’s double slit apparatus. The separation between the slits is 𝑑 and the screen is placed at a constant distance from the slits. What factor should d be multiplied by to maintain a constant fringe width for various lines, as n takes different allowed values?

Answer: (C)

55. Under parity and time reversal transformations, which of the following statements is(are) TRUE about the electric dipole moment p and the magnetic dipole moment μ ?

(A) p is odd under parity and μ is odd under time reversal

(B) p is odd under parity and μ is even under time reversal

(D) p is even under parity and μ is even under time reversal

Answer: (A)

56. Consider the complex function

At z = π, which of the following options is(are) CORRECT?

(A) The order of the pole is 4

(B) The order of the pole is 3

(D) The residue at the pole is 2π/3

Answer: (B)

57. Consider the vector field consisting of the velocities of points on a thin horizontal disc of radius of radius R = 2 m, moving anticlockwise with uniform angular speed ω = 2 rad/sec about an axis passing through its center. If then which of the following options is(are) CORRECT? (In the options, are unit vectors corresponding to the plane polar coordinates r and θ).

You may use the fact that in cylindrical coordinates (s, ϕ, z) (S is the distance from the z-axis), the gradient, divergence, curl and Laplacian operators are:

(A)

(B)

(D)

Answer: (B)

58. A slow moving π⁻ particle is captured by a deuteron (d) and this reaction produces two neutrons (n) in the final state, i.e., π⁻ + d → n + n. Neutron and deuteron have even intrinsic parities, whereas π⁻ has odd intrinsic parity. L and S are the orbital and spin angular momenta, respectively of the system of two neurons. Which of the following statements regarding the final two-neutron state is(are) CORRECT?

(A) It has odd parity

(B) L + S is odd

(D) L = 2, S = 0

Answer: (A, C)

59. Two independent electrostatic configurations are shown in the figure. Configuration (I) consists of an isolated point charge q = 1 C, and configuration (II) consists of another identical charge surrounded by a thick conducting shell of inner radius R₁ = 1 m and outer radius R₂ = 2 m, with the charge being at the center of the shell. where E_I and E_II are the magnitudes of the electric fields for configurations (I) and (II) respectively. ϵ₀ is the permittivity of vacuum, and the volume integrations are carried out over all space. If what is the value of the integer n?

Answer: (MTA)

60. In pion nucleon scattering, the pion and nucleon can combine to form a short lived bound state called the Δ particle (π + N → Δ). The masses of the pion, nucleon and the Δ particle are 140 MeV/c², 938 MeV/c² and 1230 MeV/c², respectively. In the lab frame, where the nucleon is at rest, what is the minimum energy (in MeV/c², rounded off to one decimal place) of the pion to produce the Δ particle?

Answer: (326.9 to 327.1)

61. Consider an electromagnetic wave propagating in the z-direction in vacuum, with the magnetic field given by If B₀ = 10⁻⁸ T, the average power passing through a circle of radius 1.0 m placed in the xy plane is P (in Watts). what is the value of 10³P/π (rounded off to one decimal place)?

Answer: (11.0 to 13.7)

62. An α-particle is emitted from the decay of Americium (Am) at rest, i.e., The rest masses of and α are 224.544 GeV/c², 220.811 GeV/c² and 3.728 GeV/c² What is the kinetic energy (in MeV/c², rounded off to two decimal places) of the α-particle?

Answer: (4.90 to 4.94)

63. Consider 6 identical, non-interacting, spin 1/2 atoms arranged on a crystal lattice at absolute temperature T. The z-component of the magnetic moment of each of these atoms can be ± μ_B. If P and Q are the probabilities of the net magnetic moment of the solid being 2μB and 6μB respectively, what is the value of P/Q (in integer)?

Answer: (15 to 15)

64. Two identical, non-interacting ⁴He₂ atoms are distributed among 4 different non-degenerate energy levels. The probability that they occupy different energy levels is p. Similarly, two ³He₂ atoms are distributed among 4 different non-degenerate energy levels, and the probability that they occupy different levels is q. What is the value of p/q (rounded off to one decimal place)?

Answer: (0.6 to 0.6)

65. Two identical bodies kept at temperatures 800 K and 200 K act as the hot and the cold reservoirs of an ideal heat engine, respectively. Assume that their heat capacity (C) in Joules/K is independent of temperature and that they do not undergo any phase change. Then, the maximum work that can be obtained from the heat engine is n × C Joules. What is the value of n (in integer)?

Answer: (200 to 200)

GATE Exam 2023 Petroleum Engineering (PE) Question Paper With Answer Key

August 5, 2023 by suresh84

GATE-2023

PE: Petroleum Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(D) between

Answer: (D)

2. Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(D) Refute

Answer: (C)

(A) 125

(B) 720

(D) 80

Answer: (D)

4. Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(D) At most half the candidates have a score that is larger than the mean.

Answer: (C)

5. In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(D) S

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

Answer: (MTA)

7. Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

(1) At any stage, Ankita can move either one or two stairs up.

(2) At any stage, Ankita cannot move to a lower step.

Let F(N) denote the number of possible ways in which Ankita can reach the Nth stair. For example, F(1) = 1, F(2) = 2, F(3) = 3.

The value of F(5) is _______.

(A) 8

(B) 7

(D) 5

Answer: (A)

Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.

(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(D) neither (i) nor (ii)

Answer: (D)

9. Which one of the given figures P, Q, R and S represents the graph of the following function?

f(x) = ||x + 2| – |x – 1||

(A) P

(B) Q

(D) S

Answer: (A)

(A) P

(B) Q

(D) S

Answer: (D)

PE: Petroleum Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Let z₁ and z₂ be two arbitrary complex numbers with non-zero modulus. Which of the following conditions is FALSE?

(A) |z₁ + z₂| > |z₁| + |z₂|

(B) 0 ≤ |z₁ + z₂| < ∞

(D) |z₁z₂| = |z₁||z₂|

Answer: (A)

12. In the 4th order Runge-Kutta method for solving ordinary differential equations with step size h < 1, the ratio of the order of local error to the order of global error is

(A) h

(B) h²

(D) 1/h²

Answer: (A)

13. Which of the following instruments can measure contact angle of a liquid drop placed on a surface?

(A) Goniometer

(B) Pycnometer

(D) Rheometer

Answer: (A)

14. Which of the following is the primary role of proppants in hydraulic fracturing?

(A) Keep the fractures open during production

(B) Decrease the viscosity of fracturing fluid

(D) Reduce the viscosity of crude oil in reservoir

Answer: (A)

15. A mixture of a flammable gas and air can ignite ONLY if

(A) the gas concentration is below the limiting oxygen concentration

(B) the gas concentration is above the upper flammable limit

(D) the gas concentration is below the lower flammable limit

Answer: (C)

16. Which of the following relations defines the coefficient of isothermal compressibility (C_g) for a gas?

Here, p, T, and v represent the pressure, temperature and volume of the gas, respectively.

Answer: (A)

17. Consider an ideal liquid-vapor mixture at equilibrium having liquid phase mole fraction (x_i) and gas phase mole fraction (y_i) of the component ‘i’. If at a given temperature, P_vi is the vapor pressure of pure component ‘i’ and P is the total pressure, then the equilibrium ratio (k_i) is

Answer: (C)

18. In-situ combustion method for enhanced oil recovery is commonly used for

(A) gas condensate reservoirs

(B) light oil reservoirs

(D) heavy oil reservoirs

Answer: (D)

19. Which of the following is a sedimentary rock?

(A) Amphibolite

(B) Chalk

(D) Schist

Answer: (B)

20. Kerogen is an intermediate compound in the process of petroleum formation in a sedimentary basin. This is typically classified into four categories (Type-I, Type-II, Type-III and Type-IV) based on the relative amount of carbon (C), hydrogen (H), oxygen (O) present in it (shown in the figure below).

Which of the following is the X- axis and Y-axis, respectively?

(A) H:C ratio and O:C ratio

(B) O:C ratio and H:C ratio

(D) C:O ratio and C:H ratio

Answer: (B)

21. The response of a four-arm caliper (dual caliper) log in a drilled section is shown in the figure below. The borehole features associated with the three identified sections P, Q, and R are

(A) P: washout; Q: in-gauge hole; R: key-seat

(B) P: washout; Q: in-gauge hole; R: key-seat

(D) P: dog-leg; Q: in-gauge hole; R: key-seat

Answer: (A)

22. Which of the following is necessary for the generation of electrokinetic potential across well-bore and permeable rock formation?

(A) Salinity gradient

(B) Pressure gradient

(D) Mud cake

Answer: (B)

23. A first arrival amplitude of the Cement Bond Log (CBL) of a cased hole section is given in the figure. The identified depth intervals P, Q, and R represent

(A) P: not cemented; Q: partially cemented; R: well-cemented

(B) P: not cemented; Q: well-cemented; R: partially cemented

(D) P: well-cemented; Q: not cemented; R: partially cemented

Answer: (D)

24. Contact angle measurements are often performed on smooth surfaces to gain information about the wettability of a surface. The interfacial tensions between solid-liquid, liquid-air, and air-solid are γ_SL, γ_LA and γ_AS, respectively.

Which of the following expressions describes the contact angle, θ?

Answer: (A)

25. Which of the following offshore rigs has the HIGHEST water depth of operation?

(A) Submersible drilling barge

(B) Jackup rig

(D) Semi-submersible rig

Answer: (D)

26. Consider an immiscible liquid mixture of n-decane and water containing fully dissociated NaCl. The number of degrees of freedom for this system is

(A) 3

(B) 4

(D) 2

Answer: (A)

27. The mean free path of the gas molecule is 10⁻⁶ mm, while the pore size of the rock is 10⁻³ Which of the following statements is TRUE?

(A) The Knudsen number is 10³ and the continuum principle would be applicable

(B) The Knudsen number is 10⁻³ and the continuum principle would be applicable

(D) The Knudsen number is 10⁻³ and the continuum principle would not be applicable

Answer: (B)

28. Which of the following is/are the route(s) by which a toxic substance may enter a human body?

(A) Ingestion

(B) Inhalation

(D) Asphyxiation

Answer: (A, B)

29. Select ALL the safety system(s) that is/are required in an offshore platform.

(A) Permit to work system

(B) Fire and gas alarms

(D) Financial monitoring system

Answer: (A, B, C)

30. Polymer flooding enhances oil recovery from an oil reservoir by

(A) increasing the mobility ratio

(B) reducing the mobility ratio

(D) increasing the viscous fingering

Answer: (B, C)

31. Which is/are the thermodynamic inhibitor(s) for natural gas hydrate?

(A) Tetrahydrofuran

(B) Sodium chloride

(D) Tetra n-butyl ammonium bromide

Answer: (B, C)

32. Which of the following hydrocarbon trap(s) is/are a result of sedimentary facies changes?

(A) Salt dome

(B) Unconformity

(D) Sand lens

Answer: (B, C, D)

33. Which of the following option(s) is/are indication(s) of a well kick?

(A) Decrease in mud pit volume

(B) Increase in mud pit volume

(D) Increase in pump pressure

Answer: (B, C)

34. Let be a 3 × 3 matrix.

The determinant of matrix X is 5.

The determinant of matrix is ________.

Answer: (30 to 30)

35. Consider a vector field where are the unit vectors in x, y and z directions, respectively.

The divergence of at the point (1, 2, 1) is _______ (rounded to one decimal place).

Answer: (11.5 to 11.5)

Q.36 – Q.65 Carry TWO marks Each

36. The value of is

(A) π/4

(B) π/8

(D) π/3

Answer: (D)

37. Consider the following accident scenario:

Failure of a drain connection on a rich oil line at the base of an absorber tower in a gas producing plant allowed the release of rich oil and gas. The resulting vapor cloud ignited from the ignition system of an engine-driven recompressor. The absorber tower eventually collapsed across a pipe rack. The breakage of the pipelines added more fuel to the fire and lead to the total destruction of the plant. The resulting fire burnt for 3 days.

Match the three steps of any accident (initiation, propagation, and termination) to the events that occurred in the above scenario.

(A) P-I; Q-III; R-II

(B) P-II; Q-I; R-III

(D) P-I; Q-II; R-III

Answer: (B)

38. A centrifugal pump running at 500 rpm delivers 60 liters/minute with a head of 50 m. At the same efficiency, if the rotational speed is increased to 1000 rpm, the discharge rate and head would respectively be

(A) 120 liters/minute and 200 m

(B) 120 liters/minute and 100 m

(D) 60 liters/minute and 100 m

Answer: (A)

39. Match the flow regimes associated with a vertically fractured well in a reservoir.

(A) P-I; Q-III; R-II; S-IV

(B) P-III; Q-I; R-II; S-IV

(D) P-I; Q-II; R-III; S-IV

Answer: (B)

40. The figure shows a schematic representation of the organic solid phase diagram for wax, hydrate and asphaltene deposition around the bubble point of a sample reservoir fluid. Arrowheads indicate the stable region for a corresponding organic solid.

Match the phase diagram with organic solids.

(A) I – Wax; II – Hydrate; III – Asphaltene

(B) I – Hydrate; II – Asphaltene; III – Wax

(D) I – Hydrate; II – Wax; III – Asphaltene

Answer: (D)

41. Schematic of phase diagrams for a pure gas hydrate system of methane (CH4), carbon dioxide (CO2), hydrogen sulphide (H2S) and nitrogen (N2) between the lower and upper quadruple points are shown in figure. Arrowheads indicate the stable hydrate region for a particular gas hydrate system.

Match the phase diagram with the corresponding pure gas hydrate.

(A) I – CH₄; II – N₂; III – CO₂; IV – H₂S

(B) I – H₂S; II – CH₄; III – CO₂; IV – N₂

(D) I – N₂; II – CH₄; III – CO₂; IV – H₂S

Answer: (D)

42. Match the entries between Group-I and Group-II for the seismic data acquisition, processing and interpretation.

(A) P – II; Q – IV; R – I; S – III

(B) P – II; Q – I; R – IV; S – III

(D) P – III; Q – I; R – IV; S – II

Answer: (A)

43. A build-up test is characterized by production at constant rate over time, t_p, followed by shut-in period of Δ_t. A plot of shut-in bottom hole pressure (P_ws) with Log [(t_p + Δ_t)/(Δ_t)] for pressure build-up test data is shown in the figure.

Which of the following statement(s) is/are TRUE?

(A) Early Time Region (ETR): Pressure build-up data is affected by reservoir boundaries and other reservoir heterogeneities such as sealing faults

(B) Middle Time Region (MTR): Pressure build-up data is reached after end of the wellbore storage and the pressure transient has entered the virgin reservoir

(C) Late Time Region (LTR): Pressure build-up data is affected by reservoir boundaries and other reservoir heterogeneities such as sealing faults

(D) Middle Time Region (MTR): Pressure build-up data is affected by reservoir boundaries and other reservoir heterogeneities such as sealing faults

Answer: (B, C)

44. Select the statement(s) that is/are TRUE.

(A) Combustion always occurs in the vapor phase

(B) Combustion cannot occur if air is absent

(D) The distinction between a fire and explosion is in their rate of energy release

Answer: (A, D)

45. Using Simpson’s one-third rule (with step size h = 0.25), the area under the curve y= e^−x3, from x = 0 to x = 1 is ______ (rounded to two decimal places).

Answer: (0.75 to 0.85)

46. The directional derivative of f = x³ + 4y² + z² at the point P(2, 1, 3) in the direction of the vector is _______ (rounded to one decimal place).

Answer: (2.4 to 2.4)

47. A switch-over event in a producing well occasionally results in a reportable oil leak. An analysis of the data shows that the chance of a reportable leak is 1 in 500 switch-over events. It is observed that 10 switch-over events occur every day.

If the occurrence of a reportable leak follows a Poisson distribution, the number of days in a year (of 365 days) with no reportable oil leaks from switch-over events is ____________ (rounded to nearest integer).

Answer: (357 to 358)

48. Figure shows an inextensible catenary mooring cable in still water. The submerged weight (per meter length), and the anchor radius (x) are 100 kg/m and 50 m, respectively. If horizontal tension (Th) in the catenary is 1600 kg, the catenary length (AB) is ____________ m (rounded to two decimal places).

Answer: (181 to 182)

49. An empty steel pipeline with massless endcaps has an outer diameter, D, and thickness, t. The density of steel is 7850 kg/m³. The critical D/t ratio at which the pipeline starts floating in seawater of density 1025 kg/m³ is ____________ (rounded to two decimal places).

Answer: (28 to 32)

50. Consider the flow of oil and water in one-dimensional porous medium, with S_wr = 0.2 and S_or = 0.4, where are the end point relative permeabilities of oil and water, respectively. S_or and S_wr are the residual saturations of oil and water, respectively. The viscosities of oil and water are 5 cP and 1 cP, respectively. k_ro and k_rw are the relative permeabilities of oil and water, respectively, at a given water saturation (S_w). Following relations are valid.

The total relative mobility (oil relative mobility + water relative mobility) at the water saturation of 0.4 is___________cP⁻¹ (rounded to one decimal place).

Answer: (0.2 to 0.2)

51. A binary mixture of n-butane (C₄H₁₀) and n-pentane (C₅H₁₂) is under thermodynamic equilibrium at 180 oF and 95 psia. The vapor pressures of pure C₄H₁₀ and pure C₅H₁₂ at 180°F are 160 psia and 54 psia, respectively.

Assuming ideal solution behavior (i.e., Raoult’s law and Dalton’s law are valid), the mole fraction of the n-butane in the gas phase is ________ (rounded to three decimal places).

Answer: (0.645 to 0.670)

52. A highly permeable reservoir with initial reservoir pressure of 3000 psi is under active water drive from a surrounding large aquifer. The final stabilized reservoir pressure is 2500 psi. Following data associated with the reservoir at 2500 psi are given.

Oil production rate = 30,000 STB/day

Water production rate = 0 STB/day

Oil formation volume factor, Bo = 1.5 bbl/STB

Gas formation volume factor, Bg = 0.00070 bbl/scf

Water formation volume factor, Bw = 1 bbl/STB

Producing Gas to Oil Ratio, GOR = 850 scf/STB

Gas solubility, Rs = 700 scf/STB

(bbl: reservoir barrel, STB: Stock tank barrel, scf: standard cubic feet)

If the reservoir pressure and the reservoir production rates remain constant, the water influx rate is__________bbl/day (rounded to nearest integer).

Answer: (47000 to 49000)

53. A volumetric undersaturated solution gas drive reservoir (without gas cap, no water influx, and with no initial gas saturation) has an initial water saturation of 15% which remains unchanged during production. After the production of 10% of the initial oil (measured at surface conditions), the oil formation volume factor (Bo) is reduced from its initial value of 1.4 bbl/STB to 1.2 bbl/STB.

(bbl: reservoir barrel, STB: Stock tank barrel)

The final gas saturation in percentage is _______ (rounded to one decimal place).

Answer: (19 to 20)

54. After well completion, a discovery well in an oil reservoir is produced for a short period and then closed for pressure build-up test. The production history before shut-in is given below.

The Horner’s pseudo-producing time, tpH, is__________hr (rounded to nearest integer).

Answer: (570 to 576)

55. A compressional acoustic wave takes 55 μs to travel 0.3048 m through a rock formation having bulk modulus of 37.5 GPa and shear modulus of 31 GPa. The bulk density of the rock is _______ kg/m3 (rounded to two decimal places).

Answer: (2500 to 2600)

56. A gamma ray log run across a sand-shale sequence recorded maximum and minimum values of 70 API unit and 30 API unit, respectively. A bed in this sequence has a gamma log value of 50 API unit.

Assuming a linear relationship between shale index and shale volume, the volume fraction of shale in the bed is ________ (rounded to one decimal place).

Answer: (0.5 to 0.5)

57. The resistivity reading of a flushed zone across a permeable formation (drilled with water-based mud) is 20 Ω.m. Laboratory analysis shows that the resistivity of the core plug (100% saturated with a NaCl brine) from the same formation is 6 Ω.m. The resistivity of the NaCl brine is 0.6 Ω.m.

If the resistivity of the mud filtrate is 0.9 Ω.m and Archie’s saturation exponent is 2, then the estimated residual hydrocarbon saturation (in percentage) in the flushed zone is _______ (rounded to two decimal places).

Answer: (31 to 34)

58. Consider a micellar displacement process in a homogeneous reservoir with a porosity of 30%. The volume of the microemulsion slug to be injected is 4% of the pore volume. The slug contains 4 vol% surfactant. The density of the rock and the surfactant is 2.7 g/cm3 and 1.1 g/cm3, respectively.

Assuming that the average surfactant adsorption is 0.25 mg/g of the reservoir rock, the fraction of the injected surfactant that will be adsorbed is _______________ (rounded to two decimal places).

Answer: (0.88 to 0.91)

59. A kill mud of appropriate density is required to be injected in a well such that the shut-in pressure is 6.8 x 106 Pa at a depth of 3500 m. Here, the shut-in pressure is the quantity by which the bottom-hole pressure exceeds the hydrostatic pressure of the original mud at the given depth. The density of the original mud is 1100 kg/m³.

The density of the kill mud is _________ kg/m3 (rounded to two decimal places).

Answer: (1285 to 1305)

60. A non-Newtonian drilling fluid is placed between two flat parallel rectangular plates having an area of 10 cm² The bottom plate is fixed and the vertical distance between the two plates is 1 cm, as shown in the figure. A force of 300 dyne is required to initiate the motion of the upper plate. A force of 600 dyne is needed to keep the upper plate in motion at a constant velocity of 10 cm/s. Assume that the following relationship holds for the drilling fluid.

where, τ_yx is the shear stress, τ_yx^o is the minimum shear stress to initiate fluid flow; μ_p is the Bingham plastic viscosity; and is the shear rate.

The Bingham plastic viscosity of fluid is _____________ dyne.s/cm² (rounded to nearest integer).

Answer: (3 to 3)

61. Crude oil having density and viscosity of 850 kg/m³ and 2 × 10⁻³s, respectively, is flowing at an average velocity of 0.35 m/s through a horizontal capillary tube. The inside diameter and length of the capillary tube are 2.5 × 10⁻³ m and 0.30 m, respectively. The Fanning friction factor, f, is given by,

F = 16/Re

where, Re is the Reynolds number.

The pressure drop across the capillary tube is __________Pa (rounded to one decimal place).

Answer: (1060 to 1090)

62. An oil droplet is to be mobilized by injecting water through a pore throat. The oil-water interface has the rear radius of curvature (r_A) of 25 × 10⁻⁶ m and a forward radius of curvature (r_B) of 5 × 10⁻⁶ m as shown in the figure. Assume that the pore is completely water wet (wetting contact angle is zero) and the interfacial tension between oil and water is 0.025 N/m.

The magnitude of the minimum pressure drop required to mobilize the trapped oil droplet is ___________ N/m² (rounded to nearest integer).

Answer: (7950 to 8050)

63. A four-column semi-submersible floater is located offshore. The diameter of each column is 5 m. Consider the total displaced weight of seawater of the semi-submersible as 4000 tonnes. Assume added mass contribution as 50% of the semi-submersible weight, and seawater density as 1025 kg/m³.

(Acceleration due to gravity = 9.81 m/s²)

The natural period of oscillation of the floater in vertical mode is ___________ seconds (rounded to one decimal place).

Answer: (17.0 to 17.6)

64. A shell and tube heat exchanger is used for cooling crude oil from 400 K to 360 K. Crude oil flows through the tube at 3650 kg/h. Water enters the shell side at 310 K and has a flow rate of 1600 kg/h. Assume the heat capacity of crude oil and water as 2.5 kJ/kg.K and 4.187 kJ/kg.K, respectively.

If the overall heat transfer coefficient is 300 W/m².K and the streams are counter current, the heat transfer area required is _________ m² (rounded to one decimal place).

Answer: (7.5 to 8.5)

65. An underwater riser with an outer diameter of 250 mm and wall thickness of 20 mm is subjected to tension and pressure. The effective tension is 1200 kN wherein the internal and external pressures of the riser are 25 MPa and 6 MPa, respectively.

The true wall tension in the riser is ____ ×10⁶ N (rounded to two decimal places).

Answer: (1.5 to 2.1)

GATE Exam 2023 Naval Architecture and Marine Engineering (NM) Question Paper With Answer Key

August 5, 2023 by suresh84

GATE-2023

NM: Naval Architecture and Marine Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x − 1)³(x − 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

NM: Naval Architecture and Marine Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Consider the function where x = u sin v and y = u cos v. The partial derivative, is

(A) 0

(B) 1

(D) 3

Answer: (B)

12. Consider the function z = x³ – 2x²y + xy² + 1. The directional derivative of z at the point (1, 2) along the direction is

(A) 0

(B) −1

(D) −2

Answer: (C)

13. The vapor quality of steam in the turbine of a Rankine cycle can be improved by employing

(A) regeneration of steam

(B) intercooler

(D) cogeneration

Answer: (C)

14. In the following “GZ (righting lever arm)” versus “angle of heel” curve, the point ‘X’ indicates

(A) angle of loll

(B) angle of vanishing stability

(D) trim angle

Answer: (A)

15. Comparing a catamaran (with a separation between demi-hulls) and a mono-hull craft of the same displacement and water plane area, the initial metacentric radius of the catamaran will be

(A) same as that of the mono-hull

(B) one-half of the mono-hull

(D) one-third of the mono-hull

Answer: (C)

16. The time series of rudder angle (δ) and heading angle (ψ) during a ship’s maneuver are shown in the following figure. Identify the maneuver and the associated parameters (p, q, r and s)

(A) turning maneuver

p: heading angle, q: rudder angle, r: 1st overshoot angle, s: 2nd overshoot angle

(B) spiral maneuver

p: heading angle, q: rudder angle, r: 1st overshoot angle, s: 2nd overshoot angle

p: rudder angle, q: heading angle, r: 1st overshoot angle, s: 2nd overshoot angle

(D) zig-zag maneuver

p: heading angle, q: rudder angle, r: 1st overshoot angle, s: 2nd overshoot angle

Answer: (C)

17. A closed system undergoing a thermodynamic cycle consisting of two reversible isothermal and two reversible adiabatic processes is shown in the following figure. If δQ is the infinitesimal heat transfer and T is the instantaneous temperature, then the value of the contour integral

(A) is positive

(B) is negative

(D) cannot be determined

Answer: (C)

18. In a marine steam power cycle employing regeneration, the feed water heater for waste heat recovery is placed after the

(A) boiler

(B) turbine

(D) pump

Answer: (D)

19. From the following, choose the offshore platform that can be used ONLY for offshore drilling purpose.

(A) Jacket platform

(B) Jackup platform

(D) SPAR

Answer: (B)

20. Which method among the following is based on the strain energy principle?

(A) Conjugate beam method

(B) Castigliano’s method

(D) Moment distribution method

Answer: (B)

21. In dimensional analysis, according to Buckingham’s π-theorem, if n is the total number of variables and m is the number of independent dimensions, then the maximum number of independent dimensionless π-groups will be

(A) m – n

(B) mn

(D) n – m

Answer: (D)

22. A submerged cylinder of diameter 1 m is rotating clockwise at 100 rpm, in a flow with a free stream velocity of 10 m/s. Assuming ideal flow, the number of stagnation points on the cylinder is

(A) 2

(B) 3

(D) 0

Answer: (A)

23. The buoyancy curve variation of a ship floating in still water and in waves is shown in the following figure. The total area under each curve is the same. The cases ‘X’ and ‘Y’ correspond to

(A) X: wave crest is amidships, Y: wave crest is amidships

(B) X: wave trough is amidships, Y: wave trough is amidships

(D) X: wave crest is amidships, Y: wave trough is amidships

Answer: (D)

24. Let X be any random variable and Y = −2X + 3.

If E[Y] = 1 and E[Y²]= 9, then which of the following are TRUE?

(A) E[X] = 1

(B) E[X] = −2

(D) Var(X) = 2

Answer: (A, D)

25. Consider the contour integral along the curve |z| = 3 oriented in the counterclockwise direction. If Res[f, z₀] denotes the residue of f(z) at the point z₀, then which of the following are TRUE?

(A) Res[f, 0] = −1/4

(B) Res[f, 1] = 1/3

(D) Res[f, 2] = −1

Answer: (A, B, C)

26. A stationary ship has longitudinal symmetry. The surge, sway and heave motions are represented by indices 1-2 -3, respectively and roll, pitch and yaw motions are represented by indices 4-5-6, respectively. Which of the following are TRUE about the added mass (A_ij)?

(A) A₃₅ = A₅₃

(B) A₆₂ = A₂₆

(D) A₃₃ = A₅₅

Answer: (A, B, C)

27. The failure modes that may be observed in a riveted joint to fasten two plate members, subjected to shear load are

(A) bending of the rivet

(B) shearing of the rivet

(D) tensile failure of the rivet

Answer: (A, B, C)

28. A rectangular barge is freely floating in a drydock as shown in the following figure. For longitudinal strength analysis which of the following are TRUE?

(A) The barge is considered as a free-free beam

(B) At aft and forward ends: shear force = 0, bending moment = 0

(D) At aft and forward ends: shear force ≠ 0, bending moment ≠ 0

Answer: (A, B)

29. A ship of length 180 m has a displacement of 14400 tonnes and is floating on an even keel in sea water of density 1025 kg/m³. The trim changes by 0.18 m when a weight of 120 tonnes that is already onboard, is shifted 24 m forward. The longitudinal metacentric height is ______ m.

Answer: (200 to 200)

30. A piezometer and a pitot tube measure the static and the total pressure of a fluid in a pipe flow respectively. The piezometer reads 100 kPa and the pitot tube shows 200 kPa. The density of the fluid is 1000 kg/m³. The velocity of the flow is ______ m/s (round off to one decimal place)

Answer: (13.5 to 14.5)

31. A Carnot heat engine operates between two reservoirs of temperatures 900°C (TH) and 30 oC (TL). If the heat transferred during one cycle to the engine from TH is 150 kJ, then the energy rejected to TL is _________ kJ (round off to the nearest integer)

Answer: (38 to 39)

32. An oil tanker of breadth 20 m and having a displacement of 24000 tonnes in sea water (density of sea water = 1025 kg/m³) is carrying oil of relative density 0.8 in 9 longitudinally distributed tanks which are all half-filled. Each longitudinal tank is 12 m long and 16 m wide. The apparent change in vertical center of gravity, due to the presence of oil in the tanks is _______ m (round off to one decimal place)

Answer: (1.1 to 1.3)

33. For a regular sinusoidal wave propagating in deep water having wave height of 3.5 m and wave period of 9 s, the wave steepness is _______ (round off to three decimal places)

Answer: (0.025 to 0.032)

34. A solid cantilever shaft of diameter 0.1 m and length 2 m is subjected to a torque of 10 kN-m at the free end (shear modulus is 82 GPa). The maximum induced shear stress is ______ N/mm² (round off to the nearest integer).

Answer: (50 to 52)

35. If a random variable X has the probability density function

and if Y = X², then the expected value of Y is _________ (round off to one decimal place)

Answer: (2.8 to 2.9)

Q.36 – Q.65 Carry TWO marks Each

36. The value of the surface integral ∬(x² dydz + y² dzdx + z² dxdy) over the surface of the cube given by 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2, is

(A) 12

(B) 24

(D) 48

Answer: (D)

37. If the system of linear equations, x – ay – z = 0, ax – y – z = 0, x + y – z = 0, has infinite number of solutions, then the possible values of a are

(A) 0, 1

(B) -1, 2

(D) 0, -1

Answer: (C)

38. Two 30 m long bilge keels of mass 40 tonnes each, are fitted at the turn of the bilge on port and starboard sides of a ship. The cross section of the bilge keel is shown in the following figure. Assume density of water = 1000 kg/m³. If the TPC (tonnes per centimeter) immersion of the ship is 50, then the change in the mean draft is _____ cm

(A) 1

(B) 0.8

(D) 1.6

Answer: (A)

39. The layout of a Tension Leg Platform (TLP) is shown in the following figure. It consists of four interconnected pontoons at the bottom and four cylindrical columns, which support the working platform at the top. The density of sea water is 1025 kg/m³. Neglect the weight and buoyancy of the tethers. During operation, the maximum mass (in metric tonnes) of the entire structure must lie between

(A) 18630 and 18635

(B) 28635 and 28640

(D) 24560 and 24565

Answer: (A)

40. The trajectory of a model ship during a pure sway PMM test is shown below. The steady forward speed, u is 2.0 m/s. The maximum amplitude of sway motion, y_Max is 0.5 m and its period is 8 s. The magnitude of maximum drift angle, in degrees (round off to the nearest integer), and the magnitude of maximum sway acceleration, in m/s² (round off to one decimal place), of the model respectively are

(A) 11 and 0.3

(B) 13 and 0.5

(D) 9 and 0.1

Answer: (A)

41. A ship of length 125 m has a design speed of 25 knots (1 knot = 0.5144 m/s). A 5.0 m long geometrically similar model with wetted surface area of 4 m2 has a coefficient of residuary resistance of 1.346 x 10⁻³ at the corresponding speed. The ship’s residuary resistance in kN (in sea water of density 1025 kg/m³), and the model speed in knots (round off to the nearest integer) respectively are

(A) 285 and 5

(B) 17 and 5

(D) 17 and 1

Answer: (A)

42. A fully filled water tank OABCD has a circular arc (AB) of radius 10 m at the bottom as shown in the following figure. The height BC is 10 m. The length OA and CD are 5 m and 15 m, respectively. The density of the water is ρ kg/m³ and the acceleration due to gravity is g m/s². The magnitude of the resultant hydrostatic force per unit width acting on AB in N/m lies between

(A) 190 ρg and 200 ρg

(B) 210 ρg and 220 ρg

(D) 250 ρg and 260 ρg

Answer: (C)

43. The velocity vector of a 2D flow field is given by The acceleration is

Answer: (A)

44. Water is flowing with a free stream velocity of 0.25 m/s around a submerged flat plate of 2 m length (in the direction of flow) and 1 m width. The local shear stress at a distance x from the leading edge of the plate is given by

where ρ = 1000 kg/m³ is the density of the water, u is the free stream velocity and R_ex is the Reynolds number at x. Assume that the flow is laminar, and the kinematic viscosity of water is 10⁻⁶ m²/s. The drag force (in Newton) acting on one side of the plate lies between

(A) 0 and 0.05

(B) 0.05 and 0.10

(D) 0.15 and 0.20

Answer: (C)

45. For a 2D ideal flow, let φ be the velocity potential and ψ be the stream function. Which one of the following is TRUE?

