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GATE Exam 2019 Ecology and Evolution (EY) Question Paper With Answer Key

June 7, 2023December 5, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

6. Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit interest rates.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

7. In a country of 1400 million population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country?

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

8. The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education the term gharana became acceptable. Gharana originally referred to hereditary musicians from a particular lineage, including disciples and grand disciples.

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

9. Two trains started at 7AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100 km/h. The time at which they were 540 km apart is AM.

(A) 9

(B) 10

(D) 11.30

Answer: (B)

10. “I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community.”

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Ecology and Evolution

1. Which of the following is NOT an example of cooperative behaviour?

(A) Biofilm formation

(B) Lek formation

(D) Sentinel behavior

Answer: (B)

2. In a simple linear regression, which of the following statements represents the principle underlying the estimation of the slope and intercept?

(A) The sum of the residuals is minimised

(B) The sum of the residuals is maximised

(D) The sum of the squares of the residuals is maximized

Answer: (C)

3. According to MacArthur and Wilson’s theory of island biogeography, the number species on an of land is a balance between

(A) colonisation and extinction

(B) colonisation and speciation

(D) speciation and extinction

Answer: (A)

4. A researcher wants to sample ant diversity in a landscape consisting of riverine valleys and plateaus. Which among the following is the best sampling strategy for her to employ?

(A) Once an ant is located, lay quadrats in that area

(B) Lay equal number of quadrats in valleys and plateaus

(D) Lay quadrats in both habitats in proportion to their areas

Answer: (D)

5. The rates of non-synonymous and synonymous change per site are 𝑑𝑁 and 𝑑𝑆 respectively. Which of the following mechanisms explains the evolution of a gene with 𝑑𝑁/𝑑𝑆 = 0.2?

(A) Diversifying selection

(B) Neutral evolution

(D) Negative selection

Answer: (D)

6. Which of the following assumptions allows us to use molecular clocks to estimate species divergence times?

(A) Adaptive changes accumulate at a constant rate

(B) Adaptive changes occur episodically

(D) Neutral changes occur episodically

Answer: (C)

7. A large proportion of individuals in a particular population of humans carry the allele for colour-blindness. Assuming colour-blindness does not confer any evolutionary advantage, which of the following mechanisms CANNOT explain the unusual abundance of this allele?

(A) Founder effect

(B) Genetic drift

(D) Purifying selection

Answer: (D)

8. The evolutionary change in the timing of development is known as

(A) heterochrony

(B) heterotopy

(D) homotopy

Answer: (A)

9. Which of the following habitats is best suited for infrasound (low frequency) communication in animals?

(A) Coral reef

(B) Open ocean

(D) Urban area

Answer: (B)

10. Which of the following is typical of the eyes of a nocturnal insect?

(A) High resolution and high sensitivity

(B) High resolution and low sensitivity

(D) Low resolution and low sensitivity

Answer: (C)

11. Gut passage time is defined as the time taken from ingestion to excretion of a food item. Which among the following animals has the longest gut passage time?

(A) Black bear

(B) Gaur

(D) Tiger

Answer: (B)

12. A researcher found 𝑛 number of woody species in a one hectare tropical forest plot. He employs the same method in another one hectare plot in the same forest. Based on the principle of species area curves, the expected number of new species in the second plot is

(A) equal to 𝑛 (the number of species found in the first plot)

(B) less than 𝑛 (the number of species found in the first plot)

(D) always zero

Answer: (B)

13. A phylogenetic study finds that certain plants of peninsular India are more closely related to those in Australia than to those in China. Which of the following statements best explains this result?

(A) China and Australia were part of Laurasia, but India was in Gondwana

(B) India and Australia were part of Gondwana, but China was in Laurasia

(D) India and China were part of Laurasia, but Australia was in Gondwana

Answer: (B)

14. The pattern of net primary productivity in a year for two grassland habitats (P and Q) is shown below. Which of the following statements is consistent with the figure?

(A) Habitat P is in Argentina while Q is in Canada

(B) Habitat P is in Russia while Q is in Canada

(D) Habitat P is in South Africa while Q is in Argentina

Answer: (C)

15. Which of the following statements best explains the patterns of leaf-litter decomposition over time shown in the figure below?

(A) Habitat 1 is cold and wet; Habitat 2 is warm and arid

(B) Habitat 1 is warm and arid; Habitat 2 is cold and wet

(D) Habitat 1 is warm and wet; Habitat 2 is cold and arid

Answer: (C)

16. To compare biomass of a fish species in two lakes, A and B, a researcher records live-weights of 30 individuals from each lake. She assumes that these two datasets are normally distributed and have equal variance. She calculates

where are mean values from the respective lakes, and s is the pooled standard error.

What is this quantity Q?

(A) Correlation coefficient

(B) Regression coefficient

(D) χ2-statistic

Answer: (A)

17. While developing his theory of evolution by natural selection, Charles Darwin was influenced by t he work of

(A) Charles Lyell and Thomas Malthus

(B) Francis Crick and James Watson

(D) Sewall Wright and Ronald Fisher

Answer: (C)

18. Weakly-electric fish typically produce electric voltages of less than 1 volt for communication and navigation. Which of the following features is NOT a characteristic of weakly-electric fish?

(A) Electrocytes

(B) Electroreception capabilities

(D) Mechanisms to avoid signal jamming

Answer: (B)

19. Match the combination of primates and trees to the state/union territory where they can be found.

(A) P – i; Q – iii; R – iv; S – ii

(B) P – iii; Q – i; R – iv; S – ii

(D) P – i; Q – iv; R – ii; S – iii

Answer: (B)

20. Which of the following crops should show the LOWEST proportional increase in photosynthetic rate under rising carbon dioxide levels in the atmosphere?

(A) Barley

(B) Maize

(D) Wheat

Answer: (B)

21. Which among the following is the best indicator of the precision with which a population parameter is estimated?

(A) Degrees of freedom

(B) Mean

(D) Standard error

Answer: (D)

22. Which of the following hormones regulates moulting in arthropods?

(A) Corticosterone

(B) Ecdysone

(D) Hydrocortisone

Answer: (B)

23. A study found that grazing decreased species richness when productivity was low, and increased species richness when productivity was high. Which of the following figures best represents this result? In the figure, the dotted line represents species richness in grazed plots and the solid line represents species richness in plots without grazing.

(A) i

(B) ii

(D) iv

Answer: (B)

24. The mean height of students in a class (number of students, n=10) was initially estimated to be 6 feet and 6 inches. Later an error was detected, where one boy’s height was recorded as 10 feet taller than his actual height. The correct mean height of the students in the class is _______ inches (round off to 1 decimal place).

Answer: (65.9 to 66.1)

25. Two true-breeding lines of a moth, one with black wings and the other with red wings, are crossed. All of the resulting offspring in the F1 generation had red wings. These offspring are crossed to produce the F2 generation of moths where the expected fraction of moths with black wings in the population is _________ (round off to two decimal places).

Answer: (0.24 to 0.26)

Q.26 – Q. 55 carry two marks each.

26. A teacher proposed a null hypothesis (H₀) that there is no difference in the mean heights of boys and girls in his class. His alternative hypothesis (H_a) was that boys are taller than girls.

The figure below shows the probability distribution, i.e. probability density function, of the difference in the mean height of boys and girls if the null hypothesis were true. The observed mean difference in heights is shown by the solid back circle. The dotted line represents the range μ ± 2σ whereas the solid line shows the range μ ± 3σ.

Assuming a significance level of 0.05, which of the following conclusions is correct?

(A) 𝐻₀ is accepted

(B) 𝐻₀ is rejected

(D) 𝐻_𝑎 is rejected

Answer: (B)

27. Females in many birds and mammals mate with multiple males, in addition to their paired- male. Which of the following is an INCORRECT adaptive explanation for such extra-pair mating?

(A) Increased genetic quality of offspring

(B) Increased care of offspring by the paired-male

(D) Increased resources for offspring production

Answer: (B)

28. A researcher hypothesized that females of a bird species prefer to mate with long-tailed males. To test this hypothesis, she assigned male birds of similar tail lengths to one of the following four treatments:

1. Intact – tails left unmanipulated

2. Re-attached – tails cut and re-attached without any change in length

3. Shortened – tails cut, shortened and re-attached

4. Elongated – tails cut, elongated and re-attached

She measured mating success of these experimental birds and the results from this are shown below. Error bars represent 95% confidence intervals. Which of the following inferences are consistent with these results?

i. Experimental manipulation of tails decreased male mating success

ii. Females preferred to mate with males with short tails

iii. Females preferred to mate with males with long tails

(A) i only

(B) i and iii only

(D) iii only

Answer: (B)

29. Highly repetitive sequences are most likely to be prevalent in regions of the genome with ______recombination rate and originate via ______crossing over. Choose the right pair of words that completes this statement correctly.

(A) high; equal

(B) high; unequal

(D) low; unequal

Answer: (D)

30. Which of the following is correct about first and second derivatives at points P, Q and R for f(x) = sin (x) shown below?

Answer: (C)

31. Which of the following is NOT a proximate explanation for group cohesion among animals?

(A) Animals follow a common path while foraging

(B) Animals follow their nearest neighbor while foraging

(D) Animals secrete pheromones to attract conspecifics while foraging

Answer: (C)

32. Which of the following statements is LEAST likely to explain the evolution of dispersal?

(A) Dispersal enhances chances of finding novel habitats

(B) Dispersal regulates population densities

(D) Dispersal reduces sibling conflict

Answer: (B)

33. Which of the following plots describes the expected relationship between population size (y-axis) and generation time (x-axis) in vertebrates? Here, each data point represents a different vertebrate species and the generation time is defined as the average interval between two generations.

(A) i

(B) ii

(D) iv

Answer: (B)

34. Six different species of centipedes represented by the following phylogenetic tree have these single nucleotide polymorphisms (SNPs) at a given locus. Assuming maximum parsimony (or minimum evolutionary changes), what is the most likely nucleotide in the ancestor ‘P’?

(A) A or C

(B) A or G

(D) C or T

Answer: (A)

35. Garter snakes have evolved resistance to the poisonous secretions of the rough-skinned newts. The following figure describes poison production in newts and the resistance (measured as amount of poison tolerated) in garter snakes in three different geographical areas. Given this information, which of the following statements is correct regarding the evolution of poison resistance in garter snakes?

(A) Evolution of resistance is neutral

(B) Snakes in Area 2 are more adapted than the others

(D) The resistance mechanism is costly

Answer: (D)

36. Many bird species show cooperative breeding. Offspring are cared for by parents and other individuals (helpers) who are typically offspring from previous years. Which of the following is NOT an appropriate evolutionary explanation for why helpers do not leave and breed on their own?

(A) At high population density new breeding territories are difficult to obtain and helpers gain more from staying and helping than from dispersing to breed

(B) In environments where resources are scarce, helpers gain more by suppressing their reproduction and minimizing population extinction than from dispersing to breed

(C) When complex parental care is required for offspring survival, helpers gain more by staying and learning to care than from dispersing to breed

(D) When predation risk during dispersal is high, helpers gain more by staying and helping than from dispersing to breed

Answer: (B)

37. The relative performance of amphibians adapted to tropical (dashed line) and temperate (solid line) climates as a function of temperature is shown below. Assume that global warming will result in an equal increase in mean temperatures over the next 30 years in both regions. Which of the following statements about the effects of global warming on these two amphibians is most likely?

(A) Temperate and tropical amphibians will be similarly impacted

(B) Temperate amphibians will be more negatively impacted than tropical amphibians

(D) Tropical amphibians will be positively impacted, while temperate amphibians will be negatively impacted

Answer: (C)

38. Global warming potential of different greenhouse gases (CO2, CH4, N2O, etc) is determined by their:

P: ability to absorb infrared radiation

Q: concentration in the atmosphere

R: residence time in the atmosphere

S: source of origin (whether natural, or anthropogenic)

(A) P & R only

(B) P, Q & R only

(D) Q & S only

Answer: (B)

39. A hornbill foraging exclusively on figs in a tropical forest spends an average of 36 minutes on a tree before moving to the next tree. The density of fig trees in the forest decreases by half. In accordance with optimal foraging theory, which of following represents a possible duration (in minutes) that the hornbill may spend per tree?

(A) 6

(B) 18

(D) 54

Answer: (D)

40. Type-I errors in statistical tests represent false positives, where a true null hypothesis is falsely rejected. Type-II errors represent false negatives where we fail to reject a false null hypothesis. For a given experimental system, increasing sample size will

(A) decrease both Type-I and Type-II errors

(B) decrease Type-I and increase Type-II errors

(D) increase Type-I and decrease Type-II errors

Answer: (D)

41. Semelparous species are those that produce all of their offspring in a single reproductive event. The survivorship curve of a population of a semelparous species would most likely resemble which of the following?

(A) i

(B) ii

(D) iv

Answer: (C)

42. Bergmann’s rule describes the increase in body size observed in related organisms as we go from the equator to the poles. Which of the following is a possible explanation for this pattern?

(A) Decreased body mass in smaller organisms helps generate less heat

(B) Decreased surface area to volume ratios in larger organisms helps conserve heat

(D) Increased surface area in larger organisms helps efficient gas exchange in the poles

Answer: (B)

43. To estimate the number of foxes in an area, a researcher conducted a mark-recapture survey. In the first survey, he caught and marked 90 foxes. In his second survey a week later, he caught 120 foxes of which 40 were marked (recaptures). If you are told that the actual number of foxes in this area is 400, which of the following is a plausible explanation for the anomaly in the researcher’s data?

(A) Capture increased mortality in the marked foxes

(B) Large mortality of foxes between the two surveys

(D) The marked foxes were more likely to be recaptured

Answer: (D)

44. Which one of the statements below best describes a plant species with the timing of reproductive events shown in the following figure?

(A) The plant does not require animal pollinators

(B) The plant relies on diurnal pollinators only

(D) The plant relies on nocturnal pollinators only

Answer: (D)

45. Match species in column A to its phylogenetically closest relative in column B.

(A)P – W; Q – V; R – Z; S – X; T – Y

(B) P – Y; Q – V; R – Z; S – X; T – W

(D) P – Y; Q – V; R – Z; S – W; T – X

Answer: (B)

46. Under which of the following conditions is rapid pollen tubes growth most likely to evolve?

(A) In a self-compatible species with few ovules

(B) In a self-compatible species with many ovules

(D) In a self-incompatible species with many ovules

Answer: (C)

47. Which of the following correctly represents a decreasing order of tree species richness?

P – Dry tropical forests in Maharahstra

Q – Lowland wet tropical forests in Arunachal Pradesh

R – Scrub Forest in Rajasthan

S – Wet tropical forests in Kerala

(A) Q > R > S > P

(B) Q > S > P > R

(D) S > Q > R > P

Answer: (B)

48. A forester, pictured below, is trying to measure the height of a tree. Her height is x =1.5 m. She stands y = 10 m away from a tree, from where the angle subtended to the top of the tree is z = 45°. The height of the tree is_______m (round off to 1 decimal place).

Answer: (11.49 to 11.51)

49. In a recently discovered fossil, only 0.39% of 𝐶14 found in living fossils is present. If the half-life of 𝐶¹⁴ is 5730 years, the age of the fossil is expected to be __________years (round off to the nearest integer).

Answer: (45800 to 45900)

50. A beaker contains a large number of spherical nuts of two types, one with radius 1 cm and the other with 2 cm, in the ratio 2:1. A squirrel picks one nut from a random point in this beaker. Assuming that the beaker is well-mixed, the probability of picking the smaller nut is _______(round off to 1 decimal place).

Answer: (0.19 to 0.35)

51. In a closed population following logistic growth, per capita birth rate 𝑏 and per capita death rate 𝑑 vary with population size 𝑁 as 𝑏 = 0.1 − 0.0001𝑁 and 𝑑 = 0.01 + 0.00002𝑁, respectively. The carrying capacity 𝐾 of this population is________ individuals.

Answer: (750 to 750)

52. A population of birds has a 3:2 male to female adult sex ratio at the beginning of the breeding season. During the breeding season, every female produces 8 eggs of which 4 survive to become juveniles. A census at the end of the breeding season accurately estimates the bird population to be 1300 individuals. Assuming no deaths, the number of adult males in this population is _______ individuals.

Answer: (300 to 300)

53. The coordinates of P is (0,1), Q is (0,3), R is (2,0) and S is (1,0). The area of the trapezoid PQRS is ___________ (round off to 1 decimal place).

Answer: (2.49 to 2.51)

54. Trees in two patches A and B can disperse seeds to a bare patch C. The probability of a seed being dispersed from A to C is 0.5 and the probability of germination of such a seed is 0.1. Likewise, the probability of a seed being dispersed from B to C is 0.4 and the probability of germination of such a seed is 0.2. If the number of seeds produced in patch A is 100 and that in B is 200, the expected number of germinated seeds in patch C is________.

Answer: (21 to 21)

55. A bacterial population grows from 106 cells to 5.5 × 107 cells in 20 minutes. Assuming that the growth was not resource limited, the per-capita growth rate of bacteria is ______ per minute (round off to 2 decimal places).

Answer: (0.19 to 0.21)

GATE Exam 2019 Electrical Engineering (EE) Question Paper With Answer Key

June 7, 2023December 4, 2019 by suresh84

General Aptitude

Q.1 – Q. 5 carry one mark each.

1. I am not sure if the bus that has been booked will be able to ______all the students.

(A) sit

(B) deteriorate

(D) accommodate

Answer: (D)

2. The passengers were angry______ the airline staff about the delay.

(A) on

(B) about

(D) towards

Answer: (C)

3. The missing number in the given sequence 343, 1331, _____, 4913 is

(A) 3375

(B) 2744

(D) 4096

Answer: (C)

4. It takes two hours for a person X to mow the lawn. Y can mow the same lawn in four hours. How long (in minutes) will it take X and Y, if they work together to mow the lawn?

(A) 60

(B) 80

(D) 120

Answer: (B)

5. Newspapers are a constant source of delight and recreation for me. The _______trouble is that many I read ____ of them.

(A) even, quite

(B) even, too

(D) only, too

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. How many integers are there between 100 and 1000 all of whose digits are even?

(A) 60

(B) 80

(D) 90

Answer: (C)

7. The ratio of the number of boys and girls who participated in an examination is 4:3. The total percentage of candidates who passed the examination is 80 and the percentage of girls who passed is 90. The percentage of boys who passed is _____.

(A) 55.50

(B) 72.50

(D) 90.00

Answer: (B)

8. An award-winning study by a group of researchers suggests that men are as prone to buying on impulse as women but women feel more guilty about shopping.

Which one of the following statements can be inferred from the given text?

(A) Some men and women indulge in buying on impulse

(B) All men and women indulge in buying on impulse

(D) Many men and women indulge in buying on impulse

Answer: (A)

9. Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators belong to set Y. The product of elements having minimum and maximum values in the set Z is_____ .

(A) 1/12

(B) 1/8

(D) 3/8

Answer: (D)

10. Consider five people – Mita, Ganga, Rekha, Lakshmi and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.

Which of the following conclusions are true?

1.Lakshmi is taller than Rekha

2.Rekha is shorter than Mita

3.Rekha is taller than Sana

4.Sana is shorter than Ganga

(A) 1 and 3

(B) 3 only

(D) 1 only

Answer: (C)

Electrical Engineering

Q.1 – Q. 25 carry ONE mark each.

1. The inverse Laplace transform of is

(A) 3te^−t + e^−t

(b) 3e^−t

(D) 4te^−t + e^−t

Answer: (C)

2. M is a 2 × 2 matrix with eigenvalues 4 and 9. The eigenvalues of M² are

(A) heat equation

(B) wave equation

(D) Laplace equation

Answer: (D)

3. The partial differential equation

where c ≠ 0

is known as

(A) heat equation

(B) wave equation

(D) Laplace equation

Answer: (D)

4. Which one of the following functions is analytic in the region |z| ≤ 1?

Answer: (B)

5. The mean-square of a zero-mean random process is kT/C, where k is where 𝑘 is Boltzmann’s constant, T is the absolute temperature, and C is a capacitance. The standard deviation of the random process is

(A) kT/C

(B)

(D) √kT/C

Answer: (B)

6. A system transfer function is . If a₁ = b₁ =0, and the other coefficients are positive, the transfer function represents a

(A) low pass filter

(B) high pass filter

(D) notch filter

Answer: (A)

7. The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

(A) e^+atu(t)

(B)e^{−a(t + T)}u(t)

(D) e^−a(t−T) u(t)

Answer: (C)

8. A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is

(A) 4.5%

(B) 9%

(D) 1%

Answer: (C)

9. A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50 Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is

(A) 100 Hz

(B) 150 Hz

(D) 300 Hz

Answer: (C)

10. The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is

(A) rotor resistance

(B) rotor leakage reactance

(D) stator resistance

Answer: (C)

11. A three-phase synchronous motor draws 200 A from the line at unity power factor at rated load. Considering the same line voltage and load, the line current at a power factor of 0.5 leading is

(A) 100 A

(B) 200 A

(D) 400 A

Answer: (D)

12. In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is

(A) 60

(B) −45

(D) −30

Answer: (B)

13. The output response of a system is denoted as y(t), and its Laplace transform is given by

The steady state value of y(t) is

(A) 1/10√2

(B)10√2

(D) 100√2

Answer: (A)

14. The open loop transfer function of a unity feedback system is given by

In G(s) place, the Nyquist plot of G(s) passes through the negative real axis at the point

(A) (−0.5, j0)

(B)(−0.75, j0)

(D) (−1.5, j0)

Answer: (A)

15. The characteristic equation of a linear time-invariant (LTI) system is given by

∆(s) = s⁴ + 3s³ + 3s² + s + k = 0.

The system is BIBO stable if

(A) 0 < k < 12/9

(B) k > 3

(D) k > 6

Answer: (C)

16. Given, V_gs is the gate-source voltage, V_ds is the drain source voltage, and V_th is the threshold voltage of an enhancement type NMOS transistor, the conditions for transistor to be biased in saturation are

(A) V_gs < v_th ; V_ds ≥ V_gs – V_th

(B) V_gs > v_th ; V_ds ≥ V_gs – V_th

(D) V_gs < v_th ; V_ds ≤ V_gs – V_th

Answer: (B)

17. A current controlled current source (CCCS) has an input impedance of 10 Ω and output impedance of 100 kΩ. When this CCCS is used in a negative feedback closed loop with a loop gain of 9, the closed loop output impedance is

(A) 10 Ω

(B) 100Ω

(D) 1000 kΩ

Answer: (D)

18. If 𝑓 = 2𝑥³ + 3𝑦² + 4𝑧, the value of line integral ∫_𝐶 grad𝑓 ∙ 𝑑𝐫 evaluated over contour C formed by the segments (-3, -3, 2)→(2, -3, 2) →(2, 6, 2) →(2, 6, -1) is _________.

Answer: (139 to 139)

19. The current 𝐼 flowing in the circuit shown below in amperes (round off to one decimal place) is __________.

Answer: (1.3 to 1.5)

20. A co-axial cylindrical capacitor shown in Figure (i) has dielectric with relative permittivity ε_r1 = 2. When one-fourth portion of the dielectric is replaced with another dielectric of relative permittivity ε_r2, as shown in Figure (ii), the capacitance is doubled. The value of ε_r2 is _______.

Answer: (9 to 11)

21. The 𝑌𝑏𝑢𝑠 matrix of a two-bus power system having two identical parallel lines connected between them in pu is given as_________.

Answer: (0.095 to 0.105)

22. Five alternators each rated 5 MVA, 13.2 kV with 25% of reactance on its own base are connected in parallel to a busbar. The short-circuit level in MVA at the busbar is ______.

Answer: (100 to 100)

23. The total impedance of the secondary winding, leads, and burden of a 5 A CT is 0.01 Ω. If the fault current is 20 times the rated primary current of the CT, the VA output of the CT is________.

Answer: (100 to 100)

24. The rank of the matrix, is ______.

Answer: (3 to 3)

25. The output voltage of a single-phase full bridge voltage source inverter is controlled by unipolar PWM with one pulse per half cycle. For the fundamental rms component of output voltage to be 75% of DC voltage, the required pulse width in degrees (round off up to one decimal place) is ___________.

Answer: (111.0 to 115.0)

Q.26 – Q. 55 carry TWO marks each.

26. Consider a 2 × 2 matrix 𝑴 = [𝒗_𝟏 𝒗_𝟐], where, 𝒗_𝟏 and 𝒗_𝟐 are the column vectors. Suppose are the row vectors. Consider the following statements:

Which of the following options is correct?

(A) Statement 1 is true and statement 2 is false

(B) Statement 2 is true and statement 1 is false

(D) Both the statements are false

Answer: (C)

27. The closed loop line integral

evaluated counter-clockwise, is

(A) +8jπ

(B) −8jπ

(D) +4jπ

Answer: (A)

28. A periodic function f(t), with a period of 2π, is represented as its Fourier series,

the Fourier series coefficients a₁ and b₁ of f(t) are

(A) a₁ = a/π; b₁ = 0

(B)a₁= A/2, b₁ = 0

(D) a₁ = 0; b₁ = A/2

Answer: (D)

29. The asymptotic Bode magnitude plot of a minimum phase transfer function 𝐺(𝑠) is shown below.

Consider the following two statements.

Statement I: Transfer function G(s) has three poles and one zero.

Statement II: At very high frequency (ω−∞), the phase angle ∠G (jω) = −3π/2.

Which one of the following options is correct?

(A) Statement I is true and statement II is false.

(B) Statement I is false and statement II is true.

(D) Both the statements are false.

Answer: (B)

30. The transfer function of a phase lead compensator is given by

The frequency (in rad/sec), at which ∠D(jω) is maximum, is

Answer: (B)

31. Consider a state-variable model of a system

where y is the output, and r is the input. The damping ratio ξ and the undamped natural frequency ω_n (rad/sec) of the system are given by

Answer: (A)

32. A moving coil instrument having a resistance of 10 Ω, gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to 100 V?

(A) 9 Ω

(B) 99 Ω

(D) 9990 Ω

Answer: (D)

33. The enhancement type MOSFET in the circuit below operates according to the square law. μ_nC_ox = 100 μA/V², the threshold voltage (VT) is 500 mV. Ignore channel length modulation. The output voltage V_out is

(A) 100 mV

(B)500 mV

(D) 2 V

Answer: (C)

34. In the circuit below, the operational amplifier is ideal. If V1 = 10 mV and V2 = 50 mV, the output voltage (V_out) is

(A) 100 mV

(B) 400 mV

(D) 600 mV

Answer: (B)

35. The output expression for the Karnaugh map shown below is

Answer: (A)

36. In the circuit shown below, X and Y are digital inputs, and Z is a digital output. The equivalent circuit is a

(A) NAND gate

(B)NOR gate

(D) XNOR gate

Answer: (C)

37. A DC-DC buck converter operates in continuous conduction mode. It has 48 V input voltage, and it feeds a resistive load of 24 Ω. The switching frequency of the converter is 250 Hz. If switch-on duration is 1 ms, the load power is

(A) 6 W

(B)12 W

(D) 48 W

Answer: (A OR C)

38. The line currents of a three-phase four wire system are square waves with amplitude of 100A. These three currents are phase shifted by 120° with respect to each other. The rms value of neutral current is

(A) 0 A

(B)100/√3A

(D) 300 A

Answer: (C)

39. If 𝐀 = 2𝑥𝐢 + 3𝑦𝐣 + 4𝑧𝐤 and 𝑢 = 𝑥2 + 𝑦2 + 𝑧2, then div(𝑢𝐀) at (1, 1, 1) is _____________.

Answer: (45 to 45)

40. The probability of a resistor being defective is 0.02. There are 50 such resistors in a circuit.

The probability of two or more defective resistors in the circuit (round off to two decimal places) is ____________.

Answer: (0.25 to 0.27)

41. A 0.1 µF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage across the capacitor to drop to 1 V is ________.

Answer: (0.45 to 0.47)

42. The current I flowing in the circuit shown below in amperes is _________.

Answer: (0 to 0)

43. The voltage across and the current through a load are expressed as follows

The average power in watts (round off to one decimal place) consumed by the load is _______

Answer: (585.0 to 590.0)

44. The magnetic circuit shown below has uniform cross-sectional area and air gap of 0.2 cm. The mean path length of the core is 40 cm. Assume that leakage and fringing fluxes are negligible. When the core relative permeability is assumed to be infinite, the magnetic flux density computed in the air gap is 1 tesla. With same Ampere-turns, if the core relative permeability is assumed to be 1000 (linear), the flux density in tesla (round off to three decimal places) calculated in the air gap is _________.

Answer: (0.820 to 0.850)

45. A single-phase transformer of rating 25 kVA, supplies a 12 kW load at power factor of 0.6 The additional load at unity power factor in kW (round off to two decimal places) that may be added before this transformer exceeds its rated kVA is ________.

Answer: (7.10 to 7.30)

46. A 220 V DC shunt motor takes 3 A at no-load. It draws 25 A when running at full-load at 1500 rpm. The armature and shunt resistances are 0.5 Ω and 220 Ω, respectively. The no- load speed in rpm (round off to two decimal places) is ________.

Answer: (1564.00 to 1596.00)

47. A delta-connected, 3.7 kW, 400 V(line), three-phase, 4-pole, 50-Hz squirrel-cage induction motor has the following equivalent circuit parameters per phase referred to the stator: 𝑅₁ = 5.39 Ω, 𝑅₂ = 5.72 Ω, 𝑋₁ = 𝑋₂ = 8.22 Ω. Neglect shunt branch in the equivalent circuit. The starting line current in amperes (round off to two decimal places) when it is connected to a 100 V (line), 10 Hz, three-phase AC source is__________.

Answer: (13.00 to 16.00)

48. A 220 V (line), three-phase, Y-connected, synchronous motor has a synchronous impedance of (0.25 + 𝑗2.5) Ω/phase. The motor draws the rated current of 10 A at 0.8 pf leading. The rms value of line-to-line internal voltage in volts (round off to two decimal places) is _______.

Answer: (240.00 to 250.00)

49. A three-phase 50 Hz, 400 kV transmission line is 300 km long. The line inductance is 1 mH/km per phase, and the capacitance is 0.01 µF/km per phase. The line is under open circuit ondition at the receiving end and energized with 400 kV at the sending end, the receiving end line voltage in kV (round off to two decimal places) will be______.

Answer: (414.00 to 423.00)

50. A 30 kV, 50 Hz, 50 MVA generator has the positive, negative, and zero sequence reactances of 0.25 pu, 0.15 pu, and 0.05 pu, respectively. The neutral of the generator is grounded with a eactance so that the fault current for a bolted LG fault and that of a bolted three-phase fault at the generator terminal are equal. The value of grounding reactance in ohms (round off to one decimal place) is________.

Answer: (1.7 to 1.9)

51. In the single machine infinite bus system shown below, the generator is delivering the real power of 0.8 pu at 0.8 power factor lagging to the infinite bus. The power angle of the generator in degrees (round off to one decimal place) is_______.

Answer: (19.0 to 22.0)

52. In a 132 kV system, the series inductance up to the point of circuit breaker location is 50 mH. The shunt capacitance at the circuit breaker terminal is 0.05 µF. The critical value of

resistance in ohms required to be connected across the circuit breaker contacts which will give no transient oscillation is______.

Answer: (500 to 500)

53. In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at 48 V. The input DC voltage is 24 V. The output power is 120 W. The switching frequency is 50 kHz. Assume ideal components and a very large output filter capacitor. The converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in µH) is_________.

Answer: (24 to 24)

54. A fully-controlled three-phase bridge converter is working from a 415 V, 50 Hz AC supply. It is supplying constant current of 100 A at 400 V to a DC load. Assume large inductive smoothing and neglect overlap. The rms value of the AC line current in amperes (round off to two decimal places) is _________

Answer: (81.00 to 82.00)

55. A single-phase fully-controlled thyristor converter is used to obtain an average voltage of 180 V with 10 A constant current to feed a DC load. It is fed from single-phase AC supply of 230 V, 50 Hz. Neglect the source impedance. The power factor (round off to two decimal places) of AC mains is _________.

Answer: (0.75 to 0.80)

GATE Exam 2019 Electronics and Communication Engineering (EC) Question Paper With Answer Key

June 7, 2023December 4, 2019 by suresh84

General Aptitude

Q.1 – Q. 5 carry one mark each.

1. The strategies that the company to sell its products house-to-house marketing.

(A) use, includes

(B) uses, include

(D) uses, including

Answer: (B)

2. The boat arrived dawn.

(A) in

(B) at

(D) under

Answer: (B)

3. It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is hours.

(A) 2/3

(B) 3/4

(D) 7/3

Answer: (C)

4. Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is_______.

(A) 2

(B) 6

(D) 120

Answer: (B)

5. When he did not come home, she _______him lying dead on the roadside somewhere.

(A) concluded

(B) looked

(D) pictured

Answer: (D)

Q.6 – Q. 10 carry two marks each.

6. Four One people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. is an engineer, one is a doctor, one a teacher and another a dancer. You are told that:

1.Mathew is not standing next to Seema

2.There are two people standing between Lohit and the engineer

3.Rahul is not a doctor

4 The teacher and the dancer are standing next to each other

5.Seema is turning to her right to speak to the doctor standing next to her

Who among them is an engineer?

(A) Seema

(B) Lohit

(D) Mathew

Answer: (D)

7. The bar graph in Panel (a) shows the proportion of male and female illiterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c), respectively. The total population did not change during this period.

The percentage increase in the total number of literates from 2001 to 2011 is_______ .

(A) 30.43

(B) 33.43

(D) 35.43

Answer: (A)

8. “Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latter-day Indian scholars presented a contrary picture.”

From the text above, we can infer that:

Indian history written by British historians ________

(A) was well documented and not researched but was always biased

(B) was not well documented and researched and was always biased

(D) was not well documented and researched and was sometimes biased

Answer: (C)

9. Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_____ remaining in the budget.

(A) 000.00

(B) 166.67

(D) 433.33

Answer: (B)

10. Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, who is currently sharing an office with T wants to move to the adjacent office with S, the handsome new intern. Given the floor plan, what is the current location of Q, R and T?

(O = Office, WR = Washroom)

Answer: (C)

Electronics and Communication Engineering

Q.1 – Q. 25 carry ONE mark each.

1. Which one of the following functions is analytic over the entire complex plane?

(A) ln(Z)

(B) e^1/z

(D) cos(z)

Answer: (D)

2. The families of curves represented by the solution of the equation

(A) Parabolas and Circles

(B) Circles and Hyperbolas

(D) Hyperbolas and Parabolas

Answer: (C)

3. Let H(z) be t he z-transform of a real-valued discrete-time signal ℎ[𝑛]. If P(z) = H(z)H(1/z) has a zero at and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly ?

Answer: (D)

4. Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).

Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?

(A) 0.5 A

(B) 1 A

(D) 2.5 A

Answer: (B)

5. Let Y(s) be unit-step response of a casual system having a transfer function

that is, The forced response of the system is

(A) u(t) – 2e^−tu(t) + e^−3tu(t)

(B) 2u(t) – 2e^−tu(t) + e^−3tu(t)

(D) u(t)

Answer: (D OR A)

6. For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles 𝑁𝑝 and the number of system zeros 𝑁𝑧 in the frequency range 1 Hz ≤ f ≤ 10⁷ Hz is

(A) N_p = 5, N_z = 2

(B) N_p = 6, N_z = 3

(D) N_p = 4, N_z = 2

Answer: (B)

7. A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to

(A) 0010011

(B) 1100001

(D) 1111111

Answer: (B)

8. Which one of the following options describes correctly the equilibrium band diagram at T = 300 K of a Silicon pnn⁺p⁺⁺ configuration shown in the figure?

Answer: (A)

9. The correct circuit representation of the structure shown in the figure is

Answer: (A)

10. The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with Φ_ms = 0 V and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points

(A) P, Q, R

(B) Q, R, P

(D) Q, P, R

Answer: (B)

11. What is the electric flux through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of Q?

(A) HQ/ε₀

(B) HQ/4ε₀

(D) 4H/Qε₀

Answer: (B)

12. In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side.

(A) 1 – P, 2 – R, 3 – Q, 4 – S

(B) 1 – Q, 2 – R, 3 – P, 4 – S

(D) 1 – R, 2 – Q, 3 – S, 4 – P

Answer: (B)

13. A standard CMOS inverter is designed with equal rise and fall times (β_n = β_p). If the width of the pMOS transistor in the inverter is increased, what would be the effect on the LOW noise margin (𝑁𝑀𝐿) and the HIGH noise margin NM_H?

(A) NM_L increases and NM_H decreases.

(B) NM_L decreases and NM_H increases.

(D) No change in the noise margins.

Answer: (A)

14. In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?

(A) 0 and D

(B) Hi-Z and D

(D)

Answer: (B)

15. In the circuit shown, A and B are the inputs and the circuit?

(A) Latch

(B) XNOR

(D) XOR

Answer: (B)

16. The value of the contour integral

evaluated over the unit circle |z| = 1 is________

Answer: (−0.0001 to .0001)

17. The number of distinct eigenvalues of the matrix

is equal to______.

Answer: (3 to 3)

18. If 𝑋 and 𝑌 are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] =_______.

Answer: (11 to 11)

19. The value of the integral is equal to ________.

Answer: (1.99 to 2.01)

20. Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by

Then Pr(Z > 2| Z > 1), rounded off to two decimal places, is equal to ________.

Answer: (0.36 to 0.38)

21. Consider the signal where t is in seconds. Its fundamental time period, in seconds, is ________.

Answer: (11.99 to 12.01)

22. The baseband signal 𝑚(𝑡) shown in the figure is phase-modulated to generate the PM signal φ(t) = cos(2πf_ct + k m(t)). The time 𝑡 on the x-axis in the figure is in milliseconds. If the carrier frequency is f_c = 50 kHz and k = 10π, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _______(rounded off to 2 decimal places).

Answer: (0.74 to 0.76)

23. Radiation resistance of a small dipole current element of length l at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is ______%.

Answer: (1.98 to 2.02)

24. In the circuit shown, V_s is a square wave of period 𝑇 with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and R₁ = R₂ = 50 Ω. The average value of V_L is ______-volts (rounded off to 1 decimal place).

Answer: (−3.1 to −2.9)

25. In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at Q₂ is_______kHz.

Answer: (4 to 4)

Q.26 – Q. 55 carry TWO marks each.

26. Consider a differentiable function f(x) on the set of real numbers such that f(−1) = 0 and |f′(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x ∈ [−2, 2]?

(A) f(x) ≤ 1/2|x + 1|

(B) f(x) ≤ 2|x + 1|

(D) f(x) ≤ 2|x|

Answer: (B)

27. Consider the line integral

the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of the region R shown in the figure below. The region R is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to

(A) 6 + π/2

(B) 8 + π

(D) 16 +2π

Answer: (C)

28. Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal flow graph corresponding to X[1] is shown in the figure. Let In the figure, what should be the values of the coefficients a₁, a₂, a₃ in terms of W₆ so that X[1] is obtained correctly?

(A) a₁ = −1, a₂ = W₆, a₃ = W₆²

(B) a₁ = 1, a₂ = W², a₃= W₆

(D) a₁ = −1, a₂ = W²₆, a₃ = W₆

Answer: (C)

29. It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

where c₁ and c₂ are arbitrary real numbers. The desired three-tap filter is given by

h[0] = 1, h[1] = a, h[2] = b

and

h[n] = 0, n < 0 or n > 2.

What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above?

(A) a = 1, b = 1

(B) a = 0, b = −1

(D) a = 0, b = 1

Answer: (D)

30. In the circuit shown, if v(t) = 2 sin(1000 t) volts, R = 1 kΩ and C = 1μF, t hen the steady-state current i(t) in miliamperes (mA), is

(A) sin(1000 t) + cos (1000 t)

(B) 2 sin(1000 t) + 2 cos(1000 t)

(D) sin(1000 t) + 3 cos(1000 t)

Answer: (C)

31. Consider a causal second-order system with the transfer function

with a unit-step R(s) = 1/s as an input. Let 𝐶(𝑠) be the corresponding output. The time taken by the system output 𝑐(𝑡) to reach 94% of its steady-state value rounded off to two decimal places, is

(A) 5.25

(B) 4.50

(D) 2.81

Answer: (B)

32. The block diagram of a system is illustrated in the figure shown, where X(𝑠) is the input and Y(s) is the output. The transfer function is

Answer: (B)

33. Let the state-space representation of an LTI system be , y(t) = C x(t) + d u(t) where A, B, C are matrices, d is a scalar d is a scalar, u (t) is the input to the system, and y(t) is its output. Let B = [0 0 1]^T and d = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is

Answer: (A)

34. A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density N₀/2. Binary signaling, with minimizes the bit-error probability.

Let φ₁(t), φ₂(t) form an orthonormal signal set.

It we choose p(t) = φ₁(t) and q(t) = − φ₁(t), we would obtain a certain bit-error probability P_b.

If we keep p(t) = φ₁(t), but take q(t) = √E φ₂(t), for what value of E would we obtain the same bit-error probability P_b?

(A) 0

(B) 1

(D) 3

Answer: (D)

35. The quantum efficiency (η) and responsivity (R) at a wavelength λ (in µm) in a p-i-n photodetector are related by

Answer: (A)

36. Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents I and 2I, respectively, in opposite directions. If the two wires are separated by a distance of 4r, then the magnitude of the magnetic field between the wires at a distance r from W1 is

Answer: (C)

37. The dispersion equation of a waveguide, which relates the wave number k to the frequency ω, is

where the speed of light c = 3 × 10⁸ m/s, and ω₀ is a constant. If the group velocity is 2 × 10⁸ m/s, then the phase velocity is

(A) 1.5 × 10⁸ m/s

(B) 2 × 10⁸ m/s

(D) 4.5 × 10⁸ m/s

Answer: (D)

38. In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are 20 V and 60 mA, respectively. The values of R₁ and R_L are 200 Ω and 1 kΩ, respectively. What is the range of Vi that will maintain the Zener diode in the ‘on’ state?

(A) 22 V to 34 V

(B) 24 V to 36 V

(D) 20 V to 28 V

Answer: (B)

39. The state transition diagram for the circuit shown is

Answer: (C)

40. In the circuits shown, the threshold voltage of each nMOS transistor is 0.6 V. Ignoring the effect of channel length modulation and body bias, the values of Vout1 and Vout2, respectively, in volts, are

(A) 1.8 and 1.2

(B) 2.4 and 2.4

(D) 2.4 and 1.2

Answer: (C)

41. The RC circuit shown below has a variable resistance 𝑅(𝑡) given by the following expression:

where R₀ = 1 Ω, and 𝐶 = 1 F. We are also given that T = 3 R₀C and the source voltage is V_s = 1 V. If the current at time t = 0 is 1 A, then the current I(t), in amperes, at time t = T/2 is _____(rounded off to 2 decimal places)

Answer: (0.23 to 0.27)

42. Consider a unity feedback system, as in the figure shown, with an integral compensator k/s and open-loop transfer function

where K > 0. The positive value of 𝐾 for which there are exactly two poles of the unity feedback system on the 𝑗𝜔 axis is equal to _______ (rounded off to two decimal places)

Answer: (5.99 to 6.01)

43. Consider the homogeneous ordinary differential equation

with y(x) as a general solution. Given that

y(1) = 1 and y(2) = 14

the value of y(1.5), rounded off to two decimal places, is________.

Answer: (5.24 to 5.26)

44. Let h[n] be a length-7 discrete-time finite impulse response filter, given by

h[0] = 4, h[1] = 3, h[2] = 2, h[3] = 1,

h[−1] = −3, h[−2] = −2, h[−3] = −1,

and h[n] is zero for |n| ≥ 4. A length-3 finite impulse response approximation g[n] of h[n] has to be obtained such that

is minimized, where H(e^jω) and G(e^jω) are the discrete-time Fourier transforms of h[n] and g[n], respectively. For the filter that minimizes E(h, h), the value of 10g[−1] + g[1], rounded off to 2 decimal places, is ________.

Answer: (−27.01 to 26.99)

45. Let a random process 𝑌(𝑡) be described as 𝑌(𝑡) = ℎ(𝑡) ∗ 𝑋(𝑡) + 𝑍(t), where 𝑋(𝑡) is a white noise process with power spectral density 𝑆𝑋(𝑓) = 5 W/Hz. The filter ℎ(𝑡) has a magnitude response given by |𝐻(𝑓)| = 0.5 for −5 ≤ 𝑓 ≤ 5, and zero elsewhere. 𝑍(𝑡) is a stationary random process, uncorrelated with 𝑋(𝑡), with power spectral density as shown in the figure. The power in 𝑌(𝑡), in watts, is equal to_____W (rounded off to two decimal places).

Answer: (17.40 to 17.60)

46. A voice signal 𝑚(𝑡) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude- modulated to generate an AM signal 𝑓(𝑡) = 𝐴(1 + 𝑚(𝑡)) cos 2𝜋𝑓𝑐𝑡, where 𝑓_𝑐 = 600 kHz. The AM signal 𝑓(𝑡) is to be digitized and archived. This is done by first sampling 𝑓(𝑡) at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using 𝐾 bits, where 𝐾 is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is _______Mbps.

Answer: (11.80 to 11.82)

47. A random variable 𝑋 takes values −1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise 𝑁, so that the random variable at the channel output is 𝑌 = 𝑋 + 𝑁. The noise 𝑁 is independent of 𝑋, and is uniformly distributed over the interval [−2 , 2]. The receiver makes a decision

where the threshold 𝜃 ∈ [−1,1] is chosen so as to minimize the probability of error The minimum probability of error, rounded off to 1 decimal place, is _____.

Answer: (0.1 to 0.1)

48. A Germanium sample of dimensions 1 cm × 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dioxide- Germanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is 3 × 10⁴ cm⁻¹ and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is ______µm.

Answer: (0.230 to 0.232)

49. In an ideal pn junction with an ideality factor of 1 at T=300 K, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2 decimal places, is _______mV.

