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GATE Exam 2021 Mining Engineering (MN) Question Paper With Answer Key

June 8, 2023June 15, 2022 by suresh84

GATE-2021

MN-Mining Engineering

GA-General Aptitude

Q 1 – Q5 Carry one mark each. ( for each wrong answer: −1/3)

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6-Q. 10 carry two marks (for each wrong answer: −2/3)

6. On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 18 units North of Point P.

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

7. The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play, On the other hand, I find it strange that many public speakers think key can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

10. In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Mining Engineering (MN)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Tricone roller bit is used with

(A) down-the-hole hammer.

(B) Jack hammer.

(D) rotary drill.

Answer: (D)

2. Resuing method of mining is practiced for

(A) thick vein deposit.

(B) massive shallow deposit.

(D) massive deep-seated deposit.

Answer: (C)

3. The equipment used for both drop cut and terrace cut in surface mining is

(A) surface miner.

(B) shovel.

(D) bucket wheel excavator.

Answer: (D)

4. Surface miner does NOT have a

(A) differential gear for turning.

(B) tensioning arrangement for crawler.

(D) pick cooling system.

Answer: (A)

5. Induced blasting enhances production in

(A) sublevel stoping.

(B) block caving.

(D) shrinkage stoping.

Answer: (B)

6. The measures of dispersion of a dataset are

(A) standard deviation, range and mode.

(B) standard deviation, range and interquartile range.

(D) interquartile range, median and mode.

Answer: (B)

7. NONEL is used as down-the-hole initiator to

(A) avoid generation of air overpressure.

(B) provide precise delay.

(D) reduce ground vibration.

Answer: (C)

8. The vectors act in a plane as shown below. The magnitude of the vector is

(A) zero.

(B) half to the area bounded by the vectors

(D) twice the area bounded by the vectors

Answer: (D)

9. As per MMDR Act 1957, for the allocation of lease of minor minerals

(A) the State Government is authorised to give the permit.

(B) the Central Government is authorised to give the permit.

(D) the Central Government is authorised to give permit but with the consent of State Government.

Answer: (A)

10. In photogrammetry, the ‘Tilt of a photograph’ refers to the angle between the

(A) lines joining the opposite fiducial marks of a photograph.

(B) normal to the plane of photograph and optical axis.

(D) vertical and optical axis of the camera.

Answer: (D)

11. The hydraulic sand stowing pipeline layout should be such that

(A) the geometric profile must coincide with the hydraulic gradient line.

(B) the hydraulic profile should always be below the hydraulic gradient line.

(D) the geometric profile should always be above the hydraulic gradient line.

Answer: (B)

12. For a “positive definite” square matrix, the TRUE statement is

(A) the matrix is singular.

(B) all the eigen values of the matrix are greater than zero.

(D) some of the eigen values can be less than zero.

Answer: (B)

13. The standard normal distribution is a

(A) non-parametric distribution.

(B) single parameter distribution.

(D) three-parameter distribution.

Answer: (C)

14. Variance of the sum of two statistically independent random variables X and Y, σ²_X+Y, is

Answer: (A)

15. The difference between depreciation and amortization allowances in tax calculation is that

(A) depreciation is for a tangible asset applicable on its declared life; whereas amortization is for an intangible asset applicable on a specified period.

(B) depreciation is for an intangible asset applicable on its declared life; whereas amortization is for a tangible asset applicable on a specified period.

(C) depreciation is for a tangible asset applicable on a specified period; whereas amortization is for an intangible asset applicable on its declared life.

(D) depreciation is for an intangible asset applicable on a specified period; whereas amortization is for a tangible asset applicable on its declared life.

Answer: (A)

16. Owning cost of a machine does NOT include

(A) purchase price.

(B) insurance.

(D) operating cost.

Answer: (D)

17. Folds are the structural features resulting from

(A) ductile deformation of earth crust.

(B) brittle deformation of earth crust.

(D) fracturing of earth crust.

Answer: (A)

18. The CORRECT curve showing the relationship between vertical stress on a coal pillar and extraction ratio of a bord and pillar panel in a horizontal seam is

(A) Curve A.

(B) Curve B.

(D) Curve D.

Answer: (C)

19. Given impeller diameter D, speed of rotation n and air density ρ, for geometrically similar fans, the fan pressure is proportional to

(A) nD²ρ.

(B) n²D²ρ.

(D) n³D⁵ρ.

Answer: (B)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. A coal sample having moisture content of 8.0% has unit weight 15.6 kN/m³. The dry unit weight of the sample, in kN/m³ is _____.

Answer: (14.00 to 15.00)

21. The value of the integral computed using Simpson’s 1/3 rule with 2 subintervals is_______.

[round off to 3 decimal places]

Answer: (5.000 to 5.200)

22. In the context of sound frequency analysis, the lower and upper frequencies of a 1/1 octave band are 710 Hz and 1420 Hz respectively. The corresponding centre frequency of the band in Hz, is_______. [round off to the nearest integer]

Answer: (999 to 1005)

23. In Battle Environmental Evaluation System (BEES) of Environmental Impact Assessment (EIA), “air pollution” has a Parameter Importance Unit (PIU) value of 52. The Environmental Quality (EQ) score of a project with respect to air pollution was 0.8 before the project implementation and it becomes 0.6 after the project implementation. The difference in the “Environmental Impact Unit (EIU)”, before and after the project implementation is______.

[round off to 2 decimal places]

Answer: (10.40 to 10.40)

24. A system consists of four components connected functionally in a parallel configuration. The reliability of the individual components is 0.40, 0.60, 0.50 and 0.40. The system reliability, is________. [round off to 3 decimal places]

Answer: (0.918 to 0.938)

25. A vehicle is moving at a speed of 12 m/s on a level road. It applies emergency brakes and starts to skid without rolling in a straight path. The deceleration of the vehicle is constant after braking and it comes to rest at a distance of 15 m. Assuming, g = 10 m/s², the coefficient of kinetic friction between the tyres and road is _______. [round off to 2 decimal places]

Answer: (0.45 to 0.50)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. In a bord and pillar panel six shuttle cars, each of 10 tonne capacity, are deployed to transport coal produced by two continuous miners to a belt conveyor. Each shuttle car on an average carries 80% of its rated capacity and makes 7 round trips in an hour. The belt conveyor has a capacity such that the effective material cross section area is of 0.09 m² and runs at a speed 1.1 m/s. The broken coal has a bulk density of 1.2 tonne/m³. The ratio between the production and the capacity of the belt conveyor, in percent is

(A) 65.46

(B) 71.42

(D) 82.46

Answer: (C)

27. With reference to the figure related to rock cutting by point attack tool, match the angle with corresponding name.

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

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

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

Answer: (A)

28. The pit bottom in a correlation survey is shown in the figure. Points C and D represent two suspended wires. The bearing of line CD is 286o00′00′′ and its length is 4.64 m. The angle CED is measured as 00o00′40′′. The length of line DE is 5.46 m. Considering the Weisbach triangle method, the bearing of the line CE is

(A) 286°00’47”

(B) 285°59’12.9″

(D) 285°00’47.1″

Answer: (B)

29. A dump truck moves up an incline of 50 with constant tractive force of 800 kN. The gross mass of the truck is 250 tonne and its rolling resistance is 545 kN. The acceleration due to gravity is 10 m²/s. The time required, in s, to reach a speed of 3.3 m/s from 1.0 m/s is

(A) 22.0

(B) 15.5

(D) 0.2

Answer: (B)

30. In a longwall panel, face is supported with shields of yield capacity 460 tonne per shield. The distance from the canopy tip to coal face is 0.15 m when the support is fully advanced. The depth of web is 0.60 m. The shields are set skin to skin at the face. Length of the canopy of the shield is 3.25 m and width 1.5 m. Setting capacity is 80% of the yield capacity. The setting resistance at the maximum and minimum span of the coal face, in tonne/m², respectively are

(A) 61.33 and 72.15.

(B) 63.72 and 75.48.

(D) 91.99 and 108.22.

Answer: (A)

31. A 10 ml sample of wastewater is diluted with water having no BOD, to fill a 300 ml BOD bottle. The initial DO of the diluted waste water is 9.0 mg/l. If the BOD₅ of the waste water sample is 60 mg/l, the final DO of the diluted waste water in mg/l, is

(A) 5.0

(B) 6.0

(D) 8.0

Answer: (C)

32. The Mohr circle of stress of a dry porous rock is shown in the figure. If the rock is fully saturated with a pore pressure p, then the Mohr circle takes the form of

Answer: (A)

33. The straight line shown depicts the failure criterion of a rock type. The values of stress at points A and B are as shown. The safety factor at the points A and B respectively are

(A) 1.175 and 0.755

(B) 1.324 and 0.851

(D) 0.755 and 1.175

Answer: (D)

34. Figure shown relates to the manufacture of roof bolts. With respect to the cost/revenue vs production level, match the appropriate trend line with corresponding description.

(A) (P)-(1); (R)-(3); (S)-(2).

(B) (P)-(2); (R)-(1); (S)-(3).

(D) (P)-(3); (R)-(1); (S)-(2).

Answer: (D)

35. The value of is

(A) 0

(B) b²/2

(D) b²

Answer: (B)

36. In order to check whether iron ore is supplied to the specification of 62% Fe, a steel company has conducted a hypothesis test with the null hypothesis as H0: μFe = 62% and alternative hypothesis Ha: μFe < 62%. A random sample of 5 observations reveal the following grade values of the lot, 58%, 56%, 60%, 64%, 62%. The t-test statistic for the hypothesis is

(A) – 3.000

(B) 1.414

(D) 3.000

Answer: (C)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks)

37. Production planning of a small quarry having 3 years of life is shown in the figure. The following information of revenue and cost data are available.

Selling price of ore = Rs. 1500/tonne

Ore mining cost = Rs. 500/tonne

Waste mining cost = Rs. 500/m³

Initial capital = Rs. 1000 million

Discount rate = 10 %

By neglecting depreciation, salvage value and corporate tax, the NPV of the mining project, in million Rs., is_______. [round off to 2 decimal places]

Answer: (35.50 to 38.30)

38. A triangular distributed load is applied on top of a beam as shown in the figure. The value of maximum bending moment in kN-m is______.

[round off to 2 decimal places]

Answer: (1.20 to 1.35)

39. For a dumpy level, the bubble tube has sensitivity of 40″ for one division. While taking a staff reading at a distance of 60 m, the bubble is out of centre by 2 divisions. The error in staff reading in mm is______. [round off to one decimal place]

Answer: (225 to 24.0)

40. On an old plan of scale 1:1000, leasehold area of a mine is now measured as 802 cm² using a planimeter. The plan is found to have shrunk, such that the original line of 10 cm is now measured as 9.8 cm on the plan. True lease hold mine area, in m², is _______. [round off to the nearest integer]

Answer: (83450 to 83550)

41. CO is released from a point source on a level ground at a rate of 25 g/s. The average wind speed is 5 m/s. The dispersion coefficients are 150 m and 200 m in horizontal and vertical directions, respectively, at a receiver station located on the ground along the downwind direction. Assuming the plume follows Gaussian dispersion model, the concentration of CO, in μg/m³, at the station is______.

[round off to 2 decimal places]

Answer: (50.00 to 55.00)

42. Assume that COVID-19 growth rate of number of infections per day (c) in a certain population is represented by the following differential equation.

Where, t stands for time in days. Time taken for the number of infections per day to double, in days, is______. [round off to the nearest integer]

Answer: (9 to 11)

43. Ore is hoisted from 620 m depth using a single skip of 7 tonne pay load. The skip winding system has constant acceleration/deceleration of 1 m/s² and a constant speed of 10 m/s. The skip loading time and unloading time are 120 s and 60 s, respectively. Considering the overall utilization of the skip as 70 %, the maximum daily capacity of the winding system, in tonne, is ______. [round off to the nearest integer]

Answer: (1250 to 1350)

44. In an analysis of fragmented blast muck, the mean fragment size is found to be 60 cm with uniformity index of 1.25. Considering Rosin-Ramler equation, the cumulative mass fraction, in percent, to pass the grizzly screen size of 100 cm is______. [round off to 2 decimal places]

Answer: (71.00 to 75.00)

45. A single-acting reciprocating ram pump, while running at 120 rpm, delivers water at a rate of 10 litres per second. Considering the ram diameter is 150 mm and stroke length is 300 mm, the volumetric efficiency of the pump, in percent is _______.

[round off to one decimal place]

Answer: (92.0 to 96.0)

46. In a sand stowing arrangement, the slurry has a sand concentration of 35% by volume. The specific gravity of sand grain is 2.6. The concentration of sand by weight, in percent, in the slurry is _____. [round off to one decimal place]

Answer: (57.00 to 59.80)

47. In a surface mine, third bench from the pit bottom is blasted, as shown in the figure. The width, height and slope angle of each bench are 8 m, 6 m, and 800, respectively. A fly rock is projected at an angle of 450 with the horizontal with initial velocity, v. If the acceleration due to gravity is 10 m/s² then the minimum velocity (v) in m/s required for the fly rock to reach just beyond toe of the pit slope is ______.

[round off to 2 decimal places]

Answer: (9.00 to 11.00)

48. Injury experience is studied in an underground coal mine with a random sample of 132 workers. The results of the study are tabulated below.

The odds ratio of experiencing an injury by the roof-bolter operators when compared to the loader operators is______. [round off to 2 decimal places]

Answer: (2.20 to 2.30)

49. A random variable X is defined by

The value of E(X²) is ______. [round off to one decimal place]

Answer: (6.0 to 6.0)

50. A project network consists of the following activities

If the project completion time is 30 days, then the value of ‘X’, in days, is_______.

[in integer]

Answer: (5 to 5)

51. Rate of fuel consumption f_c (litres per hour) of a truck varies with truck speed x, (kmph) as given below

The fuel price is Rs. 70 per litre. Other costs amount to Rs. 500 per hour. If the truck travels 100 km from a coal mine to a thermal plant, the speed of the truck, in kmph, that minimizes the total cost is_______. [round off to one decimal place]

Answer: (35.0 to 38.0)

52. A cement company has three factories which transport cement to four distribution centres. The daily production of each factory, the demand at each distribution centre, and the associated transportation cost per tonne from factory to distribution centre are given in the Table.

The initial basic feasible solution using the least-cost rule is _____. [in integer]

Answer: (112000 to 112000)

53. The grade-tonnage distribution for the ultimate pit of a mine is given below.

The mill cut-off grade is 0.5 % Cu. The annual mining capacity (ore + waste) is 4.5 million tonne and milling capacity is 1.0 million tonne. Excavation is planned in such a way that either of the mine or the mill runs at full capacity throughout. The planned life of the mine, in years, is _______. [round off to one decimal place]

Answer: (6.0 to 6.0)

54. A coal mine operating in three shifts produces 400 tonnes of coal per day with a face OMS of 1.0 from panel A, and 200 tonnes of coal with face OMS of 1.0 from panel B. The panel A and panel B are in parallel with resistance 0.6 Ns⁻²m⁻⁸ and 0.5 Ns⁻²m⁻⁸, respectively. If the panels are supplied with minimum permissible quantity as per CMR 2018, the requisite regulator resistance to meet the conditions in Ns⁻²m⁻⁸ [round off to 2 decimal places]

Answer: (1.80 to 2.00)

55. A set of three steel bars of equal cross-sectional area of 0.01 m² are loaded, as shown in the figure. The elastic modulus of steel is 200 GPa. The overall change of length of the complete set of bars, in mm, is_______. [round off to 3 decimal places]

Answer: (0.045 to 0.055)

GATE Exam 2021 Mechanical Engineering (ME-2) Question Paper With Answer Key

June 8, 2023June 15, 2022 by suresh84

GATE-2021

ME-2: Mechanical Engineering

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

(A) 2

(B) 3

(D) 5

Answer: (B)

2. Consider the following sentences:

(i) The number of candidates who appear for the GATE examination is staggering.

(ii) A number of candidates from my class are appearing for the GATE examination.

(iii) The number of candidates who appear for the GATE examination are staggering.

(iv) A number of candidates from my class is appearing for the GATE examination.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iii)

(D) (ii) and (iv)

Answer: (A)

3. A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.

(A) 10.08 AM

(B) 10.42 AM

(D) 10.00 PM

Answer: (A)

4. If ⊕÷⊙= 2 ; ⊕÷ Δ = 3; ⊙ +Δ = 5; Δ ×⊗ =10,

Then, the value of (⊗ − ⊕)², is:

(A) 0

(B) 1

(D) 16

Answer: (B)

5. The front door of Mr. X’s house faces East. Mr. X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is ______

(A) South-East

(B) North-East

(D) North-West

Answer: (D)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All entrepreneurs are wealthy.

Statement 2: All wealthy are risk seekers.

Conclusion I: All risk seekers are wealthy.

Conclusion II: Only some entrepreneurs are risk seekers.

Based on the above statements and conclusions, which one of the following options is CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(D) Both conclusions I and II are correct

Answer: (C)

7. A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____

(A) 3/16

(B) 45/236

(D) 3/4

Answer: (B)

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is____

(A) 1/8

(B) 1/6

(D) 1/2

Answer: (C)

9. Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _______

(A) 1/4

(B) 1/8

(D) 1/32

Answer: (B)

10. The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.

In relation to the first sentence above, what does the second sentence do?

(A) Restates an idea from the first sentence.

(B) Second sentence entirely contradicts the first sentence.

(D) States an effect of the first sentence.

Answer: (D)

Mechanical Engineering (ME, Set-2)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider an n × n matrix A and a non-zero n × 1 vector p. Their product Ap = α 2p, where α ∈ ℜ and α ∉ {−1, 0, 1}. Based on the given information, the eigen value of A² is:

(A) a

(B) a²

(D) α⁴

Answer: (D)

2. If the Laplace transform of a function f(t) is given by then f(0) is

(A) 0

(B) 1/2

(D) 3/2

Answer: (C)

3. The mean and variance, respectively, of a binomial distribution for n independent trials with the probability of success as p, are

(A) √np , np(1 − 2p)

(B)

(D) np, np(1 – p)

Answer: (D)

4. The Cast Iron which possesses all the carbon in the combined form as cementite is known as

(A) Grey Cast Iron

(B) Spheroidal Cast Iron

(D) White Cast Iron

Answer: (D)

5. The size distribution of the powder particles used in Powder Metallurgy process can be determined by

(A) Laser scattering

(B) Laser reflection

(D) Laser penetration

Answer: (A)

6. In a CNC machine tool, the function of an interpolator is to generate

(A) signal for the lubrication pump during machining

(B) error signal for tool radius compensation during machining

(D) reference signal prescribing the shape of the part to be machined

Answer: (D)

7. The machining process that involves ablation is

(A) Abrasive Jet Machining

(B) Chemical Machining

(D) Laser Beam Machining

Answer: (D)

8. A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is

(A) 3

(B) 9

(D) 81

Answer: (B)

9. The allowance provided in between a hole and a shaft is calculated from the difference between

(A) lower limit of the shaft and the upper limit of the hole

(B) upper limit of the shaft and the upper limit of the hole

(D) lower limit of the shaft and the lower limit of the hole

Answer: (C)

10. In forced convective heat transfer, Stanton number (St), Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr) are related as

Answer: (A)

11. For a two-dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression can be simplified to

Answer: (D)

12. Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?

(A) Nikuradse stresses

(B) Reynolds stresses

(D) Prandtl stresses

Answer: (B)

13. A two dimensional flow has velocities in x and y directions given by u = 2xyt and v = −y²t, where t denotes time. The equation for streamline passing through x = 1, y = 1 is

(A) x²y = 1

(B) xy² = 1

(D) x/y² = 1

Answer: (B)

14. A plane truss PQRS (PQ = RS, and ∠PQR = 90°) is shown in the figure.

The forces in the members PR and RS, respectively, are _____________

(A) F√2 (tensile) and F (tensile)

(B) F√2 (tensile) and F (compressive)

(D) F (tensile) and F√2 (tensile)

Answer: (B)

15. Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground.

Select the correct statement about instantaneous centers in the mechanism.

(A) Only points P, Q, and S are instantaneous centers of mechanism

(B) Only points P, Q, S and T are instantaneous centers of mechanism

(D) All points P, Q, R, S, T and U are instantaneous centers of mechanism

Answer: (D)

16. The controlling force curves P, Q and R for a spring controlled governor are shown in the figure, where r₁ and r₂ are any two radii of rotation.

The characteristics shown by the curves are

(A) P – Unstable; Q – Stable; R – Isochronous

(B) P – Unstable; Q – Isochronous; R – Stable

(D) P – Stable; Q – Unstable; R – Isochronous

Answer: (B)

17. The von Mises stress at a point in a body subjected to forces is proportional to the square root of the

(A) total strain energy per unit volume

(B) plastic strain energy per unit volume

(D) distortional strain energy per unit volume

Answer: (D)

18. Value of using Simpson’s one-third rule with interval size 0.3 is

(A) 1.83

(B) 1.60

(D) 1.06

Answer: (A)

19. Value of (1 + i)⁸, where i = √−1 , is equal to

(A) 4

(B) 16

(D) 16i

Answer: (B)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is 300 m/s, temperature is 330 K and pressure is 180 kPa. Assume that the air behaves as a perfect gas with constant cp =1.005 kJ/kg.K. The stagnation temperature at this point is _________ K (round off to two decimal places).

Answer: (373.00 to 377.00)

21. Consider an ideal vapour compression refrigeration cycle working on R-134a refrigerant. The COP of the cycle is 10 and the refrigeration capacity is 150 kJ/kg. The heat rejected by the refrigerant in the condenser is __________ kJ/kg (round off to the nearest integer).

Answer: (165 to 165)

22. A rigid tank of volume 50 m³ contains a pure substance as a saturated liquid vapour mixture at 400 kPa. Of the total mass of the mixture, 20% mass is liquid and 80% mass is vapour. Properties at 400 kPa are: Tsat = 143.61 °C, vf = 0.001084 m³/kg, vg = 0.46242 m³/kg. The total mass of liquid vapour mixture in the tank is ___________kg (round off to the nearest integer).

Answer: (134 to 136)

23. An object is moving with a Mach number of 0.6 in an ideal gas environment, which is at a temperature of 350 K. The gas constant is 320 J/kg.K and ratio of specific heats is 1.3. The speed of object is ____________m/s (round off to the nearest integer).

Answer: (228 to 230)

24. A column with one end fixed and one end free has a critical buckling load of 100 N. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be ___________N (round off to the nearest integer).

Answer: (800 to 840)

25. A steel cubic block of side 200 mm is subjected to hydrostatic pressure of 250 N/mm². The elastic modulus is 2 × 10⁵ N/mm² and Poisson ratio is 0.3 for steel. The side of the block is reduced by _________ mm (round off to two decimal places).

Answer: (0.08 to 0.12)

Q.26 – Q.34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The value of is

(A) 0

(B) 1/6

(D) π

Answer: (B)

27. Let the superscript T represent the transpose operation. Consider the function where x and r are n × 1 vectors and Q is a symmetric n × n matrix. The stationary point of f(x) is

(A) Q^Tr

(B) Q⁻¹r

(D) r

Answer: (B)

28. Consider the following differential equation

The solution of the equation that satisfies the condition y(1) = 1 is

(A) 2ye^y = e^x+ e

(B) y²e^y = e^x

(D) (1 + y)e^y = 2e^x

Answer: (C)

29. A factory produces m (i = 1, 2, … , m) products, each of which requires processing on n (j = 1, 2, … , n) workstations. Let a_ij be the amount of processing time that one unit of the i^th product requires on the j^th Let the revenue from selling one unit of the ith product be r_i and h_i be the holding cost per unit per time period for the i^th product. The planning horizon consists of T (t = 1, 2, …, T) time periods. The minimum demand that must be satisfied in time period t is d_it, and the capacity of the j^th workstation in time period t is c_jt. Consider the aggregate planning formulation below, with decision variables S_it (amount of product i sold in time period t), X_it (amount of product i manufactured in time period t) and I_it (amount of product i held in inventory at the end of time period t.

Answer: (A)

30. Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is _________ g/kg of dry air.

(A) 1.4

(B) 35.1

(D) 13.6

Answer: (D)

31. A plane frame PQR (fixed at P and free at R) is shown in the figure. Both members (PQ and QR) have length, L, and flexural rigidity, EI. Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end, R, is

Answer: (B)

32. A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.

Diameters of pulleys of belt drive and number of teeth (T) on the gears 2 to 7 are indicated in the figure. The speed and direction of rotation of gear 7, respectively, are

(A) 255.68 rpm; clockwise

(B) 255.68 rpm; anticlockwise

(D) 575.28 rpm; anticlockwise

Answer: (A)

33. A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness (K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:

(1) K = 640 kN/m, ξ = 0.70

(2) K = 640 kN/m, ξ = 0.07

(3) K = 22.5 kN/m, ξ = 0.70

(4) K = 22.5 kN/m, ξ = 0.07

Arrange the isolators in the ascending order of the force transmitted to the foundation.

(A) 1-3-4-2

(B) 1-3-2-4

(D) 3-1-2-4

Answer: (C)

34. Consider the system shown in the figure. A rope goes over a pulley. A mass, m, is hanging from the rope. A spring of stiffness, k, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.

The pulley radius is r and its mass moment of inertia is J. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is

Answer: (B)

Q.35 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

35. Find the positive real root of x³ − x − 3 = 0 using Newton-Raphson method. If the starting guess (x₀) is 2, the numerical value of the root after two iterations (x₂) is _____________ (round off to two decimal places).

Answer: (1.66 to 1.68)

36. Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping a bearing in the inventory is ₹ 20. The setup cost for the production of a batch is ₹ 1800. Assuming 300 working days in a year, the economic batch quantity in number of bearings is ______________ (in integer).

Answer: (40200 to 40300)

37. A cast product of a particular material has dimensions 75 mm × 125 mm × 20 mm. The total solidification time for the cast product is found to be 2.0 minutes as calculated using Chvorinov’s rule having the index, n = 2. If under the identical casting conditions, the cast product shape is changed to a cylinder having diameter = 50 mm and height = 50 mm, the total solidification time will be ____________ minutes (round off to two decimal places).

Answer: (2.60 to 3.00)

38. A spot welding operation performed on two pieces of steel yielded a nugget with a diameter of 5 mm and a thickness of 1 mm. The welding time was 0.1 s. The melting energy for the steel is 20 J/mm³. Assuming the heat conversion efficiency as 10%, the power required for performing the spot welding operation is ____________ kW (round off to two decimal places).

Answer: (39.00 to 40.00)

39. A surface grinding operation has been performed on a Cast Iron plate having dimensions 300 mm (length) × 10 mm (width) × 50 mm (height). The grinding was performed using an alumina wheel having a wheel diameter of 150 mm and wheel width of 12 mm. The grinding velocity used is 40 m/s, table speed is 5 m/min, depth of cut per pass is 50 μm and the number of grinding passes is 20. The average tangential and average normal force for each pass is found to be 40 N and 60 N respectively. The value of the specific grinding energy under the aforesaid grinding conditions is ______________ J/mm³ (round off to one decimal place).

Answer: (38.0 to 39.0)

40. In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be 400 N. The cutting velocity, V_c = 100 m/min, depth of cut, t = 2.0 mm, feed, s0 = 0.1 mm/revolution and chip velocity, V_f = 20 m/min, the shear strength, τ_s of the material will be ___________ MPa (round off to two decimal places).

Answer: (388.00 to 400.00)

41. The thickness, width and length of a metal slab are 50 mm, 250 mm and 3600 mm, respectively. A rolling operation on this slab reduces the thickness by 10% and increases the width by 3%. The length of the rolled slab is __________ mm (round off to one decimal place).

Answer: (3880.0 to 3886.0)

42. A 76.2 mm gauge block is used under one end of a 254 mm sine bar with roll diameter of 25.4 mm. The height of gauge blocks required at the other end of the sine bar to measure an angle of 30° is __________ mm (round off to two decimal places).

Answer: (200.00 to 206.00)

43. The demand and forecast of an item for five months are given in the table.

The Mean Absolute Percent Error (MAPE) in the forecast is ___________ % (round off to two decimal places)

Answer: (6.00 to 10.00)

44. A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at 300 K at a rate of 100 kg/s. The overall heat transfer coefficient is 1500 W/m².K, and total heat transfer area is 400 m2. Steam condenses at a saturation temperature of 350 K. Assume that the specific heat of coolant water is 4000 J/kg.K. The temperature of the coolant water coming out of the condenser is _________ K (round off to the nearest integer).

Answer: (337 to 341)

45. Ambient air flows over a heated slab having flat, top surface at y = 0. The local temperature (in Kelvin) profile within the thermal boundary layer is given by T(y) = 300 + 200 exp(−5y), where y is the distance measured from the slab surface in meter. If the thermal conductivity of air is 1.0 W/m.K and that of the slab is 100 W/m.K, then the magnitude of temperature gradient |dT/dy| within the slab at y = 0 is __________ K/m (round off to the nearest integer).

Answer: (10 to 10)

46. Water flows out from a large tank of cross-sectional area At = 1 m² through a small rounded orifice of cross-sectional area A_o = 1 cm², located at y = 0. Initially the water level, measured from y = 0, is H = 1 m. The acceleration due to gravity is 9.8 m/s².

Neglecting any losses, the time taken by water in the tank to reach a level of y = H/4 is __________ seconds (round off to one decimal place).

Answer: (2257.0 to 2259.0)

47. Consider the open feed water heater (FWH) shown in the figure given below:

Specific enthalpy of steam at location 2 is 2624 kJ/kg, specific enthalpy of water at location 5 is 226.7 kJ/kg and specific enthalpy of saturated water at location 6 is 708.6 kJ/kg. If the mass flow rate of water entering the open feed water heater (at location 5) is 100 kg/s then the mass flow rate of steam at location 2 will be __________ kg/s (round off to one decimal place).

Answer: (25.0 to 25.4)

48. A high velocity water jet of cross section area = 0.01 m² and velocity = 35 m/s enters a pipe filled with stagnant water. The diameter of the pipe is 0.32 m. This high velocity water jet entrains additional water from the pipe and the total water leaves the pipe with a velocity 6m/s as shown in the figure.

The flow rate of entrained water is ___________ litres/s (round off to two

decimal places).

Answer: (130.00 to 134.00)

49. A vertical shaft Francis turbine rotates at 300 rpm. The available head at the inlet to the turbine is 200 m. The tip speed of the rotor is 40 m/s. Water leaves the runner of the turbine without whirl. Velocity at the exit of the draft tube is 3.5 m/s. The head losses in different components of the turbine are: (i) stator and guide vanes: 5.0 m, (ii) rotor: 10 m, and (iii) draft tube: 2 m. Flow rate through the turbine is 20 m³/s. Take g = 9.8 m/s². The hydraulic efficiency of the turbine is ___________ % (round off to one decimal place).

Answer: (90.0 to 92.0)

50. An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, and 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K.

Assume constant specific heat of air is 1005 J/kg.K and gas constant is 287 J/kg.K. There is no work transfer across the boundary of this device. The rate of entropy generation is __________ kW/K (round off to one decimal place).

Answer: (2.1 to 2.3)

51. A block of negligible mass rests on a surface that is inclined at 30° to the horizontal plane as shown in the figure. When a vertical force of 900 N and a horizontal force of 750 N are applied, the block is just about to slide.

The coefficient of static friction between the block and surface is _______ (round off to two decimal places).

Answer: (0.16 to 0.19)

52. The wheels and axle system lying on a rough surface is shown in the figure.

Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is 0.2 m and its mass is 1.5 kg. Neglect the moment of inertia of the axle and assume g = 9.8 m/s². An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is _________ m/s² (round off to one decimal place).

Answer: (1.3 to 1.4)

53. A cantilever beam with a uniform flexural rigidity (EI = 200 × 106 N.m²) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 10000 N.m². The magnitude of the slope of the beam at its free end is _________ micro radian (round off to the nearest integer).

Answer: (48 to 52)

54. The torque provided by an engine is given by T(θ) = 12000 + 2500 sin(2θ) N.m, where θ is the angle turned by the crank from inner dead center. The mean speed of the engine is 200 rpm and it drives a machine that provides a constant resisting torque. If variation of the speed from the mean speed is not to exceed ±0.5%, the minimum mass moment of inertia of the flywheel should be ___________ kg.m² (round off to the nearest integer).

Answer: (560 to 580)

55. The figure shows the relationship between fatigue strength (S) and fatigue life (N) of a material. The fatigue strength of the material for a life of 1000 cycles is 450 MPa, while its fatigue strength for a life of 106 cycles is 150 MPa.

The life of a cylindrical shaft made of this material subjected to an alternating stress of 200 MPa will then be __________ cycles (round off to the nearest integer).

Answer: (152000 to 165000)

GATE Exam 2021 Mechanical Engineering (ME-1) Question Paper With Answer Key

June 8, 2023June 15, 2022 by suresh84

GATE-2021

ME-1: Mechanical Engineering

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider the following sentences:

(i) After his surgery, Raja hardly could walk.

(ii) After his surgery, Raja could barely walk.

(iii) After his surgery, Raja barely could walk.