(A) ∇²φ = 0 and |∇ψ|² = |∇φ|²

(B) ∇²φ = 0 and ∇ψ∙∇φ ≠ 0

(D) ∇²ψ = 0 and ∇ψ × ∇φ = 0

Answer: (A)

46. A long body with elliptical cross section is held perpendicular to a 2D uniform steady flow field of horizontal velocity U_∞ as shown in the following figure. The heights of the control volume (bounded by the dashed lines) at the inlet and outlet are 2h and 4h, respectively. The profile of the horizontal velocity far downstream is given by The density of the fluid is ρ. The magnitude of the drag force per unit length acting on the body is

Answer: (A)

47. A ‘T’ section is welded to the flat bottom shell plate of a ship as shown in the following figure (bottom shell longitudinal). The neutral axis of the ship’s midship section is 14 m above the bottom shell plate. The distance (X) of neutral axis of the ‘T’ section from the ship’s neutral axis is ________ m (round off to two decimal places)

(A) 12.63

(B) 13.63

(D) 11.24

Answer: (B)

48. A vertical frictionless piston-cylinder arrangement contains air of mass 1 kg. During a process, 50 J of heat is transferred from outside to the system such that the piston is raised slowly by 0.1 m from its initial equilibrium position. The mass of the piston is 1 kg, and the diameter is 0.1 m. Assume that g = 9.81 m/s², and Patm = 100 kPa. The change in internal energy of the air in J (round off to two decimal places) lies between

(A) 28.45 and 28.55

(B) -28.55 and -28.45

(D) 129.45 and 129.55

Answer: (C)

49. An insulated nozzle has an inlet cross-sectional area of 314 cm². Air flows through the nozzle with an inlet temperature of 300 K at a steady rate of 1.256 m³/s. The velocity at the exit is greater than that at the inlet by 210 m/s. Assume a constant C_p = 1.004 kJ/kg-K. The temperature (in K) of air at the exit of the nozzle lies between

(A) 330 and 331

(B) 269 and 270

(D) 277 and 278

Answer: (B)

50. The heave natural frequencies of a Jacket structure, FPSO and a semi-submersible are ω_J, ω_F and ω_S Each one of them has a pay load capacity of 10000 tonnes. Which of the following is TRUE?

(A) ω_J < ω_F < ω_S

(B) ω_J > ω_F > ω_S

(D) ω_J > ω_S > ω_F

Answer: (B)

51. A simply supported beam with an overhang has experienced the bending moment as shown below. The corresponding concentrated load is

(A) 5 kN at mid span of PR

(B) 10 kN at Q

(D) 5 kN at S

Answer: (D)

52. Let Which of the following are TRUE?

(A) The matrix L is row equivalent to

(B) The linear system Lx = b has a solution for all b

(D) Rank of matrix L is 3

Answer: (A, D)

53. For a given time varying load applied on a single degree of freedom system, the dynamic response amplitude is always less than the static response amplitude if

(A) the applied loading frequency is greater than 1.5 times the natural frequency of the system

(B) the damping is greater than 70% of critical damping

(D) the applied loading frequency is less than the natural frequency of the system for an undamped system

Answer: (A, B)

54. The stress field,

σ_x = 4x³ + 3x²y + 5xy²

σ_y = −x³ + 6x²y – 7xy²

τ_xy = −5x²y – 3xy²

would satisfy the strain compatibility condition if

(A) both σ_x and σ_y are multiplied by 1/2

(B) both σ_x and σ_y are multiplied by 2

(D) τ_xy is multiplied by 2

Answer: (B, C)

55. If y(x) is the solution of the differential equation

(1 + x²)yʹʹ − 2xyʹ = 0

satisfying y(0) = 0 and yʹ(0) = 3, then y(1) equals _______

Answer: (4 to 4)

56. For a ship of length L = 100 m, the distance between the bow and stern pressure system is 0.942L. Assume g = 10 m/s². The ship velocity corresponding to the prismatic hump of the wave making resistance curve is ________ m/s (round off to one decimal place)

Answer: (9.9 to 10.1)

57. A vessel of 100 m length has a constant triangular cross-section with a depth of 12 m and breadth of 15 m as shown in following figure. The vessel has a vertical center of gravity (KG) = 6.675 m. The minimum draft (d), at which the vessel will become stable is _______ m (round off to one decimal place)

Answer: (7.1 to 7.3)

58. For a marine screw propeller, the open water characteristics at J = 0.6 are K_T = 0.1336 and 10K_Q = 0.2010. The open water propeller efficiency η_o, is _______ (round off to two decimal places)

Answer: (0.62 to 0.65)

59. Saturated liquid water (m = 1 kg) initially at 0.101 MPa and 100°C is heated at constant pressure until the temperature increases to 500 oC. Assume a constant C_p of steam = 1.9 kJ/kg-K, and enthalpy of vaporization, h_fg = 2257 kJ/kg at 0.101 MPa. The change in entropy of the water is ________ kJ/K (round off to two decimal places)

Answer: (7.35 to 7.55)

60. A simple vapor compression refrigeration cycle with ammonia as the working fluid operates between 30°C and −10℃ as shown in the following figure. The saturated liquid and vapor enthalpies at 30°C and −10℃ are provided in the table below. If the COP of the cycle is 5.6, the specific enthalpy at the inlet to the condenser is ______ kJ/kg (round off to the nearest integer)

Answer: (1615 to 1617)

61. An air-standard diesel cycle, as shown in the following figure with a compression ratio of 16, has an initial pressure 0.9 bar and temperature 300 K. Assume γ = 1.4 and C_p = 1.004 kJ/kg-K. If the heat added during the constant pressure process is 900 kJ/kg, then the peak temperature during the cycle is ________ K (round off to the nearest integer)

Answer: (1805 to 1807)

62. A tsunami that originated off the Indonesian coast has propagated towards the east-coast of India. It enters the continental shelf at 150 km away from the coast of Chennai. If the average water depth is 80 m from the coast to the continental shelf and 20 minutes is the tsunami period, the time taken by the tsunami to reach the coast of Chennai on entering the continental shelf is ______ hours (round off to two decimal places)

Answer: (1.45 to 1.50)

63. A buoy of virtual mass 30 kg oscillates in a fluid medium as a single degree of freedom system. If the total damping in the system is set as 188.5 N-s/m, such that the oscillation just ceases to occur, then the natural period of the system is _________ s (round off to one decimal place)

Answer: (1.9 to 2.1)

64. Consider a truss as shown in the following figure. The length of each member is 2 m. The area of cross section of each member is 100 mm² and Young’s modulus is 2 × 10⁵ N/mm². The vertical deflection at C is _______ mm (round off to one decimal place)

Answer: (0.7 to 0.8)

65. A marker buoy of mass 1500 kg floating in sea water of density 1025 kg/m³, consists of a cylinder and cone as shown in the following figure. The buoy is suitably ballasted to make it stable in the floating condition. The buoy is subjected to an external periodic excitation force in Newton, F_e(t) = 2000 sin (1.25 t). Ignore damping effects and assume g = 9.81 m/s², added mass = 25% of the mass of the buoy. The maximum heave response amplitude of the buoy is ________ m (round off to one decimal place)

Answer: (0.9 to 1.0)

GATE Exam 2023 Metallurgical Engineering (MT) Question Paper With Answer Key

August 5, 2023 by suresh84

GATE-2023

MT: Metallurgical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x − 1)³ (x − 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

MT: Metallurgical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. At one atmosphere pressure, α-Fe transforms to γ-Fe above 912° Density of γ-Fe is more than that of α-Fe. Choose the correct statement.

(A) Increasing the pressure above one atmosphere lowers the α-Fe to γ-Fe transformation temperature.

(B) Increasing the pressure above one atmosphere raises the α-Fe to γ-Fe transformation temperature.

(D) Pressure change will not have any effect on the α-Fe to γ-Fe transformation temperature.

Answer: (A)

12. Formation of an ideal solution leads to

(A) increase in entropy

(B) decrease in volume

(D) decrease in entropy

Answer: (A)

13. Order (O) and degree (D) of the differential equation are

(A) O = 2 and D = 1

(B) O = 1 and D = 2

(D) O = 2 and D = 6

Answer: (A)

14. At one atmosphere pressure, iron (Fe) and nickel (Ni) oxidize as

2Fe + O₂ ↔ 2FeO ∆G° = −527400 + 128 T Joules

2Ni + O₂ ↔ 2NiO ∆G° = −471200 + 172 T Joules

Identify the correct statement.

Given: Temperature, T is in Kelvin

(A) Fe can reduce NiO at all temperatures

(B) Fe can reduce NiO only above 1000 K

(D) Ni can reduce FeO only above 1000 K

Answer: (A)

15. For laminar fluid flow through a smooth circular tube, the relation between friction factor (f) and Reynolds number (Re) is

(A) f = 16/Re

(B) f = 24/Re

(D) f = 24/√Re

Answer: (A)

16. Among the following options, a process for liquid-liquid separation is

(A) Smelting

(B) Roasting

(D) Calcination

Answer: (A)

17. The most effective concentration step for sulfide ores is

(A) Froth flotation

(B) Magnetic separation

(D) Electrostatic separation

Answer: (A)

18. The gas distribution in a blast furnace is controlled by the shape of

(A) Cohesive zone

(B) Deadman zone

(D) Chemical reserve zone

Answer: (A)

19. Diamond has low

(A) electrical conductivity

(B) modulus of elasticity

(D) thermal conductivity

Answer: (A)

20. For self-diffusion in polycrystalline copper with a lattice diffusion coefficient D_L, grain boundary diffusion coefficient D_GB, and surface diffusion coefficient D_S, the correct relationship is

(A) D_S > D_GB > D_L

(B) D_L > D_S > D_GB

(D) D_GB = D_S = D_L

Answer: (A)

21. Magnitude of Burgers vector of the dislocation resulting from reaction of dislocations with Burgers vectors is

(A) a/√2

(B) √2a

(D) 2a

Answer: (A)

22. The mechanism of creep for a single crystal as depicted in the schematic is

(A) Nabarro-Herring creep

(B) Grain boundary sliding

(D) Coble creep

Answer: (A)

23. The value of is

(A) −38/10

(B) −51/10

(D) undefined

Answer: (A)

24. Match the defects in Column I with corresponding metal forming techniques in Column II.

(A) P – 4, Q – 1, R – 2, S – 3

(B) P – 4, Q – 2, R – 3, S – 1

(D) P – 3, Q – 1, R – 4, S – 2

Answer: (A)

25. In rolling, the point on the surface of contact between roll and sheet where surface velocity of the roll is equal to velocity of the sheet is referred as

(A) no-slip point

(B) no-stick point

(D) maximum stick point

Answer: (A)

26. When cracks propagate in a brittle material, the following option(s) is/are correct

(A) elastic strain energy decreases

(B) surface energy increases

(D) elastic strain energy increases

Answer: (A, B)

27. Which of the following is/are responsible for reducing the high cycle fatigue life of a component?

(A) increasing the mean stress at constant amplitude

(B) increasing the surface roughness

(D) absence of sharp corners in the component

Answer: (A, B)

28. The non-destructive testing technique(s) for detecting internal defects in a steel component is/are

(A) X-ray tomography

(B) Ultrasonic technique

(D) Dye penetrant technique

Answer: (A, B, C)

29. The condition(s) for high degree of mutual substitutional solid solubility for two metals is/are

(A) metals should have same valence

(B) metals should have same crystal structure

(D) the difference in electronegativity of metals should be large

Answer: (A, B, C)

30. The sum of eigen values of the matrix is _______ (in integer).

Answer: (0 to 0)

31. The probability of setting an easy exam paper by three setters are 1/2, 1/3, and 1/4. If all three are setting one paper each, then the probability that at least one of the papers will be easy is __________ (round off to 2 decimal places).

Answer: (0.74 to 0.76)

32. Maximum number of phases that can be in equilibrium for a 5-component system at constant temperature and pressure is _________ (in integer).

Answer: (5 to 5)

33. A liquid of density 900 kg m⁻³ is flowing over a flat plate with a free stream velocity of 0.1 m s⁻¹. The laminar boundary layer thickness at a distance of 0.2 m from the leading edge of the plate is 0.007 m. The viscosity of the liquid in centipoise is __________ (round off to 2 decimal places).

Given: 1 centipoise = 10⁻³ kg m⁻¹s⁻¹

Answer: (0.84 to 0.92)

34. The rate constant of a reaction at 400 K is three times the value at 300 K. The activation energy of the reaction in kJ mol⁻¹ is __________ (round off to 1 decimal place).

Given: Universal gas constant, R = 8.314 J mol⁻¹K⁻¹

Answer: (10.5 to 11.5)

35. The maximum value of function f(x) = 4x³ – 24x² + 36 in the domain [−1, 5] is _______ (round off to nearest integer).

Answer: (36 to 36)

Q.36 – Q.65 Carry TWO marks

36. Taking S as entropy, T as temperature, P as pressure, and V as volume, match Column I with Column II.

(A) A – 2, B – 1, C – 3, D – 4

(B) A – 4, B – 3, C – 2, D – 1

(D) A – 2, B – 1, C – 4, D – 3

Answer: (A)

37. Match the transport processes in Column I with the relationships in Column II.

(A) P – 2, Q – 3, R – 4, S – 1

(B) P – 4, Q – 3, R – 2, S – 1

(D) P – 2, Q – 1, R – 4, S – 3

Answer: (A)

38. For supersonic O₂ jet in basic oxygen furnace steelmaking, choose the correct combination from the following:

(1) Converging-diverging nozzle

(2) Diverging-converging nozzle

(3) O₂ velocity greater than sound velocity at nozzle throat (Mach number > 1)

(4) O₂ velocity equal to sound velocity at nozzle throat (Mach number = 1)

(5) Exit O₂ jet pressure ≥ atmospheric pressure

(6) Exit O₂ jet pressure < atmospheric pressure

(A) (1), (4), (5)

(B) (1), (3), (6)

(D) (2), (4), (5)

Answer: (A)

39. Elutriator is used to separate particles based on their sizes in flowing air as shown in the figure.

Assuming spherical particles, the diameter (D₅₀) of the suspended particles which have 50% chance to report to overflow by turbulent air flow is expressed as

Answer: (A)

40. A fluid flow field is given by the velocity vector The curl of velocity at (1, 2, 3) is

Answer: (A)

41. Given, S is a surface bounded by the planes x = 0, y = 0, z = 0, x = 3, y = 2, and z = 1. If is the unit vector normal to S, then is

(A) 18

(B) 9

(D) 3

Answer: (A)

42. Match the processes in Column I with the corresponding applications in Column II.

(A) P – 2, Q – 1, R – 4, S – 3

(B) P – 4, Q – 3, R – 2, S – 1

(D) P – 2, Q – 4, R – 1, S – 3

Answer: (A)

43. Match Column I with Column II.

(A) P – 3, Q – 4, R – 2, S – 1

(B) P – 2, Q – 4, R – 3, S – 1

(D) P – 4, Q – 2, R – 1, S – 3

Answer: (A)

44. Match the plots in Section I with the corresponding functions in Section II.

(A) P – 3, Q – 2, R – 4, S – 1

(B) P – 2, Q – 3, R – 4, S – 1

(D) P – 2, Q – 3, R – 1, S – 4

Answer: (A)

45. Match the components in Column I with corresponding manufacturing processes in Column II.

(A) P – 2, Q – 3, R – 4, S – 1

(B) P – 3, Q – 4, R – 1, S – 2

(D) P – 2, Q – 3, R – 1, S – 4

Answer: (A)

46. Match the welding techniques in Column I with the most appropriate applications in Column II.

(A) P – 4, Q – 1, R – 2, S – 3

(B) P – 3, Q – 2, R – 1, S – 4

(D) P – 2, Q – 4, R – 3, S – 1

Answer: (A)

47. Concerning the chemical potentials of components in a binary system at constant pressure, the correct statement(s) is/are

(A) For single-phase equilibrium at a given temperature, chemical potentials of the components change with alloy composition.

(B) For two-phase equilibrium at a given temperature, chemical potential of any component in both phases is same.

(C) For two-phase equilibrium at a given temperature, chemical potentials of the components change with alloy composition.

(D) For single-phase equilibrium of a given composition, chemical potentials of the components do not change with temperature.

Answer: (A, B)

48. Which of the following is/are the role(s) of coke in a blast furnace?

(A) reducing agent

(B) heat source

(D) flux

Answer: (A, B, C)

49. Identify the INCORRECT statement(s)

(A) Calcination is typically exothermic and roasting is usually endothermic.

(B) Coking of coal is carried out in a shaft furnace.

(C) The aims of extractive metallurgy processing are separation, compound formation, metal production, and metal purification.

(D) The secondary steelmaking offers steel cleanliness, composition adjustments, and temperature adjustments.

Answer: (A, B)

50. For the given schematic TTT diagram of an eutectoid steel, the following statement(s) is/are true for the heat treatment schedules HT-1, HT-2, and HT-3.

(A) HT-3 leads to the formation of a pearlite microstructure

(B) HT-1 leads to a predominantly martensite microstructure

(D) HT-3 leads to a mixture of pearlite and bainite microstructure

Answer: (A, B, C)

51. A dislocation loop PQRSTU is on the (111) plane of a cubic single crystal with Burgers vector The dislocation segments are parallel to directions, respectively.

The correct statement(s) is/are

(A) Dislocation segment PQ is mixed in character.

(B) Dislocation segment UT is screw in character.

(D) Dislocation segment QR is edge in character.

Answer: (A, B, C)

52. Compared to top gating, the effect(s) of bottom gating in sand mold casting is/are

(A) reduced melt oxidation

(B) reduced mold erosion

(D) enhanced mold erosion

Answer: (A, B)

53. Choose the correct statement(s) in the context of fusion welding of austenitic stainless steel containing about 0.06 wt.% carbon.

(A) Corrosion resistance of heat affected zone is poorer than base material.

(B) Corrosion resistance of heat affected zone is superior than fusion zone.

(D) Corrosion resistance is same for fusion zone, heat affected zone, and base material.

Answer: (A)

54. For the equation

the value of x is ________ (in integer).

Answer: (0 to 0)

55. Enthalpy of formation of an A−B regular solution containing 80 atomic percent A is 3.36 kJ mol⁻¹. The activity coefficient of A at 500 K for the solution containing 40 atomic percent A is ____________(round off to 1 decimal place). Given: Universal gas constant, R = 8.314 J mol⁻¹K⁻¹

Answer: (6.0 to 6.5)

56. A thin plate is loaded in plane stress condition with

σ_xx = 110 MPa, σ_yy = −50 MPa, τ_xy = −70 MPa

The maximum principal stress in MPa is ____________ (round off to nearest integer).

Answer: (130 to 140)

57. A chimney as shown in the figure requires to have natural draft (pressure difference between the furnace and the bottom of chimney, P0 – P1) of 1.0133 × 10³ Pa.

Given: acceleration due to gravity, g = 9.81 m s⁻²

Assume densities of air and flue do not change along the chimney height. Neglect frictional energy loss and kinetic energy difference at the bottom and top of the chimney.

If the density difference between the air and flue is 0.5 kg m⁻³, the minimum height (h) of the chimney in meters is____________ (round off to nearest integer).

Answer: (200 to 210)

58. Two circular surfaces A and B with the values of emissivity ε, temperature T, and respective view factors are shown in the figure. Consider heat radiation only between surfaces A and B.

Given: Stefan-Boltzmann constant, σ = 5.67 × 10⁻⁸ Wm⁻² K⁻⁴

Net heat flow rate by radiation from surface A in kW is____________ (round off to 1 decimal place).

Answer: (9.2 to 9.7)

59. Copper ore assaying 10 wt.% Cu is fed to a concentration plant at the rate of 100 tons/h. If the grades of concentrate and tailing are 30 wt.% Cu and 1 wt.% Cu, respectively, the percentage recovery of copper in concentrate is __________ (round off to nearest integer).

Given:1 ton = 1000 kg

Answer: (90 to 95)

60. Diffraction pattern of a polycrystalline BCC metal is obtained using monochromatic X-rays of wavelength 0.25 nm. If the first peak occurs at Bragg angle (θ) of 30°, then the radius of the metal atom in nm is ____________ (round off to 2 decimal places).

Answer: (0.13 to 0.17)

61. The alloy A (given in the phase diagram) is cooled slowly from the liquid state to just below the eutectic temperature. The ratio of weight fractions of pro-eutectic α to eutectic α is ____________ (round off to 1 decimal place).

Answer: (2.3 to 2.7)

62. In an aqueous solution of Fe²⁺ ions with concentration of 10⁻⁴ M at 298 K and atmospheric pressure, the reduction potential of Fe in volt is ____________ (round off to 2 decimal places).

Given : Standard reduction potential

Faraday’s constant, F = 96500 C per mole of electrons Universal gas constant, R = 8.314 J mol⁻¹K⁻¹

Answer: (-0.58 to -0.54)

63. Strain hardening behavior of an alloy is given by σ = 1100 ε³, where σ and ε are true stress and true strain, respectively. The alloy is cold drawn to an unknown amount of strain, followed by tensile testing. If the tensile test showed 10 % reduction in area at maximum load, then the unknown amount of strain from prior cold work is ____________ (round off to 2 decimal places).

Answer: (0.18 to 0.21)

64. A specimen containing maximum initial surface crack of size 1.5 mm is subjected to cyclic loading with σ_max = 300 MPa and σ_min = 0 MPa. Assuming specimen geometric factor of 1, and referring to the given figure, the crack growth rate in μm cycle⁻¹ is ____________ (round off to nearest integer).

Given: N = number of cycles

a = crack length

R = stress ratio

ΔK = stress intensity range

Answer: (7 to 15)

65. A 200 mm thick slab is rolled using 500 mm diameter rolls under cold rolling and hot rolling conditions, separately. The coefficient of friction is 0.04 in cold rolling and 0.4 in hot rolling. The ratio of maximum possible thickness reduction in cold rolling to that in hot rolling is ____________ (round off to 2 decimal places).

Answer: (0.01 to 0.01)

GATE Exam 2023 Mining Engineering (MN) Question Paper With Answer Key

August 3, 2023 by suresh84

GATE-2023

MN: Mining Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark Each

1. The line ran _______ the page, right through the centre, and divided the page into two.

(A) across

(B) of

(D) about

Answer: (A)

2. Kind : ________ : : Often : Seldom

(By word meaning)

(A) Cruel

(B) Variety

(D) Kindred

Answer: (A)

3. In how many ways can cells in a 3 × 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

(A) 2

(B) 9

(D) 6

Answer: (D)

4. There are 4 red, 5 green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two balls of the same colour?

One cannot see the colour of the balls until they are picked.

(A) 4

(B) 15

(D) 2

Answer: (A)

5. Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.

Operation 1: Scale independently along the x and y axes.

Operation 2: Rotation in any direction about the origin.

Which figure among the options can be achieved through a combination of these two operations on the given circle?

Answer: (A)

Q.6 – Q.10 Carry TWO marks Each

6. Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one’s love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) In Elvesland, one always declares one’s love by gifting a white flower.

(ii) In Elvesland, all emotions are declared by gifting flowers.

(iii) In Elvesland, sometimes one expresses one’s anger by gifting a flower that is not yellow.

(iv) In Elvesland, sometimes one expresses one’s love by gifting a white flower.

(A) only (ii)

(B) (i), (ii) and (iii)

(D) only (iv)

Answer: (D)

7. Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?

(A) 16

(B) 4

(D) 720

Answer: (A)

8. Based only on the following passage, which one of the options can be inferred with certainty?

When the congregation sang together, Apenyo would also join, though her little screams were not quite audible because of the group singing. But whenever there was a special number, trouble would begin; Apenyo would try singing along, much to the embarrassment of her mother. After two or three such mortifying Sunday evenings, the mother stopped going to church altogether until Apenyo became older and learnt to behave.

At home too, Apenyo never kept quiet; she hummed or made up silly songs to sing by herself, which annoyed her mother at times but most often made her become pensive. She was by now convinced that her daughter had inherited her love of singing from her father who had died unexpectedly away from home.

[Excerpt from These Hills Called Home by Temsula Ao]

(A) The mother was embarrassed about her daughter’s singing at home.

(B) The mother’s feelings about her daughter’s singing at home were only of annoyance.

(D) When Apenyo hummed at home, her mother tended to become thoughtful.

Answer: (D)

9. If x satisfies equation then x is equal to _______.

(A) 1/2

(B) log₁₆ 8

(D) log₄ 8

Answer: (C)

10. Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds v_P, v_Q, and v_R,

Which one of the following options is CORRECT?

(A) v_P < v_R < v_Q

(B) v_P < v_Q < v_R

(D) v_P = v_R ≠ v_Q

Answer: (C)

MN: Mining Engineering

Q.11 – Q.35 Carry ONE mark Each

11. The fault pattern shown in the figure is a case of _______.

(A) Normal fault.

(B) Reverse fault.

(D) Oblique slip fault.

Answer: (D)

12. The blast pattern of a coal face shown in the figure represents____

(A) burn cut.

(B) pyramid cut.

(D) drag cut.

Answer: (B)

13. A shear stress τ acts tangentially to the upper surface of a block and causes a small deformation Δw as shown. The shear strain is calculated by

(A) ∆w/w

(B) ∆w/h

(D) 2∆w/h

Answer: (B)

14. Given two vectors the magnitude of projection of is

(A) 5/√2

(B) 5/√13

(D) 5

Answer: (A)

15. Axial stress versus axial strain curves for two test results of a porous rock from triaxial undrained compression tests are shown in the figure. The pore water pressure for the curve B can be the best explained by

(A) U < 0

(B) U = 0

(D) 0 < U < 10

Answer: (C)

16. Given two random variables X and Y, the expected value E(3X−5Y) is

(A) 3E(X) −5E(Y)

(B) 3E(X)+5E(Y)

(D) E(X) −E(Y) −E(XY)

Answer: (A)

17. The reaction products of calcium hydroxide with acidic ferruginous mine water are

(A) FeO, Ca⁺ and H⁺

(B) FeO, CaO and H₂O

(D) Fe(OH)₃, Ca²⁺ and H₂O

Answer: (D)

18. An underground coal mine experienced 5 serious injuries, 15 reportable injuries, and 25 minor injuries during 2020. If the average employment in the mine is 1200, then the total injury rate per 1000 persons employed is

(A) 54.0

(B) 20.83

(D) 60.0

Answer: (C)

19. A linear programming problem is given as:

Maximize 𝑍 = 4x₁ + 2x₂

Subject to:

2×1 – 2x₂ ≤ 20

4x₁ ≤ 80

x₁ ≥ 0, x₂ ≥ 0

The problem has

(A) Unbounded solution.

(B) Infeasible solution.

(D) Unique optimal solution.

Answer: (A)

20. A tabular, near-flat (dip < 30o), and less than 2 m thick copper orebody having erratically located grade is to be mined underground. Wall rock and orebody are competent. The most suitable mining method is

(A) Cut and fill stoping.

(B) Sub-level stoping.

(D) Breast stoping.

Answer: (D)

21. x and y are functions of independent variables r and θ as given below

x = r cos θ, y = r sin θ

The Jacobian of x, y is

(A) tan θ

(B) r² sin θ cos θ

(D) r

Answer: (D)

22. In project scheduling techniques, the CORRECT statement is

(A) Both CPM and PERT are deterministic.

(B) Both CPM and PERT are probabilistic.

(D) CPM is probabilistic and PERT is deterministic.

Answer: (C)

23. As per DGMS guidelines, the risk score in Safety Management Plan for a hazard is computed as

(A) Consequence × Exposure

(B) Consequence × Exposure × Probability

(D) Consequence × Probability

Answer: (B)

24. Match the following items with their respective contours

(A) P→1, Q→3, R→2

(B) P→3, Q→1, R→2

(D) P→2; Q→1; R→3

Answer: (C)

25. In an astronomical survey at a given station, the pole star is located at an angle of 27° from the horizon. The latitude of the survey station in degrees is

(A) 27° N

(B) 63° N

(D) 63° S

Answer: (A)

26. The position tracking of a point by GPS is based on the technique of

(A) Graphical resection.

(B) Analytical resection.

(D) Trilateration.

Answer: (D)

27. Matrix A is negative definite. Which one of the following is NOT the correct statement about the matrix?

(A) It is symmetric.

(B) Determinant of A is always less than zero.

(D) Trace of A is always less than zero.

Answer: (B)

28. The average ore grade of a copper deposit is 0.9%. The recovery of the metal after processing, smelting and refining is 85%. If the selling price of refined copper is Rs 640/kg, the sale value in Rs. from mining one tonne of ore is_____.

[rounded off to 1 decimal place]

Answer: (4895 to 4897)

29. A slope stability radar shows that the position of a point P in a mine dump shifts from (200, 700, −60) m to (200.05, 700.1, −60.75) m over a time Δ𝑡. The net displacement in cm of the point P is_____.

[rounded off to 2 decimal places]

Answer: (75.00 to 76.50)

30. A Mohr-Coulomb failure envelop of a sandstone rock is given as

σ₁ = 30 + 3.5σ₃

where σ₁ and σ₃, measured in MPa, are the major and minor principal stresses respectively. The angle of the failure plane with the 𝜎3 axis in degree is_____.

[rounded off to 1 decimal place]

Answer: (60.00 to 63.00)

31. A punch hole of diameter 10 mm is to be made in a 5 mm thick rock plate as shown. If the yield strength of rock plate is 25 MPa, the punch force P required in kN is _____.

[rounded off to 1 decimal place]

Answer: (3.50 to 4.50)

32. ‘Critical subsidence’ has occurred on the surface due to mining of a flat longwall panel at a depth of 200 m. The width of the panel is 150 m. The maximum width of the panel in m that can be mined at a depth of 300 m, to reach critical subsidence is_____.

[rounded off to 1 decimal place]

Answer: (225.00 to 225.00)

33. To increase the resistance of a mine roadway by 1.5 Ns²m⁻⁸, the size in m² of the regulator to be installed is _____.

[rounded off to 2 decimal places]

Answer: (0.95 to 1.07)

34. A coal seam of 3.0 m height is mined with a double-ended ranging drum shearer (DERDS) for a web depth of 0.5 m. The coal density is 1.4 tonne/m³. If the panel width is 150 m, the production per cycle in tonne is_____.

[rounded off to 1 decimal place]

Answer: (315.0 to 315.0 OR 630.0 OR 630.0)

35. In a panel with 50 workers, a miner typically consumes 2.5 × 10⁻³ m³/min of oxygen. The percentage of oxygen in the intake air is 20.95%. To ensure minimum permissible oxygen in the return air as per CMR 2017 the quantity of ventilating air in m3/min to be supplied to the panel is_____.

[rounded off to 2 decimal places]

Answer: (6.00 to 7.00)

Q.36 – Q.65 Carry TWO marks Each

36. In a quality control process of coal supplied to a thermal plant, the 3-sigma control limits for fixed carbon (FC) are defined by 40%±15%. The process is termed “out of control” if:

Rule 1: 4 out of 5 successive values of FC are situated at the same side of the mean and at a distance more than 1 standard deviation.

Rule 2: Any one value crosses any of the 3-sigma control limits.

For the following continuous data of FC (%) : 49, 51, 56, 20, 46, 48, 47, 49, 45, 41, 42, 40, the process is

(A) out of control because of both rules 1 & 2.

(B) out of control because of rule 1 only.

(D) not out of control.

Answer: (A)

37. A tunnel of diameter 8 m is to be driven in a rock mass having quality index, Q of 1.0. Assume the excavation support ratio (ESR) of the tunnel is 1.0. The support requirement of the tunnel wall using fibre reinforced shotcrete (based on the chart prepared by Grimstad and Barton, 1993) is

(A) Shotcrete of thickness 9-12 cm, bolt length of 2.7-2.8 m

(B) Shotcrete of thickness 9-12 cm, bolt length of 3.0-3.2 m

(D) Shotcrete of thickness 5-9 cm, bolt length of 2.5-2.6 m

Answer: (C)

38. Match the following devices with their intended applications.

(A) P→1; Q→2; R→3; S→4

(B) P→4; Q→3; R→1; S→2

(D) P→4; Q→3; R→2; S→1

Answer: (B)

39. The evaluation of the integral

yields

(A) ln(e^x + x^e)

(B)

(C)

(D) ln(e^x – x^e)

Answer: (C)

40. Given the function

f(x) = |x| + |x – 1|,

For all the real values of x, which one of the following statements is CORRECT?

(A) The function is continuous and not differentiable at one point.

(B) The function is continuous but not differentiable at two points.

(D) The function is continuous and differentiable.

Answer: (B)

41. The slope and intercept values of three linear equations are

The above system of equations has

(A) Trivial solution.

(B) A single solution.

(D) No Solution.

Answer: (D)

42. A regression line is constructed between shovel production rate and shovel swing angle for 50 observations as shown below.

t-values corresponding to level of significance (P) and degree of freedom (DF)

If residuals are normally distributed and significance tests of the parameters are conducted at 0.05 significance level, the true statement is ____

(A) Both intercept and slope are significant.

(B) Intercept is significant but slope is not significant.

(D) Both intercept and slope are not significant.

Answer: (B)

43. A duct of diameter 0.60 m with an exhausting fan has −97.5 mm wg static pressure behind the fan when the air flow rate is 4.0 m³/s. If an evasee with inlet to outlet area ratio of 1:4 and efficiency 60% is attached to the outlet of the fan, the static pressure of the fan in mm of wg becomes

(A) −104.26

(B) − 99.13

(D) −80.6

Answer: (A)

44. Coordinate of two points A and B are (E 0 m, N 200 m) and (E 300 m, N 200 m), respectively. The bearing of two lines AO and BO are 67° and 35°, respectively. The easting of point O, in m, is _____.