[𝑘 = 1.38 × 10⁻²³ JK⁻¹, ℎ = 6.625 × 10⁻³⁴ J-s, 𝑞 = 1.602 × 10⁻¹⁹C].

Answer: (34.00 to 38.00)

50. Consider a long-channel MOSFET with a channel length 1 µm and width 10 µm. The device parameters are acceptor concentration NA= 5 × 10¹⁶ cm^-3, electron mobility µn=800 cm2/V-s, oxide capacitance/area Cox= 3.45 × 10⁻⁷ F/cm², threshold voltage VT=0.7 V. The drain saturation current (IDsat) for a gate voltage of 5 V is ______ mA (rounded off to two decimal places). [𝜀₀ = 8.854 × 10⁻¹⁴F/cm, 𝜀_𝑆𝑖 = 11.9]

Answer: (25.40 to 25.60)

51. A rectangular waveguide of width w and height h has cut-off frequencies for TE₁₀ and TE₁₁ modes in the ratio 1: 2. The aspect ratio w/h, rounded off to two decimal places, is______.

Answer: (1.71 to 1.75)

52. In the circuit shown, Vs is a 10 V square wave of period, T = 4 ms with R = 500 Ω and C = 10 µF. The capacitor is initially uncharged at t=0, and the diode is assumed to be ideal. The voltage across the capacitor (V_c) at 3 ms is equal to ______volts (rounded off to one decimal place).

Answer: (3.2 to 3.4)

53. A CMOS inverter, designed to have a mid-point voltage V_I equal to half of V_dd, as shown in the figure, has the following parameters:

V_dd = 3 V

μ_nC_ox = 100 μA/V²; V_tn = 0.7 V forn MOS

μ_pC_ox = 40 μA/V²; |V_tp| = 0.9 V for pMOS

The ratio of (W/L)_n to (W/L)_p is equal to ________(rounded off to 3 decimal places).

Answer: (0.210 to 0.230)

54. In the circuit shown, the threshold voltages of the pMOS (|V_tp|) and nMOS (𝑉_tn) transistors are both equal to 1 V. All the transistors have the same output resistance r_ds of 6 MΩ. The other parameters are listed below:

μ_nC_ox = 60 μA/V² ; (W/L)_nMOS = 5

μ_pC_ox = 30 μA/V² ; (W/L)_pMOS = 10

μ_n and μ_p are the carrier mobilities, and 𝐶ox is the oxide capacitance per unit area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is (rounded off to 1 decimal place).

Answer: (-905 to -895 OR 895.0 to 905.0)

55. In the circuit shown, V₁ = 0 and V₂ = V_dd. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of Iout is _______ mA (rounded off to 1 decimal place).

Answer: (5.9 to 6.1)

GATE Exam 2019 Chemistry (CY) Question Paper With Answer Key

June 7, 2023December 3, 2019 by suresh84

General Aptitude

Q.1 – Q. 5 carry one mark each.

1. John Thomas, an writer, passed away in 2018.

(A) imminent

(B) prominent

(D) dominant

Answer: (C)

2. _________I permitted him to leave, I wouldn’t have had any problem with him being absent, _________I?

(A) Had, wouldn’t

(B) Have, would

(D) Have, wouldn’t

Answer: (C)

3. A work her staer noticed that the hour hand on the factory clock had moved by 225 degrees during y at the factory. For how long did she stay in the factory?

(A) 3.7 5 hours

(B) 4 hours and 15 mins

(D) 7.5 hours

Answer: (D)

4. The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is _______.

(A) 2

(B) 3

(D) 6

Answer: (C)

5. The minister avoided any mention of the issue of women’s reservation in the private sector. He was accused of_______the issue.

(A) collaring

(B) skirting

(D) belting

Answer: (B)

Q.6 – Q. 10 carry two marks each.

6. Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then they are shot. One prisoner made a statement and the judge had no option but to set him free. Which one of the following could be that statement?

(A) I did not commit the crime

(B) I committed the crime

(D) You committed the crime

Answer: (C)

7. A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes. In one he got 10% profit and in the other he got 12%. If the profit percentages are interchanged with these investments he would have got Rs.120 less. Find the ratio between his investments in the two schemes.

(A) 9 : 16

(B) 11 : 14

(D) 47 : 53

Answer: (D)

8. Congo was named by Europeans. Congo’s dictator Mobuto later changed the name of the country and the river to Zaire with the objective of Africanising names of persons and spaces. However, the name Zaire was a Portuguese alteration of Nzadi o Nzere, a local African term meaning ‘River that swallows Rivers’. Zaire was the Portuguese name for the Congo river in the 16th and 17th centuries.

Which one of the following statements can be inferred from the paragraph above?

(A) Mobuto was not entirely successful in Africanising the name of his country

(B) The term Nzadi o Nzere was of Portuguese origin

(D) As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire

Answer: (A)

9. A firm hires employees at five different skill levels P, Q, R, S, T. The shares of employment at these skill levels of total employment in 2010 is given in the pie chart as shown. There were a total of 600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total employment at skill levels P, Q and R remained unchanged during this period. If the employment at skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in 2016?

(A) 30

(B) 35

(D) 72

Answer: (C)

10. M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily FALSE?

(A) M is the grandmother of Y

(B) R is the father of Y

(D) W is the wife of P

Answer: (D)

Chemistry

Q .1 – Q. 25 carry one mark each.

1. The INCORRECT statement about the solid-state structure of CsCl and CaF2 is:

(A) Cations in both solids exhibit coordination number 8.

(B) CsCl has bcc type structure and CaF2 has cubic close pack structure.

(D) Both exhibit close pack structure.

Answer: (D)

2. The INCORRECT statement about the interhalogen compound ICl3 is:

(A) It exists as a dimer.

(B) Geometry around the iodine is tetrahedral in solid-state.

(D) Liquid ICl3 conducts electricity.

Answer: (B)

3. Among the following carbon allotropes, the one with discrete molecular structure is

(A) Diamond

(B) α-Graphite

(D) Fullerene

Answer: (D)

4. The INCORRECT statement about the silicones is:

(A) They are thermally unstable because of the Si–C bond.

(B) They are insoluble in water.

(D) They have stable silica-like skeleton (–Si–O–Si–O–Si–).

Answer: (A)

5. The ∆_o value of [Ni(H₂O)₆]²⁺ is 8500 cm⁻¹. The ∆₀values for [NiCl₆]⁴⁻ and [Ni(NH₃)₆]²⁺ compared to [Ni(H₂O)₆]²⁺ are

(A) higher and lower, respectively.

(B) lower and higher, respectively.

(D) lower in both complex ions.

Answer: (B)

6. The Freundich isotherm, a linear relationship is obtained in the plot of

(θ = surface coverage and p = partial pressure of the gas)

(A) θ vs p.

(B) ln (θ) vs ln(p).

(D) θ vs ln(p).

Answer: (B)

7. Micelle formation is accompanied by the

(A) decrease in overall entropy due to ordering.

(B) increase in overall entropy mostly due to increase in solvent entropy.

(D) increase in overall entropy and decrease in enthalpy.

Answer: (B)

8. Consider the following phase diagram of CO₂ (not to scale). At equilibrium, the INCORRECT statement is:

(A) At 200 K, on increasing the pressure from 1 to 50 atm, CO₂ gas condenses to liquid.

(B) It is not possible to obtain liquid CO₂ from gaseous CO2 below 5.11 atm.

(D) With increasing pressure, the melting point of solid CO₂ increases.

Answer: (A)

9. The major product formed in the following reaction is

Answer: (B)

10. The Woodward-Hoffmann condition to bring out the following transformation is

(A) ∆, conrotatory

(B) ∆, disrotatory

(D) hν, conrotatory

Answer: (D)

11. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (B)

12. In the following reaction, the stereochemistry of the major product is predicted by the

(A) Cram ’s model

(B) Cram’s chelation model

(D) Felkin-Anh model

Answer: (B)

13. The product(s) formed in the following reaction is (are)

(A) I only

(B) II only

(D) mixture of I and II

Answer: (C)

14. Among the following compounds, the number of compounds that DO NOT exhibit optical

activity at room temperature is _________.

Answer: (4 to 4)

15. The number of following diene(s) that undergo Diels-Alder reaction with methyl acrylate is______.

Answer: (5 to 5)

16. The number of 1H NMR signals observed for the following compound is_________ .

Answer: (6 to 6)

17. The number of CO stretching bands in IR spectrum of trigonal bipyramidal cis-M(CO)₃L₂ is _______.

(M = metal and L = monodentate ligand)

Answer: (3 to 3)

18. On heating a sample of 25 mg hydrated compound (molecular weight = 250 g/mol) in thermogravimetric analysis, 16 mg of dehydrated compound remains. The number of water molecules lost per molecule of hydrated compound is __________.

(Molecular weight of water = 18 g/mol)

Answer: (5 to 5)

19. The total number of α and β particles emitted in the following radioactive decay is ________.

Answer: (11 to 11)

20. An ideal gas occupies an unknown volume V liters (L) at a pressure of 12 atm. The gas is expanded isothermally against a constant external pressure of 2 atm so that its final volume becomes 3 L. The work involved for this expansion process is ________cal. (Round off to two decimal places)

(Gas constant R = 0.082 L atm mol^–1 K^–1 = 2 cal mol^–1 K^–1)

Answer: (-126.00 to -120.00)

21. The entropy change for the melting of ‘x’ moles of ice (heat of fusion is 80 cal g^–1) at 273 K and 1 atm pressure is 28.80 cal K^–1. The value of ‘x’ is ______. (Round off to two decimal places)

(Molecular weight of water =18 g/mol)

Answer: (5.410 to 5.55)

22. Consider a two-state system at thermal equilibrium having energies 0 and 2kBT for which the degeneracies are 1 and 2, respectively. The value of the partition function at the same absolute temperature T is _______. (Round off to two decimal places)

(kB is the Boltzmann constant)

Answer: (1.25 to 1.30)

23. Consider a system of three identical and distinguishable non-interacting particles and three available nondegenerate single particle energy levels having energies 0, ε and 2εThe system is in contact with a heat bath of temperature T K. A total energy of 2ɛ is shared by these three particles. The number of ways the particles can be distributed is_______.

Answer: (6 to 6)

24. In a 400 MHz 1H NMR spectrometer, a proton resonates at 1560 Hz higher than that of tetramethylsilane. The chemical shift value of this proton is _____ ppm. (Round off to one decimal place)

(Chemical shift of tetramethylsilane is fixed at zero ppm)

Answer: (3.9 to 3.9)

25. Gas phase bond length and dipole moment of a compound (MX) is 3 Å and 10.8 D, respectively. The ionic character in gas phase MX is _______%. (Round off to one decimal place)

(1D = 3.336 × 10^–30 C m)

Answer: (74.0 to 76.0)

Q.26 – Q. 55 carry two marks each.

26. The experimentally observed magnetic moment values, which match well with the spin-only values for the pair of aqueous ions is

(Atomic number: Cr = 24, Co = 27, Gd = 64, Tb = 65, Dy = 66 and Lu = 71)

(A) Cr(III)and Gd(III)

(B) Co(II) and Gd (III)

(D) Lu(III) and Tb(III)

Answer: (A)

27. Among the following compounds, a normal spinel is

(A) MgFe₂O₄

(B) ZnFe₂O4

(D) CuFe₂O₄

Answer: (B)

28. Following are the examples of silicate minerals

The correct structural description of the minerals is

(A) I – Ortho silicate, II – Cyclic silicate and III – Sheet silicate

(B) I – Ortho silicate, II – Sheet silicate and III – Cyclic silicate

(D) I – Sheet silicate, II – Ortho silicate and III – Cyclic silicate

Answer: (A)

29. In the EPR spectrum of a methyl radical, the number of lines and their relative intensities, respectively, are

(A) 1 and 1

(B) 3 and 1:2:1

(D) 4 and 1:3:3:1

Answer: (D)

30. The product obtained in the reaction of Mn₂(CO)₁₀ with Br₂ is

(A) Mn(CO)5Br

(B) Mn₂(CO)₈Br₂

(D) Mn₂(CO)₉Br

Answer: (A)

31. The correct molecular representation of W(Cp)₂(CO)₂ is

(Cp = cyclopentadienyl)

32. Match the metalloproteins with their respective functions.

(A) P – III; Q – II; R – I; S – IV

(B) P – III; Q – I; R – IV; S – II

(D) P – IV; Q – II; R – I; S – III

Answer: (B)

33. Suppose the wave function of a one dimensional system is

Ψ = sin(kx)exp(3ikx).

In an experiment measuring the momentum of the system, one of the expected outcomes is

(A) 0

(B) ћk

(D) 3 ћk

Answer: (C)

34. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (A)

35. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (B)

36. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (D)

37. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (D)

38. In the following reaction sequence, the products P and Q are

(A)

(B)

(C)

(D)

Answer: (C)

39. The major product formed in the following reaction is.

(PCC = pyridinium chlorochromate)

(A)

(B)

(C)

(D)

Answer: (C)

40. In the following reactions, the major products P and Q are

(A)

(B)

(C)

(D)

Answer: (B)

41. In the following reaction sequence, the products P and Q are

(A)

(B)

(C)

(D)

Answer: (B)

42. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Answer: (C)

43. The rate of the following redox reaction is slowest when X is

(A) H₂O

(B) NH₃

(D) N₃^–

Answer: (B)

44. A complex is composed of one chromium ion, three bromides and six water molecules. Upon addition of excess AgNO₃, 1.0 g aqueous solution of the complex gave 0.94 g of AgBr. The molecular formula of the complex is

(Atomic weight: Cr = 52, Br = 80, Ag = 108, O = 16 and H = 1)

(A) [Cr(H₂O)₆]Br₃

(B) [Cr(H₂O)₅Br]Br₂•H₂O

(D) [Cr(H₂O)₃Br₃]•3H₂O

Answer: (B)

45. The number of possible optically active isomer(s) for the following complex is ________.

en = ethylenediamine

Answer: (2 to 2 OR 4 to 4)

46. The specific rotation of optically pure (R)-2-bromobutane is –112.00. A given sample of 2-bromobutane exhibited a specific rotation of –82.88. The percentage of (S)-(+)-enantiomer present in this sample is_______.

Answer: (13 to 13)

47. Consider the following two parallel irreversible first order reactions at temperature T,

where 𝑘₁and 𝑘₂ are the rate constants and their values are 5 × 10^–2 and 15 × 10^–2 min^–1, respectively, at temperature T. If the initial concentration of the reactant ‘P’ is 4 mol L^–1, then the concentration of product ‘R’ after 10 min of reaction is _____ mol L^–1. (Round off to two decimal places)

(Assume only P is present at the beginning of the reaction.)

Answer: (2.50 to 2.65)

48. Consider the following equilibrium

At 298 K, the standard molar Gibbs energies of formation, ∆_fG⁰, of SO₂ (g) and SO₃ (g) are –300 and –371 kJ mol^{– 1}, respectively. The value of the equilibrium constant, KP, at this temperature is ______× 10¹⁰. (Round off to the nearest integer)

(Gas constant R = 8.31 J mol^–1 K^–1)

Answer: (265 to 295)

49. Consider the electrochemical cell

M(s)|MI₂(s)|MI₂(aq)|M(s)

where ‘M’ is a metal. At 298 K, the standard reduction potentials are

and the temperature coefficient is

At this temperature the standard enthalpy change for the

overall cell reaction, ∆_rH⁰, is _____kJ mol^–1. (Round off to two decimal places)

(Faraday constant F = 96500 C mol^–1)

Answer: (-38.00 to -37.00)

50. The normal boiling point of a compound (X) is 350 K (heat of vaporization, ∆_vapH, = 30 kJ mol–1). The pressure required to boil ‘X’ at 300 K is_______ Torr. (Round off to two decimal places)

(Ignore the temperature variation of ∆vapH; Gas constant R = 8.31 J mol^–1 K^–1 and 1 atm = 760 Torr)

Answer: (120.00 to 140.00)

51. For a bimolecular gas phase reaction P + Q → R, the pre-exponential factor is 1 × 10¹³ dm³ mol^–1 s^–1. The standard entropy of activation at 25°C is ______ J K^–1 mol^–1. (Round off to two decimal points)

(The standard concentration c^o = 1 mol dm^–3; Planck constant h = 6.62 × 10^–34 J s; Boltzmann constant k_B = 1.38 × 10^–23 JK^–1; Gas constant R = 8.31 J mol^–1 K^–1)

Answer: (-12.90 to -12.40)

52. Character table of point group D8 is given below.

Value of (a + b + c + d + e + f + g + h + i + j + k) is equal to _______.

Answer: (9 to 9)

53. If are spin angular momentum operators and is spin up eigen function, then the value of ‘a’ is _____ . (Round off to one decimal place)

Answer: (0.5 to 0.5)

54. A particle in one dimensional box of length 2a with potential energy

is perturbed by the potential V’ = cx eV, where c is a constant. The 1st order correction to the 1st excited state of the system is ______× c eV.

Answer: (0 to 0)

55. Consider a two dimensional harmonic oscillator with angular frequency ω_x = 2ω_y = 6.5 × 10¹⁴ rad s^–1. The wavelength of x polarized light required for the excitation of a particle from its ground state to the next allowed excited state is _____ × 10⁻⁶ m. (Round off to one decimal place)

(Speed of light c = 3.0 × 10⁸ ms^–1)

Answer: (2.8 to 3.0)

GATE Exam 2019 Computer Science and Information Technology (CS) Question Paper With Answer Key

June 7, 2023December 3, 2019 by suresh84

General Aptitude

Q. 1 – Q. 5 carry one mark each.

1. The expenditure on the project as follows: equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.

(A) break down

(B) break

(D) breaks

Answer: (C)

2. The search engine’s business model around the fulcrum of trust.

(A) revolves

(B) plays

(D) burst

Answer: (A)

3. Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 km/h and the speed of the second car is 60 km/h. The number of hours it takes for the distance between the two cars to be 20 km is ____.

(A) 1

(B) 2

(D) 6

Answer: (B)

4. Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ______.

(A) 666

(B) 3000

(D) 12000

Answer: (C)

5. A court is to a judge as ______ is to a teacher.

(A) a student

(B) a punishment

(D) a school

Answer: (D)

Q. 6 – Q. 10 carry two marks each.6

6. The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:

P says “Q committed the crime.”

Q says “S committed the crime.”

R says “I did not do it.”

S says “What Q said about me is false.”

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

(A) P

(B) R

(D) Q

Answer: (B)

7. In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of the people, the percentage of administrators shall be in the range of _____.

(A) 0 to 15

(B) 16 to 30

(D) 46 to 60

Answer: (C)

8. “A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net.”

Which one of the following statements can be inferred from the given passage?

(A) Beggars are lazy people who beg because they are unwilling to work

(B) Beggars are created because of the lack of social welfare schemes

(D) Begging has to be banned because it adversely affects the welfare of the state

Answer: (B)

9. In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths clubs, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is .

(A) 1000

(B) 975

(D) 225

Answer: (C)

10. Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests. Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell. Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

The shaded rooms are already occupied. WR is washroom.

(A)

(B)

(C)

(D)

Answer: (D)

Computer Science and Information Technology

1. A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main memory is byte addressable and uses a 32-bit address. How many bits are required for the Tag and the Index fields respectively in the addresses generated by the processor?

(A) 24 bits and 0 bits

(B) 28 bits and 4 bits

(D) 28 bits and 0 bits

Answer: (D)

2. The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system has 16 address lines denoted by A15 to A0. What is the range of addresses (in hexadecimal) of the memory system that can get enabled by the chip select (CS) signal?

(A) C800 to CFFF

(B) CA00 to CAFF

(D) DA00 to DFFF

Answer: (A)

3. Which one of the following kinds of derivation is used by LR parsers?

(A) Left most

(B) Leftmost in reverse

(D) Rightmost in reverse

Answer: (D)

4. Which one of the following kinds of derivation is used by LR parsers?

(A) Leftmost

(B) Leftmost in reverse

(D) Rightmost in reverse

Answer: (C)

5. Let U = {1, 2, …., n}. Let A = {(x, X)|x ∈ X, X ⊆}. Consider the following two statements on |A|.

Which of the above statements is/are TRUE?

(A) Only I

(B) Only II

(D) Neither I nor II

Answer: (C)

6. Which one of the following is NOT a valid identity?

Answer: (B)

7. If 𝐿 is a regular language over ∑ = {a, b}, which one of the following languages is NOT regular ?

8.Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in 𝑛 bits. To avoid overflow, the representation of Z would require a minimum of:

(A) 𝑛 bits

(B) 𝑛 − 1 bits

(D) 𝑛 + 2 bits

Answer: (B)

9. Let 𝑋 be a square matrix. Consider the following two statements on 𝑋.

I. 𝑋 is invertible.

Determinant of 𝑋 is non-zero.

Which one of the following is TRUE?

(A) I implies II; II does not imply I.

(B) II implies I; I does not imply II.

(D) I and II are equivalent statements.

Answer: (D)

10. Let 𝐺 be an arbitrary group. Consider the following relations on 𝐺:

Which of the above is/are equivalence relation/relations?

(A) 𝑅₁ and 𝑅₂

(B) 𝑅₁ only

(D) Neither 𝑅₁ nor 𝑅₂

Answer: (B)

11. Consider the following two statements about database transaction schedules:

I. Strict two-phase locking protocol generates conflict serializable schedules that are also recoverable.

II. Timestamp-ordering concurrency control protocol with Thomas’ Write Rule can generate view serializable schedules that are not conflict serializable.

Which of the above statements is/are TRUE?

(A) I only

(B) II only

(D) Neither I nor II

Answer: (C)

12. Let 𝐺 be an undirected complete graph on 𝑛 vertices, where 𝑛 > 2. Then, the number of different Hamiltonian cycles in 𝐺 is equal to

(A) 𝑛!

(B) (𝑛 − 1)!

(D)

Answer: (C OR D)

13.

(A) 1

(B) 53/12

(D) Limit does not exist

Answer: (C)

14. Which one of the following statements is NOT correct about the B+ tree data structure used for creating an index of a relational database table?

(A) B+ Tree is a height-balanced tree

(B) Non-leaf nodes have pointers to data records

(D) Each leaf node has a pointer to the next leaf node

Answer: (B)

15. For Σ = {𝑎, 𝑏}, let us consider the regular language 𝐿 = { 𝑥 |𝑥 = 𝑎²⁺³^𝑘 or 𝑥 = 𝑏¹⁰⁺¹²^𝑘,

𝑘 ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for 𝐿 ?

(A) 3

(B) 5

(D) 24

Answer: (D)

16. Which of the following protocol pairs can be used to send and retrieve e-mails (in that order)?

(A) IMAP, POP3

(B) SMTP, POP3

(D) IMAP, SMTP

Answer: (B)

17. The following C program is executed on a Unix/Linux system:

The total number of child processes created is______.

Answer: (31 to 31)

18. Consider the following C program:

The value printed by the program is_______.

Answer: (26 to 26)

19. Consider the grammar given below: S → Aa

Let a, b, d, and $ be indexed as follows:

Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210) Answer: _______.

Answer: (31 to 31)

20. An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is ______.

Answer: (0.08 to 0.08)

21. The value of 3⁵¹ mod 5 is _______.

Answer: (2 to 2)

22. Two numbers are chosen independently and uniformly at random from the set {1, 2 , . . . , 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ________.

Answer: (0.502 to 0.504)

23. Consider three concurrent processes P1, P2 and P3 as shown below, which access a shared variable D that has been initialized to 100.

The processes are executed on a uniprocessor system running a time-shared operating system. If the minimum and maximum possible values of D after the three processes have completed execution are X and Y respectively, then the value of Y – X is _______.

Answer: (80 to 80)

24. Consider the following C program:

The number that will be displayed on execution of the program is_______.

Answer: (6 to 6)

25. Consider a sequence of 14 elements: A = [−5, −10, 6, 3, −1, −2, 13, 4, −9, −1, 4, 12, −3, 0]. The subsequence sum Determine the maximum of 𝑆(𝑖, 𝑗), where 0 ≤ 𝑖 ≤ 𝑗 < 14. (Divide and conquer approach may be used.)

Answer: _____.

Answer: (29 to 29)

26. Consider the following C function.

Which one of the following will happen when the function convert is called with any positive integer n as argument?

(A) It will print the binary representation of n and terminate

(B) It will print the binary representation of n in the reverse order and terminate

(D) It will not print anything and will not terminate

Answer: (D)

27. Consider the following C program:

Which one of the following values will be displayed on execution of the programs?

(A) 41

(B) 52

(D) 630

Answer: (B)

28. Consider three machines M, N, and P with IP addresses 100.10.5.2, 100.10.5.5, and 100.10.5.6 respectively. The subnet mask is set to 255.255.255.252 for all the three machines. Which one of the following is true?

(A) M, N, and P all belong to the same subnet

(B) Only M and N belong to the same subnet

(D) M, N, and P belong to three different subnets

Answer: (C)

29. Suppose that in an IP-over-Ethernet network, a machine X wishes to find the MAC address of another machine Y in its subnet. Which one of the following techniques can be used for this?

(A) X sends an ARP request packet to the local gateway’s IP address which then finds the MAC address of Y and sends to X

(B) X sends an ARP request packet to the local gateway’s MAC address which then finds the MAC address of Y and sends to X

(D) X sends an ARP request packet with broadcast IP address in its local subnet

Answer: (C)

30. Consider three 4-variable functions f₁, f₂, and f₃, which are expressed in sum-of-minterms as

f1 = ∑ (0, 2, 5, 8, 14), f2 = ∑ (2, 3, 6, 8, 14, 15), f3 = ∑ (2, 7, 11, 14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

(A) ∑ (7, 8, 11)

(B) ∑ (2, 7, 8, 11, 14)

(D) ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)

Answer: (A)

31. Which one of the following languages over Σ = {𝑎, 𝑏} is NOT context-free?

Answer: (C)

32. Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS).

Consider the two statements given below.

(I) Both Y and Z are in BCNF

(II) Decomposition of X into Y and Z is dependency preserving and lossless

Which of the above statements is/are correct?

(A) Both I and II

(B) I only

(D) Neither I nor II

Answer: (C)

33. Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressible. The page size is 8 kB and the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss?

(A) 16 × 2¹⁰

(B) 256 × 2¹⁰

(D) 8 × 2²⁰

Answer: (B)

34. Consider the following sets:

S1 Set of all recursively enumerable languages over the alphabet {0,1}

S2 Set of all syntactically valid C programs S3. Set of all languages over the alphabet {0,1}

S4 Set of all non-regular languages over the alphabet {0,1}

Which of the above sets are uncountable?

(A) S1 and S2

(B) S3 and S4

(D) S1 and S4

Answer: (B)

35. Consider the first order predicate formula 𝜑:

∀𝑥 [(∀𝑧 𝑧|𝑥 ⇒ ((𝑧 = 𝑥) ∨ (𝑧 = 1))) ⇒ ∃𝑤 (𝑤 > 𝑥) ∧ (∀𝑧 𝑧|𝑤 ⇒ ((𝑤 = 𝑧) ∨ (𝑧 = 1)))] Here ‘𝑎|𝑏’ denotes that ‘𝑎 divides 𝑏’, where 𝑎 and 𝑏 are integers. Consider the following sets:

S1. {1,2,3, … , 100}

S2. Set of all positive integers

S3. Set of all integers

Which of the above sets satisfy 𝜑?

(A) S1 and S2

(B) S1 and S3

(D) S1, S2 and S3

Answer: (C)

36. Consider the following grammar and the semantic actions to support the inherited type declaration attributes. Let 𝑋₁, 𝑋₂, 𝑋₃, 𝑋₄, 𝑋₅, and 𝑋₆ be the placeholders for the non- terminals D, T, L or L₁ in the following table:

Which one of the following are the appropriate choices for 𝑋1, 𝑋2, 𝑋3 and 𝑋4?

(A) 𝑋₁ = 𝐿 , 𝑋₂ = 𝑇, 𝑋₃ = 𝐿₁, 𝑋₄ = 𝐿

(B) 𝑋₁ = 𝑇 , 𝑋₂ = 𝐿, 𝑋₃ = 𝐿₁, 𝑋₄ = 𝑇

(D) 𝑋₁ = 𝑇 , 𝑋₂ = 𝐿, 𝑋₃ = 𝑇, 𝑋₄ = 𝐿1

Answer: (A)

37. There are n unsorted arrays: A₁, A₂, …, An. Assume that n is odd. Each of A₁, A₂, …, An contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A₁, A₂, …, An is

(A) O(n)

(B) O(n log n)

(D) Ω(n² log n)

Answer: (C)

38. Let 𝐺 be any connected, weighted, undirected graph.

I. 𝐺 has a unique minimum spanning tree, if no two edges of 𝐺 have the same weight.

II. 𝐺 has a unique minimum spanning tree, if, for every cut of 𝐺, there is a unique minimum-weight edge crossing the cut.

Which of the above two statements is/are TRUE?

(A) I only

(B) II only

(D) Neither I nor II

Answer: (C)

39. Consider the following snapshot of a system running 𝑛 concurrent processes. Process 𝑖 is holding 𝑋𝑖 instances of a resource R, 1 ≤ 𝑖 ≤ 𝑛. Assume that all instances of R are currently in use. Further, for all 𝑖, process 𝑖 can place a request for at most 𝑌𝑖 additional instances of R while holding the 𝑋𝑖 instances it already has. Of the 𝑛 processes, there are exactly two processes 𝑝 and 𝑞 such that 𝑌_𝑝 = 𝑌_𝑞 = 0. Which one of the following conditions guarantees that no other process apart from 𝑝 and 𝑞 can complete execution?

Answer: (A)

40. Consider the following statements:

I. The smallest element in a max-heap is always at a leaf node

II. The second largest element in a max-heap is always a child of the root node

III. A max-heap can be constructed from a binary search tree in Θ(𝑛) time

IV. A binary search tree can be constructed from a max-heap in Θ(𝑛) time

Which of the above statements are TRUE?

(A) I, II and III

(B) I, II and IV

(D) II, III and IV

Answer: (A)

41. Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in milliseconds) as shown below:

These processes are run on a single processor using preemptive Shortest Remaining Time First scheduling algorithm. If the average waiting time of the processes is 1 millisecond, then the value of Z is______.

Answer: (2 to 2)

42. The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointers. The disk block size is 4 kB, and the disk block address is 32-bits long. The maximum possible file size is (rounded off to 1 decimal place)_____GB.

Answer: (3.7 to 3.8 OR 4.0 to 4.1)

43. Consider the augmented grammar given below

Let I0 = CLOSURE ({[S’ → •S]}). The number of items in the set GOTO (I₀ , 〈 ) is:_____.

Answer: (5 to 5)

44. Consider the following matrix:

The absolute value of the product of Eigen values of 𝑅 is_______.

Answer: (12 to 12)

45. A certain processor deploys a single-level cache. The cache block size is 8 words and the word size is 4 bytes. The memory system uses a 60-MHz clock. To service a cache miss, the memory controller first takes 1 cycle to accept the starting address of the block, it then takes 3 cycles to fetch all the eight words of the block, and finally transmits the words of the requested block at the rate of 1 word per cycle. The maximum bandwidth for the memory system when the program running on the processor issues a series of read operations is _______× 10⁰⁰ bytes/sec.

Answer: (160 to 160)

46. Let 𝑇 be a full binary tree with 8 leaves. (A full binary tree has every level full.) Suppose two leaves 𝑎 and 𝑏 of 𝑇 are chosen uniformly and independently at random. The expected value of the distance between 𝑎 and 𝑏 in 𝑇 (i.e., the number of edges in the unique path between 𝑎 and 𝑏) is (rounded off to 2 decimal places)______.

Answer: (4.25 to 4.25)

47. Suppose 𝑌 is distributed uniformly in the open interval (1,6). The probability that the polynomial 3𝑥² + 6𝑥𝑌 + 3𝑌 + 6 has only real roots is (rounded off to 1 decimal place) _____.

Answer: (0.8 to 0.8)

48. Let Σ be the set of all bijections from {1, … , 5} to {1, … , 5}, where 𝑖𝑑 denotes the identity function, i.e. 𝑖𝑑(𝑗) = 𝑗, ∀𝑗. Let ∘ denote composition on functions. For a string 𝑥 = 𝑥1 𝑥2 ⋯ 𝑥𝑛 ∈ Σ𝑛, 𝑛 ≥ 0 , let 𝜋(𝑥) = 𝑥1 ∘ 𝑥2 ∘ ⋯ ∘ 𝑥𝑛.

Consider the language 𝐿 = {𝑥 ∈ Σ∗| 𝜋(𝑥) = 𝑖𝑑 }. The minimum number of states in any DFA accepting 𝐿 is ________.

Answer: (120 to 120)

49. Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches.

Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is _________.

Answer: (3 to 3)

50. What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = ∑ (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer: ______.

Answer: (3 to 3)

51. A relational database contains two tables Student and Performance as shown below:

The primary key of the Student table is Roll_no. For the Performance table, the columns Roll_no. and Subject_code together form the primary key. Consider the SQL query given below:

The number of rows returned by the above SQL query is______ .

Answer: (5 to 5)

52. Consider the following C program:

The number of times the variable sum will be printed, when the above program is executed, is ________.

Answer: (5 to 5)

53. Consider the following C program:

The output of the above C program is _______.

Answer: (10 to 10)

54. In an RSA cryptosystem, the value of the public modulus parameter 𝑛 is 3007. If it is also known that φ(𝑛) = 2880, where φ () denotes Euler’s Totient Function, then the prime factor of 𝑛 which is greater than 50 is ______.

Answer: (97 to 97)

55. Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).

How many tuples will be returned by the following relational algebra query?

Answer: ________.

Answer: (1 to 1)

GATE Exam 2019 Chemical Engineering (CH) Question Paper With Answer Key

June 7, 2023December 3, 2019 by suresh84

General Aptitude

Q. 1 – Q. 5 carry one mark each.

1. The expenditure on the project as follows: equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.

(A) break down

(B) break

(D) breaks

Answer: (C)

2. The search engine’s business model around the fulcrum of trust.

(A) revolves

(B) plays

(D) burst

Answer: (A)

(A) 1

(B) 2

(D) 6

Answer: (B)

(A) 666

(B) 3000

(D) 12000

Answer: (C)

5. A court is to a judge as ______ is to a teacher.

(A) a student

(B) a punishment

(D) a school

Answer: (D)

Q. 6 – Q. 10 carry two marks each.6

6. The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:

P says “Q committed the crime.”

Q says “S committed the crime.”

R says “I did not do it.”

S says “What Q said about me is false.”

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

(A) P

(B) R

(D) Q

Answer: (B)

(A) 0 to 15

(B) 16 to 30

(D) 46 to 60

Answer: (C)

Which one of the following statements can be inferred from the given passage?

(A) Beggars are lazy people who beg because they are unwilling to work

(B) Beggars are created because of the lack of social welfare schemes

(D) Begging has to be banned because it adversely affects the welfare of the state

Answer: (B)

(A) 1000

(B) 975

(D) 225

Answer: (C)

Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell. Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

The shaded rooms are already occupied. WR is washroom.

(A)

(B)

(C)

(D)

Answer: (D)

Chemical Engineering

1. A system of n homogeneous linear equations containing n unknowns will have non-trivial solutions if and only if the determinant of the coefficient matrix is

(A) 1

(B) −1

(D) ∞

Answer: (D)

2. The value of the expression is

(A) ∞

(B) 0

(D) −1

Answer: (C)

3. Consider a rigid, perfectly insulated, container partitioned into two unequal parts by a thin membrane (see figure). One part contains one mole of an ideal gas at pressure 𝑃_𝑖 and temperature 𝑇_𝑖 while the other part is evacuated. The membrane ruptures, the gas fills the entire volume and the equilibrium pressure is 𝑃_𝑓 = 𝑃𝑖⁄4. If 𝐶_𝑝 (molar specific heat capacity at constant pressure), 𝐶_𝑣 (molar specific heat capacity at constant volume) and 𝑅 (universal gas constant) have the same units as molar entropy, the change in molar entropy (𝑆_𝑓 − 𝑆_𝑖) is

(A) C_𝑝ln2 + Rln4

(B) −C_𝑣ln2 + Rln4

(D) C_𝑝ln2

Answer: (A)

4. For a single component system, vapor (subscript 𝑔) and liquid (subscript 𝑓) coexist in mechanical, thermal and phase equilibrium when

(A) 𝑢_𝑔 = u_f (equality of specific internal energy)

(B) h_𝑔 = h_f(equality of specific enthalpy)

(D) g_g= g_f (equality of specific Gibbs free energy)

Answer: (D)

5. For a binary nonideal A-B mixture exhibiting a minimum boiling azeotrope, the activity coefficients, 𝛾𝑖 (i = A, B), must satisfy

(A) γ_A > 1, γ_B > 1

(B) γ_A < 1, γ_B > 1

(D) γ_A < 1, γ_B < 1

Answer: (A)

6. For a fully-developed turbulent hydrodynamic boundary layer for flow past a flat plate, the thickness of the boundary layer increases with distance x from the leading edge of the plate, along the free-stream flow direction, as

(A) 𝑥^0.5

(B) 𝑥^1.5

(D) 𝑥^0.8

Answer: (D)

7. Consider a cylinder (diameter D and length D ), a sphere (diameter D ) and a cube length D ). objects is true (side Which of the following statements concerning the sphericity ( Φ ) of the above :

(A) Φ_sphere > Φ_cylinder > Φ_cube

(B) Φ_sphere = Φ_cylinder = Φ_cube

(D) Φ_sphere > Φ_cylinder = Φ_cube

Answer: (A)

8. Prandtl number signifies the ratio of

Answer: (A)

9. Pool boiling equipment operating above ambient temperature is usually designed to operate

(A) far above the critical heat flux

(B) near the critical heat flux

(D) near the Leidenfrost point

Answer: (B)

10. The desired liquid-phase reaction

is accompanied by an undesired side reaction

Four isothermal reactors schemes (CS TR: ideal Continuous-Stirred Tank Reactor. PFR: ideal Plug Flow Reactor) for processing equal molar feed rates of D and E are show in figure. Each scheme is designed for t he same conversion. The scheme that gives the most favorable product distribution is

Answer: (C)

11. For a first order reaction in a porous spherical catalyst pellet, diffusional effects are most likely to lower the observed rate of reaction for

(A) slow reaction in a pellet of small diameter

(B) slow reaction in a pellet of large diameter

(D) fast reaction in a pellet of large diameter

Answer: (D)

12. A thermocouple senses temperature based on the

(A) Nernst Effect

(B) Maxwell Effect

(D) Peltier Effect

Answer: (C)

13. The correct expression for the Colburn j-factor for mass transfer that relates Sherwood number (Sh), Reynolds number (Re) and Schmidt number (Sc) is

Answer: (A)

14. In the drying of non-dissolving solids at constant drying conditions, the internal movement of moisture in the solid has a dominant effect on the drying rate during

(A) the initial adjustment period only

(B) the constant rate period only

(D) both the initial adjustment and constant rate periods

Answer: (C)

15. Three distillation schemes for separating an equimolar, constant relative volatility ABC mixture into nearly pure components are shown. The usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays are valid. All the schemes are designed for minimum total reboiler duty. Given that the relative volatilities are in the ratio α_A : α_B : α_C = 8:2:1, the correct option that arranges the optimally-designed schemes in ascending order of total reboiler duty is

(A) I, II, III

(B) III, I, II

(D) III, II, I

Answer: (B)

16. Consider the two countercurrent heat exchanger designs for heating a cold stream from 𝑡_𝑖𝑛 to 𝑡_out , as shown in figure. The hot process stream is available at 𝑇 . The inlet stream conditions and overall heat transfer coefficients are identical in both the designs. The heat transfer area in Design I and Design II are respectivel

If heat losses are neglected, and if both the designs are feasible, which of the following statements holds true:

Answer: (D)

17. Producer gas is obtained by

(A) passing air through red hot coke

(B) thermal cracking of naphtha

(D) passing air and steam through red hot coke

Answer: (D)

18. In Kraft process, the essential chemical reagents used in the digester are

(A) caustic soda, mercaptans and ethylene oxide

(B) caustic soda, sodium sulphide and soda ash

(D) baking soda, sodium sulphide and mercaptans

Answer: (B)

19. The most common catalyst used for oxidation of o-xylene to phthalic anhydride is

(A) V₂O₅

(B) Pd

(D) Ag

Answer: (A)

20.In petroleum refining operations, the process used for converting paraffins and naphthenes to aromatics is

(A) alkylation

(B) catalytic reforming

(D) isomerization

Answer: (B)

21. The combination that correctly matches the polymer in Group-1 with the polymerization type in reaction Group-2 is

(A) P-II, Q-I, R-III

(B) P-I, Q-III, R-II

(D) P-II, Q-III, R-I

Answer: (D)

22. The product of the eigenvalues of the matrix is ______ (rounded off to one decimal place).

Answer: (13.9 to 14.1)

23. For a hydraulic lift with dimensions shown in figure, assuming g =10 m/s² , the maximum diameter D_left (in m) that lifts a vehicle of mass 1000 kg using a force of 100 N is _____ (rounded off to two decimal places).

Answer: (0.19 to 0.21)

24. The liquid flow rate through an equal percentage control valve, when fully open, is 150 gal/min and the corresponding pressure drop is 50 psi. If the specific gravity of the liquid is 0.8, then the valve coefficient, C_v, in gal/(min psi^0.5) is ______ (rounded off to two decimal places).

Answer: (18.96 to 18.98)

25. Consider a sealed rigid bottle containing CO₂ and H₂O at 10 bar and ambient temperature. Assume that the gas phase in the bottle is pure CO₂ and follows the ideal gas law. The liquid phase in the bottle contains CO₂ dissolved in H₂O and is an ideal solution. The Henry’s constant at the system pressure and temperature is The equilibrium mole fraction of CO₂ dissolved in H₂O is _____ (rounded off to three decimal places).

Answer: (0.009 to 0.011)

Q. 26 – Q. 55 carry two marks each.

26. The solution of the ordinary differential equation subject to the initial condition

Answer: (D)

27. The value of the complex number i^−1/2 (where i = √−1) is

Answer: (A)

28. An incompressible Newtonian fluid flows in a pipe of diameter D₁ at volumetric flow rate Q . Fluid with same properties flows in another pipe of diameter D₂ =D₁/2 at the same flow rate Q . The transition length required for achieving fully-developed flow is l₁for the tube of diameter D₁, while it is l₂ for the tube of diameter D2 . Assuming steady laminar flow in both cases, the ratio l₁/ l₂ is:

(A) 1/4

(B) 1

(D) 4

Answer: (B)

29. A disk turbine is used to stir a liquid in a baffled tank. To design the agitator, experiments are performed in a lab-scale model with a turbine diameter of 0.05 m and a turbine impeller speed of 600 rpm. The liquid viscosity is 0.001 Pa s while the liquid density is 1000 kg/m³ . The actual application has a turbine diameter of 0.5 m, an impeller speed of 600 rpm, a liquid viscosity of 0.1 Pa s and a liquid density of 1000 kg/m³ . The effect of gravity is negligible. If the power required in the lab-scale model is P1 and the estimated power for the actual application is P₂ , then the ratio P₂/P₁ is

(A) 10³

(B) 10⁴

(D) 10⁶

Answer: (A)

30. Consider two non-interacting tanks-in-series as shown in figure. Water enters TANK 1 at q cm³/s and drains down to TANK 2 by gravity at a rate k √h₁(cm³/s). Similarly, water drains from TANK 2 by gravity at a rate of k√h₂(cm³/s) where h₁ and h₂ represent levels of TANK 1 and TANK 2, respectively (see figure). Drain valve constant k = 4 cm^2.5/s and cross-sectional areas of the two tanks are A₁ = A₂ = 28 cm².

At steady state operation, the water inlet flow rate is qss = 16 cm³/s. The transfer function relating the deviation variables

Answer: (A)

31. Choose the option that correctly matches the step response curves on the left with the appropriate transfer functions on the right. The step input change occurs at time t =0.

(A) P – III, Q – IV; R – II, S – I

(B) P – III, Q – I; R – IV, S – II

(D) P –III, Q – II; R – IV, S – I

Answer: (B)

32. 100 kg of a feed containing 50 wt.% of a solute C is contacted with 80 kg of a solvent containing 0.5 wt.% of C in a mixer-settler unit. From this operation, the resultant extract and raffinate phases contain 40 wt.% and 20 wt.% of C, respectively. If E and R denote the mass of the extract and raffinate phases, respectively, the ratio E/R is

(A) 1/4

(B) 1/2

(D) 1

Answer: (C)

33. The combination that correctly matches the process in Group-1 with the entries in Group-2 is

(A) P-II, Q-IV, R-III, S-I

(B) P-III, Q-IV, R-II, S-I

(D) P-II, Q-I, R-IV, S-III

Answer: (B)

34. If x, y and z are directions in a Cartesian coordinate system and i , j and k are the respective unit vectors, the directional derivative of the function u(x, y, z) = x² − 3yz at the point (2, 0, −4) in the direction (i + j – 2k)/√6 is _________(rounded off to two decimal places).

Answer: (6.52 to 6.54)

35. Two unbiased dice are thrown. Each dice can show any number between 1 and 6. The probability that the sum of the outcomes of the two dice is divisible by 4 is _____ (rounded off to two decimal places).

Answer: (0.24 to 0.26)

36. The Newton-Raphson method is used to determine the root of the equation f (x)= e^−x – x .If the initial guess for the root is 0, the estimate of the root after two iterations is _____ (rounded off to three decimal places).

Answer: (0.565 to 0.567)

37. Carbon monoxide (CO) reacts with hydrogen sulphide (HS) at a constant temperature of 800 K and a constant pressure of 2 bar as:

CO + H₂S ⇋ COS + H₂

The Gibbs free energy of the reaction ∆g°_rxn = 22972.3 J/mol and universal gas constant R =8.314 J/(mol K). Both the reactants and products can be assumed to be ideal gases. If initially only 4 mol of H₂S and 1 mol of CO are present, the extent of the reaction (in mol) at equilibrium is ____ (rounded off to two decimal places).