(iv) After his surgery, Raja could hardly walk.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iii)

(D) (ii) and (iv)

Answer: (D)

2. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing _________

(A) North

(B) East

(D) South

Answer: (D)

In the above figure, O is the center of the circle and, M and N lie on the circle.

The area of the right triangle MON is 50 cm².

What is the area of the circle in cm² ?

(A) 2π

(B) 50π

(D) 100π

Answer: (D)

4. If

then, the value of the expression ∆ 2 ⊕ 3 ∆ ((4 ⨁ 2) ∇ 4)=

(A) −1

(B) −0.5

(D) 7

Answer: (D)

5. “The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle”

Which of the following can be logically inferred from the information presented in the above statement?

(A) The people in the state did not consume leafy vegetables earlier.

(B) Consumption of leafy vegetables may not be the only indicator of healthy lifestyle.

(D) The people in the state have increased awareness of health hazards causing by consumption of junk foods.

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos.

In the symbiotic relationship described above, the primary benefits for oxpeckers and rhinos respectively are,

(A) Oxpeckers get a food source, rhinos have no benefit.

(B) Oxpeckers save their habitat from poachers while the rhinos have no benefit.

(D) Oxpeckers save the lives of poachers, rhinos save their own lives.

Answer: (C)

A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416. The ratio of hens: ducks: goats in farm Q is 5:14:13. All the hens, ducks and goats are sent from farm Q to farm P.

The new ratio of hens: ducks: goats in farm P is_____

(A) 5:7:13

(B) 5:14:13

(D) 21:10:26

Answer: (C)

The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000.

The total number of management degree holders among the executives in companies C2 and C5 together is_____.

(A) 225

(B) 600

(D) 2500

Answer: (D)

10. Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.

The number of distinct seating arrangements possible is:

(A) 4

(B) 8

(D) 16

Answer: (D)

Mechanical Engineering (ME, Set-1)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. If y(x) satisfies the differential equation subject to the condition y(π/2) = π/2, then y(π/6) is

(A) 0

(B) π/6

(D) π/2

Answer: (C)

2. The value of is

(A) 1/4

(B) 1/3

(D) 1

Answer: (C)

3. The Dirac-delta function (δ(t − t₀)) for t, t₀ ∈ ℝ, has the following property

The Laplace transform of the Dirac-delta function δ(t − a) for a > 0; ℒ(δ(t − a)) = F(s) is

(A) 0

(B) ∞

(D) e⁻^sa

Answer: (D)

4. The ordinary differential equation subject to an initial condition y(0) = 1 is solved numerically using the following scheme:

where h is the time step, t_n = nh, and n = 0, 1, 2, …. This numerical scheme is stable for all values of h in the interval _________.

(A) 0 < h < 2/π

(B) 0 < h < 1

(D) for all h > 0

Answer: (A)

5. Consider a binomial random variable X. If X₁,X₂, … ,X_n are independent and identically distributed samples from the distribution of X with sum then the distribution of Y as n → ∞ can be approximated as

(A) Exponential

(B) Bernoulli

(D) Normal

Answer: (D)

6. The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively, are

(A) 0.01 and 0.01

(B) 0.02 and 0.01

(D) 0.02 and 0.02

Answer: (B)

7. In a machining operation, if a cutting tool traces the workpiece such that the directrix is perpendicular to the plane of the generatrix as shown in figure, the surface generated is

(A) plane

(B) cylindrical

(D) a surface of revolution

Answer: (B)

8. The correct sequence of machining operations to be performed to finish a large diameter through hole is

(A) drilling, boring, reaming

(B) boring, drilling, reaming

(D) boring, reaming, drilling

Answer: (A)

9. In modern CNC machine tools, the backlash has been eliminated by

(A) preloaded balls crews

(B) rack and pinion

(D) slider crank mechanism

Answer: (A)

10. Consider the surface roughness profile as shown in the figure.

The center line average roughness (Ra, in μm) of the measured length (L) is

(A) 0

(B) 1

(D) 4

Answer: (B)

11. In which of the following pairs of cycles, both cycles have at least one isothermal process?

(A) Diesel cycle and Otto cycle

(B) Carnot cycle and Stirling cycle

(D) Bell-Coleman cycle and Vapour compression refrigeration cycle

Answer: (B)

12. Superheated steam at 1500 kPa, has a specific volume of 2.75 m³/kmol and compressibility factor (Z) of 0.95. The temperature of steam is______ °C (round off to the nearest integer).

(A) 522

(B) 471

(D) 198

Answer: (C)

13. A hot steel spherical ball is suddenly dipped into a low temperature oil bath.

Which of the following dimensionless parameters are required to determine instantaneous center temperature of the ball using a Heisler chart?

(A) Biot number and Fourier number

(B) Reynolds number and Prandtl number

(D) Nusselt number and Grashoff number

Answer: (A)

14. An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of Q̇₁ to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes Q̇₂. The ratio Q̇₂/Q̇₁ is

(A) √2

(B) 2

(D) 1/2

Answer: (A)

15. The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to p_v. The saturation pressure of water at 300 K is psat. The correct relation for the air-water mixture is

(A) p_v = 0.5 p_sat

(B) p_v = p_sat

(D) p_v = 2 p_sat

Answer: (A)

16. Consider a reciprocating engine with crank radius R and connecting rod of length L. The secondary unbalance force for this case is equivalent to primary unbalance force due to a virtual crank of _______

(A) radius L²/4R rotating at half the engine speed

(B) radius R/4 rotating at half the engine speed

(D) radius L/2 rotating at twice the engine speed

Answer: (C)

17. A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at x = L/2 is

(A) ML²/2EI

(B) ML²/4EI

(D) ML²/16EI

Answer: (C)

18. A prismatic bar PQRST is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are

(A) QR and PQ

(B) ST and PQ

(D) ST and RS

Answer: (D)

19. Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents

(A) direct shear stress in the coil wire cross-section

(B) torsional shear stress in the coil wire cross-section

(D) combined direct shear and torsional shear stress along with the effect of stress concentration at inside edge of the coil wire cross-section

Answer: (C)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is 95%. The lead time period is 5 days and daily customer demand can be assumed to follow the Gaussian (normal) distribution with mean 50 units and a standard deviation of 10 units. Using ϕ⁻¹(0. 95) = 1. 64, where φ represents the cumulative distribution function of the standard normal random variable, the amount of safety stock that must be maintained by Robot Ltd. to achieve this demand fulfillment probability for the lead time period is _________ units (round off to two decimal places).

Answer: (331 to 333)

21. A pressure measurement device fitted on the surface of a submarine, located at a depth H below the surface of an ocean, reads an absolute pressure of 4.2 MPa. The density of sea water is 1050 kg/m³, the atmospheric pressure is 101 kPa, and the acceleration due to gravity is 9.8 m/s². The depth H is ___________ m (round off to the nearest integer).

Answer: (397 to 399)

22. Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of U = 4 m/s. Separation between the plates is 5 mm. There is no pressure gradient in the direction of flow. The density of fluid is 800 kg/m³, and the kinematic viscosity is 1. 25 × 10−4 m²/s. The average shear stress in the fluid is _________ Pa (round off to the nearest integer).

Answer: (79 to 81)

23. A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and temperature of 250 kPa and 400 K respectively. Now the valve is opened and air is allowed to flow into the tank until the pressure inside the tank reaches to 250 kPa at which point the valve is closed. Assume that the air behaves as a perfect gas with constant properties (c_p = 1.005 kJ/kg.K, c_v = 0.718 kJ/kg.K, R = 0.287 kJ/kg.K). Final temperature of the air inside the tank is __________ K (round off to one decimal place).

Answer: (555 to 565)

24. The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is 100 kg.m². The propeller rotates at ω = 12 rad/s. The waves acting on the ship hull induces a rolling motion as shown in the figure with an angular velocity of 5 rad/s. The gyroscopic moment generated on the shaft due to the motion described is ______________ N.m (round off to the nearest integer).

Answer: (0 to 0)

25. Consider a single degree of freedom system comprising a mass M, supported on a spring and a dashpot as shown in the figure.

If the amplitude of the free vibration response reduces from 8 mm to 1.5 mm in 3 cycles, the damping ratio of the system is ______________ (round off to three decimal places).

Answer: (0.085 to 0.090)

Q.26 – Q. 34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Consider a vector p in 2-dimensional space. Let its direction (counter- clockwise angle with the positive x-axis) be θ. Let p be an eigenvector of a 2 × 2 matrix A with corresponding eigenvalue λ, λ > 0. If we denote the magnitude of a vector v by ‖v‖, identify the VALID statement regarding p′, where p′ = Ap.

(A) Direction of p′ = λθ, ||p′|| = ||p||

(B) Direction of p′ = θ, ||p′|| = λ||p||

(D) Direction of p′ = θ, ||p′|| = ||p||/λ

Answer: (B)

27. Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral (where integration is taken counter clockwise) is

(A) 0

(B) 2

(D) 2πi

Answer: (C)

28. A set of jobs A, B, C, D, E, F, G, H arrive at time t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence – first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below.

If the make span is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is

(A) A-E-D-F-H-C-G-B

(B) A-D-E-F-H-C-G-B

(D) B-G-C-H-F-D-E-A

Answer: (A)

29. The fundamental thermodynamic relation for a rubber band is given by dU = TdS + τdL, where T is the absolute temperature, S is the entropy, τ is the tension in the rubber band, and L is the length of the rubber band. Which one of the following relations is CORRECT:

Answer: (B)

30. Consider a two degree of freedom system as shown in the figure, where PQ is a rigid uniform rod of length, b and mass, m.

Assume that the spring deflects only horizontally and force F is applied horizontally at Q. For this system, the Lagrangian, L is

Answer: (B)

31. A right solid circular cone standing on its base on a horizontal surface is of height H and base radius R. The cone is made of a material with specific weight w and elastic modulus E. The vertical deflection at the mid-height of the cone due to self-weight is given by

(A) wH²/8E

(B) wH²/6E

(D) wRH/6E

Answer: (A)

32. A tappet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The mass moment of inertia of the rocker about B is 10^-4m². The rocker arm dimensions are a = 3.5 cm and b = 2.5 cm. A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at N rpm. The pushrod is assumed massless and has a stiffness of 15 N/mm. At the other end C, the rocker pushes a valve against a spring of stiffness 10 N/mm. The valve is assumed massless and rigid.

Resonance in the rocker system occurs when the cam shaft runs at a speed of _________ rpm (round off to the nearest integer).

(A) 496

(B) 4739

(D) 2369

Answer: (B)

33. Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop opens. The probability that a customer arrives within the next 3 minutes is

(A) 0.39

(B) 0.86

(D) 0.61

Answer: (A)

34. Let f(x) = x² − 2x + 2 be a continuous function defined on x ∈ [1, 3]. The point x at which the tangent of f(x) becomes parallel to the straight line joining f(1) and f(3) is

(A) 0

(B) 1

(D) 3

Answer: (C)

Q.35 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

35. Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

The probability that the project will be completed within 40 days is _________ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

Answer: (0.5 to 0.5)

36. A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of 250 mm and inner diameter of 230 mm. The value of acceleration due to gravity, g = 10 m/s². If a G-factor (ratio of centrifugal force to weight) of 60 is used for casting the tube, the rotational speed required is __________________rpm (round off to the nearest integer).

Answer: (660 to 664)

37. The resistance spot welding of two 1.55 mm thick metal sheets is performed using welding current of 10000 A for 0.25 s. The contact resistance at the interface of the metal sheets is 0.0001 Ω. The volume of weld nugget formed after welding is 70 mm3. Considering the heat required to melt unit volume of metal is 12 J/mm³, the thermal efficiency of the welding process is _______ % (round off to one decimal place).

Answer: (30 to 36)

38. An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of 12o on a lathe. During turning, the cutting force and the friction force are 1000 N and 600 N, respectively. If the chip thickness and the uncut chip thickness during turning are 1.5 mm and 0.75 mm, respectively, then the shear force is _____________ N (round off to two decimal places).

Answer: (625 to 750)

39. In a grinding operation of a metal, specific energy consumption is 15 J/mm³. If a grinding wheel with a diameter of 200 mm is rotating at 3000 rpm to obtain a material removal rate of 6000 mm³/min, then the tangential force on the wheel is ______________ N (round off to two decimal places).

Answer: (45.00 to 50.00)

40. A 200 mm wide plate having a thickness of 20 mm is fed through a rolling mill with two rolls. The radius of each roll is 300 mm. The plate thickness is to be reduced to 18 mm in one pass using a roll speed of 50 rpm. The strength coefficient (K) of the work material flow curve is 300 MPa and the strain hardening exponent, n is 0.2. The coefficient of friction between the rolls and the plate is 0.1. If the friction is sufficient to permit the rolling operation then the roll force will be __________ kN (round off to the nearest integer).

Answer: (775 to 784)

41. The XY table of a NC machine tool is to move from P(1,1) to Q(51,1); all coordinates are in mm. The pitch of the NC drive leadscrew is 1 mm. If the backlash between the leadscrew and the nut is 1.8o, then the total backlash of the table on moving from P to Q is ____________ mm (round off to two decimal places).

Answer: (0.20 to 0.30)

42. Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process time of the workstation is exponentially distributed with a mean of 4 minutes. The expected number of jobs at the workstation at any given point of time is ___________ (round off to the nearest integer).

Answer: (4 to 4)

43. An uninsulated cylindrical wire of radius 1.0 mm produces electric heating at the rate of 5.0 W/m. The temperature of the surface of the wire is 75°C when placed in air at 25°C. When the wire is coated with PVC of thickness 1.0 mm, the temperature of the surface of the wire reduces to 55°C. Assume that the heat generation rate from the wire and the convective heat transfer coefficient are same for both uninsulated wire and the coated wire. The thermal conductivity of PVC is ___________ W/m.K (round off to two decimal places).

Answer: (0.10 to 0.12)

44. A solid sphere of radius 10 mm is placed at the centroid of a hollow cubical enclosure of side length 30 mm. The outer surface of the sphere is denoted by 1 and the inner surface of the cube is denoted by 2. The view factor F₂₂ for radiation heat transfer is ___________ (rounded off to two decimal places).

Answer: (0.76 to 0.78)

45. Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is 20 kJ/kg. The work output from the high pressure turbine is 750 kJ/kg. The work output from the low pressure turbine is 1500 kJ/kg. The thermal efficiency of the cycle is 50 %. The enthalpy of saturated liquid and saturated vapour at condenser pressure are 200 kJ/kg and 2600 kJ/kg, respectively. The quality of steam at the exit of the low pressure turbine is ___________ % (round off to the nearest integer).

Answer: (92 to 96)

46. In the vicinity of the triple point, the equation of liquid-vapour boundary in the P − T phase diagram for ammonia is ln P = 24. 38 − 3063/T, where P is pressure (in Pa) and T is temperature (in K). Similarly, the solid-vapour boundary is given by ln P = 27. 92 − 3754/T. The temperature at the triple point is _________ K (round off to one decimal place).

Answer: (195.1 to 195.3)

47. A cylindrical jet of water (density = 1000 kg/m³) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a linear spring with a spring constant k = 1 kN/m. The incoming jet diameter is D = 1 cm.

If the spring shows a steady deflection of 1 cm upon impingement of jet, then the velocity of the incoming jet is ____________ m/s (round off to one decimal place).

Answer: (11.2 to 11.4)

48. A single jet Pelton wheel operates at 300 rpm. The mean diameter of the wheel is 2 m. Operating head and dimensions of jet are such that water comes out of the jet with a velocity of 40 m/s and flow rate of 5 m³/s. The jet is deflected by the bucket at an angle of 165°. Neglecting all losses, the power developed by the Pelton wheel is ______________ MW (round off to two decimal places).

Answer: (2.50 to 2.80)

49. An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoor air, the intake duct supplies a mixture of fresh air with a cold air stream. The two streams are mixed in an insulated mixing chamber located upstream of the intake duct. Cold air enters the mixing chamber at 5°C, 105 kPa with a volume flow rate of 1.25 m³/s during steady state operation. Fresh air enters the mixing chamber at 34 °C and 105 kPa. The mass flow rate of the fresh air is 1.6 times of the cold air stream. Air leaves the room through the exit duct at 24°C.

Assuming the air behaves as an ideal gas with c_p = 1.005 kJ/kg.K and R = 0.287 kJ/kg.K, the rate of heat gain by the air from the room is ________ kW(round off to two decimal places).

Answer: (4.90 to 5.10)

50. Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm.

The reaction at the point of contact between two spheres is _________ N (round off to one decimal place).

Answer: (124.0 to 126.0)

51. An overhanging beam PQR is subjected to uniformly distributed load 20 kN/m as shown in the figure.

The maximum bending stress developed in the beam is ___________ MPa (round off to one decimal place).

Answer: (249.0 to 251.0)

52. The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm.

The quick return ratio for the mechanism is _________ (round off to one decimal place).

Answer: (1.9 to 2.1)

53. A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4.

The magnitude of the torque applied by the brake is ____________ N.m (round off to one decimal place).

Answer: (199.0 to 201.0)

54. A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure. The load varies from 800 N to 1600 N. The modified endurance, yield and ultimate strengths of the material are 200 MPa, 500 MPa and 600 MPa, respectively.

The factor of safety of the beam using modified Goodman criterion is ________ (round off to one decimal place).

Answer: (1.9 to 2.1)

55. A cantilever beam of rectangular cross-section is welded to a support by means of two fillet welds as shown in figure. A vertical load of 2 kN acts at free end of the beam.

Considering that the allowable shear stress in weld is 60 N/mm², the minimum size (leg) of the weld required is _______ mm (round off to one decimal place).

Answer: (6.4 to 6.9)

GATE Exam 2021 Mathematics (MA) Question Paper With Answer Key

June 8, 2023June 15, 2022 by suresh84

GATE-2021

MA: Mathematics

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A) 21

(B) 37

(D) 73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A) (i) is grammatically correct and (ii) is unambiguous

(B) (i) is grammatically incorrect and (ii) is unambiguous

(D) (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

4. A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Plan, outline

(B) Hospital, library

(D) Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______

(A) π/2

(B) 3/π

(D) 3π

Answer: (C)

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

The discount on item Q, as a percentage of its marked price, is ______

(A) 25

(B) 12.5

(D) 5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A) 0.3024

(B) 0.4235

(D) 0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(D) Neither conclusion I nor II is correct.

Answer: (C OR D)

10. Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.

Which one of the following statements summarizes the passage?

(A) The proposed AOM addresses the core problems that cause obesity.

(B) If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(D) AOM are addressing the problem superficially.

Answer: (D)

Mathematics (MA)

Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let A be a 3 × 4 matrix and B be a 4 × 3 matrix with real entries such that AB is non-singular. Consider the following statements:

P: Nullity of A is 0.

Q: BA is a non-singular matrix.

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (D)

2. Let f(z) = u(x, y) + i v(x, y) for z = x + iy ∈ ℂ, where x and y are real numbers, be a non-constant analytic function on the complex plane ℂ. Let u_x, v_x and u_y, v_y denote the first order partial derivatives of u(x, y) = Re(f(z)) and v(x, y) = Im(f(z)) with respect to real variables x and y, respectively.

Consider the following two functions defined on ℂ:

g1(z) = ux(x, y) − i uy(x, y) for z = x + iy ∈ ℂ,

g2(z) = vx(x, y) + i vy(x, y) for z = x + iy ∈ ℂ.

Then

(A) both g₁(z) and g₂(z) are analytic in ℂ

(B) g₁(z) is analytic in C and g₂(z) is NOT analytic in ℂ

(D) neither g₁(z) nor g₂(z) is analytic in ℂ

Answer: (B)

3. Let be the Möbius transformation which maps the points z₁ = 0, z₂ = −i, z₃ = ∞ in the z-plane onto the points w₁ = 10, w₂ = 5 − 5i, w₃ = 5 + 5i in the w-plane, respectively. Then the image of the set S = {z ∈ ℂ ∶ Re(z) < 0} under the map w = T(z) is

(A) {w ∈ ℂ ∶ |w| < 5}

(B) {w ∈ ℂ ∶ |w| > 5}

(D) {w ∈ ℂ ∶ |w − 5| > 5}

Answer: (C)

4. Let R be the row reduced echelon form of a 4 × 4 real matrix A and let the third column of R be Consider the following statements:

P: If is a solution of Ax = 0, then γ = 0.

Q: For all b ∈ ℝ⁴, rank[A| b] = rank[R| b].

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (D)

5. The eigenvalues of the boundary value problem

are given by

(A) λ = (nπ)², n = 1,2,3, …

(B) λ = n², n = 1,2,3, …

(D) λ = k_n², where k_n, n = 1,2,3, … are the roots of k + tan(kπ) = 0

Answer: (C)

6. The family of surfaces given by u = xy + f(x² − y²), where f: R → R is adifferentiable function, satisfies

Answer: (A)

7. The function u(x, t) satisfies the initial value problem

Then u(5, 5) is

(A) 1 – 1/e¹⁰⁰

(B) 1 – e¹⁰⁰

(D) 1 – e¹⁰

Answer: (A)

8. Consider the fixed-point iteration

x_n+1 = φ(x_n), n ≥ 0

with φ(x) = 3 + (x – 3)³, x ∈ (2.5, 3.5),

and the initial approximation x₀ = 3.25.

Then, the order of convergence of the fixed-point iteration method is

(A) 1

(B) 2

(D) 4

Answer: (C)

9. Let {en ∶ n = 1, 2, 3, … } be an orthonormal basis of a complex Hilbert space H. Consider the following statements:

P: There exists a bounded linear functional f: H → ℂ such that f(e_n) = 1/n for n = 1, 2, 3, … .

Q: There exists a bounded linear functional g:H → ℂ such that g(e_n) = 1/√n for n = 1, 2, 3, … .

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (B)

10. Let be given by Consider the following statements:

P: |f(x) − f(y)| < |x − y| for all

Q: f has a fixed point.

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (D)

11. Consider the following statements:

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (A)

12. Let f: ℝ³ → ℝ be a twice continuously differentiable scalar field such that div(∇f) = 6. Let S be the surface x² + ^y2 + z² = 1 and n̂ be unit outward normal to S. Then the value of is

(A) 2 π

(B) 4 π

(D) 8 π

Answer: (D)

13. Consider the following statements:

P: Every compact metrizable topological space is separable.

Q: Every Hausdorff topology on a finite set is metrizable.

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (A)

14. Consider the following topologies on the set ℝ of all real numbers:

T₁ = {U ⊂ ℝ ∶ 0 ∉ U or U = ℝ },

T₂ = {U ⊂ ℝ ∶ 0 ∈ U or U = ∅} ,

T₃ = T₁ ∩ T₂.

Then the closure of the set {1} in (ℝ, T₃) is

(A) {1}

(B) {0, 1}

(D) R\{0}

Answer: (C)

Q.15 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

15. Let f : ℝ² → ℝ be differentiable. Let D_uf(0, 0) and D_vf(0, 0) be the directional derivatives of f at (0, 0) in the directions of the unit vectors u = (1/√5, 2/√5) and v = (1/√2, −1/√2), respectively. If D_uf(0, 0) = √5 and D_vf(0, 0) = √2 , then

Answer: (4 to 4)

16. Let ᴦ denote the boundary of the square region R with vertices (0, 0), (2, 0), (2, 2) and (0, 2) oriented in the counter-clockwise direction. Then

Answer: (12 to 12)

17. The number of 5-Sylow subgroups in the symmetric group S₅ of degree 5 is _______ .

Answer: (6 to 6)

18. Let I be the ideal generated by x2 + x + 1 in the polynomial ring R = ℤ₃[x], where ℤ₃ denotes the ring of integers modulo 3. Then the number of units in the quotient ring R/I is ________ .

Answer: (6 to 6)

19. Let T: ℝ³ → ℝ³ be a linear transformation such that

Then the rank of T is _____ .

Answer: (2 to 2)

20. Let y(x) be the solution of the following initial value problem

Then y(4) = _________.

Answer: (32 to 32)

21. Let f(x) = x⁴ + 2x³ − 11x² − 12x + 36 for x ∈ ℝ.

The order of convergence of the Newton-Raphson method

with x0 = 2. 1, for finding the root α = 2 of the equation f(x) = 0 is _______ .

Answer: (1 to 1)

22. If the polynomial p(x) = α + β (x + 2) + γ (x + 2)(x + 1) + δ (x + 2)(x + 1)x interpolates the data

then α + β + γ + δ = _________.

Answer: (1 to 1)

23. Consider the Linear Programming Problem P:

Maximize 2x₁ + 3x₂

subject to

2x₁ + x₂ ≤ 6,

−x₁ + x₂ ≤ 1,

x₁ + x₂ ≤ 3,

x₁ ≥ 0 and x₂ ≥ 0.

Then the optimal value of the dual of P is equal to _________ .

Answer: (8 to 8)

24. Consider the Linear Programming Problem P:

Minimize 2x₁ − 5x₂

subject to

2x₁ + 3x₂ + s₁ = 12,

−x₁ + x₂ + s₂ = 1,

−x₁ + 2x₂ + s₃ = 3,

x₁ ≥ 0, x₂ ≥ 0, s₁ ≥ 0, s₂ ≥ 0, and s₃ ≥ 0.

If is a basic feasible solution of P, then x₁ + s₁ + s₂ + s₃ =_______.

Answer: (5 to 5)

25. Let H be a complex Hilbert space. Let u, v ∈ H be such that 〈u, v〉 = 2. Then

Answer: (2 to 2)

Q.26 – Q.43 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Let ℤ denote the ring of integers. Consider the subring

R = {a + b √−17 ∶ a, b ∈ ℤ } of the field ℂ of complex numbers.

Consider the following statements:

P: 2 + √−17 is an irreducible element.

Q: 2 + √−17 is a prime element.

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (B)

27. Consider the second-order partial differential equation (PDE)

Consider the following statements:

P: The PDE is parabolic on the ellipse

Q: The PDE is hyperbolic inside the ellipse

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (A)

28. If u(x, y) is the solution of the Cauchy problem

then u(2, 1) is equal to

(A) 1 − 2 e⁻²

(B) 1 + 4 e⁻²

(D) 1 + 2 e⁻²

Answer: (C)

29. Let y(t) be the solution of the initial value problem

obtained by the method of Laplace transform. Then

(A)

(B)

(C)

(D)

Answer: (A)

30. The critical point of the differential equation is a

(A) node and is asymptotically stable

(B) spiral point and is asymptotically stable

(D) saddle point and is unstable

Answer: (A)

31. The initial value problem

where f(t, y) = −10 y, is solved by the following Euler method

y_n+1 = y_n + h f(t_n, y_n), n ≥ 0,

with step-size h. Then yn → 0 as n → ∞, provided

(A) 0 < h < 0.2

(B) 0.3 < h < 0.4

(D) 0.5 < h < 0.55

Answer: (A)

32. Consider the Linear Programming Problem P:

Maximize c₁x₁ + c₂x₂

subject to

a₁₁x₁ + a₁₂x₂ ≤ b₁,

a₂₁x₁ + a₂₂x₂ ≤ b₂,

a₃₁x₁ + a₃₂x₂ ≤ b₃,

x₁ ≥ 0 and x₂ ≥ 0, where aij, bi and cj are real numbers (i = 1, 2, 3; j = 1, 2).

Let be a feasible solution of P such that p c₁ + q c₂ = 6 and let all feasible solutions of P satisfy −5 ≤ c₁x₁ + c₂x₂ ≤ 12.

Then, which one of the following statements is NOT true?

(A) P has an optimal solution

(B) The feasible region of P is a bounded set

(D) The dual of P has at least one feasible solution

Answer: (B)

33. Let L² [−1, 1] be the Hilbert space of real valued square integrable functions on [−1, 1] equipped with the norm

Consider the subspace M = {f ∈ L²[−1, 1] :

For f(x) = x², define d = inf {‖f − g‖ ∶ g ∈ M }. Then

(A) d = √2/3

(B) d = 2/3

(D) d = 3/2

Answer: (A)

34. Let C[0, 1] be the Banach space of real valued continuous functions on [0, 1] equipped with the supremum norm. Define T: C[0, 1] → C[0, 1] by

Let R(T) denote the range space of T. Consider the following statements:

P: T is a bounded linear operator.

Q: T⁻¹: R(T) → C[0, 1] exists and is bounded.

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (B)

35. Let ℓ¹ = {x = (x(1), x(2), … , x(n), … ) be the sequence space equipped with the norm Consider the subspace and the linear transformation T:X → ℓ¹ given by

(Tx)(n) = n x(n) for n = 1, 2, 3, … . Then

(A) T is closed but NOT bounded

(B) T is bounded

(D) T⁻¹ exists and is an open map

Answer: (A)

36. Let fn:[0, 10] → ℝ be given by fn(x) = n x³ e^−nx for n = 1, 2, 3, … .

Consider the following statements:

P: (f_n) is equicontinuous on [0, 10].

does NOT converge uniformly on [0, 10].

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (B)

37. Let f: ℝ² → ℝ be given by

Consider the following statements:

P: f is continuous at (0, 0) but f is NOT differentiable at (0, 0).

Q: The directional derivative D_uf(0, 0) of f at (0, 0) exists in the direction of every unit vector u ∈ ℝ².

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (A)

38. Let V be the solid region in ℝ³ bounded by the paraboloid y = (x² + z²) and the plane y = 4. Then the value of is

(A) 128 π

(B) 64 π

(D) 256 π

Answer: (A)

39. Let f: ℝ² → ℝ be given by f(x, y) = 4xy − 2x² − y⁴. Then f has

(A) a point of local maximum and a saddle point

(B) a point of local minimum and a saddle point

(D) two saddle points

Answer: (A)

40. The equation xy − z log y + e^xz = 1 can be solved in a neighborhood of the point (0, 1, 1) as y = f(x, z) for some continuously differentiable function f.

Then

(A) ∇f(0, 1) = (2, 0)

(B) ∇f(0, 1) = (0, 2)

(D) ∇f(0, 1) = (1, 0)

Answer: (A)

41. Consider the following topologies on the set ℝ of all real numbers.

T₁ is the upper limit topology having all sets (a, b] as basis.

T₂ = {U ⊂ ℝ ∶ ℝ\U is finite} ∪ {∅}.

T₃ is the standard topology having all sets (a, b) as basis.

Then

(A) T₂ ⊂ T₃ ⊂ T₁

(B) T₁ ⊂ T₂ ⊂ T₃

(D) T₂ ⊂ T₁ ⊂ T₃

Answer: (A)

42. Let ℝ denote the set of all real numbers. Consider the following topological spaces.

X₁ = (ℝ, T₁), where T₁ is the upper limit topology having all sets (a, b] as basis.

X₂ = (ℝ, T₂), where T₂ = {U ⊂ ℝ ∶ ℝ\U is finite} ∪ {∅}.

Then

(A) both X₁ and X₂ are connected

(B) X₁ is connected and X₂ is NOT connected

(D) neither X₁ nor X₂ is connected

Answer: (C)

43. Let 〈∙, ∙〉: ℝⁿ × ℝⁿ → ℝ be an inner product on the vector space ℝⁿ over ℝ. Consider the following statements:

Then

(A) both P and Q are TRUE

(B) P is TRUE and Q is FALSE

(D) both P and Q are FALSE

Answer: (A)

Q.44 -Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

44. Let G be a group of order 5⁴ with center having 5² Then the number of conjugacy classes in G is ________.

Answer: (145 to 145)

45. Let F be a finite field and F^× be the group of all nonzero elements of F under multiplication. If F^× has a subgroup of order 17, then the smallest possible order of the field F is _______.

Answer: (103 to 103)

46. Let R = {z = x + iy ∈ 𝕔 ∶ 0 < x < 1 and − 11 π < y < 11 π} and ᴦ be the positively oriented boundary of R. Then the value of the integral is ______.

Answer: (11 to 11)

47. Let D = {z ∈ ℂ ∶ |z| < 2π} and f: D → ℂ be the function defined by

If then 6a₂ = _______.

Answer: (3 to 3)

48.The number of zeroes (counting multiplicity) of P(z) = 3z⁵ + 2i z² + 7i z +1 in the annular region {z ∈ ℂ ∶ 1 < |z| < 7} is ________ .

Answer: (4 to 4)

49. Let A be a square matrix such that det(xI − A) = x⁴(x − 1)²(x − 2)³, where det(M) denotes the determinant of a square matrix M.

If rank(A²) < rank(A³) = rank(A⁴), then the geometric multiplicity of the eigenvalue 0 of A is ________ .

Answer: (MTA)

50. If is the power series solution of the differential equation

Answer: (2 to 2)

51. If u(x, t) = A e^−t sin x solves the following initial boundary value problem

then πA = _______.

Answer: (MTA)

52. Let V = {p ∶ p(x) = a₀ + a₁x + a₂x², a₀, a₁, a₂ ∈ R} be the vector space of all polynomials of degree at most 2 over the real field R. Let T: V → V be the linear operator given by T(p) = (p(0) − p(1)) + (p(0) + p(1)) x + p(0) x².

Then the sum of the eigenvalues of T is _____ .