[rounded off to 2 decimal places]

Answer: (426.00 to 427.64)

45. Data related to a surface miner operation are given below –

Drum width (m) = 3.0

Average cutting depth (cm) = 20

Average cutting speed (m/min) = 25

Length of pit (m) = 500

Turning time (min) = 2

Truck exchange time (s) = 30

Truck capacity (m³) = 15

Considering in situ volume, the production rate of the surface miner in m³/hr, is _____.

[rounded off to 1 decimal place]

Answer: (555 to 578)

46. A continuous miner served by two shuttle cars produces 240 tonne/hr. The capacity of each shuttle car is 10 tonne. When a single shuttle car operates, the cycle time becomes 4 min. In case one of the shuttle cars is under break-down, the reduction in hourly production from that of two cars in percent is _____.

[rounded off to 1 decimal place

Answer: (37.0 to 38.0)

47. A circular tunnel is developed in a biaxial in situ stress field as shown in the figure. If the ratio between tangential stress at the boundary point A and that at the boundary point B is 2.0, the value of k is _____.

[rounded off to 2 decimal places]

Answer: (0.30 to 0.35)

48. Strength of a rectangular coal pillar in MPa is given by

Where w, l(≥ w) and h are width, length and height of the pillar, respectively. The parameter S₁ is constant.

A 30 m square pillar is split into two halves as shown in the figure. The height of the pillar is 3 m. The ratio of safety factors between one half-pillar and the original square pillar is _____.

[rounded off to 2 decimal places]

Answer: (0.49 to 0.52)

49. A dozer pushes up a 100 kg spool of cable along a 20° incline road at a constant velocity as shown in the figure. The coefficient of static friction between the dozer bucket and the spool (Point B) is 0.45, and coefficient of kinetic friction between road and the spool (Point A) is 0.15.

Consider the spool only slides up the incline. The maximum normal force in N acting at Point B, is _____.

[rounded off to 1 decimal place]

Answer: (495 to 510)

50. Stress waves are sent from the transmitter A to the receiver B through an isotropic and elastic cylindrical rock specimen as shown in the figure.

The length of the specimen is 100 mm. The travel time of longitudinal and shear waves are 0.025 ms and 0.04 ms, respectively. The Poisson’s ratio of the rock specimen is_____.

[rounded off to 2 decimal places]

Answer: (0.27 to 0.29)

51. A jointed rock sample is subjected to 20 MPa vertical stress as shown in the figure.

The modulus of elasticity of the rock is 10 GPa and the normal stiffness of the joint surface is 5 GPa/m. Assuming one-dimensional elastic behaviour of rock and joint, the displacement in mm of the loading surface AB is_____.

[rounded off to 1 decimal place]

Answer: (4.0 to 4.5)

52. An unmanned aerial vehicle (UAV) with payload of 2 kg reaches vertically 100 m in 10 s at uniform velocity. The self-weight of the UAV is 1.2 kg. The power required in lifting in kW is _____.

[rounded off to 2 decimal places]

Answer: (0.30 to 0.32)

53. An irregular shaped rock sample of mass 60 g displaces 27 g of brine when submerged in a filled jar. The specific gravity of brine is 1.05. The unit weight of the rock sample in kN/m3 is_____.

[rounded off to 2 decimal places]

Answer: (22.59 to 23.19)

54. The reliability function of a pump is given as where t stands for time in years. If the pump comes with a six-month warranty, the number of years for the pump to attain a reliability of 0.9 is _____.

[rounded off to 2 decimal places]

Answer: (14.50 to 17.00)

55. In a sample of groundwater, the concentration of Ca²⁺ is 200 mg/l. The corresponding calcium carbonate hardness in mg/l is _____.

[rounded off to 1 decimal place]

Answer: (490 to 510)

56. A thermal power station receives coal of calorific value 4000 kcal/kg and uses 7000 tonnes of coal every day. Assuming 860 kcal is the heat equivalent of 1.0 kWh, for a thermal efficiency of 40% and electrical efficiency of 85% the power generation per day in MWh is_____.

[rounded off to 1 decimal place]

Answer: (11060.0 to 11080.0)

57. A coal company has three mines which transport coal to four washeries. The daily production from each mine, the demand at each washery and unit transportation cost from each mine to each washery are given in table

The cost of initial basic feasible solution using Vogel’s approximation method is _____.

[rounded off to 1 decimal place]

Answer: (77900 to 77900)

58. A workshop has four tasks and equal number of machines to perform the tasks. Each of the machines can perform only one of the four tasks. The estimated cost at each of the machines to complete each task is given in table

The total cost of optimal assignment is_____.

[rounded off to 1 decimal place]

Answer: (210 to 210)

59. The time between consecutive accidents in days in an underground coal mine in a year are as follows

10, 15, 6, 18, 12, 14, 16, 9, 21, 15, 26, 18, 22, 25, 13

Assuming exponential distribution, the probability that there will be no accident over a 10-day period is _____.

[rounded off to 2 decimal places]

Answer: (0.52 to 0.56)

60. A surface mine blast pattern has spacing 4 m and burden 3 m. The diameter of the drill hole is 110 mm. The drilling length is 8.8 m including subgrade of 10%. The bulk explosive density is 900 kg/m³.

If the powder factor is 2.5 m³/kg, the charge length in m is _____.

[rounded off to 2 decimal places]

Answer: (4.44 to 4.55)

61. A mining company makes an initial investment of Rs 200 crore on a project.

The following data are available:

Production life : 3 years

Year wise production

after gestation period (Mtonne) : 1.0, 2.0, and 1.0

Stripping ratio : 1.5 m³/tonne

Selling price of ore : Rs. 2000 per tonne

Ore mining cost : Rs. 500 per tonne

Waste mining cost : Rs. 500 per m³

Discount rate : 10%

By ignoring any other cash-flows, if the NPV of the project becomes Rs. 5.367 crore, the gestation period of the project, in years, is _____.

[rounded off to the nearest integer]

Answer: (2 to 2)

62. A rock slope is intercepted by a joint plane at an angle 30° as shown in figure.

The following data are available

Unit weight of the rock : 20 kN/m³

Cohesion of joint : 30 kPa

Friction angle of joint : 22°

The factor of safety of the rock slope to slide along the joint plane is _____.

[rounded off to 2 decimal places]

Answer: (1.50 to 1.54)

63. A mine void of width 20 m, length 50 m and height 30 m is to be filled with mill tailings based cemented paste backfill (CPB). The CPB contains tailings: cement: water as 1.0:0.1:0.2 by weight. The specific gravity of tailings and cement are 2.8 and 2.4 respectively. Assuming 20% of the original volume of water is retained in the final backfill, the amount of cement in tonne required so as to fill the void completely is_____.

[rounded off to nearest integer]

Answer: (6800 to 6850)

64. A fan installed in a mine ventilation system circulates 30 m³/s of air to two districts A and B as shown in Figure below. It is desired to increase the quantity of air by 20% in the district B using a booster fan in it. Assuming that the main fan pressure is unchanged, the pressure of the booster fan, in Pa, is_____.

[rounded off to 2 decimal places]

Answer: (305 to 325)

65. Data related to a water turbine pump with backward bladed impellers are given below:

Impeller diameter : 35 cm

RPM : 1200

Angle of curvature of blade : 30°

Radial velocity of discharge : 2 m/s

Manometric efficiency : 0.8

The number of impellers required in the pump to lift water by a height 300 m is _____.

[rounded off to higher integer]

Answer: (10 to 10)

GATE Exam 2023 Mechanical Engineering (ME) Question Paper With Answer Key

August 3, 2023 by suresh84

GATE-2023

ME: Mechanical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. He did not manage to fix the car himself, so he _______ in the garage.

(A) got it fixed

(B) getting it fixed

(D) got fixed

Answer: (A)

2. Planting : Seed : : Raising : _____

(By word meaning)

(A) Child

(B) Temperature

(D) Lift

Answer: (A)

3. A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

(A) 22.7

(B) 23.7

(D) 66.8

Answer: (A)

4. The minute-hand and second-hand of a clock cross each other _______ times between 09:15:00 AM and 09:45:00 AM on a day.

(A) 30

(B) 15

(D) 31

Answer: (A)

5. The symbols are to be filled, one in each box, as shown below.

The rules for filling in the four symbols are as follows.

(1) Every row and every column must contain each of the four symbols.

(2) Every 2 × 2 square delineated by bold lines must contain each of the four symbols.

Which symbol will occupy the box marked with ‘?’ in the partially filled figure?

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

6. In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi’s friends at school were hardworking and kind too. But the teachers drew attention to Ravi’s complete lack of interest in sports. The teachers believed that, along with some of his friends who showed similar disinterest in sports, Ravi needed to engage in some sports for his overall development.

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) All of Ravi’s friends are hardworking and kind.

(B) No one who is not a friend of Ravi is hardworking and kind.

(D) Some of Ravi’s friends are hardworking and kind.

Answer: (D)

7. Consider the following inequalities

p² – 4q < 4

3p + 2q < 6

where p and q are positive integers.

The value of (p + q) is ______.

(A) 2

(B) 1

(D) 4

Answer: (A)

8. Which one of the sentence sequences in the given options creates a coherent narrative?

(i) I could not bring myself to knock.

(ii) There was a murmur of unfamiliar voices coming from the big drawing room and the door was firmly shut.

(iii) The passage was dark for a bit, but then it suddenly opened into a bright kitchen.

(iv) I decided I would rather wander down the passage.

(A) (iv), (i), (iii), (ii)

(B) (iii), (i), (ii), (iv)

(D) (i), (iii), (ii), (iv)

Answer: (C)

9. How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?

(A) 729

(B) 728

(D) 664

Answer: (A)

10. An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

(A) P

(B) Q

(D) S

Answer: (B)

ME: Mechanical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are

(A) 3 and 3, respectively

(B) √3 and √3 , respectively

(D) 3 and 9, respectively

Answer: (A)

12. The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?

(A) |2 – x|

(B) |2 – |x||

(D) 2 − |x|

Answer: (B)

13. With reference to the Economic Order Quantity (EOQ) model, which one of the options given is correct?

(A) Curve P1: Total cost, Curve P2: Holding cost, Curve P3: Setup cost, and Curve P4: Production cost.

(B) Curve P1: Holding cost, Curve P2: Setup cost, Curve P3: Production cost, and Curve P4: Total cost.

(D) Curve P1: Total cost, Curve P2: Production cost, Curve P3: Holding cost, and Curve P4: Setup cost.

Answer: (A)

14. Which one of the options given represents the feasible region of the linear programming model:

(A) Region P

(B) Region Q

(D) Region S

Answer: (B)

15. A cuboidal part has to be accurately positioned first, arresting six degrees of freedom and then clamped in a fixture, to be used for machining. Locating pins in the form of cylinders with hemi-spherical tips are to be placed on the fixture for positioning. Four different configurations of locating pins are proposed as shown. Which one of the options given is correct?

(A) Configuration P1 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P3 is under-constrained.

(B) Configuration P2 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P4 is under-constrained.

(C) Configuration P3 arrests 6 degrees of freedom, while Configurations P2 and P4 are over-constrained and Configuration P1 is under-constrained.

(D) Configuration P4 arrests 6 degrees of freedom, while Configurations P1 and P3 are over-constrained and Configuration P2 is under-constrained.

Answer: (A)

16. The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is

(A) 3EI/L³

(B) 2EI/L³

(D) L³/3EI

Answer: (A)

17. The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?

Answer: (C)

18. The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?

(A) S_ut

(B) S₂

(D) S₄

Answer: (D)

19. Air (density = 1.2 kg/m³, kinematic viscosity = 1.5 × 10⁻⁵ m²/s) flows over a flat plate with a free-stream velocity of 2 m/s. The wall shear stress at a location 15 mm from the leading edge is τ_w. What is the wall shear stress at a location 30 mm from the leading edge?

(A) τ_w/2

(B) √2τ_w

(D) τ_w/√2

Answer: (D)

20. Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure.

The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:

P₁ = 100 kPa, ρ₁ = 1.2 kg/m³, u₁ = 400 m/s

The duct cross-sectional area at Location 2 is given by A₂ = 2A₁, where A₁ denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity u₂ and pressure P₂ at Location 2 is TRUE?

(A) u₂ < u₁, P₂ < P₁

(B) u₂ < u₁, P₂ > P₁

(D) u₂ > u₁, P₂ > P₁

Answer: (C)

21. Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profiles. The Nusselt number for this flow depends on

(A) neither the Reynolds number nor the Prandtl number

(B) both the Reynolds and Prandtl numbers

(D) the Prandtl number but not the Reynolds number

Answer: (A)

22. A heat engine extracts heat (Q_H) from a thermal reservoir at a temperature of 1000 K and rejects heat (Q_L) to a thermal reservoir at a temperature of 100 K, while producing work (W). Which one of the combinations of [Q_H, Q_L and W] given is allowed?

(A) Q_H = 2000 J, Q_L = 500 J, W = 1000 J

(B) Q_H = 2000 J, Q_L = 750 J, W = 1250 J

(D) Q_H = 6000 J, Q_L = 600 J, W = 5500 J

Answer: (B)

23. Two surfaces P and Q are to be joined together. In which of the given joining operation(s), there is no melting of the two surfaces P and Q for creating the joint?

(A) Arc welding

(B) Brazing

(D) Spot welding

Answer: (B, C)

24. A beam is undergoing pure bending as shown in the figure. The stress (σ)-strain (ε) curve for the material is also given. The yield stress of the material is σ_Y. Which of the option(s) given represent(s) the bending stress distribution at cross-section AA after plastic yielding?

Answer: (C, D)

25. In a metal casting process to manufacture parts, both patterns and moulds provide shape by dictating where the material should or should not go. Which of the option(s) given correctly describe(s) the mould and the pattern?

(A) Mould walls indicate boundaries within which the molten part material is allowed, while pattern walls indicate boundaries of regions where mould material is not allowed.

(B) Moulds can be used to make patterns.

(C) Pattern walls indicate boundaries within which the molten part material is allowed, while mould walls indicate boundaries of regions where mould material is not allowed.

(D) Patterns can be used to make moulds.

Answer: (A, B, D)

26. The principal stresses at a point P in a solid are 70 MPa,−70 MPa and 0. The yield stress of the material is 100 MPa. Which prediction(s) about material failure at P is/are CORRECT?

(A) Maximum normal stress theory predicts that the material fails

(B) Maximum shear stress theory predicts that the material fails

(D) Maximum shear stress theory predicts that the material does not fail

Answer: (B, C)

27. Which of the plot(s) shown is/are valid Mohr’s circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)

(A) M1

(B) M2

(D) M4

Answer: (A, C)

28. Consider a laterally insulated rod of length L and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperature profile(s) can occur without internal heat generation?

Answer: (A, B)

29. Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |ω₂|/| ω₁| = 1/4, have their centers 30 mm apart. The number of teeth on the driver (gear 1) is _______. (Answer in integer)

Answer: (95.999 to 96.001)

30. The figure shows a block of mass m = 20 kg attached to a pair of identical linear springs, each having a spring constant k = 1000 N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is _________ seconds. (Rounded off to two decimal places)

Take π = 3.14.

Answer: (6.27 to 6.29)

31. A vector field is defined over a conical region having height h = 2, base radius r = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin. If n denotes the unit outward normal to the curved surface S of the cone, the value of the integral ∫_SB ∙ ndS equals ________. (Answer in integer)

Answer: (-0.001 to 0.001)

32. A linear transformation maps a point (x, y) in the plane to the point according to the rule

Then, the disc x² + y² ≤ 1 gets transformed to a region with an area equal to ________. (Rounded off to two decimals)

Use π = 3.14.

Answer: (18.80 to 18.90)

33. The value of k that makes the complex-valued function

f(z) = e⁻^kx(cos 2y – i sin 2y)

analytic, where z = x + iy, is _______.

(Answer in integer)

Answer: (1.999 to 2.001)

34. The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle α = 270 degrees. The coefficient of friction between the belt and the pulley is 0.3. The influence of centrifugal forces on the belt is negligible. During braking, the ratio of the tensions T₁ to T₂ in the belt is equal to __________. (Rounded off to two decimal places) Take π=3.14.

Answer: (4.05 to 4.15)

35. Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T_{1, in} = 300 K and T_{2, in} = 350 K. The heat capacity rates of the two fluids are C₁= 1000 W/K and C₂ = 400 W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is _____ kW.

(Answer in integer)

Answer: (9.999 to 10.001)

Q.36 – Q.65 Carry TWO marks Each

36. Which one of the options given is the inverse Laplace transform of

u(t) denotes the unit-step function.

Answer: (A)

37. A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?

Take the acceleration due to gravity to be g = 9.8 m/s². Options have been rounded off to one decimal place.

Answer: (C)

38. The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity ω₁. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.

What is the angular velocity ω₂ of the bar PQ?

(A) ω₂ = 2ω₁

(B) ω₂ = ω₁

(D) ω₂ = 0.25ω₁

Answer: (D)

39. A beam of length 𝐿 is loaded in the 𝑥𝑦−plane by a uniformly distributed load, and by a concentrated tip load parallel to the 𝑧−axis, as shown in the figure. The resulting bending moment distributions about the 𝑦 and the 𝑧 axes are denoted by M_y and M_z, respectively.

Which one of the options given depicts qualitatively CORRECT variations of M_y and M_z, along the length of the beam?

Answer: (B)

40. The figure shows a thin-walled open-top cylindrical vessel of radius r and wall thickness t. The vessel is held along the brim and contains a constant-density liquid to height h from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls.

Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress (σ₁) and circumferential wall stress (σ₂) on y?

Answer: (A)

41. Which one of the following statements is FALSE?

(A) For an ideal gas, the enthalpy is independent of pressure.

(B) For a real gas going through an adiabatic reversible process, the process equation is given by PV_γ = constant, where P is the pressure, V is the volume and γ is the ratio of the specific heats of the gas at constant pressure and constant volume.

(C) For an ideal gas undergoing a reversible polytropic process PV^1.5 = constant, the equation connecting the pressure, volume and temperature of the gas at any point along the process is where R is the gas constant and m is the mass of the gas.

(D) Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high temperature.

Answer: (B)

42. Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air (considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position L₁. The initial pressure of the air inside the cylinder is P₁ ≫ P₀, where P₀ is the atmospheric pressure. The stop S₁ is instantaneously removed and the piston moves to the position L₂, where the equilibrium pressure of air inside the cylinder is P₂ ≫ P₀. What is the work done by the piston on the atmosphere during this process?

(A) 0

(B) P₀A(L₂ – L₁)

(C)

(D)

Answer: (B)

43. A cylindrical rod of length h and diameter 𝑑 is placed inside a cubic enclosure of side length L. S denotes the inner surface of the cube. The view-factor FS-S is

(A) 0

(B) 1

(C)

(D)

Answer: (D)

44. In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool α = 5°, and the shear angle, ϕ, is known to be 45°.

Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close to each other. As they approach the thin shear zone (shown as a thick line in the figure), plane RS gets sheared with respect to PQ (point R1 shears to R2, and S1 shears to S2).

Assuming that the perpendicular distance between PQ and RS is δ = 25 μm, what is the value of shear strain rate (in s⁻¹) that the material undergoes at the shear zone?

(A) 1.84 × 10⁴

(B) 5.20 × 10⁴

(D) 1.30 × 10⁴

Answer: (B)

45. A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is mounted. The motor moves in discrete rotational steps of 50 steps per revolution. The pitch of the screw is 5 mm and the total horizontal traverse length of the table is 100 mm. What is the total number of controllable locations at which the table can be positioned on this axis?

(A) 5000

(B) 2

(D) 200

Answer: (C)

46. Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young’s modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible.

The bars are held between rigid supports as shown in the figure and the temperature is raised by Δ𝑇. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by σ₁and σ₂, respectively.

Which of the statement(s) given is/are CORRECT?

(A) The interface between P and Q moves to the left after heating

(B) The interface between P and Q moves to the right after heating

(D) σ₁ = σ₂

Answer: (A, D)

47. A very large metal plate of thickness 𝑑 and thermal conductivity k is cooled by a stream of air at temperature T_∞ = 300 K with a heat transfer coefficient h, as shown in the figure. The centerline temperature of the plate is TP. In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate?

(A) h = 10 Wm⁻²K⁻¹, k = 100 Wm⁻¹K⁻¹, d = 1 mm, T_P = 350 K

(B) h = 100 Wm⁻²K⁻¹, k = 100 Wm⁻¹K⁻¹, d = 1 m, T_P = 325 K

(D) h = 1000 Wm⁻²K⁻¹, k = 1 Wm⁻¹K⁻¹, d = 1 m, T_P = 350 K

Answer: (A, C)

48. The smallest perimeter that a rectangle with area of 4 square units can have is ______ units.

(Answer in integer)

Answer: (7.999 to 8.001)

49. Consider the second-order linear ordinary differential equation

with the initial conditions

The value of y at x = 2 equals ________.

(Answer in integer)

Answer: (8.999 to 9.001)

50. The initial value problem

is solved numerically using the forward Euler’s method with a constant and positive time step of ∆t.

Let y_n represent the numerical solution obtained after n steps. The condition |y_n+1| ≤ |y_n| is satisfied if and only if ∆t does not exceed _________.

(Answer in integer)

Answer: (0.999 to 1.001)

51. The atomic radius of a hypothetical face-centered cubic (FCC) metal is (√2/10) nm. The atomic weight of the metal is 24.092 g/mol. Taking Avogadro’s number to be 6.023 × 10²³ atoms/mol, the density of the metal is ____________ kg/m³.

(Answer in integer)

Answer: (2490 to 2510)

52. A steel sample with 1.5 wt.% carbon (no other alloying elements present) is slowly cooled from 1100°C to just below the eutectoid temperature (723°C). A part of the iron-cementite phase diagram is shown in the figure. The ratio of the pro-eutectoid cementite content to the total cementite content in the microstructure that develops just below the eutectoid temperature is ________.

(Rounded off to two decimal places)

Answer: (0.53 to 0.55)

53. A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data shows that D1 follows a normal distribution with a mean of 20 mm and a standard deviation of 0.3 mm, while D2 follows a normal distribution with a mean of 35 mm and a standard deviation of 0.4 mm. An inspection of dimension C is carried out in a sufficiently large number of parts.

To be considered under six-sigma process control, the upper limit of dimension C should be ____________ mm.

(Rounded off to one decimal place)

Answer: (16.4 to 16.6)

54. A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the datum as per the engineering drawing used for manufacturing this part. The CMM is used to measure four points P1, P2, P3, P4 on Surface SP, and four points Q1, Q2, Q3, Q4 on Surface SQ as shown. A regression procedure is used to fit the necessary planes.

The distance between the two fitted planes is ___________ mm.

(Answer in integer)

Answer: (4.999 to 5.001)

55. A solid part (see figure) of polymer material is to be fabricated by additive manufacturing (AM) in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the AM machine is a/10 mm and the nozzle follows a linear serpentine path parallel to the sides of the square layers with a feed rate of a/5 mm/min.

Ignore any tool path motions other than those involved in adding material, and any other delays between layers or the serpentine scan lines.

The time taken to fabricate this part is ___________ minutes.

(Answer in integer)

Answer: (MTA)

56. An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewing via the optical flat using a monochromatic light of wavelength 0.5 μm, 12 fringes were observed over a length of 15 mm of gauge B. If the gauges are placed 45 mm apart, the height difference of the gauges is ______________ μm.

(Answer in integer)

Answer: (8.999 to 9.001)

57. Ignoring the small elastic region, the true stress (σ) – true strain (ε) variation of a material beyond yielding follows the equation σ = 400 ε³ MPa. The engineering ultimate tensile strength value of this material is ________ MPa.

(Rounded off to one decimal place)

Answer: (206.0 to 207.0)

58. The area moment of inertia about the y-axis of a linearly tapered section shown in the figure is _____________ m⁴.

(Answer in integer)

Answer: (3023.999 to 3024.001)

59. A cylindrical bar has a length L = 5 m and cross section area S =10 m². The bar is made of a linear elastic material with a density ρ = 2700 kg/m³ and Young’s modulus E = 70 GPa. The bar is suspended as shown in the figure and is in a state of uniaxial tension due to its self-weight.

The elastic strain energy stored in the bar equals _________ J. (Rounded off to two decimal places)

Take the acceleration due to gravity as g = 9.8 m/s².

Answer: (2.00 to 2.16)

60. A cylindrical transmission shaft of length 1.5 m and diameter 100 mm is made of a linear elastic material with a shear modulus of 80 GPa. While operating at 500 rpm, the angle of twist across its length is found to be 0.5 degrees.

The power transmitted by the shaft at this speed is _______kW. (Rounded off to two decimal places)

Take π=3.14.

Answer: (237 to 240)

61. Consider a mixture of two ideal gases, X and Y, with molar masses and respectively, in a container. The total pressure in the container is 100 kPa, the total volume of the container is 10 m³ and the temperature of the contents of the container is 300 K. If the mass of gas-X in the container is 2 kg, then the mass of gas-Y in the container is ____ kg. (Rounded off to one decimal place)

Assume that the universal gas constant is 8314 J kmol⁻¹K⁻¹.

Answer: (3.9 to 4.1)

62. The velocity field of a certain two-dimensional flow is given by

where k = 2s⁻¹. The coordinates x and y are in meters. Assume gravitational effects to be negligible.

If the density of the fluid is 1000 kg/m³ and the pressure at the origin is 100 kPa, the pressure at the location (2 m, 2 m) is ___________ kPa.

(Answer in integer)

Answer: (83.999 to 84.001)

63. Consider a unidirectional fluid flow with the velocity field given by

where u(0, t) = 1. If the spatially homogeneous density field varies with time 𝑡 as

ρ(t) = 1 + 0.2e⁻^t

the value of u(2,1) is ______________. (Rounded off to two decimal places) Assume all quantities to be dimensionless.

Answer: (1.10 to 1.20)

64. The figure shows two fluids held by a hinged gate. The atmospheric pressure is Pa = 100 kPa. The moment per unit width about the base of the hinge is ____________ kNm/m. (Rounded off to one decimal place)

Take the acceleration due to gravity to be g = 9.8 m/s².

Answer: (55.9 to 58.5)

65. An explosion at time t = 0 releases energy E at the origin in a space filled with a gas of density ρ. Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure.

Let R denote the radius of the front of the hemispherical blast wave. The radius R follows the relationship R = k t^aE^bρ^c, where k is a dimensionless constant. The value of exponent a is ___________.

(Rounded off to one decimal place)

Answer: (0.39 to 0.41)

GATE Exam 2023 Mathematics (MA) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

MA: Mathematics

General Aptitude

Q.1 – Q.5 Carry ONE mark Each

1. The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(D) between

Answer: (D)

2. Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(D) Refute

Answer: (C)

(A) 125

(B) 720

(D) 80

Answer: (D)

4. Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(D) At most half the candidates have a score that is larger than the mean.

Answer: (C)

5. In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(D) S

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

Answer: (MTA)

7. Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

(1) At any stage, Ankita can move either one or two stairs up.

(2) At any stage, Ankita cannot move to a lower step.

Let F(N) denote the number of possible ways in which Ankita can reach the Nth stair. For example, F(1) = 1, F(2) = 2, F(3) = 3.

The value of F(5) is _______.

(A) 8

(B) 7

(D) 5

Answer: (A)

Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.

(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(D) neither (i) nor (ii)

Answer: (D)

9. Which one of the given figures P, Q, R and S represents the graph of the following function?

f(x) = ||x + 2| – |x – 1||

(A) P

(B) Q

(D) S

Answer: (A)

(A) P

(B) Q

(D) S

Answer: (D)

MA: Mathematics

Q.11 – Q.35 Carry ONE mark Each

11. Let f , g : ℝ² → ℝ be defined by

and g(x, y) = 4x⁴ – 5x²y + y²

for all (x, y) ∈ ℝ².

Consider the following statements:

P: f has a saddle point at (0, 0).

Q: g has a saddle point at (0, 0).

Then

(A) both P and Q are TRUE

(B) P is FALSE but Q is TRUE

(D) both P and Q are FALSE

Answer: (A)

12. Let ℝ³ be a topological space with the usual topology and ℚ denote the set of rational numbers. Define the subspaces X, Y, Z and W of ℝ3 as follows:

X = {(x, y, 𝑧) ∈ ℝ³∶ |x| + |y| + |z| ∈ ℚ}

Y = {(x, y, z) ∈ ℝ³∶ xyz = 1}

Z = {(x, y, z) ∈ ℝ³ ∶ x²+ y² + z²= 1}

W ={(x, y, z) ∈ ℝ³ ∶ xyz = 0 }

Which of the following statements is correct?

(A) X is homeomorphic to Y

(B) Z is homeomorphic to W

(D) X is NOT homeomorphic to W

Answer: (D)

13. Let P(x) = 1 + e²^π^ix + 2 e³^π^ix, x ∈ ℝ, i = √− Then

is equal to

(A) 0

(B) 1

(D) 4

Answer: (B)

14. Let T : ℝ³ → ℝ³ be a linear transformation satisfying

T(1, 0, 0) = (0, 1, 1), T(1, 1, 0) = (1, 0, 1) and T(1, 1, 1) = (1, 1, 2).

Then

(A) T is one-one but T is NOT onto

(B) T is one-one and onto

(D) T is NOT one-one but T is onto

Answer: (C)

15. Let 𝔻 = {z ∈ ℂ : |z| < 1} and f: 𝔻 → ℂ be defined by

Consider the following statements:

P: f is three zeros (counting multiplicity) in 𝔻.

Q : f has one zero in

Then

(A) P is TRUE but Q is FALSE

(B) P is FALSE but Q is TRUE

(D) both P and Q are FALSE

Answer: (A)

16. Let 𝒩 ⊆ ℝ be a non-measurable set with respect to the Lebesgue measure on ℝ.

Consider the following statements:

P: If M = {x ∈ : x is irrational}. Then M is Lebesgue measurable.

Q: The boundary of 𝒩 has positive Lebesgue outer measure.

Then

(A) both P and Q are TRUE

(B) P is FALSE and Q is TRUE

(D) both P and Q are FALSE

Answer: (B)

17. For k ∈ ℕ, let E_k be a measurable subset of [0, 1] with Lebesgue measure 1/k².

Define

and

Consider the following statements:

P: Lebesuge measure of E is equal to zero.

Q: Lebesgue measure of F is equal to zero.

Then

(A) both P and Q are TRUE

(B) both P and Q are FALSE

(D) Q is TRUE but P is FALSE

Answer: (A)

18. Consider ℝ² with the usual Euclidean metric. Let

Consider the following statements:

P: X is a connected subset of ℝ².

Q: Y is connected subset of ℝ².

Then

(A) both P and Q are TRUE

(B) P is FALSE and Q is TRUE

(D) both P and Q are FALSE

Answer: (A)

19. Let

Consider the following statements:

P: M⁸ + M¹² is diagonalizable.

Q: M⁷ + M⁹ is diagonalizable.

Which of the following statements is correct?

(A) P is TRUE and Q is FALSE

(B) P is FALSE and Q is TRUE

(D) Both P and Q are TRUE

Answer: (D)

20. Let C[0, 1] = {f : [0, 1] → ℝ : f is continuous}.

Consider the metric space (C[0, 1], d_∞), where

d_∞(f, g) = sup{|f(x) – g(x)| : x ∈ [0, 1]} for f, g ∈ C [0, 1].

Let f₀(x) = 0 for all x ∈ [0, 1] and

X = {f ∈ (C[0, 1], d_∞): d_∞(f₀, f) ≥ 1/2}.

Let f₁, f₂ ∈ C[0, 1] be defined by f₁(x) = x and f₂(x) = 1 – x for all x ∈ [0, 1].

Consider the following statements:

P: f₁ is in the interior of X.

Q: f₂ is in the interior of X.

Which of the following statements is correct?

(A) P is TRUE and Q is FALSE

(B) P is FALSE and Q is TRUE

(D) Both P and Q are TRUE

Answer: (D)

21. Consider the metrics ρ₁ and ρ₂ on ℝ, defined by

Consider the following statements:

P: The function f : (X ∪ Y, ρ₁) → (ℝ, ρ₁) is uniformly continuous.

Q: The function f : (X ∪ Y, ρ₂) → (ℝ, ρ₁) is uniformly continuous.

Then

(A) P is TRUE and Q is FALSE

(B) P is FALSE and Q is TRUE

(D) both P and Q are TRUE

Answer: (B)

22. Let T : ℝ⁴ → ℝ⁴ be a linear transformation and the null space of T be the subspace of ℝ⁴ given by

{(x₁, x₂, x₃, x₄) ∈ ℝ⁴ : 4x₁ + 3x₂ + 2x₃ + x₄ = 0}.

If Rank(T – 3I) = 3, where I is the identity map of ℝ⁴, then the minimal polynomial of T is

(A) x(x – 3)

(B) x(x – 3)³

(D) x²(x – 3)²

Answer: (A)

23. Let C[0, 1] denote the set of all real valued continuous functions defined on [0, 1] and ||f||_∞ = sup{|f(x)| : x ∈ [0, 1]} for all f ∈ C[0, 1]. Let X = {f ∈ C[0, 1] : f(0) = f(1) = 0}.

Define F : (C[0, 1], ||∙||_∞) → ℝ by

Denote S_X = {f ∈ X : ||f||_∞ = 1}.

Then the set {f ∈ X : F(f) = ||F||} ⋂ S_X has

(A) NO element

(B) exactly one element

(D) an infinite number of elements

Answer: (A)

24. Let X and Y be two topological spaces. A continuous map f ∶ X → Y is said to be proper if f⁻¹(K) is compact in X for every compact subset K of Y, where f⁻¹(K) is defined by f⁻¹(K) = {x ∈ X ∶ f(x) ∈ K} .

Consider ℝ with the usual topology. If ℝ ∖{0} has the subspace topology induced from ℝ and ℝ × ℝ has the product topology, then which of the following maps is proper?