Answer: (0.27 to 0.30)

38. For a given binary system at constant temperature and pressure, the molar volume (in m³/mol) is given by: υ = 30x_A + 20x_B + x_Ax_B (15x_A – 7x_B), where x_A and x_B are the mol fractions of components A and B, respectively. The volume change of mixing ∆υ_mix (in m³/mol) at x_A = 0.5 is _____ (rounded off to one decimal place).

Answer: (0.9 to 1.1)

39. Consider a vessel containing steam at 180℃. The initial steam quality is 0.5 and the initial volume of the vessel is 1 m³. The vessel loses heat at a constant rate q under isobaric conditions so that the quality of steam reduces to 0.1 after 10 hours. The thermodynamic properties of water at 180 ℃ are (subscript 𝑔: vapor phase; subscript 𝑓: liquid phase):

The rate of heat loss q (in kJ/hour) is ____(rounded off to the nearest integer).

Answer: (810 to 840)

40. A fractionator recovers 95 mol % n-propane as the distillate from an equimolar mixture of n-propane and n-butane. The condensate is a saturated liquid at 55 ℃. The Antoine equation is of the form , and the constants are provided below:

Assuming Raoult’s law, the condenser pressure (in bar) is _____(rounded off to one decimal place).

Answer: (17.5 to 18.5)

41. A centrifugal pump is used to pump water (density 1000 kg/m³) from an inlet pressure of 10⁵ Pa to an exit pressure of 2 ×10⁵ Pa. The exit is at an elevation of 10 m above the pump. The average velocity of the fluid is 10 m/s. The cross-sectional area of the pipes at the pump inlet and outlet is 10⁻³ m² and acceleration due to gravity is g = 10 m/s² . Neglecting losses in the system, the power (in Watts) delivered by the pump is _____ (rounded off to the nearest integer).

Answer: (1990 to 2010)

42. A solid sphere of radius 1 cm and initial temperature of 25 ℃ is exposed to a gas stream at 100 ℃. For the solid sphere, the density is 104 kg/m3 and the specific heat capacity is 500 J/(kg K). The density of the gas is 0.6 kg/m³ and its specific heat capacity is 10³ J/(kg K). The solid sphere is approximated as a lumped system (Biot number ≪ 1) and all specific heats are constant. If the heat transfer coefficient between the solid and gas is 50 W/(m² K), the time (in seconds) needed for the sphere to reach 95 ℃ is _____ (rounded off to the nearest integer)

Answer: (900 to 905)

43. Stream A with specific heat capacity C_PA = 2000 J/(kg K) is cooled from 90℃ to 45℃ in a concentric double pipe counter current heat exchanger having a heat transfer area of 8 m². The cold stream B of specific heat capacity C_PB = 1000 J/(kg K) enters the exchanger at a flow rate 1 kg/s and 40℃. The overall heat transfer coefficient U = 250 W/(m²K). Assume that the mean driving force is based on the arithmetic mean temperature difference, that is, where T_{i, in} and T_{i, out} refer to the temperature of the ith stream (i = A, B) at the inlet and exit, respectively. The mass flow rate of stream A (in kg/s), is _______ (rounded off to two decimal places).

Answer: (0.30 to 0.32)

44. A 20 cm diameter cylindrical solid pellet of a nuclear fuel with density 6000 kg/m3 and conductivity of 300 W/(m K) generates heat by nuclear fission at a spatially uniform rate of 104 W/kg. The heat from the fuel pellet is transferred to the surrounding coolant by convection such that the pellet wall temperature remains constant at 300 ℃. Neglecting the axial and azimuthal dependence, the maximum temperature (in ℃) in the pellet at steady state is _____ (rounded off to the nearest integer).

Answer: (799 to 801)

45. The elementary, irreversible, liquid-phase, parallel reactions, 2A → D and 2A → U, take place in an isothermal non-ideal reactor. The C-curve measured in a tracer experiment is shown in the figure, where C(t) is the concentration of the tracer in g/m3 at the reactor exit at time t (in min).

The rate constants are k₁ = 0.2 Liter/(mol min) and k₂ = 0.3 Liter/(mol min). Pure A is fed to the reactor at a concentration of 2 mol/Liter. Using the segregated model, the percentage conversion in the reactor is ______ (rounded off to the nearest integer).

Answer: (63 to 67)

46. A first-order irreversible liquid phase reaction A → B k = 0.1 min⁻¹ is carried out under isothermal, steady state conditions in the following reactor arrangement comprising an ideal CSTR (Continuous-Stirred Tank Reactor) and two ideal PFRs (Plug Flow Reactors). From the information in the figure, the volume of the CSTR (in Liters) is ______ (rounded off to the nearest integer).

Answer: (850 to 860)

47. The elementary liquid-phase irreversible reactions take place in an isothermal ideal CSTR (Continuous-Stirred Tank Reactor). Pure A is fed to the reactor at a concentration of 2 mol/Liter. For the residence time that maximizes the exit concentration of B, the percentage yield of B, defined as , is _____(rounded off to the nearest integer).

Answer: (65 to 68)

48. The elementary irreversible gas-phase reaction A → B + C is carried out adiabatically in an ideal CSTR (Continuous-Stirred Tank Reactor) operating at 10 atm. Pure A enters the CSTR at a flow rate of 10 mol/s and a temperature of 450 K. Assume A, B and C to be ideal gases. The specific heat capacity at constant pressure ( C_pi) and heat of formation (H⁰_i ) , of component i (i = A,B, C), are:

The reaction rate constant where E = 31.4 kJ/mol and universal gas constant R =0.082 L atm/(mol K) = 8.314 J/(mol K). The shaft work may be neglected in the analysis, and specific heat capacities do not vary with temperature. All heats of formation are referenced to 273 K. The reactor volume (in Liters) for 75% conversion is ______ (rounded off to the nearest integer).

Answer: (131 to 138)

49. For the closed loop system shown in figure, the phase margin (in degrees) is ____ (rounded off to one decimal place).

Answer: (45.3 to 45.5)

50. Two spherical camphor particles of radii 20 cm and 5 cm, far away from each other, are undergoing sublimation in a stream of air. The mass transfer coefficient is proportional to 1√r(t) , where r(t) is the radius of the sphere at time t. Assume that the partial pressure of camphor far away from the surface of the particle is zero. Also, assume quasi-steady state, identical ambient conditions, and negligible heat effects. If t₁ and t₂ are the times required for complete sublimation of the 20 cm and 5 cm camphor particles, respectively, the ratiot₁/t₂ is _____(rounded off to one decimal place).

Answer: (7.9 to 8.1)

51. A countercurrent absorption tower is designed to remove 95% of component A from an incoming binary gas mixture using pure solvent B. The mole ratio of A in the inlet gas is 0.02. The carrier gas flow rate is 50 kmol/h. The equilibrium relation is given by Y = 2X, where Y and X are the mole ratios of A in the gas and liquid phases, respectively. If the tower is operated at twice the minimum solvent flow rate, the mole ratio of A in the exit liquid stream is_______(rounded off to three decimal places).

Answer: (0.004 to 0.006)

52. A binary mixture with components A and B is to be separated in a distillation column to obtain 95 mol% A as the top product. The binary mixture has a constant relative volatility α_AB = 2. The column feed is a saturated liquid containing 50 mol% A. Under the usual simplifying assumptions such as constant molal overflow, negligible heat loss, ideal trays, the minimum reflux ratio for this separation is ______ (rounded off to one decimal place).

Answer: (1.6 to 1.8)

53. Consider the reactor-separator-recycle process operating under steady state conditions as shown in the figure. The reactor is an ideal Continuous-Stirred Tank Reactor (CSTR), where the reaction A + B → C occurs. Assume that there is no impurity in the product and recycle streams. Other relevant information are provided in the figure. The mole fraction of B (x_B) in the reactor that minimizes the recycle rate is ______ (rounded off to two decimal places).

Answer: (0.09 to 0.11)

54. Consider two competing equipment A and B. For a compound interest rate of 10% per annum, in order for equipment B to be the economically cheaper option, its minimum life (in years) is_____ (rounded off to the next higher integer).

Answer: (8 to 8)

55. A taxi-car is bought for Rs 10 lakhs. Its salvage value is zero. The expected yearly income after paying all expenses and applicable taxes is Rs 3 lakhs. The compound interest rate is 9% per annum. The discounted payback period (in years), is ________ (rounded off to the next higher integer).

Answer: (5 to 5)

GATE Exam 2019 Civil Engineering (CE-2) Question Paper With Answer Key

June 7, 2023December 1, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-9

1 – 5 carry one mark each.

1. Daytime temperatures in Delhi can 40ºC.

(A) get

(B) stand

(D) peak

Answer: (C)

2. The growth rate of ABC Motors in 2017 was the same XYZ Motors in 2016.

(A) as off

(B) as those of

(D) as that of

Answer: (D)

3. Suresh wanted to lay a new carpet in his new mansion with an area of 70 × 55 s mts. However an area of 550 s mts. had to be left out for flower pots. If the cost of carpet is Rs. 50 per s mts., how much money (in Rs.) will be spent by Suresh for the carpet now?

(A) Rs. 1,65,000

(B) Rs. 1,92,500

(D) Rs. 1,27,500

Answer: (A)

4. A retaining wall with measurements 30m × 12m × 6m was constructed with bricks of dimensions 8cm × 6cm × 6cm. If 60% of the wall consists of bricks, the number of bricks used for the construction is lakhs.

(A) 30

(B) 40

(D) 75

Answer: (C)

5. Hima Das was only Indian athlete to win _ gold for India.

(A) the, many

(B) the, a

(D) an, the

Answer: (B)

6 – 10 carry two marks each.

6. Mohan, the manager, wants his four workers to work in pairs. No pair should work for more than 5 hours. Ram and John have worked together for 5 hours. Krishna and Amir have worked as a team for 2 hours. Krishna does not want to work with Ram. Whom should Mohan allot to work with John, if he wants all the workers to continue working?

(A) Amir

(B) Krishna

(D) None of the three

Answer: (B)

7. Population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x is greater than y. Let P be the ratio of the population of state X to state Y in a given year. The percentage increase in P from 2001 to 2011 is _______.

Answer: (D)

8. The Newspaper reports that over 500 hectares of tribal land spread across 28 tribal settlements in Mohinitampuram forest division have already been “alienated”. A top forest official said, “First the tribals are duped out of their land holdings. Second, the families thus rendered landless are often forced to encroach further into the forests”.

On the basis of the information available in the paragraph, is/are responsible for duping the tribals.

(A) forest officials

(B) landless families

(D) it cannot be inferred who

Answer: (D)

9. An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it take for the tank to be filled? (Assume that the rate of drainage is independent of the Head)

(A) 1.50

(B) 2.00

(D) 4.00

Answer: (C)

10. “Popular Hindi fiction, despite – or perhaps because of – its wide reach, often does not appear in our cinema. As ideals that viewers are meant to look up to rather than identify with, Hindi film protagonists usually read books of aspirational value: textbooks, English books, or high value literature.”

Which one of the following CANNOT be inferred from the paragraph above?

(A) Though popular Hindi fiction has wide reach, it often does not appear in the movies

(B) Protagonists in Hindi movies, being ideals for viewers, read only books of aspirational value

(D) People do not look up to writers of textbooks, English books or high value literature

Answer: (B OR D)

Civil Engineering

1 – 25 carry one mark each.

1. Euclidean norm (length) of the vector [4 −2 − 6]𝑇 is

(A) √12

(B) √24

(D) √56

Answer: (D)

2. The Laplace transform of sinh (at) is

Answer: (A)

3. The following inequality is true for all x close to 0.

What is the value of

(A) 0

(B) 1/2

(D) 2

Answer: (D)

4. What is curl of the vector field 2𝑥²𝑦𝐢 + 5𝑧²𝐣 − 4𝑦𝑧𝐤 ?

(A) 6𝑧𝐢 + 4𝑥𝐣 − 2𝑥²𝐤

(B) 6𝑧𝐢 − 8𝑥𝑦𝐣 + 2𝑥²𝑦𝐤

(D) −14𝑧𝐢 − 2𝑥²𝐤

Answer: (D)

5. A closed thin-walled tube has thickness, 𝑡, mean enclosed area within the boundary of the centerline of tube’s thickness, 𝐴_m, and shear stress, 𝜏. Torsional moment of resistance, T, of the section would be

(A) 0.5𝜏𝐴_𝑚𝑡

(B) 𝜏𝐴_𝑚𝑡

(D) 4𝜏𝐴_𝑚𝑡

Answer: (C)

6 A steel column is restrained against both translation and rotation at one end and is restrained only against rotation but free to translate at the other end. Theoretical and design (IS:800- 2007) values, respectively, of effective length factor of the column are

(A) 1.0 and 1.0

(B) 1.2 and 1.0

(D) 1.0 and 1.2

Answer: (C OR D)

7 If the finenes in the sample s modulus of a sample of fine aggregates is 4.3, the mean size of the particles is between

(A) 150 μm and 300 μm

(B) 300 μm and 600 μm

(D) 2.36 mm and 4.75 mm

Answer: (C)

8. For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web?

Answer: (A)

9. Which one of the following options contains ONLY primary air pollutants?

(A) Hydrocarbons and nitrogen oxides

(B) Hydrocarbons and ozone

(D) Nitrogen oxides and peroxyacetyl nitrate

Answer: (A)

10. Analysis of a water sample revealed that the sample contains the following species.

Concentrations of which of the species will be required to compute alkalinity?

Answer: (A)

11. Structural fa ilures considered in the mechanistic method of bituminous pavement design are

(A) Fatigue and Rutting

(B) Fatigue and Shear

(D) Shear and Slippage

Answer: (A)

12. A solid sphere of radius, r, and made of material with density, ρ_s , is moving through the atmosphere (constant pressure, p) with a velocity, v. The net force ONLY due to atmospheric pressure (F_p) acting on the sphere at any time, t, is

(A) π r² p

(B) 4π r²p

(C)

(D) zero

Answer: (D)

13. The velocity field in a flow system is given by 𝑣 = 2𝐢 + (𝑥 + 𝑦)𝐣 + (𝑥𝑦𝑧)𝐤. The acceleration of the fluid at (1, 1, 2) is

(A) 2𝐢 + 10𝐤

(B) 4𝐢 + 12𝐤

(D) 4𝐣 + 10𝐤

Answer: (D)

14. An inflow hydrograph is routed through a reservoir to produce an outflow hydrograph. The peak flow of the inflow hydrograph is PI and the time of occurrence of the peak is tI. The peak flow of the outflow hydrograph is PO and the time of occurrence of the peak is tO. Which one of the following statements is correct?

(A) P_I < P_O and t_I < t_O

(B) P_I < P_O and t_I > t_O

(D) P_I > P_O and t_I > t_O

Answer: (C)

15. An earthen dam of height H is made of cohesive soil whose cohesion and unit weight are c and γ, respectively. If the factor of safety against cohesion is F_c, the Taylor’s stability number (S_n) is

Answer: (C)

16. The notation “SC” as per Indian Standard Soil Classification System refers to

(A) Sandy clay

(B) Silty clay

(D) Clayey sand

Answer: (D)

17. An anisotropic soil deposit has coefficient of permeability in vertical and horizontal directions as 𝑘_𝑧 and 𝑘_𝑥, respectively. For constructing a flow net, the horizontal dimension of the problem’s geometry is transformed by a multiplying factor of

Answer: (A)

18. The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x*, using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by IL, and then by the Newton polynomial, denoted by IN. Which one of the following statements is correct?

A) IL is always greater than IN

(B) IL and IN are always equal

(D) No definite relation exists between IL and IN

Answer: (B)

19. The speed-density relationship in a mid-block section of a highway follows the Greenshield’s model. If he free flow speed is 𝑣𝑓 and the jam density is 𝑘𝑗, the maximum flow observed on this section is

Answer: (C)

20. The degree of static indeterminacy of the plane frame as shown in the figure is______

Answer: (15 to 15)

21. The characteristic compressive strength of concrete required in a project is 25 MPa and the standard deviation in the observed compressive strength expected at site is 4 MPa. The average compressive strength of cubes tested at different water-cement (w/c) ratios using the same material as is used for the project is given in the table.

The water-cement ratio (in percent, round off to the lower integer) to be used in the mix is______

Answer: (46 to 46)

22. The data from a closed traverse survey PQRS (run in the clockwise direction) are given in the table

The closing error for the traverse PQRS (in degrees) is__________

Answer: (3 to 3)

23. A vehicle is moving on a road of grade +4% at a speed of 20 m/s. Consider the coefficient of rolling friction as 0.46 and acceleration due to gravity as 10 m/s². On applying brakes to reach a speed of 10 m/s, the required braking distance (in m, round off to nearest integer) along the horizontal, is_____

Answer: (30 to 30)

24. The command area of a canal grows only one crop, i.e., wheat. The base period of wheat is 120 days and its total water requirement, Δ, is 40 cm. If the canal discharge is 2 m³/s, the area, in hectares, rounded off to the nearest integer, which could be irrigated (neglecting all losses) is_____

Answer: (5180 to 5190)

25. Construction of a new building founded on a clayey soil was completed in January 2010. In January 2014, the average consolidation settlement of the foundation in clay was recorded as 10 mm. The ultimate consolidation settlement was estimated in design as 40 mm. Considering double drainage to occur at the clayey soil site, the expected consolidation settlement in January 2019 (in mm, round off to the nearest integer) will be _______

Answer: (15 to 15)

Q. 26 – Q. 55 carry two marks each.

26. The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is
(A) vertical-align: middle; margin-bottom: 1px;

(B)

(D) y – x

Answer: (B)

27. Consider the hemi-spherical tank of radius 13 m as shown in the figure (not drawn to scale). What is the volume of water (in m³) when the depth of water at the centre of the tank is 6 m?

(A) 78π

(B) 156π

(D) 468π

Answer: (C)

28. An ordinary differential equation is given below.

The solution for the above equation is

(Note : K denotes a constant in the options)

(A) y = Kx ln x

(B) y – Kxe^x

(D) y = K ln x

Answer: (D)

29. For a plane stress problem, the state of stress at a point P is represented by the stress element as shown in figure.

By how much angle (θ) in degrees the stress element should be rotated in order to get the planes of maximum shear stress?

(A) 13.3

(B) 26.6

(D) 48.3

Answer: (C)

30. The critical bending compressive stress in the extreme fibre of a structural steel section is 1000 MPa. It is given that the yield strength of the steel is 250 MPa, width of flange is 250 mm and thickness of flange is 15 mm. As per the provisions of IS:800-2007, the non-dimensional slenderness ratio of the steel cross-section is

(A) 0.25

(B) 0.50

(D) 2.00

Answer: (B)

31. In the context of provisions relating to durability of concrete, consider the following assertions:

Assertion (1): As per IS 456-2000, air entrainment to the extent of 3% to 6% is required for concrete exposed to marine environment.

Assertion (2): The equivalent alkali content (in terms of Na₂O equivalent) for a cement containing 1% and 0.6% of Na₂O and K₂O, respectively, is approximately 1.4% (rounded to 1 decimal place).

Which one of the following statements is CORRECT?

(A) Assertion (1) is FALSE and Assertion (2) is TRUE

(B) Assertion (1) is TRUE and Assertion (2) is FALSE

(D) Both Assertion (1) and Assertion (2) are TRUE

Answer: (A)

32. Chlorine is used as the disinfectant in a municipal water treatment plant. It achieves 50 percent of disinfection efficiency measured in terms of killing the indicator microorganisms (E-Coli) in 3 minutes. The minimum time required to achieve 99 percent disinfection efficiency would be

(A) 9.93 minutes

(B) 11.93 minutes

(D) 21.93 minutes

Answer: (C)

33. A camera with a focal length of 20 cm fitted in an aircraft is used for taking vertical aerial photographs of a terrain. The average elevation of the terrain is 1200 m above mean sea level (MSL). What is the height above MSL at which an aircraft must fly in order to get the aerial photographs at a scale of 1:8000?

(A) 2600 m

(B) 2800 m

(D) 3200 m

Answer: (B)

34. A flexible pavement has the following class of loads during a particular hour of the day.

i. 80 buses with 2-axles (each axle load of 40 kN);

ii. 160 trucks with 2-axles (front and rear axle loads of 40 kN and 80 kN, respectively)

The equivalent standard axle load repetitions for this vehicle combination as per IRC:37- 2012 would be

(A) 180

(B) 240

(D) 320

Answer: (A)

35. The inverse of the matrix is

Answer: (C)

36. A long uniformly distributed load of 10 kN/m and a concentrated load of 60 kN are moving together on the beam ABCD shown in the figure (not drawn to scale). The relative positions of the two loads are not fixed. The maximum shear force (in kN, round off to the nearest integer) caused at the internal hinge B due to the two loads is_________

Answer: (70 to 70 or -70 to -70)

37. A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are k_x = k_y = 5 × 10⁵ kN/m and k_θ = 3 × 10⁵ kNm/rad.

For the externally applied moment of 30 kNm at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is_______

Answer: (0.005 to 0.007)

38. A rolled I-section beam is supported on a 75 mm wide bearing plate as shown in the figure. Thicknesses of flange and web of the I-section are 20 mm and 8 mm, respectively. Root radius of the I-section is 10 mm. Assume: material yield stress, 𝑓_𝑦 = 250 𝑀𝑃𝑎 and partial safety factor for material, 𝛾_𝑚𝑜 = 1.10.

As per IS: 800-2007, the web bearing strength (in kN, round off to 2 decimal places) of the beam is______

Answer: (272.60 to 272.80)

39. When a specimen of M25 concrete is loaded to a stress level of 12.5 MPa, a strain of 500×10^–6 is recorded. If this load is allowed to stand for a long time, the strain increases to 1000×10^–6. In accordance with the provisions of IS:456-2000, considering the long-term effects, the effective modulus of elasticity of the concrete (in MPa) is ________

Answer: (12500 to 12500)

40. A water treatment plant treats 6000 m³ of water per day. As a part of the treatment process, discrete particles are required to be settled in a clarifier. A column test indicates that an overflow rate of 1.5 m per hour would produce the desired removal of particles through settling in the clarifier having a depth of 3.0 m. The volume of the required clarifier, (in m³, round off to 1 decimal place) would be_______

Answer: (495.0 to 505.0)

41. Raw municipal solid waste (MSW) collected from a city contains 70% decomposable material that can be converted to methane. The water content of the decomposable material is 35%. An elemental analysis of the decomposable material yields the following mass percent.

C : H : O : N : other = 44 : 6 : 43 : 0.8 : 6.2

The methane production of the decomposable material is governed by the following stoichiometric relation

C_aH_bO_cN_d + nH₂O → mCH₄ + sCO₂ + dNH₃

Given atomic weights: C = 12, H = 1, O = 16, N = 14. The mass of methane produced (in grams, round off to 1 decimal place) per kg of raw MSW will be ________

Answer: (135.0 to 140.0)

42. Consider the reactor shown in the figure. The flow rate through the reactor is Q m³/h. The concentrations (in mg/L) of a compound in the influent and effluent are C₀ and C, respectively. The compound is degraded in the reactor following the first order reaction. The mixing condition of the reactor can be varied such that the reactor becomes either a completely mixed flow reactor (CMFR) or a plug-flow reactor (PFR). The length of the reactor can be adjusted in these two mixing conditions to LCMFR and LPFR while keeping the cross-section of the reactor constant. Assuming steady state and for C/C₀ = 0.8, the value of LCMFR/LPFR (round off to 2 decimal places) is______

Answer: (1.10 to 1.15)

43. A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of 6 m are 1.22, 1.67, 2.04, 2.34, 2.14, 1.87, and 1.15 m. The area (in m², round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is_______

Answer: (67.00 to 70.00)

44. The uniform arrival and uniform service rates observed on an approach road to a signalized intersection are 20 and 50 vehicles/minute, respectively. For this signal, the red time is 30 s, the effective green time is 30 s, and the cycle length is 60 s. Assuming that initially there are no vehicles in the queue, the average delay per vehicle using the approach road during a cycle length (in s, round off to 2 decimal places) is__________

Answer: (12.00 to 13.00)

45. A broad gauge railway line passes through a horizontal curved section (radius = 875 m) of length 200 m. The allowable speed on this portion is 100 km/h. For calculating the cant, consider the gauge as centre-to-centre distance between the rail heads, equal to 1750 mm. The maximum permissible cant (in mm, round off to 1 decimal place) with respect to the centre-to-centre distance between the rail heads is________

Answer: (157.2 to 157.6)

46. The speed-density relationship of a highway is given as

𝑢 = 100 − 0.5 𝑘

where, u = speed in km per hour, k = density in vehicles per km. The maximum flow (in vehicles per hour, round off to the nearest integer) is_______

Answer: (5000 to 5000)

47. A confined aquifer of 15 m constant thickness is sandwiched between two aquicludes as shown in the figure (not drawn to scale).

The heads indicated by two piezometers P and Q are 55.2 m and 34.1 m, respectively. The aquifer has a hydraulic conductivity of 80 m/day and its effective porosity is 0.25. If the distance between the piezometers is 2500 m, the time taken by the water to travel through the aquifer from piezometer location P to Q (in days, round off to 1 decimal place) is______

Answer: (924.0 to 926.0)

48. At the foot of a spillway, water flows at a depth of 23 cm with a velocity of 8.1 m/s, as shown in the figure.

The flow enters as an M-3 profile in the long wide rectangular channel with bed slope = 1/1800 and Manning’s n = 0.015. A hydraulic jump is formed at a certain distance from the foot of the spillway. Assume the acceleration due to gravity, g = 9.81 m/s². Just before the hydraulic jump, the depth of flow 𝑦₁ (in m, round off to 2 decimal places) is______

Answer: (041 to 0.43)

49. Two identical pipes (i.e., having the same length, same diameter, and same roughness) are used to withdraw water from a reservoir. In the first case, they are attached in series and discharge freely into the atmosphere. In the second case, they are attached in parallel and also discharge freely into the atmosphere. Neglecting all minor losses, and assuming that the
friction factor is same in both the cases, the ratio of the discharge in the parallel arrangement to that in the series arrangement (round off to 2 decimal places) is_______

Answer: (2.80 to 2.90)

50. The ordinates, u, of a 2-hour unit hydrograph (i.e., for 1 cm of effective rain), for a catchment are shown in the table.

A 6-hour storm occurs over the catchment such that the effective rainfall intensity is 1 cm/hour for the first two hours, zero for the next two hours, and 0.5 cm/hour for the last two hours. If the base flow is constant at 5 m³/s, the peak flow due to this storm (in m³/s, round off to 1 decimal place) will be ______

Answer: (96.5 to 97.5)

51. The dimensions of a soil sampler are given in the table.

For this sampler, the outside clearance ratio (in percent, round off to 2 decimal places) is_______

Answer: (11.10 to 11.12)

52. A 2 m × 4 m rectangular footing has to carry a uniformly distributed load of 120 kPa. As per the 2:1 dispersion method of stress distribution, the increment in vertical stress (in kPa) at a depth of 2 m below the footing is_____

Answer: (40 to 40)

53. Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (L_S1:L_S2) is 1.5, the ratio of the diameter of specimens (D_S1:D_S2) is 0.5, and the ratio of the constant head (h_S1:h_S2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (kS₁:k_S2) is______

Answer: (2.95 to 3.05)

54. A timber pile of length 8 m and diameter 0.2 m is driven with a 20 kN drop hammer, falling freely from a height of 1.5 m. The total penetration of the pile in the last 5 blows is 40 mm. Use the Engineering News Record expression. Assume a factor of safety of 6 and empirical factor (allowing reduction in the theoretical set, due to energy losses) of 2.5 cm. The safe load carrying capacity of the pile (in kN, round off to 2 decimal places) is______

Answer: (151.00 to 152.00)

55. A square footing of 2 m sides rests on the surface of a homogeneous soil bed having the properties: cohesion c = 24 kPa, angle of internal friction Φ = 25º, and unit weight γ = 18 kN/m³. Terzaghi’s bearing capacity factors for Φ = 25º are N_c = 25.1, The ultimate bearing capacity of the foundation (in kPa, round off to 2 decimal places) is_______

Answer: (920.00 to 925.00 or 350.00 to 356.00)

GATE Exam 2019 Civil Engineering (CE-1) Question Paper With Answer Key

June 7, 2023December 1, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-7

Q. 1 – Q. 5 carry one mark each.

1. The lecture was attended by quite students, so the hall was not very .

(A) a few, quite

(B) few, quiet

(D) few, quite

Answer: (C)

2. They have come a long way in trust among the users.

(A) creating

(B) created

(D) create

Answer: (A)

3. On a horizontal ground, the base of a straight ladder is 6 m away from the base of a vertical pole. The ladder makes an angle of 45o to the horizontal. If the ladder is resting at a point located at one-fifth of the height of the pole from the bottom, the height of the pole is meters.

(A) 15

(B) 25

(D) 35

Answer: (C)

4. If E = 10; J = 20; O = 30; and T = 40, what will be P + E + S + T?

(A) 51

(B) 82

(D) 164

Answer: (C)

5. The CEO’s decision to quit was as shocking to the Board as it was to .

(A) I

(B) me

(D) myself

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. The new cotton technology, Bollgard-II, with herbicide tolerant traits has developed into a thriving business in India. However, the commercial use of this technology is not legal in India. Notwithstanding that, reports indicate that the herbicide tolerant Bt cotton had been purchased by farmers at an average of Rs 200 more than the control price of ordinary cotton, and planted in 15% of the cotton growing area in the 2017 Kharif season.

Which one of the following statements can be inferred from the given passage?

(A) Farmers want to access the new technology if India benefits from it

(B) Farmers want to access the new technology even if it is not legal

(D) Farmers want to access the new technology by paying high price

Answer: (B)

7. In a sports academy of 300 people, 105 play only cricket, 70 play only hockey, 50 play only football, 25 play both cricket and hockey, 15 play both hockey and football and 30 play both cricket and football. The rest of them play all three sports. What is the percentage of people who play at least two sports?

(A) 23.30

(B) 25.00

(D) 50.00

Answer: (B)

8. “The increasing interest in tribal characters might be a mere coincidence, but the timing is of interest. None of this, though, is to say that the tribal hero has arrived in Hindi cinema, or that the new crop of characters represents the acceptance of the tribal character in the industry. The films and characters are too few to be described as a pattern.”

What does the word ‘arrived’ mean in the paragraph above?

(A) reached a terminus

(B) came to a conclusion

(D) went to a place

Answer: (C)

9. A square has sides 5 cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is cm.

(A) 18.50

(B) 15.10

(D) 8.50

Answer: (C)

10. P, Q, R, S and T are related and belong to the same family. P is the brother of S. Q is the wife of P. R and T are the children of the siblings P and S respectively. Which one of the following statements is necessarily FALSE?

(A) S is the aunt of R

(B) S is the aunt of T

(D) S is the brother of P

Answer: (B)

Civil Engineering

1. Which one of the following is correct?

Answer: (A)

2. Consider z direction a two-dimensional flow through isotropic soil along x direction and If h is the hydraulic head, the Laplace’s equation of continuity is expressed as

Answer: (C)

3. A simple mass-spring oscillatory system consists of a mass m, suspended from a spring of stiffness k. Considering z as the displacement of the system at any time t, the equation of motion for the free vibration of the system is . The natural frequency of the system is

Answer: (B)

4. For a small value of h, the Taylor series expansion for f (x + h)

Answer: (A)

5. A plane truss is shown in the figure (not drawn to scale).

Which one of the options contains ONLY zero force members in the truss?

(A) FG, FI, HI, RS

(B) FG, FH, HI, RS

(D) FI, FG, RS, PR

Answer: (D)

6. An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal strain in the plane of maximum shear strain is

(A) Zero

(B) 0.0010

(D) 0.0050

Answer: (C)

7. Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let R_P, R_Q, R_R denote the vertical reactions (upward positive) applied by the supports at P, Q, and R, respectively, on the truss. The correct combination of (R_P, R_Q, R_R) is represented by

(A) (30, −30, 30) kN

(B) (20, 0, 10) kN

(D) (0, 60, −30) kN

Answer: (A)

8. Assuming that there is no possibility of shear buckling in the web, the maximum reduction permitted by IS 800-2007 in the (low-shear) design bending strength of a semi-compact steel section on due to high shear is

(A) zero

(B) 25%

(D) governed by the area of the flange

Answer: (A)

9. In the reinforced beam section shown in the figure (not drawn to scale), the nominal cover at provided the bottom of the beam as per IS 456-2000, is

(A) 30 mm

(B) 36 mm

(D) 50 mm

Answer: (A)

10. The interior angles of four triangles are given below

Which of the triangles are ill-conditioned and should be avoided in Trianuglation surveys?

(A) Both P and R

(B) Both Q and R

(D) Both Q and S

Answer: (D)

11. The coefficient of average rolling friction of a road is f_r and its grade is +G%. If the grade of this road is doubled, what will be the percentage change in the braking distance (for the design vehicle to come to a stop) measured along the horizontal (assume all other parameters are kept unchanged)?

Answer: (A)

12. An isolated concrete pavement slab of length L is resting on a frictionless base. The temperature of the top and bottom fibre of the slab are T_t and T_b, respectively. Given: the coefficient of thermal expansion = α and the elastic modulus = E. Assuming 𝑇_𝑡 > 𝑇_𝑏 and the unit weight of concrete as zero, the maximum thermal stress is calculated as

Answer: (D)

13. In a rectangular channel, the ratio of the velocity head to the flow depth for critical flow condition, is

(A) 1/2

(B) 2/3

(D) 2

Answer: (A)

14. If the path of an irrigation canal is below the bed level of a natural stream, the type of cross- drainage structure provided is

(A) Aqueduct

(B) Level crossing

(D) Super passage

Answer: (D)

15. A catchment may be idealised as a rectangle. There are three rain gauges located inside the catchment at arbitrary locations. The average precipitation over the catchment is estimated by two methods: (i) Arithmetic mean (PA), and (ii) Thiessen polygon (PT). Which one of the following statements is correct?

(A) P_A is always smaller than P_T

(B) P_A is always greater than P_T

(D) There is no definite relationship between P_A and P_T

Answer: (D)

16. A retaining wall of height H with smooth vertical backface supports a back-fill inclined at an angle β with the horizontal. The back-fill consists of cohesionless soil having angle of internal friction Φ. If the active lateral thrust acting on the wall is Pa, which one of the following statements is TRUE?

(A) P_a acts at a height H/2 from the base of the wall and at an angle β with the horizontal

(B) P_a acts at a height H/2 from the base of the wall and at an angle Φ with the horizontal

(D) P_a acts at a height H/3 from the base of the wall and at an angle Φ with the horizontal

Answer: (C)

17. In a soil specimen, the total stress, effective stress, hydraulic gradient and critical hydraulic are σ σ’ , i and i_c, respectively. For initiation of quicksand condition, which one of following statements is TRUE?

(A) σ’ ≠ 0 and i = i_c

(B) σ’ = 0 and i = i_c

(D) σ = 0 and i = i_c

Answer: (B)

18. Which one of the following is a secondary pollutant?

(A) Ozone

(B) Carbon Monoxide

(D) Volatile Organic Carbon (VOC)

Answer: (A)

19. For a given loading on a rectangular plain concrete beam with an overall depth of 500 mm, the compressive strain and tensile strain developed at the extreme fibers are of the same magnitude of 2.5×10^–4. The curvature in the beam cross-section (in m^–1, round off to 3 decimal places), is ________

Answer: (0.001 to 0.001)

20. A completely mixed dilute suspension of sand particles having diameters 0.25, 0.35, 0.40, 0.45 and 0.50 mm are filled in a transparent glass column of diameter 10 cm and height 2.50 m. The suspension is allowed to settle without any disturbance. It is observed that all particles of diameter 0.35 mm settle to the bottom of the column in 30 s. For the same period of 30 s, the percentage removal (round off to integer value) of particles of diameters 0.45 and 0.50 mm from the suspension is______

Answer: (100 to 100)

21. The maximum number of vehicles observed in any five minute period during the peak hour is 160. If the total flow in the peak hour is 1000 vehicles, the five minute peak hour factor (round off to 2 decimal places) is ______

Answer: (0.51 to 0.53)

22. A circular duct carrying water gradually contracts from a diameter of 30 cm to 15 cm. The figure (not drawn to scale) shows the arrangement of differential manometer attached to the duct.

When the water flows, the differential manometer shows a deflection of 8 cm of mercury (Hg). The values of specific gravity of mercury and water are 13.6 and 1.0, respectively. Consider the acceleration due to gravity, g = 9.81 m/s². Assuming frictionless flow, the flow rate (in m³/s, round off to 3 decimal places) through the duct is________

Answer: (0.078 to 0.085)

23. The probability that the annual maximum flood discharge will exceed 25000 m³/s, at least once in next 5 years is found to be 0.25. The return period of this flood event (in years, round off to 1 decimal place) is________

Answer: (17.8 to 18.0)

24. A soil has specific gravity of its solids equal to 2.65. The mass density of water is 1000 kg/m³. Considering zero air voids and 10% moisture content of the soil sample, the dry density (in kg/m³, round off to 1 decimal place) would be_______

Answer: (2086.6 to 2095.0)

25. A concentrated load of 500 kN is applied on an elastic half space. The ratio of the increase in vertical normal stress at depths of 2 m and 4 m along the point of the loading, as per
Boussinesq’s theory, would be_________

Answer: (4 to 4)

Q. 26 – Q. 55 carry two marks each.

26. Which one of the following is NOT a correct statement?

Answer: (B)

27. A one-dimensional domain is discretized into N sub-domains of width Δx with node numbers i = 0,1, 2, 3, …, N . If the time scale is discretized in steps of Δt, the forward-time and centered- space finite difference approximation at i^th node and n^th time step, for the partial differential is

Answer: (A)

28. A rectangular open channel has a width of 5 m and a bed slope of 0.001. For a uniform flow of depth 2 m, the velocity is 2 m/s. The Manning’s roughness coefficient for the channel is

(A) 0.002

(B) 0.017

(D) 0.050

Answer: (B)

29. For the following statements:

P – The lateral stress in the soil while being tested in an oedometer is always at-rest.

Q – For a perfectly rigid strip footing at deeper depths in a sand deposit, the vertical normal contact stress at the footing edge is greater than that at its centre.

R – The corrections for overburden pressure and dilatancy are not applied to measured SPT-N values in case of clay deposits.

The correct combination of the statements is

(A) P – TRUE; Q – TRUE; R – TRUE

(B) P – FALSE; Q – FALSE; R – TRUE

(D) P – FALSE; Q – FALSE; R – FALSE

Answer: (A)

30. Consider two functions: x = Ψ lnϕ and y = ϕlnΨ. Which one of the following is the correct expression for ?

Answer: (D)

31. The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of 8 kN. The beam is symmetrical about the neutral axis (N.A.) shown, and the moment of inertia about N.A. is 1.5×10⁹ mm⁴. Considering that the nails at the location P are spaced longitudinally (along the length of the beam) at 60 mm, each of the nails at P will be subjected to the shear force of

(A) 60 N

(B) 120 N

(D) 480 N

Answer: (C)

32. The rigid-jointed plane frame QRS shown in the figure is subjected to a load P at the joint v R. Let the axial deformations in the frame be neglected. If the support S undergoes a settlement of the vertical reaction at the support S will become zero when β is equal to

(A) 0.1

(B) 3.0

(D) 48.0

Answer: (C)

33. If the section shown in the figure turns from fully-elastic to fully-plastic, the depth of neutral axis (N.A.), , decreases by

(A) 10.75 mm

(B) 12.25 mm

(D) 15.25 mm

Answer: (C)

34. Sedimentation basin in a water treatment plant is designed for a flow rate of 0.2 m³/s. The basin is rectangular with a length of 32 m, width of 8 m, and depth of 4 m. Assume that the settling velocity of these particles is governed by the Stokes’ law. Given: density of the particles = 2.5 g/cm³; density of water = 1 g/cm³; dynamic viscosity of water = 0.01 g/(cm.s); gravitational acceleration = 980 cm/s2. If the incoming water contains particles of diameter 25 μm (spherical and uniform), the removal efficiency of these particles is

(A) 51%

(B) 65%

(D) 100%

Answer: (B)

35. A survey line was measured to be 285.5 m with a tape having a nominal length of 30 m. On checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work would be

(A) 283.6 m

(B) 284.5 m

(D) 285.6 m

Answer: (A)

36. A 16 mm thick gusset plate is connected to the 12 mm thick flange plate of an I-section using fillet welds on both sides as shown in the figure (not drawn to scale). The gusset plate is subjected to a point load of 350 kN acting at a distance of 100 mm from the flange plate. Size of fillet weld is 10 mm

The maximum resultant stress (in MPa, round off to 1 decimal place) on the fillet weld along the vertical plane would be_____

Answer: (78.0 to 78.2 or 105.3 to 105.5)

37. The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of all the activities are shown in the table. The indirect cost incurred by the contractor is INR 5000 per day.

If the project is targeted for completion in 16 days, the total cost (in INR) to be incurred by the contractor would be______

Answer: (149500 to 149500)

38. A box measuring 50 cm × 50 cm × 50 cm is filled to the top with dry coarse aggregate of mass 187.5 kg. The water absorption and specific gravity of the aggregate are 0.5% and 2.5, respectively. The maximum quantity of water (in kg, round off to 2 decimal places) required to fill the box completely is _____

Answer: (5.50 to 51.20)

39. A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction. The flexural rigidity, EI, of each member is 106 kNm². Under the applied load, the horizontal displacement (in mm, round off to 1 decimal place) of joint R would be_______

Answer: (24.9 to 25.1)

40. A sample of air analysed at 0ºC and 1 atm pressure is reported to contain 0.02 ppm (parts per million) of NO₂. Assume the gram molecular mass of NO₂ as 46 and its volume at 0°C and 1 atm pressure as 22.4 litres per mole. The equivalent NO₂ concentration (in microgram per cubic meter, round off to 2 decimal places) would be_______

Answer: (41.00 to 41.10)

41. A 0.80 m deep bed of sand filter (length 4 m and width 3 m) is made of uniform particles (diameter = 0.40 mm, specific gravity = 2.65, shape factor = 0.85) with bed porosity of 0.4. The bed has to be backwashed at a flow rate of 3.60 m3/min. During backwashing, if the terminal settling velocity of sand particles is 0.05 m/s, the expanded bed depth (in m, round off to 2 decimal places) is ______

Answer: (1.15 to 1.25)

42. A wastewater is to be disinfected with 35 mg/L of chlorine to obtain 99% kill of micro- organisms. The number of micro-organisms remaining alive (Nt) at time t, is modelled by Nt = N_o e^–kt , where No is number of micro-organisms at t = 0, and k is the rate of kill. The wastewater flow rate is 36 m³/h, and k = 0.23 min^‒1. If the depth and width of the chlorination tank are 1.5 m and 1.0 m, respectively, the length of the tank (in m, round off to 2 decimal places) is ________

Answer: (7.95 to 8.15)

43. A staff is placed on a benchmark (BM) of reduced level (RL) 100.000 m and a theodolite is placed at a horizontal distance of 50 m from the BM to measure the vertical angles. The measured vertical angles from the horizontal at the staff readings of 0.400 m and 2.400 m are found to be the same. Taking the height of the instrument as 1.400 m, the RL (in m) of the theodolite station is ______

Answer: (100 to 100)

44. Consider the ordinary differential equation Given the values of y(1) = 0 and y(2) = 2, the value of y(3) (round off to 1 decimal place), is ______

Answer: (5.9 to 6.1)

45. Average free flow speed and the jam density observed on a road stretch are 60 km/h and 120 vehicles/km, respectively. For a linear speed-density relationship, the maximum flow on the road stretch (in vehicles/h) is______

Answer: (1800 to 1800)

46. Traffic on a highway is moving at a rate of 360 vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the probability (round off to 2 decimal places) that the headway between successive vehicles lies between 6 and 10 seconds is ______

Answer: (0.17 to 0.19)

47. A parabolic vertical curve is being designed to join a road of grade +5% with a road of grade
–3%. The length of the vertical curve is 400 m measured along the horizontal. The vertical point of curvature (VPC) is located on the road of grade +5%. The difference in height between VPC and vertical point of intersection (VPI) (in m, round off to the nearest integer) is_____

Answer: (10 to 10 or -10 to -10)

48. Tie bars of 12 mm diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is 230 MPa, the average bond strength between a tie bar and concrete is 2 MPa, and the joint gap between the slabs is 10 mm. Ignoring the loss of bond and the tolerance factor, the design length of the tie bars (in mm, round off to the nearest integer) is_______

Answer: (700 to 700)

49. The hyetograph of a storm event of duration 140 minutes is shown in the figure.

The infiltration capacity at the start of this event (𝑡 = 0) is 17 mm/hour, which linearly decreases to 10 mm/hour after 40 minutes duration. As the event progresses, the infiltration rate further drops down linearly to attain a value of 4 mm/hour at 𝑡 = 100 minutes and remains constant thereafter till the end of the storm event. The value of the infiltration index, φ (in mm/hour, round off to 2 decimal places), is _________

Answer: (7.00 to 7.30)

50. Two water reservoirs are connected by a siphon (running full) of total length 5000 m and diameter of 0.10 m, as shown below (figure not drawn to scale).