Answer: (1 to 1)

53. The quadrature formula is exact for all polynomials of degree ≤ 2. Then 2 β − γ = _______.

Answer: (2 to 2)

54 For each x ∈ (0, 1], consider the decimal representation x = ∙ d₁d₂d₃ ⋯ d_n ⋯. Define f:[0, 1] → R by f(x) = 0 if x is rational and f(x) = 18 n if x is irrational, where n is the number of zeroes immediately after the decimal point up to the first nonzero digit in the decimal representation of x. Then the Lebesgue integral

Answer: (2 to 2)

55. Let be an optimal solution of the following Linear Programming Problem P:

Maximize 4x₁ + x₂ − 3x₃

subject to

2x₁ + 4x₂ + ax₃ ≤ 10,

x₁ − x₂ + bx₃ ≤ 3,

2x₁ + 3x₂ + 5x₃ ≤ 11,

x₁ ≥ 0, x₂ ≥ 0 and x₃ ≥ 0, where a, b are real numbers.

If is an optimal solution of the dual of P, then p + q + r = ________ (round off to two decimal places).

Answer: (3.14 to 3.18)

GATE Exam 2021 Instrumentation Engineering (IN) Question Paper With Answer Key

June 8, 2023June 15, 2022 by suresh84

GATE-2021

IN: Instrumentation Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Getting to the top is ________________ than staying on top.

(A) more easy

(B) much easy

(D) easier

Answer: (D)

2. The mirror image of the above text about the x-axis is

Answer: (B)

3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

(A) 15

(B) 25

(D) 40

Answer: (C)

4. ⊕ and ⨀ are two operators on numbers p and q such that

If x ⊕ y = 2 ⊙ 2, then x =

(A) y/2

(B) y

(D) 2y

Answer: (B)

5. Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:

(A) 2

(B) 4

(D) 8

Answer: (C)

6. Statement: Either P marries Q or X marries Y

Among the options below, the logical NEGATION of the above statement is:

(A) P does not marry Q and X marries Y.

(B) Neither P marries Q nor X marries Y.

(D) P marries Q and X marries Y.

Answer: (B)

7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm × 4 cm each.

Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.

Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.

Folding operation 1 is carried out on Sheet M three times.

Folding operation 2 is carried out on Sheet N three times.

The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

(A) 13 : 7

(B) 3 : 2

(D) 5 : 13

Answer: (A)

8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.

The value of θ, in degrees, is ______

(A) 36

(B) 45

(D) 108

Answer: (A)

9. A function, λ, is defined by

The value of the expression is:

(A) −1

(B) 0

(D) 16

Answer: (B)

10. Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.

Based on the above passage, which one of the following is TRUE?

(A) No species possess the ability to construct worlds in their minds.

(B) The terms imagination, invention and innovation refer to unrelated skills.

(D) Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Answer: (C)

Instrumentation Engineering (IN)

Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider the row vectors v = (1, 0) and w = (2, 0). The rank of the matrix M = 2v ^Tv + 3w^Tw, where the superscript T denotes the transpose, is

(A) 1

(B) 2

(D) 4

Answer: (A)

2. Consider the sequence xn = 0. 5x_n−1 + 1, n = 1, 2, … … with x₀ = 0. Then is

(A) 0

(B) 1

(D) ∞

Answer: (C)

3. An infinitely long line, with uniform positive charge density, lies along the z- axis. In cylindrical coordinates (r, ∅,z), at any point not on the z-axis, the direction of the electric field is

Answer: (A)

4. The input-output relationship of an LTI system is given below.

For an input x[n] shown below

the peak value of the output when x[n] passes through h is ____.

(A) 2

(B) 4

(D) 6

Answer: (C)

5. In an ac main, the rms voltage V_ac, rms current Iac and power Wac are measured as: V_ac = 100 V ± 1%, Iac = 1 A ± 1% and W_ac = 50 W ± 2% (errors are with respect to readings). The percentage error in calculating the power factor using these readings is

(A) 1%

(B) 2%

(D) 4%

Answer: (D)

6. Let u(t) denote the unit step function. The bilateral Laplace transform of the function f(t) = e^tu(−t) is ____.

Answer: (C)

7. Input-output characteristic of a temperature sensor is exponential for a

(A) Thermistor

(B) Thermocouple

(D) Mercury thermometer

Answer: (A)

8. The signal sin(√2πt) is

(A) periodic with period T√2π

(B) not periodic

(D) periodic with period T = 4π²

Answer: (B)

Q.9 – Q.11 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

9. The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are

(A) that it is of at least second order.

(B) that it has at least one pole-pair that is underdamped.

(D) that it is a first order system.

Answer: (A; B)

10. For a 4-bit Flash type Analog to Digital Convertor (ADC) with full scale input voltage range “V”, which of the following statement(s) is/are true?

(A) The ADC requires 15 comparators.

(B) The ADC requires one 4 to 2 priority encoder and 4 comparators.

(D) A change in the input voltage by v/16 will always flip the LSB of the output.

Answer: (A; D)

11. A 16-bit microprocessor has twenty address lines (A0 to A19) and 16 data lines. The higher eight significant lines of the data bus of the processor are tied to the 8-data lines of a 16 Kbyte memory that can store one byte in each of its 16K address locations. The memory chip should map onto contiguous memory locations and occupy only 16 Kbyte of memory space. Which of the following statement(s) is/are correct with respect to the above design?

(A) If the 16 Kbyte of memory chip is mapped with a starting address of 80000H, then the ending address will be 83FFFH.

(B) The active high chip-select needed to map the 16 Kbyte memory with a starting address at F0000H is given by the logic expression (A₁₉ · A₁₈ · A₁₇ · A₁₆).

(C) The 16 Kbyte memory cannot be mapped with contiguous address locations with a starting address as 0F000H using only A19 to A14 for generating chip select.

(D) The above chip cannot be interfaced as the width of the data bus of the processor and the memory chip differs.

Answer: (A; C)

Q.12 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

12. A single-phase transformer has a magnetizing inductance of 250 mH and a core loss resistance of 300 Ω, referred to primary side. When excited with a 230 V, 50 Hz sinusoidal supply at the primary, the power factor of the input current drawn, with secondary on open circuit, is ____ (rounded off to two decimal places).

Answer: (0.24 to 0.26)

13. Taking N as positive for clockwise encirclement, otherwise negative, the number of encirclements N of (−1 , 0) in the Nyquist plot of is _____.

Answer: (-1 to -1)

14. The diode used in the circuit has a fixed voltage drop of 0.6 V when forward biased. A signal vs is given to the ideal OpAmp as shown. When vs is at its positive peak, the output (vOA) of the OpAmp in volts is _______.

Answer: (1 to 1)

15. The transistor Q₁ has a current gain β₁ = 99 and the transistor Q₂ has a current gain β₂ = 49. The current I_B2 in microampere is _______.

Answer: (10 to 10)

16. A 300 V, 5 A, LPF wattmeter has a full scale of 300 W. The wattmeter can be used for loads supplied by 300 V ac mains with a maximum power factor of ___________ (rounded off to one decimal place).

Answer: (0.2 to 0.2)

17. A 10-bit ADC has a full-scale of 10.230 V, when the digital output is (11 1111 1111)₂. The quantization error of the ADC in millivolt is _________.

Answer: (4.9 to 5.1)

18. A strain gage having nominal resistance of 1000 Ω has a gage factor of 2.5. If the strain applied to the gage is 100 μm/m, its resistance in ohm will change to ____________ (rounded off to two decimal places).

Answer: (1000.25 to 1000.25)

19. Given: Density of mercury is 13,600 kg/m³ and acceleration due to gravity is 9.81 m/s². Atmospheric pressure is 101 kPa. In a mercury U-tube manometer, the difference between the heights of the liquid in the U-tube is 1 cm. The differential pressure being measured in pascal is ______ (rounded off to the nearest integer).

Answer: (1333 to 1360)

20. A piezoresistive pressure sensor has a sensitivity of 1 (mV/V)/kPa. The sensor is excited with a dc supply of 10 V and the output is read using a 3½ digit 200 mV full-scale digital multimeter. The resolution of the measurement set-up, in pascal is ___.

Answer: (10 to 10)

21. An amplitude modulation (AM) scheme uses tone modulation, with modulation index of 0.6. The power efficiency of the AM scheme is ____ % (rounded off to one decimal place).

Answer: (15.0 to 15.5)

22. When the movable arm of a Michelson interferometer in vacuum (n = 1) is moved by 325 μm, the number of fringe crossings is 1000. The wavelength of the laser used in nanometers is ____.

Answer: (650 to 650)

23. Consider the function f(x) = −x² + 10x + 100. The minimum value of the function in the interval [5, 10] is ___.

Answer: (100 to 100)

24. Let defined in the complex plane. The integral over the contour of a circle c with center at the origin and unit radius is _____.

Answer: (0 to 0)

25. The determinant of the matrix M shown below is ____.

Answer: (4 to 4)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. f(z) = (z − 1) ⁻¹ − 1 + (z − 1) − (z − 1)² + ⋯ is the series expansion of

Answer: (B)

27. A single-phase transformer has maximum efficiency of 98 %. The core losses are 80 W and the equivalent winding resistance as seen from the primary side is 0.5 Ω. The rated current on the primary side is 25 A. The percentage of the rated input current at which the maximum efficiency occurs is

(A) 35.7%

(B) 50.6%

(D) 100%

Answer: (B)

28. A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor circuit in comparison to the rotor being shorted is

(A) The starting torque would be higher.

(B) The power factor at start will be lower.

(D) The losses at starting would be lower.

Answer: (A)

29. Consider a unity feedback configuration with a plant and a PID controller as shown in the figure . and with K being scalar. The closed loop is

(A) only stable for K > 0

(B) only stable for K between -1 and +1

(D) stable for all values of K

Answer: (A)

30. The output Vo of the ideal OpAmp used in the circuit shown below is 5 V Then the value of resistor RL in kilo ohm (kΩ) is

(A) 2.5

(B) 5

(D) 50

Answer: (C)

31. A Boolean function F of three variables X, Y, and Z is given as

F (X, Y, Z) = (Xʹ + Y + Z)˖(X + Yʹ + Zʹ )˖(Xʹ + Y + Zʹ )˖( Xʹ Yʹ Zʹ + Xʹ Y Zʹ + X Y Zʹ )

Which one of the following is true?

(A) F (X, Y, Z) = (X + Y + Zʹ)˖( Xʹ + Yʹ +Zʹ )

(B) F (X, Y, Z) = (Xʹ + Y)˖(X + Y ʹ+ Zʹ )

(D) F (X, Y, Z) = Xʹ Yʹ Z + X Y Z

Answer: (C)

32. A 10½ digit Counter-timer is set in the ‘frequency mode’ of operation (with T_s = 1 s). For a specific input, the reading obtained is 1000. Without disconnecting this input, the Counter-timer is changed to operate in the ‘Period mode’ and the range selected is microseconds (μ_s, with f_s = 1 MHz). The counter will then display

(A) 0

(B) 10

(D) 1000

Answer: (D)

33. A J-type thermocouple has an output voltage V_θ = (13650 + 50 θ_x) μV, where θ_x is the junction temperature in Celsius (°C). The thermocouple is used with reference junction compensation, as shown in the figure. The Instrumentation amplifier used has a gain G = 20. If If θ_Ref is 1 °C, for an input θx of 100°C, the output V_o of the instrumentation amplifier in millivolt is

(A) 98 mV

(B) 99 mV

(D) 101 mV

Answer: (B)

34. A laser pulse is sent from ground level to the bottom of a concrete water tank at normal incidence. The tank is filled with water up to 2 m below the ground level. The reflected pulse from the bottom of the tank travels back and hits the detector. The round-trip time elapsed between sending the laser pulse, the pulse hitting the bottom of the tank, reflecting back and sensed by the detector is 100 ns. The depth of the tank from ground level marked as x in metre is ____.

(Refractive index of water n_water = 1. 3 and velocity of light in air c_air = 3 × 10⁸ m/s)

(A) 9

(B) 10

(D) 12

Answer: (D)

35. A 4 × 1 multiplexer with two selector lines is used to realize a Boolean function F having four Boolean variables X, Y, Z and W as shown below. S₀ and S₁ denote the least significant bit (LSB) and most significant bit (MSB) of the selector lines of the multiplexer respectively. I₀, I₁, I₂, I₃ are the input lines of the multiplexer.

The canonical sum of product representation of F is

(A) F (X, Y, Z, W) = Σ m( , ,3, 4, 5)

(B) F (X, Y, Z, W) = Σ m( , ,3,11,14)

(D) F (X, Y, Z, W) = Σ m(1,3,7,9,15)

Answer: (B)

36. Given below is the diagram of a synchronous sequential circuit with one J-K flip-flop and one T flip-flop with their outputs denoted as A and B respectively, with JA = (Aʹ + Bʹ), KA = (A + B), and TB = A.

Starting from the initial state (AB = 00), the sequence of states (AB) visited by the circuit is

(A) 00 → 01 → 10 → 11 → 00…

(B) 00 → 10 → 01 → 11 → 00…

(D) 00 → 01 → 11 → 00…

Answer: (B)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

37. Consider that X and Y are independent continuous valued random variables with uniform PDF given by X ~ U(2, 3) and Y ~ U(1, 4). Then P(Y ≤ X) is equal to __________ (rounded off to two decimal places).

Answer: (0.45 to 0.55)

38. Given The value of the determinant │A⁴ − 5A³ +6A² +2 I│= _____.

Answer: (4 to 4)

39. The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of 1 kg has a depth of 0.5 m along the y direction. The coefficient of friction between the bar and the surface is 0.1. Assume the acceleration due to gravity to be 10 m/s². The system faces a uniform flux density B = −1 ẑ T. At time t = 0, a current of 10 A is switched onto the bar and is maintained.

When the bar has moved by 1 m, its speed in metre per second is ____ (rounded off to one decimal place).

Answer: (2.7 to 2.9)

40. A toroid made of CRGO has an inner diameter of 10 cm and an outer diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper wire is wound on the core. μ_o = 4π × 10⁻⁷ H/m and μR of CRGO is 3000. When a current of 5 mA flows through the winding, the flux density in the core in millitesla is ____.

Answer: (10 to 10)

41. An air cored coil having a winding resistance of 10 Ω is connected in series with a variable capacitor C_x. The series circuit is excited by a 10 V sinusoidal voltage source of angular frequency 1000 rad/s. As the value of the capacitor is varied, a maximum voltage of 30 V was observed across it. Neglecting skin-effect, the value of the inductance of the coil in millihenry is _____.

Answer: (30 to 30)

42. A household fan consumes 60 W and draws a current of 0.3125 A (rms) when connected to a 230 V (rms) ac, 50 Hz single phase mains. The reactive power drawn by the fan in VAr is __________ (rounded off to the nearest integer).

Answer: (39 to 40)

43. Given y(t) = e^−3tu(t) ∗ u(t + 3), where * denotes convolution operation. The value of y(t) as t → ∞ is ____________ (rounded off to two decimal places).

Answer: (0.3 to 0.35)

44. The input signal shown below

is passed through the filter with the following taps

The number of non-zero output samples is ____.

Answer: (10 to 10)

45. A sinusoid (√2 sin t) μ(t), where μ(t) is the step input, is applied to a system with transfer-function The amplitude of the steady state output is ____.

Answer: (0.95 to 1.05)

46. Consider a system with transfer-function A unit step function μ(t) is applied to the system, which results in an output y(t). If e(t) = y(t) − μ(t), then is ______.

Answer: (1 to 1)

47. The circuit shown below uses an ideal OpAmp. Output V_O in volt is ________ (rounded off to one decimal place).

Answer: (1.0 to 1.1)

48. All the transistors used in the circuit are matched and have a current gain β of 20. Neglecting the Early effect, the current I_O4 in milliampere is _____.

Answer: (1 to 1)

49. The power in a 400 V (rms, line-line) three-phase, three-wire RYB sequence system is measured using the two wattmeters, as shown. The R-line current is 5∠60° Wattmeter W₁ in the R-line will read (in watt) _________.

Answer: (0 to 0)

50. A 31⁄2 digit, rectifier type digital meter is set to read in its 2000 V range. A symmetrical square wave of frequency 50 Hz and amplitude ±100 V is measured using the meter. The meter will read _____.

Answer: (111 to 111)

51. A bar primary current transformer of rating 1000/1 A, 5VA, UPF has 995 secondary turns. It exhibits zero ratio error and phase error of 30 minutes at 1000 A with rated burden. The watt loss component of the primary excitation current in ampere is __________ (rounded off to one decimal place).

Answer: (4.9 to 5.1)

52. In the bridge circuit shown, the voltmeter V showed zero when the value of the resistors are: R₁ = 100 Ω, R₂ = 110 Ω, and R₃ = 90 Ω. If (R₁/R₂) = (R_A/R_B), the value of R₄ in ohm is _____.

Answer: (99 to 99)

53. For the full bridge made of linear strain gages with gage factor 2 as shown in the diagram, R₁ = R₂ = R₃ = R₄ = 100 Ω at 0°C and strain is 0. The temperature coefficient of resistance of the strain gages used is 0.005 per ° All strain gages are made of same material and exposed to same temperature. While measuring a strain of 0.01 at a temperature of 50 °C, the output V_O in millivolt is _____ (rounded off to two decimal places).

Answer: (2.45 to 2.55)

54. A signal having a bandwidth of 5 MHz is transmitted using the Pulse code modulation (PCM) scheme as follows. The signal is sampled at a rate of 50% above the Nyquist rate and quantized into 256 levels. The binary pulse rate of the PCM signal in Mbits per second is ___.

Answer: (120 to 120)

55. In the figure shown, a large multimode fiber with ncore = 1. 5 and n_clad = 1. 2 is used for sensing. A portion with the cladding removed passes through a liquid with refractive index n_liquid. An LED is used to illuminate the fiber from one end and a paper is placed on the other end, 1 cm from the end of the fiber. The paper shows a spot with radius 1 cm. The refractive index n_liquid of the liquid (rounded off to two decimal places) is ________.

Answer: (1.30 to 1.35)

GATE Exam 2021 Geology and Geophysics (GG) Question Paper With Answer Key

June 8, 2023June 14, 2022 by suresh84

GATE-2021

GG-Geology & Geophysics

GA: General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A) whose

(B) which

(D) whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A) 396

(B) 324

(D) 144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (11¹³ + 1)?

(A) 11²⁶ + 1

(B) 11³³ + 1

(D) 11⁵² – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Stone

(B) Land

(D) Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?

(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.

(D) To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm²is:

(A) 12.50

(B) 6.25

(D) 1.5625

Answer: (C)

8. Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.

The mean of X is _____

(A) 2.5

(B) 5.0

(D) 50.0

Answer: (D)

The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the

exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A) 65 and 53

(B) 60 and 50

(D) 55 and 48

Answer: (D)

10. Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

(A) There are two cars parked in between Q and V.

(B) Q and R are not parked together.

(D) Car P is parked at the extreme end.

Answer: (A)

Geology (GG)

Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Which of the given planets has the highest average density?

(A) Mercury

(B) Venus

(D) Mars

Answer: (C)

2. In a multi-electrode resistivity tomography (ERT) survey, using equally spaced electrodes, which of the given configurations will provide the maximum number of data points?

(A) Wenner array

(B) Axial Dipole-dipole array

(D) Schlumberger array

Answer: (C)

3. In Electromagnetic methods of prospecting, which one of the given options is CORRECT about frequency and type of current source for the Primary field used?

(A) High frequency A.C.

(B) Low frequency A.C.

(D) Low frequency D.C.

Answer: (B)

4. ‘Group’ is a unit of:

(A) Lithostratigraphy

(B) Sequence stratigraphy

(D) Chronostratigraphy

Answer: (A)

5. Furongian is an Epoch of:

(A) Cambrian

(B) Ordovician

(D) Cretaceous

Answer: (A)

6. The stage of textural maturity of a clay-rich sandstone containing poorly-sorted and angular framework grains is:

(A) Mature

(B) Supermature

(D) Submature

Answer: (C)

7. Which one of the following structures indicates Synsedimentary deformation?

(A) Festoon bedding

(B) Flaser bedding

(D) Convolute bedding

Answer: (D)

8. Low value in SP log as observed in dispersed shales is mainly due to the impeded movement of:

(A) Na⁺ ion

(B) Cl ion

(D) OH⁻ion

Answer: (B)

9. In Radiometric survey, the g-ray spectrometer count rate depends on:

(A) Cracks present in the target rock volume

(B) Solid angle of the target rock about the spectrometer

(D) Pressure in the target rock

Answer: (B)

10. The dimension of radiant emittance of a blackbody as per Stefan-Boltzmann law is:

(A) M⁰L¹T⁻¹

(B) M¹L⁻¹T⁻²

(D) M¹L⁰T⁻³

Answer: (D)

11. A surface geological process that can create a landform called Cirque is:

(A) aeolian deposition

(B) fluvial deposition

(D) deposition of volcanic ash

Answer: (C)

12. If α and β P- and S-wave velocities, respectively, then α² – (4/3)β² is equal to:

(κ is the bulk modulus, μ is shear modulus and ρ is density)

(A) κ/ρ

(B) μ/ρ

(D) κ − μ/ρ

Answer: (A)

13. Which one of the following phases is P-wave that converts to S-wave during passage through the solid inner core?

(A) PKIKP

(B) PKJKP

(D) PKPPcP

Answer: (B)

14. In reduction of gravity data, the latitude correction is maximum at:

(A) 35° latitude

(B) 45° latitude

(D) 65° latitude

Answer: (B)

15. The most coaliferous unit of the Gondwana Supergroup is:

(A) Talchir Formation

(B) Barakar Formation

(D) Panchet Formation

Answer: (B)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

16. A vertical borehole encounters a shale bed of uniform thickness occurring at a depth of 5 m and dipping 60°. The borehole pierces through this shale bed for a length of 10 m to reach a sandstone layer below. The true thickness of the shale bed is ________ m. [in integer]

Answer: (5 to 5)

17. The mass and volume of a fully dried soil sample are 2200 gm and 1100 cm³, respectively. If the specific gravity of the soil particles is 2.5 and water density is 1 gm/cm³, the void ratio of the soil is ________. [round off to 2 decimal places]

Answer: (0.25 to 0.25)

18. A constant-head permeability test was performed on a vertical sand column of height 40 cm and cross-sectional area of 25 cm2. During the test, when the loss of head was 50 cm, the volume of water collected in 2 minutes was 300 cm³. Applying Darcy’s law, the calculated coefficient of permeability of the sand column is ________ cm/sec. [round off to 2 decimal places]

Answer: (0.08 to 0.08)

19. The radius (r) of the oblate spheroid at 45° latitude with ellipticity of polar flattening of 1/298.25 and equatorial radius of 6378140 m is ________ km. [round off to 2 decimal places]

Answer: (6367.44 to 6367.46)

20. Light passes through two media with refractive indices of 1.75 and 1.55, respectively. The thickness of both the media is 30 μ The resultant path difference of the yellow light component (λ = 589 nm) is ________ πm. (Take λ = 3.141) [round off to one decimal places]

Answer: (64.0 to 64.0)

21. The water table in an unconfined aquifer at a place near the coast is 1 m above the Mean Sea Level. Given the densities of fresh and saline water as 1.001 and 1.025 g/cc, respectively, the fresh-saline water interface at the same location should be at a depth of _______ m from the water table. [round off to one decimal place]

Answer: (42.6 to 42.7)

22. The volume percentage of galena and quartz in an ore body of Pb are 90 and 10, respectively. The densities of galena and quartz are 7.6 and 2.65 g/cc, respectively. The grade of the ore body in terms of weight percent of Pb is _____. (Atomic weights of Pb = 206 and S = 32) [round off to 2 decimal places]

Answer: (83.30 to 83.34)

23. Normal moveout (NMO) for reflected phase of seismic data is 2 milliseconds. Consider the diffraction source at the edge of the same reflector, where the shot point is directly above diffraction source. In this case, the NMO due to diffraction is ______ milliseconds [in integer].

Answer: (4 to 4)

24. In a 2D seismic survey, first receiver location is at (1000 m, 4000 m), second receiver location is at (2000 m, 4000 m) and the source location is at (2000 m, 1000 m). Consider P-wave velocity as 5000 m/sec. The difference in first arrival time of P-wave phase for the two receivers is ________ seconds. [round off to 2 decimal places].

Answer: (0.03 to 0.03)

25. The potential difference measured between potential electrodes using Wenner array is 500 mV when a current of 2 A is passed through the subsurface between current electrodes. If the computed apparent resistivity is 100 Ωm then the distance between the current electrodes will be ________ m. [round off to 2 decimal places] (Use π = 3.141)

Answer: (190.00 to 192.00)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. Which one of the following statements is CORRECT?

(A) Taphonomy refers to the study of fossilization pathways from death of an organism to its recovery as a fossil.

(B) Biostratinomy refers to the study of fossilization pathways from burial of an organism under sediments to its recovery as a fossil.

(C) Biostratinomy is an integral component of biostratigraphy and refers to the characterization of strata based on fossil content.

(D) Taphonomy refers to the study of fossilization pathways from death of an organism to its burial under the sediments.

Answer: (A)

27. Based on the three statements given below, choose the CORRECT option:

Statement I: Gunderdehi Formation is a stratigraphic unit of the Chattisgarh Supergroup.

Statement II: Raniganj Formation is a coal-bearing Triassic unit of the Gondwana Supergroup.

Statement III: Pitepani Volcanics is a stratigraphic unit of the Dongargarh Supergroup.

(A) All the statements are correct

(B) Statement I is correct, but statements II and III are incorrect

(D) Statements II and III are correct but statement I is incorrect

Answer: (C)

28. Which one of the following equid genera was a one-toed grazer?

(A) Merychippus

(B) Parahippus

(D) Mesohippus

Answer: (C)

29. Match the following invertebrate genera in Group I with their corresponding Class/Phylum in Group II:

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

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

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

Answer: (A)

30. Tillite with faceted boulders and green shale with dropstones characterize the lithology of:

(A) Lameta Formation

(B) Bagra Formation

(D) Panchet Formation

Answer: (C)

31. Match the following structures in Group I with the corresponding environment of deposition in Group II:

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

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

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

Answer: (A)

32. Match the items in Group-I with appropriate items in Group-II

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

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

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

Answer: (C)

33. With regard to superposed folding, the stereographic projection represents a geometry of:

(A) plane cylindrical fold.

(B) plane non-cylindrical fold.

(D) non-plane non-cylindrical fold.

Answer: (B)

34. The given outcrop pattern of a bed (shaded in grey) with respect to contours (dashed lines) indicates that the bed.

(A) dips upstream.

(B) is horizontal.

(D) dips downstream at an angle equal to the valley gradient.

Answer: (A)

35. With regard to occurrence of groundwater in an area, which of the given statements is CORRECT?

(A) Vadose water occurs in the zone of saturation.

(B) The zone of aeration lies below the zone of saturation.

(D) The depth of the perched water table is less than that of the water table.

Answer: (D)

36. There are indications of presence of a massive tabular multimetal sulfide ore body at a shallow depth from the surface. Which of the following would be the most efficient geophysical method to confirm the presence of the ore body?

(A) resistivity sounding

(B) ground geomagnetic survey

(D) ground gravity survey

Answer: (C)

37. The following reaction takes place in the amphibolite grade of metamorphism of pelitic rocks:

kyanite + chlorite ⟺ staurolite + quartz +H₂O

Which of the following is a CORRECT statement on this reaction?

(A) The reaction can be represented as a sharp univariant boundary.

(B) Initially chlorite and staurolite are Fe-rich and will gradually become Mg-rich with increasing temperature.

(D) The reaction is independent of fugacity of H₂O.

Answer: (B)

38. Match the items in Group-I with corresponding appropriate items in Group-II.

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

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

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

Answer: (A)

39. The symmetry elements of a point group are: 3 crystallographic axes of 2-fold symmetry and 3 mirror planes perpendicular to the crystallographic axes. The Hermann – Mauguin notation of the point group is:

(A) 2m2m2m

(B) 2mm

(D) 2/m

Answer: (C)

40. An aqueous polyphase (L + V + solid) inclusion contains a halite daughter crystal at room temperature and pressure. Which of the given statements is CORRECT in relation to this inclusion?

(A) The salinity of the bulk aqueous fluid can be determined from the temperature of melting of ice.

(B) The salinity of the bulk aqueous fluid can be determined from the temperature of dissolution of halite.

(D) The density in all cases can be determined from the temperature of dissolution of the halite daughter crystal.

Answer: (B)

41. Match the rock types in Group-I with their most likely corresponding lithospheric/ tectonic settings of formation in Group-II.

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

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

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

Answer: (C)

42. A mantle source rock melts at a time t0 giving rise to melt (M) and residue (R). Which of the following statements is CORRECT about evolution of the (¹⁴³Nd/¹⁴⁴Nd) and (⁸⁷Sr/⁸⁶Sr) isotope ratio in M (that crystallized to form a rock) and R?

(A) The growth of Nd isotope ratio versus time is faster in R than M and the Sr isotope ratio grows slower in R than M.

(B) The growth of Nd isotope ratio versus time is slower in R than M and the Sr isotope ratio grows faster in R than M.

(D) The growth of Nd and Sr isotope ratio in M and R would depend on the initial concentrations of Sm and Rb in the mantle source rock.

Answer: (A)

Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

43. The mole percentages of SiO₂, Al₂O₃ and K₂O in a granitic rock are 84.21, 7.89 and 7.89, respectively. The molar proportion (in %) of K-feldspar in the rock is ______. [ round off to one decimal place]

Answer: (29.9 to 30.1)

44. In a zone of active normal faulting, the maximum and minimum in situ principal stresses (compressive in nature) are 30 MPa (s1) and 10 MPa (s3), respectively. The fault plane striking N-S has a dip amount of 60° towards E. Considering Anderson theory of faulting and using the given information, the calculated normal stress on the fault plane is ________ MPa. [in integer]

Answer: (15 to 15)

45. A circular tunnel is being excavated in a blocky rock mass by drilling and blasting. An excavation disturbed zone (EDZ) around the tunnel extends 0.70 m into the rock from the excavation surface. Considering the unit weight of the rock as 25 kN/m³, the support pressure required at the crown of the tunnel to stabilize the loose blocks of the EDZ is _______ kPa. [round off to one decimal place]

Answer: (17.5 to 17.5)

46. Under uniaxial compression, a cylindrical quartzite specimen (length = 122 mm and diameter = 60 mm) showed linear elastic behaviour. The uniaxial compressive strength and the modulus ratio of the rock are 150 MPa and 500, respectively. The axial strain at 75 MPa during the loading was _________ milli-strain. [in integer]

Answer: (1 to 1)

47. The sketch shows a triangular rock mass (ABC) resting on a joint plane (AC) inclined at 35° with the horizontal. A rockbolt having an inclination of 25° with the horizontal is used to stabilize the slope. If the bolt tension (T) is 110 kN, the absolute value of shear force along the joint plane induced by the bolt tension is _________ kN. [in integer]

Answer: (55 to 55)

48. A stratified confined aquifer consists of three parallel homogeneous and isotropic horizontal layers with thickness of 10 m, 5 m and 5 m. The layers have the same width. The hydraulic conductivities of the strata are 15 m/day, 20 m/day and 30 m/day, respectively. The water flow follows Darcy’s law and is parallel to the strata. Considering the same hydraulic gradient for all the layers, the effective hydraulic conductivity of the aquifer is ________ m/day. [in integer]

Answer: (20 to 20)

49. A drainage basin of fourth order covers an area of 35 km². Within the basin, the total lengths of the 1st order, 2nd order and 3rd order drainages are 11.5 km, 8.5 km and 4.2 km, respectively. If the drainage density of the basin is 0.8 km⁻¹, the total length of the 4th order drainage is ________ km. [round off to one decimal place]

Answer: (3.8 to 3.8)

50. The grade of copper (in wt%) of an ore body determined at locations 1, 2 and 3 are indicated (in parentheses) below. The grade of copper at an unknown location x calculated using Inverse-Square Distance Weighting (IDW) is ________ wt %. [round off to 2 decimal places]

Answer: (1.67 to 1.69)

51. The heat flux at the Earth’s surface is 60 mWm⁻². If the thermal conductivity at the surface is 2.5 Wm⁻¹ °C⁻¹, the geothermal gradient is ________ °C/km. [in integer]

Answer: (24 to 24)

52. A rock formed at time t₀ = 0 with number of ¹⁴C atoms = 10⁵. The number of ¹⁴C atoms (in log₁₀) after a time of 8 × 10³ years is _______. [round off to 3 decimal places] (Use a decay constant of 1.25 × 10⁻⁴ yr⁻¹)

Answer: (4.565 to 4.567)

53. In the given reaction,

2Fe²⁺ + 3H₂O → Fe₂O₃ + 6H⁺ + 2e⁻

consider ideal condition, take concentration of Fe²⁺ as 10⁻⁵ molal, E⁰ = 0.98 V and pH=6. The value of (2.303 × R × T)/F = 0.059 (where F is the Faraday constant). The value of Eh on the Fe²⁺ / hematite boundary at 25 °C is ________ V. [round off to 2 decimal places]

Answer: (0.21 to 0.22)

54. The first and second dissociation constants of H₂CO₃ are 6.761 × 10⁻⁷ and 4.68 × 10⁻¹¹, respectively. If the concentration of H₂CO₃ is 1 molal and pH = 6, the ∑CO₂ in the solution (assuming ideal condition) is _______ molal. [round off to 3 decimal places]

Answer: (1.675 to 1.677)

55. A satellite orbits the earth at an altitude of 700 km on the equatorial plane of the earth and it revolves in the same direction as the direction of rotation of the earth. Considering the radius of a spherical earth as 6300 km and the acceleration due to gravity as 10 m/s², the tangential velocity of the satellite in the orbit is ____________ km/s. [round off to 2 decimal places]

Answer: (7.52 to 7.53)

Geophysics (GG)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. In a horizontally stratified cuboid rock sample (stratified in vertical z direction with various layers of different resistivity), bulk resistivity is measured in three perpendicular directions. If ρ₁, ρ₂, and ρ₃ are the bulk resistivities measured perpendicular to xy, xz and yz planes, respectively, then

(A) ρ₁ < ρ₂ = ρ₃

(B) ρ₁ > ρ₂ = ρ₃

(D) ρ₁ ≠ ρ₂ ≠ ρ₃

Answer: (B)

27. Which one is the CORRECT sequence of electromagnetic methods in terms of depth of investigation?

P – AFMAG method

Q – VLF method

R – GPR method

S – Magnetotelluric method

(A) P > Q > S > R

(B) P > S > R > Q

(D) S > Q > R > P

Answer: (C)

28. Which Norm gives the maximum weight to the data points having maximum deviation/outlier from the smoothly fitted curve during linearized inversion?