(A) f : ℝ \ {0} → ℝ defined by f(x) = x

(B) f : ℝ × ℝ → ℝ × ℝ defined by f(x, y) = (x + y, y)

(D) f : ℝ × ℝ → ℝ defined by f(x, y ) = x² – y²

Answer: (B)

25. Consider the following Linear Programming Problem P:

Minimize 3x₁ + 4x₂

Subject to x₁ − x₂ ≤ 1,

x₁ + x₂ ≥ 3,

x₁ ≥ 0, x₂ ≥ 0.

The optimal value of the problem P is _________.

Answer: (10 to 10)

26. Let u(x, t) be the solution of

for some positive real number c.

Let the domain of dependence of the solution 𝑢 at the point P(3, 2) be the line segment on the x-axis with end points Q and R.

If the area of the triangle PQR is 8 square units, then the value of c² is _________.

Answer: (4 to 4)

27. Let

for all z in some neighbourhood of 0 in ℂ.

Then the value of a₆ + a₅ is equal to _______.

Answer: (13 to 13)

28. Let p(x) = x³ – 2x + 2. If q(x) is the interpolating polynomial of degree less than or equal to 4 for the data

then the value of at x = 0 is ________.

Answer: (2 to 2)

29. For a fixed c ∈ ℝ, let

If the value of obtained by using the Trapezoidal rule is equal to α, then the value of c is ________ (rounded off to 2 decimal places.)

Answer: (0.24 to 0.26)

30. If for some α ∈ ℝ,

then the value of α equals _______.

Answer: (4 to 4)

31. Let S be the portion of the plane z= 2x + 2y − 100 which lies inside the cylinder x² + 𝑦² = 1. If the surface area of S is απ, then the value of α is equal to ___________.

Answer: (3 to 3)

32. Let L²[−1, 1] = {f : [−1, 1] → ℝ : f is Lebesgue measurable and the norm

Let F : (L²[−1, 1], ||∙||₂) → ℝ be defined by

for all f ∈ L²[−1, 1].

If ||F|| denotes the norm of the linear functional F, then 5||F||² is equal to ________.

Answer: (2 to 2)

33. Let y(t) be the solution of the initial value problem

If α = y(π/2), then the value of is _______ (rounded off to 2 decimal places).

Answer: (0.49 to 0.51)

34. Consider ℝ⁴ with the inner product < x, y > = for x = (x₁, x₂, x₃, x₄) and y = (y₁, y₂, y₃, y₄).

Let M = {(x₁, x₂, x₃, x₄) ∈ ℝ⁴ : x₁ = x₃} and M^⊥ denote the orthogonal complement of M. The dimension of M^⊥ is equal to ________.

Answer: (1 to 1)

35. Let and If 6M⁻¹ = M² – 6M + αI for some α ∈ ℝ, then the value of α is equal to _________.

Answer: (11 to 11)

Q.36 – Q.65 Carry TWO marks Each

36. Let GL₂(ℂ) denote the group of 2 × 2 invertible complex matrices with usual matrix multiplication. For S, T ∈ GL₂(ℂ), < S, T > denotes the subgroup generated by S and T. Let and G₁, G₂, G₃ be three subgroups of GL₂(ℂ) given by

Let Z(G_i) denote the center of G_i and i = 1, 2, 3.

Which of the following statements is correct?

(A) G₁ is isomorphic to G₃

(B) Z(G₁) is isomorphic to Z(G₂)

(C)

(D) Z(G₂) is isomorphic to Z(G₃)

Answer: (D)

37. Let ℓ² = {(x₁, x₂, x₃, …) : x_n ∈ ℝ for all n ∈ ℕ and

For a sequence (x₁, x₂, x₃, …) ∈ ℓ², define ||(x₁, x₂, x₃, …||₂ = Let S : (ℓ², ||∙||₂) → T : (ℓ², ||∙||₂) and T : (ℓ², ||∙||₂) → (ℓ², ||∙||₂) be defined by

S(x₁, x₂, x₃, …) = (y₁, y₂, y₃, …), where

T(x₁, x₂, x₃, …) = (y₁, y₂, y₃, …), where

Then

(A) S is a compact linear map and T is NOT a compact linear map

(B) S is NOT a compact linear map and T is a compact linear map

(D) NEITHER S NOR T is a compact linear map

Answer: (D)

38. Let

c₀₀ = {(x₁, x₂, x₃…) : x_i ∈ ℝ, i ∈ ℕ, x_i ≠ 0 only for finitely many indices i}.

For (x₁, x₂, x₃, …) ∈ c₀₀, let||(x₁, x₂, x₃, …)||_∞ = sup{|x_i| : i ∈ ℕ}.

Define F, G : (c₀₀, ||∙||_∞) → (c₀₀, ||∙||_∞) by

Then

(A) F is continuous but G is NOT continuous

(B) F is NOT continuous but G is continuous

(D) NEITHER F NOR G is continuous

Answer: (B)

39. Consider the Cauchy problem

u = f(t) on the initial curve Γ = (t, t); t > 0.

Consider the following statements:

P: If f(t) = 2t + 1, then there exists a unique solution to the Cauchy problem in a neighbourhood of Γ.

Q : If f(t) = 2t – 1, then there exist infinitely many solutions to the Cauchy problem in a neighbourhood of Γ.

Then

(A) both P and Q are TRUE

(B) P is FALSE and Q is TRUE

(D) both P and Q are FALSE

Answer: (D)

40. Consider the linear system Mx = b, where Suppose M = LU, where L and U are lower triangular and upper triangular square matrices, respectively. Consider the following statements:

P : If each element of the main diagonal of L is 1, then trace (U) = 3.

Q : For any choice of the initial vector x⁽⁰⁾, the Jacobi iterates x^(k), k = 1, 2, 3 … converge to the unique solution of the linear system Mx = b.

Then

(A) both P and Q are TRUE

(B) P is FALSE and Q is TRUE

(D) both P and Q are FALSE

Answer: (A)

41. Let ϕ and ψ be two linearly independent solutions of the ordinary differential equation

yʹʹ + (2 – cos x) y = 0, x ∈ ℝ.

Let α, β ∈ ℝ be such that α < β, ϕ(α) = ϕ(β) = 0 and ϕ(x) = 0 for all x ∈ (α, β).

Consider the following statements:

P : ϕʹ(α) ϕʹ(β) > 0.

Q: ϕ(x) ψ (x) ≠ 0 for all x ∈ (α, β).

Then

(A) P is TRUE and Q is FALSE

(B) P is FALSE and Q is TRUE

(D) both P and Q are TRUE

Answer: (C)

42. Let 𝔻 = {z ∈ ℂ : |z| < 1} and f : 𝔻 → ℂ be an analytic function given by the power series where a₀ = a₁ = 1 and a_n = 1/2²ⁿ for n ≥ 2.

Consider the following statements:

P: If z₀ ∈ 𝔻, then f is one-one in some neighbourhood of z₀.

Q: If E = {z ∈ ℂ : |z| ≤ 1/2}, then f(E) is a closed subset of ℂ.

Which of the following statements is/are correct?

(A) P is TRUE

(B) Q is TRUE

(D) P is FALSE

Answer: (A, B)

43. Let Ω be an open connected subset of ℂ containing U = {z ∈ ℂ : |z| ≤ 1/2}.

Let 𝔍 = {f : Ω → ℂ : f is analytic and

Consider the following statements:

P : There exists f ∈ 𝔍 such that |fʹ(0)| ≥ 2.

Q: |f⁽³⁾(0)| ≤ 48 for all f ∈ 𝔍, where f⁽³⁾ denotes the third derivative of f.

Then

(A) P is TRUE

(B) Q is FALSE

(D) Q is TRUE

Answer: (C, D)

44. Let (ℝ, τ) be a topological space, where the topology τ is defined as

τ = {U ⊆ ℝ : U = ∅ or 1 ∈ U}.

Which of the following statements is/are correct?

(A) (ℝ, τ) is first countable

(B) (ℝ, τ) is Hausdorff

(D) The closure of (1, 5) is [1, 5]

Answer: (A, C)

45. Let ℛ = {p(x) ∈ ℚ[x] : p(0) ∈ ℤ}, where ℚ denotes the set of rational numbers and ℤ denotes the set of integers. For a ∈ ℛ, let ‹a› denote the ideal generated by a in ℛ.

Which of the following statements is/are correct?

(A) If p(x) is an irreducible element in ℛ, then ‹p(x)› is a prime ideal in ℛ

(B) ℛ is a unique factorization domain

(D) ℛ is NOT a principal ideal domain

Answer: (A)

46. Consider the rings

where ‹2, x³› denotes the ideal generated by {2, x³} in ℤ[x] and ‹x²› denotes the ideal generated by x² in ℤ₂[x].

Which of the following statements is/are correct?

(A) Every prime ideal of 𝒮₁ is a maximal ideal

(B) 𝒮₂ has exactly one maximal ideal

(D) There exists an element in 𝒮₂ which is NEITHER nilpotent NOR a unit

Answer: (A, B, C)

47. Consider the sequence of Lebesgue measurable functions f_n : ℝ → ℝ given by

For a measurable subset E of ℝ, denote m(E) to be the Lebesgue measure of E.

Which of the following statements is/are correct?

Answer: (B, C, D)

48. Define the characteristic function χ_E of a subset E in ℝ by

For 1 ≤ p < 2, let

L^p[0, 1] = {f: [0, 1] → ℝ : f is Lebesgue measurable and

Let f : [0, 1] → ℝ be defined by

Consider the following two statements:

P : f ∈ L^p [0, 1] for every p ∈ (1, 2).

Q: f ∈ L¹[0, 1].

Then

(A) P is TRUE

(B) Q is TRUE

(D) P is FALSE

Answer: (B, D)

49. Let x(t), y(t), t ∈ ℝ, be two functions satisfying the following system of differential equations:

xʹ(t) = y(t).

yʹ(t) = x(t).

and x(0) = α, y(0) = β, where α, β are real numbers.

Which of the following statements is/are correct?

(A) If α = 1, β = −1, then |x(t)| + |y(t)| → 0 as t → ∞

(B) If α = 1, β = 1, then |x(t)| + |y(t)| → 0 as t → ∞

(D) If α = 1, β = 1.01, then |x(t)| + |y(t)| → 0 as t → ∞

Answer: (A)

50. For h > 0, and α, β, γ ∈ ℝ, let

be a three-point formula to approximate f ʹ (a) for any differentiable function f : ℝ → ℝ and a ∈ ℝ.

If D_hf(a) = f ʹ(a) for every polynomial f of degree less than or equal to 2 and for all a ∈ ℝ, then

(A) α + 2γ = −2

(B) α + 2β – 2γ = 0

(D) α + 2β – 2γ = 1

Answer: (A, B)

51. Let f be a twice continuously differentiable function on [a, b] such that f ʹ(x) < 0 and f ʹʹ(x) < 0 for all x ∈ (a, b). Let f(ζ) is given by

for an initial guess x₀.

If x_k ∈ (ζ, b) for some k ≥ 0, then which of the following statements is/are correct

(A) x_k+1 > ζ

(B) x_k+1 < ζ

(D) For every

Answer: (A, C)

52. Let f : ℝ² → ℝ be defined by

Then

(A) the directional derivative of f at (0,0) in the direction of (1/√2, 1/√2) is 1/√2

(B) the directional derivative of f at (0,0) in the direction of (0,1 ) is 1

(D) f is NOT differentiable at (0,0)

Answer: (A, C, D)

53. Let C[0, 1] = {f : [0, 1] → ℝ : f is continuous} and

d_∞(f, g) = sup{|f(x) – g(x)|: x ∈ [0, 1]} for f, g ∈ C[0, 1].

For each n ∈ ℕ, define f_n : [0, 1] → ℝ by f_n(x) = xⁿ for all x ∈ [0, 1].

Let P = {f_n : n ∈ ℕ}.

Which of the following statements is/are correct?

(A) P is totally bounded in (C[0, 1], d_∞)

(B) P is bounded in (C[0, 1], d_∞)

(D) P is open in (C[0, 1], d_∞)

Answer: (B, C)

54. Let G be an abelian group and Φ : G → (ℤ, +) be a surjective group homomorphism. Let 1 = Φ(a) for some a ∈

Consider the following statements.

P: For every g ∈ G, there exists an n ∈ ℤ such that gaⁿ ∈ ker(Φ).

Q: Let e be the identity of G and <a> be the subgroup generated by a. Then G = ker(Φ) < a > and ker(Φ) ∩ < a > = {e}.

Which of the following statements is/are correct?

(A) P is TRUE

(B) P is FALSE

(D) Q is FALSE

Answer: (A, C)

55. Let C be the curve of intersection of the cylinder x² + y² = 4 and the plane

z − 2 =0. Suppose C is oriented in the counterclockwise direction around the

𝑧-axis, when viewed from above. If

|∫_C(sin x + e^x)dx + 4x dy + e^z cos² z dz| = απ,

Then the value of α equals ________.

Answer: (16 to 16)

56. Let ℓ² = {(x₁, x₂, x₃…) : x_n ∈ ℝ for all n ∈ ℕ and

For a sequence (x₁, x₂, x₃, …} ∈ ℓ², define

Consider the subspace

Let M^⊥ denote the orthogonal complement of M in the Hilbert space (ℓ², ||∙||₂).

Consider (1, 1/2, 1/3, 1/4, …) ∈ ℓ².

If the orthogonal projection of (1, 1/2, 1/3, 1/4, …) onto M^⊥ is given by

for some α ∈ ℝ, then α equals ________.

Answer: (15 to 15)

57. Consider the transportation problem between five sources and four destinations as given in the cost table below. The supply and demand at each of the source and destination are also provided:

Let C_N and C_L be the total cost of the initial basic feasible solution obtained from the North-West corner method and the Least-Cost method, respectively. Then C_𝑁− C_L equals _________.

Answer: (380 to 380)

58. Let σ ∈ S₈, where S₈ is the permutation group on 8 elements. Suppose σ is the product of σ₁ and σ₂, where σ₁ is a 4-cycle and σ₂ is a 3-cycle in S₈. If σ₁ and σ₂ are disjoint cycles, then the number of elements in S₈ which are conjugate to σ is _________.

Answer: (3360 to 3360)

59. Let A be a 3 × 3 real matrix with det(A + iI) = 0, where i = √−1 and I is the 3 × 3 identity matrix. If det(A) = 3, then the trace of A² is _________.

Answer: (7 to 7)

60. Let A = [a_aj] be a 3 × 3 real matrix such that

If m is the degree of the minimal polynomial of A, then a₁₁ + a₂₁ + a₃₁ + m equals _______.

Answer: (4 to 4)

61. Let Ω be the disk x² + y² < 4 in ℝ² with boundary ∂Ω. If u(x, y) is the solution of the Dirichlet problem

then the value of u(0,1) is __________.

Answer: (4 to 4)

62. For every k ∈ ℕ ∪ {0}, let y_k(x) be a polynomial of degree k with y_k(1) = 5. Further, let y_k(x) satisfy the Legendre equation

(1 – x²)yʹʹ − 2xyʹ + k(k + 1)y = 0.

for some positive integer n, then the value of n is ___________.

Answer: (12 to 12)

63. Consider the ordinary differential equation (ODE)

4(ln x) yʹʹ + 3yʹ + y = 0, x > 1.

If r₁ and r₂ are the roots of the indicial equation of the above ODE at the regular singular point x=1, then |r₁ − r₂| is equal to _________ (rounded off to 2 decimal places).

Answer: (0.24 to 0.26)

64. Let u(x, t) be the solution of the non-homogeneous wave equation

Then the value of u(π/2, 3π/2) is _______ (rounded off to 2 decimal places).

Answer: (0.64 to 0.70)

65. Consider the Linear Programming Problem P:

Maximize 3x₁ + 2x₂ + 5x₃

subject to

x₁ + 2x₂ + x₃ ≤ 44,

x₁ + 2x₃ ≤ 48,

x₁ + 4x₂ ≤ 52,

x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0.

The optimal value of the problem P is equal to __________.

Answer: (140 to 140)

GATE Exam 2023 Instrumentation Engineering (IN) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

IN: Instrumentation Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(D) between

Answer: (D)

2. Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(D) Refute

Answer: (C)

(A) 125

(B) 720

(D) 80

Answer: (D)

4. Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(D) At most half the candidates have a score that is larger than the mean.

Answer: (C)

5. In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(D) S

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

Answer: (MTA)

7. Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

(1) At any stage, Ankita can move either one or two stairs up.

(2) At any stage, Ankita cannot move to a lower step.

Let F(N) denote the number of possible ways in which Ankita can reach the Nth stair. For example, F(1) = 1, F(2) = 2, F(3) = 3.

The value of F(5) is _______.

(A) 8

(B) 7

(D) 5

Answer: (A)

Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.

(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(D) neither (i) nor (ii)

Answer: (D)

9. Which one of the given figures P, Q, R and S represents the graph of the following function?

f(x) = ||x + 2| – |x – 1||

(A) P

(B) Q

(D) S

Answer: (A)

(A) P

(B) Q

(D) S

Answer: (D)

IN: Instrumentation Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Choose solution set S corresponding to the systems of two equations

x – 2y + z = 0

x – y = 0

Note: R denotes the set of real numbers

Answer: (A)

12. Inductance of a coil is measured as 10 mH, using an LCR meter, when no other objects are present near the coil. The LCR meter uses a sinusoidal excitation at 10 kHz. If a pure copper sheet is brought near the coil, the same LCR meter will read _________.

(A) less than 10 mH

(B) 10 mH

(D) less than 10 mH initially and then stabilizes to more than 10 mH

Answer: (A)

13. Which of the following flow meters offers the lowest resistance to the flow?

(A) Turbine flow meter

(B) Orifice flow meter*

(D) Electromagnetic flow meter

Answer: (D)

14. Pair the quantities (p) to (s) with the measuring devices (i) to (iv).

(A) (i) – (r), (ii) – (s), (iii) – (q), (iv) – (p)

(B) (i) – (p), (ii) – (s), (iii) – (r), (iv) – (q)

(D) (i) – (q), (ii) – (s), (iii) – (p), (iv) – (r)

Answer: (C)

15. Capacitance ‘C’ of a parallel plate structure is calculated as 20 pF using where ε₀ is the permittivity of free space, ε_r is the relative permittivity of the dielectric, A is the overlapping area of the electrodes and d is the distance between them. The value of C is then measured using an LCR meter. If the meter is assumed to be ideal and it introduces no error due to cable capacitance, which one of the following readings is likely to be correct?

(A) 20.5 pF

(B) 20 pF

(D) 10 pF

Answer: (A)

16. The table shows the present state Q(t), next state Q(t + 1), and the control input in a flip-flop. Identify the flip-flop.

(A) T flip-flop

(B) D flip-flop

(D) JK flip-flop

Answer: (A)

17. Match the Exclusive-OR (XOR) operations (i) to (iv) with the results (p) to (s), where X is a Boolean input.

(A) (i) – (q), (ii) – (r), (iii) – (s), (iv) – (p)

(B) (i) – (q), (ii) – (r), (iii) – (p), (iv) – (s)

(D) (i) – (q), (ii) – (p), (iii) – (s), (iv) – (r)

Answer: (D)

18. A light emitting diode (LED) emits light when it is _____biased. A photodiode provides maximum sensitivity to light when it is_____ biased.

(A) forward, forward

(B) forward, reverse

(D) reverse, forward

Answer: (B)

19. when expanded as a power series around z = 2, would result in with the region of convergence (ROC) |z − 2| < 1. The coefficients a_k, k ≥ 0, are given by the expression _________.

(A) (−1)^k

(B) (−1)^k+1

(D) (−1/2)^k+1

Answer: (B)

20. The solution x(t), t ≥ 0, to the differential equation k > 0 with initial conditions x(0) = 1 andis

(A) x(t) = 2e⁻^kt + 2kt – 1

(B) x(t) = 2e⁻^kt – 1

(D) x(t) = 2e⁻^kt – kt – 1

Answer: (C)

21. A system has the transfer-function

Let u(t) be the unit-step function. The input x(t) that results in a steady-state output y(t) = sin πt is ___________.

Answer: (C)

22. Choose the fastest logic family among the following:

(A) Transistor-Transistor Logic

(B) Emitter-Coupled Logic

(D) Resistor-Transistor Logic

Answer: (B)

23. What is

(A) 0

(B) 1

(D) Limit does not exist

Answer: (A)

24. The number of zeros of the polynomial P(s) = s³ + 2s² + 5s + 80 in the right-half plane is ___________.

Answer: (2 to 2)

25. The number of times the Nyquist plot of encircles the origin is ________.

Answer: (2 to 2)

26. The opamp in the circuit shown is ideal, except that it has an input bias current of 1 nA and an input offset voltage of 10 μV. The resulting worst-case output voltage will be ± _____ μV (rounded off to the nearest integer).

Answer: (1110 to 1110)

27. The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them is 10 μN/m. When the gap is doubled, the force per unit length will be __________ μN/m (rounded off to one decimal place).

Answer: (4.9 to 5.1)

28. Consider the discrete-time signal x[n] = u[−n + 5] – u[n + 3], where

The smallest 𝑛 for which x[n] = 0 is _______.

Answer: (-3 to -3)

29. Let y(t) = x(4t), where x(t) is a continuous-time periodic signal with fundamental period of 100 s. The fundamental period of y(t) is _____ s(rounded off to the nearest integer).

Answer: (25 to 25)

30. When the bridge given below is balanced, the current through the resistor R_a is _____mA (rounded off to two decimal places).

Answer: (0.99 to 1.01)

31. In the circuit given, the Thevenin equivalent resistance Rth across the terminals ‘a’ and ‘b’ is ___________Ω (rounded off to one decimal place).

Answer: (1.0 to 1.0)

32. X is a discrete random variable which takes values 0, 1 and 2. The probabilities are P(X = 0) = 0.25 and P(X = 1) = 0.5. With E[.] denoting the expectation operator, the value of E[X] – E[X²] is _______ (rounded off to one decimal place).

Answer: (-0.5 to -0.5)

33. The diode in the circuit is ideal. The current source i_s(t) = π sin (3000π t) mA. The magnitude of the average current flowing through the resistor R is ______mA (rounded off to two decimal places).

Answer: (0.95 to 1.05)

34. The full-scale range of the wattmeter shown in the circuit is 100 W. The turns ratio of the individual transformers are indicated in the figure. The RMS value of the ac source voltage V_s is 200 V. The wattmeter reading will be __________W (rounded off to the nearest integer).

Answer: (0 to 0)

35. The no-load steady-state output voltage of a DC shunt generator is 200 V when it is driven in the clockwise direction at its rated speed. If the same machine is driven at the rated speed but in the opposite direction, the steady-state output voltage will be ________V (rounded off to the nearest integer).

Answer: (0 to 0)

Q.36 – Q.65 Carry TWO marks Each

36. The impulse response of an LTI system is h(t) = δ(t) + 0.5δ(t – 4), where δ(t) is the continuous-time unit impulse signal. If the input signal output is _____.

Answer: (A)

37. The Laplace transform of the continuous-time signal x(t) = e⁻^3tu(t – 5) is ________, where u(t) denotes the continuous-time unit step signal.

Answer: (C)

38. In a p-i-n photodiode, a pulse of light containing 8 × 10¹² incident photons at wavelength λ₀ = 1.55 μm gives rise to an average 4 × 10¹² electrons collected at the terminals of the device. The quantum efficiency of the photodiode at this wavelength is _______%.

(A) 50

(B) 54.2

(D) 80

Answer: (A)

39. Let where z denotes a complex number and j denotes √− The inverse function f⁻¹(z) maps the real axis to the _________.

(A) unit circle with centre at the origin

(B) unit circle with centre not at the origin

(D) real axis

Answer: (A)

40. The simplified form of the Boolean function F (W, X, Y, Z) = Σ (4, 5, 10, 11, 12, 13, 14, 15) with the minimum number of terms and smallest number of literals in each term is_________.

Answer: (C)

41. For the given digital circuit, A = B = 1. Assume that AND, OR, and NOT gates have propagation delays of 10 ns, 10 ns, and 5 ns respectively. All lines have zero propagation delay. Given that C = 1 when the circuit is turned on, the frequency of steady-state oscillation of the output Y is ______.

(A) 20 MHz

(B) 15 MHz

(D) 50 MHz

Answer: (A)

42. In the circuit shown, the initial binary content of shift register A is 1101 and that of shift register B is 1010. The shift registers are positive-edge triggered, and the gates have no delay.

When the shift control is high, what will be the binary content of the shift registers A and B after four clock pulses?

(A) A = 1101, B = 1101

(B) A = 1110, B = 1001

(D) A = 1010, B = 1111

Answer: (C)

43. The magnitude and phase plots shown in the figure match with the transfer-function_______.

Answer: (B)

44. A continuous real-valued signal x(t) has finite positive energy and

x(t) = 0, ∀ t < 0. From the list given below, select ALL the signals whose continuous-time Fourier transform is purely imaginary.

(A) x(t) + x(−t)

(B) x(t) – x(−t)

(D) j(x(t) – x(−t))

Answer: (B, C)

45. A silica-glass fiber has a core refractive index of 1.47 and a cladding refractive index of 1.44. If the cladding is completely stripped out and the core is dipped in water having a refractive index of 1.33, the numerical aperture of the modified fiber is_______ (rounded off to three decimal places).

Answer: (0.620 to 0.640)

46. In the circuit shown, ω = 100π rad/s, R₁ = R₂ = 2.2 Ω and L = 7 mH. The capacitance C for which Yin is purely real is ____________ mF (rounded off to two decimal places).

Answer: (1.40 to 1.50)

47. The R-L circuit with R = 10 kΩ and L = 1 mH is excited by a step current I0u(t). At t = 0⁻, there is a current I_L = I₀/5 flowing through the inductor. The minimum time taken for the current through the inductor to reach 99% of its final value is _____ μs (rounded off to two decimal places).

Answer: (0.43 to 0.45)

48. Consider a standard negative feedback configuration with and the controller The root-locus of G(s)C(s) is presented in the figure below. The gain C(jω) = 2 at ω = 1 rad/s. The value of K_D is ________ (rounded off to one decimal place).

Answer: (0.9 to 1.1)

49. How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with exactly one digit appearing twice?

Answer: (240 to 240)

50. The phase margin of the transfer function is ________ degrees. (rounded off to the nearest integer).

Answer: (-2 to 2)

51. A wire-wound ‘resistive potentiometer type’ angle sensor with 72 turns is used in an application. The first turn of the potentiometer is connected to ground while its last turn is connected to 3.6 V. The width of the wiper covers two turns ensuring make-before-break. The output (wiper) voltage when the wiper is on top of both the turns 35 and 36 is _______V (rounded off to two decimal places).

Answer: (1.77 to 1.78)

52. The two secondaries of a linear variable differential transformer (LVDT) showed a magnitude of 2 V (RMS) for zero displacement position of the core. It is noted that the phase of one of the secondaries has a deviation of one degree from the expected phase. Other than this deviation, the LVDT is ideal.

If the differential output sensitivity of the LVDT is 1 mV (RMS)/1 μm, the output for zero displacement is __________ μm (rounded off to one decimal place).

Answer: (34.5 to 35.5)

53. Five measurements are made using a weighing machine, and the readings are 80 kg, 79 kg, 81 kg, 79 kg and 81 kg. The sample standard deviation of the measurement is ______________ kg (rounded off to two decimal places).

Answer: (0.98 to 1.02)

54. Four strain gauges R_A, R_B, R_C and R_D, each with nominal resistance R, are connected in a bridge configuration. When a force is applied, R_A and R_D increase by ΔR and R_B and R_C decrease by ΔR as shown. A potentiometer with total resistance Rv is connected as shown. If R = 100 Ω, and ΔR = 1 Ω, the minimum value of resistance Rv required to balance the bridge is ______Ω (rounded off to two decimal places).

Answer: (4.00 to 4.10)

55. A sinusoidal current of i₁(𝑡)=1 sin(200𝜋𝑡) mA is flowing through a 4 H inductor which is mutually coupled to another 5 H inductor carrying i₂(t) = 2 sin(200 πt) mA as shown in the figure. The coupling coefficient between the inductors is 0.6. The peak energy stored in the circuit is _______ μJ (rounded off to two decimal places).

Answer: (17.00 to 18.00)

56. The figure below shows a feedback amplifier constructed using an nMOS transistor. Assume that μ_nC_ox = 1 mA/V², threshold voltage V_T = 1V and W/L = 2. The bias voltage at the drain terminal is 4 V. The capacitors C∞ offer zero impedance at the signal frequency. The ratio V_out/V_in is __________ (rounded off to two decimal places).

Answer: (0.64 to 0.70)

57. Consider the real-valued function g(x) = max{(x – 2)², −2x + 7},

where x ∈ (−∞, ∞). The minimum value attained by g(x) is _______ (rounded off to one decimal place).

Answer: (0.9 to 1.1)

58. A short-circuit test is conducted on a single-phase transformer by shorting its secondary. The frequency of input voltage is 1 kHz. The corresponding wattmeter reading, primary current and primary voltage are 8 W, 2 A and 6 V respectively. Assume that the no-load losses and the no-load currents are negligible, and the core has linear magnetic characteristics. Keeping the secondary shorted, the primary is connected to a 2 V (RMS), 1 kHz sinusoidal source in series with a The primary current (RMS) will be _______ A(rounded off to decimal places).

Answer: (0.95 to 1.05)

59. The opamps in the circuit are ideal. The input signals are

V_S1 = 3 + 0.10 sin(300t) V and V_S2 = −2 + 0.11 sin(300t) V.

The average value of the voltage V₀ is ______V (rounded off to two decimal places).

Answer: (0.49 to 0.51)

60. In the circuit shown, the input voltage V_in = 100 mV. The switch and the opamp are ideal. At time t = 0, the initial charge stored in the 10 nF capacitor is 1 nC, with the polarity as indicated in the figure. The switch S is controlled using a 1 kHz square-wave voltage signal V_s as shown. Whenever V_s is ‘High’, S is in position ‘1’ and when V_s is ‘Low’, S is in position ‘2’.

At t = 20 ms, the magnitude of the voltage V_o will be _______ mV (rounded off to the nearest integer).

Answer: (99 to 101)

61. In the diagram shown, the frequency of the sinusoidal source voltage V_S is 50 Hz. The load voltage is 230 V (RMS), and the load impedance is The value of attenuator A₁ = 1/50√ The multiplier output voltage V_o = V_xV_y/1V, where V_x and V_y are the inputs. The magnitude of the average value of the multiplier output V_o is _______ V (rounded off to one decimal place).

Answer: (2.1 to 2.5)

62. In the circuit shown, assuming an ideal opamp, the value of the output voltage V_o = ____ V (rounded off to one decimal place).

Answer: (1.9 to 2.1)

63. The rank of the matrix A given below is one. The ratio α/β is _________ (rounded off to the nearest integer).

Answer: (-8 to -8)

64. A 1.999 V True RMS 3-1/2 digit multimeter has an accuracy of ±1 % of reading ±2 digits.

It is used to measure 100 A (RMS) current flowing through a line using a 100:5 ratio, Class-1 current transformer with a burden of 0.1 Ω ±0.5 %.

The worst-case absolute error in the multimeter output is _________ V (rounded off to three decimal places).

Answer: (0.009 to 0.011)

65. The voltage source V_s = 10√2 sin(20000πt) V has an internal resistance of 50 Ω. The RMS value of the current through R is _______mA (rounded off to one decimal place).

Answer: (99.0 to 101.0)

*This option did not appear in GATE 2023 Examination. It appeared as “Turbine flow meter”, that is, “Turbine flow meter” option was repeated.

GATE Exam 2023 Geology and Geophysics (GG) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

GG: Geology and Geophysics

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The village was nestled in a green spot, _______ the ocean and the hills.

(A) through

(B) in

(D) between

Answer: (D)

2. Disagree : Protest : : Agree : _______

(By word meaning)

(A) Refuse

(B) Pretext

(D) Refute

Answer: (C)

(A) 125

(B) 720

(D) 80

Answer: (D)

4. Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

(A) The median is at least as large as the mean.

(B) The mean is at least as large as the median.

(D) At most half the candidates have a score that is larger than the mean.

Answer: (C)

5. In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

(A) P

(B) Q

(D) S

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A) Some residents of the complex who are well established in their fields are also authors of some best-selling books.

(B) All academicians residing in the complex are well established in their fields.

(D) Some academicians residing in the complex are well established in their fields.

Answer: (MTA)

7. Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:

(1) At any stage, Ankita can move either one or two stairs up.

(2) At any stage, Ankita cannot move to a lower step.

Let F(N) denote the number of possible ways in which Ankita can reach the Nth stair. For example, F(1) = 1,F(2) = 2,F(3) = 3.

The value of F (5) is _______.

(A) 8

(B) 7

(D) 5

Answer: (A)

Based only on the information provided above, which of the following statements can be logically inferred with certainty?

(i) The majority of human DNA has no role in the synthesis of proteins.

(ii) The function of about 98% of human DNA is not understood.

(A) only (i)

(B) only (ii)

(D) neither (i) nor (ii)

Answer: (D)

9. Which one of the given figures P, Q, R and S represents the graph of the following function?

f(x) = ||x + 2| – |x – 1||

(A) P

(B) Q

(D) S

Answer: (A)

(A) P

(B) Q

(D) S

Answer: (D)

GG: Geology and Geophysics

PART A: COMPULSORY SECTION FOR ALL CANDIDATES

Q.11 – Q.17 Carry ONE mark Each

11. Which of the following is a chronostratigraphic unit?

(A) Member

(B) Stage

(D) Period

Answer: (B)

12. During contact metamorphism, with increasing temperature,

(A) the ratio of volume to surface area of mineral grains increases.

(B) the ratio of volume to surface area of mineral grains decreases.

(D) hydrous minerals become more stable.