The inlet leg length of the siphon to its summit is 2000 m. The difference in the water surface levels of the two reservoirs is 5 m. Assume the permissible minimum absolute pressure at the summit of siphon to be 2.5 m of water when running full. Given: friction factor f = 0.02 throughout, atmospheric pressure = 10.3 m of water, and acceleration due to gravity g = 9.81 m/s². Considering only major loss using Darcy-Weisbach equation, the maximum height of the summit of siphon from the water level of upper reservoir, h (in m, round off to 1 decimal place) is _______

Answer: (5.7 to 5.9)

51. Consider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocity of 1 cm/s in the x-direction. The distance between the plates is 5 mm and the dynamic viscosity of the fluid is 0.01 N-s/m². If the shear stress on the lower plate is zero, the pressure gradient, ∂p/∂x (in N/m² per m, round off to 1 decimal place) is________

Answer: (7.9 to 8.1)

52. A reinforced concrete circular pile of 12 m length and 0.6 m diameter is embedded in stiff clay which has an undrained unit cohesion of 110 kN/m². The adhesion factor is 0.5. The Net Ultimate Pullout (uplift) Load for the pile (in kN, round off to 1 decimal place) is_______

Answer: (1240.0 to 1250.0)

53. A granular soil has a saturated unit weight of 20 kN/m³ and an effective angle of shearing resistance of 30°. The unit weight of water is 9.81 kN/m³. A slope is to be made on this soil deposit in which the seepage occurs parallel to the slope up to the free surface. Under this seepage condition for a factor of safety of 1.5, the safe slope angle (in degree, round off to 1 decimal place) would be_______

Answer: (10.8 to 11.3)

54. A 3 m × 3 m square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as shown in the figure. A reaction arrangement using precast PCC blocks placed on the ground is to be made for the jacks.

At each stage, the jacks are required to apply a force of 1875 kN to push the segment. The jacks will react against the rigid steel plate placed against the reaction arrangement. The footprint area of reaction arrangement on natural ground is 37.5 m². The unit weight of PCC block is 24 kN/m³. The properties of the natural ground are: c = 17 kPa; ϕ = 25º and γ = 18 kN/m3. Assuming that the reaction arrangement has rough interface and has the same properties that of soil, the factor of safety (round off to 1 decimal place) against shear failure is _________

Answer: (1.8 to 2.1)

55. A square footing of 4 m side is placed at 1 m depth in a sand deposit. The dry unit weight (γ) of sand is 15 kN/m³. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors: dq = d_γ = 1.0 and the bearing capacity factor: N_γ = 18.75. This footing is placed at a depth of 2 m in the same soil deposit. For a factor of safety of 3.0 as per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be _______

Answer: (240 to 240 or 250 to 250 or 270 to 270)

GATE Exam 2019 Biotechnology (BT) Question Paper With Answer Key

June 7, 2023November 28, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ______ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Q. 1 – Q. 25 carry one mark each.

Q.1 The Bt toxin gene from Bacillus thuringiensis used to generate genetically modified crops is
(A) cry (B) cro (C) cdc (D) cre

n p

Q.3 Tetracycline inhibits the
(A) interaction between tRNA and mRNA
(B) translocation of mRNA through ribosome
(C) peptidyl transferase activity
(D) binding of amino-acyl tRNA to ribosome

Q.4 Which one of the following is a database of protein sequence motifs?
(A) PROSITE (B) TrEMBL (C) SWISSPROT (D) PDB

Q.5 Which one o
genome? f the following enzymes is encoded by human immunodeficiency virus (HIV)
(A) Reverse transcriptase (B) Phospholipase
(C) Phospha tase (D) ATP synthase

Q.6 DNA synthesis in eukaryotes occurs during which phase of the mitotic cell cycle?
(A) M (B) G1 (C) S (D) G0

Q.7 Match the human diseases in Group I with the causative agents in Group II.

Group I Group II
P. Amoebiasis 1. Leishmania donovani
Q. African sleeping sickness 2. Trypanosoma cruzi
R. Kala azar 3. Entamoeba histolytica
S. Chagas’ disease 4. Trypanosoma gambiense

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

Q.8 Which one of t
number of gen he following techniques can be used to compare the expression of a large es in two biological samples in a single experiment?
(A) Polymerase chain reaction (B) DNA microarray
(C) Northern h ybridization (D) Southern hybridization

Q.9 Which of the following processes can increase genetic diversity of bacteria in nature?

P. Conjugation
Q. Transformation
R. Transduction
S. Transfection
(A) P only (B) P and Q only (C) P, Q and R only (D) P, Q, R and S

Q.10 Which one of the following is NOT a part of the human nonspecific defense system?
(A) Interferon (B) Mucous (C) Saliva (D) Antibody

Q.11 A mutation i
the last three n a gene that codes for a polypeptide results in a variant polypeptide that lacks amino acids. What type of mutation is this?
(A) Synonym ous mutation (B) Nonsense mutation
(C) Missens e mutation (D) Silent mutation

Q.12 Which one of the following equations represents a one-dimensional wave equation?
(A) 𝜕𝑢 = 𝑐2 𝜕2𝑢
𝜕𝑡 𝜕𝑥2 (B) 𝜕2𝑢 = 𝑐2 𝜕2𝑢
𝜕𝑡2 𝜕𝑥2 (C) 𝜕2𝑢 = 𝑐2 𝜕𝑢
𝜕𝑡2 𝜕𝑥 (D) 𝜕2𝑢 + 𝜕2𝑢 = 0
𝜕𝑡2 𝜕𝑥2

Q.13 Which of the following are geometric series?

P. 1, 6, 11, 16, 21, 26, …
Q. 9, 6, 3, 0, -3, -6, …
R. 1, 3, 9, 27, 81, …
S. 4, -8, 16, -32, 64, …
(A) P and Q only (B) R and S only (C) Q and S only (D) P, Q and R only

Q.14 Which one of the following statements is CORRECT for enzyme catalyzed reactions? (𝛥𝐺 is Gibbs free energy change, 𝐾𝑒𝑞 is equilibrium constant)
(A) Enzymes affect 𝛥𝐺, but not 𝐾𝑒𝑞
(B) Enzymes affect 𝐾𝑒𝑞, but not 𝛥𝐺
(C) Enzymes affect both 𝛥𝐺 and 𝐾𝑒𝑞
(D) Enzymes do not affect 𝛥𝐺 or 𝐾𝑒𝑞

Q.15 Which one of the following can NOT be a limiting substrate if Monod’s growth kinetics is applicable?
(A) Extracellular carbon source
(B) Extracellular nitrogen source
(C) Dissolved oxygen
(D) Intracellular carbon source

Q.16 Which one of the following is the unit of heat transfer coefficient?
(A) W m2 K-1 (B) W m-2 K (C) W m-2 K-1 (D) W m2 K

Q.17 Which one o
bacterial cult f the following is catabolized during endogenous metabolism in a batch ivation?
(A) internal r eserves (B) extracellular substrates
(C) extracell ular products (D) toxic substrates

Q.18 Which one of the f ollowing need NOT be conserved in a biochemical reaction?
(A) Total mass (B) Total moles
(C) Number of ato ms of each element (D) Total energy

Q.19 The number of possible rooted trees in a phylogeny of three species is .

Q.20 Matrix A = [0 6 will be skew-symmetric when 𝑝 = .
𝑝 0]

Q.21 The solution of lim (𝑥2−64) is .
𝑥→8 𝑥−8

Q.22 The median value for the dataset (12, 10, 16, 8, 90, 50, 30, 24) is .

Q.23 The degree of reduction for acetic acid (C2H4O2) is .

Q.24 The mass of 1 kmol of oxygen molecules is g (rounded off to the nearest integer).

Q.25 Protein concentration of a crude enzyme preparation was 10 mg mL-1. 10 µL of this sample gave an activity of 5 µmol min-1 under standard assay conditions. The specific activity of
this crude enzyme preparation is units mg-1.

Q. 26 – Q. 55 carry two marks each.

Q.26 In general, which one of the following statements is NOT CORRECT?
(A) Hydrogen bonds result from electrostatic interactions
(B) Hydrogen bonds contribute to the folding energy of proteins
(C) Hydrogen bonds are weaker than van der Waals interactions
(D) Hydrogen bonds are directional

Q.27 For site-directed mutagenesis, which one of the following restriction enzymes is used to digest methylated DNA?
(A) KpnI (B) DpnI (C) XhoI (D) MluI

Q.28 Match the organelles in Group I with their functions in Group II.

Group I Group II
P. Lysosome 1. Digestion of foreign substances
Q. Smooth ER 2. Protein targeting
R. Golgi apparatus 3. Lipid synthesis
S. Nucleolus 4. Protein synthesis
5. rRNA synthesis
(A) P-1, Q-3, R-2, S-5 (B) P-1, Q-4, R-5, S-3
(C) P-2, Q-5, R-3, S-4 (D) P-1, Q-3, R-4, S-5

Which of
searched u

P. A large
Q. E-valu
R. A high
S. E-value the following statements are CORRECT when a protein sequence database is sing the BLAST algorithm?

r E-value indicates higher sequence similarity e < 10-10 indicates sequence homology
er BLAST score indicates higher sequence similarity
> 1010 indicates sequence homology
(A) P, Q a nd R only (B) Q and R only
(C) P, R a nd S only (D) P and S only

Which o
reaction

P. Mg2+
Q. pH
R. Ann f the following factors affect the fidelity of DNA polymerase in polymerase chain
?
concentration ealing temperature
(A) P an d Q only (B) P and R only
(C) Q an d R only (D) P, Q and R

Q.32 Group I lists spectroscopic methods and Group II lists biomolecular applications of these methods. Match the methods in Group I with the applications in Group II.

Group I Group II
P. Infrared 1. Identification of functional groups
Q. Circular Dichroism 2. Determination of secondary structure
R. Nuclear Magnetic Resonance 3. Estimation of molecular weight
4. Determination of 3-D structure

(A) P-4, Q-3, R-1 (B) P-2, Q-1, R-3
(C) P-1, Q-2, R-4 (D) P-3, Q-2, R-4

Q.33 The hexapeptide P has an isoelectric point (pI) of 6.9. Hexapeptide Q is a variant of P that contains valine instead of glutamate at position 3. The two peptides are analyzed by polyacrylamide gel electrophoresis at pH 8.0. Which one of the following statements is CORRECT?
(A) P will migrate faster than Q towards the anode
(B) P will migrate faster than Q towards the cathode
(C) Both P and Q will migrate together
(D) Q will migrate faster than P towards the anode

Q.34 Antibody-produci ng hybridoma cells are generated by the fusion of a
(A) T cell with a myeloma cell (B) B cell with a myeloma cell
(C) macrophage w ith a myeloma cell (D) T cell and a B cell

Q.35 Which of the following statements are CORRECT about the function of fetal bovine serum in animal cell culture?

P. It stimulates cell growth
Q. It enhances cell attachment
R. It provides hormones and minerals
S. It maintains pH at 7.4
(A) P and Q only (B) P and S only (C) P, Q and R only (D) P, Q, R and S

Q.36 Which one
and mRN of the following covalent linkages exists between 7-Methyl guanosine (m7G) As?
(A) 2’–3′ tr iphosphate (B) 3’–5′ triphosphate
(C) 5’–5′ tr iphosphate (D) 2’–5′ triphosphate

Q.37 Which one of the following amino acid residues will destabilize an α-helix when inserted in the middle of the helix?
(A) Pro (B) Val (C) Ile (D) Leu

Q.38 What is the solution of the differential equation 𝑑𝑦 = 𝑥 , with the initial condition, at 𝑥 =
𝑑𝑥 𝑦
0, 𝑦 = 1?
(A) 𝑥2 = 𝑦2 + 1 (B) 𝑦2 = 𝑥2 + 1 (C) 𝑦2 = 2𝑥2 + 1 (D) 𝑥2 – 𝑦2 = 0

Q.39 The Laplace transform of the function 𝑓(𝑡) = 𝑡2 + 2𝑡 + 1 is
(A) 1 + 3 + 1
𝑠3 𝑠2 𝑠 (B) 4 + 4 + 1
𝑠3 𝑠2 𝑠 (C) 1 + 2 + 1
𝑠3 𝑠2 𝑠 (D) 2 + 2 + 1
𝑠3 𝑠2 𝑠

Q.40 Which of the following factors can influence the lag phase of a microbial culture in a batch fermentor?

P. Inoculum size
Q. Inoculum age
R. Medium composition
(A) P and Q only (B) Q and R only (C) P and R only (D) P, Q and R

Q.41 Which one of the following statements is CORRECT about proportional controllers?
(A) The initial change in control output signal is relatively slow
(B) The initial corrective action is greater for larger error
(C) They have no offset
(D) There is no corrective action if the error is a constant

Q.42 Match the instruments in Group I with their corresponding measurements in Group II.

Group I Group II
P. Manometer 1. Agitator speed
Q. Rotameter 2. Pressure difference
R. Tachometer 3. Cell number
S. Haemocytometer 4. Air flow rate

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

Q.43 Which of the following statements is ALWAYS CORRECT about an ideal chemostat?

P. Substrate concentration inside the chemostat is equal to that in the exit stream
Q. Optimal dilution rate is lower than critical dilution rate
R. Biomass concentration increases with increase in dilution rate
S. Cell recirculation facilitates operation beyond critical dilution rate
(A) P and Q only (B) P, R and S only (C) P and S only (D) P, Q and S only

Q.44 Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]

Assertion [a]: It is possible to regenerate a whole plant from a single plant cell. Reason [r]: It is easier to introduce transgenes in to plants than animals.
(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]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false

Q.45 A UV-visible spectrophotometer has a minimum detectable absorbance of 0.02. The minimum concentration of a protein sample that can be measured reliably in this
instrument with a cuvette of 1 cm path length is µM. The molar extinction coefficient of the protein is 10,000 L mol-1 cm-1.

Q.46 The difference in concentrations of an uncharged solute between two compartments is 1.6-fold. The energy required for active transport of the solute across the membrane separating the two compartments is cal mol-1 (rounded off to the nearest integer). (R
= 1.987 cal mol-1 K-1, T = 37 ºC)

Q.47 In pea plants, purple color of flowers is determined by the dominant allele while white color is determined by the recessive allele. A genetic cross between two purple flower- bearing plants results in an offspring with white flowers. The probability that the third offspring from these parents will have purple flowers is (rounded off to 2 decimal
places).

Q.48 The molecular mass of a protein is 22 kDa. The size of the cDNA (excluding the untranslated regions) that codes for this protein is kb (rounded off to 1 decimal
place).

A new game is being introduced in a casino. A player can lose Rs. 100, break even, win Rs. 100, or win Rs. 500. The probabilities (𝑃(𝑋)) of each of these outcomes (𝑋) are given in the following table:

𝑋 (in Rs.) -100 0 100 500
𝑃 (𝑋) 0.25 0.5 0.2 0.05

The standard deviation (σ) for the casino payout is Rs. (rounded off to the nearest integer).

∫−1 𝑓(𝑥)𝑑𝑥 calculated using trapezoidal rule for the values given in the table is
(rounded off to 2 decimal places).

𝑥 −1 −2⁄3 −1⁄3 0 1⁄3 2⁄3 1
𝑓(𝑥) 0.37 0.51 0.71 1.0 1.40 1.95 2.71

Q.51 Yeast biomass (C6H10O3N) grown on glucose is described by the stoichiometric equation given below:
C6H12O6 + 0.48 NH3 + 3 O2  0.48 C6H10O3N + 3.12 CO2 + 4.32 H2O

The amount of glucose needed for the production of 50 g L-1 of yeast biomass in a batch reactor with a working volume of 1,00,000 L is _ kg (rounded off to the nearest integer).

Q.52 Phenolic wastewater discharged from an industry was treated with Pseudomonas sp. in an aerobic bioreactor. The influent and effluent concentrations of phenol were 10,000 and 10 ppm, respectively. The inlet feed rate of wastewater was 80 L h-1. The kinetic properties of the organism are as follows:
Maximum specific growth rate (µ𝑚) = 1 h-1 Saturation constant (𝐾𝑆) = 100 mg L-1
Cell death rate (𝑘𝑑) = 0.01 h-1
Assuming that the bioreactor operates under ‘chemostat’ mode, the working volume required for this process is L (rounded off to the nearest integer).

Q.53 In a cross-flow filtration process, the pressure drop (𝛥𝑃) driving the fluid flow is 2 atm, inlet feed pressure (𝑃𝑖) is 3 atm and filtrate pressure (𝑃𝑓) is equal to atmospheric pressure.
The average transmembrane pressure drop (𝛥𝑃𝑚) is atm.

Q.54 An industrial fermentor containing 10,000 L of medium needs to be sterilized. The initial spore concentration in the medium is 106 spores mL-1. The desired probability of contamination after sterilization is 10-3. The death rate of spores at 121 ºC is 4 min-1.
Assume that there is no cell death during heating and cooling phases. The holding time of the sterilization process is min (rounded off to the nearest integer).

Q.55 The dimensions and operating condition of a lab-scale fermentor are as follows: Volume = 1 L
Diameter = 20 cm Agitator speed = 600 rpm
Ratio of impeller diameter to fermentor diameter = 0.3
This fermentor needs to be scaled up to 8,000 L for a large scale industrial application. If the scale-up is based on constant impeller tip speed, the speed of the agitator in the larger reactor is rpm. Assume that the scale-up factor is the cube root of the ratio of fermentor volumes.

GATE Exam 2019 Architecture and Planning (AR) Question Paper With Answer Key

June 7, 2023November 28, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ______ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Architecture and Planning

Q. 1 – Q. 25 carry one mark each.

1. Which of the following commands in AUTOCAD is used to create 3D solid between various cross sections?

(A) LOFT

(B) MESH

(D) PFACE

Answer: (A)

2. Name the architect who criticized ornament in useful objects in his essay ‘Ornament and Crime’.

(A) John Ruskin

(B) H P Berlage

(D) Walter Gropius

Answer: (C)

3. A sanit ground ary landfill is provided with High Density Poly Ethylene (HDPE) lining along the surface. This is provided primarily to prevent

(A) Bleaching

(B) Leaching

(D) Plant growth

Answer: (B)

4. Super-ele vation of a road with pre-determined radius of curvature is primarily dependent on

(A) Altitude

(B) Soil bearing capacity

(D) Design traffic speed

Answer: (D)

5. In a mono-centric urban model, land rent is expected to

(A) diminish as one moves towards the center

(B) diminish as one moves away from the center

(D) be unrelated with distance from center

Answer: (B)

6. Fineness modulus of sand measures its

(A) Compressive strength

(B) Grading according to particle size

(D) Ratio of coarse and fine sand

Answer: (B)

7. The spherical surface of the geodesic dome comprises of

(A) Equilateral triangles of various sizes

(B) Isosceles triangles of various sizes

(D) Isosceles triangles of uniform size

Answer: (C)

8. The abrup t change or junction between two ecological zones is termed as

(A) Ecological niche

(B) Ecosystem

(D) Ecotone

Answer: (D)

9. Complementary colours in a Munsell pigment colour wheel refers to

(A) Colours in alternate positions

(B) Colours opposite to one another

(D) A pair of secondary colours

Answer: (B)

10. The closing syntax, for an executable command line in C or C++ program, is

(A) :

(B) ,

(D) .

Answer: (C)

11. The term ‘Necropolis’ refers to

(A) Orginacally growing Settlment

(B) Origin of settlement

(D) Merging of two settlements

Answer: (C)

12. Which of the following projection types is adopted in the Universal Transeverse Mercator (UTM)?

(A) Spherical Conical

(B) Planar

Answer: (D)

13. The ing redient to be added to produce Aerated Cement Concrete, is

(A) Aluminum

(B) Calcium chloride

(D) Sulphur

Answer: (A)

14. The cause of short column effect, during seismic occurrence, is due to

(A) Centralized rupture of the column

(B) Tearing of reinforcement bars

(D) Stress concentration

Answer: (D)

15. The solar protection system consisting of fixed slats or grids, outside a building façade in front of openings, is known as

(A) Brise–soleil

(B) Solarium

(D) Trombe wall

Answer: (A)

16. The Indian property inscribed by UNESCO on the World Heritage List in the year 2018 is

(A) Mattanchery Palace, Ernakulam

(B) The Victorian Gothic and Art Deco Ensembles of Mumbai

(D) Mughal Gardens in Kashmir

Answer: (B)

17. Typical features of Buddhist architecture are

(A) Mandapa, Chattri, Amalaka, Torana

(B) Stambha, Torana, Vimana , Harmika

(D) Vedika , Stupa, Chaitya, Vimana

Answer: (C)

18. Identify the Queen closure

(A)

(B)

(C)

(D)

Answer: (A)

19. Identify th e role of Vermiculate in vertical landscapes

(A) Fertilizer

(B) Holding material

(D) Water retention element

Answer: (Mark to All)

20. Which of the following parameters is essential to estimate the Envelope Performance Factor (EPF) of a building as per the Energy Conservation Building Code (ECBC), 2011?

(A) Building Type

(B) Maximum humidity

(D) Building occupancy duration

Answer: (D)

21. The illumination level of a room is 300 lux and the efficacy of the lamps is 60. The Light Power Density (LPD) of the room in Watt/m² is _____.

Answer: (5 to 5)

22. The load on a RCC column is 150 kN. The soil bearing capacity is 80 kN/m². Assuming a factor of safety of 1.2, the side of the square column footing is meter (rounded off to one decimal place)________.

Answer: (1.49 to 1.51)

23. A room is separated by a partition wall. The average intensities of sound in the source and
receiving sides across the partition are 10-4 W/m² and 10^-7 W/m² respectively. The transmission loss (TL) of the partition wall is dB______.

Answer: (30 to 30)

24. If the purchase price of 2BHK flat rises by 10 percent, the demand for such flats is observed to decrease by 8 percent. The price elasticity of the housing demand for 2BHK flats is (rounded off to one decimal place)________.

Answer: (0.75 to 0.85)

25. ‘Threshold of enclosure’ created by vertical surfaces or series of vertical elements in an urban plaza, represented by the ratio of height and distance, is given by an angle of degrees (rounded off to one decimal place)_______.

Answer: (260.0 to 30.0)

Q. 26 – Q. 55 carry two marks each.

26. Match the instruments in Column – I with the various types of surveying in Column – II and select the appropriate option.

(A) P-3, Q-4, R-2, S-5

(B) P-2, Q-4, R-1, S-5

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

Answer: (D)

27. Match the characteristics of settlement systems in Column – I with their corresponding theory/rules in Column – II and select the appropriate option.

(A) P-4, Q-1, R-2, S-5

(B) P-2, Q-5, R-3, S-1

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

Answer: (D)

28. Match the architectural projects in Column – I with the architect in Column – II, and select the appropriate option.

(A) P-3, Q-1, R-2, S-5

(B) P-1, Q-2, R-5, S-3

(D) P-3, Q-4, R-1, S-5

Answer: (A)

29. Match the Name of the book provided in Column – I with the corresponding author in Column – II and select the appropriate option.

(A) P-2, Q-3, R-1, S-5

(B) P-5, Q-2, R-3, S-4

(D) P-2, Q-1, R-4, S-5

Answer: (A)

30. Match the thermal properties in the Column – I and their respective units in Column – II and select the appropriate option.

(A) P-4, Q-1, R-5, S-2

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

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

Answer: (B)

31. Match the application in the field of construction in the Column – I and the respective items in Column – II and select the appropriate option.

(A) P-5, Q-1, R-4, S-3

(B) P-4, Q-3, R-1, S-5

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

Answer: (C)

32. Match the following types of masonry joints in Column – I with their corresponding description in Column – II, and select the appropriate option.

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

(B) P-4, Q-3, R-2, S-5

(D) P-4, Q-3, R-1, S-5

Answer: (B OR D)

33. Match the following in Column – I with their suitable description in Column – II, and select the appropriate option.

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

(B) P-2, Q-4, R-3, S-5

(D) P-3, Q-4, R-1, S-5

Answer: (D)

34. Match the units provided in Column – I with their corresponding items in Column – II, and select the appropriate option.

(A) P-5, Q-1, R-4, S-3

(B) P-2, Q-3, R-4, S-5

(D) P-5, Q-4, R-1, S-2

Answer: (D)

35. Match the scientific names of the trees provided in Column – I with the corresponding color of their bloom in Column – II, and select the appropriate option.

(A) P-4, Q-5, R-4, S-1

(B) P-1, Q-5, R-2, S-3

(D) P-4, Q-5, R-2, S-1

Answer: (D)

36. Match the items in Column – I and their respective location in building/site in Column – II, and select the appropriate option.

(A) P-4, Q-5, R-2, S-3

(B) P-5, Q-1, R-3, S-2

(D) P-3, Q-4, R-5, S-2

Answer: (C)

37. As per the Handbook on Barrier Free and Accessibility, CPWD – 2014, match the design guidelines in Column – I with their appropriate standards in Column – II and select the appropriate option.

(A) P-3, Q-4, R-1, S-5

(B) P-5, Q-3, R-2, S-4

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

Answer: (C)

38. Match the contemporary Urban Design Movements listed in Column – I with the corresponding principles listed in Column – II and select the appropriate option.

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

(B) P-1, Q-5, R-3, S-2

(D) P-2, Q-5, R-4, S-1

Answer: (A OR D)

39. Match the figures of vaults in Column – I with their corresponding types in Column – II and select the appropriate option.

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

(B) P-3, Q-1, R-4, S-5

(D) P-2, Q-3, R-1, S-5

Answer: (A)

40. A colony of 50 people is served by a septic tank. The rate of water supply is 90 lpcd in the colony and 40% of it is going to the septic tank. The retention period of the tank is 24 hours. The length of the septic tank is meter (rounded off to two decimal places)__________.

Assume, storage capacity/person = 0.085m³ (3 years)

Space for digestion = 0.0425 m³/person

Depth of tank = 1.4 m Length: Width = 2:1

Answer: (3.40 to 3.45)

41. A cone, with a base of 10 cm diameter and axis of 12 cm, is lying on Horizontal Plane (HP) along its generator. The internal angle which the base of the cone makes with the HP is _____ degrees.

Answer: (67.0 to 68.0)

42. A public utility building of 5000 m² was constructed 5 years before, on a site of 1 hectare. The present value of open land in that location is Rs. 100/m² and present construction cost of such building is Rs. 2500/m². If the value of the building is assumed to be depreciating at a constant rate of 6 percent per annum, then the present value of the property using ‘Valuation by Cost Method’ is___ (in Rs. lakhs) (rounded off to one decimal place).

Answer: (101.0 to 104.0)

43. A residential area of 20 hectares is planned for three different types of plots of 500 m², 300 m² and 200 m² with numbers of plot in each category are 100, 120 and 150 respectively. The rest of the area is allocated for roads and facilities such as schools, shops and parks. Each plot has one dwelling unit and the average household size is 5 persons.

The net residential density of the area in persons per hectare is ______.

Answer: (159 to 160)

44. In a single lane road, traffic volume of 1000 vehicle/h moving at 20 km/h, comes to a halt due to an accident. If jam density is 150 vehicle/km, the velocity of the shock wave generated (in absolute value) is _____ km/h.

Answer: (9.9 to 10.1)

45. In a site map, a rectangular residential plot measures 150 mm × 40 mm, and the width of the front road in the map measures 16 mm. Actual width of the road is 4 m. If the permissible F.A.R. is 1.2, the maximum built-up area for the residential building will be ____ m².

Answer: (450 to 450)

46. The internal dimension of a room is 10m × 10m × 4m (height). The total area of the doors and windows are 16 m2. Keeping the doors and windows closed, the reverberation time of the room becomes 1.2 second. Assume all the interior surfaces including doors and windows have same sound absorption coefficient. If all the doors and windows of the room are kept fully open, the reverberation time will be_____ second (rounded off to two decimal places).

Answer: (0.93 to 0.97)

47. A depressed portion of a land is identified by three closed contours, as shown in the figure below. The area bounded by three contour lines are 6 m2, 24 m² and 96 m² respectively.

The contour interval is 1 m. Using prismoidal method, the volume of the earth needed to fill the land depression is_____ m³.

Answer: (65 to 76)

48. Solar panels are proposed to be installed on a building roof top to generate electricity. The size of each solar panel is 2 m². The efficiency of each panel is 75%. The orientations of the solar panel and related solar data are given in the table below.

As per the above proposal ____ kWh solar power will be generated daily. (rounded off to one decimal place)

Answer: (28.4 to 28.6)

49. A power shovel is having 1.8 m³ excavation output per batch of operation. The average cycle time of the batch operation is 45 seconds. The lost time per hour of the excavation activity is 10 minutes. Assume six working hours of operation per day. The amount of soil excavated by the power shovel per day is _____ m³ (rounded off to two decimal places).

Answer: (719.75 to 720.25)

50. A room having dimension 12 m × 10 m × 3.5 m is required to be mechanically ventilated by air-conditioner. The temperature difference between outdoor ambient air and the supply air is 12°C. Consider three air exchanges per hour. The volumetric specific heat of the air is 1250 J/m³°C. Assume one ton of refrigeration (TR) is equal to 3.5 kW. The capacity of the air-conditioner for the room in TR will be _____.

Answer: (1.49 to 1.51)

51. A simply supported beam AB has a clear span of 7 meter. The bending moment diagram (BMD) of the beam due to a single concentrated load is shown in the figure below.

The magnitude of the concentrated load in kN is _____ .

Answer: (21 to 21)

52. For a symmetrical trapezoidal open drain in a landscape with grass and loose rock surface, the velocity of flow of water is _____ m/sec, (rounded off to two decimal places), given the following data.

Water edge width at the top = 750 mm

Water edge width at the bottom = 450 mm

Water depth = 600 mm

Manning’s coefficient of roughness = 0.05

Slope along the drain = 1 in 250

Answer: (0.40 to 0.50)

53. The stack pressure is created by 10 m height of stack and 15°C temperature difference. The motive force due to the stack pressure over a cross section area of 2.5 m² is ____ N.

Answer: (15.0 to 16.0)

54. An industrial building contains 3000 kg of combustible materials, in dry state, distributed over three rooms of area 100 m², 500 m² and 300 m² each, in a proportion of 30%, 50% and 20% of the contents, respectively. Calorific value of the material is 4400 kCal/kg.

The Total Fire Load of the rooms is equal to _____ kCal/ m².

Answer: (61500 to 61700 OR 14600 to 14700)

55. A simple truss is shown in the figure below. The truss is loaded with horizontal and vertical force 15 kN and 25 kN, respectively. The force in the member AB will be _____ kN.

Answer: (20 to 20)

GATE Exam 2019 Agricultural Engineering (AG) Question Paper With Answer Key

June 7, 2023November 27, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ______ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Agricultural Engineering

Q. 1 – Q. 25 carry one mark each.

1. has the value

(A) 0.785

(B) 0.915

(D) 1.245

Answer: (A)

2. The determinant of the matrix is

(A) 1

(B) 0

(D) 2

Answer: (C)

3. In a relay race there are five teams A, B, C, D and E. Assuming that each team has an equal chance of securing any position (first, second, third, fourth or fifth) in the race, the probability that A, B and C finish first, second and third, respectively is

(A) 1/60

(B) 1/20

(D) 3/10

Answer: (A)

4. The path traced by the material threshed between the cylinder and the concave of an axial flow thresher is

(A) straight single pass and perpendicular to the cylinder shaft

(B) curved and perpendicular to the cylinder shaft

(D) straight and parallel to the cylinder shaft

Answer: (C)

5. The farm machine/implement used only for preparing wetland is

(A) rotavator

(B) disk harrow

(D) cultivator

Answer: (C)

6. The type of typical spray distribution profile of a hollow cone nozzle is

(A) steep sided slo pes

(B) gradual sloping sides

(D) narrow topped with steep sides

Answer: (A)

7. The amount of biogas required to run a diesel engine is 0.65 m3 kW^-1h^-1. The minimum size of the Deenbandhu model biogas plant in m3 required to run a 1 kW (brake power) diesel engine daily for one hour is

(A) 1

(B) 2

(D) 4

Answer: (B)

8. A soil sample has a porosity of 40%. Void ratio of the soil sample is

(A) 0.367

(B) 0.467

(D) 0.667

Answer: (D)

9. In the Muskingum method of channel routing, the routing equation is written as 𝑄₂ = 𝐶𝑜𝐼₂ + 𝐶₁𝐼₁ + 𝐶₂𝑄₁. If the storage-time constant K = 12 h, weighting factor x = 0.15 and the time step for routing ∆𝑡 = 4 h, the coefficient 𝐶_𝑜 is

(A) 0.016

(B) 0.048 .

(D) 0.656

Answer: (A)

10. Match the following items between Column-I and Column-II with the most appropriate combinations:

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

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

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

Answer: (B)

11. Tensiometer installed in the soil measures

(A) osmotic suction of soil moisture

(B) soil permeability

(D) capillary potential of the soil

Answer: (D)

12. Head pulley of a bucket elevator has an effective radius of 150 mm. In order to obtain the most satisfactory discharge from this elevator, the speed of the head pulley in rpm is

(A) 36

(B) 44

(D) 77

Answer: (D)

13. The clean paddy production per annum is 160 million tonnes. Average milling quality analysis indicates the husk content, total yield and degree of polish as 22%, 73.32% and 6%, respectively. For an average bran oil yield of 20%, the annual rice bran oil potential in million tonnes is

(A) 1.268

(B) 1.498

(D) 1.945

Answer: (B)

14. A batch of 10000 L milk is to be sterilized and thereafter packed in 20000 packets of 500 ml each. The mean Standard Plate Count (SPC) of Bacillus subtilis in 100 samples of fresh milk was found to be 50 ml -1. The milk is to be sterilized such that each 500 ml packet is completely devoid of the same organism. Minimum number of log cycle reduction for sterilization of this batch is_______ .

(A) 8

(B) 9

(D) 12

Answer: (B)

15. A tube-in-tube counter-flow heat exchanger is heating oil from 35°C to 77°C by circulating hot water at 100°C. The outlet temperature of water is 70 °C. The log-mean-temperature difference (LMTD) is

(A) exactly equal to the mean arithmetic temperature difference

(B) significantly greater than the mean arithmetic temperature difference

(D) very nearly equal to the mean arithmetic temperature difference

Answer: (D)

16. Using trapezoidal rule, the value of (rounded off to three decimal places)is_______ .

Answer: (1.820 to 1.830)

17. Two cards are drawn at random and without replacement from a pack of 52 playing cards. The probability that both the cards are black (rounded off to three decimal places) is__________.

Answer: (0.244 to 0.246)

18. The total width between the two extreme furrow openers in a tractor drawn 9-row wheat seed drill is 1.6 m. The average mass of wheat seeds dropped per meter of row length in each furrow opener is 2.15 g. Seed rate obtained with the seed drill in kg ha-1 (rounded off to one decimal place) is ________.

Answer: (107.4 to 107.8)

19. The purchase price of a tractor is Rs. 5,50,000. Useful life of the tractor is 10 years and its salvage value is 10% of the purchase price. Following the sum of the years digit method, the depreciation in 3rd year in Rs. is________ .

Answer: (72000 to 72000)

20. A pair of straight teeth spur gears is transmitting power at 500 rpm. The pinion has 16 standard full depth involute teeth of module 8 mm. The pitch line velocity of the pinion in m s-1 (rounded off to two decimal places) is __________.

Answer: (3.30 to 3.40)

21. A soil conservation structure has an expected life of 10 years and is designed for a flood magnitude of return period 50 years. The risk of this hydrologic design in percentage (rounded off to two decimal places) is _________.

Answer: (18.00 to 18.40)

22. A watershed of area 80 ha has a runoff coefficient of 0.3. A storm of intensity 5 cm h-1 occurs for a duration more than the time of concentration of the watershed. The peak discharge in m³ s^-1 (rounded off to two decimal places) is _________.

Answer: (3.30 to 3.35)

23. A lateral has 12 sprinklers spaced 14 m apart in a sprinkler irrigation system. The laterals are spaced 20 m apart on the main line. If the recommended fertilizer dose is 80 kg ha-1, the amount of fertilizer to be applied at each setting in kg (rounded off to two decimal places) is_______.

Answer: (26.87 to 26.89)

24. In a rubber roll sheller, 250 mm diameter rolls are set at a clearance of 1 mm. If the mean thickness of paddy grains being shelled is 2 mm, the length of husking zone in mm (rounded off to two decimal places) is ________.

Answer: (22.20 to 22.35)

25. Air-water vapour mixture at 1 atmosphere pressure has 0.035 kg water vapour (kg dry air)-1 and dry bulb temperature of 37 oC. The value of Universal gas constant is 8.314 kJ (kg mole K)^-1. The humid volume of this air-water vapour mixture in m³ (kg dry air)-1 (rounded off to three decimal places) is _________.

Answer: (0.920 to 0.930)

Q. 26 – Q. 55 carry two marks each.

Q.26 General soluti on to the differential equation y″ + 4y’ + 5y = 0 is

(A) 𝑒^2𝑥(𝑎 𝑐𝑜𝑠 𝑥 + 𝑏 sin 𝑥)

(B) 𝑒^−2𝑥(𝑎 cos 𝑥 + 𝑏 sin 𝑥)

(D) 𝑒^−𝑥(𝑎 cos 2𝑥 + 𝑏 sin 2𝑥)

Answer: (B)

27. For vectors on the curve C (y = 2x²) in the x-y plane from (0, 0) to (1, 2) is

(A) -1.17

(B) 1.50

(D) 2.67

Answer: (A)

28. A 3-cylinder 4-stroke CI engine coupled with a turbocharger has a bore and stroke length of 120 mm and 130 mm, respectively. The engine is running at 1600 rpm with a volumetric efficiency of 150%. The air to fuel ratio for complete combustion on weight basis is 14.9:1 and the density of air entering the cylinder is 1.2 kg m-3. The fuel consumption in kg h^-1 is

(A) 17.05

(B) 25.57

(D) 51.14

Answer: (B)

29. A level field of 1.2 ha (120 m × 100 m) is ploughed using a reversible mould board plough with a total effective cutting width of 0.64 m. The average field overlap is 80 mm between two consecutive laps. The average time taken for each turn is 30 seconds and the mean operating speed is 5.0 km h-1. The maximum effective field capacity in ha h^-1 is

(A) 0.207

(B) 0.236

(D) 0.318

Answer: (A)

30. The thresher ‘A’ has output capacity of 170 kg h^-1 while threshing paddy crop at 14% moisture content (m.c.) with a grain to straw ratio 45:55. The thresher ‘B’ has output capacity of 160 kg h-1 while threshing paddy crop at 13% m.c. with a grain to straw ratio 40:60. Both the threshers have threshing efficiency of 97%. If a farmer has to carry out threshing of paddy crop at 12% m.c. with a grain to straw ratio 40:60 in the least time, the selected thresher and its output in kg when operated for 5 hours will be

(A) A and 738

(B) A and 850

(D) B and 800

Answer: (C)

31. A horizontal axis drag type wind rotor, fitted with 4 thin rectangular blades having drag coefficient 1.29, is used to extract power when the average wind velocity in the rotor plane is 10 km h-1. The maximum power coefficient is

(A) 0.148

(B) 0.191

(D) 0.593

Answer: (B)

32. A two-wheel drive tractor while operating a plough at a forward speed of 5 km h^-1 experiences a wheel slip of 15%. If the angular speed of the rear axle is 2.4 rad s^-1, the rolling radius of the traction wheel in meter will be

(A) 0.49

(B) 0.58

(D) 0.75

Answer: (C)

33. The combined mass of a tractor seat and operator is 75 kg and the undamped natural frequency of the operator seat is 10 rad s^-1. If the seat suspension damping rate is 600 N m^-1 s^-1, the damping ratio is

(A) 0.2

(B) 0.4

(D) 0.8

Answer: (B)

34. A catchment has eight raingauge stations. In a year, the annual rainfall recorded by the gauges (in cm) are 93.8, 106.5, 170.6, 138.7, 87.8, 156.2, 180.9 and 110.3. For a 10% error in the estimation of the mean rainfall, the optimum number of stations in the catchment is

(A) 4

(B) 6

(D) 10

Answer: (C)

35. On a 4% land slope in a medium rainfall zone, the horizontal spacing of bunds in meter and the length of bunds per hectare in meter, respectively are

(A) 25 and 300

(B) 25 and 400

(D) 30 and 400

Answer: (B)

36. In a drainage area of 15 ha, the slope and drainage coefficient are 0.4% and 11 mm/day, respectively. The value of Manning’s roughness coefficient is 0.016. The inside diameter (in mm) of the corrugated plastic tubing used for drainage is

(A) 200.51

(B) 205.52

(D) 215.23

Answer: (C)

37. A 20 cm diameter well fully penetrates a confined aquifer of thickness 20 m. After a long period of pumping at the rate of 1500 L min^-1, the steady drawdowns in the wells at 30 m and 50 m from the pumping well are found to be 2.0 m and 1.5 m, respectively. Assuming π = 3.14, the transmissivity of the aquifer in m² s^-1 is

(A) 0.244

(B) 14.676

(D) 880.560

Answer: (Marks to All)

38. Water is flowing at a velocity of 1.6 m s^-1 in a pipe of diameter 8 cm and length 100 m. Assuming the value of coefficient of friction for pipe, f = 0.005 and acceleration due to gravity, g = 9.81 m s-2, the head loss (in meter) due to friction in the pipe is

(A) 1.28

(B) 2.28

(D) 3.26

Answer: (D)

39. A cream separator has discharge radii of 6 cm and 9 cm and the density of cream and skim milk are 860 and 1035 kg m^-3, respectively. The ideal radius (in meter) for placing the feed inlet is

(A) 0.085

(B) 0.098

(D) 0.174

Answer: (D)

40. Head rice contents in the samples collected at feed inlet, head rice outlet and broken rice outlet of an indented cylinder grader are 82%, 94% and 15%, respectively. If the grader receives the feed at 1200 kg h^-1, the flow rate (in kg h-¹) of head rice in the broken rice stream is

(A) 20.17

(B) 27.34

(D) 1017.72

Answer: (B)

41. A batch of 100 kg grain at 32% moisture content (wet basis) is being dried using hot air at 70 °C and 30% RH. The values of Henderson equation’s constants c and n for the grain are 8.5×10^-6 and 2.07, respectively. Considering the maximum possible drying of the batch, the quantity of moisture removed in kg is

(A) 10.20

(B) 17.05

(D) 25.07

Answer: (D)

42. A chiller used for 3 hours. kW and working on mechanical vapour compression refrigeration system (COP = 4.5) is cooling 12500 kg of fresh cow milk (cp = 3.8 kJ kg^-1 K^-1) from 30°C to 4°C in Assuming ideal compression process, the power consumed by the electric motor in the tonnage of refrigeration (TR), respectively are

(A) 25.4 and 32.5

(B) 25.4 and 114.3

(D) 114.3 and 25.4

Answer: (A)

43. Two streams of air with the following conditions are adiabatically mixed:

Latent heat of vapourization of water at 0°C = 2501 kJ kg^-1 Specific heat capacity of dry air = 1.005 kJ kg^-1 K^-1 Specific heat capacity of water vapour = 1.880 kJ kg^-1 K^-1

Using above values, the dry bulb temperature and the absolute humidity of the mixed air in o°C and g water vapour (kg dry air)^-1, respectively are

(A) 43 and 30

(B) 44 and 31

(D) 46 and 35

Answer: (D)

44. Directional derivative of 𝑓(𝑥, 𝑦, 𝑧) = 𝑥𝑦² + 𝑦𝑧³ at the point (2, -1, 1) in the direction of vector (rounded off to two decimal places) is __________.

Answer: (-3.70 TO -3.60)

45. The mean absolute deviation about the median for the data 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21
(rounded off to two decimal places) is ___________.

Answer: (5.26 to 5.28)

46. The application rate of an 18-nozzle hydraulic sprayer is 1120 L ha^-1. The nozzle spacing and forward speed are 400 mm and 3.4 km h^-1, respectively. The operating pressure is 2.1 MPa and the pump efficiency is 60%. If 10% of the pump output power is used for agitating the liquid, the power needed to operate the sprayer in kW (rounded off to three decimal places) is ________.

Answer: (2.900 to 3.000)

47. A two-wheel drive tractor is taking a turn with a radius of curvature 5.0 m. The minimum horizontal distance between the tipping axis and line of action of the CG is 800 mm. The angle between the line of action of centrifugal force and perpendicular direction to the tipping plane is 15o. If the vertical distance of the CG from the ground level is 900 mm, the limiting speed (in km h-1) of the tractor to prevent overturning (rounded off to two decimal places) is __________.

Answer: (24.00 to 24.45)

48. During operation, a two-wheel drive tractor with a total weight of 2000 kg has a weight distribution of 35% and 65% in front and rear axles, respectively. The width and diameter of the tyres fitted to the front axle are 0.18 m and 0.56 m, and those of the rear axle are 0.34 m and 1.10 m, respectively. If tyre deflection is 20%, then rolling resistance (in kN) of the tractor in a soil with average cone index 1000 kPa at a wheel slip of 15% (rounded off to two decimal places) will be __________.

Answer: (1.31 to 1.36)

49. The peak of a flood hydrograph due to a 5-hour storm is 670 m³ s^-1. The total depth of rainfall is 9 cm. Assuming an average infiltration loss of 0.2 cm h^-1 and a constant baseflow of 30 m3 s-1, the peak discharge of the 5-hour unit hydrograph for this catchment in m³ s^-1 is ________.

Answer: (80 to 80)

50. A parabolic grassed water channel 8 m wide at the top and 60 cm deep is laid on a slope of 3%. Assuming the value of ‘n’ in Manning’s formula as 0.04 m^-1/3 s, the discharge capacity (in m3 s-1) of the channel (rounded off to two decimal places) is __________.

Answer: (7.35 to 7.55)

51. Undisturbed soil sample is collected from a field when the soil moisture is at field capacity. The inside diameter of the core sampler is 7.5 cm with a height of 15 cm. Weight of the core sampling cylinder with moist soil is 2.81 kg and that with oven dry soil is 2.61 kg. The weight of the core sampling cylinder is 1.56 kg. Assuming π = 3.14, the water depth in centimeter per meter depth of soil (rounded off to two decimal places) is _________.