(A) L1-Norm

(B) L2-Norm

(D) L∞-Norm

Answer: (D)

29. Which one of the following statements is CORRECT for the Quenching agent used in the tube of Geiger-Muller counter?

(A) It enhances the emission of secondary electrons from the cathode.

(B) It reduces the emission of secondary electrons from the cathode.

(D) It reduces the emission of secondary electrons from the anode.

Answer: (B)

30. Which one of the following statements is CORRECT regarding the property of Laplacian operator for vector/scalar fields?

(A) Laplacian of a vector field is zero if the Laplacian of each of its components are zero.

(B) Laplacian of a vector field is zero if the Laplacian of any one of its component is zero.

(D) If the Laplacian of a scalar field is finite (non-zero) then the scalar field is harmonic.

Answer: (A)

31. The most desirable interaction of γ-ray with matter for γ-ray spectroscopy is

(A) Photoelectric effect only

(B) Both Photoelectric effect and Compton scattering

(D) Photoelectric effect, Compton scattering and Pair production

Answer: (A)

32. Which one of the following is the CORRECT sequence for a 2D seismic reflection data processing prior to Time-depth conversion?

(A) Migration → Deconvolution → Filtering → Equalization → Coherency

(B) Deconvolution → Migration → Filtering → Coherency → Equalization

(D) Deconvolution → Filtering → Equalization → Migration → Coherency

Answer: (D)

33. Choose the CORRECT procedure to avoid the area of cracked, altered formation in Sonic log.

(A) Measure interval transit times using long-spacing sonic tools.

(B) Use more number of sets of sources.

(D) Use more number of sets of detectors.

Answer: (A)

34. The factor that DOES NOT influence measurement of Nuclear Magnetic Resonance log is

(A) mineral composition of the rock.

(B) bound water (irreducible water).

(D) pore fluid pressure.

Answer: (D)

35. Consider a time-invariant geophysical filter with the given input as:

x(t) = e^−αt when t ≥ 0 ; x(t) = 0 when t < 0 and output y(t) = e⁻^β^t when t ≥ 0 ; y(t) = 0 when t < 0. The transfer function for the given input and output of time-invariant filter will be:

Answer: (B)

36. Which of the given figures is the Hilbert transform of the Dirac delta function δ(ξ) :

(A) Figure 1

(B) Figure 2

(D) Figure 4

Answer: (A)

37. If a mountain range is 100% isostatically compensated (Airy’s type), what would be the expected nature of the Bouguer anomaly and free air anomaly?

(A) Bouguer anomaly is very large and negative; free air anomaly is small and positive.

(B) Bouguer anomaly is very large and negative; free air anomaly is large and positive.

(D) Bouguer anomaly is very large and negative; free air anomaly is large and negative.

Answer: (A)

38. Which of the following is INCORRECT for a recorded nuclear explosion event?

(A) The first P-wave from an explosion to arrive at any seismic station, irrespective of Azimuth, should be compressional.

(B) Nuclear explosions are not as good as earthquakes at generating surface waves or S-waves.

(D) Nuclear explosions have all been shallower than 2 km depth.

Answer: (C)

39. Focal depth can be determined from measurement of the difference in the travel time between:

(A) pP and P

(B) PP and P

(D) PPP and P

Answer: (A)

40. Of the following options, at which discontinuity both P-wave and S-wave have maximum velocity drop?

(A) Conard

(B) Mohorovicic

(D) Lehman

Answer: (C)

41. In data enhancement techniques, what is the advantage of magnetic anomaly being ‘Reduced to the pole’?

(A) Enhances the signal to noise ratio.

(B) Estimates the depth to the basement.

(D) Helps in pseudo-gravity transformation.

Answer: (C)

42. Match the source in Group – I with their half-width (X_1/2) / δg_max and depth (d) relation in Group –II.

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

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

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

Answer: (C)

Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

43. If a gravity determination is made at an elevation of 150 m above mean sea level, the Bouguer correction required for a density contrast of 250 kg m⁻³ with the surroundings is________ mgal. [round off to 2 decimal places]

Answer: (1.55 to 1.65 OR -1.65 to -1.55)

44. An infinite horizontal cylinder of radius 40 km is buried at a depth of 100 km and yields the same maximum gravity anomaly as that of an infinite horizontal cylinder of radius 1 km, buried at a depth of 1 km having density contrast with the surroundings of 200 kgm⁻³. The density contrast of the deeper cylinder with respect to the surrounding is ________ kg/m³. [round off to one decimal place]

Answer: (12.5 to 12.5)

45. An earthquake causes an average of 25 m strike slip displacement over a 50 km long, 25 km deep portion of a transform fault. Assuming that the rock rigidity is 3 × 10¹⁰ Nm⁻², the moment magnitude (Mw) of the earthquake is ______ . [round off to 2 decimal places]

Answer: (3.24 to 3.26 OR 7.90 to 7.92)

46. Lithological unit X is sandwiched between Y1 above and Y2 below it. Now consider a log across lithology X, where Gamma ray (GR) reading is given by 100API; Y₁ lithology, where minimum GR reading is 10API; and Y₂ lithology of shale, where GR reading is 200API. Then the shale-free fractional volume in the X lithology will be________. [round off to 2 decimal places]

Answer: (0.52 to 0.53)

47. In a 2D seismic survey, 25 receivers are placed in a group and 25 sources are placed in another group, where random noise is present. The signal to noise ratio for this arrangement will be_______. [in integer]

Answer: (25 to 25)

48. In a VSP survey, the tube wave passage through borehole causes cross-section area change from 0.79 m² to 1.13 m². The transmission coefficient will be ______. [round off to 2 decimal places]

Answer: (0.82 to 0.82)

49. In a cratonic region, radioactive heat generation decreases exponentially with depth. Assuming characteristic depth as 10 km and surface heat generation as 3 μWm⁻³ and neglecting mantle heat flow, the heat production per unit volume for a 30 km thick layer will be_______ μWm⁻³. [round off to 2 decimal places]

Answer: (0.95 to 0.95)

50. In an Induced Polarization survey, 50 milliseconds chargeability was measured for steady state voltage (full saturation reached) of 200 V between potential electrodes. When the current was switched off, the voltage across potential electrodes drops instantaneously (time t = 0 s) to a level V_a and thereafter decays linearly with time and becomes zero in 10 seconds. The magnitude of instantaneous voltage V_a (at time t = 0 s) will be________ mV. [in integer]

Answer: (2000 to 2000)

51. Apparent resistivity sounding data for Schlumberger array is theoretically generated by the teacher for the following 4-layer model as: ρ₁ = 100 Ωm, ρ₂ = 20 Ωm, ρ₃ = 500 Ωm, ρ₄ = 10 Ωm and layer thicknesses h1 = 50 m, h₂ = 20 m and h₃ = 50 m. If the student interprets this theoretical sounding data for ρ₃ as 750 Ωm, then according to the Principle of Equivalence, the thickness h₃ would be ________ m. [round off to 2 decimal places]

Answer: (33.00 to 34.00)

52. A 3D conducting body is located at a depth of 50 m in a homogeneous medium of resistivity 500 Ω A frequency of f₁ Hz is appropriate to detect this conducting body in a plane wave EM survey. When the same conducting body is located in a host medium of resistivity 100 Ωm at the same depth then a frequency of f2 Hz is found to be appropriate. Then the value of f₂/f₁ will be __________. [round off to 2 decimal places]

Answer: (0.19 to 0.21)

53. The apparent resistivity and phase computed for MT measurement at 10⁻³ Hz frequency is 500 Ωm and 30°, respectively. Ratio of Imaginary to Real component of the Impedance tensor is ______. [round off to 2 decimal places]

Answer: (0.57 to 0.59)

54. The diagonal elements of a covariance matrix computed for a linearized inverse problem having model parameters m₁, m₂, m₃, m₄, m₅ are 49, 15, 3, 200, 40, respectively. The standard deviation (uncertainty) in the estimation of model parameters m4 is ________. [round off to 2 decimal places]

Answer: (14.00 to 15.00)

55. Electric current density incident at an angle 40° from vertical at the horizontal interface between two layers with resistivity ρ₁ = 100 Ωm and ρ₂ = 500 Ωm (from layer 1 to layer 2). The current density will enter into the second layer at an angle ________ degrees from vertical. [round off to 2 decimal places]

Answer: (9.45 to 9.55)

GATE Exam 2021 Ecology and Evolution (EY) Question Paper With Answer Key

June 8, 2023June 14, 2022 by suresh84

GATE-2021

EY-Ecology and Evolution

GA- General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A) whose

(B) which

(D) whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A) 396

(B) 324

(D) 144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (11¹³ + 1)?

(A) 11²⁶ + 1

(B) 11³³ + 1

(D) 11⁵² – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Stone

(B) Land

(D) Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Which one of the following statements is the CORRECT inference from the above passage?

(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.

(D) To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm²is:

(A) 12.50

(B) 6.25

(D) 1.5625

Answer: (C)

The mean of X is _____

(A) 2.5

(B) 5.0

(D) 50.0

Answer: (D)

exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A) 65 and 53

(B) 60 and 50

(D) 55 and 48

Answer: (D)

Based on the above statements, the only INCORRECT option given below is:

(A) There are two cars parked in between Q and V.

(B) Q and R are not parked together.

(D) Car P is parked at the extreme end.

Answer: (A)

EY: Ecology and Evolution

Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Animal species can vary in whether dispersal is more likely among male offspring (male-biased), female offspring (female-biased), or similar between the sexes. Dispersal in birds and mammals is most commonly

(A) female-biased and male-biased, respectively.

(B) female-biased and similar between the sexes, respectively.

(D) similar between the sexes, and female-biased respectively.

Answer: (A)

2. Of the following, which one is the most direct measure of Darwinian fitness?

(A) Adult body size

(B) Lifetime reproductive success

(D) Maximum sprint speed

Answer: (B)

3. The marginal value theorem in optimal foraging theory examines which one of the following foraging decisions?

(A) How long to stay in a patch of food

(B) How to allocate time to foraging versus reproduction

(D) How to select between different food types within a patch

Answer: (A)

4. Which one of the following shows the highest degree of endemism?

(A) Birds of the Himalayas

(B) Mammals of central India

(D) Trees of the Gangetic basin

Answer: (C)

5. Which one of the following Mendelian disorders is influenced by diet?

(A) Cystic fibrosis

(B) Haemophilia

(D) Thalassemia

Answer: (C)

6. Which one of the following mammalian DNA regions exhibits the highest level of sequence variation?

(A) Homeobox transcription factor binding domain

(B) Hox genes

(D) Histone protein-encoding genes

Answer: (C)

7. Which one of the following makes a species most vulnerable to extinction?

(A) Low density throughout a large geographic range and in several habitat types

(B) Locally common in a restricted geographic range and in several habitat types

(D) Locally common in a restricted geographic range and in a specific habitat type

Answer: (D)

8. The frequency distributions of a trait in two populations, X and Y, are shown in the figure.

Which one of the following statements about the mean and standard deviation (SD) of the two populations is accurate?

(A) X has higher mean, and Y has higher SD.

(B) Y has higher mean, and X has higher SD.

(D) Y has higher mean, and Y has higher SD.

Answer: (D)

9. Two sister species of bulbuls have non-overlapping distributions. One is distributed in India and the other in Sri Lanka. Which one of the following modes of speciation is the most parsimonious explanation for this pattern?

(A) Allopatric speciation

(B) Sympatric speciation

(D) Peripatric speciation

Answer: (A)

10. In an Arctic Ocean food chain, killer whales feed on sea otters, which feed on sea urchins, which in turn feed on kelp (a type of seaweed). An increase in the abundance of killer whales causes sea otter abundance to decline, leading to higher sea urchin densities, which in turn reduces the abundance of kelp. Which one of the following terms describes this phenomenon?

(A) Trophic cascade

(B) Prey switching

(D) Productivity-stability relationship

Answer: (A)

11. Listed below are hypotheses for the evolution of monogamy. Which one of these is NOT based on the concept of individual selection?

(A) Food provisioning by both parents is crucial for offspring survival.

(B) Biparental protection from predators is essential for offspring survival.

(D) Forming monogamous pairs allows individuals to regulate their reproductive output and ensure the survival of the species.

Answer: (D)

12. Rising temperature due to global warming can stimulate decomposition of organic matter and release CO₂ into the atmosphere. This is an example of

(A) positive feedback.

(B) negative feedback.

(D) environmental stochasticity.

Answer: (A)

13. Ant-mimic spiders of the genus Myrmarachne are known for which one of the following evolutionary phenomena?

(A) Aposematism

(B) Aggressive mimicry

(D) Muellerian mimicry

Answer: (B)

14. The probability of local extinction increases with body size when there is forest degradation, loss, and fragmentation. Consider the following hypotheses for the vulnerability of larger-bodied species:

(P) Larger-bodied species tend to have smaller population sizes.

(Q) Larger-bodied species require larger territories/home ranges.

(R) Larger-bodied species have higher absolute resource and energy requirements.

Which one of the following options correctly lists all potential reasons for the vulnerability of larger-bodied species?

(A) P and Q only

(B) P only

(D) P, Q, and R

Answer: (D)

15. Grazing by large mammalian herbivores can have a strong influence on ecosystem structure, and can cause ecosystems to transition between alternative states over decades. Which one of the following transitions can result from grazing?

(A) Mangrove to coral reef

(B) Terai grassland to alpine meadow

(D) Tropical rainforest to arid desert

Answer: (C)

16. The effective population size of a sexually reproducing, diploid, animal species will be highest when the sex ratio (number of reproducing males /number of reproducing females) is

(A) 1

(B) 0.5

(D) 2

Answer: (A)

Q.17 – Q. 22 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

17. The theory of evolution by natural selection was proposed by which one (or more) of the following?

(A) Charles Darwin

(B) Jean Baptiste Lamarck

(D) Georges Cuvier

Answer: (A; C)

18. According to the MacArthur – Wilson equilibrium model of island biogeography, which one (or more) of the following factors affect(s) extinction rate on an island?

(A) Interspecific competition

(B) Island area

(D) Species identity

Answer: (B)

19. Which of the following is/are necessary condition(s) for natural selection to shape limb lengths in a population?

(A) Individuals in a population vary in the length of their limbs.

(B) Limb length increases in individuals with repeated use.

(D) Limb length influences running speed and thus, their ability to survive and reproduce.

Answer: (A; C; D)

20. Which of the following is/are possible reason(s) for linkage disequilibrium between alleles at two loci?

(A) Low recombination rate between loci

(B) High recombination rate between loci

(D) Polyploidy

Answer: (A; C)

21. Metabolism includes the processes of catabolism and anabolism. Select the anabolic process(es).

(A) Growth

(B) Storage

(D) Excretion

Answer: (A; B)

22. SARS-CoV-2 is hypothesised to have jumped from bats to pangolins before infecting humans. Which one (or more) of the following methods can be effectively used for testing this hypothesis?

(A) Comparative genomics

(B) DNA fingerprinting

(D) Transgenesis

Answer: (A; C)

Q.23 – Q. 25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

23. A sample of heights of trees follows a normal distribution. In this sample, 68% of height measurements are expected to fall in the interval: mean ± _____ standard deviation. (Round off to the nearest integer.)

Answer: (0.99 to 1.01)

24. A bird species has an annual survival probability of 0.30. While sampling the population of this species, the probability that any individual is captured in a given year is 0.40. A bird is captured, tagged and released in Year one. The probability that it is re-captured in Year two is _____. (Round off to two decimal places.)

Answer: (0.11 to 0.13)

25. Sex ratio at birth is biased towards females in a mongoose population. If the probability of having a daughter is 0.7 in this population, and if sex determination of each offspring is an independent event, then the probability that a female with a litter of four offspring has at least one son is _______. (Round off to two decimal places.)

Answer: (0.74 to 0.77)

Q.26 – Q.46 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. In a species of gecko, males are polymorphic such that some males are yellow and other males are white. A student hypothesises that body colour is a signal of aggression. To test this, he measures aggression in yellow and white males. He also measures body size in every individual he tests. He plots the data in the following way (yellow males: solid line and filled dots; white males: dashed line and open dots). Which one of the following statements is correct based on these data?

(A) All yellow males are more aggressive than white males.

(B) Body size is correlated with aggression in all males.

(D) Small yellow males are more aggressive than small white males.

Answer: (C)

27. Homing pigeons can perceive the pattern of polarized light in the sky (which depends on the position of the sun relative to the earth). This enables homing pigeons to orient and navigate home if released in any location. One can reset their biological clock in captivity by artificially controlling the light conditions. If you acclimatize a pigeon to a new lighting cycle with “sunrise” at 6 PM and “sunset” at 6 AM, instead of 6 AM sunrise and 6 PM sunset that naturally occurs, the bird will be clock- shifted by 12 hours within a few days. Suppose you release two birds, a normal bird (N) and a 12-hr clock-adjusted bird (C), 30 km East of their home at 6 AM. In which direction will each bird fly?

(A) Both birds will fly West.

(B) Both birds will fly East.

(D) Bird C will fly West, bird N will fly East.

Answer: (C)

28. Demographic stochasticity introduces random variation in population growth because

(A) changing weather conditions from year-to-year can result in good and bad years for reproduction.

(B) the discrete nature of births and deaths introduces uncertainty in population parameters.

(D) of predictable time lags between change in population size and reproduction.

Answer: (B)

29. In an island chain, species richness (S) increases with island area (A) according to the equation, S = 4.3 A⁵⁵.

(A) (i)

(B) (ii)

(D) (iv)

Answer: (B)

30. A researcher measures the abundance of a tree species in 10 plots in each of two habitats. She tests for differences in abundance between the two habitats using an ANOVA. The results from the ANOVA are as follows:

• Mean abundance in habitat A = 30 trees

• Mean abundance in habitat B = 50 trees

• F-statistic (on 1 and 18 degrees of freedom) = 6.04

• P-value = 0.02

Here, a P-value of 0.02 means that

(A) repeating this study 100 times will provide a result of “no difference” in abundance between the two habitats with a probability of 0.02.

(B) there is a 2% chance that abundances differ between habitats.

(C) the probability that an F-statistic with a value of 6.04 or greater falls within theF-distribution for 1 and 18 degrees of freedom is 0.02.

(D) there is a very large difference in the abundance of the species between the two habitats because the P-value is less than 0.05.

Answer: (C)

31. In the graph shown, the solid line represents the best fit from an ordinary least-squares regression, where X is the predictor variable and Y is the response variable. In this case, which one of the following assumptions of the linear regression is violated?

(A) Equal variances in Y across values of X

(B) Normal distribution of residuals

(D) Linear relationship between X and Y

Answer: (A)

32. Consider the following list of bacteria and the infections they cause in humans.

Which one of the following combinations correctly matches these micro-organisms and the infections they cause in humans?

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

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

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

Answer: (C)

33. Which one of the following statements is INCORRECT with respect to the tree of life?

(A) Ctenophora is more closely related to Cnidaria than it is to Echinodermata.

(B) Porifera is more closely related to Ctenophora than it is to Echinodermata.

(D) Arthropoda is more closely related to Mollusca than it is to Nematoda.

Answer: (D)

34. Consider a population that shows logistic growth of the form is the population growth rate, r is the instantaneous rate of increase, K is the carrying capacity and N is the population size.

For such a population (N > 0), which one of the following graphs shows the correct relationship between per capita growth rate on the y-axis, and population size (N) on the x-axis?

(A) (i)

(B) (ii)

(D) (iv)

Answer: (A)

35. Which one of the following represents the correct chronological order of geological periods (from oldest to most recent)?

(A) Devonian → Jurassic → Cambrian → Neogene

(B) Devonian → Cambrian → Neogene → Jurassic

(D) Cambrian → Neogene → Devonian → Jurassic

Answer: (C)

36. Soils undergo weathering over large time-scales (millions of years). Over time, concentration of phosphorus (P) declines monotonically (solid line), while nitrogen (N) shows a unimodal pattern (dotted line) as shown.

Based on this pattern, which one of the following diagrams represents the likely trend in N:P ratio?

(A) (i)

(B) (ii)

(D) (iv)

Answer: (A)

37. A large forest area is fragmented into multiple smaller patches of different sizes. A researcher estimates the number of bird species in these forest fragments immediately following fragmentation, and then again 20 years later. The relationship between fragment size and species richness is shown in the graph for the two sampling events (immediately after fragmentation: closed circles and solid line; 20 years after fragmentation: open circles and dashed line). The best explanation for the differences in species richness with fragment size between the two sampling events is

(A) Allen’s rule.

(B) K-selection.

(D) Bergmann’s rule.

Answer: (C)

38. The table shows a list of analysis goals (i, ii, iii) and different statistical tests (P, Q, R).

Match the analysis goal to the most appropriate statistical test.

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

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

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

Answer: (C)

39. Shifting cultivation is a form of agricultural practice in the hills of Northeast India, where a forest patch is cleared and cultivated for a few years, after which it is left fallow and allowed to regenerate. Succession occurs on such previously cultivated plots. Over time, the plant community should move towards which region in the graph?

(A) P

(B) Q

(D) S

Answer: (B)

40. Consider 1000 terrestrial species that have geographical ranges of different shapes and sizes. If the Earth were entirely covered by land (no oceans), and the ranges of these species were overlaid on the surface of the Earth at random, which one of the following patterns is expected?

(A) Highest species richness per unit area in the tropics

(B) Highest species richness per unit area at higher latitudes

(D) Geographically restricted species found only near the poles

Answer: (C)

41. The graph below shows how the lower limits of the elevational ranges of bird species on a tropical mountain have changed over 20 years (2000 to 2020) because of climate change. Each point below represents a bird species. Points would cluster on the dashed line if species had the same lower elevational range limits in 2000 and 2020. Given that the mountain summit is at an elevation of 3500 m (solid horizontal line), and assuming that the trend shown by the graph continues over the next 20 years, what would you expect in 2040?

(A) Low-elevation species will become locally extinct.

(B) Mid-elevation species will become locally extinct.

(D) All species will return to their original elevational ranges.

Answer: (C)

42. Behavioural ecologists exploring a newly discovered island find 20 new species of terrestrial lizards. Males of these species have a dorsal ridge that varies in size from large in some species to entirely lacking in others. The scientists hypothesise that dorsal ridges in males evolved by runaway sexual selection stemming from sensory bias in females. Which one of the following would provide the necessary evidence to support this hypothesis?

(A) Females of species in which males lack this trait are attracted to males that have a large dorsal ridge artificially attached to them.

(B) Males without a ridge are more likely to attract females of all species than males with a ridge.

(D) Females of species whose males have a dorsal ridge do not show a preference for this trait.

Answer: (A)

43. The graph shows the relationship between a variable on the x-axis and genetic diversity on the y-axis. Each point represents a species and the trend line describes the relationship across species.

Select the most appropriate variable for the x-axis.

(A) Evolutionary age of species

(B) Abundance

(D) Geographic range

Answer: (C)

44. Hunting is a major source of mortality for large frugivorous birds. These birds disperse the seeds of forest trees and are the primary contributors to forest regeneration. The graphs show the distribution of different age-classes of a frugivore-dispersed tree species at two isolated sites.

Based on the graphs, select the most likely conclusion.

(A) Hunting is higher at site (i) than at site (ii).

(B) Hunting is higher at site (ii) than at site (i).

(D) Frugivores are not hunted at either site.

Answer: (B)

45. The following phylogeny shows how species P to T are related to each other. The branch lengths indicate the degree of evolutionary change.

The species composition of three areas is given below

Area 1: PQR; Area 2: RST; Area 3: QRS

Given this information, the phylogenetic diversity of

(A) Area 1 > Area 3 > Area 2

(B) Area 1 = Area 2 = Area 3

(D) Area 1 < Area 3 < Area 2

Answer: (A)

46. The IUCN Red List provides information on the conservation status of different species. Match the species to their status in the table below.

(A) Tiger: NT; Great Indian Bustard: EX; Passenger Pigeon: EN; Blackbuck: CR

(B) Tiger: EN; Great Indian Bustard: CR; Passenger Pigeon: EX; Blackbuck: NT

(D) Tiger: NT; Great Indian Bustard: EN; Passenger Pigeon: EX; Blackbuck: CR

Answer: (B)

Q.47 – Q.52 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

47. A gene duplication event in an organism results in two copies of a gene. Which one (or more) of the following outcomes is/are possible for the duplicated copy?

(A) It retains the original function.

(B) It acquires a new function.

(D) It gets translated but not transcribed.

Answer: (A; B; C)

48. The egg-laying mammal, platypus, is known for its ability to inject venom by stabbing with spurs on its hindlimbs. Which one (or more) of the following statements supports the hypothesis that venom in this species is used for intrasexual competition?

(A) Only males produce venom.

(B) Venom is secreted only during the breeding season.

(D) Venom is ineffective against conspecifics.

Answer: (A; B)

49. All octopi dream every night, and sometimes change colour while dreaming. A student hypothesises that octopi change colour only when they dream about the food they ate that day. To test this hypothesis, the student conducts an experiment with two treatments that are randomly ordered, and separated by 2 days. In one treatment, she places 10 octopi in individual tanks in captivity and provides each one with a large crab to eat during the day. She then records the dream state colour of these octopi that night. Which one (or more) of the following would be an appropriate NEGATIVE control to test this hypothesis?

(A) Provide the same 10 octopi with the same food source (crab), and then record their colour that night when they are dreaming.

(B) Provide the same 10 octopi with a new food object (e.g. sea stars) and record the colour that night when they are dreaming.

(C) Provide the same 10 octopi with a non-food object (e.g. rock), and record their colour that night when they are dreaming.

(D) Provide 10 squid with the same food source (crab) and record the colour that night when they are dreaming.

Answer: (C)

50. Which one (or more) of the following conservation actions would NOT benefit native species?

(A) Planting Prosopis juliflora in the Thar desert to reduce erosion.

(B) Stringing rope ladders across roads to connect the canopy for facilitating the movement of arboreal animals in the Western Ghats.

(D) Growing native species in urban gardens of Bengaluru to attract pollinators.

Answer: (A; C)

51. In cooperatively breeding animals, offspring from one year stay back and help their parents to rear offspring born in successive breeding episodes. Kin selection has been used to explain such helping behaviour. Which of the following result(s) support(s) the kin selection hypothesis?

(A) Helpers provide more care in populations where extra-pair paternity is low, than in populations where extra-pair paternity is high.

(B) Individuals who choose to stay and help are more likely to inherit their parents’ territory than individuals who stay but do not help.

(C) Individuals who choose to disperse from their natal territory rather than stay and help have a lower survival because of predation during dispersal, when compared with individuals who stay and help.

(D) Helpers whose parents continue to form the breeding pair provide more care than helpers whose parents are replaced by a new breeding pair.

Answer: (A; D)

52. Which one (or more) of the following genetic processes is/are likely to be affected by the disruption of codon usage bias in highly expressed genes?

(A) Translation rate

(B) Translation accuracy

(D) Transcription accuracy

Answer: (A; B)

Q.53 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

53. Male beetles are of two phenotypes: horned and hornless. Horned males mate with twice as many females compared with hornless males. But females mated to hornless males produce one-third more offspring. The reproductive success of a male (number of offspring fathered) is the number of females he mates with multiplied by the number of offspring each female produces. The reproductive success of horned males is ________ times that of hornless males. (Round off to one decimal place.)

Answer: (1.40 to 1.60)

54. A population shows exponential growth of the form N_t = N₀e^rt where N_t is increase. If r = 0.1, then the doubling time for this population is __________. (Round off to two decimal places.)

Answer: (6.80 to 7.00)

55. At a locus with two alleles A1 and A2, the genotype A1A1 produces white flowers, A2A2 produces red flowers, and A1A2 produces pink flowers. For a population in Hardy-Weinberg equilibrium, the frequency of red flowers is 0.25. If the white flowered plants are removed, and all pink and red flowered-plants in this population are randomly crossed amongst each other, the frequency of white flowered plants in the next generation will be ______. (Round off to two decimal places.)

Answer: (0.10 to 0.12)

GATE Exam 2021 Electrical Engineering (EE) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

EE: Electrical Engineering

GA- General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A) whose

(B) which

(D) whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A) 396

(B) 324

(D) 144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (11¹³ + 1)?

(A) 11²⁶ + 1

(B) 11³³ + 1

(D) 11⁵² – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Stone

(B) Land

(D) Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Which one of the following statements is the CORRECT inference from the above passage?

(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.

(D) To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm²is:

(A) 12.50

(B) 6.25

(D) 1.5625

Answer: (C)

The mean of X is _____

(A) 2.5

(B) 5.0

(D) 50.0

Answer: (D)

exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A) 65 and 53

(B) 60 and 50

(D) 55 and 48

Answer: (D)

Based on the above statements, the only INCORRECT option given below is:

(A) There are two cars parked in between Q and V.

(B) Q and R are not parked together.

(D) Car P is parked at the extreme end.

Answer: (A)

Electrical Engineering (EE)

Q.1 – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let p and q be real numbers such that p² + q² = 1. The eigenvalues of the matrix are

(A) 1 and 1

(B) 1 and -1

(D) pq and −pq

Answer: (B)

2. Let p(z) = z³ + (1 + j)z² + (2 + j)z + 3, where z is a complex number. Which one of the following is true?

(A) conjugate {p(z)} = p(conjugate{z}) for all z

(B) The sum of the roots of p(z) = 0 is a real number

(D) All the roots cannot be real

Answer: (D)

3. Let f(x) be a real-valued function such that f'(x₀) = 0 for some x₀ ∈ (0, 1), and f”(x) > 0 for all x ∈ (0, 1). Then f(x) has

(A) no local minimum in (0, 1)

(B) one local maximum in (0, 1)

(D) two distinct local minima in (0, 1)

Answer: (C)

4. For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘ab’ is

(A) 10 V in series with 12 Ω

(B) 65 V in series with 15 Ω

(D) 35 V in series with 2 Ω

Answer: (B)

5. Which one of the following vector functions represents a magnetic field are unit vectors along x-axis, y-axis, and z-axis, respectively)

Answer: (A)

6. If the input x(t) and output y(t) of a system are related as y(t) = 0 max(0, x(t)), then the system is

(A) linear and time-variant

(B) linear and time-invariant

(D) non-linear and time-invariant

Answer: (D)

7. Two discrete-time linear time-invariant systems with impulse responses h₁[n] = δ[n – 1] + δ[n+ 1] and h₂[n] = δ[n] + δ[n – 1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is

(A) δ[n – 2] + δ[n + 1]

(B) δ[n – 1] δ[n] + δ[n + 1] δ[n – 1]

(D) δ[n] δ[n – 1] + δ[n – 2] δ[n + 1]

Answer: (C)

8. Consider the table given:

The correct combination that relates the constructional feature, machine type and mitigation is

(A) P-V-X, Q-U-Z, R-T-Y

(B) P-U-X, Q-S-Y, R-V-Z

(D) P-U-X, Q-V-Y, R-T-Z

Answer: (B)

9. Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is N_L. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:

The dimension of the sub-matrix M is

(A) N_L × (N – 1)

(B) (N – 1) × (N – 1 – N_L)

(D) (N – 1) × (N – 1 + N_L)

Answer: (A)

10. Two generators have cost functions F₁ and F₂. Their incremental-cost characteristics are

They need to deliver a combined load of 260 MW. Ignoring the network losses, for economic operation, the generations P₁ and P₂ (in MW) are

(A) P₁ = P₂ = 130

(B) P₁ = 160, P₂ = 100

(D) P₁ = 120, P₂ = 140

Answer: (B)

11. For the closed-loop system shown, the transfer function is

Answer: (C)

12. Inductance is measured by

(A) Schering bridge

(B) Maxwell bridge

(D) Wien bridge

Answer: (B)

Q.13 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

13. Suppose the circles x² + y² = 1 and (x – 1)² + (y – 1)² = r² intersect each other orthogonally at the point (u, v). Then u + v = ______.