Answer: (A)

13. The dimension of dynamic viscosity is

(A) M¹L⁻¹T⁻²

(B) M¹L¹T⁻¹

(D) M⁰L⁰T⁰

Answer: (B)

14. At a depth of about 400 km inside the Earth, which one of the following occurs?

(A) Conversion of most silicates to perovskite structure

(B) Conversion of plagioclase-peridotite to spinel-peridotite

(D) Conversion of spinel-peridotite to plagioclase-peridotite

Answer: (C)

15. Equatorial radius of which one of the following planets is closest to that of the Earth?

(A) Mercury

(B) Venus

(D) Neptune

Answer: (B)

16. Variation of Bouguer anomaly obtained along a profile after applying all the necessary corrections is due to

(A) topographic undulation above the datum plane.

(B) increase in densities of crustal rocks with depth.

(D) vertical density contrast across Moho.

Answer: (C)

17. The heat production (Qr) of a granitic rock due to decay of the radioactive elements U, Th and K having concentration CU, CTh, and CK, respectively, is given by the expression

Q_r = αC_U + βC_Th + γC_K

Which one of the following correctly represents the relation between the magnitude of coefficients α, β, γ (in μWkg⁻¹)?

(A) α > β > γ

(B) α < β > γ

(D) α < β < γ

Answer: (A)

Q.18 – Q.26 Carry TWO marks Each

18. Which one of the following Phanerozoic periods has the shortest duration of time?

(A) Cambrian

(B) Devonian

(D) Silurian

Answer: (D)

19. Based on the given mineral proportions, which one of the following statements is CORRECT?

(A) Y is more felsic compared to X & Z

(B) X is more felsic compared to Y & Z

(D) Y is the most felsic and Z is the most mafic

Answer: (A)

20. The CORRECT sequence(s) of electromagnetic radiations in terms of increasing wavelength is/are

(A) Gamma ray < UV < Near-IR

(B) X-ray < Visible light < Thermal IR

(D) Microwave < Thermal IR < Near-IR

Answer: (A, B)

21. Which of the given folds is/are represented by the stereoplot?

(A) Horizontal fold

(B) Vertical fold

(D) Recumbent fold

Answer: (B, C)

22. The bulk density and water content of a soil are 1800 kg/m3 and 18%, respectively. The dry density of the soil calculated from the given information is __________ kg/m³. [round off to 2 decimal places]

Answer: (1525.41 to 1525.43)

23. In a seismic reflection survey over a two-layered Earth model having densities and seismic velocities ρ₁=2000 kg/m³, V₁=1800 m/s for the first layer and ρ₂ = 3000 kg/m³, V₂ = 2100 m/s for the second layer, the normal incidence P-wave reflection coefficient is ____________. [round off to 3 decimal places]

Answer: (0.272 to 0.274)

24. The resistivity of a rock, 100% saturated with water of resistivity 0.25 Ωm, is 60 Ω Assuming tortuosity and cementation exponents to be 1 and 2, respectively, the porosity of the rock is ________ (in %). [round off to 2 decimal places]

Answer: (6.45 to 6.46)

25. Let us consider that a student misses cancelling the self-potential between potential electrodes before injecting current into the subsurface, in a Wenner electrical resistivity survey using DC resistivity meter over a horizontally stratified Earth. In direct and reverse modes of measurement (when current flows from C1 to C2 and C2 to C1, respectively) with the same magnitude of current flow, the potential differences recorded are +158 mV and −214 mV, respectively. The self-potential between the potential electrodes before injecting current was _________mV. [in integer]

Answer: (-28 to -28)

26. For the given figure, considering Pratt’s model of isostatic compensation at the crust mantle boundary, the crustal density (ρ₁) that explains 1.5 km deep lake is __________kg/m³. (Consider density of water ρ_w = 1000 kg/m3) [round off to 2 decimal places]

Answer: (2789.00 to 2790.00)

PART B (SECTION 1): FOR GEOLOGY CANDIDATES ONLY

Q.27 – Q.44 Carry ONE mark Each

27. Which one of the following mineral pairs shows solid solubility through coupled substitution of elements?

(A) Albite – Anorthite

(B) Albite – Orthoclase

(D) Jadeite – Aegirine

Answer: (A)

28. The behavior of trace elements in magmatic systems follows

(A) Henry’s Law

(B) Raoult’s Law

(D) First Law of Thermodynamics

Answer: (A)

29. Choose the CORRECT statement regarding crystallization of a single feldspar of composition Or50Ab50 in the Albite-Orthoclase system.

(A) The mineral can form in hypersolvus but not in subsolvus feldspar system.

(B) The mineral can form in subsolvus but not in hypersolvus feldspar system.

(D) The mineral can crystallize neither in hypersolvus nor in subsolvus feldspar system.

Answer: (MTA)

30. Given ΔV_r and ΔS_r are the volume and entropy of reaction, respectively, the most suitable conditions for the reaction to be used as a geothermometer are

(A) small ΔV_r but large ΔS_r

(B) small ΔS_r but large ΔV_r

(D) negative ΔV_r but positive ΔS_r

Answer: (A)

31. In which one of the given mass extinction events, global cooling that resulted in glaciation and lowering of sea level, is considered as major cause of extinction for more than 50% of marine fauna?

(A) Cretaceous – Paleogene

(B) Permian – Triassic

(D) Holocene

Answer: (C)

32. Processes of fossilization affecting an organism from its death to burial under sediments come under the study of

(A) Biostratinomy

(B) Biostratigraphy

(D) Taxonomy

Answer: (A)

33. The dip and dip direction of the lee side of a straight crested ripple on modern sediments are found to be 15° and N10°W, respectively. Considering unidirectional water movement, the flow direction is towards

(A) N10°W

(B) N70°W

(D) S70°W

Answer: (A)

34. Rhodocrosite in hand specimen is most likely to be confused with certain varieties of

(A) Wollastonite

(B) Orthoclase

(D) Biotite

Answer: (B)

35. Which of the following is NOT an essential property of a mineral?

(A) Natural occurrence

(B) Regular internal structure

(D) Solid state

Answer: (C)

36. The number of lattice points in a face-centered cubic unit cell is

(A) 1

(B) 2

(D) 4

Answer: (D)

37. All the faces of an octahedron can be collectively symbolized by

(A) 111

(B) [111]

(D) {111}

Answer: (D)

38. Shallow-focus earthquakes with tensional focal mechanism are characteristic of

(A) subduction zones.

(B) continental shear zones.

(D) mid-ocean ridges.

Answer: (D)

39. 90% of the bulk Earth is constituted of Fe, Si, O and

(A) Al

(B) Ca

(D) Na

Answer: (C)

40. Which of the following is/are slope stabilization method(s)?

(A) Bolting

(B) Application of shotcrete

(D) Use of geogrid

Answer: (A, B, D)

41. The amount of Fe in a sample of 25 g of pyrrhotite (FeS) is __________ g. (Atomic wt. of Fe = 55.85 and S = 32.06) [round off to 2 decimal places]

Answer: (15.87 to 15.89)

42. The rate of spreading about a symmetric spreading center at the middle of a 4000 km wide sea is 40 mm/year. The spreading began ________ million years before present. [in integer]

Answer: (100 to 100)

43. A vertical aerial photograph is obtained over flat terrain with a 30 cm focal-length camera lens from an altitude of 18288 m. If the width of a dolerite dyke on this vertical photograph is 2 mm, its actual width on the terrain is ____________ m. [round off to 2 decimal places]

Answer: (121.91 to 121.93)

44. The decay constant of a radioactive isotope is 1.21 × 10⁻⁴ year⁻¹. The half-life of the isotope is __________ years. [round off to nearest integer]

Answer: (5727 to 5729)

Q.45 – Q.65 Carry TWO marks Each

45. The given outcrop pattern on a flat topography represents

(A) antiform with axial culmination.

(B) horizontal fold.

(D) synform with axial depression.

Answer: (D)

46. Match the following fossil taxa in Group I with their corresponding features in Group II.

(A) P-4, Q-3, R-2, S-1

(B) P-3, Q-4, R-2, S-1

(D) P-3, Q-1, R-4, S-2

Answer: (A)

47. In the given schematic diagram, cross beds are exposed on a vertical rock face. The feature XY (bold line) represents a/an

(A) reactivation surface.

(B) foreset of cross bed.

(D) angular unconformity.

Answer: (A)

48. The schematic diagram represents thin section of a carbonate rock. The type of cement formed by large calcite crystals is known as

(A) overgrowth cement.

(B) poikilotopic cement.

(D) meniscus cement.

Answer: (B)

49. Based on the three statements given below, choose the CORRECT option.

Statement I: Echinoids have water vascular system.

Statement II: Delthyrium and pedicle foramen are found in the brachial valve of brachiopods.

Statement III: Cardinal teeth, adductor muscles and chondrophore are found in bivalves.

(A) Statements I and III are correct, statement II is incorrect.

(B) Statements II and III are correct, statement I is incorrect.

(D) Statements I, II and III are correct.

Answer: (A)

50. The total number of symmetry elements in the crystal class represented by the point group

(A) 21

(B) 22

(D) 24

Answer: (C)

51. The ratio of bridging to non-bridging oxygen atoms in the amphibole structure is

(A) 4:11

(B) 5:6

(D) 1:2

Answer: (B)

52. Match the following basins in Group I with their corresponding formations in Group II.

(A) P-4, Q-3, R-1, S-2

(B) P-3, Q-4, R-2, S-1

(D) P-2, Q-3, R-1, S-4

Answer: (A)

53. Based on the three statements given below, choose the CORRECT option.

Statement I: Gigantopithecus is a genus of the family Hominidae

Statement II: Equus is a living genus of the family Equidae

Statement III: Gomphotherium is a genus belonging to the order Proboscidea

(A) Statements I and II are correct, statement III is incorrect.

(B) Statements I and III are correct, statement II is incorrect.

(D) Statements I, II and III are correct.

Answer: (D)

54. In porphyry copper deposits, the order of alteration zones from the intrusive body outwards is

(A) propylitic→argillic→phyllic→potassic

(B) argillic→phyllic→potassic→propylitic

(D) potassic→argillic→phyllic→propylitic

Answer: (C)

55. Which is the CORRECT sequence of ore minerals in their increasing order of reflectance?

(A) Galena, Sphalerite, Magnetite, Pyrite

(B) Magnetite, Sphalerite, Galena, Pyrite

(D) Galena, Magnetite, Sphalerite, Pyrite

Answer: (C)

56. Which of the following stratigraphic successions is/are arranged in CORRECT chronological order?

(A) Muth Quartzite-Syringothyris Limestone-Fenestella Shale-Panjal Volcanics

(B) Barakar Formation-Bijori Formation-Pachmarhi Formation-Bagra Formation

(D) Kaimur Group-Semri Group-Bhander Group-Rewa Group

Answer: (A, B)

57. Which of the following options represent(s) simultaneous crystallization of two minerals in the given feature(s) ?

(A) Granophyric texture

(B) Myrmekite

(D) Cumulate pyroxene with interstitial plagioclase

Answer: (A, B)

58. Which of the following textures suggest(s) post-kinematic growth of the mentioned mineral?

(A) Randomly oriented chlorite grain aggregates pseudomorphing porphyroblast

(B) Garnet porphyroblast wrapped by external foliation

(D) Porphyroblastic garnet containing helicitic fold as internal schistosity

Answer: (A, D)

59. In the schematic cross-section of a hill, a planar discontinuity intersects a planar slope face. Using kinematic analysis, which of the following conditions favor(s) plane failure to occur?

(A) The dip of the discontinuity surface is less than that of the slope face.

(B) Friction angle on the discontinuity surface is more than the dip of the slope face.

(D) The dip direction of the discontinuity surface is same as that of the slope face.

Answer: (A, C, D)

60. In a drainage basin, the number of the 1st, 2nd, 3rd, 4th and 5th order streams are 240, 40, 8, 2 and 1, respectively. The average of all calculated bifurcation ratios is __________. [round off to 2 decimal places]

Answer: (4.25 to 4.25)

61. A sandstone follows Mohr-Coulomb failure criterion. If the uniaxial compressive strength and the angle of the internal friction of the sandstone are 7 MPa and 30, respectively, the calculated cohesion of the rock is _____________ MPa. [round off to 2 decimal places]

Answer: (2.01 to 2.03)

62. At a certain depth in the crust, the maximum and minimum principal compressive stresses are 150 MPa and 75 MPa, respectively, which lead to normal faulting. If the average density of the crust is 2700 kg/m3, the crustal depth of fracture initiation according to Anderson’s theory of faulting is __________ km. (g = 10 m/s²) [round off to one decimal place]

Answer: (5.5 to 5.6)

63. A cylindrical soil sample of 10 cm diameter is tested in a constant-head permeameter. A volume of 250 cm³ of water is collected in 5 minutes when the constant-head difference between tapping points 15 cm apart is 5 cm. Considering Darcy flow, the absolute value of coefficient of permeability in cm/s is ____________. (π = 3.14) [round off to 3 decimal places]

Answer: (0.030 to 0.032)

64. The minimum anion-to-cation radius ratio at which a 3-fold coordination becomes possible is _________. [round off to 2 decimal places]

Answer: (4.42 to 4.46)

65. The mole fraction of jadeite in the pyroxene of composition (Ca₆₆₇Na_0.333Fe²⁺_0.121Fe³⁺_0.125Mg^0.546A_l0.208)Si₂O₆ is _________. [round off to 3 decimal places]

Answer: (0.208 to 0.208)

PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY

Q.27 – Q.44 Carry ONE mark Each

27. Young’s Modulus of granite is

(A) 5 × 10¹⁰ to 7 × 10¹⁰ Newton/m².

(B) 5 × 10¹⁰ to 7 × 10¹⁰ Newton/cm².

(D) 5 × 10¹⁰ to 7 × 10¹⁰ Newton m.

Answer: (A)

28. The resultant stress obtained from normal stress measurements that are corrected for the mean stress is

(A) hydrostatic stress.

(B) lithostatic stress.

(D) shear stress.

Answer: (C)

29. Which one of the following options is CORRECT for the arrangement of magnetic moment of dipoles in ferrimagnetic material?

(A) Equal and anti-parallel in nature

(B) Unequal and anti-parallel in nature

(D) Unequal and parallel in nature

Answer: (B)

30. Choose the CORRECT earthquake body wave phase which travels as S-wave through the inner core of the Earth.

(A) SKIKS

(B) SKKS

(D) PKiKP

Answer: (C)

31. If the divergence and curl of a vector field are zero, then the field will be

(A) solenoidal and irrotational.

(B) solenoidal but not irrotational.

(D) neither solenoidal nor irrotational.

Answer: (A)

32. The equipotential surface due to a line current electrode placed horizontally over the surface of a homogeneous Earth is

(A) cylindrical.

(B) spherical.

(D) hemi-spherical.

Answer: (C)

33. The basic working principle of a standard Proton Precession Magnetometer is based on

(A) Faraday’s law of induction.

(B) Nuclear magnetic resonance.

(D) Gauss’s law for magnetization.

Answer: (B)

34. The working principle of a modern absolute gravimeter is based on

(A) free-fall method.

(B) simple pendulum method.

(D) principle of zero length spring.

Answer: (A)

35. The given figure shows the self-potential (S.P.) anomaly observed over a polarized spherical body. The direction of polarization with respect to horizontal is

(A) 0°

(B) 45°

(D) 90°

Answer: (A)

36. Geiger-Muller counter responds primarily to

(A) α-radiation.

(B) β-radiation.

(D) α, β, γ-radiations all, equally.

Answer: (B)

37. The damping parameter in the Damped Least-squares solution of a geophysical inverse problem is primarily used to

(A) stabilize the inverse solution.

(B) increase the resolution of estimated model parameters.

(D) obtain a unique solution.

Answer: (A)

38. A seismic wave with a wavelength of 25 m propagates through a sedimentary basin with a phase velocity of 280 m/s. The rate of change of phase velocity with respect to wavelength is 4 per second. The group velocity of the seismic wave propagating in the same dispersive medium is _________ m/s. [round off to nearest integer]

Answer: (180 to 180)

39. The gravity anomaly value estimated at the base of a 10 m tall building is 20 mGal. The gravity anomaly value at the top of the building is ________ mGal. (Ignore the mass of the building in both cases) [round off to 1 decimal place]

Answer: (16.7 to 17.0)

40. In a VLF EM measurement, the vertical and horizontal components of secondary magnetic field observed at any observation point are +10 SI units and -2 SI units, respectively. If the magnitude of the primary magnetic field at the observation point is +50 SI units, then magnitude of the measured dip angle with respect to the horizontal at the observation point is_________ degree. [round off to 2 decimal place]

Answer: (10.50 to 12.50)

41. A geothermal gradient of 32°C/km is measured in the upper few meters of sediments covering the ocean floor. If the mean thermal conductivity of the oceanic sediments is 1.9 Wm⁻¹°C⁻¹, then the absolute value of local heat flow is _________milli-Wm⁻². [round off to 1 decimal place]

Answer: (60.5 to 61.1)

42. A seismic refraction survey is done over a two-layered Earth having P-wave velocities of 2000 m/s and 3500 m/s for the first and second layers, respectively. Given the thickness of the first layer to be 2000 m, the critical distance for the refracted wave is ________ m. [round off to nearest integer]

Answer: (2784 to 2786)

43. The given figure shows the time domain convolution of two boxcar functions. The duration (t) of the output pulse as shown in the figure is _________ milli-second. [in integer]

Answer: (5 to 5)

44. For a given rock formation, the porosity (ϕ) is 23 % and water saturation (S_w) is 25 %. The proportion of water (bulk volume of water) in the total rock formation is ________%. [round off to 2 decimal places]

Answer: (5.50 to 6.00)

Q.45 – Q.65 Carry TWO marks Each

45. Electrical Resistivity Tomography (ERT) survey is performed in a noisy background along a 1000 m long profile with 10 m equi-spaced electrodes using different electrode configurations. Which electrode configuration will produce maximum number of negative apparent resistivity data?

(A) Dipole-dipole configuration

(B) Wenner-Schlumberger configuration

(D) All configurations will produce the same number of negative apparent resistivity data

Answer: (A)

46. Consider a signal whose original real part is given by f(t) = sin (t) and its Hilbert transform is given by f(t)_H. Then, the complex signal f_C is

(A) sin(t) – isin(t)

(B) cos(t) – icos(t)

(D) cos(t) – isin(t)

Answer: (C)

47. Mathematically, the geometrical factor for a Two-electrode array and Wenner array is the same. Which one of the following statements is CORRECT?

(A) Lateral resolution of Two-electrode array is better than the Wenner array

(B) Lateral resolution of Wenner array is better than the Two-electrode array

(D) Vertical resolution of both arrays will be the same

Answer: (B)

48. Laminar shale, structural shale and dispersed shale can be distinguished by which one of the following cross-plots?

(A) Self-potential (S_P) log value and formation water resistivity (R_w)

(B) Laterolog Deep (LLD) resistivity and formation resistivity (Rt)

(D) Neutron porosity and Density porosity

Answer: (D)

49. The factor by which the magnetic field decreases with respect to the gravity field caused by the same source at a distance (r) is

(A) 1/r

(B) r

(D) 1/r²

Answer: (A)

50. The total excess mass of an irregular shaped body can be calculated from the corresponding gravity anomaly measured over a horizontal plane on the surface of the Earth using

(A) Divergence theorem.

(B) Stoke’s theorem.

(D) Laplace’s equation.

Answer: (A)

51. Select the CORRECT equation for Euler deconvolution solution of the total magnetic field B_T observed along a profile on the surface of the Earth for ith point, with background magnetic field value B, and structural index N.

Answer: (A)

52. The potential field U due to a source follows a spherical symmetry. Which among the following is/are CORRECT statement(s)?

Answer: (B, C, D)

53. In Magnetotelluric survey, three magnetic field components (H_x, H_y, H_z) and two electric field components (E_x and E_y) are measured and two apparent resistivities ρ_xy and ρ_yx are computed. Which of the following is/are CORRECT?

(A) ρ_xy = ρ_yx over horizontally stratified layered structure

(B) ρ_xy = ρ_yx when 2D strike is in x-direction

(D) ρxy = ρyx when 2D strike is at 45° from x-direction

Answer: (A, D)

54. Singular Value Decomposition (SVD) decomposes a matrix A into 3 orthogonal matrices. If V is one of the orthogonal matrices, then which among the following is/are CORRECT? (superscript T-represents transpose and I is the Identity matrix)

(A) V^TV = VV^T ≠ I

(B) V^TV ≠ VV^T ≠ I

(D) VV^T = I

Answer: (C, D)

55. If g_A, g_B and g_C are the observed gravity values in a valley below mean sea level, on a plane surface at mean sea level and on the top of a mountain above mean sea level at the same latitude, respectively, then which of the following option(s) is/are CORRECT?

(A) g_A and g_B less than g_C

(B) g_A and g_C less than g_B

(D) g_C and g_B less than g_A

Answer: (C, D)

56. The CORRECT option(s) for the generation of point M in a seismic reflection survey as shown in the given figure is/are

(A) The curvature of the reflector is greater than that of the incident wavefront

(B) Focusing effect

(D) The curvature of the incident wavefront is greater than that of the reflector.

Answer: (A, B)

57. In the X² – T² seismic reflection method, the travel time (T) is expressed as

T₀ is the normal incidence two-way travel time at zero offset distance (X = 0), RMS velocities Which of the following options apply(ies) to the third term?

(A) Heterogeneous medium

(B) Isotropic medium.

(D) Geometrical spreading to correct AVO data.

Answer: (A, D)

58. The coefficient of electrical anisotropy and mean resistivity of a horizontally stratified rock sample is 1.10 and 150 Ωm, respectively. The longitudinal resistivity of the rock sample is _______ Ω [round off to 2 decimal places]

Answer: (136.00 to 137.00)

59. The amplitude of a plane EM wave travelling vertically downward in a homogeneous medium of resistivity ‘ρ’ decreases with depth as where z is depth. If the frequency of the EM wave is 10 kHz, then the resistivity of the medium is _______ Ω (use μ = μ₀ = 4π × 10⁻⁷ H/m and π = 3.14)

[round off to nearest integer]

Answer: (125 to 131)

60. In a seismic survey using a Vibroseis source, the source wavelet used is S(t) = (0.3, 0.5, 0.6, 0.7) and the data acquired is X(t) = (0.5, 0.3, 0.7, 0.2) (as shown in the figure). Consider the unit delay (lag) to be 0.1 second (i.e., two-way travel time), which corresponds to a depth of 300 m. The cross correlation of S(t) with X(t) leads to maximum cross-correlated value of ________. [round off to 2 decimal places]

Answer: (0.92 to 0.92)

61. In the given figure, the rupture propagates from left to right along a fault with a rupture velocity of 1.5 km/sec. Given the P-wave velocity of the medium to be 6 km/sec, the apparent rupture time observed at point ‘O’ at the right edge of the fault is _________ sec. [round off to nearest integer]

Answer: (14 to 16)

62. Given the following well logging parameters

Flushed zone resistivity R_XO = 0.4 Ωm, Formation resistivity R_t = 5 Ωm, Mud-filtrate resistivity R_mf = 0.02 Ωm, Formation water resistivity R_w = 0.10 Ωm, Tortuosity factor 𝑎 = 1, and Cementation and Saturation exponents m = n = 2, Porosity = 30 %.

The movable hydrocarbon saturation is _________%. [round off to 1 decimal places]

Answer: (27.1 to 27.7)

63. The horizontal and vertical components of the geomagnetic field at a location are 40000 nT and 30000 nT, respectively. If the horizontal and vertical components of the induced field at the same location are −1000 nT and −600 nT, respectively, then the total magnetic field anomaly for that location is _______ nT. [round off to nearest integer]

Answer: (-1160 to -1159)

64. There is a major water supply well in a fully saturated sandy medium which has a porosity of 40% and a density of 2600 kg/m³. Water extracted from this well creates a depression in the shape of a vertical cylinder to a depth of 300 m from the surface and with a radius of 1000 m about the well. The maximum change in gravity anomaly due to the 100% extraction of water is __________ mGal. (use π = 3.14 and G = 6.67 × 10⁻¹¹ Nm²kg⁻²) [round off to 2 decimal places]

Answer: (17.01 to 17.31)

65. The given figure is a seismogram of a local earthquake which occurred at a depth of 10 km. Considering the P-wave and S-wave velocities as 6 km/s and 3 km/s respectively for the medium, the epicentral distance is________ km. [round off to nearest integer]

Answer: (34 to 35)

GATE Exam 2023 Geomatics Engineering (GE) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

GE: Geomatics Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x − 1)³(x − 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

GE: Geomatics Engineering

PART A: Common FOR ALL CANDIDATES

Q.11 – Q.27 Carry ONE mark Each

11. An angle was measured with a standard error of 5ʺ. How many observations a surveyor needs to take in order to obtain a standard error of 1ʺ for the mean value of this angle?

(A) 5

(B) 1

(D) 25

Answer: (D)

12. What are the Manhattan and Pythagorean distances (in m), respectively between points A and B in the figure below, where the Euclidean distance between A and C is 4 m, and the Euclidean distance between C and B is 4 m? All the cells have the same edge lengths.

(A) 9.0 and 5.7

(B) 5.7 and 8.0

(D) 8.0 and 5.7

Answer: (D)

13. Which of the following is tested using the Chi-square test in least squares adjustment?

(A) Adjusted and observed values of observations are statistically similar

(B) Presence of gross errors in observations

(D) High correlation between observations and residuals

Answer: (B)

14. In active remote sensing of Earth objects from a satellite-borne sensor, the source of the energy used for sensing, lies at the _________.

(A) satellite

(B) Sun

(D) ground station

Answer: (A)

15. For a push-broom sensor, the following details are given:

Number of detectors = 3000

Height above the ground = 900 km

Swath on the ground = 30 km

The spatial resolution of the sensor is _______ m.

(A) 30

(B) 270

(D) 10

Answer: (D)

16. To visually distinguish between a river channel and a canal on an image, having similar widths and located in the same area, the most important parameter used is ___________.

(A) size

(B) shape

(D) texture

Answer: (B)

17. The unit of spectral radiance is ________.

(A) W sr⁻¹ μm⁻¹

(B) W m⁻² sr⁻¹

(D) W m⁻² sr⁻¹ μm⁻¹

Answer: (D)

18. The ratio between the reflected to the incident energy on a surface at a particular wavelength gives the __________ of the surface.

(A) spectral reflectance

(B) spectral transmittance

(D) spectral irradiance

Answer: (A)

19. GNSS stands for Global Navigation Satellite Systems. As of today, which of the following is the complete set of GNSS constellations that cover the entire globe?

(A) GPS, GLONASS, Galileo, BeiDou, IRNSS, QZSS

(B) GPS, GLONASS, Galileo, BeiDou, IRNSS, QZSS, GAGAN, WAAS, EGNOS

(D) GPS, GLONASS, Galileo, BeiDou

Answer: (D)

20. The basic premise for using the DGPS technique is to reduce the errors due to

(A) atmosphere, satellite orbit, multipath

(B) atmosphere, satellite orbit, satellite clock

(D) atmosphere, satellite orbit, satellite clock, receiver clock, multipath

Answer: (B)

21. The orbital period of GPS satellites is determined by the __________ of their orbits.

(A) semi-major axis

(B) eccentricity

(D) semi-major axis, inclination and eccentricity

Answer: (A)

22. Which vector data analysis tool combines geometries and attributes from different layers?

(A) Overlay

(B) Map Manipulation

(D) Cartesian distance measurement

Answer: (A)

23. A GIS analyst has two raster datasets with the same number of rows and columns. The analyst computes the average of the two input raster layers to generate a new raster layer with the same size as the input raster layers. What type of raster data analysis operation is performed?

(A) Local

(B) Neighborhood

(D) Global

Answer: (A)

24. Match the following errors (Column 1) in spatial data digitization with their descriptions (Column 2).

(A) P-2, Q-4, R-3, S-5, T-1

(B) P-1, Q-2, R-3, S-5, T-4

(D) P-2, Q-4, R-3, S-1, T-5

Answer: (A)

25. Which of the following statement(s) is/are TRUE for the least squares adjustment of observations?

(A) Observations have a Chi-square distribution

(B) Random errors in the observations are assumed to have a symmetrical distribution

(D) The adjusted parameters are independent of a priori reference variance

Answer: (B, C, D)

26. Which of the following statement(s) is/are TRUE for the systematic errors?

(A) These can be corrected by applying a suitable mathematical model

(B) The least squares adjustment automatically removes unmodelled systematic errors

(D) Removal of gross errors automatically removes systematic errors

Answer: (A, C)

27. In the following figure, A and B are fixed points with known plane rectangular coordinates. C and D are the new points in the control survey whose coordinates are to be determined. For this network, the surveyor has measured all 8 internal angles (1 to 8) and 5 sides BC, CD, DA, AC and BD. The value of redundancy (r) for the given figure will be equal to ________ (In integer).

Answer: (9 to 9)

Q.28 – Q.46 Carry TWO marks Each

28. As shown in the following figure, let d₁, d₂, d₃ denote three uncorrelated clockwise directions, observed at point P with equal standard errors for each direction, i.e., σd₁ = σd₂ = σd₃ = ±√2ʺ. Let α₁ and α₂ be two included angles formed by these three directions. The covariance matrix (in arcsecond²) for these included angles will be given as:

Answer: (B)

29. The figure shows three distance observations D₁, D₂ and D₃. The table lists values of these observations and the corresponding weights. Assuming uncorrelated observations, the most probable values by the least squares approach for these measurements are _______ (Rounded off to 3 decimal places).

Answer: (B)

30. Which of the following methods is widely used by the GNSS constellations to distinguish the satellites from each other at the GNSS receiver?

(A) Code Division Multiple Access (CDMA)

(B) Time Division Multiple Access (TDMA)

(D) Phase Division Multiple Access (PDMA)

Answer: (A)

31. For the following data, the slope (m) and intercept (c) of the least squares fitted straight line (Y = mX + c) are given as:

(A) Slope = 0.750, Intercept = 5.167

(B) Slope = 0.850, Intercept = 6.180

(D) Slope = 0.750, Intercept = 5.555

Answer: (A)

32. Which of the following statement(s) is/are CORRECT for sun-synchronous Earth observation satellites?

(A) They are in near-polar orbit around the Earth

(B) They cross the equator at different longitudes at nearly the same local solar time

(D) The angle of inclination of their orbit is < 1 degree

Answer: (A, B, C)

33. Which of the following statement(s) is/are CORRECT?

(A) In optical remote sensing, more often we are interested in diffuse reflections

(B) The reflection will be diffuse if the incident wavelength is comparatively much larger than the surface roughness

(D) All wavelengths emitted by the Sun reflect in diffuse manner from the objects on the surface of the Earth

Answer: (A, C)

34. The spectral reflectance curves of three materials (A, B, and C) are shown in the figure below. Also shown are three wavelength bands at X, Y and Z. Which of the following statement(s) is/are CORRECT?

(A) Each of the curve is the spectral signature of the respective material

(B) A sensor designed for the wavelength band ‘Y’ will best distinguish these materials in the image captured by the sensor

(C) A sensor designed for the wavelength band ‘Z’ will best distinguish these materials in the image captured by the sensor

(D) These curves are normally produced using a spectro-radiometer

Answer: (A, B, D)

35. Which of the following statement(s) is/are TRUE?

(A) Topography is an example of continuous spatial feature

(B) Geo-relational data model stores spatial data and attribute data separately

(D) Land surface temperature is an example of discrete spatial feature

Answer: (A, B, C)

36. In the network shown below, after converting it to a topological graph, which of the following statement(s) is/are TRUE? (Assume there are no pseudo-nodes)

(A) The correct number of nodes (or vertices) are 7

(B) The correct number of edges (or links) are 9

(D) The correct number of edges (or links) are 8

Answer: (A, B, C)

37. Which of the following type(s) of tolerances is/are used in editing GIS data?

(A) Snap tolerance

(B) Weed tolerance

(D) Polygon tolerance

Answer: (A, B, C)

38. Choose the CORRECT statement(s) regarding microwave remote sensing.

(A) Spatial resolution of passive microwave remote sensor is coarser than that of active microwave remote sensor from the same platform

(B) The intensity of signal returned by an object depends on its geometric as well as dielectric properties

(C) It is possible to “see through” the dense forest canopy using X-band active microwave remote sensing (i.e. signals can penetrate the dense forest canopy)

(D) Microwave remote sensing can be used in soil moisture studies

Answer: (A, B, D)

39. Consider the Sun and the Earth as blackbodies at 6000 K and 300 K temperatures, respectively. Which of the following statement(s) is/are INCORRECT?

(A) Sun emits maximum energy at 9.3 μm

(B) Sun does not emit energy at microwave

(D) Earth does not emit energy at green wavelength

Answer: (A, B, C)

40. Which of the following statement(s) concerning GNSS errors is/are CORRECT?

(A) Tropospheric delay increases with increasing relative humidity

(B) Ionospheric error is highly correlated with the position of the Moon

(D) The observed range is called as pseudorange because of its erroneous nature

Answer: (A, D)

41. For a push-broom (along-track) sensor the following are known:

Field of view (FoV) = 2 degrees

Instantaneous FoV = 1 milli-radian

Time to scan one full scanline = 2 × 10⁻² s

Height above ground = 100 km

The dwell time for a single pixel of this sensor is ___________ s.

(Rounded off to 2 decimal places)

Answer: (0.02 to 0.02)

42. The range accuracy with a microsecond accurate clock in the GNSS receiver is about 300 m. If we improve the clock accuracy to 3.33 × 10^−x s, the range accuracy becomes 1 cm. The value of x is ________ (In integer).

Assume the speed of light to be c = 3 × 10⁸ m/s and that no other errors are being considered.

Hint: error-free range = speed of light × time of travel of the signal

Answer: (11 to 11)

43. A GPS satellite is flying at a distance of 20,000 km from the observer. The phase of the L1 carrier (1575.42 MHz) in degrees as received by the observer is _______ (Rounded off to 2 decimal places).

Assume that the signal did not experience any refraction, reflection or other errors and the speed of light to be 𝑐 = 3 × 10⁸ m/s.