Answer: (30.10 to 30.30)

52. An irrigation stream of 27 L s^-1 is diverted to a check basin of size 12 m × 12 m. The water holding capacity of the soil is 15% and the average soil moisture content in the crop root zone prior to applying water is 7.5%. The depth of crop root zone is 1.2 m and apparent specific gravity of the soil is 1.5. Assuming no loss due to deep percolation, irrigation time (in minute) required to replenish the root zone moisture to its field capacity is _______.

Answer: (12 to 12)

53. Angle of internal friction of a certain grain (bulk density = 650 kg m^-3) is 30°. A bin filled with this grain experiences a pressure of 60 kPa at its base. Ignoring the factor of safety, the safe height (in meter) to which water (density = 1000 kg m^-3) can be filled in this bin (rounded off to two decimal places) is ________.

Answer: (2.00 to 2.10)

54. The steady-state mass transfer coefficient (kg) based on water vapour pressure differential (VPD) operating across stagnant, non-diffusing air was estimated to be 0.05 g mole s^-1 m^-2 kPa^-1. If VPD varies from 12 kPa to 7 kPa over a distance of 2 mm, then the mass transfer coefficient (kyˈ) based on equimolar counter-diffusion in g mole s-1 m^-2 (mole fraction)^-1 (rounded off to one decimal place) is __________.

Answer: (4.5 to 4.7)

55. In an air blast freezing operation, a flat tray of 1.0 m×1.0 m×0.02 m dimensions is used to freeze filled depodded peas. Bulk density and moisture content of peas are 550 kg m^-3 and 85% (w.b.), respectively. Latent heat of freezing from water to ice at -1 −°C is 335 kJ kg-1 and heat transfer occurs identically from the top and the bottom surfaces of the tray. Convective film heat transfer coefficient on the heat transfer surfaces of the tray is 30 W m^-2 K^-1 and the thermal conductivity of frozen peas is 0.54 W m^-1 K^-1. Assuming the tray to be a semi-infinite slab, the freezing time (in minutes) to completely freeze the product (rounded off to one decimal place) is ________.

Answer: (Marks to All)

GATE Exam 2019 Aerospace Engineering (AE) Question Paper With Answer Key

June 7, 2023November 27, 2019 by suresh84

GATE 2019 General Aptitude (GA) Set-8

Q. 1 – Q. 5 carry one mark each.

1. The fishermen, ________ the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(D) that

Answer: (C)

2. Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

1. Some who were involved in the strike were students.

2. No student was involved in the strike.

3. At least one student was involved in the strike.

4. Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(D) 2 and 3

Answer: (C)

3. The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is .

(A) 17.1

(B) 21.0

(D) 72.8

Answer: (C)

4. Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

1. No two odd or even numbers are next to each other.

2. The second number from the left is exactly half of the left-most number.

3. The middle number is exactly twice the right-most number.

Which is the second number from the right?

(A) 2

(B) 4

(D) 10

Answer: (C)

5. Until Iran came along, India had never been in kabaddi.

(A) defeated

(B) defeating

(D) defeatist

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India

Answer: (C)

(A) 10.50

(B) 14.70

(D) 50.00

Answer: (A)

Which one of the following pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(D) gharana, lineage

Answer: (C)

(A) 9

(B) 10

(D) 11.30

Answer: (B)

Based on the paragraph above, the prestige of a head-hunter depended upon

(A) the prestige of the kingdom

(B) the prestige of the heads

(D) the number of heads he could gather

Answer: (D)

Aerospace Engineering

Q. 1 – Q. 25 carry one mark each.

1. The maximum value of the function 𝑓(𝑥) = 𝑥𝑒^−𝑥 (where x is real) is

(A) 1/𝑒

(B) 2/𝑒²

(D) ∞

Answer: (A)

2. Vector 𝑏⃗ is obtained by rotating 𝑎 = 𝑖̂ + 𝑗̂ by 90° about 𝑘̂, where 𝑖̂, 𝑗̂ and 𝑘̂ are unit vectors along the x, y and z axes, respectively. 𝑏⃗ is given by

(A) 𝑖̂ − 𝑗̂

(B) −𝑖̂ + 𝑗̂

(D) −𝑖̂ − 𝑗̂

Answer: (B)

3. A scalar function is given by 𝑓(𝑥, 𝑦) = 𝑥² + 𝑦². Take 𝑖̂ and 𝑗̂ as unit vectors along the x and y axes, respectively. At (𝑥, 𝑦) = (3, 4), the direction along which 𝑓 increases the fastest is

Answer: (C)

4. The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

(A) LT⁻¹

(B) L²T ⁻¹

(D) L⁻²T

Answer: (B)

5. ϕ(𝑥, 𝑦) represents the velocity potential of a two-dimensional flow with velocity field are unit vectors along the x and y axes, tively. Which of the following is necessarily true?

(A) ∇²ϕ

(D) 𝑢 = −𝜕𝜙/𝜕𝑦, 𝑣 = 𝜕𝜙/𝜕𝑥

Answer: (B)

6. For a quasi-one-dimensional isentropic supersonic flow through a diverging duct, which of the following is true in the direction of the flow?

(A) Both the Mach number and the static temperature increase.

(B) The Mach number increases and the static temperature decreases.

(D) Both the Mach number and the static temperature decrease.

Answer: (B)

7. For a NACA2415 airfoil of chord length c, which of the following is true?

(A) Maximum camber is located at 0.2c from the leading edge.

(B) Maximum thickness is located at 0.15c from the leading edge.

(D) Maximum thickness is 0.05c.

Answer: (C)

8. When a propeller a the following state irplane in ground-roll during take-off experiences headwind, which of ments is FALSE?

(A) The drag on the airplane increases.

(B) The thrust from the propellers decreases.

(D) The ground-roll distance increases.

Answer: (D)

9. Which of the following graphs represents the response of a dynamically unstable airplane?

(A)

(B)

(C)

(D)

Answer: (A)

10. The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine

(A) has larger kinetic energy lost in the exhaust jet.

(B) has lower thrust power.

(D) has higher thrust to weight ratio.

Answer: (A)

11. While flying at order from the l Mach 2.0, 11 km altitude and producing the same thrust, what is the correct owest thrust specific fuel consumption (tsfc) to the highest tsfc?

(A) Turbofan, R amjet, Turbojet

(B) Turbofan, Turbojet, Ramjet

(D) Turbojet, Turbofan, Ramjet

Answer: (B)

12. For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

(A) CPR of an axial compressor > CPR of centrifugal compressor.

(B) CPR of an axial compressor < CPR of centrifugal compressor.

(D) CPR of any value can be attained with either an axial or a centrifugal compressor.

Answer: (B)

13. For a beam subjected to a transverse shear load through its shear center,

(A) the twist per unit length is zero.

(B) the shear stress is uniform throughout the cross-section.

(D) the shear strain is zero at the shear center.

Answer: (A)

14. A function 𝑓(𝑥) is defined by The value of

is (round off to 1 decimal place).

Answer: ()

15. The value of the following limit is______ (round off to 2 decimal places).

Answer: (0.5 to 0.5)

16. To simulate the aerodynamic forces on a cylinder of 1 m diameter due to a uniform air flow of 1 m/s at standard temperature and pressure (STP), low-speed wind tunnel experiments at STP are conducted on a 0.1 m diameter cylinder. The free stream air speed in the wind tunnel experiments should be _____ m/s (round off to the nearest integer).

Answer: (0.16 to 0.17)

17. The power-off glide range for an airplane with a maximum Lift to Drag ratio of 18, when the glide starts at an altitude of 4 km, is _______ km (round off to the nearest integer).

Answer: (10 to 10)

18. For an airplane flying in a vertical plane, the angle of attack is 3°, the horizontal and vertical components of velocity in wind axis are 300 km/h and 15.72 km/h, respectively. The pitch attitude of the airplane is _______ degrees (round off to 2 decimal places).

Answer: (5.98 to 6.00)

19. An airplane is in steady level flight with a true air speed of 50 m/s. The ambient air density and ambient pressure at the flight altitude are 0.91 kg/m³ and 7×10⁴N/m^2, respectively. At sea level, air density is 1.225 kg/m³ and ambient pressure is 1.01×10⁵ N/m². The equivalent or indicated air speed of the airplane is ______ m/s (round off to 2 decimal places).

Answer: (43.05 to 43.15)

20. For the complete combustion of 1 mole of ethanol (C₂H₅OH), the required number of moles of oxygen is _____ .

Answer: (3 to 3)

21. One kg of diatomic gas is heated and its temperature increases from 100 K to 600 K. The energy added at constant pressure during this process is 500 kJ. The specific heat at constant volume for the gas is _____ kJ/kgK. (round off to 2 decimal places).

Answer: (0.70 to 0.72)

22. The number of independent elastic constants for a homogeneous isotropic linear elastic material is______ .

23. A thin plate with Young’s modulus 210 GPa and Poisson’s ratio 0.3 is loaded as shown in the figure. The change in length along the y-direction________ is mm (round off to 1 decimal place).

Answer: (2 to 2)

24. For the state of stress shown in the figure, the normal stress, 𝜎_𝑛 , on a plane inclined at 45 degrees to the x-axis is MPa (round off to the nearest integer).

Answer: (247 to 255)

25. In the spring-mass system, shown in the figure, mass m = 3 kg and the spring stiffness k = 20 kN/m. The natural frequency of the system is _____ Hz (round off to the nearest integer).

Answer: (16 to 16)

Q. 26 – Q. 55 carry two marks each.

26. The following system of equations

2𝑥 − 𝑦 − 𝑧 = 0,

−𝑥 + 2𝑦 − 𝑧 = 0,

−𝑥 − 𝑦 + 2𝑧 = 0

(A) has no solution.

(B) has a unique solution.

(D) has an infinite number of solutions.

Answer: (D)

27. A supersonic flow in a constant area duct at Mach number M₁ encounters a ramp of angle θ₁ (see Figure 1). The resulting oblique shock with shock angle β₁ is then reflected from the top wall. For the reflected shock, the turn angle is θ2 and the shock angle is β₂.

Use the weak shock solution from the θ-β-M plot shown in Figure 2 to choose the correct option from the following.

(A) β₁ > β₂

(B) β₁ < β₂

(D) θ₁ < θ₂

Answer: (B)

28. Which of the following statements about adverse yaw of an airplane is/are correct?

P. It is caused by flow separation resulting from large rudder deflection.

Q. It is caused by dissimilar drag forces acting on the two halves of the wing resulting from aileron deflections of same magnitude.

R. It can be eliminated by ensuring that the upward deflection of one aileron is greater than the downward deflection of the opposite aileron.

(A) P only

(B) Q only

(D) Q and R

Answer: (D)

29. In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine

(A) decreases, as the heat input is lower.

(B) remains unchanged.

(D) decreases, as the thrust produced is higher.

Answer: (C)

30. For a 1 m long simply supported beam with a concentrated vertical load of 200 N and a concentrated bending moment of 100 Nm at the center as shown in the figure, the correct bending moment diagram is :

(A)

(B)

(C)

(D)

Answer: (A)

31. For real x, the number of points of intersection between the curves 𝑦 = 𝑥 and 𝑦 = cos 𝑥 is_________.

Answer: (1 to 1)

32. One of the eigenvalues of the following matrix is 1.

The other eigenvalue is ______ .

Answer: (2 to 2)

33. The curve 𝑦 = 𝑓(𝑥) is such that its slope is equal to 𝑦² for all real x. If the curve passes through (1, -1), the value of y at 𝑥 = −2 is_______ (round off to 1 decimal place).

Answer: (0.5 to 0.5)

34. The inviscid, incompressible flow field resulting from a uniform flow past a circular cylinder of radius R centered at the origin is given by:

where u_r and u_θ are the radial and azimuthal velocity components in polar coordinates, (r, θ), as shown in the figure. U is the free stream speed. Ignore the effects of gravity. The azimuthal location (in the first quadrant) on the cylinder at which the pressure coefficient is zero is ______ degrees (round off to the nearest integer).

Answer: (30 to 30)

35. A cylindrical container of radius R = 50 cm is filled with water up to a height ho. Upon rotating the cylinder about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaced upwards by h₁ = 10 cm at r = R. The magnitude of the downward displacement h₂ of the free surface at r = 0 _____ is cm (round off to the nearest integer).

Answer: (10 to 10)

36. A two-dimensional, incompressible fluid flow is described by the stream function Ψ = xy³ m²/s on the Cartesian x-y plane. If the density and dynamic viscosity of the fluid are 1 kg/m3 and 0.1 kg/m-s, respectively, the magnitude of the pressure gradient in the x direction at x=1 m and y=1 m is _______ N/m³ (round off to 1 decimal place).

Answer: (3.5 to 3.7 or 2.3 to 2.5)

37. The static pressure ratio across a stationary normal shock is given by

where M₁ is the upstream Mach number. For a stationary normal shock in air (γ = 1.4, 𝑅 = 287 J/kg-K) with upstream flow conditions given by: speed 800 m/s, static temperature 300 K and static pressure 1 atm., the static pressure downstream of the shock is ____atm. (round off to 2 decimal places).

Answer: (5.95 to 6.10)

38. For a symmetric airfoil at an angle of attack of 10º, assuming thin airfoil theory, the magnitude of the pitching moment coefficient about the leading edge is ______ (round off to 2 decimal places).

Answer: (0.24 to 0.30)

39. The span-wise distribution of circulation over a finite wing of span b = 10 m is

If Γ₀ = 20 m²/s and the free stream density and speed are 1.2 kg/m³ and 100 m/s, respectively, the total lift is _______ kN (round off to 2 decimal places).

Answer: (18.00 to 19.20)

40. The airplane shown in figure starts executing a symmetric pull-up maneuver from steady level attitude with a constant nose-up pitch acceleration of 20 deg/s². The vertical load factor measured at this instant at the centre of gravity (CG) is 2. Given that the acceleration due to gravity is 9.81 m/s², the vertical load factor measured at point P on the nose of the airplane, which is 2 m ahead of the CG, is _______ (round off to 2 decimal places).

Answer: (2.06 to 2.08)

41. Consider an airplane with a weight of 8000 N, wing area of 16 m², wing zero-lift drag coefficient of 0.02, Oswald’s efficiency factor of 0.8, and wing aspect ratio of 6, in steady level flight with wing lift coefficient of 0.375. Considering the same flight speed and ambient density, the ratio of the induced drag coefficient during steady level flight to that during a 30o climb is ______ (round off to 2 decimal places).

Answer: (1.32 to 1.35)

42. The product of earth’s mass (M) and the universal gravitational constant (G) is GM = 3.986×1014 m³/s². The radius of earth is 6371 km. The minimum increment in the velocity to be imparted to a spacecraft flying in a circular orbit around the earth at an altitude of 4000 km to make it exit earth’s gravitational field is______ km/s (round off to 2 decimal places).

Answer: (2.54 to 2.62)

43. A propeller driven airplane has a gross take-off weight of 4905 N with a wing area of 6.84 m². Assume that the wings are operating at the maximum of 13, the propeller efficiency is 0.9 and the specific fuel consumption of the engine is 0.76 kg/kW-hr. Given that the density of air at sea level is 1.225 kg/m³ and the acceleration due to gravity is 9.81 m/s², the weight of the fuel required for an endurance of 18 hours at sea level is ________ N (round off to the nearest integer).

Answer: (1440 to 1490)

44. The design of an airplane is modified to increase the vertical tail area by 20% and decrease the moment arm from the aerodynamic centre of the vertical tail to the airplane centre of gravity by 20%. Assuming all other factors remain unchanged, the ratio of the modified to the original directional static stability ( due to tail fin) is ______ (round off to 2
decimal places).

Answer: (0.96 to 0.96)

45. For a rocket engine, the velocity ratio r is V_a/V_e, where Va is the vehicle velocity and V_e is the exit velocity of the exhaust gases. Assume the flow to be optimally expanded through the nozzle. For r = 2, if F is the thrust produced and 𝑚̇ is the mass flow rate of exhaust gases, then, 𝐹/(𝑚̇𝑉_𝑒) is__________ .

Answer: (1 to 1)

46. The specific impulse of a rocket engine is 3000 Ns/kg. The mass of the rocket at burnout is 1000 kg. The propellant consumed in the process is 720 kg. Assume all factors contributing to velocity loss to be negligible. The change in vehicle velocity Δu is ____ km/s (round off to 2 decimal places).

Answer: (1.60 to 1.65)

47. The combustion products of a gas turbine engine can be assumed to be a calorically perfect gas with γ = 1.2. The pressure ratio across the turbine stage is 0.14. The measured turbine inlet and exit stagnation temperatures are 1200 K and 900 K, respectively. The total-to- total turbine efficiency is_______ % (round off to the nearest integer).

Answer: (88 to 90)

48. The figure shows the velocity triangles for an axial compressor stage. The specific work input to the compressor stage is kJ/kg_______ (round off to 2 decimal places).

Answer: (2.50 to 2.60)

49. As shown in the figure, a rigid slab CD of weight W (distributed uniformly along its length) is hung from a ceiling using three cables of identical length and cross-sectional area. The central cable is made of steel (Young’s modulus = 3E) and the other two cables are made of aluminium (Young’s modulus = E). The percentage of the total weight taken by the central cable is______ % (round off to the nearest integer).

Answer: (60 to 60)

50. All the bars in the given truss are elastic with Young’s modulus 200 GPa, and have identical cross-sections with moment of inertia 0.1 cm⁴. The lowest value of the load P at which the truss fails due to buckling is _____ kN (round off to the nearest integer).

Answer: (550 to 570)

51. A solid circular shaft is designed to transmit a torque T with a factor of safety of 2. It is proposed to replace the solid shaft by a hollow shaft of the same material and identical outer radius. If the inner radius is half the outer radius, the factor of safety for the hollow shaft is (round off to 1 decimal place).

Answer: (1.8 to 1.9)

52. In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load along the z- direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is N (round off to the nearest integer).

Answer: (310 to 320)

53. A thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of T = 1 kN-m. The walls have uniform thickness t = 1 mm and shear modulus G = 26 GPa. Assume that the curved portion is semi-circular. The shear stress in the wall is_____ MPa (round off to 1 decimal place).

Answer: (17.0 to 17.5)

54. For a damped spring-mass system, mass m = 10 kg, stiffness k = 103 N/m, and damping coefficient c = 20 kg/s. The ratio of the amplitude of oscillation of the first cycle to that of the fifth cycle is______ (round off to 1 decimal place).

Answer: (12.3 to 12.6)

55. For the system of springs and masses shown below, k = 1250 N/m and m = 10 kg. The highest natural frequency, ω, of the system is _____ radians/s (round off to the nearest integer).

Answer: (25 to 25)

GATE Exam 2018 Life Sciences (XL) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

4. A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m² of area. What is the area of the original rectangle in square meters?

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

8. From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Life Sciences (XL)

Chemistry (COMPULSORY) – XL-P

XL-P: Q. 1 – Q. 5 carry one mark each & Q. 6 – Q. 15 carry two marks each

1. F or the complete combustion of graphite and diamond in oxygen individually, the standard
enthalpy change (ΔH°₂₉₈) values are –393.5 kJ mol–1 and –395.4 kJ mol–1, respectively. Then, the ΔH° ₂₉₈ for the conversion of graphite into diamond is

(A) +1.9 kJ mol^–1

(B) –1.9 kJ mol^–1

(D) –3.8 kJ mol^–1

Answer: (A)

2. F or a 4s orbital of hydrogen atom, the magnetic quantum number (m_l) is

(A) 4

(B) 3

(D) 0

Answer: (D)

3. Hybridization of xenon in XeF₂ is

(A) sp

(B) sp²

(D) sp³d

Answer: (D)

4. Two equivalents of P react with one equivalent of Q to produce a major product R.

The number of double bonds present in the major product R is _______.

Answer: (11 to 11)

5. T he total number of possible stereoisomers for the compound with the structural formula CH₃CH(OH)CH=CHCH₂CH₃ is _______.

Answer: (4 to 4)

6. Among B—H, C—H, N—H and Si—H bonds in BH₃, CH₄, NH₃ and SiH₄, respectively, the polarity of the bond which is shown INCORRECTLY is

(A) B^δ+– H^δ–

(B) C^δ–– H^δ–

(D) Si^δ–– H^δ+

Answer: (D)

7. Among the following statements,

(i) [NiCl₄]^2– (atomic number of Ni = 28) is diamagnetic

(ii) Ethylamine is a weaker Lewis base compared to pyridine

(iii) [NiCl₂{P(C₆H₅)₃}₂] has two geometrical isomers

(iv) Bond angle in H₂O is greater than that in H₂S,

the CORRECT one is

(A) (i)

(B) (ii)

(D) (iv)

Answer: (D)

8. In [Mn(H₂O)₆]²⁺ (atomic number of Mn = 25), the d-d transitions according to crystal field theory (CFT) are

(A) Laporte forbidden and spin forbidden

(B) Laporte allowed and spin allowed

(D) Laporte allowed and spin forbidden

Answer: (A)

9. The major product M in the reaction

Answer: (D)

10. The two major products of the reaction

are

Answer: (A)

11. The compound, which upon mono-nitration using a mixture of HNO₃ and H₂SO₄, does NOT give the meta-isomer as the major product, is

Answer: (C)

12. The standard reduction potential (E°) for the conversion of CrO₇^2– to Cr³⁺ at 25°C in an aqueous solution of pH 3.0 is 1.33 V. The concentrations of CrO₇^2–to Cr³⁺ are 1.0 × 10^–4 M and 1.0 × 10^–3 M, respectively. Then the potential of this half-cell reaction is (Given: Faraday constant = 96500 C mol^–1, Gas constant R = 8.314 J K^–1 mol^–1)

(A) 1.04 V

(B) 0.94 V

(D) 0.74 V

Answer: (B)

13. The solubility product (Ksp) of Mg(OH)₂ at 25 °C is 5.6 × 10^–11. Its solubility in water is S × 10^–2 g/L, where the value of S is _______ (up to two decimal places). (Given: Molecular weight of Mg(OH)₂ = 58.3 g mol^–1)

Answer: (1.39 to 1.43)

14. The activation energy (Ea) values for two reactions carried out at 25°C differ by 5.0 kJ mol^–1. If the pre-exponential factors (A₁ and A₂) for these two reactions are of the same magnitude, the ratio of rate constants (k₁/k₂) is _______ (up to two decimal places). (Given: Gas constant R = 8.314 J K^–1 mol^–1)

Answer: (7.39 to 7.54)

15. One mole of helium gas in an isolated system undergoes a reversible isothermal expansion at 25 °C from an initial volume of 2.0 liters to a final volume of 10.0 liters. The change in entropy (ΔS) of the surroundings is ______ J K^–1 (up to two decimal places). (Given: Gas constant R = 8.314 J K^–1 mol^–1)

Answer: (-13.40 to -13.36)

Biochemistry-XL(Q)

Q. 1 – Q. 10 carry one mark each & Q.11 – Q.20 carry two marks each.

1. To which one of the following classes of enzymes does chymotrypsin belong?

(A) Oxidoreductase

(B) Hydrolase

(D) Isomerase

Answer: (B)

2. The substrate saturation profile of an enzyme that follows Michaelis-Menten kinetics is depicted in the figure. What is the order of the reaction in the concentration range between 0.8 to 1.4 M?

(A) Zero

(B) Fraction

(D) Second

Answer: (A)

3. Which one of the following conformations of glucose is most stable?

(A) Boat

(B) Half Chair

(D) Planar

Answer: (C)

4. Which one of the following profiles represent the phenomenon of cooperativity?

Answer: (C)

5. Which one of the following amino acids is responsible for the intrinsic fluorescence of proteins?

(A) Pro

(B) Met

(D) Trp

Answer: (D)

6. The glycosylation of the proteins occurs in_____.

(A) glyoxysomes

(B) lysosomes

(D) plasma membrane

Answer: (C)

7. Which one of the following properties of the myeloma cells is used in the hybridoma technology to generate monoclonal antibody?

(A) lack of thymidylate synthase

(B) over-expression of hypoxanthine-guanine phosphoribosyl transferase

(D) lack of hypoxanthine-guanine phosphoribosyl transferase

Answer: (D)

8. The movement of protons through the FoF1-ATPase during mitochondrial respiration is required for ____

(A) the increase in pH of mitochondrial matrix.

(B) changing the conformation of FoF1-ATPase to expel the ATP.

(D) decreasing the affinity of ADP to FoF1-ATPase.

Answer: (B)

9. The number of NADP⁺ molecules required to completely oxidize one molecule of glucose to CO2 through pentose phosphate pathway is ____ (correct to integer number).

Answer: (12 to 12)

10. Measurement of the absorbance of a solution containing NADH in a path length of 1cm cuvette at 340 nm shows the value of 0.31. The molar extinction coefficient of NADH is 6200 M-1 cm-1. The concentration of NADH in the solution is ___ μM (correct to integer number).

Answer: (50 to 50)

Q. 11 – Q. 20 carry two marks each.

11. Among the reagents given below which one of the combination of reagents will NOT break the disulphide bonds in the immunoglobulin molecules?

(P) Reduced glutathione

(Q) Dithiothritol

(R) Sodium dodecyl sulphate

(S) Methionine

(A) R&S

(B) P&R

(D) Q&R

Answer: (A)

12. Match the protein elution condition given in Group I with the appropriate chromatography matrices from Group II.

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

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

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

Answer: (A)

13. Which one of the following is NOT a neurotransmitter?

(A) Adrenaline

(B) Glutamate

(D) Histidine

Answer: (D)

14. The type-II hypersensitivity reaction is mainly mediated by____.

(A) IgE

(B) IgM

(D) T cells

Answer: (B)

15. Which one the following reaction mechanisms drives the conversion of low energy 3-phosphoglyceraldehyde to high energy 1,3-bisphosphoglycerate?

(A) Oxidation without anhydride bond formation

(B) Oxidation coupled with anhydride bond formation

(D) Formation of carboxylate

Answer: (B)

16. A polymerase reaction is carried out for 10 cycles in a volume of 1 ml with 5 molecules of template DNA. Assuming that the efficiency of the reaction is 100 %, the number of molecules of DNA present in 100 μl at the end of the reaction is ___ (correct to integer number).

Answer: (512 to 512)

17. The secondary structure topology diagram of 400 amino acid long “Protein-X” is depicted in the figure. The start and end amino acid residue numbers of each α-helix are marked. The percentage (correct to integer number) of residues forming α-helix is____.

Answer: (20 to 20)

18. An enzyme follows Michaelis-Menten kinetics with substrate S. The fraction of the maximum velocity (V_max) will be observed with the substrate concentration [S] = 4K_m is _____ (correct to one decimal place). (K_m is Michaelis-Menten constant)

Answer: (0.8 to 0.8)

19. The mass spectrum of benzoic acid will generate the fragment as a base peak (100% relative abundance) of m/z (mass to charge ratio) at ____ (correct to integer number).

Answer: (77 to 77)

20. The standard free energy(ΔG´) values of reactions catalyzed by citrate lyase and citrate synthetase are -670 and -8192 cal/mol, respectively.

The standard free energy (in cal/mol) of acetyl-CoA hydrolysis is ___ (correct to integer number).

Answer: (-8862 to -8862)

Botany (XL-R)

XL-R: Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. Which of the following genera produces dimorphic seeds that help to broaden the time of germination in a variable habitat?

(A) Xanthium

(B) Pisum

(D) Linum

Answer: (A)

2. The genes for microRNA (miRNA) in plants are usually transcribed by

(A) RNA polymerase I

(B) RNA polymerase II

(D) RNA polymerase IV

Answer: (B)

3. Which of the statements is TRUE for transposable elements Ac and Ds?

(A) Both Ac and Ds are autonomous because they encode their own transposase

(B) Both Ac and Ds are non-autonomous because they do not encode their own transposase

(D) Only Ds is autonomous because it encodes its own transposase

Answer: (C)

4. Identify the CORRECT statement.

(A) Receptor-like kinases play role in gametophytic self-incompatibility in Brassicaceae

(B) Receptor-like kinases play role in sporophytic self-incompatibility in Solanaceae

(D) Ribonucleases play role in gametophytic self-incompatibility in Solanaceae

Answer: (D)

5. Which of the following statements is TRUE for an ecotone?

(A) An ecotone is the synonym of an ecosystem

(B) An ecotone is an interface zone of two or more ecosystems

(D) An ecotone is exclusively characterized by decreased biodiversity

Answer: (B)

6. Acid rain with a pH of 4.0 is more acidic than the rain with a pH of 6.0 by

(A) 2 times

(B) 10 times

(D) 1000 times

Answer: (C)

7. Which of the following plants produces Ylang-ylang oil?

(A) Cananga odorata

(B) Carcum copticum

(D) Pimenta racemosa

Answer: (A)

8. Identify the INCORRECT statement in connection with polar transport of auxin.

(A) The putative influx carrier AUX1 is a cytosolic protein

(B) Polar auxin transport in root tends to be both acropetal and basipetal in direction

(D) AUX1 and PIN1 proteins are located in the opposite ends of a cell for polar transport

Answer: (A)

9. Which of the following stains is used to visualize callose under the microscope?

(A) Alcian blue

(B) Aniline blue

(D) Thymol blue

Answer: (B)

10. The coding sequence of a gene XLR18 has the single ORF of 783 bp. The pproximate molecular weight of the XLR18 protein in kDa is ______.

Answer: (28.00 to 31.00)

11. Statements given below are either TRUE (T) or FALSE (F). Select the CORRECT combination.

P. Mitosis occurs exclusively in diploid mother cell

Q. Mitosis occurs both in diploid and haploid mother cells

R. Meiosis occurs exclusively in diploid mother cell

S. Meiosis occurs both in diploid and haploid mother cells

(A) P-T, Q-F, R-T, S-F

(B) P-F, Q-T, R-F, S-T

(D) P-F, Q-T, R-T, S-F

Answer: (D)

12. You are asked to design a genetic construct for high-level expression of a gene encoding the therapeutic protein 18 (TP18) via plastid transformation. Select the CORRECT set ofgenetic elements for this construct.

(A) Actin1 promoter → TP18 coding sequence → Actin1 transcription terminator

(B) Ubiquitin1 promoter → TP18 coding sequence → Ubiquitin1 transcription terminator

(D) rbcL promoter → TP18 coding sequence → rbcL transcription terminator

Answer: (D)

13. Select the CORRECT combination of the following statements.

P. The cyclic electron transport chain involving PSI results in net production of both ATP and NADPH

Q. The cyclic electron transport chain involving PSI results in net production of ATP

R. Rubisco enzyme usually converts RuBP and CO2 into 2-phosphoglycolate and 3-phosphoglycerate

S. Rubisco enzyme usually converts RuBP and O2 into 2-phosphoglycolate and 3-phosphoglycerate

(A) P, Q

(B) R, S

(D) P, R

Answer: (C)

14. Match the fruit characters with their families and representative plant species.

(A) P-2-iv, Q-3-ii, R-1-vi, S-4-v

(B) P-1-iii, Q-3-iv, R-2-i, S-4-ii

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

Answer: (B)

15. Select the CORRECT combination by matching the disease, affected plant and the causal organism.

(A) P-2-v, Q-1-iv, R-3-iii, S-4-vi

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

(D) P-4-vi, Q-1-iii, R-3-ii, S-2-v

Answer: (C)

16. Select the CORRECT combination by matching Group-I with Group-II.

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

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

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

Answer: (D)

17. Match the plant alkaloids with their uses and source species.

(A) P-2-iv, Q-1-iii, R-4-i, S-3-ii

(B) P-4-iii, Q-2-v, R-1-vi, S-3-i

(D) P-3-ii, Q-4-iii, R-1-iv, S-2-i

Answer: (A)

18. Identify the CORRECT combination of statements with respect to chemical defense in plants.

P. Pisatin, a phytoalexin produced by Ricinus communis is a constitutive defense compound

Q. Phaseolus vulgaris produces Phaseolus agglutinin I, which is toxic to the cowpea weevil

R. A single step non-enzymatic hydrolysis of cyanogenic glycoside releases the toxic hydrocyanic acid (HCN) to protect plant against herbivores and pathogens

S. Avenacin, a triterpenoid saponin from oat prevents infection by Gaeumannomyces graminis, a major pathogen of cereal roots

(A) P, Q

(B) Q, S

(D) P, S

Answer: (B)

19. In garden pea, dwarf plants with terminal flowers are recessive to tall plants with axial flowers. A true-breeding tall plant with axial flowers was crossed with a true-breeding dwarf plant with terminal flowers. The resulting F1 plants were testcrossed, and the following progeny were obtained:

Tall plants with axial flowers = 320

Dwarf plants with terminal flowers = 318

Tall plants with terminal flowers = 79

Dwarf plants with axial flowers = 83

The map distance between the genes for plant height and flower position is______cM.

Answer: (20.25 to 20.25)

20. Two true-breeding snapdragon (Antirrhinum majus) plants, one with red flowers and another with white flowers were crossed. The F1 plants were all with pink flowers. When the F1 plants were selfed, they produced three kinds of F2 plants with red, pink and white flowers in a 1:2:1 ratio. The probability that out of the five plants picked up randomly, two would be with pink flowers, two with white flowers and one with red flowers is _____%.

Answer: (11.00 to 12.00)

Microbiology (XL-S)

XL (S): Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. David Baltimore’s classification of viruses is based on differences in

(A) host cell receptors used by viruses

(B) the pathways required to synthesize virus mRNA

(D) the envelope proteins on the surface of viruses

Answer: (B)

2. Which of the following immune system components can function as an opsonin?

(A) Antibodies

(B) T-cell receptors

(D) Interferons

Answer: (A)

3. The oral polio vaccine (OPV) consists of

(A) live attenuated virus

(B) killed virus

(D) viral capsid subunit

Answer: (A)

4. Which of the following eukaryotic cellular components carries out intracellular degradation during autophagy?

(A) Nucleus

(B) Golgi bodies

(D) Lysosomes

Answer: (D)

5. A nalysis of DNA sequences suggest that eukaryotic mitochondrial genomes primarily originated from

(A) fungi

(B) protozoa

(D) bacteria

Answer: (D)

6. Binomial nomenclature has NOT yet been adopted for

(A) bacteria

(B) fungi

(D) protozoa

Answer: (C)

7. Which of the following is NOT an accepted method for sterilization?

(A) Autoclaving

(B) X-rays

(D) UV rays

Answer: (D)

8. The primary product of nitrogen fixation is

(A) N₂

(B) NH₄⁺

(D) NO₃

Answer: (B)

9. In humans, the key stages in the life cycle of malarial parasites occur in

(A) red blood cells and the liver

(B) red blood cells and platelets

(D) red blood cells and the gut

Answer: (A)

10. You have a 50 mg/mL stock solution of arginine. To prepare 1 liter of growth medium for an arginine auxotroph that requires 70 μg/mL of arginine, the volume of this stock solution that should be added is _____________ mL (up to 1 decimal point) .

Answer: (1.38 to 1.42)

11. Accumulating evidence suggest that Domain Archaea is more closely related to Domain Eukarya than to Domain Bacteria. Which of the following properties are shared between eukaryotes and archaea ?

(i) Protein biogenesis

(ii) Presence of sterol containing membranes

(iii) Ribosomal subunit structures

(iv) Adaptation to extreme environmental conditions

(v) Fatty acids with ester linkages in the cell membrane

(A) (ii), (iii) and (v)

(B) (i), (ii), (iv), and (v)

(D) (iii) and (iv)

Answer: (C)

12. Match the antimicrobial agents in group I with their category/mode of action in group II.

(A) (i)-(q), (ii)-(s), (iii)-(r), (iv)-(p)

(B) (i)-(s), (ii)-(r), (iii)-(p), (iv)-(q)

(D) (i)-(s), (ii)-(r), (iii)-(q), (iv)-(p)

Answer: (C)

13. Match the microorganisms to their predominant modes of transmission.

(A) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

(B) (i)-(s), (ii)-(q), (iii)-(p), (iv)-(r)

(D) (i)-(s), (ii)-(r), (iii)-(p), (iv)-(q)

Answer: (A)

14. Match the precursors/intermediates with the corresponding metabolic pathways.

(A) (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)

(B) (i)-(p), (ii)-(r), (iii)-(s), (iv)-(q)

(D) (i)-(r), (ii)-(s), (iii)-(q), (iv)-(p)

Answer: (D)

15. Match the scientists to their area of major contribution

(A) (i)-(s), (ii)-(q), (iii)-(p), (iv)-(r)

(B) (i)-(s), (ii)-(p), (iii)-(q), (iv)-(r)

(D) (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s)

Answer: (B)

16. Which of the following combinations would improve the resolution of a microscope?

(i) Increasing the half aperture angle of the objective lens

(ii) Decreasing the wavelength of the illumination source

(iii) Decreasing the numerical aperture of the objective lens

(iv) Decreasing the refractive index of immersion medium

(A) (i) and (ii)

(B) (ii) and (iii)

(D) (i) and (iii)

Answer: (A)

17. Active transport involves the movement of a biomolecule against a concentration gradient across the cell membrane using metabolic energy. If the extracellular concentration of a biomolecule is 0.005M and its intracellular concentration is 0.5M, the least amount of energy that the cell would need to spend to transport this biomolecule from the outside to the inside of the cell is ________ kcal/mol (up to 2 decimal points). (Temperature T = 298K and universal gas constant R= 1.98 cal/mol·K)

Answer: (2.60 to 2.80)

18. A continuous cell culture being carried out in a stirred tank reactor is described in terms of its cell mass concentration X and substrate concentration S. The concentration of the substrate in the sterile feed stream is SF = 10 g/L and yield coefficient Y_x/s = 0.5. The flow rates of the feed stream and the exit stream are equal (F=5 mL/min) and constant. If the
specific growth rate the steady state concentration of S is _____ g/L (up to 1 decimal point).

Answer: (0.5 to 0.5)

19. The initial concentration of cells (N₀) growing unrestricted in a culture is 1.0×10⁶cells/mL. If the specific growth rate (μ) of the cells is 0.1 h^-1, the time required for the cell concentration to become 1.0×10⁸ cells/mL is _________ hours (up to 2 decimal points).

Answer: (45.50 to 46.50)

20. The following stoichiometric equation represents the conversion of glucose to lactic acid in a cell:

Glucose + 2Pi + 2ADP → 2Lactate + 2ATP +2H₂O

If the free energy of conversion of glucose to lactic acid only is ΔG⁰ = –47000 cal/mol, the efficiency of energy transfer is _______ % (up to 1 decimal point). (ΔG⁰ for ATP hydrolysis is –7.3 kcal/mol)

Answer: (30.5 to 31.5)

Zoology (XL-T)

XL (T): Q. 1 – Q. 10 carry one mark each & Q. 11 – Q. 20 carry two marks each.

1. Animals belonging to phylum Echinodermata are closer to chordates than other invertebrate phyla. Which ONE of the following reasons can account for this relatedness?

(A) Highly evolved nervous system

(B) Radially symmetric body plan

(D) Well-developed muscles

Answer: (C)

2. A zoologist recovered some tissue from preserved skin of a woolly mammoth. Further genetic analysis requires DNA isolation and increasing its amount. Which ONE of the following techniques would be most useful for increasing the amount of DNA?

(A) RFLP analysis

(B) Polymerase chain reaction (PCR)

(D) Chromatography

Answer: (B)

3. In a chemical reaction where the substrate and product are in equilibrium in solution, what will occur if an enzyme is added?

(A) The equilibrium of the reaction will not change.

(B) There will be a decrease in product formed.

(D) The free energy of the system will change.

Answer: (A)

4. Tay-Sachs disease is a human genetic disorder that is associated with defects in which ONE of the following cellular organelles?

(A) Endoplasmic reticulum

(B) Mitochondria

(D) Lysosome

Answer: (D)

5. Increase in the existent population of grey peppered moth, Biston betularia, during industrial revolution in Britain is an example of which ONE of the following evolutionary processes?

(A) Neutral selection

(B) Disruptive selection

(D) Stabilizing selection

Answer: (C)

6. Which ONE of the following is NOT a characteristic of a cancer cell?

(A) Increase in cell motility

(B) Loss of contact inhibition

(D) Uncontrolled meiosis

Answer: (D)

7. Cardiac and cerebral tissues are derived from the following germ layers respectively

(A) Ectoderm and mesoderm

(B) Mesoderm and ectoderm

(D) Endoderm and ectoderm

Answer: (B)

8. An animal’s ability to escape from a predator by using the explored knowledge of home area is an example of

(A) Latent learning

(B) Insight learning

(D) Imprinting

Answer: (A)

9. Bowman’s capsules are present in which ONE of the following organs/ tissues?

(A) Renal cortex

(B) Urinary bladder

(D) Ureter

Answer: (A)

10. Which ONE of the following is the primary function of lung surfactants?

(A) Remove dust particles from bronchi

(B) Provide immunity to respiratory tract

(D) Aid in carbon dioxide exchange

Answer: (B)

11. Match the disorders/diseases listed in Column I to their respective causative agents listed in Column II.

(A) I-iv, II-iii, III-ii, IV-i

(B) I-iii, II-iv, III-ii, IV-i

(D) I-iii, II-i, III-iv, IV-ii

Answer: (B)

12. Glucose monomers are joined together by glycosidic linkages to form a cellulose polymer. During this process, changes in the free energy, total energy, and entropy respectively are represented correctly by which ONE of the following options?

(A) +ΔG, +ΔH, +ΔS.

(B) +ΔG, -ΔH, -ΔS.

(D) +ΔG, +ΔH, -ΔS.

Answer: (D)

13. In Drosophila melanogaster, a mutation in Ultrabithorax which defines the third segment of the thorax or T3 leads to development of four winged flies, as the halteres develop into a second pair of wings. Which ONE of the following phenotypes in fly will result from overexpression of Ultrabithorax in the second thoracic segment?

(A) Four winged flies.

(B) Two wings and two halteres flies.

(D) Flies with two halteres.

Answer: (C)

14. Which ONE of the following is TRUE in case of respiratory acidosis?

(A) Increased rate of ventilation is a cause of respiratory acidosis

(B) Blood pH more than 7

(D) Acidosis can be compensated through reduction of bicarbonate levels in plasma

Answer: (C)

15. Match the proteins / molecules listed in column I with the cellular location mentioned in the column II.

(A) I-ii; II-iii; III-i; IV-iv

(B) I-iii; II-iv; III-i; IV-ii

(D) I-iv; II-iii; III-ii; IV-i

Answer: (B)

16. In an experiment, nucleus from a Drosophila oocyte was transplanted into the anterior part of another oocyte, at a region opposite to the existing nucleus. Which ONE of the following phenotypes will the developing egg show?

(A) A ventralized egg with no dorsal appendages

(B) A dorsalized egg with two dorsal appendages

(D) A dorsalized egg with four dorsal appendages

Answer: (D)

17. Match the organisms listed in Column I with the features listed in Column II

(A) I-iii; II-i; III-iv; IV-ii

(B) I-ii; II-iv; III-i; IV-iii

(D) I-iv; II-iii; III-ii; IV-i

Answer: (C)

18. Which ONE of the following statements is NOT part of the classical Darwinian theory of evolution by natural selection?

(A) A trait which is constantly used will get inherited by next generation.

(B) Phenotypic variations exist among the individuals of a population of a species

(D) Each population can randomly acquire a distinct and separate suite of variations.

Answer: (A)

19. A population of rabbits was determined to have a birth rate of 200 and mortality rate of 50 per year. If the initial population size is 4000 individuals, after 2 years of non-interfered breeding the final population size will be _______________.

Answer: (5270 to 5310)

20. In a population which is in Hardy-Weinberg equilibrium, the frequency of occurrence of a disorder caused by recessive allele (q) is 1 in 1100. The frequency of heterozygotes in the population will be ______________. (Give the answer to three decimal places).

Answer: (0.056 to 0.062)

Food Technology ( XL-U)

Q. 1 – Q. 10 carry one mark each & Q.11 – Q.20 carry two marks each.

1. Which of the following is an oil soluble pigment present in fruits and vegetables?

(A) Flavonoids

(B) Carotenoids

(D) Tannins

Answer: (B)

2. Which of the following represent the group of saturated fatty acids?

(A) Lauric, Myristic, Arachidic

(B) Palmitic, Linoleic, Linolenic

(D) Behenic, Caprylic, Arachidonic

Answer: (A)

3. The anti-nutritional factor present in fava bean is

(A) Gossypol

(B) Curcine

(D) Cyanogen

Answer: (C)

4. Which of the following is a Gram positive bacteria?

(A) Listeria monocytogenes

(B) Proteus vulgaris

(D) Shigella dysenteriae

Answer: (A)

5. Irradiation carried out to reduce viable non-spore forming pathogenic bacteria using a dose between 3 to 10 kGy is

(A) Radurization

(B) Thermoradiation

(D) Radicidation

Answer: (D)

6. Identify the correct statement related to the viscosity of Newtonian fluids from the following.

(A) It is not influenced by temperature

(B) It increases with shearing rate

(D) It is not influenced by shearing rate

Answer: (D)

7. Adult male Wistar rats were fed with a protein based diet. Total 150 g of protein was ingested per animal. If the average weight increased from 110 g to 350 g after the end of experiment, the Protein efficiency ratio of the given protein would be _______. (up to two decimal points).

Answer: (1.55 to 1.65)

8. The initial moisture content of a food on wet basis is 50.76%. Its moisture content (%) on dry basis is _______.(up to two decimal points)

Answer: (103.0 to 103.2)

9. The oxygen transmission rate through a 2.54 × 10^-3cm thick low density polyethylene film with air on one side and inert gas on the other side is 3.5 × 10^-6 mL cm^-2 s^-1. Oxygen partial pressure difference across the film is 0.21 atm. The permeability coefficient of the film to oxygen is _______ × 10^-11 mL (STP) cm cm^-2 s^-1 (cm Hg)^-1.

Answer: (54 to 56)

10. Ambient air at 30°C dry bulb temperature and 80% relative humidity was heated to a dry bulb temperature of 80°C in a heat exchanger by indirect heating. The amount of moisture gain (g kg^-1 dry air) during the process would be _______.