Answer: (1 to 1)

14. In the given circuit, the value of capacitor C that makes current I=0 is________ μF.

Answer: (20.00 to 20.00)

15. Two single-core power cables have total conductor resistances of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is _____×10⁶.

Answer: (300 to 300)

16. In the given circuit, for voltage V_y to be zero, the value of β should be _____. (Round off to 2 decimal places).

Answer: (-3.30 to -3.20)

17. A 1 μC point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 μC is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is ____ mJ. (Round off to 2 decimal places).

Take in SI units. All coordinates are in meters.

Answer: (8.90 to 9.10)

18. The power input to a 500 V, 50 Hz, 6-pole, 3-phase induction motor running at 975 RPM is 40 kW. The total stator losses are 1 kW. If the total friction and windage losses are 2.025 kW, then the efficiency is __________%.

Answer: (89.50 to 90.50)

19. An alternator with internal voltage of 1 ∠δ₁u and synchronous reactance of 0.4 p.u is connected by a transmission line of reactance 0.1 p.u to a synchronous motor having synchronous reactance 0.35 p.u and internal voltage of 0.85 ∠δ₂ p.u. If the real power supplied by the alternator is 0.866 p.u, then (δ₁ – δ₂) is ____ degrees. (Round off to 2 decimal places.)

(Machines are of non-salient type. Neglect resistances.)

Answer: (59.00 to 61.00)

20. The Bode magnitude plot for the transfer function of the circuit is as shown. The value of R is _______ Ω. (Round off to 2 decimal places.)

Answer: (0.09 to 0.11)

21. A signal generator having a source resistance of 50 Ω is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is ______ μ (Round off to 2 decimal places.)

Answer: (2.30 to 2.50)

22. A 16-bit synchronous binary up-counter is clocked with a frequency f_CLK. The two most significant bits are OR-ed together to form an output Y. Measurements show that Y is periodic, and the duration for which Y remains high in each period is 24 ms. The clock frequency f_CLK is __________ MHz. (Round off to 2 decimal places.)

Answer: (2.00 to 2.10)

23. In the BJT circuit shown, beta of the PNP transistor is 100. Assume V_BE = −7 V. The voltage across R_C will be 5 V when R₂ is ____ kΩ. (Round off to 2 decimal places.)

Answer: (16.70 to 17.70)

24. In the circuit shown, the input Vi is a sinusoidal AC voltage having an RMS value of 230 V ±20%. The worst-case peak-inverse voltage seen across any diode is ________ V. (Round off to 2 decimal places.).

Answer: (389 to 391)

25. In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load R₀. The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V. The value of R_S is 6 Ω. The Zener diode has a maximum rated power dissipation of 2.5 W. Assuming the Zener diode to be ideal, the minimum value of R₀ is _______ Ω.

Answer: (29.00 to 31.00)

Q.26 – Q.37 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. In the open interval (0, 1) , the polynomial p(x) = x⁴ – 4x³ + 2 has

(A) two real roots

(B) one real root

(D) no real roots

Answer: (B)

27. Suppose the probability that a coin toss shows “head” is p, where 0 < p < 1. The coin is tossed repeatedly until the first “head” appears. The expected number of tosses required is

(A) p/(1 – p)

(B) (1 – p)/p

(D) 1/p²

Answer: (C)

28. Let (−1 – j), (3 – j), (3 + j) and (−1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the contour integral is

(A) jπ/2

(B) 0

(D) jπ/16

Answer: (C)

29. In the circuit, switch ‘S’ is in the closed position for a very long time. If the switch is opened at time t = 0, then i_L (t) in amperes, for t ≥ 0 is

(A) 8e⁻^10t

(B) 10

(D) 10(1 − e⁻^2t)

Answer: (C)

30. The input impedance, Z_in(s), for the network shown is

(A)

(B) 6s + 4

(D)

Answer: (A)

31. The causal signal with z-transform z²(z – a)⁻² is (u[n] is the unit step signal)

(A) a²ⁿu[n]

(B) (n+1)aⁿu[n]

(D) n²aⁿu[n]

Answer: (B)

32. Let f(t) be an even function, i.e. f(−t) = f(t) for all t. Let the Fourier transform of f(t) be defined as Suppose for all ω, and F(0) = 1. Then

(A) f(0) < 1

(B) f(0) > 1

(D) f(0) = 0

Answer: (A)

33. In a single-phase transformer, the total iron loss is 2500 W at nominal voltage of 440 V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss respectively are

(A) 1600 W and 900 W

(B) 900 W and 1600 W

(D) 600 W and 250 W

Answer: (B)

34. In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and Z_m = 0.5j p.u is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that δ > 0, the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is

(A) |E||V|

(B) |E||V|/2

(D) 3|E||V|/2

Answer: (A)

35. A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the Y_Bus matrix correspond to Bus 1, 2 and 3, respectively, then Y_Bus of the network is

Answer: (C)

36. Suppose I_A, I_B and I_C are a set of unbalanced current phasors in a three- phase system. The phase-B zero-sequence current I_B0 = 0.1∠0°u. If phase-A current I_A = 1.1∠0° p.u and phase-C current I_C= (1∠120° + 0.1)p.u, then I_B in p.u is

(A) 1∠240° − 0.1∠0°

(B) 1.1∠240° − 0.1∠0°

(D) 1∠−120° + 0.1∠0°

Answer: (D)

37. A counter is constructed with three D flip-flops. The input-output pairs are named (D₀, Q₀), (D₁, Q₁), and (D₂, Q₂), where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the Q₂ Q₁ Q₀ The combinational logic expression for D₁ is

Answer: (C)

Q.38 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

38. Let A be a 10 × 10 matrix such that A⁵ is a null matrix, and let I be the 10 × 10 identity matrix. The determinant of A + I is _______.

Answer: (1 to 1)

39. A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratio is ________.

Answer: (1 to 1)

40. In the given circuit, for maximum power to be delivered to R_L, its value should be _________ Ω. (Round off to 2 decimal places.)

Answer: (1.40 to 1.42)

41. One coulomb of point charge moving with a uniform velocity m/s enters the region x ≥ 0 having a magnetic flux density The magnitude of force on the charge at x = 0⁺ is _______ N.

( are unit vectors along x-axis, y-axis, and z-axis, respectively.)

Answer: (100 to 100)

42. Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field E₂ in the gap to the original electric field E₁ is __________.

Answer: (5 to 5)

43. Consider a continuous-time signal x(t) defined by x(t) = 0 for |t| > 1, and x(t) = 1 – |t| for |t| ≤ Let the Fourier transform of x(t) be defined as The maximum magnitude of X(ω) is______.

Answer: (1 to 1)

44. A belt-driven DC shunt generator running at 300 RPM delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is 0.025 Ω, field resistance is 50 Ω, and brush drop is 2 V. Ignoring armature reaction, the speed of the motor is _____________ RPM. (Round off to 2 decimal places.)

Answer: (273.00 to 277.00)

45. An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is __________ Ω. (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.

Answer: (0.50 to 0.54)

46. Consider a closed-loop system as shown . is the plant transfer function and G_c(s) = 1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ________________ rad/s. (Round off to 2 decimal places.)

Answer: (10.80 to 11.00)

47. In the given figure, plant and compensator The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is ________. (Round off to 2 decimal places.)

Answer: (9.50 to 9.60)

48. The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the RMS value of the full- wave rectified waveform to the RMS value of the clipped waveform is _____. (Round off to 2 decimal places.)

Answer: (1.20 to 1.23)

49. The state space representation of a first-order system is given as

where, x is the state variable, u is the control input and y is the controlled output. Let u x =−K be the control law, where K is the controller gain. To place a closed-loop pole at −2, the value of K is ___________.

Answer: (1 to 1)

50. An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ______ μ (Round off to 2 decimal places.)

Answer: (50.00 to 52.00)

51. A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is 820 Ω, then the value C is _____ μ (Round off to 2 decimal places.)

Answer: (12.30 to 12.60)

52. A CMOS Schmitt-trigger inverter has a low output level of 0 V and a high output level of 5 V. It has input thresholds of 1.6 V and 2.4 V. The input capacitance and output resistance of the Schmitt-trigger are negligible. The frequency of the oscillator shown is _______ Hz. (Round off to 2 decimal places.)

Answer: (3150.00 to 3170.00)

53. Consider the boost converter shown. Switch Q is operating at 25 kHz with a duty cycle of 0.6. Assume the diode and switch to be ideal. Under steady-state condition, the average resistance R_in as seen by the source is ______ Ω. (Round off to 2 decimal places.)

Answer: (1.55 to 1.65)

54. Consider the buck-boost converter shown. Switch Q is operating at 25 kHz and 0.75 duty-cycle. Assume diode and switch to be ideal. Under steady- state condition, the average current flowing through the inductor is_______ A.

Answer: (24 to 24)

55. A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across ‘ab’ as shown. To achieve a modulation index of 0.8, the angle θ expressed in degrees should be ________. (Round off to 2 decimal places.)

(Modulation index is defined as the ratio of the peak of the fundamental component of v_ab to the applied DC value.)

Answer: (50.00 to 52.00)

GATE Exam 2021 Electronics and Communication Engineering (EC) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

EC: Electronics and Communication Engineering

GA: General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A) 9,92,500

(B) 9,95,006

(D) 12,51,506

Answer: (C)

2. p and q are positive integers and

(A) 3

(B) 7

(D) 11

Answer: (B)

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A) 4

(B) 3

(D) 7

Answer: (C)

4. Nostalgia is to anticipation as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Present, past

(B) Future, past

(D) Future, present

Answer: (C)

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iii)

(D) (i) and (iv)

Answer: (B)

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct.

(B) Only conclusion II is correct.

(D) Both conclusion I and II are correct.

Answer: (C)

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A) (ii) and (iii)

(B) (ii) and (iv)

(D) (i) and (iii)

Answer: (D)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A) π/3

(B) 2π/3

(D) 3π

Answer: (A)

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A) 4

(B) 5

(D) 7

Answer: (C)

10.

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A) 2 : 3

(B) 3 : 4

(D) 5 : 6

Answer: (A)

Electronics and Communication Engineering (EC)

Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The vector function is defined over a circular arc C shown in the figure.

The line integral of ∫_C F(r).dr is

(A) 1/2

(B) 1/4

(D) 1/3

Answer: (A)

2. Consider the differential equation given below.

The integrating factor of the differential equation is

(A) (1 – x²)⁻^3/4

(B) (1 – x²)⁻^1/4

(D) (1 – x²)⁻^1/2

Answer: (B)

3. Two continuous random variables X and Y are related as

Y = 2X + 3

Let denote the variances of X and Y, respectively. The variances are related as

Answer: (B)

4. Consider a real-valued base-band signal x(t), band limited to 10 kHz. The Nyquist rate for the signal is

(A) 15 kHz

(B) 30 kHz

(D) 20 kHz

Answer: (B)

5. Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of x[n] and h[n]. The value(s) of k for which z[k] = y[k] is/are

(A) k = 0, 1, 2, … , 15

(B) k = 0

(D) k = 0 and k = 15

Answer: (C)

6. A bar of silicon is doped with boron concentration of 10¹⁶ cm⁻³ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of 10²⁰ cm⁻³s⁻¹. If the recombination lifetime is 100 μs, intrinsic carrier concentration of silicon is 10¹⁰ cm⁻³ and assuming 100% ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is

(A) 10²⁰ cm⁻⁶

(B) 2 × 10²⁰ cm⁻⁶

(D) 2 × 10³² cm⁻⁶

Answer: (D)

7. The energy band diagram of a p-type semiconductor bar of length L under equilibrium condition (i.e., the Fermi energy level EF is constant) is shown in the figure. The valance band EV is sloped since doping is non-uniform along the bar. The difference between the energy levels of the valence band at the two edges of the bar is ∆.

If the charge of an electron is q, then the magnitude of the electric field developed inside this semiconductor bar is

(A) ∆/qL

(B) 2∆/qL

(D) 3∆/2qL

Answer: (A)

8. In the circuit shown in the figure, the transistors M₁ and M₂ are operating in saturation. The channel length modulation coefficients of both the transistors are non-zero. The trans conductance of the MOSFETs M₁ and M₂ are g_m1 and g_m2, respectively, and the internal resistance of the MOSFETs M₁ and M₂ are r₀₁ and r₀₂, respectively.

Ignoring the body effect, the ac small signal voltage gain (∂V_out⁄∂V_in) of the circuit is

Answer: (D)

9. For the circuit with an ideal OPAMP shown in the figure, VREF is fixed.

If V_OUT = 1 volt for V_IN = 0. 1 volt and V_OUT = 6 volt for V_IN = 1 volt, where V_OUT is measured across R_L connected at the output of this OPAMP, the value of R_F⁄R_IN is

(A) 3.285

(B) 2.860

(D) 5.555

Answer: (MTA)

10. Consider the circuit with an ideal OPAMP shown in the figure.

Assuming |V_IN| ≪ |V_CC| and |V_REF| ≪ |V_CC|, the condition at which V_OUT equals to zero is

(A) V_IN = V_REF

(B) V_IN = 0.5 VREF

(D) V_IN = 2 + V_REF

Answer: (A)

11. If (1235)_x = (3033)_y, where x and y indicate the bases of the corresponding numbers, then

(A) x = 7 and y = 5

(B) x = 8 and y = 6

(D) x = 9 and y = 7

Answer: (B)

12. Addressing of a 32K × 16 memory is realized using a single decoder. The minimum number of AND gates required for the decoder is

(A) 2⁸

(B) 2³²

(D) 2¹⁹

Answer: (C)

13. The block diagram of a feedback control system is shown in the figure.

The transfer function of the system is

Answer: (C)

14. The complete Nyquist plot of the open-loop transfer function G(s)H(s) of a feedback control system is shown in the figure.

If G(s)H(s) has one zero in the right-half of the s-plane, the number of poles that the closed-loop system will have in the right-half of the s-plane is

(A) 0

(B) 1

(D) 3

Answer: (D)

15. Consider a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. A plane wave traveling in the region z ≥ 0 with electric field vector E = 10 cos(2 × 10⁸t + βz)ay is incident normally on the plane at z = 0, where β is the phase constant. The region z ≥ 0 is in free space and the region z < 0 is filled with a lossless medium (permittivity ε = ε₀, permeability μ = 4μ₀, where ε₀ = 8. 85 × 10⁻¹² F/m and μ0 = 4π × 10⁻⁷ H/m). The value of the reflection coefficient is

(A) 1/3

(B) 3/5

(D) 2/3

Answer: (A)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

16. If the vectors (1. 0, −1. 0, 2. 0), (7. 0, 3. 0, x) and (2. 0, 3. 0, 1. 0) in ℝ³ are linearly dependent, the value of x is __________

Answer: (8.0 to 8.0)

17. Consider the vector field F = a_x(4y − c₁z) + ay (4x + 2z) + az(2y + z) in a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. If the field F is irrotational (conservative), then the constant c₁ (in integer) is __________

Answer: (0 to 0)

18. Consider the circuit shown in the figure.

The current I flowing through the 7 Ω resistor between P and Q (rounded off to one decimal place) is __________ A.

Answer: (0.5 to 0.5)

19. Consider the circuit shown in the figure.

The value of v₀ (rounded off to one decimal place) is __________ V.

Answer: (1.0 to 1.0)

20. An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7. 68 V. If the digital input code is 10010110 (the leftmost bit is MSB), then the analog output voltage of the DAC (rounded off to one decimal place) is __________ V.

Answer: (4.5 to 4.5)

21. The autocorrelation function R_X(τ) of a wide-sense stationary random process X(t) is shown in the figure.

The average power of X(t) is __________

Answer: (2.0 to 2.0)

22. Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is __________

Answer: (94.2 to 94.6)

23. A speech signal, band limited to 4 kHz, is sampled at 1. 25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range −5 V to +5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is __________ kHz.

Answer: (9.24 to 9.28)

24. A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is __________ V.

Answer: (2.80 to 3.20)

25. The refractive indices of the core and cladding of an optical fiber are 1. 50 and 1. 48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is __________ degree.

Answer: (9.30 to 9.44)

Q.26 – Q. 35 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. Consider the integral

where C is a counter-clockwise oriented circle defined as |x − i| = 2. The value of the integral is

Answer: (MTA)

27. A box contains the following three coins.

(I) A fair coin with head on one face and tail on the other face.

(II) A coin with heads on both the faces.

(III) A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

(A) 2/5

(B) 1/3

(D) 2/3

Answer: (B)

28. The switch in the circuit in the figure is in position P for a long time and then moved to position Q at time t = 0.

The value of at t = 0⁺ is

(A) 0 V/s

(B) 3 V/s

(D) −5 V/s

Answer: (C)

29. Consider the two-port network shown in the figure.

The admittance parameters, in siemens, are

(A) y₁₁ = 2, y₁₂ = −4, y₂₁ = −4, y₂₂ = 2

(B) y₁₁ = 1, y₁₂ = −2, y₂₁ = −1, y₂₂ = 3

(D) y₁₁ = 2, y₁₂ = −4, y₂₁ = −4, y₂₂ = 3

Answer: (C)

30. For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity (∂V_T/∂|V_BS|) is found to be 50 mV/V at a substrate voltage |V_BS| = 2 V, where V_T is the threshold voltage of the MOSFET. Assume that, |V_BS| ≫ 2Φ_B, where qΦ_B is the separation between the Fermi energy level E_F and the intrinsic level E_i in the bulk. Parameters given are

Electron charge (q) = 1. 6 × 10⁻¹⁹ C

Vacuum permittivity (ε₀) = 8. 85 × 10⁻¹² F/m

Relative permittivity of silicon (ε_Si) = 12

Relative permittivity of oxide (ε_ox) = 4

The doping concentration of the substrate is

(A) 7.37 × 10¹⁵ cm⁻³

(B) 4.37 × 10¹⁵ cm⁻³

(D) 9.37 × 10¹⁵ cm⁻³

Answer: (A)

31. The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are 4 ns, 2 ns and 1 ns, respectively.

If all the inputs P, Q, R, S and T are applied simultaneously and held constant, the maximum propagation delay of the circuit is

(A) 3 ns

(B) 5 ns

(D) 7 ns

Answer: (C)

32. The content of the registers are R₁ = 25H, R₂ = 30H and R₃ = 40H. The following machine instructions are executed.

PUSH{R₁}

PUSH{R₂}

PUSH{R₃}

POP{R₁}

POP{R₂}

POP{R₃}

After execution, the content of registers R₁, R₂, R₃ are

(A) R₁ = 40H, R₂ = 30H, R₃ = 25H

(B) R₁ = 25H, R₂ = 30H, R₃ = 40H

(D) R₁ = 40H, R₂ = 25H, R₃ = 30H

Answer: (A)

33. The electrical system shown in the figure converts input source current i_s(t) to output voltage v_o(t).

Current i_L(t) in the inductor and voltage v_C(t) across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e., i_L(0) = and v_C (0) = 0 The system is

(A) completely state controllable as well as completely observable

(B) completely state controllable but not observable

(D) neither state controllable nor observable

Answer: (D)

34. A digital transmission system uses a (7, 4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code (m_i; c_i) where c_i is the codeword corresponding to the i^th message mi, are known to be ( 1 1 0 0 ; 0 1 0 1 1 0 0 ), ( 1 1 1 0 ; 0 0 1 1 1 1 0 ) and (0 1 1 0 ; 1 0 0 0 1 1 0 ), then which of the following is a valid codeword in this code?

(A) 1 1 0 1 0 0 1

(B) 1 0 1 1 0 1 0

(D) 0 1 1 0 1 0 0

Answer: (C)

35. The impedance matching network shown in the figure is to match a lossless line having characteristic impedance Z₀ = 50 Ω with a load impedance Z_L. A quarter-wave line having a characteristic impedance Z₁ = 75 Ω is connected to Z_L. Two stubs having characteristic impedance of 75 Ω each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length 0. 25λ connected across PQ and the other one is an open-circuited (O.C.) stub of length 0. 5λ connected across RS.

The impedance matching is achieved when the real part of Z_L is

(A) 112.5 Ω

(B) 75.0 Ω

(D) 33.3 Ω

Answer: (A)

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

36. A real 2 × 2 non-singular matrix A with repeated eigenvalue is given as

where x is a real positive number. The value of x (rounded off to one decimal place) is __________

Answer: (10.0 to 10.0)

37. For a vector field D = ρ cos² φ aρ + z² sin² φ a_φ in a cylindrical coordinate system (ρ, φ, z) with unit vectors a_ρ, a_φ and a_z, the net flux of D leaving the closed surface of the cylinder (ρ = 3, 0 ≤ z ≤ 2) (rounded off to two decimal places) is __________

Answer: (56.50 to 56.60)

38. In the circuit shown in the figure, the switch is closed at time t = 0, while the capacitor is initially charged to −5 V (i.e., v_c(0) = −5 V).

The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is __________ ms.

Answer: (0.132 to 0.146)

39. The exponential Fourier series representation of a continuous-time periodic signal x(t) is defined as

where ω₀ is the fundamental angular frequency of x(t) and the coefficients of the series are a_k. The following information is given about x(t) and a_k.

(I) x(t) is real and even, having a fundamental period of 6

(II) The average value of x(t) is 2

The average power of the signal x(t) (rounded off to one decimal place) is __________

Answer: (31.9 to 32.1)

40. For a unit step input u[n], a discrete-time LTI system produces an output signal ( 2δ[n + 1] + δ[n] + δ[n − 1] ). Let y[n] be the output of the system for an input The value of y[0] is __________

Answer: (0.0 to 0.0)

41. Consider the signals x[n] = 2ⁿ⁻¹ u[−n + 2] and y[n] = 2⁻ⁿ⁺² u[n + 1], where u[n] is the unit step sequence. Let X(e^jω) and Y(e^jω) be the discrete- time Fourier transform of x[n] and y[n], respectively. The value of the integral (rounded off to one decimal place) is _________

Answer: (7.9 to 8.1)

42. A silicon P-N junction is shown in the figure. The doping in the P region is 5 × 10¹⁶ cm⁻³ and doping in the N region is 10 × 10¹⁶ cm⁻³. The parameters given are

The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place)

is ________V.

Answer: (8.1 to 8.4)

43. An asymmetrical periodic pulse train v_in of 10 V amplitude with on-time T_ON = 1 ms and off-time T_OFF = 1 μs is applied to the circuit shown in the figure. The diode D₁ is ideal.

The difference between the maximum voltage and minimum voltage of the output waveform v_o (in integer) is __________ V.

Answer: (10 to 10)

44. For the transistor M1 in the circuit shown in the figure, μ_nC_ox = 100 μA/V² and (W⁄L) = 10, where μ_n is the mobility of electron, C_ox is the oxide capacitance per unit area, W is the width and L is the length.

The channel length modulation coefficient is ignored. If the gate-to-source voltage V_GS is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is __________ V.

Answer: (0.5 to 0.5)

45. A circuit with an ideal OPAMP is shown in the figure. A pulse VIN of 20 ms duration is applied to the input. The capacitors are initially uncharged.

The output voltage V_OUT of this circuit at t = 0⁺ (in integer) is __________V.

Answer: (-12 to -12)

46. The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is 500 MHz.

Starting from the initial value of the flip-flop outputs Q₂Q₁Q₀ = 1 1 1 with

D₂ = 1, the minimum number of triggering clock edges after which the flip-flop outputs Q₂Q₁Q₀ becomes 1 0 0 (in integer) is __________

Answer: (5 to 5)

47. The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time t = 0.

Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is __________ A.

Answer: (1.40 to 1.50)

48. A unity feedback system that uses proportional-integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters K_P and K_I. The maximum value of K_I that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is _________.

Answer: (3.125 to 3.125)

49. A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant 2 rad/volt. If the carrier signal is c(t) = 2 cos(2π10⁶t), the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is __________ Hz.

Answer: (1011310.0 to 1011320.0)

50. Consider a super heterodyne receiver tuned to 600 kHz. If the local oscillator feeds a 1000 kHz signal to the mixer, the image frequency (in integer) is __________ kHz.

Answer: (1400 to 1400)

51. In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is _______ bits.

Answer: (3.320 to 3.325)

52. A message signal having peak-to-peak value of 2 V, root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps. Assuming that the quantization error is uniformly distributed, the maximum signal to quantization noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is __________

Answer: (30.00 to 34.00)

53. Consider a polar non-return to zero (NRZ) waveform, using +2 V and −2 V for representing binary ‘1’ and ‘0’ respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance 0. 4 V². If the a priori probability of transmission of a binary ‘1’ is 0. 4, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is __________ V.

Answer: (0.03 to 0.05)

54. A standard air-filled rectangular waveguide with dimensions a = 8 cm, b = 4 cm, operates at 3. 4 GHz. For the dominant mode of wave propagation, the phase velocity of the signal is v_p. The value (rounded off to two decimal places) of v_p⁄c, where c denotes the velocity of light, is __________

Answer: (1.15 to 1.25)

55. An antenna with a directive gain of 6 dB is radiating a total power of 16 kW. The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of 6 dB gain (rounded off to three decimal places) is __________ V/m.

Answer: (0.224 to 0.264)

GATE Exam 2021 Chemistry (CY) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CY: Chemistry

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Getting to the top is ___________than staying on top.

(A) more easy

(B) much easy

(D) easier

Answer: (D)

2. The mirror image of the above text about the x-axis is

Answer: (B)

3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

(A) 15

(B) 25

(D) 40

Answer: (C)

4. ⊕ and ⨀ are two operators on numbers p and q such that

If x ⊕ y = 2 ⊙ 2, then x =

(A) y/2

(B) y

(D) 2y

Answer: (B)

(A) 2

(B) 4

(D) 8

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Statement: Either P marries Q or X marries Y

Among the options below, the logical NEGATION of the above statement is:

(A) P does not marry Q and X marries Y.

(B) Neither P marries Q nor X marries Y.

(D) P marries Q and X marries Y.

Answer: (B)

7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each.

Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.

Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.

Folding operation 1 is carried out on Sheet M three times.

Folding operation 2 is carried out on Sheet N three times.

The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

(A) 13 : 7

(B) 3 : 2

(D) 5 : 13

Answer: (A)

8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.

The value of θ, in degrees, is ______

(A) 36

(B) 45

(D) 108

Answer: (A)

9. A function, λ, is defined by

The value of the expression is:

(A) −1

(B) 0

(D) 16

Answer: (B)

Based on the above passage, which one of the following is TRUE?

(A) No species possess the ability to construct worlds in their minds.

(B) The terms imagination, invention and innovation refer to unrelated skills.

(D) Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Answer: (C)

Chemistry (CY)

Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The rates of alkaline hydrolysis of the compounds shown below

follow the order:

(A) I > II > III

(B) II > I > III

(D) III > I > II

Answer: (C)

2. The major product formed in the following reaction

Answer: (A)

3. The major product formed in the following reaction

Answer: (C)

4. The least acidic among the following compounds

(A) M

(B) N

(D) P

Answer: (A)

5. The major product formed in the following reaction

Answer: (A)

6. The reagent(s) required for the conversion of hex-3-yne to (E)-hex-3-ene is/are:

(A) H₂, Pd/BaSO₄

(B) Bu₃SnH

(D) LiAlH₀

Answer: (C)

7. An organic compound exhibits the [M]⁺, [M+2]⁺ and [M+4]⁺ peaks in the intensity ratio 1:2:1 in the mass spectrum, and shows a singlet at δ49 in the ¹H NMR spectrum in CDCl₃. The compound is:

(A) 1,4-dichlorobenzene

(B) 1,4-dibromobenzene

(D) 1,2-dichlorobenzene

Answer: (B)

8. Reaction of LiAlH₄ with one equivalent of Me₃N∙HCl gives a tetrahedral compound, which reacts with another equivalent of Me₃N∙HCl to give compound N. The compound N and its geometry, respectively, are:

(A) LiAlH₄NMe₃ and trigonal bipyramidal

(B) Li₂AlH₄Cl and square pyramidal

(D) AlH₃(NMe₃)₂ and pentagonal

Answer: (C)

9. Which one of the following is a non-heme protein?

(A) hemoglobin

(B) hemocyanin

(D) cytochrome P-450

Answer: (B)

10. A correct example of a nucleotide is:

(A) adenosine monophosphate (AMP)

(B) RNA

(D) DNA

Answer: (A)

11. The equilibrium constant for the reaction

3 NO (g) ⇌ N₂O (g) + NO₂ (g)

at 25 °C is closest to:

[ΔG° = −104.18 kJ; R = 8.314 J mol⁻¹ K⁻¹]

(A) 1.043

(B) 1.8 × 10⁸

(D) 5.7 × 10⁻¹⁹

Answer: (B)

12. The reaction of NiBr₂ with two equivalents of PPh₃ in CS₂ at –78 °C gives a red-colored diamagnetic complex, [NiBr₂(PPh₃)₂]. This transforms to a green-colored paramagnetic complex with the same molecular formula at 25 °C. The geometry and the number of unpaired electrons in the green-colored complex, respectively, are:

(A) tetrahedral and 1

(B) tetrahedral and 2

(D) square planar and 4

Answer: (B)

13. The rate of the substitution reaction of [Co(CN)₅Cl]^3– with OH^– to give [Co(CN)₅(OH)]^3–

(A) depends on the concentrations of both [Co(CN)₅Cl]^3– and OH^–

(B) depends on the concentration of [Co(CN)₅Cl]^3– only

(D) is inversely proportional to the concentration of OH^–

Answer: (B)

14. The ∆_o of [Cr(H₂O)₆]³⁺, [CrF₆]^3– and [Cr(CN)₆]^3– follows the order:

(A) [Cr(H₂O)₆]³⁺ > [CrF₆]^3– > Cr(CN)₆]^3–

(B) [CrF₆]^3– > [Cr(H₂O)₆]³⁺ > [Cr(CN)₆]^3–

(D) [CrF₆]^3– > [Cr(CN)₆]^3– > [Cr(H₂O)₆]³⁺

Answer: (C)

Q.15 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

15. The phase diagram of CO₂ is shown below:

The correct statement(s) about CO₂ is/are:

(A) Below T_c, it does not exist in liquid state.

(B) Above T_c, it does not exist in liquid state.

(D) Above T₁, it does not exist in solid state.

Answer: (A; C)

16. Acceptable wavefunctions for a quantum particle must be:

(A) odd

(B) even

(D) continuous

Answer: (C; D)

17. The characters of E, C₂, σ_v, and σ’_v symmetry operations, in this order, for valid irreducible representation(s) of the C_2v point group is/are:

(A) 1, 1, 1, 1

(B) −1, 1, 1, −1

(D) 1, −1, −1, −1

Answer: (A; C)

18. The normal mode(s) of vibration of H₂O is/are:

Answer: (A; B; C)

Q.19 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

19. A reversible heat engine absorbs 20 kJ of heat from a source at 500 K and dissipates it to the reservoir at 400 K. The efficiency of the heat engine is _______%.

Answer: (20 to 20)

20. Among the following eight compounds,

the number of compound(s) which can exhibit stereoisomerism is _______.

Answer: (6 to 6)

21. The Mo−Mo bond order in [(η⁵-C₅H₅)Mo(CO)₂]₂ which obeys the 18-electron rule is _______.

Answer: (3 to 3)

22. The change in enthalpy (ΔH) for the reaction

2 P (s) + 3 Br₂ (l) → 2 PBr₃ (l)

is −243 kJ. In this reaction, if the amount of phosphorus consumed is 3.1 g, the change in enthalpy (rounded off to two decimal places) is ______ kJ.

[Atomic Wt. of P = 31]

Answer: (-12.16 to -12.14)

23. The number of signal(s) in the ¹H NMR spectrum of the following compound

recorded at 25 °C in CDCl₃ is __________.

Answer: (3 to 3)

24. A 5 V battery delivers a steady current of 1.5 A for a period of 2 h. The total charge that has passed through the circuit is ______ Coulombs.