Answer: (0.00 to 0.00)

44. For a profile given in the figure in the form of three steps A, B and C, the following information is available:

Height of step A (H_A) with respect to a reference line = 10 m (known and error free)

Difference in height between step A and step B (h₁) = 5 m ± 2 mm

Difference in height between step B and step C (h₂) = 8 m ± 3 mm

H_B and H_C are the unknown heights of step B and C, respectively. The step B is higher than step C and D.

The coefficient of correlation, between the height differences = 0.25

The coefficient of correlation between estimated heights of points B and C will be _________ (Rounded off to 2 decimal places).

Answer: (0.39 to 0.41)

45. The relative radiance value of a facet of a Triangulated Irregular Network (TIN) can be computed using:

R_f = cos(A_f – A_s) sin(H_f) cos (H_s) + cos(H_f) sin(H_s)

Where, R_f is the relative radiance value of a facet, A_f is the facet’s aspect, 𝐴𝑠 is the sun’s azimuth angle, H_f is the facet’s slope and H_s is the sun’s altitude. Suppose a facet of a TIN has a slope value of 10° and an aspect value of 297° and sun’s azimuth of 315°. For sun’s altitude angle of 65°, the relative radiance value of this facet is ______ (Rounded off to 2 decimal places).

Answer: (0.95 to 0.97)

46. The table provides the X- and Y-coordinates of the points, measured in row and column of a raster with cell size of 1 meter, and their known values. Using inverse distance weighted (IDW) interpolation method and Euclidean distance, the interpolated value at Point 0 is_______ (Rounded to 2 decimal places).

A constant rate of change in value between points should be assumed.

Answer: (17.24 to 17.86)

PART B: FOR Section I: Surveying and Mapping CANDIDATES ONLY

Q 47 – Q 54 Carry ONE mark Each

47. The bearing of the line AB from North is 143°40ʹ and angle ABC measured in clockwise direction is 309°30ʹ. The bearing of line BC in Quadrantal Bearing System is ________.

(A) N3°10ʹW

(B) N86°50ʹE

(D) N3°10ʹE

Answer: (C)

48. Which of the following map scale is most suitable for urban planning?

(A) 1:10,000

(B) 1:25,000

(D) 1:100,000

Answer: (A)

49. Which of the following statement is NOT true regarding relief displacement in vertical photographs in the context of aerial photogrammetry?

(A) Relief displacement is the shift in the photographic position of an object caused by the elevation of the object (above or below the datum)

(B) Relief displacement is always in non-radial direction from the principal point

(C) Relief displacement can cause straight roads (not passing through the ground principal point) to appear crooked in undulating terrain

(D) The magnitude of relief displacement is affected by the flying height of the camera (assuming everything else to be same)

Answer: (B)

50. A square grid is laid on a flat terrain and is photographed from an aerial camera. The flying height and camera parameters are assumed to be constant. The camera and lens are assumed to be perfect (i.e. free from any distortions). The image of the grid obtained from the camera is shown below. Select the CORRECT statement from the statements given below.

(A) Camera is looking directly downwards (towards nadir)

(B) The given photograph is a vertical photograph

(D) Scale over the given photograph is constant

Answer: (C)

51. Which of the following statement is TRUE for the World Geodetic System 1984 (WGS84)?

(A) The WGS84 ellipsoid best fits the shape of the earth including its topography

(B) The WGS84 ellipsoid and the Geodetic Reference System 1980 (GRS80) ellipsoid are one and the same

(D) The WGS84 ellipsoid can be used to determine the geoid

Answer: (D)

52. Which of the following map(s) is/are published by Survey of India?

(A) Topographical Maps

(B) Geological Maps

(D) Thematic Maps

Answer: (A)

53. Which of the following triangles are well conditioned and may be suitable for control establishment using triangulation?

(A) I

(B) II

(D) IV

Answer: (A, C)

54. An angle of 90° is to be laid out with a theodolite having a least count of 30ʺ. The angle was measured by repetition method and was found to be 90° 00ʹ 25ʺ. The offset value at a distance of 300 m from the theodolite to set-out the correct angle is _________ m. (Rounded off to 3 decimal places).

Answer: (0.035 to 0.037)

Q 55 – Q 65 Carry TWO marks Each

55. The following vertical circle readings were taken by a theodolite set up at station A to observe targets located at P and Q

The value of the vertical angle PAQ is _________.

(A) 1° 51ʹ 25ʺ

(B) 1° 51ʹ 30ʺ

(D) 5° 51ʹ 30ʺ

Answer: (D)

56. Aerial photograph is to be taken from a flying height of 2 km above a flat ground with a camera having a focal length of 200 mm. The image format used is 23 cm × 23 cm. The ground area covered by a single photograph is __________km².

(A) 5.29

(B) 1.48

(D) 2.22

Answer: (A)

57. The scaled and rotated versions of vectors [1, 2] and [−3, 4] are ________

(A) [−1, 3], [−7,1]

(B) [5, 7], [−7, 3]

(D) [2, −3], [−7, 3]

Answer: (A)

58. Find the best match between Column 1 and Column 2

(A) P – 4; Q – 2; R – 3; S-1

(B) P – 1; Q – 3; R – 2; S-4

(D) P – 2; Q – 3; R – 1; S-4

Answer: (D)

59. Which of the following statement(s) is/are CORRECT?

(A) WGS84 ellipsoid is an oblate ellipsoid

(B) GPS positioning gives the orthometric height of a place

(D) Shape of geoid changes with time

Answer: (A, D)

60. For a constant flying height, the average scale of an aerial photograph depends on which of the following parameter(s)?

(A) Focal length of the camera

(B) Size of the photograph

(D) Topography of the ground

Answer: (A, D)

61. Which of the following statement(s) is/are CORRECT?

(A) Mean sea level is defined as the long-term mean of the tide gauge measurements at a given location

(B) Mean sea level is the same as the mean tide level

(D) Mean sea level is an approximation of geoid

Answer: (A, D)

62. Following is the page of a field book used for levelling. Few readings marked with ‘−’ are illegible. The Reduced Level (RL) of the Temporary Bench Mark (TBM) is__________ m (Rounded off to 2 decimal places). All the readings are in m.

Answer: (104.50 to 101.50)

63. The zone number of Universal Transverse Mercator (UTM) projection having a longitude of 67° 20ʹ 30ʺE is _______ (In integer).

Answer: (42 to 42)

64. A pair of overlapping vertical photographs were taken from a flying height of 1230 m above sea level with a camera having a focal length of 152.4 mm. The distance between the consecutive exposure stations is 350 m. The parallax bar reading of a point A on the photograph is observed as 10.96 mm. The parallax bar constant for this setup is given as 80.71 mm. The elevation of point A above sea level is found to be _________ m (Rounded off to 2 decimal places).

Answer: (647.68 to 648.32)

65. A perfectly adjusted tachometer is set at a point A having Reduced Level (RL) of 80.50 m and the following readings are taken to the staff held at point B having RL of 80.10 m.

The height of the instrument from the ground above point A is ________ m (Rounded off to 2 decimal places).

Answer: (1.60 to 1.60)

PART B: FOR Section II: Image Processing and Analysis CANDIDATES ONLY

Q 66 – Q 73 Carry ONE mark Each

66. The purpose of thresholding in supervised classification is

(A) to reject homogeneous classes

(B) to correct the geometry of the image

(D) to identify and reject pixels not belonging to pre-defined training classes

Answer: (D)

67. The pixel values for a 3 band and 8-bit image are (127, 127, 127). On an RGB colour display, this pixel will appear __________.

(A) green

(B) black

(D) white

Answer: (C)

68. The value at the center pixel of the image at (1) obtained after applying the filter given at (2) is _________

(A) 70

(B) 68

(D) 71

Answer: (A)

69. To store a 3 band, 4-bit, 512×512 size image (without header) the number of storage bits required are __________.

(A) 31,45,728

(B) 6,144

(D) 1,25,82,912

Answer: (A)

70. A child travelling in a bus is staring at the wheels of a car. To the child’s amusement the car wheels appear to spin backwards, but the car moves forward. This perception is because of the nature of our human visual sensory system, and is attributed to ________.

(A) aliasing

(B) convolution

(D) modulation

Answer: (A)

71. Which one of the following is NOT a linear operation?

(A) Convolution

(B) Moving average

(D) Similarity transformation

Answer: (C)

72. The minimum number of 2-dimensional ground control points (GCP’s) required for second order polynomial mapping for image georeferencing is:

(A) 4

(B) 5

(D) 7

Answer: (C)

73. Consider an across-track multispectral scanner with ground pixel size of 56 m x 79 m in the along-track and across-track directions. Which of the following statement is TRUE?

(A) Aspect ratio distortion of the image will be greater than 1

(B) Aspect ratio distortion of the image will be less than 1

(D) Aspect ratio distortion is a type of radiometric distortion

Answer: (A)

Q 74 – Q 84 Carry TWO marks Each

74. The contingency table as given below is obtained after an image classification. The overall classification accuracy (O) is given as

(A) O = 0.795

(B) O = 0.850

(D) O = 0.754

Answer: (A)

75. Divergence analysis in classification is used:

(A) to decorrelate a given set of bands used in classification

(B) to logically smooth the classified image

(D) to evaluate statistical separability amongst class pairs

Answer: (D)

76. Consider the histogram of an 8-bit image given below at (1). A piece-wise linear contrast stretch given at (2) is applied on the said image. The minimum and maximum pixel values of the image obtained after applying the given contrast stretch are __________ (minimum value) and ____________ (maximum value), respectively.

(A) 17, 176

(B) 17, 120

(D) 20, 120

Answer: (A)

77. The variance-covariance matrix for a 3-band image is given below (in the sequence of bands 1, 2 and 3). Which of the statement(s) is/are CORRECT?

(A) The standard deviation of all bands is the same

(B) The bands 1 and 2 are positively correlated

(D) A line fitted to the scattergram between band 1 and band 3 will have a positive slope

Answer: (A, B, D)

78. Which of the following statement(s) is/are TRUE regarding color theory:

(A) Subtractive color theory is used for color printing

(B) Additive color theory is used to display images on a color television screen

(D) White light projected on a translucent filter made of cyan dye would subtract the green light

Answer: (A, B, C)

79. Pixel (x, y) indicates a pixel at location x, y in the image coordinate system. Which of the following statement(s) is/are CORRECT?

(A) Pixels (x+1, y) and (x, y+1) are the adjacent horizontal and vertical neighbors of pixel (x, y), respectively

(B) The digital number at pixel (x, y) will always be the average of the digital numbers of pixels (x-1, y) and (x+1, y)

(D) Pixel (x, y) has only four diagonal adjacent neighbors

Answer: (A, C, D)

80. Which of the following statement(s) is/are CORRECT in the context of image enhancement?

(A) Histogram equalization carries out a contrast stretch such that output values are displayed on the basis of their frequency of occurrence

(B) Compared to a linear contrast stretch, histogram equalization is computationally more expensive

(D) Histogram equalization and linear contrast stretch will produce identical results if the histogram of the input image is uniform

Answer: (A, B, D)

81. The value of the convolution of f(x) = 3 cos 2x and where x ∈ [0, 2π], at x = π/3, is _______ (Rounded off to 2 decimal places).

Answer: (2.71 to 2.73 OR 0.42 to 0.44)

82. A sensor converts the influx of light linearly to digital code through voltage changes. The sensor has a voltage range of 0-5 V and the maximum number of codes that it can quantize the voltage change is 2048. The bit-size of the quantizer is _________ (In integers).

Answer: (11 to 11)

83. The following digital numbers are given for a pixel of multispectral sensor. The NDWI (normalized difference water index) for this pixel is __________ (Rounded off to 1 decimal place).

Blue = 136

Green = 200

Red = 245

NIR = 150

TIR = 50

Answer: (0.1 to 0.2)

84. In the grid below, the four corners A, B, C and D are the pixel locations on an image. The brightness values at pixels A, B, C and D are 10, 20, 5 and 30, respectively. Using bilinear interpolation, the brightness value determined at point P is ______ (Rounded off to 1 decimal place).

Answer: (20.3 to 20.3)

GATE Exam 2023 Ecology and Evolution (EY) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

EY: Ecology and Evolution

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A) you are

(B) your

(D) yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A) Sight

(B) Site

(D) Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A) 20/7

(B) 28/5

(D) 35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A) Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B) Everyone who has dropped out of college has won the Fields medal.

(D) Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

(A) 3

(B) 4

(D) 6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A) only (i)

(B) only (iii) and (iv)

(D) (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A) 400

(B) 600

(D) 200

Answer: (A)

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A) According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x⁴ in the polynomial (x – 1)³ (x – 2)³ is equal to _______.

(A) 33

(B) −3

(D) 21

Answer: (A)

(A) circle

(B) regular octagon

(D) rhombus

Answer: (D)

EY: Ecology and Evolution

Q.11 – Q.35 Carry ONE mark Each

11. Which one of the following is an example of mechanical potential energy?

(A) Activated neuron

(B) Polarized cell membrane

(D) Relaxed muscle

Answer: (C)

12. A research team studies the probability of crop damage by wild boar in crop fields. For each crop field sampled, they record ‘1’ if damage was observed, and ‘0’ if damage was not observed. Which one of the following distributions is most appropriate to analyse the probability of crop damage?

(A) Binomial distribution

(B) Poisson distribution

(D) Gamma distribution

Answer: (A)

13. To test whether body size differs between two populations of a field mouse species, a researcher measured 100 individuals in each population and calculated the statistic

where are the mean body sizes of the two populations, respectively, S_p is the pooled standard deviation, and n₁ and n₂ are the sample sizes for the two populations, respectively.

This statistic is used in the

(A) Chi–square test

(B) Kruskal–Wallis test

(D) Mann–Whitney U test

Answer: (C)

14. Which one of the following ecological processes best explains the observation that seedling establishment increases with distance from the parent tree in a forest?

(A) Competition between species

(B) Competition within species

(D) Facilitation within species

Answer: (B)

15. In the early 20th century, which one of these scientists made fundamental contributions to both the fields of evolution and statistics?

(A) R. A. Fisher

(B) Niko Tinbergen

(D) Thomas Huxley

Answer: (A)

16. The figure depicts how body temperature changes for two species (L and M) as a function of ambient temperature.

Which one of the following statements about how L and M regulate temperature is correct?

(A) L and M are both homeotherms.

(B) L and M are both poikilotherms.

(D) L is a poikilotherm, whereas M is a homeotherm.

Answer: (C)

17. You are a deep–sea organism and your potential mates are several hundreds of kilometers away from you. Which one of the following kinds of mating signals is most likely to help them locate you?

(A) Display gestures

(B) Electric pulses

(D) Sounds

Answer: (D)

18. Which one of the following options represents the correct order with respect to levels of organization?

B – biomes; E – ecosystems; P – populations; I – individuals; C – communities

(A) I < P < C < E < B

(B) I < C < P < E < B

(D) I < P < E < C < B

Answer: (A)

19. Which one of the following options describes the difference between abiotic resources and abiotic conditions?

(A) Resource levels can fluctuate but conditions do not.

(B) Conditions can fluctuate but resource levels do not.

(D) Conditions can be used up by organisms, whereas resources cannot.

Answer: (C)

20. Which one of the following ranges correctly represents the percentage of energy that is transferred from a lower to the next higher trophic level in most terrestrial systems?

(A) 0.01% to 1%

(B) 33% to 66%

(D) 90% to 95%

Answer: (C)

21. Whales and dolphins are hypothesized to have evolved along the northern shore of the Tethys Sea, prior to the Indian plate’s collision with the Eurasian plate. To which one of the following animals are these aquatic mammals most closely related?

(A) pigs

(B) elephants

(D) zebras

Answer: (A)

22. Which one of the following options represents the correct order of decreasing average net primary productivity (g / m² / year) in natural ecosystems?

(A) Swamp and marshes > Tropical forests > Temperate forests > Temperate grasslands > Tundra

(B) Swamps and marshes > Tropical forests > Temperate forests > Tundra > Temperate grasslands

(D) Tropical forests > Swamps and marshes > Temperate forests > Temperate grasslands > Tundra

Answer: (A)

23. The increase in mean global temperature since the industrial revolution falls in the range of

(A) 0 °C to 0.5 °C

(B) 0.5 °C to 2 °C

(D) > 5 °C

Answer: (B)

24. Which one of the following endangered species has been the subject of a reintroduction plan in India?

(A) Rusty spotted cat

(B) Jungle cat

(D) Jaguar

Answer: (C)

25. Compared with bony fish, many shark species show steeper population declines in response to heavy fishing pressure. Which one of the following options explains this?

(A) Sharks are dangerous to humans.

(B) Sharks evolved over 400 million years ago.

(D) Sharks are only found in open oceans.

Answer: (C)

26. Which one or more of the following options describe(s) how ferns differ from angiosperms and gymnosperms?

(A) Ferns lack a vascular system.

(B) Ferns have separate haploid and diploid generations.

(D) Ferns are known only from the fossil record.

Answer: (B)

27. The IUCN Red List is based on a set of criteria to evaluate species vulnerability to extinction. Which one or more of the options is/are used as criteria?

(A) Absolute population size

(B) Geographic range

(D) Change in population size over time

Answer: (A, B, D)

28. Which one or more of the following processes contribute(s) substantially to increased mean global temperatures?

(A) Decreased greenhouse gases in the atmosphere

(B) Increased tropical deforestation

(D) Increased fossil fuel use

Answer: (B, D)

29. Depending on soil nutrient availability, which one or more of the following interaction(s) can occur between soil mycorrhizal fungi and plants?

(A) Parasitism

(B) Predation

(D) Commensalism

Answer: (A, C, D)

30. Which one or more of the following is/are characteristic of r-selected animals?

(A) They have a long lifespan.

(B) They produce a large number of offspring in each reproductive event.

(D) They reproduce at a young age.

Answer: (B, D)

31. Which one or more of the following represent(s) benefits of Batesian mimicry to the mimic?

(A) Increased toxicity against potential predators

(B) Reduced cooperation

(D) Reduced competition

Answer: (C)

32. Which one or more of the following is/are developmental feature(s) of hatchlings of an altricial bird species?

(A) Eyes open

(B) Eyes closed

(D) Down feathers absent

Answer: (B, D)

33. You have a biased coin with the probability of getting a head being 0.6. The probability of getting at least 1 head in 3 tosses is ____. (Rounded off to three decimal places)

Answer: (0.930 to 0.940)

34. A lake has 20 blue male, 30 red male, 60 blue female and 80 red female fish. A researcher catches one individual at random from the lake. If the caught fish is blue, the probability that it is female is ____________.

(Rounded off to two decimal places)

Answer: (0.74 to 0.76)

35. A researcher fitted a function to data on how foraging rate (F, number of items consumed per 10 minutes) of a shorebird varied with its group size (G, number of individuals) and obtained the following equation:

log_eF = 3 – 0.2 – log_e G

According to this equation, the foraging rate (F) of a solitary forager is ___________ items per 10 minutes.

(Rounded off to the nearest integer)

Answer: (19 to 21)

Q.36 – Q.65 Carry TWO marks Each

36. Two species of birds, A and B, are found together in region X. Only species A is present in region Y. Both species produce species-specific alarm calls in response to a predator P. A researcher conducts experiments where she plays recorded calls of both species to species A in regions X and Y. The response of species A to the recorded calls are summarized in the table below.

Based on the results, the most appropriate inference is that

(A) species A’s response to species B’s alarm call is a learned behavior.

(B) species A’s response to species B’s alarm call is an innate behavior.

(D) predator P exclusively preys on species B.

Answer: (A)

37. The table below lists different insects and taxonomic orders. Choose the option that matches the animal to its correct taxonomic order.

(A) P-ii; Q-i; R-v; S-iv

(B) P-iii; Q-v; R-iv; S-i

(D) P-iv; Q-ii; R-i; S-v

Answer: (C)

38. Islands I, II, and III lie off a mainland coast. Which one of the following statements about species richness is consistent with the theory of island biogeography?

(A) Island II has the highest species richness because it has the lowest area.

(B) Island III has the highest species richness because it is large and farthest from the mainland.

(D) Islands I and III have equally high species richness because they have roughly the same area.

Answer: (C)

39. In a polygynous hummingbird species, males defend and monopolize nectar–rich plants (resource). Females visit these plants for nectar and the defending male will have access to all visiting females for mating. Under which scenario is polygyny expected to be the highest?

(A) Resources are abundant and evenly distributed.

(B) Resources are abundant and clumped.

(D) Resources are scarce and randomly distributed.

Answer: (B)

40. A researcher estimates the relationship between reproductive success (N, number of offspring) and horn length (H, in cm) in a wild goat as

N = 40 – 2.2H + 0.04H²

Horn length typically varies from 10 cm to 50 cm in this species. Which one of the following graphs correctly represents this relationship?

(A) P

(B) Q

(D) S

Answer: (B)

41. Overfishing reduced food availability for sea lions in California, causing a decline in their population size. In 1972, under the US Endangered Species Act, fishing was banned from sea lion foraging areas. Subsequently, the population of sea lions increased in a logistic form as shown in the figure.

The per capita growth rate is highest in the interval ______ and the population growth rate is highest in the interval ____.

(A) I, II

(B) I, III

(D) III, II

Answer: (A)

42. A locus at Hardy-Weinberg equilibrium in a diploid organism has n alleles. The maximum heterozygosity (i.e., proportion of heterozygotes) for this locus is

(A) n

(B) I/n

(D) I – n

Answer: (C)

43. Match the diseases to the pathogens that cause them.

(A) P-i; Q-iii; R-iv

(B) P-iii; Q-i; R-ii

(D) P-iv; Q-i; R-ii

Answer: (C)

44. The production of anthocyanin pigments in pea flowers requires the presence of at least one dominant allele in each of two independently assorting genes, C and P. The presence of anthocyanin results in purple flowers, whereas its absence gives white flowers. A cross between two double heterozygous (CcPp) plants is performed. What is the expected ratio of plants with purple flowers to plants with white flowers?

(A) 1 : 3

(B) 3 : 1

(D) 9 : 7

Answer: (D)

45. In the phylogenetic trees shown, the tips represent different species of geckos (labeled A to E) and the areas to which they belong. Which one of these is most consistent with the hypothesis that the geckos colonized the Western Ghats from Northeast India through the Eastern Ghats?

(A) P

(B) Q

(D) S

Answer: (B)

46. The phylogenetic tree depicts the relationship between 5 species of snakes (labelled A to E) and provides information about their habitat specialization. Given the principle of parsimony (least number of evolutionary changes required) and that ancestor Y was terrestrial, which one of the options given is correct?

(A) X was more likely to be aquatic than terrestrial.

(B) X was more likely to be terrestrial than aquatic.

(D) X was neither aquatic nor terrestrial.

Answer: (C)

47. The mode of speciation in snakes in the Western Ghats is predominantly allopatric. A researcher wants to quantify diversification of snakes in this range. From the options given, choose the most cost and time efficient way to sample snakes.

(A) Across an elevational gradient

(B) Across barriers such as valleys and rivers

(D) Intensively across the entire mountain range

Answer: (B)

48. All else being equal, which one of the following population sizes (N) and migration rates (𝑚) would result in the most genetic differentiation between populations (F_st)?

Note that F_st is computed as

(A) N = 500, m = 1

(B) N = 200, m = 200

(D) N = 40, m = 1

Answer: (D)

49. Which one or more of the following is/are prediction(s) or assumption(s) of the handicap principle for the evolution of sexual signals?

(A) Females prefer costly signals.

(B) Honest signals are costly to produce.

(D) Costly signals are reliable indicators of signaller quality.

Answer: (A, B, D)

50. A research team assesses the impact of the invasive species Lantana camara on the seed set of a native flowering plant S. The plant S usually grows in clumps with other individuals of the same or different flowering species. They measure the seed set of flowering individuals of S grown (i) alone; (ii) with a conspecific (same species); (iii) with a native species Q; (iv) with a native species R; (v) with Lantana camara. The figure below shows the mean seed set with 95% confidence intervals for the different treatments.

Based on the figure provided, which one or more of the options given is/are correct?

(A) Seed set is higher in the presence of both the native species than in the presence of a conspecific.

(B) Seed set is lower in the presence of Lantana camara than in the presence of both the native species.

(D) Seed set is always higher in the presence of other plants than when grown alone.

Answer: (C)

51. There are two palatable prey species, Q and R, for an insectivorous bird species in a forest. However, the bird searches for and consumes only species Q. According to optimal foraging theory, which one or more of the following conditions can explain the bird choosing to forage only for Q?

(A) The handling time for Q > the handling time of R

(B) The handling time for Q < the handling time of R

(D) The relative abundance of Q < the relative abundance of R

Answer: (B, C)

52. Conservation biologists have debated whether protected areas should be designed as a single large patch or as several small patches. Assuming that the total area is the same for the two designs, which one or more of the options describe(s) the conservation benefit(s) of several small patches?

(A) Lower rates of local extinction

(B) Lower rates of diversification

(D) Lower population sizes

Answer: (C)

53. Which one or more options is/are example(s) of niche partitioning between species?

(A) Temporal separation of activity

(B) Diet specialization

(D) Vertical stratification of foraging heights

Answer: (A, B, D)

54. In an assemblage of coexisting wild cat species, the size of canine teeth was found to be strikingly different between these species. Which one or more of the following statements explain(s) this observation?

(A) Differences in the size of canine teeth were driven by the size of prey captured by the different species.

(B) Differences in the size of canine teeth are an example of divergent evolution.

(D) Differences in the size of canine teeth were driven by past competition.

Answer: (A, B, D)

55. The Biological Species Concept (BSC) states that ‘species are groups of interbreeding natural populations that are reproductively isolated from other such groups’. Which one or more of the options could pose challenges for defining species using the BSC?

(A) Fertile interspecies hybrids

(B) Extinct fossil species

(D) Inbreeding depression

Answer: (A, B)

56. The barnacle species, Chthamalus stellatus (CS), is found only in the high intertidal zone whereas Balanus glandula (BG) is found only in the low intertidal zone. A researcher transplanted CS from the high to low (T-CS), and BG from the low to high (T-BG) intertidal zones. Additionally, they allowed the species to grow alone or in competition with each other, and quantified survival.

Which one or more of the following inferences is/are consistent with the experimental results shown below?

(A) Only abiotic conditions increase mortality of BG in the high intertidal zones.

(B) Only abiotic conditions increase mortality of CS in the low intertidal zones.

(D) Interspecific competition increases mortality of CS in the low intertidal zone.

Answer: (A, D)

57. In the figure below, ellipse X represents the combinations of salt concentrations and temperatures that a marine invertebrate species can tolerate. Ellipse Y represents the combinations of salt concentrations and temperatures that this species is actually found in.

Which one or more of the following statements about X and Y is/are correct?

(A) X is the fundamental niche of the species, whereas Y is the realized niche.

(B) The difference between X and Y can result from biotic interactions.

(D) The difference between X and Y results from the species’ tolerance to salt concentrations.

Answer: (A, B, C)

58. A butterfly species inhabits four types of patchy landscapes (P, Q, R, S). Grey shapes represent occupied habitat and white shapes are unoccupied. Arrows represent the occurrence and directions of possible dispersal.

Which one or more of the options is/are likely to be correct?

(A) In landscape Q, patch w is a source population.

(B) Landscape R represents a metapopulation.

(D) Landscape S has the highest level of inbreeding.

Answer: (A, B, C)

59. A new food requesting behaviour has been observed in bonnet macaques in Bandipur National Park. The macaques extend their hand and make a cooing sound only towards humans, which effectively results in food given to them. If this behaviour is to increase in frequency in the population over time by the process of natural selection, which one or more of the options below is/are necessary condition(s)?

(A) Food requesting behaviour must be transmitted from one generation to the next.

(B) All bonnet macaques in the area must show this behaviour.

(D) Food requesting behaviour must only be taught by parents to offspring.

Answer: (A, C)

60. Two co-occurring plant species, A and B, flower at the same time. They are visited by the same pollinator species. If these plants are pollinator-limited, then which one or more of the following statements is/are correct with regard to the figure shown below?

(A) Line 1 represents competition.

(B) Line 2 represents mutualism.

(D) Line 1 represents facilitation.

Answer: (D)

61. Scorpions on the sand dunes in Syria in September 2022 have the age distribution as shown in Figure P. Scorpions can live to a maximum of 90 days. In all the figure panels, the x-axis represents age class and the y-axis represents number of individuals.

Assuming no immigration or emigration, which one or more of the age distribution panels Q, R, S, T is/are possible 30 days later?

(A) Q

(B) R

(D) T

Answer: (A, B)

62. The Shannon-Weaver index H is a measure of diversity and is calculated as

where S is the total number of species and p_i is the proportional abundance of a species i.

The table below gives the abundance of different species in a community. The Shannon-Weaver index of reptile diversity in this community is ___________.

(Rounded off to two decimal places)

Answer: (1.18 to 1.20)

63. In haplodiploid organisms, males are haploid and females are diploid. Consider the relatedness diagram shown below. Female A has a full-sister, Y, who has a daughter, B. The relatedness between A and B is ___________. (Rounded off to three decimal places)

Answer: (0.374 to 0.376)

64. Mixed species flocks of birds include social and solitary species. There are 5 social species and 10 solitary species in a forest. Flocks always have a total of 5 species, of which 2 are social and 3 are solitary. The number of types of flocks with unique species composition is _________. (Answer in integer)

Answer: (1200 to 1200)

65. In a zoo, three lions and four tigers eat 390 kg of food every week. In another zoo, four lions and five tigers eat 500 kg of food every week. Lions and tigers eat different amounts of food, but all individuals of the same species eat the same amount. The amount of food a single lion eats per week is _______ kg. (Answer in integer)

Answer: (50 to 50)

GATE Exam 2023 Environmental Science and Engineering (ES) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

ES: Environmental Science and Engineering

General Aptitude (GA)

Q.1 – Q.5 Carry ONE mark each.

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x2⁻^|x|

(D) f(x) = x2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

We tend to think of cancer as a ‘modern’ illness because its metaphors are so modern. It is a disease of overproduction, of sudden growth, a growth that is unstoppable, tipped into the abyss of no control. Modern cell biology encourages us to imagine the cell as a molecular machine. Cancer is that machine unable to quench its initial command (to grow) and thus transform into an indestructible, self-propelled automaton.

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product

3⁹⁹⁹ × 7¹⁰⁰⁰ is _______.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

ES: Environmental Science and Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Given are two ordinary differential equations

The correct choice is

(A) P is linear; Q is nonlinear

(B) P is nonlinear; Q is linear

(D) Both P and Q are nonlinear

Answer: (B)

12. P and Q are square matrices. Consider the following

X: (P⁻¹)⁻¹ = P

Y: Symmetric if Q = −Q^T

The correct choice is

(A) X is TRUE; Y is FALSE

(B) X is FALSE; Y is TRUE

(D) Both X and Y are FALSE

Answer: (A)

13. Given are two infinite series

The correct choice is

(A) P is convergent series; Q is divergent series

(B) P is divergent series; Q is convergent series

(D) Both P and Q are divergent series

Answer: (D)

14. For testing alkalinity for a water sample, first phenolphthalein indicator is added. The water remains colorless. However, when a few drops of methyl orange is added to the sample, the color turns yellow. As per these observations, the correct choice is

(A) Absence of CO₃^2– and/or HCO₃^– but the presence of OH^– ions in the sample

(B) Presence of CO₃^2– and/or HCO₃^– but the absence of OH^– ions in the sample

(D) Presence of CO₃^2–, HCO₃^– and OH^– ions in the sample

Answer: (B)

15. Read the following statements

(I) Photosynthesis takes place within the chloroplasts of the eukaryotes, whereas the breakdown of complex molecules to yield energy takes place in the cytoplasm and in the mitochondria.

(II) Photosynthesis takes place within the chloroplasts of the prokaryotes, whereas the breakdown of complex molecules to yield energy takes place in the cytoplasm and in the mitochondria.

(III) All living organisms retain the enzymatic machinery to partially oxidise glucose without the help of oxygen. This breakdown of glucose to pyruvic acid is called glycolysis.

(IV) All living organisms retain the enzymatic machinery to completely oxidise glycerol without the help of oxygen. This breakdown of glycerol to citric acid is called glycolysis.

The correct choice is

(A) I and III are correct

(B) II and IV are correct

(D) II is correct whereas IV is incorrect

Answer: (A)

16. Read the following statements

(i) Aerobic heterotrophic bacteria uses organic matter for carbon source and energy source.

(ii) Aerobic heterotrophic bacteria uses carbon dioxide for carbon source and energy source.

(iii) Aerobic autotrophic bacteria uses carbon dioxide for carbon source and reduced substances for energy source.

(iv) Aerobic autotrophic bacteria uses organic matter for getting energy.

The correct choice is

(A) (i) is correct; (iii) is correct

(B) (iv) is correct; (i) is incorrect

(D) (ii) is correct; (iv) is incorrect

Answer: (A)

17. A student wants to decide electron acceptor for aerobic, facultative and anaerobic bacteria. In this context, read the following statements

(i) Dissolved Oxygen (DO) can act as electron acceptor for aerobic bacteria.

(ii) Nitrite can act as electron acceptor for aerobic bacteria.

(iii) Dissolved Oxygen (DO) can act as electron acceptor for anaerobic bacteria.

(iv) Nitrite can act as electron acceptor for facultative bacteria.

The correct choice is

(A) (i) is correct; (iv) is correct

(B) (ii) is correct; (iii) is incorrect

(D) (i) is correct; (ii) is correct

Answer: (A)

18. Which of the following is true according to the Central Pollution Control Board (CPCB), Government of India’s notification issued in the year 2009?