Answer: (0 to 0)

Q. 11 – Q. 20 carry two marks each.

11. Match the commodity in Group I with the bioactive constituent in Group II

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

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

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

Answer: (B)

12. Match the process operation in Group I with the separated constituent in Group II

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

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

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

Answer: (C)

13. Match the spoilage symptom in Group I with the causative microorganism in Group II

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

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

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

Answer: (C)

14. Match the fermented product in Group I with the base material in Group II

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

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

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

Answer: (A)

15. Match the operation in Group I with the process in Group II

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

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

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

Answer: (D)

16. Out of 7 principles of HACCP system, 4 are listed below. Arrange these principles in the order in which they are applied.

(P) Conduct a hazard analysis

(Q) Establish monitoring process

(R) Establish critical limit

(S) Establish record keeping and documentation process

(A) P, R, Q, S

(B) Q, R, P, S

(D) R, S, P, Q

Answer: (A)

17. Identify an example of a classical diffusional mass transfer process without involving heat, among the following.

(A) Drying of food grains

(B) Carbonation of beverages

(D) Concentration of fruit juice

Answer: (B)

18. For an enzyme catalyzed reaction S → P the kinetic parameters are:

[S] = 40 μM, V₀ = 9.6 μM s-1 and V_max = 12.0 μM s^-1.

The K_m of the enzyme in μM will be _______.(up to one decimal points)

Answer: (9.8 to 10.2)

19. A microbial sample taken at 10 AM contained 1 × 10⁵ CFU/mL. The count reached to 1 × 10¹⁰ CFU/mL at 8 PM of the same day. The growth rate (h-1) of the microorganism would be _______.(up to two decimal points)

Answer: (1.1 to 1.8)

20. The rate of heat transfer per unit area from a metal plate is 1000 W m^-2. The surface temperature of the plate is 120°C and ambient temperature is 20°C. The convective heat transfer coefficient (W m^-2 °C^-1) using the Newton’s law of cooling will be _______.

Answer: (10 to 10)

GATE Exam 2018 Engineering Sciences (XE) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Engineering Sciences

Engineering Mathematics (XE-A)

XE-A: Q. 1 – Q. 7 carry one mark each & Q. 8 – Q. 11 carry two marks each.

1. The largest interval in which the initial value problem

has a unique solution is

(A) (–∞, ∞)

(B) (–5, 5)

(D) (0, 5)

Answer: (D)

2. The sum of the roots of the indicial equation at 0x of the differential equation

(A) 0

(B) 1

(D) –2

Answer: (A)

3. Let f be a three times continuously differentiable real valued function on (0, 5) such that its third derivative for all x ∈ (0, 5). If P(x) is a polynomial of degree ≤ 2 such that P(1) = f(1), P(2) = f(2) and P(3) = f(3) then |f(4) – P(4)| equals _______________

Answer: (0.01 to 0.01)

4. For real numbers α₁ and α₂ if the formula is exact for all polynomials of degree ≤ 1 then 2α₁ + 3α₂ equals _______

Answer: (5 to 5)

5. Raju has four fair coins and one fair dice. At first Raju tosses a coin. If the coin shows head then he rolls the dice and the number that dice shows is taken as his score. If the coin shows tail then he tosses three more coins and the total number of tails shown (including the first one) is taken as his score. If Raju tells that his score is 2 then the probability that he rolled the dice is (up to two decimal places) _______________

Answer: (0.29 to 0.32)

6. Let f be a continuously differentiable real valued function defined by

Then the value of a²b is _______________

Answer: (250 to 250)

7. A rectangular box without top cover having a square base is to be made from a sheet of 108 square meters. Then the largest possible volume of the box in cubic meters is ______________

Answer: (108 to 108)

8. Let Then the trace of A¹⁰⁰⁰ equals

(A) 2¹⁰⁰⁰ – 1

(B) 2¹⁰⁰⁰ + 1

(D) 2¹⁰⁰⁰

Answer: (B)

9. Let ℂ denote the set of complex numbers and i² = –1. Let ϒ be the simple positively oriented circle |z| = 1 and S = {z ∈ ℂ| 0 <|z| < 2}. If f : S → ℂ is analytic in S and is given by

then the value of the contour integral

(A) 0

(B) 1/8

(D) 7/2

Answer: (C)

10. Let ℝ³ denote the three dimensional Euclidean space and for all (x, y, z) ∈ ℝ³. If C is the curve described by the parametric equation then the value of the line integral i is ______________

Answer: (3 to 3)

11. Let u(x, t) satisfy the initial and boundary value problem

Then the value of is __________

Answer: (0.04 to 0.04)

Fluid Mechanics (XE (B))

XE (B): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. Rheological diagram of different types of fluids is shown in figure. Column I represents the nature of the fluid and column II represents the curve showing the variation of shear stress against shear strain rate.

The most appropriate match between columns I and II is,

(A) (i) – O; (ii) – N ; (iii) – P; (iv) – M

(B) (i) – O; (ii) – P ; (iii) – N; (iv) – M

(D) (i) – P; (ii) – O ; (iii) – N; (iv) – M

Answer: (B)

2. In a two-dimensional, incompressible and irrotational flow, stream function (Ψ = Ψ (x, y) ) and velocity potential (Φ = Φ(x, y) exist. The velocities in x and y directions are non-zero. The product of , is

(A) −1

(B) 0

(D) ∞

Answer: (A)

3. The inviscid flow past a rotating circular cylinder can be generated by the superposition of

(A) uniform flow, source and vortex

(B) uniform flow, doublet

(D) uniform flow, doublet and vortex

Answer: (D)

4. The velocity field and the surface normal vector are given by, and respectively. If Euler equations are to be solved, the boundary condition that must be satisfied at the wall is,

Answer: (A)

5. The influence of Froude number is most significant in

(A) capillary flows

(B) creeping flows

(D) compressible flows

Answer: (C)

6. If the stream function (Ψ(x, y)) for a two-dimensional incompressible flow field is given as 2y(x² − y²), the corresponding velocity field is

Answer: (B)

7. Water is flowing in two different tubes of diameters D and 2D, with the same velocity. The ratio of laminar friction factors for the larger diameter tube to the smaller diameter tube is

(A) 0.5

(B) 1.0

(D) 4.0

Answer: (A)

8. If the velocity field is vorticity of the fluid element in the field at (x=1, y=2) in s^-1 is ____.

Answer: (4 to 4)

9. A pitot-static tube is used to measure air velocity in a duct by neglecting losses. The density of air is 1.2 kg/m³. If the difference between the total and static pressures is 1 kPa, the velocity of air at the measuring location, in m/s, is _______.

Answer: (39 to 42)

10. A parallelepiped of (2 m × 2 m) square cross-section and 10 m in length, is partially floating in water upto a depth of 1.2 m, with its longest side being horizontal. The specific gravity of the block is

(A) 0.8

(B) 0.6

(D) 0.4

Answer: (B)

11. The velocity field in a two-dimensional, unsteady flow is given by The magnitude of acceleration of a fluid particle located at x = 1 m, y = 1 m at the time t = 1 s, in m/s², is

(A) 16.0

(B) 18.1

(D) 34.1

Answer: (C)

12. In a two-dimensional, incompressible and irrotational flow, fluid velocity (v) in the ydirection is given by v = 2x−5y . The velocity (u) in the x-direction is

(A) u = 2x−5y

(B) u = 2x − 5y

(D) u = 5x−2y

Answer: (C)

13. A two-dimensional laminar viscous liquid film of constant thickness (h) steadily flows down an incline as shown in figure. Acceleration due to gravity is g. If the velocity profile in the liquid film is given as, u = ky(2h– y); v = 0, the value of constant k is

Answer: (A)

14. A water jet of 100 mm diameter issuing out of a nozzle at a speed of 50 m/s strikes a vane and flows along it as shown in figure. The vane is attached to a cart which is moving at a constant speed of 20 m/s on a frictionless track. The jet is deflected at an angle of 30o. Take the density of water as 1000 kg/m³. Neglecting the friction between the vane and the fluid, the magnitude of the force exerted by water on the cart in the x-direction, in N, is ______.

Answer: (900 to 990)

15. Capillary waves are generated in the sea. The speed of propagation (C) of these waves is known to be a function of density (ρ), wave length (λ), and surface tension (σ). Assume, ρ and λ to be constant. If the surface tension is doubled, in the functional form of the relevant non-dimensional group, the percentage increase in propagation speed (C) is _______

Answer: (40 to 42)

16. Consider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________.

Answer: (2.9 to 3.1)

17. A 2.6 gram smooth table-tennis (ping-pong) ball has a diameter of 38 mm. Density (ρ) of air is 1.2 kg/m3. Neglect the effect of gravity. Take coefficient of drag as 0.5. If the ball is struck with an initial velocity of 30 m/s, the initial deceleration, in m/s², is _________.

Answer: (107 to 127)

18. O n a flat plate, transition from laminar to turbulent boundary layer occurred at a critical Reynolds number (Re_cr). The empirical relations for the laminar and turbulent boundary layer thickness are given by respectively. The ratio of laminar to turbulent boundary layer thickness, at the location of transition, is 0.3. The value of Recr is _______.

Answer: (440000 to 442000)

19. In a capillary tube of radius R = 0.25 mm, a fully developed laminar velocity profile is defined as, MPa/m, μ is the dynamic viscosity of the fluid, and r is the radial position from the centerline of the tube. If the flow rate through the tube is 1000 mm³/s, the viscosity of the fluid, in Pa-s, is ______________.

Answer: (0.001 to 0.002)

20. The skin friction coefficient for a turbulent pipe flow is defined as, where τ_w is the wall shear stress and V is the average flow velocity. The value of f C is empirically given by the relation: C_f = 0.065(2/Re)^0.25where Re is the Reynolds number. If the average flow velocity is 10 m/s, diameter of the pipe is 250 mm, kinematic viscosity of the fluid is 0.25×10^–6 m²/s, and density of the fluid is 700 kg/m³, the skin friction drag induced by the flow over 1 m length of the pipe, in N, is ___________.

Answer: (30 to 45)

21. A (150 mm × 150 mm) square pillar is located in a river with water flowing at a velocity of 2 m/s, as shown in figure. The height of the pillar in water is 8 m. Take density of water as 1000 kg/m³ and kinematic viscosity as 1×10^–6 m/s². The coefficient of drag of the pillar is 2.0. The drag force exerted by water on the pillar in N is _______.

Answer: (4800 to 4800)

22. An orifice plate is used to measure flow rate of air (density = 1.23 kg/m³) in a duct of 250 mm diameter as shown in figure. The volume flow rate is 1 m³/s. Flow at sections 1 and 3 is uniform and section 2 is located at vena contracta. The diameter ratio, D_t/D₁, is 0.66. The flow area at vena contracta, A₂ = 0.65At, where At is area of the orifice. The pressure difference between locations 2 and 3 in N/m² is ____________.

Answer: (1200 to 1350)

Materials Science (XE-C)

XE (C): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. The stress ratio for a completely reversed cyclic loading during a fatigue test is

(A) 0

(B) 1

(D) –1/2

Answer: (C)

2. Minimum symmetry that a cubic crystal must possess is

(A) four 3-fold rotation axes.

(B) three 4-fold rotation axes.

(D) centre of symmetry.

Answer: (A)

3. If a material is repelled in an external magnetic field then it is

(A) Ferromagnetic

(B) Diamagnetic

(D) Antiferromagnetic

Answer: (B)

4. An electron makes a transition from the valence band to the conduction band in an indirect band gap semiconductor. Which one of the following is true?

(A) Energy of the electron decreases.

(B) A photon is emitted in the process.

(D) A photon is created in the process.

Answer: (C)

5. Which one of the following is the characteristic of a screw dislocation?

(A) Dislocation line and Burgers vector are parallel.

(B) Direction of motion of dislocation is parallel to the Burgers vector.

(C) Atomic displacement due to the movement of the dislocation is in the direction of the motion of the dislocation line.

(D) It has a unique slip plane.

Answer: (A)

6. The number of vibrational degrees of freedom for a non-linear triatomic molecule are

(A) 9

(B) 6

(D) 3

Answer: (D)

7. An atom is restricted to move in one dimension by making unit jumps either to the left or right, as shown in the figure. Assuming that a jump to the left or right is equally probable, the probability of the atom returning back to the starting point after four jumps is

(A) 0.250

(B) 0.333

(D) 0.500

Answer: (C)

8. For a two-dimensional solid, the variation of lattice specific heat as a function of temperature T (in K, at low temperatures) is given as: 𝐶_𝑝=𝑏𝑇^𝑛, where b is a constant. The value of n is ____________.

Answer: (2 to 2)

9. If the cation (C) to anion (A) radius ratio,r_C/r_Ais 0.6, then the coordination number (i.e., number of A ions surrounding a C ion) is likely to be ____________.

Answer: (6 to 6)

10. Match the invariant reactions in Column I with the names in Column II (L is liquid phase, and α, β, γ are solid phases). All reactions proceed to the right on cooling.

(A) P-5, Q-1, R-4, S-3

(B) P-5, Q-3, R-4, S-2

(D) P-2, Q-1, R-4, S-5

Answer: (B)

11. Consider the following anodic (oxidation) reaction in an acidic solution:

Mg → Mg⁺² + 2e^–

If 48250 Coulomb charge is produced during this anodic reaction then the amount of Mg (in g) dissolved into the solution is
(Given: Faraday Constant =96500 C/mole of electrons, Atomic weight of Mg = 24)

(A) 6

(B) 12

(D) 48

Answer: (A)

12. An intrinsic semiconductor has conduction electron concentration, n = 10¹² cm^–3. The mobility of both electrons and holes are identical = 4 × 10⁴ cm² V^–1 s^–1. If a voltage of 100 V is applied on two parallel end faces of the cube (edge length 1 cm) through Ohmic contacts, the current through the cube would be (in mA)
(Given: charge of electron = 1.6 × 10^–19 C)

(A) 640

(B) 1280

(D) 12800

Answer: (B)

13. An infinite plate with a through-thickness crack of length 2 mm is subjected to a tensile stress (as shown in the figure). Assuming the plate to be linear elastic, the fracture stress is ____________ MPa (round off to the nearest whole number)

(Given: Fracture toughness, 𝐾_𝐼𝐶=25 𝑀𝑃𝑎 √m)

Answer: (430 to 500)

14. A unidirectionally aligned carbon fibre reinforced epoxy composite is loaded as shown in the figure. The volume fraction of the fibre is 0.6. The Young’s modulus of the composite is ____________ GPa.

(Given: Young’s Modulus of the fibre and the matrix are 200 GPa and 10 GPa, respectively)

Answer: (124 to 124)

15. A sintered sample was weighed in air and water using an analytical balance. The mass of the sample in air is 2.67 g and its apparent mass in water is 1.67 g. The density of the sample is __________ g cm^–3 (give answer up to 2 decimal places)
(Given: Density of water = 1.00 g cm^–3)

Answer: (2.60 to 2.70)

16. The atoms in a gas laser have two energy levels such that a transition from the higher to the lower level releases a photon of wavelength 500 nm. If 7 × 10²⁰ atoms are pumped into the upper level with 4 × 10²⁰ atoms in the lower level, the amount of energy released in a single pulse is ____________ Joules (give answer up to 2 decimal places)
(Given: Planck’s constant, h = 6.6 × 10^–34 J s; speed of light, c = 3 × 10⁸ m s^–1)

Answer: (59.00 to 60.00)

17. The speed of an electron is measured to be 300 m s^–1 with an uncertainty of 0.01%. The fundamental accuracy with which the position of the electron can be determined simultaneously with the speed in the same experiment is _________ mm (give answer up to 2 decimal places)
(Given: Planck’s constant, h = 6.6 × 10^–34 J s; mass of electron = 9.1 × 10^–31 J kg)

Answer: (1.85 to 2.00)

18. When 3 identical non-interacting spin ½ particles are put in an infinite potential well, the ground state energy of the system is 18 meV. If instead, seven particles are put inside the potential well, the new ground state energy is ________ meV.

Answer: (132 to 132)

19. If the value of the integral (I) is 4, the value of the constant b is ___________ (give answer up to 2 decimal places).

Answer: (5.01 to 5.17)

20. X-ray diffraction pattern is obtained from FCC polycrystalline aluminium (lattice parameter = 0.405 nm) using Cr-K radiation of wavelength 0.229 nm. The maximum number of peaks that can be observed in the pattern is ____________.

Answer: (5 to 5)

21. The planar atomic density in the (110) plane of a BCC iron crystal is ____________ nm^–2 (give answer up to 2 decimal places)
(Given: lattice parameter of iron is 0.287 nm)

Answer: (15.5 to 18.5)

22. Mild steel is carburized at 1300 K for 1 hour to obtain a certain case depth. Keeping the time as 1 hour, the case depth can be doubled by increasing the temperature to ______________K (round off to the nearest whole number)

(Given: Activation energy Q = 148 kJ mol^–1, Gas constant, R = 8.314 J mol^–1 K^–1)

Answer: (1420 to 1480)

SOLID MECHANICS (XE-D)

XE (D): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. A thin cylinder (thickness, t and diameter, d) with closed ends is subjected to an internal pressure, p. The ratio of hoop stress to longitudinal stress developed in the wall of the cylinder is

(A) 1:4

(B) 1:2

(D) 2:1

Answer: (D)

2. A steel rod is fixed at one end and free at the other end. The coefficient of thermal expansion of the steel is α, and modulus of elasticity is E. If the temperature of the rod is increased by ΔT then the stress and strain developed in the rod are respectively

(A) zero, αΔT

(B) EαΔT, αΔT

(D) zero, zero

Answer: (A)

3. The effective lengths of the columns with ideal boundary conditions shown in Case-I, Case-II, and Case-III are respectively

(A) L, 4L, 2L

(B) L, 2L, L/4

(D) L, 2L, L/2

Answer: (D)

4. At a point in a stressed body, sum of the normal stresses acting on perpendicular faces of an arbitrarily oriented plane stress element is always

(A) dependent on the angle of orientation of the element

(B) constant and independent of angle of orientation of the element

(D) zero

Answer: (B)

5. The principal stresses on a plane stress element are shown in the figure. The maximum shear stress (in MPa) is

(A) 200

(B) 100

(D) 0

Answer: (B)

6. A rigid and thin L-shaped bracket is fixed to the wall at point B, and a force F is applied at point A as shown. For a given force F, the point B experiences the maximum clockwise moment when the inclination θ (in degrees) with the x-axis is……….[up to two decimal places].

Answer: (52.50 to 53.50)

7. A cantilever beam with length, L = 1 m, modulus of elasticity, E = 210 GPa, and area moment of inertia, I = 1.2 × 10^–7m⁴ carries a concentrated mass m = 100 kg at its freeend. By idealizing it as a single degree-of-freedom system and neglecting the mass of the cantilever beam, the natural frequency (in rad/s) of small transverse oscillations of the mass m is …….. [up to two decimal places]

Answer: (27.00 to 28.00)

8. For a typical grade of steel, the value of modulus of elasticity (E) and Poisson’s ratio (ν) are 208 GPa and 0.3 respectively. The value of shear modulus (G) of the steel (in GPa) is ……..

Answer: (80 to 80)

9. A tensile test is performed on a metallic specimen of diameter 8 mm and gauge length 50 mm. When the tensile load P reaches a value of 20 kN, the distance between the gauge marks increases by 0.09 mm. If the sample remains within the elastic limit, the modulus of elasticity (in GPa) of the test metal is………..[up to two decimal places]

Answer: (220.00 to 222.00)

10. A beam ABC is subjected to load P at its free end C as shown in the figure. The flexural rigidity of the beam is EI. The vertical support reaction at point B is

(A) 5P/4

(B) 5P/2

(D) 2P/5

Answer: (B)

11. A horizontal effort P is applied to raise a block of weight W on a rough surface inclined at an angle θ with the horizontal. If μ_s is the coefficient of static friction between the block and the surface, the minimum effort P required to impend the upward motion of the block along the surface is

Answer: (B)

12. Three round bars of same material, equal lengths, and different cross-sectional dimensions are shown in the figures as Case-I, Case-II and Case-III. All the bars are clamped at the upper end, and a concentrated load P is applied at the lower end of each bar. If the elastic strain energy stored in the bar shown in Case-I is U₁ then the elastic strain energy stored in Case-II and Case-III respectively is

(A) (8/5)U₁, (5/8)U₁

(B) (5/16)U₁, (5/16)U₁

(D) (5/8)U₁, (5/8)U₁

Answer: (D)

13. A rigid uniform rod with mass m, length L and center of gravity G is freely suspended from a hinge as shown in the figure. The rod is given a small angular displacement θ in the counter-clockwise direction from the position in which it hangs vertically (θ = 0). If g is the acceleration due to gravity, the natural frequency of oscillations (in rad/s) is

Answer: (C)

14. A cylindrical member, made up of ductile material, is subjected to pure torsion as shown in the figure. The failure plane (from Option-I to Option-IV) for ductile material as per maximum shear stress theory is represented by

(A) Option I

(B) Option II

(D) Option IV

Answer: (C)

15. A simply supported beam of span L is subjected to a couple Mo at a distance a from support A. Among the four options (Option-I to Option-IV) shown, the correct shear force diagram of the beam is

(A) Option-I

(B) Option-II

(D) Option-IV

Answer: (A)

16. A circular shaft ABC of diameter, L and length, A is fixed at end A. It is subjected to the torsional moments at point B and point C as shown in the figure. The ratio of angle of twists at point B to point C is

(A) 1.5 : 1

(B) 1 : 3

(D) 1 : 1.5

Answer: (D)

17. A circular steel bar of diameter 10 mm is bent into the shape as shown in figure, and lies in x-z plane. A horizontal force P is applied along the positive z-direction as shown. The yield strength of the steel is 200 MPa. Neglecting the effect of transverse shear, the load P (in Newton) required to initiate yielding as per maximum shear stress theory of failure is…………[up to two decimal places]

Answer: (195.00 to 197.00)

18. Two sliders A and B, connected by a rigid link of length L, slide in two mutually perpendicular and frictionless guide-ways. At a particular instance, the slider A is moving in the downward direction with a speed of 0.05 m/s. At this instance, the magnitude of the velocity of slider B (in m/s) is ……[up to two decimal places]

Answer: (0.01 to 0.02)

19. A simply supported beam ABC is subjected to load as shown in the figure. The 20 kN load is applied at point B with the help of a welded bracket as shown. The beam has a rectangular cross-section of 15 mm width and 100 mm depth as shown. The maximum transverse shear stress developed in the beam (in MPa) is ……..[up to one decimal place]

Answer: (14.5 to 15.5)

20. A rigid rod ABC, in the form of a quarter-circular arc of radius R, is hinged at C and supported by a roller at B. A vertical force P is applied at the end A of the bar. For the reactions at B and C to be equal in magnitude, the value of the angle θ (in degrees) is ………. [up to two decimal places].

Answer: (26.00 to 27.00)

21. A marble of mass m slides along a frictionless linear slide AB kept in a vertical plane. The marble is released from point A with zero initial velocity, and it reaches point B under the action of gravity. Assuming the acceleration due to gravity to be 9.81 m/s², the speed (in m/s) of the marble when it just reaches point B is………[up to two decimal places].

Answer: (3.10 to 3.20)

22. A horizontal force 10 N is applied at support B on the frame as shown in figure. Considering only bending deformation, the vertical reaction (in N) at support B is ………. [up to one decimal place]

Answer: (13.5 to 14.5)

Thermodynamics (XE-E)

XE (E): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, C_p : molar heat capacity at constant pressure, C_v : molar heat capacity at constant volume, R : universal gas constant

1. When a fixed mass of air-water vapour mixture is heated at constant pressure,

(A) both relative and specific humidity decrease.

(B) relative humidity decreases, but specific humidity remains unchanged.

(D) both relative and specific humidity increase.

Answer: (B)

2. For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the magnitude of work done is

Answer: (A)

3. The statement which is NOT a consequence of the first law of thermodynamics is

(A)Heat is a path function

(B) Energy is a property of a system

(D)A perpetual motion machine of the first kind is not possible

Answer: (C)

4. For a refrigerator absorbing heat Q_L from a cold region and rejecting heat Q_H to a hot region, the coefficient of performance is written as

Answer: (A)

5. The value of the compressibility factor at the critical point evaluated using the van der Waals equation of state is

(A) 2/7

(B) 5/8

(D) 1/7

Answer: (C)

6. The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour pressure of 13.5 kPa is

(A) 58.7

(B) 51.4

(D) 35.2

Answer: (D)

7. One kmol of an ideal gas (C_p = 21 kJ/kmol.K) undergoes a constant pressure process from 300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy (in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.

Answer: (160.0 t0 161.0)

8. A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.

Answer: (14.5 to 15.0)

9. An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of 2 bar and a temperature of 300 K, the volume (in m³) of 1 kg of this gas (up to 2 decimal places) is ________.

Answer: (0.30 to 0.32)

10. Consider the following statements for an ideal gas undergoing a reversible non-flow process:

P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero.

Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero.

R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero.

S. If the process is isothermal, the change in entropy of the gas is necessarily zero.

Which one of the following options is valid?

(A) Only P is correct

(B) Only S is correct

(D) Only P and S are correct

Answer: (C)

11. An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature and reject equal amount of heat. Also, the working fluid enters at the same state before compression. One of the following statements always true about their efficiencies (𝜂) is

(A) 𝜂_O > 𝜂_D

(B) 𝜂_O= 𝜂_D

(D) 𝜂_O= 1−𝜂_D

Answer: (C)

12. A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection (in kJ/s) to the reservoir at 650 K is

(A) 11

(B) 31

(D) 52

Answer: (D)

13. A gas obeys the following equation of state:

where is molar volume, and a, b are constants with values a = 10^–5 J.K/Pa² and b = 8 × 10^–2 m³/mol. Take C_p = 30 kJ/kmol.K. At 10 bar and 500 K, the value of the Joule-Thomson coefficient (in K/Pa) is

(A) –2 × 10^–6

(B) –4 × 10^–6

(D) 4 × 10^–6

Answer: (B)

14. In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (ℎ = 3375.1 kJ/kg, 𝑠 = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa, ℎ_𝑓 = 191.81 kJ/kg, 𝑠_𝑓 = 0.6492 kJ/kg.K, ℎ_𝑔 = 2583.9 kJ/kg and 𝑠_𝑔 = 8.1488 kJ/kg.K. The heat rejected in the condenser (in kJ/kg) is

(A) 1898

(B) 3796

(D) 2847

Answer: (A)

15. Methane has compressibility factor value of 0.9 at reduced pressure of 1.0 and reduced temperature of 1.5. For propane, the critical temperature and pressure are 369.8 K and 42.48 bar, respectively. Take R = 8.314 kJ/kmol.K. Applying the principle of corresponding states, the molar volume of propane (in m3/kmol) at the same reduced pressure and temperature is

(A) 0.355

(B) 0.526

(D) 0.977

Answer: (D)

16. A rigid insulated vessel is divided into two compartments by a partition. One compartment contains 12 kg of oxygen at 200 kPa and 280 K. The other compartment contains 26 kg of carbon dioxide at 400 kPa and 360 K. The specific heats at constant volume in kJ/kg.K for oxygen and carbon dioxide are 0.662 and 0.653, respectively. The partition is removed and the gases are allowed to mix. Considering both gases are ideal, the final temperature (in K) of the mixture (up to 1 decimal place) is ________.

Answer: (332.5 to 336.5)

17. Moist air having 60% relative humidity, enters a steady-flow air-conditioning unit at 102 kPa and 30 °C. The volume flow rate of the moist air entering the unit is 0.1 m³/s. The moist air leaves the unit at 95 kPa and 15 °C with a relative humidity of 100%. Liquid condensate leaves the unit at 15 °C.

For water: at 15 °C, ℎ_𝑓 = 62.982 kJ/kg, ℎ_𝑔 = 2528.3 kJ/kg, 𝑃_𝑠𝑎𝑡 = 1.7057 kPa. at 30 °C, ℎ_𝑓 = 125.74 kJ/kg, ℎ_𝑔 = 2555.6 kJ/kg, 𝑃_𝑠𝑎𝑡 = 4.2469 kPa.

For air, specific heat at constant pressure is 1.004 kJ/kg.K and the specific gas constant is 0.287 kJ/kg.K.

Neglecting heat leakage to the surrounding, the magnitude of heat extracted (in kW) from the air stream (up to 2 decimal places) is __________.

Answer: (3.01 to 3.07)

18. Air at 150 kPa and 323 K is filled in a rigid vessel of 0.05 m³ capacity. For air, assumed as an ideal gas, specific heat at constant volume is 0.7163 kJ/kg.K and the specific gas constant is 0.287 kJ/kg.K. Neglect kinetic and potential energy changes. If 30 kJ of heat is added, the final temperature (in K) of air (up to 1 decimal place) is __________.

Answer: (838.0 to 844.0)

19. Superheated steam at 2 bar and 300 °C, with an enthalpy of 3072.1 kJ/kg, enters a horizontal adiabatic nozzle with negligible velocity and leaves at 0.2 bar as saturated vapour with an enthalpy of 2609.9 kJ/kg. Assuming steady flow and neglecting the potential energy changes, the exit velocity (in m/s) of the steam (up to 1 decimal place) is __________.

Answer: (961.0 to 962.0)

20. A given mass of a simple compressible substance undergoes a reversible cycle, as shown in the P-V diagram. The magnitude of the net work done during the cycle is 3 kJ. The pressure (in bar) at point C (up to 1 decimal place) is ________.

Answer: (5.7 to 6.1)

21. One kmol of an ideal gas at 300 K and 10 bar is reversibly heated in a constant volume process to 500 K. It is then reversibly and isothermally expanded to 2 bar. Take C_v = 20.8 kJ/kmol.K and R = 8.314 kJ/kmol.K. The total heat supplied (in kJ) to the gas (up to 1 decimal place) is ________.

Answer: (12950.0 to 13000.0)

22. A rigid container is completely filled with a liquid having a constant isothermal compressibility of 1.09 × 10^–4 bar^–1 and a constant coefficient of volume expansion of 1.12 × 10^–3 K^–1 . The liquid is initially at 300 K and 1 bar. Heat is supplied to the liquid to raise its temperature to 350 K. Assuming that no phase change occurs, the final pressure (in bar) of the liquid (up to 1 decimal place) is ________.

Answer: (513.0 to 517.0)

Polymer Science & Engineering (XE – F)

XE (F): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. Which one of the following polymers occurs naturally?

(A) Bakelite

(B) Teflon

(D) Perspex

Answer: (C)

2. The order of average molecular weights of a polymer is

Answer: (A)

3. Rubbers are a class of polymer known for

(A) High intermolecular forces

(B) High T_g polymers

(D) Low intermolecular forces

Answer: (D)

4. Nylon 6 is manufactured from

(A) Sebacic acid and hexamethylene diamine

(B) Caprolactam

(D) Caprolactone

Answer: (B)

5. S torage modulus and tan δ of a polymer are experimentally measured by

(A) Differential scanning calorimetry

(B) Thermogravimetric analysis

(D) Dynamic mechanical thermal analysis

Answer: (D)

6. A plastic bucket is manufactured by

(A) Compression moulding

(B) Injection moulding

(D) Blow moulding

Answer: (B)

7. T he monomers, A and B with reactivity ratios rA and rB, form alternate copolymers when,

(A) r_A = r_B = 0

(B) r_A = r_B = 1

(D) r_A < 1, r_B < 1

Answer: (A)

8. The degree of polymerization of a poly(methyl methacrylate) sample having number average molecular weight of 1,50,000 g/mol is___________.

(C = 12, H = 1, O = 16 g/mol).

Answer: (1500.00 to 1500.00)

9. If the heat of fusion of 100 % crystalline polyethylene is 290 mJ/mg, a sample of polyethylene with heat of fusion of 141 mJ/mg will have_______ % crystallinity.

Answer: (48.52 to 48.72)

10. Match the following:

(A) P-3; Q-1; R-2; S-1

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

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

Answer: (D)

11. Match the following:

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

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

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

Answer: (A)

12. Flexible PVC tubes are used for watering. If some organic solvents are passed through this tube, it becomes stiff. This is due to the fact that the organic solvents

(A) plasticize PVC and raise Tg.

(B) remove plasticizer and raise Tg.

(D) react with PVC and increase Tg

Answer: (B)

13. Match the following:

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

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

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

Answer: (D)

14. Match the following:

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

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

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

Answer: (B)

15. A plot of strain (%) versus time of a polymer is given below. Based on this plot and the properties as mentioned below, find out the correct combination.

1 = Viscoelastic deformation; 2 = Elastic deformation

3 = Viscoelastic recovery; 4 = Elastic recovery

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

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

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

Answer: (D)

16. T he plot shows apparent viscosity versus shear rate of Newtonian, Dilatent and Pseudoplastic fluids. Based on this plot and the fluid behaviour as mentioned below, find out the correct combination.

1 = Dilatent fluid; 2 = Newtonian fluid, 3 = Pseudoplastic fluid

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

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

(D) P-2; Q-3; Q-1

Answer: (C)

17. Plot of the modulus versus temperature of different types of polymers is given below. Based on this plot and the nature of the polymers as mentioned below, find out the correct combination.

1 = An amorphous polymer of high molecular weight having entanglements

2 = An amorphous polymer of moderate molecular weight

3 = Highly crosslinked polymer

4 = Semi-crystalline polymer

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

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

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

Answer: (C)

18. The T_g of homopolymers of A and B are +100°C and -70°C respectively. The T_g of a random copolymer of A and B having 40 wt% A and 60 wt% B is _________°C.

Answer: (-25.00 to -24.50)

19. The number average molecular weight of a polymer prepared from HO(CH₂)₁₄COOH is 24,000 g/mol. The conversion of the monomer required to reach the above molecular weight is__________%. (C = 12, H = 1, O = 16 g/mol).

Answer: (98.80 to 99.10)

20. Glass fibers in nylon provide reinforcement. The modulus of elasticity for each component of the composite is; E_glass = 10.5 x 10⁶ psi; E_nylon = 0.4 x 10⁶ psi. If the nylon contains 30 vol % E-glass, the fraction of the applied force is carried by the glass fiber is__________. (Assume that both glass fiber and nylon have equal strain).

Answer: (0.90 to 0.93)

21. The solubility parameter of a polymer having cohesive energy density (E_coh) 43870 J/mol and molar volume (V) 136 cm³/mol is _________ (J/cm³)^1/2.

Answer: (17.91 to 18.00)

22. T he heat of polymerization of styrene is 20 Kcal/mol. Heat of 5 x10⁵ Kcal will be released on polymerization of __________ Kg of styrene (C = 12 and H = 1 g/mol).

Answer: (2600 to 2600)

Food Technology – XE-G

XE (G): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. Which of the following is oil soluble pigment present in fruits and vegetables?

(A) Flavonoids

(B) Carotenoids

(D) Tannins

Answer: (B)

2. Which of the following represent the group of saturated fatty acids?

(A) Lauric, Myristic, Arachidic

(B) Palmitic, Linoleic, Linolenic

(D) Behenic, Caprylic, Arachidonic

Answer: (A)

3. The anti-nutritional factor present in fava bean is

(A) Gossypol

(B) Curcine

(D) Cyanogen

Answer: (C)

4. Irradiation carried out to reduce viable non-spore forming pathogenic bacteria using a dose between 3 to 10 kGy is called

(A) Radurization

(B) Thermoradiation

(D) Radicidation

Answer: (D)

5. Identify the correct statement related to the viscosity of Newtonian fluids from the following

(A) It is not influenced by temperature

(B) It increases with shearing rate

(D) It is not influenced by shearing rate

Answer: (D)

6. Adult male Wistar rats were fed with a protein based diet. Total 150 g of protein was ingested per animal. If the average weight increased from 110 g to 350 g after the end of the experiment, the Protein efficiency ratio of the given protein would be _______. (up to two decimal points)

Answer: (1.55 to 1.65)

7. The initial moisture content of a food on wet basis is 50.76%. Its moisture content (%) on dry basis is _______.(up to two decimal points)

Answer: (103.0 to 103.2)

8. The oxygen transmission rate through a 2.54 x 10^-3 cm thick low density polyethylene film with air on one side and inert gas on the other side is 3.5 x 10^-6 mL cm^-2 s^-1. Oxygen partial pressure difference across the film is 0.21 atm. The permeability coefficient of the film to oxygen is _______ x 10^-11 mL (STP) cm cm^-2 s^-1 (cm Hg)^-1.

Answer: (54 to 56)

9. A mbient air at 30°C dry bulb temperature and 80% relative humidity was heated to a dry bulb temperature of 80°C in a heat exchanger by indirect heating. The amount of moisture gain (g kg^-1 dry air) during the process would be _______.

Answer: (0 to 0)

10. Match the commodity in Group I with the bioactive constituent in Group II

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

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

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

Answer: (B)

11. Match the process operation in Group I with the separated constituent in Group II

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

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

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

Answer: (C)

12. Match the spoilage symptom in Group I with the causative microorganism in Group II

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

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

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

Answer: (C)

13. Match the fermented product in Group I with the base material in Group II

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

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

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

Answer: (A)

14. Match the operation in Group I with the process in Group II

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

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

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

Answer: (D)

15. Out of 7 principles of HACCP system, 4 are listed below. Arrange these principles in the order in which they are applied.

(P) Conduct a hazard analysis

(Q) Establish monitoring process

(R) Establish critical limit

(S) Establish record keeping and documentation process

(A) P, R, Q, S

(B) Q, R, P, S

(D) R, S, P, Q

Answer: (A)

16. Apple juice of 10% total solids (TS) is being concentrated in a single effect evaporator working with a surface condenser to 40% TS under a vacuum of 20 kPa. After some time the vacuum pump stops but the evaporation process continued. Choose the combination of possible implications from the following.

(P) Product quality is affected

(Q) Substantial increase in thermal energy requirement

(R) Decrease in the rate of evaporation

(A) P & Q

(B) Q & R

(D) P,Q & R

Answer: (C)

17. Identify an example of a classical diffusional mass transfer process without involving heat, among the following.

(A) Drying of food grains

(B) Carbonation of beverages

(D) Concentration of fruit juice

Answer: (B)

18. For an enzyme catalyzed reaction S → P, the kinetic parameters are:

[S] = 40 μM, V₀ = 9.6 μM s^-1 and V_max = 12.0 μM s^-1.

The K_m of the enzyme in μM will be _______.(up to one decimal points)

Answer: (9.8 to 10.2)

19. A microbial sample taken at 10 AM contained 1 × 10⁵ CFU/mL. The count reached to 1 × 10¹⁰ CFU/mL at 8 PM of the same day. The growth rate (h^-1) of the microorganism would be _______.(up to two decimal points)

Answer: (1.1 to 1.8)

20. Black pepper is ground from an equivalent particle size of 6 mm to 0.12 mm using a 10 hp motor. Assuming Rittinger’s equation and that 1 hp = 745.7 W, the power (hp) of motor required to fine grind black pepper to 0.08 mm would be _______.(up to two decimal points)

Answer: (14.5 to 15.5)

21. Green pea (average diameter 0.8 cm) is frozen in a blast freezer operating at -40°C and with a surface heat transfer coefficient of 30 W m^-2 K^-1. The thermal conductivity of pea is 2.5 W m^-1K^-1, and latent heat of crystallization is 2.74 × 10² kJ kg^-1. If the freezing point of pea is -1°C and the density is 1160 kg m^-3, the freezing time in minutes will be _______.(up to two decimal points)

Answer: (6.0 to 6.4)

22. The rate of heat transfer from a metal plate is 1000 W m^-2. The surface temperature of the plate is 120°C and ambient temperature is 20°C. The convective heat transfer coefficient (W m^-2°C^-1) using the Newton’s law of cooling will be _______.

Answer: (10 to 10)

Atmospheric and Oceanic Sciences (XE-H)

Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

1. The most abundant gas in the atmosphere among inert gases is

(A) Helium

(B) Argon

(D) Krypton

Answer: (B)

2. The pair of variables that always exhibit monotonic decrease with height in the atmosphere is

(A) Pressure, Temperature

(B) Pressure, Ozone concentration

(D) Temperature, Water Vapour

Answer: (C)

3. Correct order of the maximum vertical extent of atmospheric circulation cells is

(A) Hadley > Ferrel > Polar

(B) Polar > Hadley > Ferrel

(D) Ferrel > Hadley > Polar

Answer: (A)

4. Analysis of an atmospheric variable shows prominent modes at 5, 40 and 1460 days. These modes correspond respectively to

(A) Tidal, MJO and ENSO

(B) Synoptic, MJO and ENSO

(D) Tidal, Milankhovich and ENSO

Answer: (B)

5. Atmospheric vertical profile of temperature is measured by radiosonde. Equivalent instruments for measuring ocean temperature profile among the following are:

(P) drifting buoy (Q) ARGO float (R) current mooring (S) XBT

(A) Q, R, S

(B) Q, S

(D) P, R, S

Answer: (B)

6. When deep water sinks in the North Atlantic and moves away from where it formed, it gets

(A) richer in oxygen and nutrients

(B) less acidic and richer in metals

(D) richer in CO₂ and O₂

Answer: (C)

7. The speed of sound in the ocean depends on

(A) temperature alone

(B) temperature and pressure

(D) temperature, salinity and pressure

Answer: (D)

8. In a numerical weather prediction model with a horizontal grid resolution of 50 km, convective cloud processes are parameterized, because

(A) Cloud physics is not known for modelling

(B) Models cannot handle phase change

(D) Cloud size is much smaller than the grid size

Answer: (D)

9. Figure below shows SST anomaly (in °C). It is associated with the phenomenon known as

(A) El Nino

(B) Indian Ocean dipole

(D) MJO

Answer: (B)

10. For an inviscid and barotropic ocean of constant depth (D), a water parcel with initial vorticity 2Ω is displaced from the equator to the north pole. Latitudinal variation of the parcel vorticity (ζ ) is well represented by the curve

(A) S

(B) Q

(D) R

Answer: (A)

11. A wave progresses up an estuary of decreasing water depth. If friction is neglected, then

(A) wave amplitude decreases and wave length increases

(B) wave amplitude increases and wave length decreases

(D) wave amplitude increases and wave length increases

Answer: (B)

12. In the Ekman flow limit, directions of ocean surface current and the geostrophic wind are

(A) the same

(B) surface current is 45° to the left of the geostrophic wind

(D) exactly opposite to each other

Answer: (A)

13.

P and Q respectively describe flow fields corresponding to

(A) Mid latitude Rossby and Polar gravity waves

(B) Equatorial Rossby and Equatorial Kelvin waves

(D) Equatorial Kelvin and Equatorial Rossby waves

Answer: (B)

14. On the summer solstice day, the maximum incident shortwave radiation at the top of the atmosphere over the equator (up to one decimal place) is __________ W m^–2. (Take solar constant as 1368 W m^–2).

Answer: (1254 to 1256)

15. In an isothermal atmosphere having a temperature of 15°C, the height at which pressure decreases to 1/10 of its value at the surface is __________ km. (Give the answer to two decimal places.) Take g = 9.8 m s^–2, gas constant R = 287 J kg^–1 K^–1

Answer: (19.42 to 19.44)

16. At 30°N and 700 hPa pressure level, wind field is in gradient balance. If the gradient wind speed is 50 m s–1 and radius of curvature of the flow is 50 km, the corresponding geostrophic wind speed is __________ m s^–1. (Give the answer to one decimal place.) Take the angular velocity of the Earth as 7.3 × 10^–5 s^–1

Answer: (734.8 to 735.0)

17. In a tropical cyclone over the Pacific Ocean, surface pressure at 500 km from the cyclone centre is 1000 hPa. Surface pressure at the centre is 900 hPa. Sea surface temperature and surface air temperature remain constant at 28°C and 27°C, respectively. Difference in potential temperature between 500 km and cyclone centre is __________ K. (Give the answer to two decimal places.) Take g = 9.8 m s^–2, Cp = 1005 J kg^–1 K^–1, gas constant R = 287 J kg^–1 K^–1

Answer: (9.16 to 9.18)

18. A cloud forms by the lifting of moist air from the surface with the initial conditions T_o = 30°C, RH = 80% and P_o = 1005 hPa. If the vapour pressure of this parcel at 500 hPa is 6.5 hPa, the liquid water content of the parcel if no precipitation takes place is __________ gm kg^–1. (Give the answer to one decimal place.) Saturation vapour pressure of water at 30°C is 42.43 hPa.

Answer: (12.8 to 13.2)

19. A numerical model of the atmosphere uses sigma (𝜎) coordinate system in vertical. At locations P and Q, surface pressures are 1005 hPa and 500 hPa, respectively. Absolute difference in the heights of 𝜎 = 0.9 level between these locations is __________ meters. (Give the answer to one decimal place.) Layer mean temperatures at P and Q are 300 K and 270 K, respectively. (Take g = 9.8 m s^–2 gas constant R = 287 J kg^–1 K^–1)

Answer: (92.4 to 92.8)

20. If difference in sea surface elevation is 1 m in 100 km at 30°N latitude, the corresponding geostrophic current is __________ m s^–1. (Give the answer to one decimal place.) Take g = 9.8 m s^–2 and angular velocity of the Earth = 7.3 × 10^–5s^–1.

Answer: (1.3 to 1.4)

21. If wind speed over ocean surface is 10 m s^–1, air-sea interface momentum flux is __________ N m^–2. (Give the answer to two decimal places.) Surface air temperatureand pressure are 27°C and 1000 hPa, respectively. Take drag coefficient as 0.001 and gas constant R = 287 J kg^–1K^–1.

Answer: (0.11 to 0.12)

22. Let L_x, L_y be length scales in x- and y-directions and corresponding mass transports are Mx and My. The ratio of M_x and M_y (to nearest integer) is __________ , if the ratio of L_xand L_y is 10 and vertical velocity is zero.