Answer: (10800 to 10800)

25. The spin-only magnetic moment of [Co(H₂O)₆]²⁺ (rounded off to one decimal place) is _______ BM.

Answer: (3.8 to 4.0)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The geometry and the number of unpaired electrons in tetrakis(1-norbornyl)Co

respectively, are:

(A) tetrahedral and one

(B) tetrahedral and five

(D) square planar and three

Answer: (A)

27. The yellow color of an aqueous solution of K₂CrO₄ changes to red-orange upon the addition of a few drops of HCl. The red-orange complex, the oxidation state of its central element(s), and the origin of its color, respectively, are:

(A) chromium chloride, +3, d-d transition

(B) dichromate ion, +6 and +6, charge transfer

(D) chromic acid, +6, charge transfer

Answer: (B)

28. The shapes of the compounds

ClF₃, XeOF₂, N₃⁻and XeO₃F₂

respectively, are:

(A) T-shape, T-shape, linear and trigonal bipyramidal

(B) trigonal planar, T-shape, V-shape and square pyramidal

(D) trigonal planar, trigonal planar, V-shape and trigonal bipyramidal

Answer: (A)

29. The metal borides that contain isolated boron atoms are:

(A) Tc₇B₃ and Re₇B₃

(B) Cr₅B₃ and V₃B₂

(D) TiB and HfB

Answer: (A)

30. The major product formed in the following reaction

(A) non-6-yn-2-one

(B) non-3-yn-8-one

(D) non-3-en-8-one

Answer: (A)

31. The major product formed in the following reaction

is:

Answer: (B)

32. The major product formed in the following reaction

is:

Answer: (D)

33. In the following reaction sequence

the major products P and Q, respectively, are:

Answer: (B)

34. In an electrochemical cell, Ag⁺ ions in AgNO₃ are reduced to Ag metal at the cathode and Cu is oxidized to Cu²⁺ at the anode. A current of 0.7 A is passed through the cell for 10 min. The mass (in grams) of silver deposited and copper dissolved, respectively, are:

[Faraday Constant = 96,485 C mol⁻¹, Atomic Weight of Ag = 107.9, Atomic Weight of Cu = 63.55]

(A) 0.469 and 0.138

(B) 0.235 and 0.138

(D) 0.235 and 0.069

Answer: (A)

35. Among the following

the compounds which can be prepared by nucleophilic substitution reaction are:

(A) III, IV, and V

(B) I, II, and VI

(D) I, III, and V

Answer: (C)

36. In the following reaction

the major products X and Y, respectively, are:

Answer: (C)

37. The major products P and Q formed in the following reactions

respectively, are:

Answer: (B)

38. The major product formed in the reaction of (2R,3R)-2-bromo-3-methylpentane with NaOMe is:

(A) (Z)-3-methylpent-2-ene

(B) (E)-3-methylpent-2-ene

(D) (2S,3R)-2-methoxy-3-methylpentane

Answer: (B)

39. The major product formed in the following reaction

is:

Answer: (A)

40. Hexane and heptane are completely miscible. At 25 °C, the vapor pressures of hexane and heptane are 0.198 atm and 0.06 atm, respectively. The mole fractions of hexane and heptane in the vapor phase for a solution containing 4 M hexane and 6 M heptane, respectively, are:

(A) 0.688 and 0.312

(B) 0.400 and 0.600

(D) 0.600 and 0.400

Answer: (A)

41. The correct order of Lewis acid strengths of BF₂Cl, BFClBr, BF₂Br and BFBr₂ is:

(A) BF₂Cl > BFClBr > BF₂Br > BFBr₂

(B) BFBr₂> BFClBr > BF₂Br > BF₂Cl

(D) BFClBr > BFBr₂ > BF₂Cl > BF₂Br

Answer: (B)

42. The correct order of increasing intensity (molar absorptivity) of the UV-visible absorption bands for the ions [Ti(H₂O)₆]³⁺, [Mn(H₂O)₆]²⁺, [CrO₄]^2–, and [NiCl₄]^2– is:

(A) [Ti(H₂O)₆]³⁺ < [Mn(H₂O)₆]²⁺ < [CrO₄]^2– < [NiCl₄]^2–

(B) [Mn(H₂O)₆]²⁺ < [Ti(H₂O)₆]³⁺ < [NiCl₄]^2– < [CrO₄]^2–

(D) [Ti(H₂O)₆]³⁺ < [NiCl₄]^2– < [CrO₄]^2– < [Mn(H₂O)₆]²⁺

Answer: (B)

Q.43 – Q.44 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

43. The correct statement(s) about the concentration of Na⁺ and K⁺ ions in animal cells is/are:

(A) [K⁺] inside the cell > [K⁺] outside the cell

(B) [Na⁺] inside the cell > [Na⁺] outside the cell

(D) [K⁺] inside the cell < [K⁺] outside the cell

Answer: (A; C)

44. The correct statement(s) about actinides is/are:

(A) The 5f electrons of actinides are bound less tightly than the 4f electrons.

(B) The trans uranium elements are prepared artificially.

(D) Actinides do not exhibit actinide contraction.

Answer: (A; B; C)

Q.45 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

45. The number of photons emitted per nanosecond by a deuterium lamp (400 nm) having a power of 1 microwatt (rounded off to the nearest integer) is ______.

[h = 6.626 × 10⁻³⁴ kg m²s⁻¹; c = 3.0 10⁸ m s⁻¹]

Answer: (2000 to 2020)

46. Given the initial weight of 1 mg of radioactive (half-life = 5.27 years), the amount disintegrated in 1 year (rounded off to two decimal places) is _______mg.

Answer: (0.11 to 0.13)

47. The de Broglie wavelength of an argon atom (mass = 40 amu) traveling at a speed of 250 ms⁻¹ (rounded off to one decimal place) is __________ picometers.

[N = 6.022 × 10²³; h = 6.626 × 10⁻³⁴ kg m²s⁻¹]

Answer: (39.5 to 40.5)

48. The molar absorption coefficient of a substance dissolved in cyclohexane is 1710 L mol⁻¹ cm⁻¹ at 500 nm. The reduction in intensity of light of the same wavelength that passes through a cell of 1 mm path length containing a 2 m mol L⁻¹solution (rounded off to one decimal place) is ___________%.

Answer: (54.0 to 55.0)

49. The fundamental vibrational frequency of ¹H¹²⁷I is 2309 cm⁻¹. The force constant for this molecule (rounded off to the nearest integer) is _____N m⁻¹.

[N = 6.022 × 10²³, c = 3.0 × 10⁸ m s⁻¹]

Answer: (309 to 315)

50. A laser Raman spectrometer operating at 532 nm is used to record the vibrational spectrum of Cl₂ having its fundamental vibration at 560 cm⁻¹. The Stokes line corresponding to this vibration will be observed at _______ cm⁻¹. (Rounded off to the nearest integer)

Answer: (18225 to 18245)

51. The vapor pressure of toluene (Mol. Wt. = 92) is 0.13 atm at 25°C. If 6 g of a hydrocarbon is dissolved in 92 g of toluene, the vapor pressure drops to 0.12 atm. The molar mass of the hydrocarbon (rounded off to the nearest integer) is _______.

Answer: (71 to 73)

52. The reaction

CO (g) + Cl₂ (g) ⇌ COCl₂ (g)

at 500°C, with initial pressures of 0.7 bar of CO and 1.0 bar of Cl₂, is allowed to reach equilibrium. The partial pressure of COCl₂ (g) at equilibrium is 0.15 bar. The equilibrium constant for this reaction at 500°C (rounded off to two decimal places) is ________.

Answer: (0.30 to 0.34)

53. The rate constants for the decomposition of a molecule in the presence of oxygen are 0.237 × 10⁻⁴ L mol⁻¹ s⁻¹ at 0 °C and 2.64 × 10⁻⁴ L mol−1 s⁻¹ at 25 °C (R = 8.314 J mol⁻¹ K⁻¹).

The activation energy for this reaction (rounded off to one decimal place) is ___________ kJ mol⁻¹.

Answer: (151 to 153)

54. 2 L of a gas at 1 atm pressure is reversibly heated to reach a final volume of 3.5 L. The absolute value of the work done on the gas (rounded off to the nearest integer) is _______ Joules.

Answer: (151 to 153)

55. The quantity of the cobalt ore [Co₃(AsO₄)₂∙H₂O] required to obtain 1 kg of cobalt (rounded off to two decimal places) is _________ kg.

[Atomic Wt. of Co = 59, As = 75, O = 16, H = 1]

Answer: (2.50 to 2.80)

GATE Exam 2021 Computer Science and Information Technology (CS-2) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CS-2: Computer Science and Information Technology

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Gauri said that she can play the keyboard __________ her sister.

(A) as well as

(B) as better as

(D) as worse as

Answer: (A)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (B)

3. If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =

(A) 1/2

(B) 1/√3

(D) √3/2

Answer: (B)

4. If then the value of x is:

(A) 2

(B) 4

(D) 8

Answer: (B)

5. Pen : Write :: Knife : _________

Which one of the following options maintains a similar logical relation in the above?

(A) Vegetables

(B) Sharp

(D) Blunt

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.

Which one of the following statements is the CORRECT inference of the above passage?

(A) Listening to music has no effect on learning and a positive effect on physical exercise.

(B) Listening to music has a clear positive effect both on physical exercise and on learning.

(C) Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.

(D) Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.

Answer: (C)

7. A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.

The total number of students in all the three classes in the beginning was:

(A) 22

(B) 66

(D) 110

Answer: (C)

9. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.

(A) 4:3

(B) 1:1

(D) 1:2

Answer: (A)

10. Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.

Observation I: S is taller than R.

Observation II: Q is the shortest of all.

Observation III: U is taller than only one student.

Observation IV: T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than ______.

(A) T

(B) R

(D) P

Answer: (C)

Computer Science and Information Technology (CS, Set-2)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let G be a connected undirected weighted graph. Consider the following two statements.

S₁: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.

S₂: If every edge in has distinct weight, then G has a unique minimum spanning tree.

Which one of the following options is correct?

(A) Both S₁ and S₂ are true.

(B) S₁ is true and S₂ is false.

(D) Both S₁ and S₂ are false.

Answer: (C)

2. Let H be a binary min-heap consisting of n elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element is H?

(A) Θ(1)

(B) Θ(log n)

(D) Θ(n log n)

Answer: (C)

3. Consider the following ANSI C program:

Which one of the following phases in a seven-phase C complier will throw an error?

(A) Lexical analyzer

(B) Syntax analyzer

(D) Machine dependent optimizer

Answer: (C)

4. The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?

(A) exponent = 00000000 and nmantissa = 000000000000000000000000

(B) exponent = 00000000 and nmantissa = 000000000000000000000001

(D) exponent = 00000001 and nmantissa = 000000000000000000000001

Answer: (C)

5. Which one of the following circuits implements the Boolean function given below?

f(x, y, z) = m₀ + m₁ + m₃ + m₄ + m₅ + m₆, where m_i is the i^th minterm.

Answer: (A)

6. Consider the following statements S1 and S2 about the relational data model:

S1: A relation scheme can have at most one foreign key.

S2: A foreign key in a relation scheme R cannot be used to refer to tuples of R.

Which one of the following choices is correct?

(A) Both S1 and S2 are true.

(B) S1 is true and S2 is false.

(D) Both S1 and S2 are false.

Answer: (D)

7. Consider the three-may handshake mechanism followed during TCP connection establishment between hosts P and Q. Let X and Y be two random 32-bit starting sequence numbers chosen by P and Q respectively. Suppose P sends a TCP connection request message to Q with a TCP segment having SYN bit = 1, SEQ number = X, and ACK bit = 0. Suppose Q accepts the connection request. Which one of the following choices represents the information present in the TCP segment header that is sent by Q to P ?

(A) SYN bit = 1, SEQ number = X + 1, ACK bit = 0, ACK number = Y, FIN bit =0

(B) SYN bit = 0, SEQ number = X+1, ACK bit = 0, ACK number = Y, FIN bit = 1

(D) SYN bit = 1, SEQ number = Y, ACK bit = 1, ACK number = X, FIN bit = 0

Answer: (C)

8. What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n ?

(A) Θ(√n)

(B) Θ(log₂(n))

(D) Θ(n)

Answer: (B)

9. Let L ⊆ {0, 1}* be an arbitrary regular language accepted by a minimal DFA with k states. Which one of the following languages must necessarily be accepted by a minimal DFA with k states?

(A) L – {01}

(B) L ⋃ {01}

(D) L ∙ L

Answer: (C)

10. Consider the following ANSI C program.

What is the output of the above program?

(A) 14

(B) 20

(D) 30

Answer: (C)

Q.11 – Q.15 Multiple Select Question (MSQ), carry ONE marks each (no negative marks).

11. Consider the following sets, where n ≥

S₁: Set of all n × n matrices with entries from the set {a, b, c}

S₂: Set of all functions from the set {0, 1, 2, …, n² – 1} to the set {0, 1, 2}

Which of the following choice(s) is/are correct?

(A) There does not exist a bijection from S₁ to S₂

(B) There exists a surjection from S₁ to S₂.

(D) There does not exist an injection from S₁ to S₂

Answer: (B; C)

12. Let L₁ be a regular language and L₂ be a context-free language. Which of the following languages is/are context-free?

Answer: (B; C; D)

13. In the context of compilers, which of the following is/are NOT an intermediate representation of the source program?

(A) Three address code

(B) Abstract Syntax Tree (AST)

(D) Symbol table

Answer: (D)

14. Which of the following statement(s) is/are correct in the context of CPU scheduling?

(A) Turnaround time includes waiting time.

(B) The goal is to only maximize CPU utilization and minimize throughput.

(D) Implementing preemptive scheduling needs hardware support.

Answer: (A; C; D)

15. Choose the correct choice(s) regarding the following propositional logic assertion S:

S : ((P ⋀ Q) → R) → ((P ⋀ Q) → (Q → R))

(A) S is neither a tautology nor a contradiction.

(B) S is a tautology.

(D) The antecedent of S is logically equivalent to the consequent of S.

Answer: (B; D)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

16. Consider a complete binary tree with 7 nodes. Let A denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let B denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root.

The value of |A – B| is _______

Answer: (1 to 1)

17. Consider the following deterministic finite automaton (DFA).

The number of strings of length 8 accepted by the above automaton is _________.

Answer: (256 to 256)

18. If x and y are two decimal digits and (0.1101)₂ = (0.8xy5)₁₀, the decimal value of x + y is ________

Answer: (3 to 3)

19. Consider a set-associative cache of size 2KB (1KB = 2¹⁰ bytes) with cache block size of 64 bytes. Assume that the cache is byte-addressable and a 32-bit address is used for accessing the cache. If the width of the tag field is 22 bits, the associativity of the cache is _________.

Answer: (2 to 2)

20. Consider a computer system with DMA support. The DMA module is transferring one 8-bit character in one CPU cycle from a device to memory through cycle stealing at regular intervals. Consider a 2 MHz processor. If 0.5% processor cycles are used for DMA, the data transfer rate of the device is _______ bits per second.

Answer: (80000 to 80000)

21. A data file consisting of 1,50,000 student-records is stored on a hard disk with block size of 4096 bytes. The data file is sorted on the primary key RollNo. The size of a record pointer for this disk is 7 bytes. Each student-record has a candidate key attribute called ANum of size 12 bytes. Suppose an index file with records consisting of two ields, ANum value and the record pointer to the corresponding student record, is built and stored on the same disk. Assume that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ________.

Answer: (698 to 698)

22. For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is ________.

Answer: (15.00 to 16.00)

23. Consider the following ANSI C function:

The value returned by SomeFunction (15, 255) is ______.

Answer: (15 to 15)

24. Suppose that P is a 4 × 5 matrix sch that every solution of the equation P_x = 0 is a scalar multiple of [2 5 4 3 1]^T. The rank of P is _______.

Answer: (4 to 4)

25. Suppose that f : ℝ → ℝ is a continuous function on the interval [−3, 3] and a differentiable function in the interval (−3, 3) such that for every x in the interval f'(x) ≤ If f(−3) = 7, then f(3) is at most _______.

Answer: (19 to 19)

Q.26 – Q.39 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: −2/3).

26. Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties:

(1) For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter.

(2) For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter.

Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?

(A) 21

(B) 23

(D) 30

Answer: (B)

27. Assume a two-level inclusive cache hierarchy, L1 and L2, where L2 is the larger of the two. Consider the following statements.

S₁ : Read misses in a write through L1 cache do not result in writebacks of dirty lines to the L2.

S₂ : Write allocate policy must be used in conjunction with write through caches and no-write allocate policy is used with writeback caches.

Which of the following statements is correct?

(A) S₁ is true and S₂ is false

(B) S₁ is false and S₂ is true

(D) S₁ is false and S₂ is false

Answer: (A)

28. Suppose we want to design a synchronous circuit that processes a string of 0’s and 1’s. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1’s by a 0. Consider the following example.

Input sequence: 00100011000011100

Output sequence : 00000001000001100

A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input.

The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables s, t, b and y respectively.

Assume the initial state of the Mealy machine is 0.

What are the Boolean expressions corresponding to t and y in terms of s and b?

Answer: (B)

29. In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.

– If the first question is answered wrong, the student gets zero marks.

– If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.

-If both the questions are answered correctly, the student gets the sum of the marks of the two questions.

The following table shows the probability of correctly answering a question and the marks of the question respectively.

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

(A) First QuesA and then QuesB. Expected marks 14.

(B) First QuesB and then QuesA. Expected marks 14.

(D) First QuesA and then QuesB. Expected marks 16.

Answer: (D)

30. Consider the following ANSI C code segment:

Assume that the variable y points to a struct (allocated on the heap) containing two fields f1 and f2, and the local variables x, y, z, p, q, and i are allotted registers. Common sub-expression elimination (CSE) optimization is applied on the code. The number of addition and dereference operations (of the form y ->f1 or y->f2) in the optimized code, respectively, are:

(A) 403 and 102

(B) 203 and 2

(D) 303 and 2

Answer: (D)

31. The relation scheme given below is used to store information about the employees of a company, where empId is the key and deptId indicates the department to which the employee is assigned. Each employee is assigned to exactly one department.

Consider the following SQL query:

The above query gives, for each department in the company, the number of female employees whose salary is greater than the average salary of

(A) employees in the department.

(B) employees in the company.

(D) female employees in the company.

Answer: (B)

32. Let S be the following schedule of operations of three transactions T₁, T₂ and T₃ in a relational database system:

R₂(Y), R₁(X), R₃(Z), R₁(Y), W₁(X), R₂(Z), W₂(Y), R₃(X), W₃(Z)

Consider the statement P and Q below:

P: S is conflict-serializable.

Q: If T₃ commits before T₁ finishes, then S is recoverable.

Which one of the following choices is correct?

(A) Both P and Q are true.

(B) P is true and Q is false.

(D) Both P and Q are false.

Answer: (B)

33. A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?

Answer: (A)

34. Consider the cyclic redundancy check (CRC) based error detecting scheme having the generator polynomial X³ + X + 1. Suppose the message m₄m₃m₂m₁m₀ = 11000 is to be transmitted. Check bits c₂c₁c₀ are appended at the end of the message by the transmitter using the above CRC scheme. The transmitted bit string is denoted by m₄m₃m₂m₁m₀c₂c₁c₀. The value of the checkbit sequence c₂c₁c₀ is

(A) 101

(B) 110

(D) 111

Answer: (C)

35. Consider the following ANSI C program:

Which one of the statements below is correct about the program?

(A) Upon execution, the program creates a linked-list of five nodes.

(B) Upon execution, the program goes into an infinite loop.

(D) It dereferences an uninitialized pointer that may result in a run-time error.

Answer: (D)

36. Consider the following two statements about regular languages:

S₁: Every infinite regular language contains an undecidable language as a subset.

S₂: Every finite language is regular.

Which one of the following choices is correct ?

(A) Only S₁ is true.

(B) Only S₂is true.

(D) Neither S₁ nor S₂ is true.

Answer: (C)

37. For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows:

Let ℒ be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P, Q, ∈ ℒ s(P, Q) = 0.

(A) 9

(B) 10

(D) 100

Answer: (B)

38. For a statement S in a program, in the context of liveness analysis, the following sets are defined:

USE(S) : the set of variables used in S

IN(S) : the set of variables that are live at the entry of S

OUT(S) : the set of variables that are live at the exit of S

Consider a basic block that consists of two statements, S₁ followed by S₂. Which one of the following statements is correct?

(A) OUT(S₁) = IN(S₂)

(B) OUT(S₁) = IN(S₁) ⋃ USE(S₁)

(D) OUT(S₁) = USE(S₁) ⋃ IN(S₂)

Answer: (A)

39. For constants a ≥ 1 and b > 1, consider the following recurrence defined on the non-negative integers:

Which one of the following options is correct about the recurrence T(n)?

Answer: (C)

Q.40 – Q.47 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

40. Suppose the following functional dependencies hold on a relation U with attributes P, Q, R, S, and T.

P → QR

RS → T

Which of the following functional dependencies can be inferred from the above functional dependencies?

(A) PS → T

(B) R → T

(D) PS → R

Answer: (A; C; D)

41. For a string 𝓌, we define 𝓌^R to be the reverse of 𝓌. For example if 𝓌 = 01101 then 𝓌^R = 10110.

Which of the following languages is/are context-free?

Answer: (B; C; D)

42. Consider the following multi-threaded code segment (in a mix of C and pseudocode), invoked by two processes P1 and P2, and each of the processes spawns two threads T1 and T2:

Which of the following statement(s) is/are correct?

(A) Both P1 and P2 will print the value of x as 2.

(B) At least one of P1 and P2 will print the value of x as 4.

(D) Both T1 and T2, in both the processes, will print the value of y as 1.

Answer: (A; D)

43. Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock (L). The following scheme is used to own a resource instance:

Which of the following choice(s) about the above scheme is/are correct?

(A) The scheme ensures that deadlocks will not occur.

(B) The scheme may lead to live-lock.

(D) The scheme violates the mutual exclusion property.

Answer: (A; B; C)

44. If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?

(A) 0x6665

(B) 0x0001

(D) 0x0100

Answer: (A; D)

45. Consider a computer network using the distance vector routing algorithm in its network layer. The partial topology of the network is as shown below.

The objective is to find the shortest-cost path from the router R to routers P and Q. Assume that R does not initially known the shortest routes to P and Q. Assume that R has three neighbouring routers denotes as X, Y, and Z. During one iteration, R measures its distance to its neighbours X, Y, and Z as 3, 2, and 5, respectively. Router R gets routing vectors from its neighbours that indicate that the distance to router P from routers X, Y and Z are 7, 6, and 5 respectively. The routing vector also indicates that the distance to router Q from routers X, Y, and Z are 4, 6, and 8, respectively. Which of the following statement(s) is/are correct with respect to the new routing table of R, after updation during this iteration?

(A) The distance from R to P will be stored as 10.

(B) The distance from R to Q will be stored as 7.

(D) The next hop router for a packet from R to Q is Z.

Answer: (B; C)

46. Consider the following directed graph:

Which of the following is/are correct about the graph?

(A) The graph does not have a topological order.

(B) A depth-first traversal starting at vertex S classifies three directed edges as back edges.

(D) For each pair of vertices u and v, there is a directed path from u to v.

Answer: (A; B)

47. Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that string ϵ is divisible by three.

(A) (0 + 1(01*0)*1)*

(B) (0 + 11 + 10(1 + 00)*01)*

(D) (0 + 11 + 11(1 + 00)*00)*

Answer: (A; B; C)

Q.48 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

48. Consider a three-level page table to translate a 39-bit virtual address to a physical address as shown below.

The page is size is 4KB(1KB = 2¹⁰ bytes) and page table entry size at every level is 8 bytes. A process P is currently using 2GB (1GB = 2³⁰ bytes) virtual memory which is mapped to 2GB of physical memory. The minimum amount of memory required for the page table of P across all levels is ______KB.

Answer: (4108 to 4108)

49. Consider the following ANSI C program.

The output of the program upon execution is ________

Answer: (60 to 60)

50. Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B are subsets of S, and A ⊆ B is ________

Answer: (59049 to 59049)

51. Consider the following augmented grammar with {#, @, <, >, a, b, c} as the set of terminals.

Answer: (8 to 8)

52. Consider a Boolean function f(w, x, y, z) such that

f(w, 0, 0, z) = 1

f(1, x, 1, z) = x + z

f(w, 1, y, z) = wz + y

The number of literals in the minimal sum-of-products expression of f is _________

Answer: (6 to 6)

53. Consider a pipelined processor with 5 stages, Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Write Back (WB). Each stage of the pipeline, except the EX stage, takes one cycle. Assume that the ID stage merely decodes the instruction and the register read is performed in the EX stage. The EX stage takes one cycle for ADD instruction and two cycles for MUL instruction. Ignore pipeline register latencies.

ADD, MUL, ADD, MUL, ADD, MUL, ADD, MUL

Assume that every MUL instruction is data-dependent on the ADD instruction just before it and every ADD instruction (except the first ADD) is data-dependent on the MUL instruction just before it. The Speedup is defined as follows:

The Speedup achieved in executing the given instruction sequence on the pipelined processor (rounded to 2 decimal places) is _________.

Answer: (1.87 to 1.88)

54. Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (= 10⁶ bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modeled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is _________.

Answer: (130 to 140)

55. In a directed acyclic graph with a source vertex s, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex v other than s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1.

The sum of the quality-scores of all the vertices in the graph shown above is_________.

Answer: (929 to 929)

GATE Exam 2021 Computer Science and Information Technology (CS-1) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CS-1: Computer Science and Information Technology

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A) 21

(B) 37

(D) 73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A) (i) is grammatically correct and (ii) is unambiguous

(B) (i) is grammatically incorrect and (ii) is unambiguous

(D) (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Plan, outline

(B) Hospital, library

(D) Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

(A) π/2

(B) 3/π

(D) 3π

Answer: (C)

The discount on item Q, as a percentage of its marked price, is ______

(A) 25

(B) 12.5

(D) 5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A) 0.3024

(B) 0.4235

(D) 0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(D) Neither conclusion I nor II is correct.

Answer: (C OR D)

Which one of the following statements summarizes the passage?

(A) The proposed AOM addresses the core problems that cause obesity.

(B) If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(D) AOM are addressing the problem superficially.

Answer: (D)

Computer Science and Information Technology (CS, Set-1)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Suppose that L₁ is a regular-language and L₂ is a context-free language. Which one of the following languages is NOT necessarily context-free?

(A) L₁ ⋂ L₂

(B) L₁ ⋅ L₂

(D) L₁ ⋃ L₂

Answer: (C)

2. Let P be an array containing n integers. Let t be the lowest upper bound on the under of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of n elements. Which one of the following choices is correct?

(A) t > 2n – 2

(B)

(D) t > [log₂(n)] and t ≤ n

Answer: (C)

3. Consider the following three functions.

f₁ = 10ⁿ f₂ = n^{log n} f₃ n^√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate ?

(A) f₃, f₂, f₁

(B) f₂, f₁, f₃

(D) f₂, f₃, f₁

Answer: (D)

4. Consider the following statements,

S₁ : The sequence of procedure calls corresponds to a preorder traversal of the activation tree.

S₂ : The sequence of procedure returns corresponds to a postorder traversal of the activation tree.

Which one of the following options is correct?

(A) S₁ is true and S₂ is false

(B) S₁ is false and S₂ is true

(D) S₁ is false and S₂ is false

Answer: (C)

5. Consider the following statements.

S₁ : Every SLR(1) grammar is unambiguous but there are certain unambiguous grammas that are not SLR(1)

S₂ : For any context-free grammar, there is a parser that takes at most O(n³) time to parse a string of length n.

Which one of the following options is correct?

(A) S₁ is true and S₂ is false

(B) S₁ is false and S₂ is true

(D) S₁ is false and S₂ is false

Answer: (C)

6. Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

(A) 15

(B) 21

(D) 528

Answer: (A)

7. Let p and q be two propositions. Consider the following two formulae in propositional logic.

Which one of the following choices is correct?

(A) Both S₁ and S₂ are tautologies

(B) S₁ is a tautology but S₂ is not a tautology.

(D) Neither S₁ nor S₂ is a tautology

Answer: (B)

8. Consider the following two statements.

S₁ : Destination MAC address of an ARP reply is a broadcast address.

S₂ : Destination MAC address of an ARP request is a broadcast address.

Which one of the following choices is correct?

(A) Both S₁ and S₂ are true.

(B) S₁ is true and S₂ is false.

(D) Both S₁ and S₂ are false

Answer: (C)

9. Consider the following array.

Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order?

(A) Selection sort

(B) Mergesort

(D) Quicksort using the last element as pivot

Answer: (C)

10. A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?

(A) Θ(n log n)

(B) Θ(n)

(D) Θ(1)

Answer: (D)

11. In the context of operating systems, which of the following statement is/are correct with respect to paging?

(A) Paging helps solve the issue of external fragmentation.

(B) Page size has no impact on internal fragmentation.

(D) Multi-level paging is necessary to support pages of different sizes.

Answer: (A; C)

12. Let denote an encoding of an automation M. Suppose that ∑ = {0, 1}.Which of the following languages is/are NOT recursive?

Answer: (D)

13. Suppose a database system crashes gain while recovering from a previous crash. Assume check pointing is not done by the database either during the transactions or during recovery.

Which of the following statements is/are correct?

(A) The same undo and redo list will be used while recovering again.

(B) The system cannot recover any further.

(D) The database will become inconsistent.

Answer: (A)

14. Which of the following standard C library functions will always invoke a system call when executed from a single-threaded process in a UNIX/Linux operating system?

(A) exit

(B) malloc

(D) strlen

Answer: (A; C)

15. Consider a linear list based directory implementation in a file system. Each directory is a list of nodes, where each node contains the file name along with the file metadata, such as the list of pointers to the data blocks. Consider a given directory foo.

Which of the following operations will necessarily require a full scan of foo for successful completion?

(A) Creation of a new file in foo

(B) Deletion of an existing file from foo

(D) Opening of an existing file in foo

Answer: (A; C)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks)

16. In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______.

Answer: (11 to 11)

17. Consider the following undirected graph with edge weights as shown:

The number of minimum-weight spanning trees of the graph is _____.

Answer: (3 to 3)

18. The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.

Answer: (0.35 to 0.39)

19. There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

– The fastest computer gets the toughest job and the slowest computer gets the easiest job.

-Every computer gets at least one job.

The number of ways in which this can be done is _______

Answer: (65 to 65)

20. Consider the following expression.

The value of the above expression ( rounded to 2 decimal places) is ________

Answer: (0.25 to 0.25)

21. Consider the following sequence of operations of an empty stack.

Consider the following sequence of operations on any empty queue.

The value of s + q is ______.

Answer: (86 to 86)

22. Consider a computer system with a byte-addressable primary memory of size 2³² Assume the computer system has a direct-mapped cache of size 32 KB (1 KB = 2¹⁰ bytes), and each cache block is of size 64 bytes.

The size of the tag field is ______ bits.

Answer: (17 to 17)

23. A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed.

The estimated number of tuples in the output of σ _(A>10)_⋁_(B=18)(r) is _________.

Answer: (819 to 820 OR 205 to 205)

24. Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S:1 E: 10000001 F: 111110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is _______.

Answer: (-7.75 to -7.75)

25. Three processes arrive at time zero with CPU bursts of 16, 20 and 10 milliseconds. If the scheduler has prior knowledge about the length of the CPU bursts, the minimum achievable average waiting time for these three processes in a non-preemptive scheduler (round to nearest integer) is ______ milliseconds.

Answer: (12 to 12)

Q.26 – Q.39 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: -2/3)

26. Consider the following grammar (that admits a series of declarations, followed by expressions) and the associated syntax directed translation (SDT) actions, given as pseudo-code:

With respect to the above grammar, which one of the following choices is correct?

(A) The actions can be used to correctly type-check any syntactically correct program.

(B) The actions can be used to type-check syntactically correct integer variable declarations and integer expressions.

(D) The actions will lead to an infinite loop.

Answer: (B)

27. The following relation records the age of 500 employees of a company, where empNo (indicating the employee number) is the key:

Consider the following relational algebra expression:

What does the above expression generate?

(A) Employee numbers of only those employees whose age is the maximum.

(B) Employee numbers of only those employees whose age is more than the age of exactly one other employee.

(D) Employee numbers of all employees whose age is the minimum.

Answer: (C)

28. Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?

(A) 011, 101, 000

(B) 001, 010, 111

(D) 001, 010, 000

Answer: (A)

29. Assume that a 12-bit hamming codeword consisting of 8-bit data and 4 check bits is d₈d₇d₆d₅c₈d₄d₃d₂c₄d₁c₂c₁, where the data bits and the check bits are given in the following tables:

Which one of the following choices gives the correct values of x and y?

(A) x is 0 and y is 0.

(B) x is 0 and y is 1.

(D) x is 1 and y is 1.

Answer: (A)

30. Consider the following recurrence relation.

Which one of the following options is correct?

(A) T(n) = Θ(n^5/2)

(B) T(n) = Θ(n log n)

(D) T(n) = Θ((log n)^5/2

Answer: (C)

31. Consider the following context-free grammar where the set of terminals is {a, b, c, d, f}.

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table (“blank” denotes that the corresponding cell is empty)?

Answer: (A)

32. Let r_i(z) and w_i(z) denote read and write operations respectively on a data item z by a transaction T_i. Consider the following two schedules.

Which one of the following option sis correct?

(A) S₁ is conflict serializable, and S₂ is not conflict serializable

(B) S₁ is not conflict serializable, and S₂ is conflict serializable.

(D) Neither S₁ nor S₂ is conflict serializable.

Answer: (B)

33. Consider the relation R(P, Q, S, T, X, Y, Z W) with the following functional dependencies.

PQ → X; P → YX; Q → Y; Y → ZW

Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D₁: R = {(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]

D₂: R = [(P, Q, S); (T, X), (Q, Y); (Y, Z, W)]

Which one of the following options is correct?

(A) D₁ is a lossless decomposition, but D₂ is a lossy decomposition.

(B) D₁ is a lossy decomposition, but D₂ is a lossless decomposition.

(D) Both D₁ and D₂ are lossy decompositions.

Answer: (A)

34. Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

(A) Both G and H are always cyclic.

(B) G may not be cyclic, but H is always cyclic.

(D) Both G and H may not be cyclic.

Answer: (B)

35. Consider the two statements.

Which one of the following choices is correct?

(A) Both S₁ and S₂ are true

(B) S₁ is true, but S₂ is false.