(A) 24 hour averaged standard for PM_2.5 in ambient air is 60 μg/m³; 24 hour averaged standard for PM₁₀ in ambient air is 100 μg/m³

(B) 24 hour averaged standard for PM_2.5 in indoor air is 60 μg/m³; 24 hour averaged standard for PM₁₀ in ambient air is 100 μg/m³

(C) 24 hour averaged standard for PM_2.5 in ambient air is 60 μg/m³; 24 hour averaged standard for PM₁₀ in indoor air is 100 μg/m³

(D) 24 hour averaged standard for PM_2.5 in indoor air is 60 μg/m³; 24 hour averaged standard for PM₁₀ in indoor air is 100 μg/m³

Answer: (A)

19. The sub index values of NO₂, SO₂ and PM₁₀ are 80, 80 and 100, respectively. According to the National Air Quality Index (NAQI) released by the Government of India in the year 2015, the overall NAQI is

(A) 80

(B) 260

(D) 151

Answer: (C)

20. Which of the following is NOT a designated waste category under Bio-medical Waste Management Rules, 2016 of Government of India?

(A) Yellow

(B) Green

(D) Blue

Answer: (B)

21. Consider the following waste categories

(i) Domestic Hazardous Waste

(ii) Nuclear Waste

(iii) Sludge from wet scrubbers of hazardous waste treatment processes

(iv) Chromium bearing residue and sludge from leather tanneries

Which one of the options correctly represents the waste categories NOT covered under Hazardous and Other Wastes (Management and Trans boundary Movement) Rules, 2016 of Government of India?

(A) (i) and (ii) only

(B) (i) and (iii) only

(D) (i), (ii) and (iii) only

Answer: (A)

22. Match the following

(A) P – (iv), Q – (i), R – (iii), S – (ii)

(B) P – (i), Q – (iii), R – (ii), S – (iv)

(D) P – (ii), Q – (iii), R – (iv), S – (i)

Answer: (A)

23. Place the following international conventions/conferences/protocols/declarations in the chronological order (oldest to latest) of their happening

(i) United Nations conference in Stockholm which resulted in the establishment of the United Nations Environmental Program (UNEP)

(ii) Vienna convention for the protection of the Ozone layer

(iii) United Nations climate change conference in Glasgow commonly referred as COP26

(iv) Montreal protocol on phasing out production of substances related to Ozone layer depletion

(A) i, ii, iv, iii

(B) i, ii, iii, iv

(D) iv, iii, ii, i

Answer: (A)

24. The correct ascending order of the following greenhouse gases with respect to their global warming potential relative to CO2 in the time horizon of 100 years is

(A) CH₄ < N₂O < CFCl₃ < CF₂Cl₂

(B) CF₂C_l2 < CH₄ < N₂O < CFCl₃

(D) N₂O < CFCl₃ < CH₄ < CF₂Cl₂

Answer: (A)

25. Read the following statements with reference to the Kyoto Protocol on Climate Change

(i) Each signatory (country) has common and equal responsibility.

(ii) Clean development mechanism (CDM), joint implementation (JI) and international emission trading are the three mechanisms under Kyoto Protocol to reduce the greenhouse gas emissions.

(iii) Under Kyoto Protocol, India has agreed to reduce its greenhouse gas emissions by half by 2050 as compared to 2005 emissions.

Which one of the following is correct choice?

(A) only (i) is TRUE

(B) only (ii) is TRUE

(D) only (ii) and iii) are TRUE

Answer: (B)

26. Read the following statements

(I) In environmental laws, the polluter pays principle is enacted to make the polluter responsible for paying for the damage done to the natural environment.

(II) The precautionary principle emphasizes caution, pausing and review before going for an innovation that may prove disastrous.

(III) The precautionary principle is often used by policy makers in situations where there is the possibility of harm from making a certain decision and conclusive evidence is not yet available.

The correct choice is

(A) I is correct; II and III are incorrect

(B) I, II and III are correct

(D) I and II are correct; III is incorrect

Answer: (B)

27. Read the following statements

(I) The goal of Life Cycle Analysis (LCA) is to assess the environmental impact of products from a system perspective and to identify possible improvement strategies.

(II) Environmental Impact Assessment (EIA) is defined as a process of identifying, predicting, and evaluating the likely impacts of a proposed project or development to define mitigation actions to reduce negative impacts and to provide positive contributions to the natural environment and well-being.

The correct choice is

(A) I is correct; II is incorrect

(B) II is correct; I is incorrect

(D) Both I and II are incorrect

Answer: (C)

28. For the following major Indian environmental acts

(i) Environmental Protection Act

(ii) Water Act (Prevention and Control of Pollution)

(iii) Air Act (Prevention and Control of Pollution)

(iv) The National Green Tribunal Act

the correct chronological order (oldest to latest of their enactment) is

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iii), (iv)

(D) (ii), (iii), (i), (iv)

Answer: (D)

29. The kinematic viscosity of glycerin and kerosene are 1.2 times and 0.95 times of that of water, respectively. Glycerin and kerosene flow through two identical porous media having same hydraulic gradient. Assuming Darcy’s law is valid for the porous media, the ratio of flow rate of kerosene to that of glycerin is

(A) 1.052

(B) 1.140

(D) 1.263

Answer: (D)

30. A researcher compiled the following information about the performance of a kit in an outbreak

Infection state Kit response

Disease (probability = 0.002) Positive response (probability = 0.98)

No Disease Positive response (probability = 0.03)

The probability of detecting an infection for a positive result through the kit would be _____________ (rounded off to three decimal places).

Answer: (0.060 to 0.066)

31. The critical depth in a 2 m wide rectangular channel carrying a discharge of 10 m³/s and taking value of acceleration due to gravity (g) as 9.81 m/s² is __________(in m, rounded off to two decimal places).

Answer: (1.35 to 1.40)

32. The ratio of the moles of CO₂ evolved to the moles of O₂ consumed in respiration also called the respiratory quotient, is calculated for a carbohydrate (C₆H₁₂O₆) as substrate and found to be 1. Under similar conditions, for a fatty acid (C₅₁H₉₈O₆) as substrate, the respiratory quotient is __________ (rounded off to two decimal place).

Answer: (0.65 to 0.75)

33. The value of is _________ (rounded off to two decimal places).

Answer: (1.00 to 1.00)

34. An S-hydrograph was prepared for a catchment of 240 km² using 3-hour unit hydrograph (1 cm rainfall excess). The equilibrium discharge for the S-hydrograph would be _________ (in m³/s, rounded off to two decimal places).

Answer: (220.00 to 225.00)

35. River water containing two types of spherical suspended particles (clay particles, metal particles) is retained in a sedimentation tank. The clay particles having diameter of 75 μm and specific gravity of 2.65 is settling in the tank with a constant velocity. The velocity of clay particles is 2 times of that of metal particles having specific gravity of 8. Assume discrete settling and laminar flow conditions within the sedimentation tank. The estimated diameter of the metal particles is ____________ (in μm, rounded off to integer)

Answer: (24 to 26)

Q.36 – Q.65 Carry TWO marks Each

36. W1, W2, W3…W9 represent the holding times of 9 water samples, which follow a normal distribution with mean = 8.33 and standard deviation = 4.472. M represents the sample mean value of holding times, which also has a normal distribution. Assuming Z has a standard normal distribution (mean = 0 and standard deviation = 1), select the correct statement which describes the expression for calculating the value of type 1 error where

null hypothesis (H0): M > 6

alternate hypothesis (Ha): M ≤ 6

(A) P{Z < (–1.565)}

(B) P{Z < 1.565}

(D) P{Z > 1.565}

Answer: (A)

37. Which one of the following statements is NOT correct?

(A) Photophosphorylation is the synthesis of ATP from ADP and inorganic phosphate in the presence of light.

(B) The process through which ATP is synthesised by cells (in mitochondria and chloroplasts) is called phosphorylation.

(C) The Calvin cycle (carboxylation, reduction, and regeneration) occurs in all photosynthetic plants (C3, C4 or any other).

(D) C3 plants have a special type of leaf anatomy, they tolerate higher temperatures, they show a response to high light intensities, have high rate of photosynthesis and reduced rate of photorespiration as compared to C4 plants.

Answer: (D)

38. Read the following statements

(I) Bacteriophage is an anaerobic bacterium.

(II) Male-specific bacteriophage infect via the pili of other microorganisms including viruses.

(III) Bacteriophage is found in human as well as in animal excreta.

(IV) Bacteriophage can not indicate the presence of bacteria.

The correct choice is

(A) (I), (III) and (IV) are correct

(B) (IV) is correct; (III) is incorrect

(D) Both (III) and (IV) are correct

Answer: (D)

39. Read the following statements

(i) In endogenous metabolism by aerobic bacteria, electron acceptor is present inside the cells.

(ii) In endogenous metabolism by aerobic bacteria, electron acceptor is dissolved oxygen.

(iii) The endogenous metabolism is linked to fermentative metabolism.

(iv) In exogenous metabolism by aerobic bacteria, enzyme mediated electron transfer happens within the cells.

The correct choice is

(A) (i) is correct; (iii) is correct

(B) (ii) is correct; (iii ) is incorrect

(D) (iii) is correct; (iv) is correct

Answer: (A)

40. A boiler in an industry, located where high plume rise is expected, releases flue gas with fine particulate matter. Which one of the following options is most suited and efficient if this particulate matter is intended for reuse?

(A) reduce stack height and increase stack diameter

(B) use of wet collectors

(D) use of electrostatic precipitator (ESP)

Answer: (D)

41. Match the following

(A) J – ii; K – i; L – iv; M – iii

(B) J – iii; K – ii; L – i; M – iv

(D) J – i; K – iv; L – ii; M – iii

Answer: (A)

42. Read the following statements

(I) According to the Liebig’s law of minimum, the growth is regulated by the limited factors i.e., resources in scarcity and not by the resources in abundance.

(II) Shelford’s law of tolerance states that, only the factors present in excess/abundance can affect the growth, development of an organism or rate of biological process.

(III) Shelford’s law of tolerance states that, an organism’s success is based on a complex set of conditions and that each organism has a certain minimum, maximum, and optimum levels of environmental factor or combination of factors that determine success.

The correct choice is

(A) I and II are correct; III is incorrect

(B) I and III are correct; II is incorrect

(D) III is correct; I and II are incorrect

Answer: (B)

43. Read the following statements

(I) Trivalent chromium has relatively low aqueous solubility, and low mobility in the soil environment. By contrast, hexavalent chromium has a higher aqueous solubility and greater mobility in the soil environment.

(II) The chemical reaction between trivalent chromium and zero-valent iron will result in transformed version called hexavalent chromium.

(III) Hexavalent chromium is a known carcinogen.

(IV) Trivalent chromium has relatively higher human toxicity as compared to hexavalent chromium.

The correct choice is

(A) IV is correct; I and III are incorrect

(B) II is correct; I and IV are incorrect

(D) I, II and IV are correct; III is incorrect

Answer: (C)

44. Which of the following statements is/are NOT true?

(A) Urban heat island effect in a city can be reduced by increasing trees and vegetation cover in the city.

(B) Urban heat island intensity is affected by PM2.5 concentrations in a city.

(D) In comparison with the non-urban areas, urban heat island effect raises night-time temperatures more than daytime temperatures in cities.

Answer: (C)

45. Read the following statements about aerobic composting of organic fraction of municipal solid waste

(I) The majority of the odour problem in an aerobic composting process is due to the development of anaerobic conditions within the compost pile.

(II) All organic carbon present in the waste will completely biodegrade in 14 days.

(III) At high C/N ratio, ammonia would be released and biological activity may also be impeded.

(IV) Optimum moisture content for aerobic composting process would be 50–60%. Lower moisture would slow down the biological process. Excessive moisture will make it difficult to maintain aerobic conditions.

The correct choice(s) is/are

(A) I and IV are correct

(B) II and III are incorrect

(D) II is correct; IV is incorrect

Answer: (A, B)

46. Products P and Q have life cycle phases of material extraction, production, use, and end of life disposal. CH₄, CO₂ emissions and mass used per functional unit (f.u.) from the different phases of the products are given in the following tables.

Based upon the information given in the tables and using global warming potential of CH₄ equal to 23 kg of CO₂ per kg of CH₄, which of the following statement(s) is/are true?

(A) Greenhouse gas emissions (kg CO₂ equivalent/f.u.) from the ‘Material extraction’ phase of product P is higher than that of product Q.

(B) Greenhouse gas emissions (kg CO₂ equivalent/f.u.) from the ‘Production phase’ of product Q is higher than that of product P.

(C) Greenhouse gas emissions (kg CO₂ equivalent/f.u.) from the ‘End of life disposal’ is higher for product Q than that of product P.

(D) Greenhouse gas emissions (kg CO₂ equivalent/f.u.) from the ‘complete life cycle’ of the product P is higher than that of product Q.

Answer: (A, B, D)

47. Second order ordinary differential equation has values y = 2 and at x = 0. The value of y at x = 1 is _______ (rounded off to three decimal places).

Answer: (7.700 to 7.800)

48. Consider two matrices If R = (PQ)^T then det R is _________ (in integer).

Answer: (50 to 50)

49. For the function the maximum value in the range −2 ≤ x ≤ 2 is __________ (rounded off to two decimal places).

Answer: (1.9 to 2.1)

50. The solubility of gas A is 16 mg/L in water and its vapor pressure is 0.042 atm. at 25° In a closed system, the gas phase concentration of A is 10⁻³ mol/L. Assuming Ideal gas constant (R) value as 0.0821 L-atm/mol-K, the concentration of gas A in water at 25°C is ________ (in mg/L, rounded off to two decimal places).

Answer: (9.1 to 9.7)

51. The following figure (not to the scale) shows a catchment (Q, S, U, T, Q) and adjoining raingauge stations P, Q, R, S, U and V. Due to a storm, 20 mm, 25 mm, 30 mm, 15 mm, 22 mm and 18 mm rainfall depths were recorded by raingauges at P, Q, R, S, U and V, respectively.

The corresponding mean rainfall over the catchment using Thiessen polygon method is __________ (in mm, rounded off to two decimal places).

Answer: (20.00 to 22.00)

52. A trapezoidal canal lined with cement concrete (n = 0.01) is designed to carry a discharge of 20 m³/s at a bed slope 1 in 400. If the bed width is twice of the depth of flow and side slope of the canal section is 2 (1 vertical:2 horizontal) then the corresponding depth of flow will be ___________ (in m, rounded off to two decimal places).

Answer: (1.00 to 1.20)

53. A plunger weighing 314 kN is balanced in a cylindrical vessel of diameter 1.5 m and filled with an oil (specific gravity 0.9) as shown in the following figure (not to the scale).

If a pressure gauge is connected with the vessel using 1.5 cm diameter tube, the reading of the gauge will be __________ (in kPa, rounded off to two decimal places).

Answer: (162.00 to 166.00)

54. A fully penetrating well is installed in a homogenous and isotropic confined aquifer. The aquifer has uniform thickness of 16 m and hydraulic conductivity of 25 m/d. Water is being pumped out from the well at a constant rate of 0.1 m³/s till steady state condition is reached. If a drawdown of 3.5 m is observed at a distance of 75 m from the well then the drawdown at a distance of 150 m from the well will be __________ (in m, rounded off to two decimal places).

Answer: (1.00 to 1.15)

55. A biological reactor is getting wastewater containing 1 mole/L acetate ions as carbon source. The following reaction takes place in the bio-reactor:

0.125CH₃COO^– + 0.0295NH₄⁺ + 0.103O₂ → 0.0295C₅H₇O₂N + 0.0955H₂O + 0.095HCO₃^– + 0.007CO₂

Assume that all acetate ions are consumed and ammonia serves as a nutrient source. Given that 1 g acetate exerts 1.07 g COD; 1 mole bacteria =113 g VSS; 1 mole acetate ion = 59 g. Value of observed yield is ___________ (in g VSS/g COD, rounded off to two decimal places).

Answer: (0.40 to 0.44)

56. A flask (100 ml volume) has wastewater, which has 0.12 mg/L geosmin. Activated carbon is added in this flask for adsorbing geosmin as per the Freundlich isotherm model (Q = 2.6 × C⁷³ where Q is mg adsorbate/mg adsorbent and C is the equilibrium concentration in mg/L). Activated carbon to be added in this flask for getting final remaining geosmin concentration of 0.05 mg/L would be ___________ (in mg/L, rounded off to three decimal places).

Answer: (0.230 to 0.245)

57. A pipeline is designed to deliver 20 L/s of an oil (kinematic viscosity = 6 × 10^–6 m²/s and specific gravity = 0.9) under the laminar flow condition. The minimum diameter of the pipe will be _______ (in m, rounded off to two decimal places).

Answer: (1.90 to 2.20)

58. You are doing an experiment to find out BOD₅ of a wastewater. You have taken 25 mL wastewater having ultimate BOD of 75 mg/L and placed it in 300 mL BOD bottle and filled it with dilution water. The initial DO of the diluted sample is 6.5 mg/L. On the 5th day, you were not able to measure the DO due to some unavoidable circumstances. However, the DO at the end of the 7th day is found to be 1.25 mg/L. Assume all the experiments are done at the same temperature, and no biodegradable organics are present in the dilution water. The BOD₅ of the wastewater sample is __________ (in mg/L, rounded off to two decimal places).

Answer: (54.4 to 54.8)

59. In a 30 m³ room, a stove in operation consumes wood at the rate of 0.25 kg/h. The inflow and outflow rate of air in the room is the same, i.e. 500 m³/h. This stove emits a VOC species at a rate of 0.2 g/kg-wood. The VOC species gets converted to CO₂ at a rate of 0.4 per hour. Given: (i) the air in the room is completely mixed, (ii) initial concentration of the VOC species in the room is negligible, and (iii) concentration of the VOC species in the air entering the room is negligible. The concentration of the VOC species due to two hours of stove operation in the room is __________ (in μg/m³, rounded off to one decimal place).

Answer: (95 to 100)

60. A city generates on average 1000 metric tonnes/day of municipal solid waste and follows integrated waste management system. 15% of the total waste is recycled, 40% of the total waste is used to produce compost. 25% of the total waste is converted to refuse derived fuel (RDF) with 80% efficiency. Remaining is disposed of in a sanitary landfill. The calorific value of the RDF is 15 MJ/kg, which is further used to generate electricity. The electrical energy that could be generated from the RDF with a thermal to electrical energy conversion efficiency of 20% is ___________ (in MWh/d, rounded off to two decimal places).

Answer: (165.00 to 168.00)

61. An industry with an effective stack height of 80 m emits 1200 g/h of CO. The windrose plotted using the meteorological data at the top of the stack, and the relation between dispersion coefficients and wind direction are given below:

During the maximum duration of the year, the ground level PM_2.5 concentration at the downwind distance of 2 km (at the plume centerline) from the stack is _________ (in μg/m³, rounded off to two decimal places).

Answer: (1.75 to 1.95)

62. Anita uses a BS-IV two wheeler petrol scooter, with a mileage of 50 km/L, to travel 30 km every day. She exchanges this two wheeler with an electric scooter, which consumes electricity at 0.1 kWh/10 km. Assuming the cost of petrol and electricity are fixed at Rs. 90 per L and Rs. 3.5 per kWh, respectively, and maintenance cost of both BS-IV two wheeler and electric scooter is negligible, the operational cost saved in a year by Ms. Anita is _________ (in Rs., in integer).

Answer: (19300 to 19400)

63. Ultimate analysis of a municipal solid waste sample is given below

For 1 kg of the municipal solid waste burnt, assuming that air contains only nitrogen and oxygen, maximum CO₂ emitted is ___________ (in kg, rounded off to three decimal places).

Answer: (1.700 to 1.800)

64. An adult of 65 kg weight and life span of 65 years drinks water for 5 years, which is contaminated with toluene of concentration 0.15 mg/L. For toluene, reference dose is 0.200 mg/kg-d. The person drinks 2 L of water per day. The hazard quotient from the toluene exposure for the adult will be __________ (rounded off to three decimal places).

Answer: (0.022 to 0.024)

65. An aeration tank needs to be installed for the removal of VOC from water, where the required rate of flow of water through the aeration tank is 180,000 m³/d. Permissible limit of VOC in the water is 12 μg/L. The saturation concentration of VOC is 5 μg/L and gas transfer rate constant is 0.40 per second at 25° The initial concentration of VOC in the water is 33 μg/L. The volume of the aeration tank to satisfy the permissible limit of VOC at 25°C is ____________ (in m³, rounded off to two decimal places).

Answer: (7.1 to 7.3)

GATE Exam 2023 Electrical Engineering (EE) Question Paper With Answer Key

August 2, 2023 by suresh84

GATE-2023

EE: Electrical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark Each

1. Rafi told Mary, “I am thinking of watching a film this weekend.”

The following reports the above statement in indirect speech:

Rafi told Mary that he _______ of watching a film that weekend.

(A) thought

(B) is thinking

(D) was thinking

Answer: (D)

2. Permit : _______ : : Enforce : Relax

(By word meaning)

(A) Allow

(B) Forbid

(D) Reinforce

Answer: (B)

(A) 1/36

(B) 1/6

(D) 1/3

Answer: (A)

4. A recent survey shows that 65% of tobacco users were advised to stop consuming tobacco. The survey also shows that 3 out of 10 tobacco users attempted to stop using tobacco.

Based only on the information in the above passage, which one of the following options can be logically inferred with certainty?

(A) A majority of tobacco users who were advised to stop consuming tobacco made an attempt to do so.

(B) A majority of tobacco users who were advised to stop consuming tobacco did not attempt to do so.

(D) Approximately 65% of tobacco users successfully stopped consuming tobacco.

Answer: (B)

5. How many triangles are present in the given figure?

(A) 12

(B) 16

(D) 24

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences.

(ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time.

(iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.

(A) (i) and (ii)

(B) (i) and (iii)

(D) only (iii)

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x² 2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x 2⁻^x

Answer: (B)

8. Which one of the options does NOT describe the passage below or follow from it?

[Adapted from The Emperor of All Maladies by Siddhartha Mukherjee]

(A) It is a reflection of why cancer seems so modern to most of us.

(B) It tells us that modern cell biology uses and promotes metaphors of machinery.

(D) Modern cell biology never uses figurative language, such as metaphors, to describe or explain anything.

Answer: (D)

9. The digit in the unit’s place of the product 3⁹⁹⁹ × 7¹⁰⁰⁰ is _______.

(A) 7

(B) 1

(D) 9

Answer: (A)

10. A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the square, as shown.

The area of the shaded region is _______ cm².

(A) 6π

(B) 18

(D) 9π

Answer: (B)

EE: Electrical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. For a given vector w = [1 2 3]^T, the vector normal to the plane defined by w^Tx = 1 is

(A) [−2 −2 2]^T

(B) [3 0 −1]^T

(D) [1 2 3]^T

Answer: (D)

12. For the block diagram shown in the figure, the transfer function Y(s)/R(s) is

Answer: (B)

13. In the Nyquist plot of the open-loop transfer function corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at

(A) G(s)H(s) = ∞

(B) G(s)H(s) = 0

(D) G(s)H(s) = −5

Answer: (C)

14. Consider a unity-gain negative feedback system consisting of the plant G(s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are

(A) ∞, ∞

(B) 1, 0

(D) -1, 1

Answer: (D)

15. The following columns present various modes of induction machine operation and the ranges of slip

The correct matching between the elements in column A with those of column B is

(A) a-r, b-p, and c-q

(B) a-r, b-q, and c-p

(D) a-q, b-p, and c-r

Answer: (A)

16. A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is

(A) 100 Hz

(B) 95 Hz

(D) 5 Hz

Answer: (B)

17. A continuous-time system that is initially at rest is described by where x(t) is the input voltage and y(t) is the output voltage. The impulse response of the system is

(A) 3e⁻^2t

(B)

(D) 2e⁻^3t

Answer: (C)

18. The Fourier transform X(ω) of the signal x(t) is given by

X(ω) = 1, for |ω| < W₀

= 0, for |ω| > W₀

Which one of the following statements is true?

(A) x(t) tends to be an impulse as W₀ → ∞

(B) x(0) decreases as W₀ increases.

(C)

(D)

Answer: (A)

19. The 𝑍-transform of a discrete signal x[n] is

with ROC = R.

Which one of the following statements is true?

(A) Discrete-time Fourier transform of x[n] converges if R is |z| > 3

(B) Discrete-time Fourier transform of x[n] converges if R is

(D) Discrete-time Fourier transform of x[n] converges if R is such that x[n] is a right-sided sequence

Answer: (B)

20. For the three-bus power system shown in the figure, the trip signals to the circuit breakers B₁ to B₉ are provided by overcurrent relays R₁ to R₉, respectively, some of which have directional properties also. The necessary condition for the system to be protected for short circuit fault at any part of the system between bus 1 and the R-L loads with isolation of minimum portion of the network using minimum number of directional relays is

(A) R₃ and R₄ are directional overcurrent relays blocking faults towards bus 2

(B) R₃ and R₄ are directional overcurrent relays blocking faults towards bus 2 and R₇ is directional overcurrent relay blocking faults towards bus 3

(C) R₃ and R₄ are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively, R₇ is directional overcurrent relay blocking faults towards Line 3 and R5 is directional overcurrent relay blocking faults towards bus 2

(D) R₃ and R₄ are directional overcurrent relays blocking faults towards Line 1 and Line 2, respectively.

Answer: (A)

21. The expressions of fuel cost of two thermal generating units as a function of the respective power generation PG1 and PG2 are given as

where a is a constant. For a given value of a, optimal dispatch requires the total load of 290 MW to be shared as PG1 = 175 MW and PG2 = 115 MW. With the load remaining unchanged, the value of a is increased by 10% and optimal dispatch is carried out. The changes in PG1 and the total cost of generation, F (= F₁ + F₂) in Rs/hour will be as follows

(A) PG1 will decrease and F will increase

(B) Both PG1 and F will increase

(D) Both PG1 and F will decrease

Answer: (A)

22. The four stator conductors (A, Aʹ, B and Bʹ) of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils a-aʹ and b-bʹ are formed by connecting the back ends of conductors ‘a’ and ‘aʹ’ and ‘b’ and ‘bʹ’, respectively, as shown in figure (ii). The e.m.f. induced in coil a-aʹ and coil b-bʹ are denoted by Ea-aʹ and Eb-bʹ, respectively. If the rotor is rotated at uniform angular speed ω rad/s in the clockwise direction then which of the following correctly describes the E_a-aʹ and E_b-bʹ ?

(A) E_a-aʹ and E_b-bʹ have finite magnitudes and are in the same phase

(B) E_a-aʹ and E_b-bʹ have finite magnitudes with E_b-bʹ leading E_a-aʹ

(D) E_a-aʹ = E_b-bʹ = 0

Answer: (D)

23. The chopper circuit shown in figure (i) feeds power to a 5 A DC constant current source. The switching frequency of the chopper is 100 kHz. All the components can be assumed to be ideal. The gate signals of switches S₁ and S₂ are shown in figure (ii). Average voltage across the 5 A current source is

(A) 10 V

(B) 6 V

(D) 20 V

Answer: (B)

24. In the figure, the vectors u and v are related as: Au = v by a transformation matrix A. The correct choice of A is

Answer: (A)

25. One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation σ₀.

The σ₀ is estimated by randomly drawing out 10,000 numbers of samples (x_n). The estimates are computed in the following two ways.

Which of the following statements is true?

Answer: (C)

26. A semiconductor switch needs to block voltage V of only one polarity (V > 0) during OFF state as shown in figure (i) and carry current in both directions during ON state as shown in figure (ii). Which of the following switch combination(s) will realize the same?

Answer: (A, D)

27. Which of the following statement(s) is/are true?

(A) If an LTI system is causal, it is stable

(B) A discrete time LTI system is causal if and only if its response to a step input u[n] is 0 for n < 0

(D) If the impulse response 0 < |h[n]| < 1 for all n, then the LTI system is stable.

Answer: (B)

28. The bus admittance (Y_bus) matrix of a 3-bus power system is given below.

Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

(A) Line charging capacitor of finite value is present in all three lines

(B) Line charging capacitor of finite value is present in line 2-3 only

(C) Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 1 only

(D) Line charging capacitor of finite value is present in line 2-3 only and shunt capacitor of finite value is present in bus 3 only

Answer: (A, C)

29. The value of parameters of the circuit shown in the figure are

R₁ = 2Ω, R₂ = 2 Ω, R3 = 3 Ω, L = 10 mH, C = 100 μF

For time t < 0, the circuit is at steady state with the switch ‘K’ in closed condition. If the switch is opened at t = 0, the value of the voltage across the inductor (V_L) at t = 0+ in Volts is ____________ (Round off to 1 decimal place).

Answer: (7.9 to 8.1)

30. A separately excited DC motor rated 400 V, 15 A, 1500 RPM drives a constant torque load at rated speed operating from 400 V DC supply drawing rated current. The armature resistance is 1.2 Ω. If the supply voltage drops by 10% with field current unaltered then the resultant speed of the motor in RPM is ___________ (Round off to the nearest integer).

Answer: (1340 to 1345)

31. For the signals x(t) and y(t) shown in the figure, z(t) = x(t) ∗ y(t) is maximum at t = T₁. Then T₁ in seconds is __________ (Round off to the nearest integer).

Answer: (4 to 4)

32. For the circuit shown in the figure, V₁ = 8 V, DC and I1 = 8 A, DC. The voltage V_ab in Volts is _________ (Round off to 1 decimal place).

Answer: (5.9 to 6.1)

33. A 50 Hz, 275 kV line of length 400 km has the following parameters:

Resistance, R = 0.035 Ω/km;

Inductance, L = 1 mH /km;

Capacitance, C = 0.01 μF/km;

The line is represented by the nominal-π model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by V_S and V_R, respectively) maintained at 275 kV, the phase angle difference (θ) between VS and VR required for maximum possible active power to be delivered to the receiving end, in degree is ____________ (Round off to 2 decimal places).

Answer: (83 to 84)

34. In the following differential equation, the numerically obtained value of y(t), at t =1, is _______________ (Round off to 2 decimal places).

Answer: (0.48 to 0.52)

35. Three points in the x-y plane are (-1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is ___________ (Round off to 2 decimal places).

Answer: (0.9 to 1.1)

Q.36 – Q.65 Carry TWO marks Each

36. The magnitude and phase plots of an LTI system are shown in the figure. The transfer function of the system is

(A) 2.51e⁻^0.032s

(B)

(D) 2.51e⁻^1.047s

Answer: (D)

37. Consider the OP AMP based circuit shown in the figure. Ignore the conduction drops of diodes D₁ and D₂. All the components are ideal and the breakdown voltage of the Zener is 5 V. Which of the following statements is true?

(A) The maximum and minimum values of the output voltage V_O are +15 V and -10 V, respectively.

(B) The maximum and minimum values of the output voltage V_O are +5 V and -15 V, respectively.

(D) The maximum and minimum values of the output voltage V_O are +5 V and -10 V, respectively.

Answer: (D)

38. Consider a lead compensator of the form

The frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of K(s), is 6 dB. The values of α, β, respectively, are

(A) 1, 16

(B) 2, 4

(D) 2.66, 2.25

Answer: (B)

39. 3-phase, star-connected, balanced load is supplied from a 3-phase, 400 V (rms), balanced voltage source with phase sequence R-Y-B, as shown in the figure. If the wattmeter reading is −400 W and the line current is I_R = 2 A (rms), then the power factor of the load per phase is

(A) Unity

(B) 0.5 leading

(D) 0.707 lagging

Answer: (C)

40. An 8 bit ADC converts analog voltage in the range of 0 to +5 V to the corresponding digital code as per the conversion characteristics shown in figure. For V_in = 1.9922 V, which of the following digital output, given in hex, is true ?

(A) 64H

(B) 65H

(D) 67H

Answer: (C)

41. The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude |V₃| =1.0 p.u. and angle of −15°. A variable current source, |I|∠ϕ is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, where θ₁ is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as

Answer: (D)

42. Consider the following equation in a 2-D real-space.

|x₁|^p + |x₂|^p = 1 for p > 0

Which of the following statement(s) is/are true.

(A) When p = 2, the area enclosed by the curve is π.

(B) When p tends to ∞, the area enclosed by the curve tends to 4.

(D) When p = 1, the area enclosed by the curve is 2.

Answer: (A, B, D)

43. In the figure, the electric field E and the magnetic field B point to x and z directions, respectively, and have constant magnitudes. A positive charge ‘q’ is released from rest at the origin. Which of the following statement(s) is/are true.

(A) The charge will move in the direction of z with constant velocity.

(B) The charge will always move on the y-z plane only.

(D) The charge will progress in the direction of y.

Answer: (MTA)

44. All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?

(A) When switch S is ON, both D₁ and D₂ conducts and D₃ is reverse biased

(B) When switch S is ON, D₁ conducts and both D₂ and D₃ are reverse biased

(D) When switch S is OFF, D₁ conducts, D₂ is reverse biased and D₃ conducts

Answer: (B, C)

45. The expected number of trials for first occurrence of a “head” in a biased coin is known to be 4. The probability of first occurrence of a “head” in the second trial is __________ (Round off to 3 decimal places).

Answer: (0.187 to 0.188)

46. Consider the state-space description of an LTI system with matrices

For the input, sin(ωt), ω > 0, the value of ω for which the steady-state output of the system will be zero, is ___________ (Round off to the nearest integer).

Answer: (2 to 2)

47. A three-phase synchronous motor with synchronous impedance of 0.1 + j0.3 per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per unit is ___________ (Round off to 2 decimal places).

Answer: (1.58 to 1.59)

48. A three phase 415 V, 50 Hz, 6-pole, 960 RPM, 4 HP squirrel cage induction motor drives a constant torque load at rated speed operating from rated supply and delivering rated output. If the supply voltage and frequency are reduced by 20%, the resultant speed of the motor in RPM (neglecting the stator leakage impedance and rotational losses) is _________ (Round off to the nearest integer).

Answer: (760 to 760)

49. The period of the discrete-time signal x[n] described by the equation below is N = _____________ (Round off to the nearest integer).

Answer: (48 to 48)

50. The discrete-time Fourier transform of a signal x[n] is X(Ω)=(1 + cos Ω)e^−jΩ. Consider that xp[n] is a periodic signal of period N = 5 such that

X_p[n] = x[n], for n = 0, 1, 2

= 0, for n = 3, 4

Note that The magnitude of the Fourier series coefficient 𝑎3 is ____________ (Round off to 3 decimal places).