Answer: (9.99 to 10.01)

GATE Exam 2018 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

(D) (iv), (iii), (ii), (i)

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

6. An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

8. To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

10. In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another unrelated study, it was found that the revenue from cracker sales in India which remained fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. The solid line in the graph below refers to annual sale of crackers and the dashed line refers to the annual crow births in India. Choose the most appropriate inference from the above data.

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Textile Engineering and Fibre Science

Q. 1 – Q. 25 carry one mark each.

1. Let then |𝐴| is equal to

(A) 2

(B) −2

(D) 6

Answer: (D)

2. If 𝐴 and 𝐵 are two independent events such that then 𝑃(𝐴 ∪ 𝐵) is equal to

(A) 11/12

(B) 1/12

(D) 5/6

Answer: (C)

3. Which one of the following is a leaf fibre?

(A) Coir

(B) Sisal

(D) Hemp

Answer: (B)

4. The pair of fibres most prone to accumulation of static charge is

(A) Cotton and Polyester

(B) Silk and Polyester

(D) Silk and Polypropylene

Answer: (C)

5. H eat-setting of melt-spun and drawn Nylon 6 filament yarn under slack condition leads to increase in its

(A) Tenacity

(B) Molecular orientation

(D) Dimensional stability

Answer: (D)

6. Which one of the fibres, having stress-strain curves as shown in the figure, is the most suitable for making mountaineering ropes?

(A) P

(B) Q

(D) S

Answer: (C)

7. The technology that produces yarn with the maximum fibre migration is

(A) Rotor spinning

(B) Friction spinning

(D) Ring spinning

Answer: (A (or) D)

8. The cleaning machine, located in the fine cleaning zone of blowroom, uses the following as the opening element

(A) Roller with saw tooth wire points

(B) Drum with large spikes

(D) Drum with large bladed discs

Answer: (A)

9. The purpose of having grooves or notches in modern flyer tops in speed frames is to

(A) Increase real twist in roving

(B) Insert false twist in roving

(D) Increase fineness of roving

Answer: (B)

10. With time, wind per double traverse in a drum-driven winder

(A) Increases

(B) Decreases

(D) First increases and then decreases

Answer: (B)

11. In a loom, seven-wheel take-up motion is

(A) Negative and intermittent

(B) Negative and continuous

(D) Positive and continuous

Answer: (C)

12. The relative humidity (in %) and temperature (in °C) of standard testing atmosphere are respectively

(A) 65 and 25

(B) 65 and 20

(D) 60 and 20

Answer: (B)

13. In Stelometer, if F is the force acting on a fibre bundle and θ is the angle through which the pendulum is moved, then F is directly proportional to

(A) sin θ

(B) cos θ

(D) cot θ

Answer: (A)

14. Yarn diameter varies

(A) Directly with yarn packing density

(B) Inversely with yarn packing density

(D) Inversely with square root of yarn packing density

Answer: (D)

15. The constant-rate-of-extension type tensile tester is NOT used for

(A) Tongue tear test

(B) Wing rip tear test

(D) Trapezoid tear test

Answer: (C)

16. During bleaching of cotton with hydrogen peroxide, addition of sodium silicate

(A) Reduces the viscosity of bath

(B) Controls the rate of decomposition of perhydroxyl ions (HO₂⁻)

(D) Enhances swelling of cotton

Answer: (B)

17. In dyeing of wool with levelling acid dyes, with time, the pH of dye bath

(A) Increases

(B) Decreases

(D) First increases and then decreases

Answer: (A)

18. The discharging agent used in discharge printing of cotton with reactive dyes is

(A) Citric acid

(B) Sodium dithionite

(D) Sodium formaldehyde sulphoxylate

Answer: (D)

19. A pplication of a fluorochemical based finish on a textile fabric imparts

P. Water repellency
Q. Oil repellency
R. Soil repellency
S. Soil release property

(A) P, Q & R only

(B) Q, R & S only

(D) P, Q & S only

Answer: (Marks to All)

20. If are three vectors such that is perpendicular to then the value of 𝜆 is ______________

Answer: (-1 to -1)

21. If 𝑦(𝑥) is the solution of the differential equation 𝑦 𝑦′ = 8 𝑥 , 𝑦(0) = 2 , then the absolute value of 𝑦(2) is _______________

Answer: (6 to 6)

22. If is a continuous function for all real values of 𝑥 , then 𝑓(8) is equal to _______________

Answer: (20 to 20)

23. A twistless polyester yarn has 90 filaments, each of 2 denier. The metric count of the yarn is ______________

Answer: (49.8 to 50.2)

24. Bottom shaft of a shuttle loom, weaving 2 up 1 down twill weave, is rotating at 90 rpm. The speed of cam shaft (in rpm) is ____________

Answer: (60 to 60)

25. If wale constant and course constant for knitted fabrics are 4.2 and 5.46, respectively, then the value of the loop shape factor, accurate to one decimal place, is ______________

Answer: (1.3 to 1.3)

Q. 26 – Q. 55 carry two marks each.

26. The cross-sectional shape of a fibre affects the following properties of yarn

P. Lustre
Q. Torsional rigidity
R. Flexural rigidity
S. Packing density

(A) P & Q only

(B) P & R only

(D) P, Q, R & S

Answer: (D)

27. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

[a]: The reaction temperature and rate of agitation during polymerization of polyethylene terephthalate have an important effect on molecular weight of the polymer produced.

[r]: Polymerization of polyester by melt polycondensation is a predominantly diffusion controlled process.

(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: (A)

28. Group I gives a list of fibres and Group II contains their applications. Match the fibre with its application.

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

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

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

Answer: (B)

29. Techniques used to determine the glass transition temperature of textile fibres are

P. X-ray diffraction (XRD)
Q. Differential scanning calorimetry (DSC)
R. Thermogravimetric analysis (TGA)
S. Dynamic mechanical analysis (DMA)

(A) P & Q only

(B) Q & R only

(D) R & S only

Answer: (C)

30. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

[a]: In a carding machine, carding type of wire point configuration is used between cylinder and doffer.

[r]: Carding type of wire point configuration gives the best fibre transfer without disturbing the fibre alignment.

(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: (D)

31. Match the spinning technology listed in Group I with the machine component / function listed in Group II.

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

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

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

Answer: (C)

32. Compared to filaments in spunbonded nonwovens, those in meltblown nonwovens have

P. Lower orientation of molecular chains
Q. Higher orientation of molecular chains
R. Lower variability in diameter
S. Higher variability in diameter

(A) P & R only

(B) P & S only

(D) Q & S only

Answer: (B)

33. Match the weave in Group I with fabric attribute in Group II.

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

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

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

Answer: (A)

34. Match the test in Group I with fabric property in Group II.

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

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

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

Answer: (D)

35. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

[a]: The work factor of silk fibre is greater than 0.5.

[r]: The work factor is calculated by assuming the following as the stress-strain curve of silk fibre.

(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: (D)

36. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

[a]: As the concentration of a surfactant in water increases, the surface tension of water initially decreases and then becomes constant.

[r]: After reaching the Critical Micelle Concentration, additional surfactant molecules do not further reduce the surface tension.

(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: (A)

37. A dye is applied on a fibre using Na2S2O4 as an auxiliary. Washing fastness of the dye on fibre is good. The correct combination of the dye and the fibre is

(A) Cationic dye, acrylic fibre

(B) Vat dye, cotton fibre

(D) Reactive dye, cotton fibre

Answer: (B)

38. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

[a]: Emulsion thickener is used in pigment printing of textiles.

[r]: Emulsion thickener has high solid content.

(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: (D)

39. Match the dye-fibre in Group I with the interactions in Group II.

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

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

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

Answer: (C)

40. Let 𝑋 be a random variable following the binomial distribution. If 𝐸(𝑋) = 2 and 𝑉𝑎𝑟(𝑋) = 1.2 , then 𝑃(𝑋 = 2) , accurate to three decimal places, is equal to ____________

Answer: (0.325 to 0.365)

41. The value of the integral is ____________

Answer: (64 to 64)

42. Starting from the initial point 𝑥0 = 10, if the sequence {𝑥_𝑛} is generated using Newton Raphson method to compute the root of the equation 𝑥⁴ − 600 = 0, then 𝑥², accurate to two decimal places, is equal to _____________

Answer: (5.95 to 6.25)

43. If then the sum of all eigenvalues of the matrix 𝑀 = 𝐴² − 4 𝐴⁻¹ is equal to _____________

Answer: (17 to 17)

44. If the density of 100% crystalline polyethylene is 1000 kg·m^-3 and that of 100% amorphous polyethylene is 865 kg·m^-3, then the mass fractional crystallinity of a polyethylene fibre with density 970 kg·m^-3, accurate to two decimal places, is ___________

Answer: (0.79 to 0.81)

45. In winding zone of ring spinning, the permissible minimum angle of lead is 30°. For a ring of 40 mm diameter, the minimum diameter (in mm) of bobbin required is _________

Answer: (20 to 20)

46. A sliver of 4.2 kilotex is fed in a rotor spinning machine with opening zone draft of 1400. The draft in the transport duct is 5 and the sliding draft on the rotor wall till the rotor groove is 2. If the total back doubling within the rotor is 120, then the linear density (in tex) of the output yarn is ___________

Answer: (35.0 to 38.0)

47. An eight head comber is running at 400 nips/min. The lap fed is 60 kilotex and noil extracted is 20%. If the feed/nip is 7 mm, then with machine utilization of 80%, the production rate (in kg/h), accurate to one decimal place, is ____________

Answer: (51.0 to 52.0)

48. A shuttle loom having 1.75 m reed width is running at 180 rpm. The shuttle enters and leaves the shed at 120° and 240° angular positions of crankshaft, respectively. If length of the shuttle is 0.25 m, then the mean velocity (in m/s) of the shuttle within the shed is ___________

Answer: (18.0 to 18.2)

49. The diameter and length of torsion rod used in a projectile loom are increased by 5% and 20%, respectively. If the torque required to twist the rod increases by X%, then the value of X, accurate to two decimal places, is _____________

Answer: (1.247 to 1.31)

50. Cloth cover factor of a square plain jammed cotton fabric, accurate to one decimal place, is _____________

Answer: (22.8 to 23.1)

51. In a vibroscope, a cotton fibre of 25 mm length is clamped at one end, led over a knifeedge support, tensioned by a weight of 350 mg, and is inclined to vibrate at a fundamental resonant frequency of 2.6 kHz. The linear density of the fibre (in tex), accurate to two decimal places, is ____________

Answer: (0.19 to 0.21)

52. The theoretical limit coefficient of variation (V_r in %) of the weight per unit length of cotton sliver is where N is the average number of fibres present in the crosssection of the sliver. To derive this expression, the coefficient of variation (in %) of the fibre weight per unit length, accurate to two decimal places, is considered as ______________

Answer: (35.00 to 36.00)

53. The bending length of a nonwoven fabric in machine direction is two times the bending length in cross-machine direction. The ratio of flexural rigidities of this fabric in machine direction to cross-machine direction is ______________

Answer: (8 to 8)

54. The standard deviation of population P is two times the standard deviation of population Q. The size of a random sample from population P is four times the size of a random sample from population Q. If 𝑒_P and 𝑒_Q denote the standard error of means of the samples from P and Q, respectively, then the ratio of 𝑒_P to 𝑒_Q is _____________

Answer: (1 to 1)

55. A crease resist (CR) agent is applied by padding on a fabric of 1 m width and 200 g/m²areal density. The concentration of CR agent in the pad bath is 100 gpl and the fabric speed is 50 m/min. The expression is 110% and the specific gravity of the pad liquor is 1.1. In order to maintain the bath concentration, the rate (in kg/min) at which the CR agent needs to be added to the bath, accurate to one decimal place, is_______________

Answer: (0.9 to 1.1)

GATE Exam 2018 Production and Industrial Engineering (PI) Question Paper With Answer Key

June 7, 2023November 26, 2018 by suresh84

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _________.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

6. Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

(A) 0

(B) 2

(D) 8

Answer: (C)

7. A wire would enclose an area of 1936 m², if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

8. A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

10. An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Production and Industrial Engineering

Q. 1 – Q. 25 carry one mark each.

1. Vector triple product a × (b × c) of three vectors a, b and c is given by

(A) (a • c)b – (a • b)c

(B) (b • c)a – (a • c)b

(D) (b • c)a – (a • b)c

Answer: (A)

2. A real-valued function y of real variable x is such that y = 5|x|. At x = 0 the function is

(A) discontinuous but differentiable

(B) both continuous and differentiable

(D) continuous but not differentiable

Answer: (D)

3. Considering the coordinate system shown in the figure, a force of magnitude 10 kN has x-component of –6 kN. Possible y-component (s) of the force is/are

(A) +8 kN only

(B) +5 kN only

(D) +5 kN and –5 kN

Answer: (C)

4. When austenite decomposes upon cooling into two phases— ferrite and cementite, the reaction is called

(A) Eutectic

(B) Eutectoid

(D) Peritectoid

Answer: (B)

5. Match the geometric tolerances with their correct symbols:

(A) P – 1, Q – 3, R – 4, S – 2

(B) P – 3, Q – 1, R – 4, S – 2

(D) P – 3, Q – 2, R – 1, S – 4

Answer: (B)

6. Which one of the following instruments makes use of the principle of interference of light?

(A) Optical flat

(B) Auto-collimator

(D) Coordinate measuring machine

Answer: (A)

7. In ASME process chart, the symbol represents

(A) operation

(B) inspection

(D) transport

Answer: (B)

8. Which one of the following is the most appropriate control chart for measuring the variability of individual readings within a sample?

(A)

(B) R-chart

(D) c-chart

Answer: (B)

9. The machines and auxiliary facilities are located according to processing sequence of the product (produced in very large quantities) in

(A) Process Layout

(B) Fixed Position Layout

(D) Cellular Layout

Answer: (C)

10. Which one of the following defects is NOT associated with the casting process?

(A) Hot tear

(B) Porosity

(D) Central burst

Answer: (D)

11. In an oxy-acetylene gas welding process, oxygen and acetylene are mixed in a ratio of 1.5:1 (by volume). The flame is

(A) neutral

(B) carburizing

(D) oxidizing

Answer: (D)

12. Each of three firms P, Q and R manufactures 100 lakhs components. The number of defective components produced by P, Q and R are 30, 42 and 47, respectively. The firm(s) in conformance with Six Sigma standard is/are

(A) only P

(B) P and Q

(D) Q and R

Answer: (A)

13.To make holes of 0.5 mm diameter and 30 mm depth in a mild steel component, the most
suitable process is

(A) chemical machining

(B) electrochemical machining

(D) plasma arc machining

Answer: (B)

14. Which one of the following processes is NOT used for producing powders?

(A) Atomization

(B) Ball milling

(D) Electrolysis

Answer: (C)

15. The process in which molten thermoplastic is forced between rolls to produce thin sheets is called

(A) blow moulding

(B) compression moulding

(D) extrusion

Answer: (C)

16. The diagonal elements of a 3-by-3 matrix are –10, 5 and 0, respectively. If two of its eigenvalues are –15 each, the third eigenvalue is _______

Answer: (24.5 to 25.5)

17. Weights (in kg) of six products are 3, 7, 6, 2, 3 and 4. The median weight (in kg, up to one decimal place) is _______

Answer: (3.19 to 3.51)

18. The probabilities of occurrence of events F and G are P(F) = 0.3 and P(G) = 0.4, respectively. The probability that both events occur simultaneously is P(F∩G) = 0.2. The probability of occurrence of at least one event P(F∪G) is _______

Answer: (0.49 to 0.51)

19. A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______

Answer: (9.9 to 10.1)

20. A cylindrical wooden block of length 50 cm is floating in water in such a way that its axis is vertical. The densities of wood and water are 800 kg/m³ and 1000 kg/m³, respectively. The submerged depth, i.e., depth of immersion (in cm) of the cylinder is _______

Answer: (39 to 41)

21. A machine consists of three components P, Q and R connected serially. The reliabilities of P, Q and R are 0.97, 0.86 and 0.93, respectively. To increase the reliability of the machine, two additional stand-by units of Q are attached. The overall reliability (up to two decimal places) of the machine is _______

Answer: (0.88 to 0.91)

22. The mean time between failures of a machine is 400 hour. If the availability of the machine is 80%, the mean time to repair (in hour) is _______

Answer: (79 to 81)

23. Processing times on a single machine for 3 jobs are given below. All the jobs are available at time t = 0.

The mean flow time (in minute) as per the shortest processing time (SPT) sequence is _______

Answer: (11.8 to 12.2)

24. In a two-pass wire drawing process, there is a 40% reduction in wire cross-sectional area in 1st pass and further 30% reduction in 2nd pass. The overall reduction (in percentage) is ______

Answer: (57 to 59)

25. A double-start thread with a pitch of 2 mm is to be cut using a lathe machine. The pitch of the leadscrew of the lathe is 6 mm. The job rotates at 60 revolution per minute (RPM). The RPM of the leadscrew is ______

Answer: (39 to 41)

Q. 26 – Q. 55 carry two marks each.

26. Consider the analytic function f(z) = x2 – y2 + i2xy of the complex variable z = x + iy where The derivative f′(z) is

(A) 2x + i2y

(B) x² + iy²

(D) 2x – i2y

Answer: (A)

27. In order to evaluate the integral with Simpson’s 1/3rd rule, values of the function e^x are used at x = 0.0, 0.5 and 1.0. The absolute value of the error of numerical integration is

(A) 0.000171

(B) 0.000440

(D) 0.002718

Answer: (C)

28. A rigid link PQ of length 1.0 m is pinned at P. It rotates about P in a vertical plane with a uniform angular acceleration of 1.0 rad/s². At an instant when the angular velocity of the link is 1.0 rad/s, the magnitude of total acceleration (in m/s²) of point Q relative to point P is

(A) 1.41

(B) 1.73

(D) 2.83

Answer: (A)

29. In a shaft-hole system, the dimensions with tolerances (in mm) are as follows:

where both x and y are positive real numbers. Which one of the following will provide an interference fit?

(A) x = 0.05, y = 0.040

(B) x = 0.04, y = 0.035

(D) x = 0.02, y = 0.035

Answer: (D)

30. A machine is procured at a price of Rs. 47000 with a 2-year warranty. After two years, the annual maintenance cost (AMC) in Rs. is given by the following formula:

AMC = (i – 2) × 2000, for i > 2,

where i is the number of years elapsed since the machine was purchased. Neglect the scrap value of the machine, inflation, interest, etc. For minimizing the average cost, the machine should be replaced at the end of the year

(A) 2

(B) 4

(D) 10

Answer: (C)

31. In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per hour. The time for servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is

(A) 10

(B) 15

(D) 30

Answer: (B)

32. Actual and forecasted demands of a product are as follows:

The forecast error measured in terms of mean absolute deviation (MAD) and mean absolute percentage error (MAPE), respectively, are

(A) 13 and 7.84%

(B) 13 and 9.85%

(D) 17 and 9.85%

Answer: (D)

33. In a mass production firm, measurements are carried out on 10000 pairs of shaft and hole. The mean diameters of the shaft and the hole are 37.53 mm and 37.59 mm, respectively. The corresponding standard deviations are 0.03 mm and 0.04 mm. The mean clearance and its standard deviation (both in mm), respectively, are

(A) 0.06 and 0.07

(B) 0.06 and 0.06

(D) 0.07 and 0.01

Answer: (C)

34. A pressure die casting set-up was tested by injecting water (density 1000 kg/m³) at a pressure of 200 bar. Mould-filling time was found to be 0.05 s. Afterwards, the actual casting is made by injecting the liquid metal (density 2000 kg/m³) at an injection pressure of 400 bar. Neglect all losses (friction, viscous-effect, etc.). The approximate mould-filling time (in s) is

(A) 0.05

(B) 0.075

(D) 0.2

Answer: (A)

35. The value of the surface integral over the surface S of the sphere x² + y² +z² = 9, where n is the unit outward normal to the surface element d,S is ______

Answer: (675 to 681)

36. Consider the differential equation

The value of y (up to two decimal places) at t =1 is ______

Answer: (4.52 to 4.56)

37. One kg of air (that can be considered a calorically perfect gas with characteristic gas constant R = 287 J/kg-K and specific heat ratioΥ = 1.4 ) undergoes a constant-volume process from an initial static pressure of 1 bar to a final static pressure of 4 bar. The increase in entropy (in J/kg-K) of air is ______

Answer: (990 to 1000)

38. If u = 2(x² – y²) and v = –axy represent the x- and y-components of the two-dimensional velocity field of an incompressible flow, the value of the constant a is ______

Answer: (3.9 to 4.1)

39. A spherical pressure vessel (made of mild steel) of internal diameter 500 mm and thickness 10 mm is subjected to an internal gauge pressure of 4000 kPa. If the yield stress of mild steel is 200 MPa, the factor of safety (up to one decimal place) is ______

Answer: (3.6 to 4.4)

40. A square cross-section wooden column of length 3140 mm is pinned at both ends. For the wood, Young’s modulus of elasticity is 12 GPa and allowable compressive stress is 12 MPa. The column needs to support an axial compressive load of 200 kN. Using a factor of safety of 2.0 in the computation of Euler’s buckling load, the minimum cross-sectional area (in mm²) of the column is ______

Answer: (1575 to 1650)

41. Length, width and thickness of a plate are 400 mm, 400 mm and 30 mm, respectively. For the material of the plate, Young’s modulus of elasticity is 70 GPa, yield stress is 80 MPa and Poisson’s ratio is 0.33. When the plate is subjected to a longitudinal tensile stress of 70 MPa, the increase in the volume (in mm³) of the plate is ______

Answer: (1575 to 1650)

42. In a V-thread, a wire is fitted such that it makes contact with the flank of the thread on the pitch line as shown in the figure. If the pitch p of the thread is 3 mm and the included angle is 60°, the diameter (in mm, up to one decimal place) of the wire is ______

Answer: (1.6 to 1.8)

43. A project consists of three activities P, Q and R. The durations of activities follow Beta distribution. The predecessors and durations of activities are as per the following table:

The expected project completion time (in month) is ______

Answer: (13.9 to 14.1)

44. A company has two manufacturing plants (C₁ and C₂) and two distribution centres (D₁ and D₂). The capacities of C₁ and C₂ are 100 and 200 units, respectively. The demand for D₁ and D₂ are 190 and 110 units, respectively. The costs per unit (in Rs.) of transportation at different routes are as per the following matrix:

Answer: (6165 to 6175)

45. The annual demand of an item is 19845 units and the production rate is 100 units per day. The per-unit production cost (excluding setup cost) is Rs. 50, the per-unit holding cost is Rs. 10 per year and setup cost is Rs. 520 per setup. To minimize the total annual cost, the optimum quantity to be produced per setup is ______

Answer: (2100 to 2155)

46. A production line operates 7 hours a day in a 5-day week. The processing times for various job elements are as follows

If the line is designed for an output of 8400 units per week, the theoretical minimum number of work stations required is ______

Answer: (2.8 to 3.2)

47. In a work sampling study of a worker, the information available are as follows: total time of study: 30 hour, number of items produced: 320, total number of observations: 1000, number of observations when worker is found working: 850 and average performance rating: 105%. Company policy is to give allowance of 10% of total time on the job. The standard time (in minute per item, up to one decimal place) for manufacturing the item is ______

Answer: (5.2 to 5.8)

48. The breakeven point of a manufacturing company is 50000 units. The fixed cost is Rs. 200000 and the variable cost per unit is Rs. 20. The selling price per unit (in Rs.) of the product at this breakeven point is ______

Answer: (23.8 to 24.2)

49. A 10 mm thick plate is rolled to 7 mm thickness in a rolling mill using 1000 mm diameter rigid rolls. The neutral point is located at an angle of 0.3 times the bite angle from the exit. The thickness (in mm, up to two decimal places) of the plate at the neutral point is ______

Answer: (7.1 to 7.4)

50. A cylindrical workpiece is turned at a feed of 0.1 mm/rev with a perfectly sharp tool. In ASA system, the side and end cutting edge angles are 15° and 5°, respectively, as shown in the figure. The peak-to-valley roughness (in μm, up to one decimal place) of the machined surface is ______

Answer: (8.4 to 8.7)

51. The worktable in a CNC machine is driven by a leadscrew with a pitch of 2 mm. The leadscrew is directly coupled to a stepper motor of step angle 1.8°. The number of pulses required to move the worktable by 50 mm is ______

Answer: (4999 to 5001)

52. During orthogonal machining of a job at a cutting speed of 90 m/min with a tool of 10° rake angle, the cutting force and thrust force are 750 N and 390 N, respectively. Assume a shear angle of 35°. The power (in W) expended for shearing along the shear plane is ______

Answer: (630 to 641)

53. I n an electrochemical machining of aluminium with plane parallel electrodes, the current density is 70 A/cm². Cross-sectional area of each electrode is 3 cm². The current efficiency (i.e., the fraction of current used for dissolution of metal) is 80%. Gram atomic weight, valency and density of aluminium are 27 gram, 3 and 2700 kg/m³, respectively. Take Faraday’s constant as 96500 Coulomb. The volumetric material removal rate (in mm³/min) is ______

Answer: (345 to 351)

54. Two metallic sheets are spot welded by passing a current of 8000 A for 0.2 s. Assume that a cylindrical nugget of 8 mm diameter and 3 mm depth is formed. The density of the nugget is 7500 kg/m³, effective resistance of the total system is 222 micro-Ohm and heat required to produce 1.0 gram of nugget is 1400 J. The percentage of heat actually utilized in producing the nugget is ______

Answer: (53 to 58)

55. In a planar 2-degree-of-freedom robot, Link 1 of 30 cm length is connected to base by a revolute joint and Link 2 of length 20 cm is connected to Link 1 with a revolute joint as shown in the figure. The work-envelope area (in cm²), covered by point P, is ______

Answer: (3760 to 7600)

GATE Exam 2018 Physics (PH) Question Paper With Answer Key

June 7, 2023November 24, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

(D) (iv), (iii), (ii), (i)

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Physics

Q. 1 – Q. 25 carry one mark each.

1. The eigenvalues of a Hermitian matrix are all

(A) real

(B) imaginary

(D) real and positive

Answer: (A)

2. Which one of the following represents the 3p radial wave function of hydrogen atom? (a₀ is the Bohr radius)

Answer: (B)

3. Given the following table,

which one of the following correctly matches the experiments from Group I to their inferences in Group II?

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

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

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

Answer: (C)

4. In spherical polar coordinates (𝑟,𝜃,𝜙), the unit vector at (10,𝜋/4,𝜋/2) is

Answer: (D)

5. The scale factors corresponding to the covariant metric tensor 𝑔_𝑖𝑗 in spherical polar coordinates are

(A) 1,𝑟²,𝑟²sin²𝜃

(B) 1,𝑟²,sin²𝜃

(D) 1,𝑟,𝑟sin𝜃

Answer: (D)

6. In the context of small oscillations, which one of the following does NOT apply to the normal coordinates?

(A) Each normal coordinate has an eigen-frequency associated with it

(B) The normal coordinates are orthogonal to one another

(D) The potential energy of the system is a sum of squares of the normal coordinates with constant coefficients

Answer: (B)

7. For the given unit cells of a two dimensional square lattice, which option lists all the primitive cells?

Answer: (C)

8. Among electric field and vector potential which is/are odd under parity (space inversion) operation?

Answer: (B)

9. The expression for the second overtone frequency in the vibrational absorption spectra of a diatomic molecule in terms of the harmonic frequency 𝜔_𝑒 and anharmonicity constant 𝑥_𝑒 is

(A) 2𝜔_𝑒(1−𝑥_𝑒)

(B) 2𝜔_𝑒(1−3𝑥_𝑒)

(D) 3𝜔_𝑒(1−4𝑥_𝑒)

Answer: (D)

10. Match the physical effects and order of magnitude of their energy scales given below, where is fine structure constant; 𝑚_𝑒 and 𝑚_𝑝 are electron and proton mass, respectively.

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

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

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

Answer: (C)

11. The logic expression can be simplified to

(A) 𝐴 XOR 𝐶

(D) 1

Answer: (A)

12. A t low temperatures (𝑇), the specific heat of common metals is described by (with 𝛼 and 𝛽 as constants)

(A) 𝛼 𝑇 + 𝛽 𝑇³

(B) 𝛽 𝑇³

(D) 𝛼 𝑇 + 𝛽 𝑇⁵

Answer: (A)

13. In a 2-to-1 multiplexer as shown below, the output X = A₀ if C = 0, and X = A₁ if C = 1.

Which one of the following is the correct implementation of this multiplexer?

Answer: (A)

14. T he elementary particle is placed in the baryon decuplet, shown below, at

(A) P

(B) Q

(D) S

Answer: (C)

15. The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (𝑎0 is the Bohr radius)

(A) −3𝑒𝑎₀

(B) zero

(D) 3𝑒𝑎₀

Answer: (B)

16. The high temperature magnetic susceptibility of solids having ions with magnetic moments can be described by with 𝑇 as absolute temperature and 𝜃 as constant. The three behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described, respectively, by

(A) 𝜃<0,𝜃>0,𝜃=0

(B) 𝜃>0,𝜃<0,𝜃=0

(D) 𝜃=0,𝜃>0,𝜃<0

Answer: (C)

17. Which one of the following is an allowed electric dipole transition?

(A) ¹ S₀ → ³ S₁

(B) ² P_3/2 → ² D_5/2

(C)² D_5/2 → ² P_1/2

(D) ³ P₀ → ⁵ D₀

Answer: (B)

18. In the decay, 𝜇⁺→𝑒⁺⁺𝜈_𝑒+𝑋, what is 𝑋?

(A) 𝛾

Answer: (D)

19. A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station would see the probe moving at a speed Xc, where the value of X is ________ (up to three decimal places).

Answer: (0.185 to 0.189)

20. For an operational amplifier (ideal) circuit shown below,

if V₁ = 1 V and V₂ = 2 V, the value of V₀ is ________V (up to one decimal place).

Answer: (-3.7 to -3.5)

21. An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy density at distance 𝑟₁ to that at 𝑟₂(=2 𝑟₁) from the wire is ________.

Answer: (4 to 4)

22. A light beam of intensity 𝐼0 is falling normally on a surface. The surface absorbs 20% of the intensity and the rest is reflected. The radiation pressure on the surface is given by 𝑋_𝐼0/c, where X is ________ (up to one decimal place). Here 𝑐 is the speed of light.

Answer: (1.8 to 1.8)

23. The number of independent components of a general electromagnetic field tensor is ________.

Answer: (6.6)

24. If 𝑋 is the dimensionality of a free electron gas, the energy (𝐸) dependence of density of states is given by where 𝑌 is ________.

Answer: (1 to 1)

25. For nucleus ¹⁶⁴Er, a 𝐽^𝜋=2⁺ state is at 90 keV. Assuming ¹⁶⁴Er to be a rigid rotor, the energy of its 4⁺ state is ________ keV (up to one decimal place).

Answer: (297.0 to 300.1)

Q. 26 – Q. 55 carry two marks each.

26. Given which one of the following makes a complete set for a three dimensional real linear vector space ?

Answer: (D)

27. An interstellar object has speed 𝑣 at the point of its shortest distance 𝑅 from a star of much larger mass 𝑀. Given 𝑣2=2 𝐺𝑀/𝑅, the trajectory of the object is

(A) circle

(B) ellipse

(D) hyperbola

Answer: (C)

28. A particle moves in one dimension under a potential 𝑉(𝑥)=𝛼|𝑥| with some non-zero total energy. Which one of the following best describes the particle trajectory in the phase space?

Answer: (A)

29. Consider an infinitely long solenoid with 𝑁 turns per unit length, radius 𝑅 and carrying a current 𝐼(𝑡)=𝛼cos𝜔𝑡, where 𝛼 is a constant and 𝜔 is the angular frequency. The magnitude of electric field at the surface of the solenoid is

(D) 𝜇₀𝜔𝑁𝑅cos𝜔𝑡

Answer: (A)

30. A constant and uniform magnetic field pervades all space. Which one of the following is the correct choice for the vector potential in Coulomb gauge?

Answer: (C)

31. If 𝐻 is the Hamiltonian for a free particle with mass 𝑚, the commutator [𝑥,[𝑥,𝐻]] is

(A) ℏ²/𝑚

(B) −ℏ²/𝑚

(D) ℏ²/(2𝑚)

Answer: (B)

32. A long straight wire, having radius 𝑎 and resistance per unit length 𝑟, carries a current 𝐼. The magnitude and direction of the Poynting vector on the surface of the wire is

(A) 𝐼²𝑟2𝜋𝑎⁄ , perpendicular to axis of the wire and pointing inwards

(B) 𝐼²𝑟2𝜋𝑎⁄ , perpendicular to axis of the wire and pointing outwards

(D) 𝐼²𝑟𝜋𝑎⁄ , perpendicular to axis of the wire and pointing outwards

Answer: (A)

33. Three particles are to be distributed in four non-degenerate energy levels. The possible number of ways of distribution: (i) for distinguishable particles, and (ii) for identical Bosons, respectively, is

(A) (i) 24, (ii) 4

(B) (i) 24, (ii) 20

(D) (i) 64, (ii) 16

Answer: (C)

34. The term symbol for the electronic ground state of oxygen atom is

(A) ^1𝑆0

(B) ¹𝐷₂

(D) ³𝑃₂

Answer: (D)

35. The energy dispersion for electrons in one dimensional lattice with lattice parameter 𝑎 is given by where 𝑊 and 𝐸₀ are constants. The effective mass of the electron near the bottom of the band is

Answer: (A)

36. Amongst electrical resistivity (𝜌), thermal conductivity (𝜅), specific heat (𝐶), Young’s modulus (Y), and magnetic susceptibility (𝜒), which quantities show a sharp change at the superconducting transition temperature?

(A) 𝜌,𝜅,𝐶, Y

(B) 𝜌,𝐶, 𝜒

(D) 𝜅, Y, 𝜒

Answer: (B)

37. A quarter wave plate introduces a path difference of 𝜆/4 between the two components of polarization parallel and perpendicular to the optic axis. An electromagnetic wave with is incident normally on a quarter wave plate which has its optic axis making an angle 135° with the 𝑥-axis as shown.

The emergent electromagnetic wave would be

(A) elliptically polarized

(B) circularly polarized

(D) linearly polarized but with polarization at 90° to that of the incident wave

Answer: (C)

38. A p-doped semiconductor slab carries a current 𝐼=100 mA in a magnetic field 𝐵=0.2 T as shown. One measures 𝑉_𝑦=0.25 mV and 𝑉_𝑥=2 mV. The mobility of holes in the semiconductor is ________ m²V^–1s^–1 (up to two decimal places).

Answer: (1.55 to 1.58)

39. An n-channel FET having Gate-Source switch-off voltage V_GS(OFF) = – 2 V is used to invert a 0 – 5 V square-wave signal as shown. The maximum allowed value of R would be ________ k (up to two decimal places).

Answer: (0.70 to 0.73)

40. Inside a large nucleus, a nucleon with mass 939 MeVc^–2 has Fermi momentum 1.40 fm^–1 at absolute zero temperature. Its velocity is Xc, where the value of X is ________ (up to two decimal places).

(ℏ𝑐=197 MeV-fm)

Answer: (0.28 to 0.31)

41. 4 MeV 𝛾-rays emitted by the de-excitation of ¹⁹F are attributed, assuming spherical symmetry, to the transition of protons from 1d_3/2 state to 1d5/2 state. If the contribution of spin-orbit term to the total energy is written as the magnitude of 𝐶 is ________ MeV (up to one decimal place).

Answer: (1.6 to 1.6)

42. An 𝛼 particle is emitted by a nucleus. Assuming the potential to be purely Coulombic beyond the point of separation, the height of the Coulomb barrier is ________ MeV (up to two decimal places).

Answer: (24.4 to 27.6)

43. For the transformation

(where 𝛼 is a constant) to be canonical, the value of 𝛼 is________.

Answer: (2 to 2)

44. Given

and boundary conditions 𝑓(0)=1 and 𝑓(1)=0, the value of 𝑓(0.5) is ________ (up to two decimal places).

Answer: (0.81 to 0.84)

45. The absolute value of the integral

over the circle |𝑧−1.5|=1 in complex plane, is ________ (up to two decimal places).

Answer: (81.60 to 81.80)

46. A uniform circular disc of mass 𝑚 and radius 𝑅 is rotating with angular speed 𝜔 about an axis passing through its center and making an angle 𝜃=30∘ with the axis of the disc. If the kinetic energy of the disc is 𝛼𝑚𝜔²𝑅², the value of 𝛼 is ________ (up to 2 decimal places).

Answer: (0.21 to 0.23)

47. The ground state energy of a particle of mass 𝑚 in an infinite potential well is 𝐸0. It changes to 𝐸₀(1+𝛼×10⁻³), when there is a small potential bump of height and width 𝑎=𝐿/100, as shown in the figure. The value of 𝛼 is ________ (up to two decimal places).

Answer: (0.78 to 0.82)

48. An electromagnetic plane wave is propagating with an intensity 𝐼=1.0×10⁵ Wm–2 in a medium with 𝜖=3𝜖₀ and 𝜇=𝜇₀. The amplitude of the electric field inside the medium is ________ ×10³ Vm^–1 (up to one decimal place).

(𝜖₀= 8.85×10⁻¹² C₂ N^–1 m^–2, 𝜇₀=4𝜋×10⁻⁷NA^–2, 𝑐 = 3×10⁸ ms^–1)

Answer: (6.5 to 6.7)

49. A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or energy 𝜖 state. Both states are non-degenerate. If the total energy of this ensemble is 4𝜖, its entropy will be ________ 𝑘_𝐵 (up to one decimal place), where 𝑘_𝐵 is the Boltzmann constant.

Answer: (6.1 to 6.3)

50. A two-state quantum system has energy eigenvalues ±𝜖 corresponding to the normalized states At time 𝑡=0, the system is in quantum state The probability that the system will be in the same state at 𝑡=ℎ/(6𝜖) is ________ (up to two decimal places).

Answer: (0.25 to 0.25)

51. An air-conditioner maintains the room temperature at 27°C while the outside temperature is 47°C. The heat conducted through the walls of the room from outside to inside due to temperature difference is 7000 W. The minimum work done by the compressor of the air-conditioner per unit time is ________ W.

Answer: (466 to 4.67)

52. Two solid spheres A and B have same emissivity. The radius of A is four times the radius of B, and temperature of A is twice the temperature of B. The ratio of the rate of heat radiated from A to that from B is ________.

Answer: (256 to 256)

53. The partition function of an ensemble at a temperature 𝑇 is

where 𝑘_𝐵 is the Boltzmann constant. The heat capacity of this ensemble at is 𝑋 𝑁𝑘_𝐵, where the value of 𝑋 is ________ (up to two decimal places).

Answer: (0.41 to 0.43)

54. An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its 650 nm spectral line is 0.03 nm. The magnitude of the field is ________ Tesla (up to two decimal places).

( 𝑒=1.60×10⁻¹⁹ C, 𝑚𝑒=9.11×10⁻³¹ kg, 𝑐=3.0×108 ms^–1)

Answer: (1.51 to 1.53)

55. The quantum effects in an ideal gas become important below a certain temperature 𝑇_𝑄 when de Broglie wavelength corresponding to the root mean square thermal speed becomes equal to the inter-atomic separation. For such a gas of atoms of mass 2×10⁻²⁶ kg and number density 6.4×10²⁵ m^–3, 𝑇𝑄= __________ ×10⁻³ K (up to one decimal place).
(𝑘𝐵=1.38×10⁻²³ J/K, ℎ=6.6×10⁻³⁴ J-s)

Answer: (78 to 90)

GATE Exam 2018 Petroleum Engineering (PE) Question Paper With Answer Key

June 7, 2023November 24, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Petroleum Engineering

Q. 1 – Q. 25 carry one mark each.

1. The Taylor series expansion of the function,

around 𝑥 = 0 (up to 4th order term) is:

Answer: (B)

2. The inverse of the matrix is

Answer: (C)

3. The line integral of a vector function over a curve C in a simply connected domain D in space, is defined by:

The line integral is independent of path in D. 𝐹₁, 𝐹₂, and 𝐹₃ are continuous, and have continuous first partial derivatives in D. 𝐶′ is a closed curve in D.
Which one of the following is NOT ALWAYS true in domain D?

Answer: (B)

4. Which one of the following is the integrating factor (IF) for the differential equation, ?

(A) 𝑒^{tan 𝑥}

(B) 𝑒^{cos 𝑥}

(D) 𝑒^{sin 𝑥}

Answer: (A)

5. A phase diagram of a black oil is shown in the figure (Y is the critical point).

Match the following:

(P) Curve XY (I) Dew point curve

(Q) Curve YZ (II) Single phase liquid

(R) Phase I (III) Bubble point curve

(S) Phase II (IV) Single phase gas

(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)

6. Match the following chemicals to their respective oilfield applications:

(P) Hydrate inhibitor

(I) Formaldehyde

(Q) Well stimulation

(II) Xanthan gum

(R) Drilling fluid biocide

(III) Methanol

(S) Viscosifier

(IV) Hydrochloric acid

(A) P-IV, Q-III, R-II, S-I

(B) P-III, Q-I, R-IV, S-II

(D) P-III, Q-IV, R-I, S-II

Answer: (D)

7. The CH₄-hydrate equilibrium curve (dashed) and CO₂-hydrate equilibrium curve (solid) on a pressure-temperature plane above 0°C are shown in the figure. The two curves divide the plane in four non-overlapping regions. In which region are CO₂-hydrates stable and CH₄– hydrates unstable?

(A) I

(B) II

(D) IV

Answer: (B)

8. Plot of ratio of pressure to gas compressibility factor (P/Z) vs. cumulative gas production (G_p) for a gas reservoir (represented by solid curve in the figure) was shown to a reservoir engineering student.

The student made the following statements:

(I) A water aquifer is attached to this gas reservoir.

(II) P/Z vs. Gp curve must always be a straight line for water encroachment in a gas reservoir.

(III) The ultimate gas recovery is diminished due to water encroachment.

Which of the above statements are TRUE?

(A) Only I and II

(B) Only II and III

(D) I, II, and III

Answer: (C)

9. Waste water from oil industry consists of oil in free and emulsified forms. The oil in the free form can be recovered by:

(A) Aerated lagoons

(B) Trickling filters

(D) Biological oxygen pond

Answer: (C)

10. A reservoir model consisting of two porous matrices M and N, separated by a fracture, is shown in the figure. The matrices are strongly water-wet and are saturated with oil of specific gravity 0.8. Water is injected only in the fracture at injection well A. If the Reynolds number for the flow in the fracture conduit is assumed to be less than unity, which one of the following force will dominate oil recovery from the porous matrix M during the water-flood operation?

(A) Capillary force

(B) Gravity force

(D) Inertial force

Answer: (A)

11. A fractional flow curve is given for a core for which the irreducible water saturation is 0.2 and the residual oil saturation is 0.3. The initial water saturation in the core is 0.3. If Welge’s method is applied to find the breakthrough saturation and fraction flow of water at breakthrough, which point should be used in the figure to draw a tangent line to the fractional flow curve.

(A) I

(B) II

(D) IV

Answer: (D)

12. Which one of the following curves represents behavior of oil phase viscosity as a function of pressure in the reservoir (where, P_b is the bubble point pressure of oil)?

(A) Curve I

(B) Curve II

(D) Curve IV

Answer: (D)

13. Pick out the INCORRECT statement.

(A) Flash point is always lower than fire point.

(B) Pour point of lube oil can be reduced by removing the wax from it.

(D) Coal bed methane typically contains more than 60% CO₂.

Answer: (D)

14. Which one of the following phenomena encountered during flooding is desirable for increasing oil recovery from a reservoir?

(A) Viscous fingering

(B) Formation damage

(D) Decrease in capillary pressure

Answer: (D)

15. CO₂ foams are used for enhanced oil recovery due to which of the following reasons?

(I) It can be used for CO₂ sequestration

(II) CO₂ can exist in the form of a dense fluid at reservoir conditions

(III) CO₂ can convert to hydrocarbon at the reservoir temperature and pressure

(IV) Solubility of CO₂ in oil is higher compared to gases like N₂

(A) Only I, II, and III

(B) Only I, II, and IV

(D) Only I, III, and IV

Answer: (B)

16. Which one of the following is FALSE about a typical offshore deepwater oil spill?

(A) Using boom boats to prevent spilled oil from spreading

(B) Allowing the spill to reach the shore before clearing

(D) Using a skimmer to collect the oil

Answer: (B)

17. Which one of these methods is NOT commonly used to deal with the problem of soil contamination by oil spillage?

(A) Biodegradation

(B) Leaching out the oil

(D) Using rain water to wash the contaminants

Answer: (D)

18. The factor on which the selection of an offshore platform for the reservoir does NOT depend:

(A) Water depth

(B) Reservoir fluid properties

(D) Best case weather forecast

Answer: (D)

19. Which one of the following options is correct about the effects of steam stimulation in increasing the oil production rate?

(I) Reduces the oil viscosity

(II) Increases the formation damage

(III) Reduces the interfacial tension

(IV) Increases the oil viscosity

(A) Only I and II

(B) Only II and III

(D) Only I and III

Answer: (D)

20. Which one of the following is INCORRECT about oil based drilling muds?

(A) Good rheological properties at higher temperatures (as high as 250oC)

(B) Effective against corrosion

(D) Less inhibitive than water based muds

Answer: (D)

21. Assume that viscous, gravity, and capillary are the only dominant forces for fluid flow in a given reservoir, a cone formed around the perforation zone will break into the well, when

(A) capillary forces are more than viscous and gravity forces.

(B) viscous forces are more than gravity forces.

(D) viscous and gravity forces are equal.