(D) Both S₁ and S₂ are false

Answer: (D)

36. Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:

Let M be the adjacency matrix of G.

Define graph G₂ on the same set of vertices with adjacency matrix N, where

Which one of the following statements is true?

(A)

(B)

(D) diam(G) < diam(G₂) ≤ 2 diam(G)

Answer: (A)

37. Consider the following ANSI C program.

Which one of the following options is correct?

(A) The program will not compile successfully.

(B) The program will compile successfully and output 1- when executed.

(D) The program will compile successfully and output 13 when executed.

Answer: (B)

38. Consider the following language.

L = {w ∈ {0, 1}* | w ends with the substring 011}

Which one of the following deterministic finite automata accepts L?

Answer: (D)

39. For a Turing machine M, denotes an encoding of M. Consider the following two languages.

Which one of the following options is correct?

(A) Both L₁ and L₂ are decidable

(B) L₁ is decidable and L₂ is undecidable

(D) Both L₁ and L₂ are undecidable

Answer: (A)

Q.40 – Q.47 Multiple Select Question (MSQ), carry two mark each (no negative marks).

40. Define R_n to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i > 0, let p[i] denote the selling price of a rod whose length is i meters. Consider the array of prices:

p[1] = 1, p[2] = 5, p[3] = 8, p[4] 9, p[5] = 10, p[6] = 17, p[7] = 18

Which of the following statements is/are correct about R₇?

(A) R₇ = 18

(B) R₇ = 19

(D) R₇ cannot be achieved by a solution consisting of three pieces.

Answer: (A; C)

41. An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following options is/are correct?

(A) Root of T can never be an articulation point in G.

(B) Root of T is an articulation point in G if and only if it has 2 or more children.

(D) If u is an articulation point in G such that x is an ancestor of u in T and y is a descendent of u in T, then all paths from x to y in G must pass through u.

Answer: (B)

42. Consider the following Boolean expression.

Which of the following Boolean expressions is/are equivalent to (complement of F)?

Answer: (B; C; D)

43. A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?

(A) If a relation S is reflexive and symmetric, then S is an equivalence relation.

(B) If a relation S is circular and symmetric, then S is an equivalence relation.

(D) If a relation S is transitive and circular, then S is an equivalence relation.

Answer: (C)

44. A TCP server application is programmed to listen on port number P on host S. A TCP client is connected to the TCP server over the network.

Consider that while the TCP connection was active, the server machine S crashed and rebooted. Assume that the client does not use the TCP keep alive timer. Which of the following behaviors is/are possible?

(A) If the client was waiting to receive a packet, it may wait indefinitely.

(B) The TCP server application on S can listen on P after reboot.

(D) If the client sends a packet after the server reboot, it will receive a FIN segment.

Answer: (A; B; C)

45. Consider two hosts P and Q connected through a router R. The maximum transfer unit (MTU) value of the link between P and R is 1500 bytes, and between R and Q is 820 bytes.

A TCP segment of size 1400 bytes was transferred from P to Q through R, with IP identification value as 0 x1234. Assume the IP header size is 20 bytes. Further, the packet is allowed to be fragmented, i.e., Don’t Fragment (DF) flag in the IP header is not set by P.

Which of the following statements is/are correct?

(A) Two fragments are created at R and the IP datagram size carrying the second fragment is 620 bytes.

(B) If the second fragment is lost, R will resent the fragment with the IP identification value 0x1234.

(D) TCP destination port can be determined by analyzing only the second fragment.

Answer: (A; C)

46. Consider the following pseudocode, where S is a semaphore initialized to 5 in line ≠2 and counter is a shared variable initialized to 0 in line ≠ Assume that the increment operation in line ≠7 is not atomic.

If five threads execute the function parop concurrently,, which of the following program behavior(s) is/are possible?

(A) The value of counter is 5 after all the threads successfully complete the execution of parop.

(B) The value of counter is 1 after all the threads successfully complete the execution of parop.

(D) There is a deadlock involving all the threads.

Answer: (A; B; D)

47. Consider a dynamic hashing approach for 4-bit integer keys:

(1) There is a main has table of size 4.

(2) The 2 least significant bits of a key is used index into the main has table.

(3) Initially, the main has table entries are empty.

(4) Thereafter, when more keys are hashed into it, to resolve collisions, the set of all keys corresponding to a main hash table entry is organized as a binary tree that grows on demand.

(5) First, the 3^rd least significant bit is used to divided the keys into left and right subtrees.

(6) To resolve more collisions, each node of the binary tree is further sub-divided into left and right subtrees based on the 4^th least significant bit.

(7) A split is done only if it is needed i.e.., only when there is a collision.

Consider the following state of the hash table.

Which of the following sequences of key insertions can cause the above state of the hash table (assume the keys are in decimal notation)?

(A) 5, 9, 4, 13, 10, 7

(B) 9, 5, 10, 6, 7, 1

(D) 9, 5, 13, 6, 10, 14

Answer: (C)

Q.48 – Q.55Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

48. Consider the following ANSI-C function:

Let Z be an array of 10 elements with Z[i] = 1, for all i such that 0 ≤ i ≤ 9. The value returned by SimpleFunction(Z, 10, 2) is ______.

Answer: (1023 to 1023)

49. Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following:

• The time taken for processing the data frame by the receiver is negligible.

• The time taken for processing the acknowledgement frame by the sender is negligible.

• The sender has infinite number of frames available for transmission.

• The size of the data frame is 2,000 bits and the size of the acknowledgement frame is 10 bits.

• The link data rate in each direction is 1 Mbps (= 10⁶ bits per second).

• One way propagation delay of the link is 100 milliseconds.

The minimum value of the sender’s window size in terms of the number of frames, (rounded to the nearest integer) needed to achieve a link utilization of 50% is _______.

Answer: (50 to 52)

50. Consider the following C code segment:

In a complier, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes in the DAG is ________.

Answer: (6 to 6)

51. In a pushdown automaton P = (Q, ∑, Γ, δ, q₀, F) a transition of the form,

where p, q ∈ Q, a ∈ ∑ ⋃ {ϵ], and X, Y ∈ Γ ⋃ {ϵ}, represents (q, Y) ∈ δ(p, a, X).

Consider the following pushdown automaton over the input alphabet ∑ = {a, b} and stack alphabet Γ = {≠, A}.

The number of strings of length 100 accepted by the above pushdown automaton is ______.

Answer: (50 to 50)

52. Consider the following matrix.

The largest eigenvalue of the above matrix is ______.

Answer: (3 to 3)

53. A five-stage pipeline has stage delays of 150, 120, 150, 160 and 140 nanoseconds. The registers that are used between the pipeline stages have a delay of 5 nanoseconds each.

The total time to execute 100 independent instructions on this pipeline, assuming there are no pipeline stalls, is _________ nanoseconds.

Answer: (17160 to 17160)

54. A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).

In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.

If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ________.

Answer: (0.04 to 0.04)

55. Consider the following instruction sequence where registers R1, R2 and R3 are general purpose and MEMORY[X] denotes the content at the memory location X.

Assume that the content of the memory location 5000 is 10, and the content of the register R3 is 3000. The content of each of the memory locations from 3000 to 3010 is 50. The instruction sequence starts from the memory location 1000. All the numbers are in decimal format. Assume that the memory is byte addressable.

After the execution of the program, the content of memory location 3010 is _______.

Answer: (50 to 50)

GATE Exam 2021 Chemical Engineering (CH) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CH: Chemical Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A) 21

(B) 37

(D) 73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A) (i) is grammatically correct and (ii) is unambiguous

(B) (i) is grammatically incorrect and (ii) is unambiguous

(D) (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Plan, outline

(B) Hospital, library

(D) Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

(A) π/2

(B) 3/π

(D) 3π

Answer: (C)

The discount on item Q, as a percentage of its marked price, is ______

(A) 25

(B) 12.5

(D) 5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A) 0.3024

(B) 0.4235

(D) 0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(D) Neither conclusion I nor II is correct.

Answer: (C OR D)

Which one of the following statements summarizes the passage?

(A) The proposed AOM addresses the core problems that cause obesity.

(B) If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(D) AOM are addressing the problem superficially.

Answer: (D)

Chemical Engineering (CH)

Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. An ordinary differential equation (ODE), with an initial condition y(0) = 1, has the analytical solution y = e^2x.

Using Runge-Kutta second order method, numerically integrate the ODE to calculate y at x = 0. 5 using a step size of h = 0. 5.

If the relative percentage error is defined as, then the value of ε at x = 0.5 is ________.

(A) 0.06

(B) 0.8

(D) 8.0

Answer: (D)

2. The function cos(x) is approximated using Taylor series around x = 0 as cos(x) ≈ 1 + a x + bx² + cx³ + d x⁴. The values of a, b, c and d are

(A) a = 1, b = −0.5, c = −1, d = −0.25

(B) a = 0, b = −0.5, c = 0, d = 0.042

(D) a = −0.5, b = 0, c = 0.042, d = 0

Answer: (B)

3. The heat of combustion of methane, carbon monoxide and hydrogen are P, Q and R respectively. For the reaction below, CH₄ + H₂O → CO + 3H₂ the heat of reaction is given by

(A) P − Q − 3R

(B) Q + 3R − P

(D) Q + R − P

Answer: (A)

4. A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of type A and type B in water (density 1000 kg m^–3) at room temperature.

Type A are spherical particles of diameter 30 μm and density 1100 kg m^–3.

Type B are spherical particles of diameter 10 μm and density 1900 kg m^–3.

Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would

(A) consist of a homogeneous mixture of type A and type B particles

(B) consist of type B particles only

(D) be completely segregated with type A particles on top of type B particles

Answer: (A)

5. A three-dimensional velocity field is given by V = 5x²y i + Cy j − 10xyz k, where i,j, k are the unit vectors in x, y, z directions, respectively, describing a cartesian coordinate system. The coefficient C is a constant. If V describes an incompressible fluid flow, the value of C is

(A) −1

(B) 0

(D) 5

Answer: (B)

6. Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given by

(A) Dittus-Boelter equation

(B) Nusselt theory

(D) Sieder-Tate equation

Answer: (B)

7. In a double-pipe heat exchanger of 10 m length, a hot fluid flows in the annulus and a cold fluid flows in the inner pipe. The temperature profiles of the hot (T_h) and cold (T_c) fluids along the length of the heat exchanger (x, such that x ≥ 0), are given by

Th(x) = 80 − 3x

Tc(x) = 20 + 2x

where T_h and T_c are in °C, and x is in meter.

The logarithmic mean temperature difference (in °C) is

(A) 24.6

(B) 27.9

(D) 50.0

Answer: (B)

8. For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as 250 Wm^–2K^–1 for a specific process condition. It is expected that the heat exchanger may be fouled during the operation, and a fouling resistance of 0.001 m²KW^–1 is prescribed. The dirt overall heat transfer coefficient is _____ W m^–2 K^–1.

(A) 100

(B) 150

(D) 250

Answer: (C)

9. In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are P₁ and π₁, respectively. The corresponding values are P₂ and π₂ at the permeate side. The membrane, feed, and permeate are at the same temperature. For equilibrium to prevail, the general criterion that should be satisfied is

(A) π₁ = π₂

(B) P₁ = P₂

(D) P₁ – π₁ = P₂ – π₂

Answer: (D)

10. Ethylene adsorbs on the vacant active sites V of a transition metal catalyst according to the following mechanism.

If NT, NV and denote the total number of active sites, number of vacant active sites and number of adsorbed C2H4 molecules, respectively, the balance on the total number of active sites is given by

Answer: (B)

11. Which of the following is NOT a standard to transmit measurement and control signals?

(A) 4 – 20 mA

(B) 3 – 15 psig

(D) 1 – 5 VDC

Answer: (C)

12. A feedforward controller can be used only if

(A) the disturbance variable can be measured

(B) the disturbance variable can be manipulated

(D) regulatory control is not required

Answer: (A)

13. Turnover ratio is defined as

Answer: (B)

14. A principal amount is charged a nominal annual interest rate of 10%. If the interest rate is compounded continuously, the final amount at the end of one year would be

(A) higher than the amount obtained when the interest rate is compounded monthly

(B) lower than the amount obtained when the interest rate is compounded annually

(D) equal to the amount obtained when using an effective interest rate of 27.18%

Answer: (A)

15. Match the common name of chemicals in Group – 1 with their chemical formulae in Group – 2.

The correct combination is:

(A) P – III, Q – II, R – I

(B) P – III, Q – I, R – II

(D) P – II, Q – I, R – III

Answer: (C)

Q.16 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

16. For the function the CORRECT statement(s) is/are

(A) f(x) is continuous at x = 1

(B) f(x) is differentiable at x = 1

(D) f(x) is differentiable at x = 0

Answer: (A; B; C)

17. Feed solution F is contacted with solvent B in an extraction process. Carrier liquid in the feed is A and the solute is C. The ternary diagram depicting a single ideal stage extraction is given below. The dashed lines represent the tie-lines.

The CORRECT option(s) is/are

(A) For the tie-lines shown, concentration of solute in the extract is higher than that in the raffinate

(B) Maximum amount of solvent is required if the mixture composition is at W

(D) U represents the raffinate composition if the mixture composition is at M

Answer: (A; C; D)

18. The inherent characteristics of three control valves P, Q and R are shown in the figure.

The CORRECT option(s) is/are

(A) P is a quick opening valve

(B) Q is a quick opening valve

(D) R is an equal percentage valve

Answer: (A; D)

Q.19 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

19. A source placed at the origin of a circular sample holder (radius r = 1 m) emits particles uniformly in all directions. A detector of length l = 1 cm has been placed along the perimeter of the sample holder. During an experiment, the detector registers 14 particles.

The total number of particles emitted during the experiment is ______.

Answer: (8790 to 8800)

20. A, B, C and D are vectors of length 4.

It is known that B is not a scalar multiple of A. Also, C is linearly independent of A and B. Further, D = 3 A + 2 B + C.

The rank of the matrix is _______.

Answer: (3 to 3)

21. The van der Waals equation of state is given by

where P_r, T_r and v_r represent reduced pressure, reduced temperature and reduced molar volume, respectively. The compressibility factor at critical point (z_c) is 3/8.

If v_r = 3 and T_r = 4/3, then the compressibility factor based on the van der Waals equation of state is _________ (round off to 2 decimal places).

Answer: (0.83 to 0.85)

22. Consider a steady flow of an incompressible, Newtonian fluid through a smooth circular pipe. Let α_laminar and α_turbulent denote the kinetic energy correction factors for laminar and turbulent flow through the pipe, respectively. For turbulent flow through the pipe

Here, is the average velocity, V0 is the centerline velocity, and n is a parameter. The ratio of average velocity to the centerline velocity for turbulent flow through the pipe is given by

For n = 7, the value of is ______ (round off to 2 decimal places.)

Answer: (0.52 to 0.54)

23. The molar heat capacity at constant pressure Cp (in J mol^–1 K^–1) for n-pentane as a function of temperature (T in K) is given by 46 + 45.4 × 10⁻³T – 14.1 × 10⁻⁶ T². Take R = 8.314 J mol⁻¹K⁻¹.

At 1000 K, the rate of change of molar entropy of n-pentane with respect to temperature at constant pressure is ___________ J mol^–1 K^–2 (round off to 2

decimal places).

Answer: (0.27 to 0.29)

24. The following homogeneous liquid phase reactions are at equilibrium.

The values of rate constants are given by: k₁ = 0.1 s^–1, k^–1 = 0.2 s^–1, k₂ = 1 s^–1 k_–2 = 10 s^–1, k₃ = 10 s^–1.

The value of rate constant k^–3 is ______________ s^–1 (round off to 1 decimal

place).

Answer: (0.5 to 0.5)

25. A company invests in a recovery unit to separate valuable metals from effluent streams. The total initial capital investment of this unit is Rs. 10 lakhs. The recovered metals are worth Rs. 4 lakhs per year.

If the annual return on this investment is 15%, the annual operating costs should be ________ lakhs of rupees (correct to 1 decimal place).

Answer: (2.5 to 2.5)

Q.26 – Q.33 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Let A be a square matrix of size n × n (n > 1). The elements of A = {a_ij} are given by

The determinant of A is

(A) 0

(B) 1

(D) (n!)²

Answer: (D)

27. Consider a fluid confined between two horizontal parallel plates and subjected to shear flow.

In the first experiment, the plates are separated by a distance of 1 mm. It is found that a shear stress of 2 N m^–2 has to be applied to keep the top plate moving with a velocity of 2 m s^–1, while the other plate is fixed.

In the second experiment, the plates are separated by a distance of 0.25 mm. It is found that a shear stress of 3 N m^–2 has to be applied to keep the top plate moving with a velocity of 1 m s^–1, while the other plate is fixed.

In the range of shear rates studied, the rheological character of the fluid is

(A) Newtonian

(B) Pseudoplastic

(D) Ideal and inviscid

Answer: (B)

28. Water of density 1000 kg m^–3 flows in a horizontal pipe of 10 cm diameter at an average velocity of 0.5 m s^–1. The following plot shows the pressure measured at various distances from the pipe entrance.

Using the data shown in the figure, the Fanning friction factor in the pipe when the flow is FULLY DEVELOPED is

(A) 0.0012

(B) 0.0074

(D) 0.0106

Answer: (B)

29. In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating under isothermal condition. Pure gas is used in this stripping operation. All solutions are dilute and Henry’s law, y* = mx, is applicable. Here, y* is the mole fraction of the solute in the gas phase in equilibrium with the liquid phase of solute mole fraction x, and m is the Henry’s law constant.

Let x₁ be the mole fraction of the solute in the leaving liquid, and x₂ be the mole fraction of solute in the entering liquid.

When the value of the ratio of the liquid-to-gas molar flow rates is equal to m, the overall liquid phase Number of Transfer Units, NTUOL, is given by

Answer: (A)

30. Which of these symbols can be found in piping and instrumentation diagrams?

(A) (Q) and (S) only

(B) (P), (Q) and (R) only

(D) (P), (Q), (R) and (S)

Answer: (C)

31. It is required to control the volume of the contents in the jacketed reactor shown in the figure.

Which one of the following schemes can be used for feedback control?

(A) Measure L101 and manipulate valve V-2

(B) Measure T101 and manipulate valve V-1

(D) Measure F101 and manipulate valve V-1

Answer: (C)

32. Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?

(A) Dead-time term(s) must be absent in the open-loop transfer function

(B) Roots of the characteristic equation must have negative real part

(D) Open-loop transfer function must have an amplitude ratio less than 1 at the critical frequency

Answer: (A)

33. Match the reaction in Group – 1 with the reaction type in Group – 2.

The correct combination is:

(A) P – II, Q – III, R – I, S – IV

(B) P – III, Q – IV, R – I, S – II

(D) P – I, Q – IV, R – III, S – II

Answer: (B)

Q.34 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

34. To solve an algebraic equation f(x) = 0, an iterative scheme of the type x_n+1 = g(x_n) is proposed, where

At the solution x = s, g’(s) = 0 and g’’(s) ≠ 0.

The order of convergence for this iterative scheme near the solution is __________.

Answer: (2 to 2)

35. The probability distribution function of a random variable X is shown in the following figure.

From this distribution, random samples with sample size n = 68 are taken. If is the sample mean, the standard deviation of the probability distribution of , i.e. is ______ (round off to 3 decimal places).

Answer: (0.069 to 0.071)

36. For the ordinary differential equation

with initial conditions y(0) = y'(0) = y”(0) = ”'(0) = 0, the value of _______ (round off to 3 decimal places).

Answer: (0.161 to 0.169)

37. Formaldehyde is produced by the oxidation of methane in a reactor. The following two parallel reactions occur.

CH₄ + O₂ → HCHO + H₂O

CH₄ + 2O₂ → CO₂ + 2H₂O

Methane and oxygen are fed to the reactor. The product gases leaving the reactor include methane, oxygen, formaldehyde, carbon dioxide and water vapor.

60 mol s–1 of methane enters the reactor. The molar flowrate (in mol s^–1) of CH₄, O₂ and CO₂ leaving the reactor are 26, 2 and 4, respectively. The molar flowrate of oxygen entering the reactor is _______________ mol s^–1.

Answer: (40 to 40)

38. The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. 1 mol of CO, 0.5 mol of O₂ and 2 mol of N₂ are taken initially at 1 bar and 298 K, and the combustion is carried out to completion.

The standard molar internal energy change of reaction (∆u°_R) for the combustion of carbon monoxide at 298 K = –282 kJ mol^–1. At constant pressure, the molar heat capacities of N₂ and CO₂ are 33.314 J mol^–1 K^–1 and 58.314 J mol^–1 K^–1, respectively. Assume the heat capacities to be independent of temperature, and the gases are ideal. Take R = 8.314 J mol^–1 K^–1.

The final pressure in the vessel at the completion of the reaction is _______ bar (round off to 1 decimal place).

Answer: (8.9 to 9.1)

39. A gaseous mixture at 1 bar and 300 K consists of 20 mol % CO₂ and 80 mol% inert gas.

Assume the gases to be ideal. Take R = 8.314 J mol^–1 K^–1.

The magnitude of minimum work required to separate 100 mol of this mixture at 1 bar and 300 K into pure CO₂ and inert gas at the same temperature and pressure is __________ kJ (round off to nearest integer).

Answer: (124 to 126)

40. A binary liquid mixture consists of two species 1 and 2. Let γ and x represent the activity coefficient and the mole fraction of the species, respectively. Using a molar excess Gibbs free energy model, ln γ₁ x₁and ln γ₂ vs. x₁ are plotted. A tangent drawn to the ln γ₁ vs. x₁ curve at a mole fraction of x₁ = 0. 2 has a slope = −1.728.

The slope of the tangent drawn to the ln γ₂ vs. x₁ curve at the same mole fraction is ______ (correct to 3 decimal places).

Answer: (0.432 to 0.432)

41. Consider a tank filled with 3 immiscible liquids A, B and C at static equilibrium, as shown in the figure. At 2 cm below the liquid A – liquid B interface, a tube is connected from the side of the tank. Both the tank and the tube are open to the atmosphere.

At the operating temperature and pressure, the specific gravities of liquids A, B and C are 1, 2 and 4, respectively. Neglect any surface tension effects in the calculations. The length of the tube L that is wetted by liquid B is _____________ cm.

Answer: (8 to 8)

42. Seawater is passed through a column containing a bed of resin beads.

Density of seawater = 1025 kg m^–3

Density of resin beads = 1330 kg m^–3

Diameter of resin beads = 50 μm

Void fraction of the bed at the onset of fluidization = 0.4

Acceleration due to gravity = 9.81 m s^–2

The pressure drop per unit length of the bed at the onset of fluidization is ___________ Pa m^–1 (round off to nearest integer).

Answer: (1790 to 1800)

43. A straight fin of uniform circular cross section and adiabatic tip has an aspect ratio (length/diameter) of 4. If the Biot number (based on radius of the fin as the characteristic length) is 0.04, the fin efficiency is __________ % (round off to nearest integer).

Answer: (42 to 44)

44. A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at 110°C and the boiling point of the solution in the second effect is 63.3° The overall heat transfer coefficient in the first effect and second effect are 2000 W m^–2 K^–1 and 1500 W m^–2 K^–1, respectively. The heat required to raise the temperature of the feed to the boiling point can be neglected. The heat flux in the two evaporators can be assumed to be equal.

The temperature at which the solution boils in the first effect is _______ °C (round off to nearest integer).

Answer: (89 to 91)

45. Consider a solid slab of thickness 2L and uniform cross section A. The volumetric rate of heat generation within the slab is ġ (W m^–3). The slab loses heat by convection at both the ends to air with heat transfer coefficient h. Assuming steady state, one-dimensional heat transfer, the temperature profile within the slab along the thickness is given by:

where k is the thermal conductivity of the slab and T_s is the surface temperature. If T_s = 350 K, ambient air temperature T_∞ = 300 K, and Biot number (based on L as the characteristic length) is 0.5, the maximum temperature in the slab is ___________ K (round off to nearest integer).

Answer: (362 to 363)

46. A distillation column handling a binary mixture of A and B is operating at total reflux. It has two ideal stages including the reboiler. The mole fraction of the more volatile component in the residue (x_W) is 0.1. The average relative volatility α_AB is 4. The mole fraction of A in the distillate (x_D) is ___________ (round off to 2 decimal places).

Answer: (0.63 to 0.65)

47. In a batch drying experiment, a solid with a critical moisture content of 0.2 kg H₂O/kg dry solid is dried from an initial moisture content of 0.35 kg H₂O/kg dry solid to a final moisture content of 0.1 kg H₂O/kg dry solid in 5 h. In the constant rate regime, the rate of drying is 2 kg H₂O/(m².h).

The entire falling rate regime is assumed to be uniformly linear. The equilibrium moisture content is assumed to be zero.

The mass of the dry solid per unit area is ___________ kg/m² (round off to nearest integer).

Answer: (34 to 35)

48. As shown in the figure below, air flows in parallel to a freshly painted solid surface of width 10 m, along the z-direction.

The equilibrium vapor concentration of the volatile component A in the paint, at the air-paint interface, is C_A,i. The concentration C_A decreases linearly from this value to zero along the y-direction over a distance δ of 0.1 m in the air phase. Over this distance, the average velocity of the air stream is 0.033 m s^–1 and its velocity profile (in m s-1) is given by v_z(y) = 10 y²

where y is in meter.

Let C_A,m represent the flow averaged concentration. The ratio of C_A,m to C_A,i , is _______________ (round off to 2 decimal places).

Answer: (0.24 to 0.26)

49. The following isothermal autocatalytic reaction, A + B → 2B (−r_A) = 0.1C_AC_B (mol L⁻¹ s⁻¹) is carried out in an ideal continuous stirred tank reactor (CSTR) operating at steady state. Pure A at 1 mol L^–1 is fed, and 90% of A is converted in the CSTR. The space time of the CSTR is ___________ seconds.

Answer: (100 to 100)

50. Reactant A decomposes to products B and C in the presence of an enzyme in a well-stirred batch reactor. The kinetic rate expression is given by

If the initial concentration of A is 0.02 mol L^–1, the time taken to achieve 50% conversion of A is _________ min (round off to 2 decimal places).

Answer: (4.44 to 4.51)

51. The following homogeneous, irreversible reaction involving ideal gases, A → B + C (−r_A) = 0.5C_A (mol L⁻¹s⁻¹) is carried out in a steady state ideal plug flow reactor (PFR) operating at isothermal and isobaric conditions. The feed stream consists of pure A, entering at 2 m s^–1.

In order to achieve 50% conversion of A, the required length of the PFR is _____________ meter (round off to 2 decimal places).

Answer: (3.49 to 3.61)

52. A system has a transfer function When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is ___________.

Answer: (40 to 40)

53. A process has a transfer function Initially the process is at steady state with x(t = 0) = 0. 4 and y(t = 0) = 100. If a step change in x is given from 0.4 to 0.5, the maximum value of y that will be observed before it reaches the new steady state is ___________ (round off to 1 decimal place).

Answer: (102.4 to 102.6)

54. Operating labor requirements L in the chemical process industry is described in terms of the plant capacity C (kg day^–1) over a wide range (10³ – 10⁶) by a power law relationship L = αC^β

where α and β are constants. It is known that

L is 60 when C is 2 × 10⁴

L is 70 when C is 6 × 10⁴

The value of L when C is 10⁵ kg day^–1 is ______________ (round off to nearest integer).

Answer: (73 to 77)

55. A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of pipe is given by

The annual cost of the installed piping system per unit length of pipe is given by C_piping = 45.92D

Here, D is the inner diameter of the pipe in meter, q is the volumetric flowrate of the liquid in m³ s^–1 and μ is the viscosity of the liquid in Pa.s. and the volumetric flow rate of the liquid is 10^–4 m³ s^–1, the economic inner diameter of the pipe is ________ meter (round off to 3 decimal places).

Answer: (0.014 to 0.016)

GATE Exam 2021 Civil Engineering (CE-2) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CE2: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Civil Engineering (CE, Set-2)

Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The value of is

(A) 0

(B) 1.0

(D) ∞

Answer: (A)

2. The rank of the matrix is

(A) 1

(B) 2

(D) 4

Answer: (C)

3. The unit normal vector to the surface X² + Y² + Z² – 48 = 0 at the point (4, 4, 4) is

Answer: (B)

4. If A is a square matrix then orthogonality property mandates

(A) AA^T = I

(B) AA^T = 0

(D) AA^T = A²

Answer: (A)

5. In general, the CORRECT sequence of surveying operations is

(A) Field observations → Reconnaissance → Data analysis → Map making

(B) Data analysis → Reconnaissance → Field observations → Map making

(D) Reconnaissance → Data analysis → Field observations → Map making

Answer: (C)

6. Strain hardening of structural steel means

(A) experiencing higher stress than yield stress with increased deformation

(B) strengthening steel member externally for reducing strain experienced

(D) decrease in the stress experienced with increasing strain

Answer: (A)

7. A single story building model is shown in the figure. The rigid bar of mass ‘m’ is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force (P) and corresponding moment (M) are also shown in the figure. The lateral deflection (δ) of the bar is given by where L is the effective length of the column, E is the Young’s modulus of elasticity and I is the area moment of inertia of the column cross-section with respect to its neutral axis.

For the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation is

Answer: (A)

8. Seasoning of timber for use in construction is done essentially to

(A) increase strength and durability

(B) smoothen timber surfaces

(D) cut timber in right season and geometry

Answer: (A)

9. In case of bids in Two-Envelop System, the correct option is

(A) Technical bid is opened first

(B) Financial bid is opened first

(D) Either of the two (Technical and Financial) bids can be opened first

Answer: (A)

10. The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is

(A) consolidated drained test

(B) unconsolidated undrained test

(D) unconfined compression test

Answer: (A)

11. As per the Unified Soil Classification System (USCS), the type of soil represented by ‘MH’ is

(A) Inorganic silts of high plasticity with liquid limit more than 50%

(B) Inorganic silts of low plasticity with liquid limit less than 50%

(D) Inorganic clays of low plasticity with liquid limit more than 50%

Answer: (A)

12. The ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe is

(A) 1/2

(B) 2/3

(D) 3/2

Answer: (B)

13. Relationship between traffic speed and density is described using a negatively sloped straight line. If v_f is the free-flow speed then the speed at which the maximum flow occurs is

(A) 0

(B) v_f/4

(D) v_f

Answer: (C)

14. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce the consumption of raw materials.

Reason [r]: Solid wastes are seldom generated when raw materials are converted to goods for consumption.

(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)

15. The hardness of a water sample is measured directly by titration with 0.01 M solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The EBT reacts and forms complexes with divalent metallic cations present in the water. During titration, the EDTA replaces the EBT in the complex. When the replacement of EBT is complete at the end point of the titration, the colour of the solution changes from

(A) blue-green to reddish brown

(B) blue to colourless

(D) wine red to blue

Answer: (D)

16. The softening point of bitumen has the same unit as that of

(A) distance

(B) temperature

(D) viscosity

Answer: (B)

Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks).

17. Which of the following statement(s) is/are correct?

(A) Increased levels of carbon monoxide in the indoor environment result in the formation of carboxyhemoglobin and the long term exposure becomes a cause of cardiovascular diseases.

(B) Volatile organic compounds act as one of the precursors to the formation of photochemical smog in the presence of sunlight.

(C) Long term exposure to the increased level of photochemical smog becomes a cause of chest constriction and irritation of the mucous membrane.

(D) Increased levels of volatile organic compounds in the indoor environment will result in the formation of photochemical smog which is a cause of cardiovascular diseases.

Answer: (A; B; C)

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

18. The value (round off to one decimal place) of is______

Answer: (0.0 to 0.0)

19. A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa.

The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is ______________

Answer: (14 to 16)

20. A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure.

The vertical reaction at support X (in kN, in integer) is _____________

Answer: (30 to 30)

21. The internal (d_i) and external (d_o) diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio (A_r) of the sampler (in %, round off to two decimal places) is ____________

Answer: (17.25 to 17.45)

22. A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m³/s. The area of the catchment (in km2, round off to the nearest integer) is ____________

Answer: (595 to 598)

23. A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 N/m³, the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is ___________

Answer: (677.50 to 679.50)

24. In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are 0.18, 0.32, and 0.22. The total loss time in each of the phases is 2 s. As per Webster’s formula, the optimal cycle length (in s, round off to the nearest integer) is _______.

Answer: (48 to 52)

25. A horizontal angle θ is measured by four different surveyors multiple times and the values reported are given below.

The most probable value of the angle θ (in degree, round off to two decimal places) is _________

Answer: (36 to 36)

Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. If k is a constant, the general solution of will be in the form of

(A) y = xln( kx)

(B) y = k ln(kx)

(D) y = xkln(k)

Answer: (A)

27. The smallest eigenvalue and the corresponding eigenvector of the matrix respectively are

Answer: (A)

28. A prismatic steel beam is shown in the figure.

The plastic moment, M_p calculated for the collapse mechanism using static method and kinematic method is

Answer: (C)

29. A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load w per unit length. Axial deformation of any member is neglected.