Answer: (0.037 to 0.039)

51. For the circuit shown, if 𝑖=𝑠𝑖𝑛1000𝑡, the instantaneous value of the Thevenin’s equivalent voltage (in Volts) across the terminals a-b at time t = 5 ms is __________ (Round off to 2 decimal places).

Answer: (-12.1 to -11.9)

52. The admittance parameters of the passive resistive two-port network shown in the figure are

y₁₁ = 5 S, y₂₂ = 1 S, y₁₂ = y₂₁ = −2.5 S

The power delivered to the load resistor RL in Watt is ________ (Round off to 2 decimal places).

Answer: (237 to 239)

53. When the winding c-d of the single-phase, 50 Hz, two winding transformer is supplied from an AC current source of frequency 50 Hz, the rated voltage of 200 V (rms), 50 Hz is obtained at the open-circuited terminals a-b. The cross sectional area of the core is 5000 mm² and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is B_max = 1 Wb/m² and the relative permeability of the core material is 5000. The leakage impedance of the winding a-b and winding c-d at 50 Hz are (5 + j100π × 0.16) Ω and (11.25 + j100π × 0.36) Ω, respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is __________ (Round off to 1 decimal place).

Answer: (2150 to 2250)

54. The circuit shown in the figure is initially in the steady state with the switch K in open condition and in closed condition. The switch K is closed and is opened simultaneously at the instant t = t₁, where t₁ > 0. The minimum value of t₁ in milliseconds, such that there is no transient in the voltage across the 100°F capacitor, is ___________ (Round off to 2 decimal places).

Answer: (1.56 to 1.58)

55. The circuit shown in the figure has reached steady state with thyristor ‘T’ in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned ON at t = 0 sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _____ (Round off to 2 decimal places).

Answer: (7.1 to 7.5)

56. Neglecting the delays due to the logic gates in the circuit shown in figure, the decimal equivalent of the binary sequence [ABCD] of initial logic states, which will not change with clock, is _________.

Answer: (8 to 8)

57. In a given 8-bit general purpose micro-controller there are following flags. C-Carry, A-Auxiliary Carry, O-Overflow flag, P-Parity (0 for even, 1 for odd) R0 and R1 are the two general purpose registers of the micro-controller. After execution of the following instructions, the decimal equivalent of the binary sequence of the flag pattern [CAOP] will be ________.

MOV R0, +0x60

MOV R1, +0x46

ADD R0, R1

Answer: (2 to 2)

58. The single phase rectifier consisting of three thyristors T₁, T₂, T₃ and a diode D₁ feed power to a 10 A constant current load. T₁ and T₃ are fired at α = 60° and T₂ is fired at α = 240°. The reference for α is the positive zero crossing of Vin. The average voltage V_O across the load in volts is _____ (Round off to 2 decimal places).

Answer: (39 to 40.5)

59. The Zener diode in circuit has a breakdown voltage of 5 V. The current gain β of the transistor in the active region in 99. Ignore base-emitter voltage drop V_BE. The current through the 20 Ω resistance in milliamperes is ________(Round off to 2 decimal places).

Answer: (245 to 255)

60. The two-bus power system shown in figure (i) has one alternator supplying a synchronous motor load through a Y-Δ transformer. The positive, negative and zero-sequence diagrams of the system are shown in figures (ii), (iii) and (iv), respectively. All reactances in the sequence diagrams are in p.u. For a bolted line-to-line fault (fault impedance = zero) between phases ‘b’ and ‘c’ at bus 1, neglecting all pre-fault currents, the magnitude of the fault current (from phase ‘b’ to ‘c’) in p.u. is ___________ (Round off to 2 decimal places).

Answer: (7.1 to 7.3)

61. An infinite surface of linear current density exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1, 1 ,1) due to the surface current in Ampere/meter is _______ (Round off to 2 decimal places).

Answer: (2.49 to 2.51)

62. The closed curve shown in the figure is described by

r = 1 + cos θ, where x = r cos θ, y = r sin θ

The magnitude of the line integral of the vector field around the closed curve is __________ (Round off to 2 decimal places).

Answer: (9 to 10)

63. A signal x(t) = 2cos(180πt) cos (60πt) is sampled at 200 Hz and then passed through an ideal low pass filter having cut-off frequency of 100 Hz.

The maximum frequency present in the filtered signal in Hz is _____________ (Round off to the nearest integer).

Answer: (80 to 80)

64. A balanced delta connected load consisting of the series connection of one resistor (R = 15 Ω) and a capacitor (C = 212.21 μF) in each phase is connected to three-phase, 50 Hz, 415 V supply terminals through a line having an inductance of L = 31.83 mH per phase, as shown in the figure. Considering the change in the supply terminal voltage with loading to be negligible, the magnitude of the voltage across the terminals V_AB in Volts is ____________ (Round off to the nearest integer).

Answer: (414 to 416)

65. A quadratic function of two variables is given as

The magnitude of the maximum rate of change of the function at the point (1,1) is _________ (Round off to the nearest integer).

Answer: (10 to 10)

GATE Exam 2023 Electronics and Communication Engineering (EC) Question Paper With Answer Key

August 1, 2023 by suresh84

GATE-2023

EC: Electronics and Communications Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “I cannot support this proposal. My ________ will not permit it.”

(A) conscious

(B) consensus

(D) consent

Answer: (C)

2. Courts : _______ : : Parliament : Legislature

(By word meaning)

(A) Judiciary

(B) Executive

(D) Legal

Answer: (A)

3. What is the smallest number with distinct digits whose digits add up to 45?

(A) 123555789

(B) 123457869

(D) 99999

Answer: (C)

4. In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies,

(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and

(iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

(A) 40

(B) 20

(D) 30

Answer: (C)

5. How many rectangles are present in the given figure?

(A) 8

(B) 9

(D) 12

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A) All creatures with claws are animals.

(B) Some creatures with claws are non-ferocious.

(D) Some ferocious creatures are creatures with claws.

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x² 2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x 2⁻^x

Answer: (A)

8. Which one of the following options can be inferred from the given passage alone?

When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.

[Excerpt from The Truth about Stories by T. King]

(A) It is a child’s description of what he or she likes.

(B) It is an adult’s memory of what he or she liked as a child.

(D) It teaches us that stories are good for children.

Answer: (B)

9. Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.

(ii) Mix the samples within each set and test the mixed sample for covid.

(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.

(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A) 700

(B) 600

(D) 1000

Answer: (A)

10. A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm × 1 cm.

The total number of creases visible when the sheet is unfolded is _______.

(A) 32

(B) 5

(D) 63

Answer: (C)

EC: Electronics and Communications Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Let be two vectors. The value of the coefficient α in the expression v₁ = αv₂ + e, which minimizes the length of the error vector e, is

(A) 7/2

(B) −2/7

(D) −7/2

Answer: (C)

12. The rate of increase, of a scalar field f(x, y, z) = xyz, in the direction v = (2, 1, 2) at a point (0,2,1) is

(A) 2/3

(B) 4/3

(D) 4

Answer: (B)

13. Let w⁴ = 16j. Which of the following cannot be a value of w?

(A) 2e^j2^π^/8

(B) 2e^j^π^/8

(D) 2e^j9^π^/8

Answer: (A)

14. The value of the contour integral, where the contour C is taken in the counter clockwise direction, is

(A) –π(1 + j)

(B) π(1 + j)

(D) –π(1 – j)

Answer: (B)

15. Let the sets of eigenvalues and eigenvectors of a matrix B be {λ_k |1 ≤ k ≤ n} and {v_k | 1 ≤ k ≤ n}, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where B = P⁻¹ AP, respectively, are

(A) {λ_k det(A) | 1 ≤ k ≤ n} and {Pv_k | 1 ≤ k ≤ n}

(B) {λ_k | 1 ≤ k ≤ n} and {v_k | 1 ≤ k ≤ n}

(D) {λ_k | 1 ≤ k ≤ n} and {P⁻¹v_k | 1 ≤ k ≤ n}

Answer: (C)

16. In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

(A) degenerate n-type.

(B) degenerate p-type.

(D) non-degenerate p-type.

Answer: (A)

17. For an intrinsic semiconductor at temperature T = 0 K, which of the following statement is true?

(A) All energy states in the valence band are filled with electrons and all energy states in the conduction band are empty of electrons.

(B) All energy states in the valence band are empty of electrons and all energy states in the conduction band are filled with electrons.

(D) All energy states in the valence and conduction band are filled with electrons.

Answer: (A)

18. A series RLC circuit has a quality factor Q of 1000 at a center frequency of 10⁶ rad/s. The possible values of R, L and C are

(A) R = 1 Ω, L = 1 μH and C = 1 μF

(B) R = 0.1 Ω, L = 1 μH and C = 1 μF

(D) R = 0.001 Ω, L = 1 μH and C = 1 μF

Answer: (D)

19. For a MOS capacitor, V_fb and V_t are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width (W_dep) for varying gate voltage (V_g) is best represented by

Answer: (B)

20. Consider a narrow band signal, propagating in a lossless dielectric medium (ε_r = 4, μ_r = 1), with phase velocity v_p and group velocity v_g. Which of the following statement is true? (c is the velocity of light in vacuum.)

(A) v_p > c, v_g > c

(B) v_p < c, v_g > c

(D) v_p < c, v_g < c

Answer: (D)

21. In the circuit shown below, V₁ and V₂ are bias voltages. Based on input and output impedances, the circuit behaves as a

(A) voltage controlled voltage source.

(B) voltage controlled current source.

(D) current controlled current source.

Answer: (D)

22. A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when

(A) the closed loop gain is less than 1 and the phase shift is less than 180°.

(B) the closed loop gain is greater than 1 and the phase shift is less than 180°.

(D) the closed loop gain is greater than 1 and the phase shift is greater than 180°.

Answer: (MTA)

23. In the circuit shown below, P and Q are the inputs. The logical function realized by the circuit shown below is

(A) Y = PQ

(B) Y = P + Q

(C)

(D)

Answer: (A)

24. The synchronous sequential circuit shown below works at a clock frequency of 1 GHz. The throughput, in Mbits/s, and the latency, in ns, respectively, are

(A) 1000, 3

(B) 333.33, 1

(D) 333.33, 3

Answer: (A)

25. The open loop transfer function of a unity negative feedback system is where k₁, T₁ and T₂ are positive constants. The phase cross-over frequency, in rad/s, is

Answer: (A)

26. Consider a system with input x(t) and output y(t) = x(e^t). The system is

(A) Causal and time invariant.

(B) Non-causal and time varying.

(D) Non-causal and time invariant.

Answer: (B)

27. Let m(t) be a strictly band-limited signal with bandwidth B and energy E. Assuming ω₀ = 10B, the energy in the signal m(t) cos ω₀t is

(A) E/4

(B) E/2

(D) 2E

Answer: (B)

28. The Fourier transform X(ω) of is

Answer: (C)

29. In the table shown below, match the signal type with its spectral characteristics.

(A) (i) → (a), (ii) → (b), (iii) → (c), (iv) → (d)

(B) (i) → (a), (ii) → (c), (iii) → (b), (iv) → (d)

(D) (i) → (a), (ii) → (c), (iii) → (d), (iv) → (b)

Answer: (B)

30. For a real signal, which of the following is/are valid power spectral density/densities?

(A)

(B)

(C)

(D)

Answer: (A, B)

31. The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is ________ bits (rounded off to the nearest integer).

Answer: (10 to 10)

32. In the circuit shown below, the current i flowing through 200 Ω resistor is ______ mA (rounded off to two decimal places).

Answer: (1.30 to 1.40)

33. For the two port network shown below, the [Y]-parameters is given as

The value of load impedance Z_L, in Ω, for maximum power transfer will be _______ (rounded off to the nearest integer).

Answer: (80 to 80)

34. For the circuit shown below, the propagation delay of each NAND gate is 1 ns. The critical path delay, in ns, is __________ (rounded off to the nearest integer).

Answer: (02 to 02)

35. In the circuit shown below, switch S was closed for a long time. If the switch is opened at 𝑡 = 0, the maximum magnitude of the voltage VR, in volts, is _________ (rounded off to the nearest integer).

Answer: (04 to 04)

Q.36 – Q.65 Carry TWO marks Each

36. A random variable X, distributed normally as N(0, 1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is

(In the options given below, a, b, c are non-zero constants and g(y) is piece-wise continuous function)

(A) aδ(y – 1) + bδ(y + 1) + g(y)

(B) aδ(y + 1) + bδ(y) + cδ(y – 1) + g(y)

(D) aδ(y + 2) + bδ(y – 2) + g(y)

Answer: (B)

37. The value of the line integral along the straight line joining the points P(1, 1, 2) and Q(2, 3, 1) is

(A) 20

(B) 24

(D) -5

Answer: (B)

38. Let x be an n × 1 real column vector with length The trace of the matrix P = xx^T is

(A) l²

(B) l²/4

(D) l²/2

Answer: (A)

39. The v_OUT/v_IN of the circuit shown below is

(A) –R₄/R₃

(B) R₄/R₃

(D) 1 – R₄/R₃

Answer: (A)

40. In the circuit shown below, D₁ and D₂ are silicon diodes with cut-in voltage of 0.7 V. V_IN and V_OUT are input and output voltages in volts. The transfer characteristic is

Answer: (A)

41. A closed loop system is shown in the figure where k > 0 and α > 0. The steady state error due to a ramp input (R(s) = α/s²) is given by

(A) 2α/k

(B) α/k

(D) α/4k

Answer: (A)

42. In the following block diagram, R(s) and D(s) are two inputs. The output Y(s) is expressed as Y(s) = G₁(s)R(s) + G₂(s)D(s).

G₁(s) and G₂(s) are given by

Answer: (A)

43. The state equation of a second order system is

is the initial condition.

Suppose λ₁ and λ₂ are two distinct eigenvalues of A and v₁ and v₂ are the corresponding eigenvectors. For constants α₁ and α₂, the solution, x(t) of the state equation is

Answer: (A)

44. The switch S₁ was closed and S₂ was open for a long time. At t = 0, switch S₁ is opened and S₂ is closed, simultaneously. The value of i_c(0⁺), in amperes, is

(A) 1

(B) −1

(D) 0.8

Answer: (B)

45. Let a frequency modulated (FM) signal where m(t) is a message signal of bandwidth W. It is passed through a non-linear system with output y(t) = 2x(t) + 5(x(t))². Let BT denote the FM bandwidth. The minimum value of ω_c required to recover x(t) from y(t) is

(A) B_T + W

(B)

(D)

Answer: (B)

46. The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain V_out/V_s is

(A) h₁₁ = 0, h₁₂ = 0, h₂₁ = very high and h₂₂ = 0

(B) h₁₁ = very high, h₁₂ = 0, h₂₁ = very high and h₂₂ = 0

(D) h₁₁ = 0, h₁₂ = 0, h₂₁ = very high and h₂₂ = very high

Answer: (MTA)

47. Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be where a₀ = 1, a₁ = 3j, a₂ = 2j, a₃ = −2j and a₄ = − The value of the sum is

(A) −10

(B) 10

(D) 2

Answer: (A)

48. Let an input x[n] having discrete time Fourier transform X(e^j^Ω) = 1 – e⁻^j^Ω + 2e⁻^3j^Ω be passed through an LTI system. The frequency response of the LTI system is The output y[n] of the system is

Answer: (C)

49. Let x(t) = 10 cos(10.5 Wt) be passed through an LTI system having impulse response The output of the system is

Answer: (A)

50. Let x₁(t) and x₂(t) be two band-limited signals having bandwidth B = 4π × 10³ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

(A) 20π × 10³

(B) 40π × 10³

(D) 32π × 10³

Answer: (D)

51. The S-parameters of a two port network is given as with reference to Z₀. Two lossless transmission line sections of electrical lengths θ₁ = βl₁ and θ₂ = βl₂ are added to the input and output ports for measurement purposes, respectively. The S-parameters [Sꞌ] of the resultant two port network is

Answer: (A)

52. The standing wave ratio on a 50 Ω lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. Z_L can be replaced by an equivalent length l_m and terminating resistance R_m of the same line. The value of R_m and l_m, respectively, are

(A) R_m = 100 Ω, l_m = 20 cm

(B) R_m = 25 Ω, l_m = 20 cm

(D) R_m = 25 Ω, l_m = 5 cm

Answer: (B, C)

53. The electric field of a plane electromagnetic wave is

E = a_xC_1xcos(ωt – βz) + a_yC_1ycos(ωt – βz + θ) V/m.

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

(A) C_1x = 1, C_1y = 1, θ = π/4

(B) C_1x = 2, C_1y = 1, θ = π/2

(D) C_1x = 2, C_1y = 1, θ = 3π/4

Answer: (A, B, D)

54. The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

Answer: (B, C, D)

55. The value of the integral over the region R, given in the figure, is ________ (rounded off to the nearest integer).

Answer: (0 to 0)

56. In an extrinsic semiconductor, the hole concentration is given to be 1.5n_i where n_i is the intrinsic carrier concentration of 1 × 10¹⁰ cm⁻³. The ratio of electron to hole mobility for equal hole and electron drift current is given as __________ (rounded off to two decimal places).

Answer: (2.20 to 2.30)

57. The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is where k, z, p, a, b and c are positive constants. The value (a + b + c) is _______ (rounded off to the nearest integer).

Answer: (4 to 4)

58. Let x₁(t) = u(t + 1.5) − u(t − 1.5) and x₂(t) is shown in the figure below. For y(t) = x₁(t) ∗ x₂(t), the is __________ (rounded off to the nearest integer).

Answer: (15 to 15)

59. Let X(t) be a white Gaussian noise with power spectral density If X(t) is input to an LTI system with impulse response e⁻^tu(t). The average power of the system output is _________ W (rounded off to two decimal places).

Answer: (0.24 to 0.26)

60. A transparent dielectric coating is applied to glass (ε_r = 4, μ_r = 1) to eliminate the reflection of red light (λ₀ = 0.75 μm). The minimum thickness of the dielectric coating, in μm, that can be used is ________ (rounded off to two decimal places).

Answer: (0.12 to 0.14)

61. In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band at T = 300 K is 1 × 10¹⁹cm⁻³. The thermal equilibrium hole concentration in silicon at 400 K is ____________ × 10¹³cm⁻³ (rounded off to two decimal places).

Given kT at 300 K is 0.026 eV.

Answer: (60.00 to 70.00)

62. A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 μs. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is _______ μs (rounded off to two decimal places).

Answer: (8.30 to 8.34)

63. In a given sequential circuit, initial states are Q₁ = 1 and Q₂ = 0. For a clock frequency of 1 MHz, the frequency of signal Q₂ in kHz, is ___________ (rounded off to the nearest integer).

Answer: (250 to 250 OR 500 to 500)

64. In the circuit below, the voltage V_L is ____________ V (rounded off to two decimal places).

Answer: (2.00 to 2.00)

65. The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of “yes/no” questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______ (rounded off to two decimal places).

Answer: (1.97 to 1.99)

GATE Exam 2023 Chemistry (CY) Question Paper With Answer Key

August 1, 2023 by suresh84

GATE-2023

CY: Chemistry

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “I cannot support this proposal. My ________ will not permit it.”

(A) conscious

(B) consensus

(D) consent

Answer: (C)

2. Courts : _______ : : Parliament : Legislature

(By word meaning)

(A) Judiciary

(B) Executive

(D) Legal

Answer: (A)

3. What is the smallest number with distinct digits whose digits add up to 45?

(A) 123555789

(B) 123457869

(D) 99999

Answer: (C)

4. In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies,

(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and

(iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

(A) 40

(B) 20

(D) 30

Answer: (C)

5. How many rectangles are present in the given figure?

(A) 8

(B) 9

(D) 12

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A) All creatures with claws are animals.

(B) Some creatures with claws are non-ferocious.

(D) Some ferocious creatures are creatures with claws.

Answer: (D)

7. Which one of the following options represents the given graph?

(A) f(x) = x²2⁻^|x|

(B) f(x) = x 2⁻^|x|

(D) f(x) = x 2⁻^x

Answer: (A)

8. Which one of the following options can be inferred from the given passage alone?

When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.

[Excerpt from The Truth about Stories by T. King]

(A) It is a child’s description of what he or she likes.

(B) It is an adult’s memory of what he or she liked as a child.

(D) It teaches us that stories are good for children.

Answer: (B)

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.

(ii) Mix the samples within each set and test the mixed sample for covid.

(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.

(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A) 700

(B) 600

(D) 1000

Answer: (A)

The total number of creases visible when the sheet is unfolded is _______.

(A) 32

(B) 5

(D) 63

Answer: (C)

CY: Chemistry

Q.11 – Q.35 Carry ONE mark Each

11. The major product formed in the given reaction is

DME: 1,2-Dimethoxyethane

Answer: (A)

12. The compound which gives a fragment at m/z = 124[M + H]⁺ is

Answer: (B)

13. The major product formed in the given reaction is

Answer: (A)

14. The major product formed in the given reaction is

Answer: (A)

15. On irradiation using UV light (>300 nm), compounds X and Y, predominantly, undergo

(A) X: Norrish type I reaction and Y: Norrish type II reaction

(B) X: Norrish type II reaction and Y: Norrish type I reaction

(D) Both X and Y: Norrish type II reaction

Answer: (B)

16. The topicity relationship of H_a and H_b in X, Y and Z are, respectively,

(A) Diastereotopic, Homotopic and Enantiotopic

(B) Homotopic, Enantiotopic and Enantiotopic

(D) Diastereotopic, Enantiotopic and Homotopic

Answer: (B)

17. Compound P was prepared based on a four-component reaction at room temperature in methanol. The required starting materials for the synthesis are

Answer: (A)

18. The major product formed in the following reaction is

Answer: (B)

19. The reaction of Ph₃PCl₂ with PhNH₂ primarily produces

(A) Ph₃P=NPh

(B) PhP=NPh

(D) Ph₂ClP=NPh

Answer: (A)

20. Formation of [M(en)₃]²⁺ from [M(H₂O)₆]²⁺ and three equivalents of ethylenediamine (en) is LEAST favored when M is

(A) Co

(B) Ni

(D) Fe

Answer: (D)

21. Wacker oxidation of alkenes is catalyzed by a combination of

(A) Pd(II) and Cu(II)

(B) Co(II) and Cu(II)

(D) Pd(II) and Co(II)

Answer: (A)

22. For the conversion of [Pt(L)Cl₃]⁻ to trans-[Pt(L)Cl₂(H₂O)], the trans-effect is LEAST when the ligand L is

(A) H₂O

(B) NH₃

(D) C₂H₄

Answer: (A)

23. The tetracoordinated copper center in the oxidized and reduced forms of plastocyanin exhibits longest bond with

(A) cysteine-S and methionine-S, respectively

(B) methionine-S and cysteine-S, respectively

(D) methionine-S and methionine-S, respectively

Answer: (D)

24. The packing efficiency (in %) of spheres for a body-centered cubic (bcc) lattice is approximately

(A) 74

(B) 68

(D) 52

Answer: (B)

25. The magnitudes of CFSE in [M(H₂O)₆]ⁿ⁺ for Mn and Fe ions satisfy the relations

(A) Mn²⁺ < Mn³⁺ and Fe²⁺ < Fe³⁺

(B) Mn²⁺ > Mn³⁺ and Fe²⁺ > Fe³⁺

(D) Mn²⁺ > Mn³⁺ and Fe²⁺ < Fe³⁺

Answer: (C)

26. The organometallic catalyst for the following transformation is

Answer: (A)

27. Point group of naphthalene (C₁₀H₈) is

(A) D_2d

(B) D_2h

(D) D_3h

Answer: (B)

28. The INCORRECT statement is

(A) Zero-point energy of a quantum mechanical harmonic oscillator of frequency v is hv/2

(B) Energy level of a quantum mechanical rigid rotor is inversely proportional to its moment of inertia

(D) Total angular momentum of an atomic system is equal to the sum of orbital angular momentum and spin angular momentum

Answer: (C)

29. For an ideal gas, the molecular partition function in the canonical ensemble, that is proportional to the system volume (V), is the

(A) vibrational partition function

(B) rotational partition function

(D) translational partition function

Answer: (D)

30. Assertion (S): The total angular momentum for light atoms (low atomic number) is obtained by Russell-Saunders coupling, whereas jj-coupling is used for heavy atoms (high atomic number).

Reasoning (R): The spin-orbit interactions are weak in light atoms (low atomic number) and strong in heavy atoms (high atomic number).

The correct option is

(A) S and R are true; and R is the correct reason for S

(B) S and R are true; but R is NOT the correct reason for S

(D) S is false but R is true

Answer: (A)

31. The acetolysis product(s) of the given reaction is(are)

Answer: (A, C)

32. Product(s) formed in the given reaction is(are)

Answer: (A, B, C)

33. The choice(s) that correctly identify radioisotopes (P, Q, R, S) shown in the following nuclear reaction is(are)

Answer: (A, B, D)

34. For the Lindemann-Hinshelwood mechanism of gas phase unimolecular reactions, the true statement(s) is(are)

(A) Only molecules with three or more atoms can follow the Lindemann-Hinshelwood mechanism

(B) Lindemann-Hinshelwood mechanism involves bimolecular elementary steps

(D) The overall reaction is of second order at high pressure

Answer: (A, B, C)

35. The calculated magnetic moment of [Ce(NO₃)₅]²⁻ is _______ BM. (rounded off to two decimal places)

(Given: atomic number of Ce is 58)

Answer: (2.51 to 2.55)

Q.36 – Q.65 Carry TWO marks Each

36. A compound, C₁₅H₁₆O₂ , has the following spectral data;

¹H NMR (ppm): 9.16 (s), 6.89 (d, J = 8 Hz), 6.64 (d, J = 8 Hz), 1.53 (s)

¹³C NMR (ppm): 154.7, 140.9, 127.1, 114.4, 40.7, 30.7

The structure of the compound is

Answer: (A)

37. The major product formed in the given reaction sequence is

Answer: (B)

38. E and F in the given reaction scheme are

Answer: (A)

39. M and N in the given reaction scheme are

NMO: N-Methylmorpholine-N-oxide

Answer: (C)

40. In the ¹H NMR spectrum, multiplicity of the signal (bold and underlined H atom) in the following species is

(A) I- pentet, II- quartet, III- doublet and IV- singlet

(B) I- pentet, II- singlet, III- singlet and IV- doublet

(D) I- singlet, II- quartet, III- singlet and IV- singlet

Answer: (A)

41. The major product obtained by the treatment of (η⁵-C₅H₅)2Ni with Na/Hg in ethanol is

(A) (η⁵-C₅H₅)( η³-C₅H₅)Ni

(B) (η³-C₅H₅)₂Ni

(D) (η³-C₅H₇)₂Ni

Answer: (C)

42. The number of shared corners of the constituent SiO₄ units in orthosilicate, pyrosilicate, cyclic silicate and sheet silicate, respectively, are

(A) 0, 1, 2 and 3

(B) 2, 3, 0 and 1

(D) 1, 2, 3 and 0

Answer: (A)

43. Concentration of Q in a consecutive reaction is given by where [P]₀ is the initial concentration of P.

If the value of k₂ = 25 s⁻¹, the value of k₁ that leads to the longest waiting time for Q to reach its maximum is

(A) k₁ = 20 s⁻¹

(B) k₁ = 25 s⁻¹

(D) k₁ = 35 s⁻¹

Answer: (A)

44. The wave function for Be³⁺ in a certain state is given by where N is the normalization constant, r is the distance of electron from the nucleus and 𝑎0 is the Bohr radius. The most probable distance of the electron from the nucleus in this state is

(A) 4a₀

(B) a₀/4

(D) a₀/8

Answer: (B)

45. Match the following

(A) P→III, Q→I, R→IV, S→II

(B) P→III, Q→IV, R→II, S→I

(D) P→II, Q→III, R→IV, S→I

Answer: (A)

46. In the scheme below,

I_α represents the intensity of the light absorbed. Assuming that the quantum yield of the first step is one, the steady state concentration of Q is given by

Answer: (A)

47. Product(s) formed in the given reaction sequence is(are)

Answer: (A, B)

48. Product(s) formed in the reaction below is(are)

Answer: (A, C)

49. The stereoisomer(s) of G giving the depicted product is(are)

Answer: (A, C)

50. Product(s) formed in the given reaction sequence is(are)

Answer: (A, C)

51. The reaction(s) in which inversion of configuration occur(s) is(are)

Answer: (A, B)

52. The correct statement(s) regarding myoglobin (Mb) and haemoglobin (Hb) is(are)

(A) At low partial pressure of O₂ (e.g., 5 kPa), the O₂ affinity of Hb lowers upon lowering the pH

(B) Binding of the first O₂ molecule to Hb results in lower affinity for the binding of second O₂ molecule

(D) One end of O₂ binds to the metal center in oxy-Mb and the other end of the bound O₂ is H-bonded with imidazole-NH of a distal histidine

Answer: (A, D)

53. The correct statement(s) regarding Co₂(CO)₈ is(are)

(A) It reacts with Na to give Na[Co(CO)₄]

(B) It contains three bridging carbonyls

(D) Two isomers exist in hexane solution

Answer: (A, C, D)

54. The compound(s) having [Xe]4f¹ configuration is(are)

(Given the atomic numbers Ce:58, Lu:71, Pr:59 and Nd:60)

(A) Na₃[Ce(NO₃)₆]

(B) Na₃[LuCl₆]

(D) Nd(NR₂)₃ (R = SiMe₃)

Answer: (A, C)

55. The correct statement(s) for XeF₂ is(are)

(A) Its bonding is best explained by classical 2-centered-2-electron bonds

(B) Its bonding is best explained by a non-classical 3-centered-4-electron bond

(D) Its point group is D_∞h

Answer: (B, C, D)

56. For the non-dissociative adsorption of a gas on solid,

(i) the Freundlich isotherm is given by θ = kp^1/n where θ is surface coverage, p is pressure, k and n are empirical constants; and

(ii) the BET isotherm is given by

where p* and c empirical constants, and p < p*.

The correct statement(s) is(are)

(A) At low surface coverage, the Langmuir isotherm reduces to the Freundlich isotherm with n = 1

(B) At high surface coverage, the Langmuir isotherm reduces to the Freundlich isotherm with n = ∞

(D) At very high pressure (p → p*), the BET isotherm reduces to the Langmuir isotherm

Answer: (A, B, C)

57. Two different enzyme catalysis reactions I and II have identical Y-intercepts for the Lineweaver-Burke (equation given below) plots. The slope for reaction I is twice than that of reaction II.

If the initial concentrations of enzymes in I and II are same, the correct statement(s) is(are)

where v and v_max are rate and maximum rate; K_M is Michaelis-Menten constant, and [S] is substrate concentration.

(A) Reactions I and II have same turn over number

(B) Michaelis-Menten constants for reactions I and II are identical

(D) The rates of the elementary steps for reactions I and II are identical

Answer: (A, C)

58. The enthalpy change for the exothermic reaction between BeI2 and HgF₂ is _______kJ mol⁻¹ (rounded off to the nearest integer)

(Given: Bond dissociation energy (in kJ mol⁻¹) for Be−F = 632, Be−I = 289, Hg−F = 268 and Hg−I = 145)

Answer: (-440 to -440)

59. Number of carbon atoms connected to the metal center in [W(C₆₀)(CO)₅] is _______ (rounded off to the nearest integer)

(Given: atomic number of W is 74)

Answer: (7 to 7)

60. Two-component solid-liquid system of naphthalene-benzene forms a simple eutectic mixture. Assuming that naphthalene-benzene forms an ideal solution, the mole fraction of naphthalene in benzene at 300 K and 1 bar is _______ (rounded off to two decimal places)

(Given: Freezing point (T_fp) and enthalpy of fusion (∆H_fus) of naphthalene are 353 K and 19.28 kJ mol⁻¹, respectively and gas constant (R) =8.31 J K⁻¹ mol⁻¹)

Answer: (0.30 to 0.32)

61. The intrinsic viscosity of a sample of polystyrene in toluene is 84 cm³ g⁻¹ at 30° It follows Mark-Houwink equation with empirical constant values of K = 1.05 × 10⁻² cm³ g⁻¹ and a = 0.75. The molecular weight of the polymer is ________ × 10³ g mol⁻¹ (rounded off to the nearest integer)

Answer: (158 to 160)

62. According to Debye-Hückel limiting law, the mean molal activity coefficient for 0.87 g K₂SO₄ (molar mass = 174 g mol⁻¹) in 1 kg of water at 25°C is _________ (rounded off to two decimal places)

Answer: (0.74 to 0.76)

63. A solution is prepared by dissolving 128 g of naphthalene (C₁₀H₈) in 780 g of benzene (C₆H₆). The vapor pressure of pure benzene is 12.6 kPa at 25° Assuming that naphthalene in benzene is an ideal solution, the partial vapor pressure of benzene is _________ kPa (rounded off to two decimal places)

Answer: (11.34 to 11.47)

64. For the galvanic cell: H₂ (g) | HCl (aq) | Cl₂ (g)

the standard electromotive force (E⁰) value is given by

E⁰ = 1.73 – (1.25 × 10⁻³)T + (1.00 × 10⁻⁶)T²

where E⁰ is in Volts and T is in Kelvin.

For the cell reaction, the standard enthalpy change (∆_rH⁰) at 300 K is _________ kJ mol⁻¹(rounded off to the nearest integer)

(Given: Faraday constant, F = 96500 C mol⁻¹)

Answer: (-164 to -154)

65. A solution of three non-interacting compounds P, Q, and R is taken in a cuvette of 1 cm path length. Their concentrations are [P] = 1 × 10⁻⁶ M, [Q] = 2 × 10⁻⁶ M, [R] = 3 × 10⁻⁶ M and the molar extinction coefficients at 300 nm are εP =1 × 10⁵ M⁻¹ cm⁻¹, εQ = 2 × 10⁵ M⁻¹ cm⁻¹ and εR = 3 × 10⁵ M⁻¹ cm⁻¹. The % transmittance at 300 nm is __________ (rounded off to two decimal places)

Answer: (3.98 to 4.00)