Answer: (B)

22. Two complex numbers, are related as follows:

where, is a scalar. Given principal argument of the principal argument of ______________. (rounded-off to two decimal places. (Use 𝜋 = 3.14)

Answer: (2.50 to 2.70)

23. A cylindrical sandstone core, 7.5 cm long and 3.5 cm diameter has grain density of 3 g/cm³. If the mass of the dry core is 200 g, the porosity of the core is __________%. (rounded-off to two decimal places)

Answer: (7.25 to 7.75)

24. In an oil reservoir the current average pressure is below bubble point pressure of the oil. The current oil production rate is 103 m³/day and total gas production rate is 105 m³/day at STP conditions (25°C and 1 atm). The formation volume factor of the oil is 1.2 and that of gas is 0.01 The dissolved gas oil ratio is 10 of soil

The gas flow rate at bottom-hole conditions is ______× 10² m³ per day. (rounded-off to two decimal places)

Answer: (8.90 to 9.10)

25. Exponential decline curve is to be used to estimate the oil reserves of a well. The current oil production rate is 1000 m³ per day and yearly decline rate is 6% per year. If the minimum oil flow rate economically sustainable for the well is 1 m³ per day, the reserves (economically producible) associated with the well are _____ × 10⁶ m³. (rounded-off to two decimal places. Use 1 year = 365 days)

Answer: (5.80 to 6.20)

Q. 26 – Q. 55 carry two marks each.

26. The probability density for three binomial distributions (D1, D2, and D3) is plotted against number of successful trials in the given figure.

Each of the plotted distributions corresponds to a unique pair of (n, p) values, where, n is the number of trials and p is the probability of success in a trial. Three sets of (n, p) values are provided in the table.

Pick the correct match between the (n, p) set and the plotted distribution.

(A) Set I – D1, Set II – D2, Set III – D3

(B) Set I – D3, Set II – D1, Set III – D2

(D) Set I – D2, Set II – D1, Set III – D3

Answer: (B)

27. Which of the following statements are true about Natural Gas Hydrates?

Natural gas hydrates:

(I) are formed under low temperature and high pressure.

(II) can store approximately 160 m3 of gas per m3 of hydrate at 25 oC and 1 atm.

(III) formation is an endothermic process.

(IV) are potential sources of methane.

(A) Only II, III & IV

(B) Only I, II & III

(D) Only I, III & IV

Answer: (C)

28. P_wf (bottom-hole well flowing pressure) vs. Q (flow rate) plots show the inflow performance relation (IPR) and vertical lift performance (VLP) curves. Figure I shows VLP curves for two well head pressures P_hw1 and P_hw2. Figure II shows VLP curves for two well diameters D₁ and D₂. Which one of the following statements is true?

(A) P_hw1 > P_hw2 and D₁ < D₂

(B) P_hw1 > P_hw2 and D₁ > D₂

(D) P_hw1 < P_hw2 and D₁ > D₂

Answer: (A)

29. Match the following:

(P) Weber Number (I) Ratio of inertial force to viscous force

(Q) Froude Number (II) Ratio of convective heat transfer to conductive heat transfer

(R) Reynolds number (III) Ratio of inertial force to interfacial force

(S) Nusselt number (IV) Ratio of inertial force to gravitational force

(A) P-III, Q-IV, R-I, S-II

(B) P-III, Q-II, R-I, S-IV

(D) P-IV, Q-III, R-I, S-II

Answer: (A)

30. A dilute mixture of coal and sand particles, both of diameter 100 μm and densities 1800 kg/m³ and 2600 kg/m³, respectively, is to be classified by elutriation technique using water (density 1000 kg/m³, viscosity 10^-3 Pa.s). Assuming Stokes law is applicable, the minimum settling velocity of the particles in the mixture is (g = 9.81 m/s²):

(A) 4.36 × 10^-3 m/s

(B) 8.72 × 10^-3 m/s

(D) 1.29 × 10^-3 m/s

Answer: (A)

31. Oil flow rate and flowing bottom-hole pressure (FBHP) recorded with time during a multirate well test are shown.

Let k is the reservoir permeability, h is the formation thickness and μ is the viscosity of the oil. Δ𝑃_𝐷(𝑡) is constant-rate dimensionless pressure drop as a function of time. The total pressure drop till time, t, where t > t₁, will be:

Answer: (A)

32. Which one of the following options presents the correct combination?

(P) Reservoir limit test (I) Communication between wells

(Q) Modified isochronal test (II) Ideally zero flowing bottom hole pressure

(R) Interference test (III) Extended drawdown test

(S) Absolute open flow potential (IV) Drawdown and build-up test of equal duration

(A) P-II, Q-III, R-I, S-IV

(B) P-IV, Q-I, R-III, S-II

(D) P-I, Q-III, R-IV, S-II

Answer: (C)

33. Which one of the following options presents the correct combination?

(P) Roller Cone bits (I) Long and widely spaced teeth

(Q) PDC bits (II) Journal (Pin) angle

(R) Soft formation (III) Short and wider teeth

(S) Hard formation (IV) Size of the cutting

(T) Back rake angle (V) 1400oC and 6×105 psi

(A) P-II, Q-V, R-I, S-III, T-IV

(B) P-III, Q-IV, R-I, S-II, T-V

(D) P-II, Q-V, R-III, S-I, T-IV

Answer: (A)

34. Primary and secondary indicators of kick in a well where the indicators are:

1) flow rate increase,

2) gas, oil or water-cut muds,

3) pit volume increase,

4) flowing well with mud pump shut-off,

5) reduction in drill-pipe weight,

6) drilling break.

Which one of the following presents the correct combination?

(A) Primary (1, 3, 5) and Secondary (2, 4, 6)

(B) Primary (1, 2, 3) and Secondary (4, 5, 6)

(D) Primary (1, 3, 4) and Secondary (2, 5, 6)

Answer: (D)

35. Relative permeability curve for the two rock types (X: solid line and Y: dashed line) are shown in the diagram, where Sw is the fractional water saturation. Which one of the following statements is correct about wettability and consolidated nature of the two rock types?

(A) X is more consolidated and mixed wet, Y is less consolidated and water wet

(B) X is more consolidated and water wet, Y is less consolidated and mixed wet

(D) X is less consolidated and water wet, Y is more consolidated and mixed wet

Answer: (C)

36. Which one of the following options presents correct combinations of exploration methods with their respective frequency of operation?

(P) Seismic (I) ~106 Hz

(Q) Sonic (II) ~102 Hz

(R) Controlled Source EM (III) ~104 Hz

(S) Ultrasonic (IV) ~1 Hz

(A) P-IV, Q-II, R-I, S-III

(B) P-II, Q-III, R-IV, S-I

(D) P-IV, Q-I, R-II, S-III

Answer: (B)

37. Which one of the following options presents the correct combinations?

(P) Borisov’s (I) Critical rate correlation in vertical wells with coning

(Q) Schols’ ( I I ) H o r i zontal well performance relation

(R) Efros’ (III) Vertical well performance relation

(S) Wiggins’ (IV) Critical rate correlation in horizontal wells with coning

(A) P-II, Q-IV, R-I, S-III

(B) P-IV, Q-III, R-II, S-I

(D) P-II, Q-I, R-IV, S-III

Answer: (D)

38. Which one of the following options represents the typical sequence of applying cut-offs for pay zone identification in a conventional reservoir?

(A) porosity, saturation, shale

(B) porosity, permeability, saturation

(D) shale, porosity, permeability

Answer: (C)

39. Which one of the following options represents the correct sequence of arrival of acoustic wave energy recorded in a sonic log?

(A) shear, surface, compressional

(B) compressional, shear, surface

(D) compressional, surface, shear

Answer: (B)

40. The variation of the amount of salt in a tank with time is given by,

where, 𝑥 is the amount of salt in kg and 𝑡 is the time in minutes. Given that there is no salt in the tank initially, the time at which the amount of salt increases to 200 kg is __________ minutes. (rounded-off to two decimal places)

Answer: (10.50 to 12.50)

41. Solve the given differential equation using the 2nd order Runge-Kutta (RK2) method:

Use the following form of RK2 method with an integration step-size, ℎ = 0.5:

The value of 𝑦(𝑡 = 0.5) =__________________. (rounded-off to two decimal places)

Answer: (3.12 to 3.26)

42. A box contains 100 balls of same size, of which, 25 are black and 75 are white. Out of 25 black balls, 5 have a red dot. A trial consists of randomly picking a ball and putting it back in the same box, i.e., sampling is done with replacement. Two such trials are done. The conditional probability that no black ball with a red dot is picked given that at least one black ball is picked, is __________. (in fraction rounded-off to two decimal places)

Answer: (0.76 to 0.80)

43. A cylindrical pipeline of length 30 km is transporting naphtha. Pressure sensors are attached along pipe length to detect leaks. Under steady-state, leak-free operation, there is a linear pressure drop along the length (z) of the pipeline. If a leak occurs, the pressure profile develops a kink at the leak point 𝑧_leak.

Assume that there is only one leak-point (4 km < 𝑧_leak < 27 km) and a new steady-state is reached. The steady-state pressure measurements at four locations along the pipe-length are provided in the table. The location of the leak-point using the gradient intersection method is _______________km. (rounded-off to two decimal places)

Answer: (7.20 to 7.80)

44. A dry core was subjected to the mercury injection test in the laboratory. Following are the related details:

Average formation porosity = 0.2

Formation volume factor, BO = 1.2 reservoir-bbl/STB

Oil API° = 32, Specific gravity of water = 1.1

Hydrostatic gradient = 0.433 psi/ft

(𝜎_𝑂𝑊 cos 𝜃)res = 26 dyne/cm, where 𝜎_𝑂𝑊 is the oil-water interfacial tension and 𝜃 is the contact angle

(𝜎_𝐴𝑀 cos 𝜃)lab = 367 dyne/cm, where 𝜎_𝐴𝑀 is air- mercury interfacial tension and 𝜃 is the contact angle

Average drainage area = 80 acres

(1 acre-ft = 7758 bbl)

The Table shows the laboratory data for capillary pressure at different mercury saturations.

and the average water saturation (𝑆_𝑊) for the productive column is 0.25. The Original Oil in Place (OOIP) in the productive column where 𝑆_𝑊 ≤ 0.5 is ___________ MMSTB. (rounded-off to one decimal place)

Answer: (105.00 to 109.00)

45. A well is drilled with water based mud. The water saturation in the completely flushed zone (no formation fluid residual) is given by,

where, R_mf and R_xo are the mud filtrate resistivity and flushed zone resistivity, respectively.

Use, a = 1.0 and R_xo = 25 R_mf.

The calculated porosity (ϕ) of the formation is ______. (in fraction rounded-off to two decimal places)

Answer: (0.19 to 0.21)

46. An oil well is tested at a flow rate (Q) of 50 BOPD. The bottom hole flowing pressure (P_wf) is 500 psia. The shut-in pressure is 1000 psia. If P_wf is lowered to 300 psia and assuming the Vogel’s correlation holds, the estimated flow rate in the oil well is ______BOPD (rounded-off to two decimal places). The Vogel’s correlation is:

Answer: (61.00 to 63.00)

47. Using Miller, Dyes and Hutchinson (MDH) method, the skin factor of an oil well is found to be 𝑠 = – 3.5.

The reservoir and fluid properties are:

Formation porosity is 0.20

Total compressibility is 2.5 × 10-5 psia-1

Oil viscosity is 1.5 cP

Wellbore radius is 0.5 ft

Flowing bottom hole pressure at Δt = 0 is 2830 psia

Shut in pressure at Δt = 1 hr (PΔt=1hr) is 3000 psia

Slope of middle time region (MTR) line in MDH plot is 190 psia/cycle.

The permeability of the reservoir is __________mD. (rounded-off to two decimal places)

Answer: (25.00 to 29.00)

48. An oil well (producing under expansion drive only) in a reservoir is subjected to two pressure build-up tests. The average formation thickness of the reservoir is 13 ft, the total compressibility is 1×10^-5 psia^-1, and porosity is 0.2. The average formation volume factor of oil is 1.3 reservoir-bbl/STB. Average reservoir pressure during the first test and the second test was found to be 3500 psia and 3200 psia, respectively. If the oil produced between the two pressure build-up tests in 180 days is 250 STB/day, the area of the reservoir is __________acres. (rounded-off to two decimal places) (Use: 1 acre = 43560 ft², 1 bbl = 5.615 ft³)

Answer: (960.00 to 970.00)

49. A well in a very large reservoir has a wellbore radius of 10 cm. The sandstone, with a porosity of 0.25 and 12% (by grain volume) calcite (CaCO₃), is to be acidized with a preflush (HCl solution) so as to dissolve all the calcite upto a distance of 1 m from the wellbore. 1 m³ of preflush is able to dissolve 0.082 m³ CaCO₃. Assume that the reaction between HCl and CaCO₃ is instantaneous. The minimum preflush volume required per meter of the formation thickness is ______________m³. (rounded-off to two decimal places)

Answer: (4.40 to 5.50)

50. At a particular temperature, the vapour pressure of benzene and toluene are 4 atm and 1.2 atm, respectively. The composition of the liquid at equilibrium is 0.5 moles of benzene and 0.5 moles of toluene. Assuming ideal gas and ideal solution, the equilibrium vapour phase mole fraction of benzene is ________ . (rounded-off to two decimal places)

Answer: (0.72 to 0.80)

51. Saturated steam at 0.7 atm and 90°C condenses on a vertical pipe of 2 cm outside diameter and 40 cm length. The average condensation heat transfer coefficient on the tube is 12000 W/m²K. The outside surface temperature of the pipe is maintained constant at 85°C. The enthalpy values for saturated steam and condensate are 2660 kJ/kg and 375 kJ/kg, respectively. The rate of steam condensation is ____ kg/h. (rounded-off to two decimal places)

Answer: (2.10 to 2.60)

52. Oil is being transported between two reservoirs with the help of three parallel pipes at steady state. The diameters of these pipes are 2 cm, 3 cm and 4 cm, respectively. The pipes are equal in length and the flow is laminar. The discharge through the 4 cm diameter pipe is 50 liters/s. The discharge through the 2 cm diameter pipe is _____ liters/s. (rounded-off to two decimal places)

Answer: (3.00 to 3.20)

53. A driller finds an oil reservoir with a gas cap starting at a depth of 1000 m from the surface. The gas-oil contact was found at 1100 m depth and water-oil contact was found at 1300 m depth. The water pressure in the aquifer below the oil zone varies with depth from the surface (h, in meters) as, P = h × 10⁴ Pa. The density of the oil is 900 kg/m³ and that of the gas is 5 kg/m³ at the reservoir condition. The minimum density of the mud needed to stop the gas kick when the driller reaches at the top of the gas cap is _____kg/m³. (rounded-off to two decimal places. Use g = 9.81 m/s²)

Answer: (1115.00 to 1160.00)

54. The viscosity, μ (in Pa.s) of a power law fluid as a function of shear rate, 𝛾̇ (in s^-1) is given by the following relation:

This power law fluid lies between two infinitely large horizontal parallel plates separated by a distance (h) of 10^-3 m. The top plate is moving horizontally at a velocity (v) of 10^-3 m/s and the bottom plate is held stationary. Assuming laminar flow and neglecting gravity, the absolute value of steady-state shear stress acting on the bottom plate is ______ Pa. (rounded-off to two decimal places)

Answer: (0.49 to 0.51)

55. A heterogeneous rectangular rock of cross-sectional area 1 m² perpendicular to the flow is being flooded by water to measure the effective permeability from cross-section AA’ to cross-section CC’.

The pressure at the cross-sections AA’, BB’, and CC’ is 2 bar, 1.5 bar, and 1 bar, respectively. The permeability in mili-Darcy and lengths AB and BC in meters are given in the figure. The effective permeability of the rock from AA’ to CC’ is ______mD.
(rounded-off to two decimal places)

Answer: (2.00 to 2.50)

GATE Exam 2018 Metallurgical Engineering (MT) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

(A) (i), (ii), (iii), (iv)

(B) (ii), (i), (iv), (iii)

(D) (iv), (iii), (ii), (i)

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Metallurgical Engineering

Q. 1 – Q. 25 carry one mark each.

1. For a laminar flow of a liquid metal over a flat plate, the thicknesses of the velocity and thermal boundary layers are δv and δt respectively. Kinematic viscosity (viscosity/density) of liquid metal is significantly lower than its thermal diffusivity
[thermal conductivity / (density × specific heat)]. Based on this information, pick the correct option.

(Note: The temperature of the liquid metal is different from that of the plate).

(A) δ_v < δ_t

(B) δ_v > δ_t

(D) Information insufficient

Answer: (A)

2. What is the most-abundant anion in a 2CaO.SiO₂ melt?

(A) (SiO₄)^4–

(B) (Si₂O₇)^6–

(D) (Si₄O₁₄)^10–

Answer: (A)

3. Analysis of a flow phenomenon in a system requires the following variables:

i. Pressure [M L^–1 T^–2]

ii. Velocity of the fluid [L T ^–1]

iii. Size of the system [L]

iv. Density of the fluid [M L^–3]

v. Viscosity of the fluid [M L^–1 T ^–1]

According to Buckingham Pi theorem (dimensional analysis) what is the number of independent DIMENSIONLESS variables needed to describe this system?

(A) 2

(B) 3

(D) 5

Answer: (A)

4. In froth flotation, the primary purpose of adding collectors is to:

(A) make the surface of the mineral hydrophobic.

(B) make the surface of the mineral hydrophilic.

(D) adjust the pH.

Answer: (A)

5. A rrange the following in the correct sequence of operations in an integrated steel plant:

i. Basic Oxygen Furnace (BOF)

ii. Blast Furnace (BF)

iii. Ruhrstahl Heraeus Degassing Process (RH)

iv. Ladle Furnace Process (LF)

(A) BOF→BF→LF→RH

(B) BF→LF→BOF→RH

(D) BF→BOF→LF→RH

Answer: (D)

6. During decarburization in a steel bath at 1550°C, the compositions of dissolved C (wt.%C) and dissolved O (wt.%O) follow the relation:

(wt.%C)(wt.%O) = K

When the partial pressure of CO (𝑝_𝐶𝑂) is 1 atm, K = 0.002. If 𝑝_𝐶𝑂 = 0.1 atm, what is the value of K, at the same temperature?
Note: Assume Henry’s law is applicable.

(A) 0.06

(B) 0.002

(D) 0.0002

Answer: (D)

7. During upset forging, and considering friction, which of the following profiles represents the axial compressive stress?

Note: In these profiles, the absolute value of the axial compressive stress is plotted on the y-axis.

(A) P

(B) Q

(D) S

Answer: (A)

8. Consider the following engineering components:

P. Gas turbine blades

Q. Tungsten-based heavy alloy penetrators

R. Self-lubricating bearings

S. Engine block of an automobile

Which of the following two components are produced by powder metallurgy?

(A) P & Q

(B) Q & R

(D) P & S

Answer: (B)

9. Which of the following materials are protected by passivation (i.e., formation of a thin adherent film on the surface) from corrosion?

P. Aluminium alloys

Q. Mild steel

R. Stainless steel

S. Silver

(A) P & Q

(B) Q & R

(D) P & R

Answer: (D)

10. The c/a ratio of Zn (hcp) is 1.856. Slip at room temperature occurs most easily on which of the following slip systems in Zn:

Note: In hcp metals, the ideal c/a ratio is 1.633.

Answer: (C)

11. At equilibrium, the maximum number of phases in a three-component system at CONSTANT PRESSURE is:

(A) 1

(B) 2

(D) 4

Answer: (D)

12. For a single phase system with K components, the exact differential of Gibbs free energy is given as :

Which one of the following can be derived from the above expression as a Maxwell’s relation?

Answer: (A)

13. For intrinsic Si at room temperature, the electron concentration = the hole concentration = 1 × 10¹⁶ m^–3, and the electron and hole mobilities are 0.1 and 0.2 m². V^–1. s^–1 respectively. What is the room temperature electrical conductivity?

The charge of an electron is 1.6 × 10⁻¹⁹C.

(A) 0 (Ω.m)^–1

(B) 1.6 × 10^–4 (Ω.m)^–1

(D) 4.8 × 10^–4 (Ω.m)^–1

Answer: (D)

14. To minimize refractory loss during BOF steel-making, slag is supersaturated with which of the following:

(A) Al₂O₃

(B) Fe₂O₃

(D) MgO

Answer: (D)

15. Which of the following welding processes is NOT suitable for joining thin metal sheets?

(A) Gas Metal Arc Welding

(B) Electro Slag Welding

(D) Laser Beam Welding

Answer: (B)

16. Which of the following categories of materials is suitable as a filler for brazing of steel sheets?

(A) Epoxy resins

(B) Near-eutectic alloys

(D) Large freezing range alloys

Answer: (B)

17. Arrange the following processes in INCREASING magnitude of surface roughness of the casting.

P. Investment casting

Q. Permanent mould casting

R. Pressure die casting

S. Sand casting

(A) R < S < Q < P

(B) P < S < Q < R

(D) Q < P < R < S

Answer: (B)

18. In a Jominy end-quench test of the eutectoid plain-carbon steel, which of the following represents the sequence of microstructures observed from the quenched end of the specimen?

(A) Fine Pearlite, Coarse Pearlite, Martensite and Pearlite, Martensite

(B) Martensite, Martensite and Pearlite, Fine Pearlite, Coarse Pearlite

(D) Martensite, Martensite and Pearlite, Coarse Pearlite, Fine Pearlite

Answer: (B)

19. A long oil pipeline made of steel is suspected to have developed a scale on the inner surface due to corrosion. Which of the following non-destructive techniques is the most suitable for detecting and quantifying such a defect?

(A) Dye penetrant test

(B) Magnetic particle inspection

(D) Acoustic emission

Answer: (C)

20. A steel is plastically worked in the temperature range below the nose of the TTT curve and above M_s, followed by quenching to produce fine martensite. What is this process called?

(A) Martempering

(B) Ausforming

(D) Normalizing

Answer: (B)

21. What is the requirement for equilibrium at a triple junction as shown in the schematic, with γ₁₂, γ₂₃ and γ₁₃ as grain boundary tensions and θ₁, θ₂ and θ₃ as dihedral angles?

Answer: (B)

22. In the A-rich end of the A-B binary eutectic phase diagram (shown below), the solidus and liquidus are straight lines.

The freezing range of the alloy with 16% B is _________ (in °C to one decimal place)

Answer: (95 to 105)

23. A vector field is given as follows:

The divergence of this field evaluated at (𝑥, 𝑦) = (2, 2) is _______________ .

Answer: (-0.1 to 0.1)

24. A plate of thickness h = 120 mm is cold rolled in a mill with a roll diameter of 200 mm. If the coefficient of friction μ is 0.1, the maximum possible reduction Δh in a single pass is ________ (in mm to one decimal place)

Answer: (0.9 to 1.1)

25. A copper-aluminium diffusion couple develops a certain concentration profile after an isothermal treatment at 600°C for 10 hours. The time required to achieve the same concentration profile at 500°C is _________ (in hours to 1 decimal place)

Given: The interdiffusion coefficient for copper in aluminium at 500°C and 600°C are 4 × 10^–14 ms^–1 and 8 × 10^–13 m² s^–1.

Answer: (180 to 220)

Q. 26 – Q. 55 carry two marks each.

26. T he molar free energy (J mol^–1) of a liquid solution of a binary A-B alloy as a function of temperature ( T ) and composition (x, the mole fraction of B) is given by:

where are the molar free energies of pure liquid A and pure liquid B. What is the excess molar free energy, G^{XS, L} , for an alloy with 𝑥 = 0.5 at 𝑇 = 1000 K?

Given: Gas constant R = 8.314 J K^–1 mol^–1

(A) 1000 J mol^–1

(B) –2000 J mol^–1

(D) –5763 J mol^–1

Answer: (A)

27. Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Assertion [A]: For a material exhibiting Coble creep, a reduction in grain size results in a significant increase in creep rate

Reason [R]: Grain boundaries act as a barrier to motion of dislocations

(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)

28. Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Assertion [A]: Refractory BCC metals like W and Mo are less ductile than FCC metals like Ni and Pt at room temperature

Reason [R]: BCC metals have fewer independent slip systems than FCC metals

(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: (D)

29. A glass fibre of 5 micron diameter is subjected to a tensile stress of 20 MPa. The surface energy and elastic modulus of this material are 0.3 Jm^–2 and 70 GPa, respectively. Pick the correct answer based on the information provided above:

Note: The glass fibre contains a population of flaws of different lengths.

(A) The fibre will undergo brittle fracture

(B) The fibre will undergo plastic deformation, but not fracture

(D) The fibre will undergo buckling

Answer: (C)

30.

Two equal and opposite point charges + Q and –Q are located as shown in the figure above. A surface integral, 𝐹_𝑖 is defined on surface 𝑆_𝑖 of a sphere of radius 𝑟_𝑖 as follows:

where is the electric field, and is the unit normal to the surface of integration.

If 𝑟₁: 𝑟₂: 𝑟₃ are in the ratio 1: 2: 5, use the Gauss divergence theorem to determine the ratio 𝐹₁: 𝐹₂: 𝐹₃ .

(A) 1 : 2 : 5

(B) 5 : 2 : 1

(D) 1 : 1 : 0

Answer: (C)

31. Match the four tensile stress-strain curves (P,Q, R, S) with the materials listed in the box:

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

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

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

Answer: (C)

32. Match the metal in Group 1 with the appropriate extractive process in Group 2

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

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

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

Answer: (C)

33. Fe is produced in a reactor using pure Fe₂O₃, C and O₂. For every mole of Fe produced, 2.38 moles of C is used. The exit gas from the reactor contains CO and CO₂ in the molar ratio of 1:1. How many moles of O₂ is consumed for every mole of Fe produced?

(A) 1.035

(B) 2.072

(D) 4.147

Answer: (A)

34. What is the voltage required to electrolytically refine impure copper of activity 𝑎_𝐶𝑢 = 0.9

(Raoultian standard state) to pure copper at 300 K

Given: Gas constant R = 8.314 J mol^–1 K^–1, and Faraday’s constant F = 96500 C mol^–1.

(A) 1.36 mV

(B) 2.72 mV

(D) 5.44 mV

Answer: (A)

35. Consider the following Ordinary Differential Equation:

In a domain 0 ≤ 𝑥 ≤ 𝑡, with boundary conditions 𝑐(0) = 0.5 and 𝑐(𝑡) = 1.0, pick the appropriate choice for 𝑐(𝑥) from the following options:

(A) P

(B) Q

(D) S

Answer: (B)

36. Match the manufacturing processes in Group 1, with the types of cracks in Group 2:

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

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

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

Answer: (C or D)

37. Consider a dilute substitutional solid solution of X in a metal A. The powder diffraction pattern of this alloy reveals that all the peaks have shifted to the left when compared to those for pure A (with no splitting of peaks). If such a solute interacts and segregates to an edge dislocation, which of the following positions around the dislocation will it preferentially occupy?

(A) P

(B) Q

(D) S

Answer: (D)

38. A classroom of 20 students can be categorized on the basis of blood-types: 5 students each with “A”, “B”, “AB”, and “O” blood-types. If four students are selected at random from this class, what is the probability that each student has a different blood-type?

(A) 0.2500

(B) 0.1289

(D) 0.0156

Answer: (B)

39. If the solid-liquid interfacial energy increases by 10%, the energy barrier for homogeneous nucleation of a spherical solid from the liquid, will change by:

(A) 21%

(B) 33%

(D) 46%

Answer: (B)

40. Consider the following stress state imposed on a material:

If the material responds elastically with a volumetric strain Δ = 3.5 × 10^–4, what is its bulk modulus?

(A) 150 GPa

(B) 350 GPa

(D) 400 GPa

Answer: (C)

41. A continuous and aligned carbon-fiber composite consists of 25 vol. % of fibers in an epoxy matrix. The Young’s modulus of fiber and matrix, respectively are E_f = 250 GPa and E_m = 2.5 GPa.

If the composite is subjected to longitudinal loading (iso-strain condition and assuming elastic response), the fraction of load borne by the reinforcement is ________ (to two decimal places)

Answer: (0.96 to 0.98)

42. Pure iron transforms from body centered cubic (BCC) to face centered cubic (FCC) crystal structure at 912 °C. If the lattice parameter of the BCC phase is 0.293 nm and that of the FCC phase is 0.363 nm, the associated volume change is _______ (in % to one decimal place)

Answer: (-5.5 to -4.5)

43. A s shown in schematic below, an alloy is cast as a rectangular slab between two thick mould walls that differ in their thermal conductivities. Shrinkage defects are found at a distance L₁ from Mould-1 with thermal conductivity 𝑘₁ and distance L₂ from Mould-2 with thermal conductivity 𝑘₂. If the ratio L₁:L₂ = 3:2, and assuming 1-D heat transfer, the ratio (k₁/k₂) is _______ (to two decimal places)

Answer: (2.2 to 2.3)

44. The temperature profile (T in Kelvin) of an arc weld across its width is given as 𝑇 = 2000 exp(−0.3𝑥²) where 𝑥 (in mm) is the distance from the weld centre. The melting point of the base material is 1500 K. The width of the fusion zone is _______ (in mm to two decimal places).

Answer: (1.9 to 2.0)

45. The terminal velocity (𝑣) of a spherical inclusion of diameter D = 50 micrometers rising in liquid steel is __________ (in mm s^–1 to two decimal places)

Assume Stokes law; i.e., drag force 𝐹𝑑 = 3𝜋𝜇𝐷𝑣, where 𝜇 is the viscosity of steel.

Given: Density of liquid steel = 7900 kg m^–3; Viscosity of liquid steel = 0.0079 Pa s;

Density of the inclusion = 2500 kg m^–3; Acceleration due to gravity = 9.8 m s^–2

Answer: (0.9 to 1.0)

46. A single crystal of aluminium is subjected to 10 MPa tensile stress along the [321] crystallographic direction. The resolved shear stress on the slip system is ______ (in MPa to two decimal places)

47. If the net magnetic moment of an Fe atom in BCC structure is 2 𝜇_𝐵, then the saturation magnetization of Fe is ___________ (kA m^–1 to one decimal place)

Given: 𝜇_𝐵 = 9.273 × 10^–24 A m²; Lattice parameter of BCC iron is 0.287 nm

Note: kA is kiloAmperes

Answer: (1500 to 1600)

48. If 2 moles of Au and 3 moles of Ag are mixed to form a single-phase ideal solid solution, the total entropy of mixing is __________ (on J K^–1 to one decimal place )

Given: Gas constant R = 8.314 J K^–1 mol^–1

Answer: (24.9 to 29.0)

49. A spherical liquid metal droplet of diameter 1 mm is solidified in a stream of gas at 300 K. Assuming that the metal droplet remains at its melting point of 900 K and neglecting radiative losses, the time to complete the solidification is __________ (in seconds to one decimal place).

Given: The enthalpy of fusion for the metal is 4000 kJ kg^–1; The gas-droplet convective heat transfer coefficient is 200 W m^–2 K^–1; Density of liquid metal is 2700 kg m^–3.

Answer: (14.9 to 15.1)

50. At a temperature of 710 K, the vapour pressure of pure liquid Zn is given by:

pzn (Xzn = 1.0) = 3.6 × 10^–4 atm.

The Raoultian activity coefficient (𝛾_𝑍𝑛 ) of Zn in Zn-Cd alloy liquid at 710 K is approximated by:

ln(𝛾_𝑍𝑛 ) = 0.875 (1 – X_zn)²

The ratio for a liquid alloy with 𝑋_𝑧𝑛 = 0.7 is __________ (to two decimal places).

Answer: (0.74 to 0.78)

51. For the reaction: 4Ag(s, pure) + O₂(g) ⟶ 2Ag₂O(s, pure), the standard enthalpy change, Δ𝐻⁰ = − 61080 J, and the standard entropy change, Δ𝑆⁰ = − 132.22 J K⁻¹, in the temperature range from 298 K to 500 K. The temperature above which Ag2O decomposes in an atmosphere containing oxygen at a partial pressure 𝑝_𝑂2 = 0.3 atm is __________ (in K to one decimal place).

Given: Gas constant R = 8.314 J K⁻¹ mol⁻¹

Answer: (427 to 432)

52. In a powder diffraction experiment on BCC iron, the first peak occurs at 2𝜃 = 68.7°. The wavelength of X-rays is _________ (in nm to three decimal places).

Given: The lattice parameter of iron = 0.287 nm

Answer: (0.225 to 0.235)

53. A 1 mol piece of copper at 400 K is brought in contact with another 1 mol piece of copper at 300 K, and allowed to reach thermal equilibrium. The entropy change for this process is __________ (in J K⁻¹ to three decimal places)

Given: Specific heat capacity of copper (between 250 K and 500 K) is 22.6 J K⁻¹mol⁻¹.

Assume that the system containing the two pieces of copper remains isolated during this process.

Answer: (0.450 to 0.480)

54. Using the trapezoidal rule with two equal intervals (n = 2, Δ𝑥 = 1), the definite integral ______________ (to two decimal places).

Answer: (1.95 to 2.05)

55. The ideal plastic work involved in extruding a cylindrical billet of length 100 mm, from an initial diameter of 20 mm to a final diameter of 16 mm is __________ (in J to one decimal place).

The flow stress in compression is 40 MPa, and remains constant throughout the process.

Answer: (555.5 to 565.5)

GATE Exam 2018 Mining Engineering (MN) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-3

1. “ From where are they bringing their books? ________ bringing _______ books from _____.”

The words that best fill the blanks in the above sentence are

(A) Their, they’re, there

(B) They’re, their, there

(D) They’re, there, there

Answer: (B)

2. A _________ investigation can sometimes yield new facts, but typically organized ones are more successful.”

The word that best fills the blank in the above sentence is

(A) meandering

(B) timely

(D) systematic

Answer: (A)

3. The area of a square is 𝑑. What is the area of the circle which has the diagonal of the square as its diameter?

(A) πd

(B) πd²

Answer: (D)

4. What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of 7 in ach case?

(A) 3047

(B) 6047

(D) 63847

Answer: (C)

5. What is the missing number in the following sequence?

2, 12, 60, 240, 720, 1440, _____, 0

(A) 2880

(B) 1440

(D) 0

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen in the town and Rs 1000 to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only 8/9th of the eligible men and 2/3rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

(A) 1,50,000

(B) 2,00,000

(D) 1,51,000

Answer: (B)

7. If pqr ≠ 0 and what is the value of the product 𝑥𝑦𝑧?

(A) –1

(B) 1/pqr

(D) pqr

Answer: (C)

8. In a party, 60% of the invited guests are male and 40% are female. If 80% of the invited guests attended the party and if all the invited female guests attended, what would be the ratio of males to females among the attendees in the party?

(A) 2:3

(B) 1:1

(D) 2:1

Answer: (B)

9. In the figure below, ∠DEC + ∠BFC is equal to ____________.

(A) ∠𝐵𝐶𝐷 − ∠𝐵𝐴𝐷

(B) ∠𝐵𝐴𝐷 + ∠𝐵𝐶𝐹

(D) ∠𝐶𝐵𝐴 + ∠𝐴𝐷𝐶

Answer: (A)

10. A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

(A) Three green faces and four red faces.

(B) Four green faces and three red faces.

(D) Six green faces and one red face.

Answer: (C)

Mining Engineering

Q. 1 – Q. 25 carry one mark each.

Answer: (C)

2. The values of x satisfying the following condition are

(A) 6, 4

(B) 4, 9

(D) 3,7

Answer: (D)

3. An azimuth of 330° corresponds to a quadrant bearing of

(A) W60°N

(B) N30°W

(D) S30°E

Answer: (B)

4. Tri-cone drill bit is a type of

(A) cross bit

(B) button bit

(D) button drag bit

Answer: (C)

5. Exposure of weak roof in junctions of a development district in a coal mine can be decreased by

(A) increasing dimension of panel barrier

(B) stitching side walls

(D) staggering the junctions

Answer: (D)

6. The property that CANNOT be determined from uniaxial compressive strength test of a rock sample fitted with strain gauges is

(A) cohesion

(B) Poisson’s ratio

(D) dilation

Answer: (A)

7. The radial stress concentration around a long circular tunnel excavated in rock is given by the curve

(A) m

(B) n

(D) p

Answer: (D)

8. Ward-Leonard system is provided in the winding system in order to restrict

(A) over-winding of the cage

(B) deceleration of the cage

(D) over-speeding of the cage

Answer: (D)

9. The equipment NOT related to extraction of coal from longwall face operation is

(A) AFC

(B) road header

(D) DERD shearer

Answer: (B)

10. The correct figure depicting the extraction of contiguous seams in bord and pillar working is indicated by

Answer: (C)

11. The significance of ‘potentially explosive mixture’ in Coward flammability diagram is –

(A) leakage of fresh air may lead to explosive condition for the mixture

(B) leakage of firedamp may lead to explosive condition for the mixture

(D) introduction of a source of ignition may result in explosion of the mixture

Answer: (A)

12. Considering ‘I’ as ‘intake’ and ‘R’ as ‘return’, the ventilation symbol for the shaft-bottom air-lock in a coal mine is

Answer: (A)

13. From a coal seam of a mine 1000 tonnes of coal is produced per day. The seam has inflammable gas emission rate of 14000 m³ per day. Percentage of inflammable gas in general body of air is 0.14. The gassiness of the seam is

(A) Degree IV

(B) Degree III

(D) Degree I

Answer: (B)

14. The temperature profiles and the plume patterns that are most likely to result are given in the figures. The dotted line represents ‘adiabatic lapse rate’ and the bold line represents ‘environmental lapse rate’. The WRONG combination is

Answer: (C)

15. The inventory pattern shown does NOT represent the following.

(A) Inventory is replenished instantaneously

(B) Demand decreases with time

(D) Demand is uniform

Answer: (B)

16. The figure depicts a transportation problem along with the solution. The correct statement is

(A) unbalanced problem, optimal solution

(B) unbalanced problem, sub-optimal solution

(D) balanced problem, sub-optimal solution

Answer: (C)

17. The degree of the differential equation is ______________.

Answer: (1.0 to 1.0)

18. The slope of the line connecting the points (20, 6) and (40, 8) is ______________.

Answer: (0.1 to 0.1)

19. Two contours of RL 60 m and 70 m are separated by 34 m measured along dip of the seam. The dip of the seam in degree is ________________.

Answer: (16.5 to 17.5)

20. The RL of the initial station is 200 m. If ΣBS = 1.54m and ΣFS = 0.45 m, then the RL of the last station in m is ________________.

Answer: (201.09 to 201.09)

21. For the conveyor belt drive shown, the tension on the tight side (T1) is double that of the slack side. The coefficient of friction between belt and drum is 0.21. The minimum angle of lap (in degree) to avoid slippage of the belt is ________________.

Answer: (185.0 to 195.0)

22. In a bord and pillar development district, 6 headings driven along the strike direction are surrounded by panel barriers on the dip and rise sides. The maximum possible number of faces for the panel is ___________________.

Answer: (16.0 to 16.0)

23. A roadway in a mine, a single light source as shown, emits light uniformly in all directions. The floor level illumination at station A is 20 lux. The floor level illumination at a point B in lux is ______________.

Answer: (8.5 to 9.5)

24. A system of two identical components connected in series has reliability of 0.25. The reliability of each component is _______________.

Answer: (0.5 to0.5)

25. The operational status of an HEMM in a shift is shown in the diagram. The availability of the machine in % is _____________________.

Answer: (56.0 to 56.5)

Q. 26 – Q. 55 carry two marks each.

26. If c is a constant, the solution of the differential equation is

Answer: (D)

27. Match the following blasting elements with the corresponding initiators.

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

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

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

Answer: (B)

28. The following plot is developed for a rock type after a series of triaxial tests. The uniaxial compressive strength and tensile strength of the rock type, respectively, in MPa, are

(A) 30, 5

(B) 30, 6

(D) 24, 5

Answer: (A)

29. Match the following in the context of environmental management.

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

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

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

Answer: (D)

30. A panel in coal mine produces 400 tonne per day. The number of persons employed in each of the three shifts is 110, 130 and 120. As per CMR, the minimum quantity of air that needs to be circulated at the last ventilation connection of the panel in m³/min is

(A) 780

(B) 900

(D) 2400

Answer: (C)

31. A right conical iron ore stack on level ground of height 10 m has 60% Fe. The height of the conical stack is extended up to 20 m using iron ore of 50% Fe. The angle of repose of iron ore is 38°. The mean grade of the final stack in % Fe is ___________________.

Answer: (51.0 to 52.0)

32. The feasible region of a linear programming problem is shown in the figure. The maximum value of the objective function Z = 4X + 3Y is ____________________.

Answer: (74.0 to 74.0)

33. Cash flow of a project of duration 4 years is shown. The uniform income ‘R’, in Rs. crores, at the end of 2nd, 3rd and 4th years for an internal rate of return of 10% is ______________.

Answer: (4.4 to 4.5)

34. The grade values of alumina at three sample locations (A, B and C) in a bauxite deposit are as shown. Using the ‘inverse distance’ method, the computed grade in % alumina at location ‘Z’ is ___________________.

Answer: (36.0 to 37.5)

35. Economic feasibility of two methods is examined for meeting a targeted mine production. On a yearly basis, the following cost parameters (Rs in crores) are applicable for these methods.

The annual rate of production, ‘X’ in million tonnes for which both the methods will yield the same operating cost is ___________________.

Answer: (5.0 to 5.0)

36. A person standing 50 m away from an HEMM experiences 90 dB sound pressure level. If the person moves to a new location that is 70 m away from the HEMM, the sound pressure level experienced by the person, in dB, becomes _________________.

Answer: (86.75 to 87.25)

37. A portion of a ventilation system has two splits as shown. Split ‘A’ has a resistance of 0.2 Ns²/m⁸ and a regulator of size 2.0 m². The resistance of split ‘B’ in Ns²/m⁸ is ________

Answer: (0.24 to 0.28)

38. Air enters a bord and pillar panel at 10 ppm CO and 20.78% O₂. The air at the panel return has 80 ppm CO and 20.52% O₂. The ‘Graham’s ratio’ for the status of fire in the panel in % is __________________.

Answer: (2.65 to 2.75)

39. In a sublevel stope, 20 m high excavation is made with ring drilling in a 6 m wide orebody. In an effective shift time of 6 hrs, three rings are blasted resulting in 9 m extraction length. LHDs of 5.0 m³ bucket capacity and cycle time of 5 minutes are used for ore transportation. The number of LHDs required for this operation is _________________.

Answer: (3.0 to 3.0)

40. A coal seam lying at a depth of 200 m is developed by bord and pillar method. Pillars are 30 m centre to centre with a gallery width of 4 m. Unit weight of the overlying strata is 28 kN/m³. If the pillar strength is 9.32 MPa, the factor of safety of pillar is ____________.

Answer: (1.2 to 1.3)

41. Following information about a longwall retreating panel is given.

Panel length = 1800 m

Face length = 150 m

Depth of web = 0.6 m

Shearer travels at a speed of 1.5 m/min along the face.

Each cutting cycle requires a non-operational time of 2 h 20 min. The panel is fully extractable. The number of working days required to extract the panel is ______________.

Answer: (500.0 to 500.0)

42. In a direct rope haulage operating along a 1500 m long incline, 180 tonne of coal is hauled in 7 hours. The average rope speed is 7.5 km/h. The set changing time for the tubs is 2 minutes each at the top and bottom of the incline. If the tub capacity is 1.0 tonne, the number of tubs in the set is __________________.

Answer: (12.0 to 12.0)

43. An SDL of 1.0 tonne capacity operates with a cycle time of 6 minutes. The dimension of the face is 4 m x 3 m. Five blasts are conducted per shift with an average pull of 1.2 m. If the density of blasted coal is 0.8 tonne/m³, the time required by the SDL in the shift to lift all the prepared coal in hours is _________________.

Answer: (5.6 to 5.8)

44. A force diagram is shown below. Considering clockwise moments to be positive, the resultant moment about A in Nm is _________________.

Answer: (-400.0 to -400.0)

45. The experiment to determine permeability of a soil sample is illustrated below. The crosssectional area of the sample is 20.0 cm². The permeability of the soil sample in cm/s is ______________.

Answer: (0.02 to 0.02)

46. In underground face blasting, the pull is found to be 10% less than the drillhole length. The headings of 3.6 m width are supported by prop density of 1.44/m². The hole length is 1.5 m, and 6 rounds of blasting are done in the panel per shift. The number of props to be erected in a shift is ____________________.

Answer: (41.0 to 43.0)

47. T he immediate roof of a mine is supported by bolts of length 1.5 m, arranged in 1.2 m x 1.2 m grid pattern. If the unit weight of roof rock is 2.25 tonne/m³ and load carrying capacity of each bolt is 7.5 tonne, the factor of safety of the support system is _______________.

Answer: (1.4 to 1.6)

48. In a level terrain, a vertical orebody of 20 m uniform width is worked by surface mining method. The density of the ore is 2.5 tonne/m³. The ultimate pit has a depth of 60 m, width of 20 m at pit bottom, and a pit slope of 45°. The overall stripping ratio for this condition in m³/tonne is ____________________.

Answer: (1.2 to 1.2)

49. A 20 m long steel tape used for survey is found to be short by 10 cm. If the area measured with the steel tape is 5000 m², the actual area in m² is __________________.

Answer: (4945.0 to 4955.0)

50. The following figure shows the designed blast pattern of a bench. The explosive column is charged at 18 kg/m. If the unit weight of the blasted material is 2.5 tonne/m³, the powder factor for the blast in tonne/kg is _______________.

Answer: (2.00 to 2.15)

51. Two points on the equator have longitudes 55°E and 25°W. Considering radius of earth as 6400 km, the distance between the two points in km is ________________.

Answer: (8930.0 to 8940.0)

52. Sum of the series 5, 10, 15, ……….., 500 is __________________.

Answer: (25250.0 to 25250.0)

53. The sample standard deviation for the following set of observations is _______________. 40, 45, 50 and 55

Answer: (6.4 to 6.5)

54. For the given function f (x, y) = (3 + x) (4 + y), the value of and y = 1 is _________.

Answer: (10.0 to 10.0)

55. Given y = x² + x + 6, the value of is ________________.

Answer: (0.40 to 0.45)