Considering the joint F being rigid, the support reaction at G is

(A) 0.375 wL

(B) 0.453 wL

(D) 0.500 wL

Answer: (C)

30. A clay layer of thickness H has a preconsolidation pressure p_c and an initial void ratio e₀. The initial effective overburden stress at the mid-height of the layer is p₀. At the same location, the increment in effective stress due to applied external load is Δ_p. The compression and swelling indices of the clay are Cc and Cs, respectively. If p₀ < p_c < (p₀ + ∆p), then the correct expression to estimate the consolidation settlement (s_c ) of the clay layer is

Answer: (B)

31. A rectangular open channel of 6 m width is carrying a discharge of 20 m³/s. Consider the acceleration due to gravity as 9.81 m/s² and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for the given discharge will then be

(A) 0.82 m

(B) 1.04 m

(D) 3.18 m

Answer: (B)

32. Read the statements given below.

(i) Value of the wind profile exponent for the ‘very unstable’ atmosphere is smaller than the wind profile exponent for the ‘neutral’ atmosphere.

(ii) Downwind concentration of air pollutants due to an elevated point source will be inversely proportional to the wind speed.

(iii)Value of the wind profile exponent for the ‘neutral’ atmosphere is smaller than the wind profile exponent for the ‘very unstable’ atmosphere.

(iv) Downwind concentration of air pollutants due to an elevated point source will be directly proportional to the wind speed.

Select the correct option.

(A) (i) is False and (iii) is True

(B) (i) is True and (iv) is True

(D) (iii) is False and (iv) is False

Answer: (D)

33. A water filtration unit is made of uniform-size sand particles of 0.4 mm diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity is

(A) 5.79 × 10⁻³ m/s

(B) 6.35 × 10⁻³ m/s

(D) 0.75 cm/s

Answer: (B)

34. For a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to +2.1 m and the sum of departures is equal to –2.8 m. The length and bearing of the closing error, respectively, are

(A) 3.50 m and 53°7’48” NW

(B) 2.45 m and 53°7’48” NW

(D) 3.50 m and 53.13° SE

Answer: (A)

35. From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as 60%, 27%, 32% and 27, respectively. The corresponding toughness index and liquidity index of the soil specimen, respectively, are

(A) 0.15 and 1.22

(B) 0.19 and 6.60

(D) 6.60 and 0.19

Answer: (C)

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

36. A function is defined in Cartesian coordinate system as f (x, y) = xe^y. The value of the directional derivative of the function (in integer) at the point (2, 0) along the direction of the straight line segment from point (2, 0) to point (1/2, 2) is _______

Answer: (1 to 1)

37. An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of 1.5 m. It is supported on a solid steel circular column of diameter 75 mm and total height (L) of 4 m. Take, water density = 1000 kg/m³ and acceleration due to gravity = 10 m/s².

If elastic modulus (E) of steel is 200 GPa, ignoring self-weight of the tank, for the supporting steel column to remain unbuckled, the maximum depth (h) of the water permissible (in m, round off to one decimal place) is _________

Answer: (2.5 to 2.9)

38. A prismatic fixed-fixed beam, modelled with a total lumped-mass of 10 kg as a single degree of freedom (SDOF) system is shown in the figure.

If the flexural stiffness of the beam is 4π² kN/m, its natural frequency of vibration (in Hz, in integer) in the flexural mode will be __________

Answer: (10 to 10)

39. A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at F and G are acting vertically.

The magnitude of tension in the cable segment FG (in kN, round off to two decimal places) is ____________

Answer: (8.10 to 8.40)

40. A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s². The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be ________________

Answer: (63.50 to 63.90)

41. A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is 16 mm. The values of modulus of elasticity of concrete and steel are 2.0 × 10⁴ MPa and 2.1 × 10⁵ MPa, respectively.

The distance of the centroidal axis from the centerline of the reinforcement (x) for the uncracked section (in mm, round off to one decimal place) is _______

Answer: (129.0 to 130.0)

42. The activity details for a small project are given in the Table.

The total time (in days, in integer) for project completion is __________

Answer: (56 to 56)

43. An equipment has been purchased at an initial cost of Rs.160000 and has an estimated salvage value of Rs. 10000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of 4th year using straight line method and sum of years digit method of depreciation is______

Answer: (20000 to 20000)

44. A rectangular footing of size 2.8 m × 3.5 m is embedded in a clay layer and a vertical load is placed with an eccentricity of 0.8 m as shown in the figure (not to scale). Take Bearing capacity factors: N_c = 5.14, N_q = 1.0, and N_γ = 0.0; Shape factors: s_c = 1.16, s_q = 1.0 and s_γ = 1.0; Depth factors: d_c = 1.1, d_q = 1.0 and d_γ = 1.0; and Inclination factors: ic = 1.0 and iq = 1.0 and i_γ = 1.0.

Using Meyerhoff’s method, the load (in kN, round off to two decimal places) that can be applied on the footing with a factor of safety of 2.5 is ________

Answer: (439.00 to 442.00)

45. The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at the surface of the clay layer, and the capillary rise in the sandy soil is negligible. The effective stress at the middle of the clay layer after the application of the embankment loading is 180 kN/m². Take unit weight of water, γ_w = 9.81 kN/m³.

The primary consolidation settlement (in m, round off to two decimal places) of the clay layer resulting from this loading will be _______

Answer: (0.32 to 0.34)

46. Numerically integrate, f (x) =10x − 20x² from lower limit a = 0 to upper limit b = 0.5. Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is _______

Answer: (0.38 to 0.42)

47. The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of coefficient of consolidation of sample M to sample N (round off to three decimal places) is _______

Answer: (0.090 to 0.105)

48. The hyetograph in the figure corresponds to a rainfall event of 3 cm.

If the rainfall event has produced a direct runoff of 1.6 cm, the ϕ-index of the event (in mm/hour, round off to one decimal place) would be_______

Answer: (4.2 to 4.2)

49. A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of 20 cm diameter.

Assume g = 9.8 m/s². When the deflection in the mercury manometer is 15 cm, the flow rate (in lps, round off to two decimal places) considering no loss

in the venturimeter is _________

Answer: (49.0 to 50.0)

50. A reservoir with a live storage of 300 million cubic metre irrigates 40000 hectares (1 hectare = 10⁴ m²) of a crop with two fillings of the reservoir. If the base period of the crop is 120 days, the duty for this crop (in hectares per cumec, round off to integer) will then be _______

Answer: (689 to 693)

51. An activated sludge process (ASP) is designed for secondary treatment of 7500 m³/day of municipal wastewater. After primary clarifier, the ultimate BOD of the influent, which enters into ASP reactor is 200 mg/L. Treated effluent after secondary clarifier is required to have an ultimate BOD of 20 mg/L. Mix liquor volatile suspended solids (MLVSS) concentration in the reactor and the underflow is maintained as 3000 mg/L and 12000 mg/L, respectively. The hydraulic retention time and mean cell residence time are 0.2 day and 10 days, respectively. A representative flow diagram of the ASP is shown below.

The underflow volume (in m³/day, round off to one decimal place) of sludge

wastage is _________

Answer: (37.0 to 38.0)

52. A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of 0.25 mm and specific gravity of 2.70. The terminal settling velocity of the particles is estimated as 2.5 cm/s. The chamber is having a width of 0.50 m and has to carry a peak wastewater flow of 9720 m³/d giving the depth of flow as 0.75 m. If a flow-through velocity of 0.3 m/s has to be maintained using a proportional weir at the outlet end of the chamber, the minimum length of the chamber (in m, in integer) to remove 0.25 mm particles completely is ______

Answer: (9 to 9)

53. In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are 55%, 40% and 5%, respectively. The values of bulk specific gravity of the coarse aggregate, fine aggregate and mineral filler are 2.55, 2.65 and 2.70, respectively. The bulk specific gravity of the aggregate mix (round off to two decimal places) is _______

Answer: (2.58 to 2.61)

54. The stopping sight distance (SSD) for a level highway is 140 m for the design speed of 90 km/h. The acceleration due to gravity and deceleration rate are 9.81 m/s2 and 3.5 m/s², respectively. The perception/reaction time (in s, round off to two decimal places) used in the SSD calculation is________

Answer: (1.90 to 2.10)

55. For a 2° curve on a high speed Broad Gauge (BG) rail section, the maximum sanctioned speed is 100 km/h and the equilibrium speed is 80 km/h. Consider dynamic gauge of BG rail as 1750 mm. The degree of curve is defined as the angle subtended at its center by a 30.5 m arc. The cant deficiency for the curve (in mm, round off to integer) is __________

Answer: (55 to 59)

GATE Exam 2021 Civil Engineering (CE-1) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CE1: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Getting to the top is ___________than staying on top.

(A) more easy

(B) much easy

(D) easier

Answer: (D)

2. The mirror image of the above text about the x-axis is

Answer: (B)

3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

(A) 15

(B) 25

(D) 40

Answer: (C)

4. ⊕ and ⨀ are two operators on numbers p and q such that

If x ⊕ y = 2 ⊙ 2, then x =

(A) y/2

(B) y

(D) 2y

Answer: (B)

(A) 2

(B) 4

(D) 8

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Statement: Either P marries Q or X marries Y

Among the options below, the logical NEGATION of the above statement is:

(A) P does not marry Q and X marries Y.

(B) Neither P marries Q nor X marries Y.

(D) P marries Q and X marries Y.

Answer: (B)

7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each.

Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.

Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.

Folding operation 1 is carried out on Sheet M three times.

Folding operation 2 is carried out on Sheet N three times.

The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

(A) 13 : 7

(B) 3 : 2

(D) 5 : 13

Answer: (A)

8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.

The value of θ, in degrees, is ______

(A) 36

(B) 45

(D) 108

Answer: (A)

9. A function, λ, is defined by

The value of the expression is:

(A) −1

(B) 0

(D) 16

Answer: (B)

Based on the above passage, which one of the following is TRUE?

(A) No species possess the ability to construct worlds in their minds.

(B) The terms imagination, invention and innovation refer to unrelated skills.

(D) Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Answer: (C)

Civil Engineering (CE, Set-1)

Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The rank of matrix is

(A) 1

(B) 2

(D) 4

Answer: (B)

2. If and then Q^TP^T is

Answer: (D)

3. The shape of the cumulative distribution function of Gaussian distribution is

(A) Horizontal line

(B) Straight line at 45 degree angle

(D) S-shaped

Answer: (D)

4. A propped cantilever beam EF is subjected to a unit moving load as shown in the figure (not to scale). The sign convention for positive shear force at the left and right sides of any section is also shown.

The CORRECT qualitative nature of the influence line diagram for shear force at G is

Answer: (B)

5. Gypsum is typically added in cement to

(A) prevent quick setting

(B) enhance hardening

(D) decrease heat of hydration

Answer: (A)

6. The direct and indirect costs estimated by a contractor for bidding a project is Rs.160000 and Rs. 20000 respectively. If the mark up applied is 10% of the bid price, the quoted price (in ₹) of the contractor is

(A) 200000

(B) 198000

(D) 182000

Answer: (A)

7. In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m² and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m², respectively are

(A) 150 kN/m²and 0

(B) 100 kN/m² and 50 kN/m²

(D) 0 and 150 kN/m²

Answer: (C)

8. A partially-saturated soil sample has natural moisture content of 25% and bulk unit weight of 18.5 kN/m³. The specific gravity of soil solids is 2.65 and unit weight of water is 9.81 kN/m³. The unit weight of the soil sample on full saturation is

(A) 21.15 kN/m³

(B) 19.03 kN/m³

(D) 18.50 kN/m³

Answer: (B)

9. If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections then the ratio of hydraulic radius of triangular section to that of rectangular section is

(A) 1/√2

(B) √2

(D) 2

Answer: (A)

10. ‘Kinematic viscosity’ is dimensionally represented as

(A) M/LT

(B) M/L²T

(D) L²/T

Answer: (D)

11. Which one of the following statements is correct?

(A) Pyrolysis is an endothermic process, which takes place in the absence of oxygen.

(B) Pyrolysis is an exothermic process, which takes place in the absence of oxygen.

(D) Combustion is an exothermic process, which takes place in the absence of oxygen.

Answer: (A)

12. Which one of the following is correct?

(A) The partially treated effluent from a food processing industry, containing high concentration of biodegradable organics, is being discharged into a flowing river at a point P. If the rate of degradation of the organics is higher than the rate of aeration, then dissolved oxygen of the river water will be lowest at point P.

(B) The most important type of species involved in the degradation of organic matter in the case of activated sludge process based wastewater treatment is chemoheterotrophs.

(D) A young lake characterized by low nutrient content and low plant productivity is called eutrophic lake.

Answer: (B)

13. The liquid forms of particulate air pollutants are

(A) dust and mist

(B) mist and spray

(D) fly ash and fumes

Answer: (B)

14. The shape of the most commonly designed highway vertical curve is

(A) circular (single radius)

(B) circular (multiple radii)

(D) spiral

Answer: (C)

15. A highway designed for 80 km/h speed has a horizontal curve section with radius 250 m. If the design lateral friction is assumed to develop fully, the required super elevation is

(A) 0.02

(B) 0.05

(D) 0.09

Answer: (B)

16. Which of the following is NOT a correct statement?

(A) The first reading from a level station is a ‘Fore Sight’.

(B) Basic principle of surveying is to work from whole to parts.

(D) Planimeter is used for measuring ‘area’.

Answer: (A)

Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks).

17. Which of the following is/are correct statement(s)?

(A) Back Bearing of a line is equal to Fore Bearing ±180°.

(B) If the whole circle bearing of a line is 270°, its reduced bearing is 90° NW.

(D) In the case of fixed hair stadia tachometry, the staff intercept will be larger, when the staff is held nearer to the observation point.

Answer: (A; B; C)

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

18. Consider the limit:

The limit (correct up to one decimal place) is __________.

Answer: (0.5 to 0.5)

19. The volume determined from ∭_V 8 xyz dV for V = [2, 3] × [1, 2] × [0, 1] will be (in integer) ______

Answer: (15 to 15)

20. The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle θ, locating the X-axis, is assumed to be positive when measured from the x-axis in counter-clockwise direction.

The absolute magnitude of the shear stress component σ_xy (in MPa, round off to one decimal place) in x-y coordinate system is ___________

Answer: (95 to 97)

21. The equation of deformation is derived to be y = x² – xL for a beam shown in the figure.

The curvature of the beam at the mid-span (in units, in integer) will be _______

Answer: (2 to 2)

22. A truss EFGH is shown in the figure, in which all the members have the same axial rigidity R. In the figure, P is the magnitude of external horizontal forces acting at joints F and G.

If R = 500 ×10³ kN, P = 150 kN and L = 3 m, the magnitude of the horizontal displacement of joint G (in mm, round off to one decimal place) is _________

Answer: (0.9 to 0.9)

23. The cohesion (c), angle of internal friction (ϕ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m³, respectively. The maximum depth of unsupported excavation in the soil (in m, round off to two decimal places) is ____________

Answer: (4.80 to 5.00)

24. Two reservoirs are connected through a homogeneous and isotropic aquifer having hydraulic conductivity (K) of 25 m/day and effective porosity (η) of 0.3 as shown in the figure (not to scale). Ground water is flowing in the aquifer at the steady state.

If water in Reservoir 1 is contaminated then the time (in days, round off to one decimal place) taken by the contaminated water to reach to Reservoir 2 will be_______

Answer: (2400 to 2400)

25. A signalized intersection operates in two phases. The lost time is 3 seconds per phase. The maximum ratios of approach flow to saturation flow for the two phases are 0.37 and 0.40. The optimum cycle length using the Webster’s method (in seconds, round off to one decimal place) is ______

Answer: (60.7 to 61.1)

Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The solution of the second-order differential equation with boundary conditions y(0) = 1 and y(1) = 3 is

(A) e⁻^x + (3e – 1)xe⁻^x

(B) e⁻^x – (3e – 1)xe⁻^x

(C)

(D)

Answer: (A)

27. The value of using the trapezoidal rule with four equal subintervals is

(A) 1.718

(B) 1.727

(D) 2.718

Answer: (B)

28. A 50 mL sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g. The crucible with the sample is dried in a hot air oven at 104°C till a constant weight of 55.129 g. Thereafter, the crucible with the dried sample is fired at 600°C for 1 h in a muffle furnace, and the weight of the crucible along with residue is determined as 54.783 g. The concentration of total volatile solids is __________.

(A) 15540 mg/L

(B) 8620 mg/L

(D) 1700 mg/L

Answer: (C)

29. A wedge M and a block N are subjected to forces P and Q as shown in the figure. If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the block are negligible compared to the forces P and Q. The coefficient of friction (μ) along the inclined surface between the wedge and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°.

The limiting force P, in terms of Q, required for impending motion of block N

to just move it in the upward direction is given as P = αQ. The value of the coefficient ‘α’ (round off to one decimal place) is

(A) 0.6

(B) 0.5

(D) 0.9

Answer: (D)

30. Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y’s bid price to X’s cost for the 30 previous bids in which Contractor X has competed against Contractor Y is given in the Table

Based on the bidding behaviour of the Contractor Y, the probability of winning against Contractor Y at a mark up of 8% for the next project is

(A) 0%

(B) more than 0% but less than 50%

(D) 100%

Answer: (B)

31. Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain (∆V/V) with the shear strain (γ) is shown in the figure.

Choose the CORRECT option regarding the representative behaviour exhibited by Curve P and Curve Q.

(A) Curve P represents dense sand and over consolidated clay, while Curve Q represents loose sand and normally consolidated clay

(B) Curve P represents dense sand and normally consolidated clay, while Curve Q represents loose sand and over consolidated clay

(C) Curve P represents loose sand and over consolidated clay, while Curve Q represents dense sand and normally consolidated clay

(D) Curve P represents loose sand and normally consolidated clay, while Curve Q represents dense sand and over consolidated clay

Answer: (A)

32. A fluid flowing steadily in a circular pipe of radius R has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distribution along the radial direction is where r is the radial distance as measured from the pipe axis and U is the maximum velocity at r = 0. The average velocity of the fluid in the pipe is

(A) U/2

(B) U/3

(D) (5/6)U

Answer: (A)

33. A water sample is analyzed for coliform organisms by the multiple-tube fermentation method. The results of confirmed test are as follows:

The most probable number (MPN) of coliform organisms for the above results is to be obtained using the following MPN Index.

The MPN of coliform organisms per 100 mL is

(A) 1100000

(B) 110000

(D) 110

Answer: (B)

34. Ammonia nitrogen is present in a given wastewater sample as the ammonium ion (NH₄⁺) and ammonia (NH₃). If pH is the only deciding factor for the proportion of these two constituents, which of the following is a correct statement?

(A) At pH above 9.25, only NH₄⁺ will be present.

(B) At pH below 9.25, NH₃ will be predominant.

(D) At pH 7.0, NH₄⁺ will be predominant.

Answer: (D)

35. On a road, the speed – density relationship of a traffic stream is given by u k = − 70 0.7 (where speed, u, is in km/h and density, k, is in veh/km). At the capacity condition, the average time headway will be

(A) 0.5 s

(B) 1.0 s

(D) 2.1 s

Answer: (D)

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

36. The values of abscissa (x) and ordinate (y) of a curve are as follows:

By Simpson’s 1/3rd rule, the area under the curve (round off to two decimal places) is ____________

Answer: (20.00 to 21.00)

37. Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicle per minute. The probability (round off to two decimal places) that at least 2 vehicles will arrive in any given 1-minute interval is __________

Answer: (0.58 to 0.60)

38. Refer the truss as shown in the figure (not to scale).

If load, F = 10√3 kN, moment of inertia, I = 8.33 × 10⁶ mm⁴ , area of cross-section, A = 10⁴ mm², and length, L = 2 m for all the members of the truss, the compressive stress (in kN/m², in integer) carried by the member Q-R is _______

Answer: (490 to 510)

39. A prismatic cantilever prestressed concrete beam of span length, L = 1.5 m has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The total prestressing force of 50 kN in the tendon is applied at dc = 50 mm from the top in the cross-section of width, b = 200 mm and depth, d = 300 mm.

If the concentrated load, P = 5 kN, the resultant stress (in MPa, in integer) experienced at point ‘Q’ will be ________

Answer: (0 to 0)

40. A column is subjected to a total load (P) of 60 kN supported through a bracket connection, as shown in the figure (not to scale).

The resultant force in bolt R (in kN, round off to one decimal place) is ______________

Answer: (27.0 to 29.0)

41. Employ stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements/rotations. Take length, L = 8 m; modulus of elasticity, E = 3 × 10⁴ N/mm²; moment of inertia, I = 225 × 10⁶ mm⁴

The mid-span deflection of the beam (in mm, round off to integer) under P = 100 kN in downward direction will be ________

Answer: (100 to 130)

42. A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O-P’-Q’-R’ as shown in the figure (not to scale). Under the given deformation, the edges of the plate remain straight.

The horizontal displacement of the point (0.5 m, 0.5 m) in the plate O-P-Q-R (in mm, round off to one decimal place) is ___________

Answer: (2.4 to 2.6)

43. A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The relationship among these activities and the duration of these activities are given in the Table.

The total float of the activity “V” (in weeks, in integer) is ___________

Answer: (0 to 0)

44. The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the ground water table was as low as 10 m below the ground level in the past. Take unit weight of water, γ_w = 9.81 kN/m³.

The over consolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is __________

Answer: (1.18 to 1.26)

45. A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is 20°. The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine’s earth pressure theory. Take unit weight of water, γ_w = 9.81 kN/m³.

The factor of safety (round off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be _________

Answer: (4.20 to 4.35)

46. A combined trapezoidal footing of length L supports two identical square columns (P₁ and P₂) of size 0.5 m × 0.5 m, as shown in the figure. The columns P₁ and P₂ carry loads of 2000 kN and 1500 kN, respectively.

If the stress beneath the footing is uniform, the length of the combined footing L (in m, round off to two decimal places) is _________

Answer: (5.70 to 5.90)

47. An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle 50° with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle 60° at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface.

Considering the trial slip circle KLM, the factor of safety against the failure of slope under undrained condition (round off to two decimal places) is __________

Answer: (1.94 to 1.98)

48. An unlined canal under regime conditions along with a silt factor of 1 has a width of flow 71.25 m. Assuming the unlined canal as a wide channel, the corresponding average depth of flow (in m, round off to two decimal places) in the canal will be __________

Answer: (2.80 to 2.95)

49. A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity = 0.8) on other side as shown in the figure.

The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (round off to two decimal places) is __________

Answer: (0.35 to 0.40)

50. A tube-well of 20 cm diameter fully penetrates a horizontal, homogeneous and isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m uniform thickness. A steady pumping at the rate of 40 litres/s from the well for a long time results in a steady drawdown of 4 m at the well face. The subsurface flow to the well due to pumping is steady, horizontal and Darcian and the radius of influence of the well is 245 m. The hydraulic conductivity of the aquifer (in m/day, round off to integer) is _________

Answer: (34 to 38)

51. A baghouse filter has to treat 12 m³/s of waste gas continuously. The bag house is to be divided into 5 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 4 sections continue to operate. An air-to-cloth ratio of 6.0 m³/min-m² cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in length. The total number of bags (in integer) required in the bag house is __________

Answer: (30 to 30)

52. A secondary clarifier handles a total flow of 9600 m³/d /d from the aeration tank of a conventional activated-sludge treatment system. The concentration of solids in the flow from the aeration tank is 3000 mg/L. The clarifier is required to thicken the solids to 12000 mg/L, and hence it is to be designed for a solid flux of 3.2 kg/m².h. The surface area of the designed clarifier for thickening (in m², in integer) is ___________

Answer: (375 to 375)

53. Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 80 km/h. The space-mean speed (in km/h, round off to two decimal places) of the observed vehicles is ________

Answer: (55.50 to 58.50)

54. The longitudinal section of a runway provides the following data:

The effective gradient of the runway (in %, round off to two decimal places) is _____

Answer: (0.30 to 0.34)

55. Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R and S are measured as 92°, 68°, 123°, and 77°, respectively. If fore bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer) is_______

Answer: (196 to 196 OR 218 to 218)

GATE Exam 2021 Biomedical Engineering (BM) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

BM: Biomedical Engineering

GA-General Aptitude

Q 1 – Q5 Carry one mark each. ( for each wrong answer: −1/3)

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 carry two marks (for each wrong answer: −2/3)

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Biomedical Engineering (BM)

Q.1 – Q.25 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. For to be a valid probability distribution function of a random variable X, the value of q is _____.

(A) 2

(B) π

(D) −π

Answer: (A)

2. Given a scalar function the directional derivative of V in the direction of the vector field 3yi – 3xj at the point (1, 1) is _____. (Note: i and j are the unit vectors along the x and y directions, respectively.)

(A) √18

(B) 0

(D) 3/2

Answer: (B)

3. Three resistive loads are connected to ideal voltage and current sources as shown in the circuit below. The voltage VAB across the terminals A and B is equal to ________ V.

(A) +10

(B) −10

(D) +6

Answer: (B)

4. An ideal inductor with an inductance value of 1/3 H is connected to a 50 Hz sinusoidal AC voltage source. The energy stored in the inductor is 6 J. The value of the maximum power delivered to the inductor is ____ W.

(A) 1200π

(B) 600π

(D) 0

Answer: (A)

5. Let X(jω) denote the Fourier transform of x(t). If then (where ω = 2πf)

(A) 10π

(B) 100

(D) 20π

Answer: (C)

6. In the circuit shown below, Y is a 2-bit (Y₁Y₀) output of the combinational logic. What is the maximum value of Y for any given digital inputs, A₁A₀ and B₁B₀?

(A) 01

(B) 10

(D) 11

Answer: (A)

7. In the block diagram shown below, an analog signal, V_IN = sin(2π10⁶t) is quantized by a 10-bit Nyquist ADC. Later, 4 LSBs are dropped and 6 MSBs are converted to an analog signal (V_OUT) while using a 6-bit DAC. Assume uniform distribution for the quantization noise. The peak SQNR at the output of DAC is _____ dB.

(A) 61.96

(B) 25.84

(D) 37.88

Answer: (D)

8. For a linear stable second order system, if the unit step response is such that the peak time is twice the rise time, then the system is _____.

(A) underdamped

(B) undamped

(D) critically damped

Answer: (B)

9. Which of the following displacement sensors is known to have a high sensitivity and a relatively larger measurement range?

(A) Strain gauge

(B) Capacitive sensor

(D) Piezoelectric sensor

Answer: (C)

10. Which of the following temperature sensors is used in contact-type digital thermometers for measuring body temperature?

(A) Thermocouple

(B) Thermistor

(D) Infrared LED-photodetector pair

Answer: (B)

11. The pH of blood in a healthy human is precisely in the range of ______.

(A) 7.10 – 8.10

(B) 6.95 – 7.05

(D) 7.35 – 7.45

Answer: (D)

12. Which of the following is a cranial bone in the human body?

(A) Occipital

(B) Mandible

(D) Sternum

Answer: (A)

13. Which of the following glands produces the thyroid stimulating hormone (TSH)?

(A) Thyroid

(B) Parathyroid

(D) Pineal

Answer: (C)

14. Which of the following causes Myocardial Infarction (MI)?

(A) Obstruction in one of the arteries supplying blood to the heart

(B) Obstruction in one of the arteries supplying blood to the brain

(D) Obstruction in one of the veins draining blood from the brain

Answer: (A)

15. If we consider blood as a suspension of RBCs in a Newtonian fluid, the shear forces experienced by the RBCs during blood flow would ___________.

(A) Randomize the orientation of blood cells

(B) Align RBCs along their long axes with streamlines

(D) Create an equal distribution of RBCs aligned in their long and short axes

Answer: (B)

16. As shown in the figure, the water contact angles of surfaces A and B are θA and θB, respectively. Based on the figure, which of the following statements given below is TRUE?

(A) Surface A is hydrophilic and surface B is hydrophobic

(B) Surface A is hydrophobic and surface B is hydrophilic

(D) Both surfaces are hydrophobic

Answer: (A)

17. Which of the following is a bone resorbing cell?

(A) Osteoblasts

(B) Osteoclasts

(D) Osteocalcin

Answer: (B)

Q.18 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

18. Which of the following statements are CORRECT in the context of planar X-ray imaging?

(A) Using fast X-ray screen improves spatial resolution

(B) Using fast X-ray screen worsens spatial resolution

(D) Decreasing tube current increases signal to noise ratio

Answer: (B; C)

19. While comparing parallel fiber and pinnate muscles of a given volume, which of the following statements are TRUE?

(A) Pinnate muscles provide more muscle force

(B) Parallel fiber muscles provide more muscle force

(D) Parallel fiber muscles facilitate better muscle shortening

Answer: (A; D)

20. Which of the following may cause failure of bone implants?

(A) Stress shielding – reduction of bone density due to removal of a typical stress from bone by an implant

(B) Aseptic loosening – loss of bond between bone and implant in the absence of an infection

(D) Osseointegration – formation of a direct interface between an implant and a bone, without intervening soft tissues

Answer: (A; B; C)

Q.21 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

21. The minimum value, fmin, of the function given below is _________. (rounded off to the nearest integer)

Answer: (-6 to -6)

22. A continuous time transfer function is converted to a discrete time transfer function H(z) using a bilinear transform at 100 MHz sampling rate. The pole of H(z) is located at z = ____.

Answer: (1 to 1)

23. Consider a type 2, unity feedback system. The intersection of the initial −40 dB/dec segment, of its Bode plot, with the zero dB line occurs at a frequency of 2 rad/s. The acceleration error constant of the system K_a is ___.

Answer: (4 to 4)

24. The radioactivity of a radionuclide with decay constant of 3. 22 × 10⁻⁵ s⁻¹is 6 mCi at 10:30 AM. The radioactivity of the radionuclide at 4:30 PM on the same day will be _________ mCi. (rounded off to two decimal places)

Answer: (2.96 to 3.02)

25. A polymeric scaffold has been developed for cartilage tissue engineering. To understand the biodegradability of the material, this polymeric scaffold with a dry weight of 20 mg is kept in a lysozyme solution for 7 days. At the end of 7 days, the scaffold is freeze-dried, and the dry weight is measured to be 18 mg. The degradation of the polymeric scaffold after 7 days is ______ %.

Answer: (10 to 10)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The Trace and Determinant of a 2 × 2 nonsingular matrix A are 12 and 32, respectively. The eigen values of A⁻¹are ____ and _____.

(A) 0.6, 0.8

(B) 0.25, 0.125

(D) 1/12, 1/32

Answer: (B)

27. A unit step input is applied to a system with impulse response at t = 0. The output of the system y(t) at t = 0⁺ is ______.

(A) 1

(B) −ω_z/ω_p

(D) 0

Answer: (C)

28. Consider the following first order partial differential equation, also known as the transport equation with initial conditions given by y(x, 0) = sin x, − ∞ < x < ∞. The value of y(x, t) at x = π and t = π/6 is _______.

(A) 1

(B) 2

(D) 0.5

Answer: (D)

29. In the circuit shown below, V_s = 100 V, R₁ = 30 Ω, R₂ = 60 Ω, R₃ = 90 Ω, R₄ = 45 Ω, and R₅ = 30 Ω. The current flowing through resistor R₃ is ___ A. (rounded off to two decimal places)

(A) +0.30

(B) +0.21

(D) −0.30

Answer: (B)

30. x[n] is convolved with h[n] to give y[n]. If y[2] = 1 and y[3] = 0, h[0] =______. (Graphs are not uniformly scaled)

(A) 1.85

(B) −2.50

(D) 2.38

Answer: (D)

31. In the block diagram shown below, an infinite tap FIR filter with transfer function H(z) = Y(z)/X(z) is realized. If the value of α is ______.

(A) 2

(B) 1/√2

(D) √2

Answer: (B)

32. An analog signal is sampled at 100 MHz to generate 1024 samples. Only these samples are used to evaluate 1024-point FFT. The separation between adjacent frequency points (ΔF) in FFT is __________ kHz.

(A) 102.16

(B) 97.66

(D) 95.63

Answer: (B)

33. In the circuit diagram shown below, all OPAMPs are ideal with infinite gain and bandwidth. V_OUT/V_IN for this circuit is ______.

(A) 5.00

(B) 5.33

(D) 6.00

Answer: (C)

34. In the circuit diagram shown below, NMOS is in saturation region, μ_nC_ox = 200 μ_A/V², width W = 40 μm, length L = 1 μm, the threshold voltage is 0.4 V, and the ratio of body-effect transconductance (g_mb) to transconductance (g_m) is 0.1. A small input voltage vin is applied at the bulk-terminal to produce a small change in the output voltage v_out. The dc gain for v_out/v_in is _______. (Neglect channel-length modulation for NMOS and all intrinsic capacitors)

(A) −0.4

(B) −4.0

(D) −3.6

Answer: (A)

35. As shown in the circuit below, a constant voltage source is connected to two ideal resistors.

The voltage drop across a resistor is measured using two different voltmeters V1 and V2 at five different time instances and the following values are recorded from V1 and V2.

Which of the following is TRUE?

(A) V1 is less accurate, V2 is more precise

(B) V1 is more accurate, V2 is more precise

(D) V1 is more accurate, V2 is less precise

Answer: (B)

36. The closed-loop characteristic equation of a system is given by s⁴ + 2s³ + 8s² + 8s + 16 = 0.

The frequency of oscillations of this closed-loop system at steady state is ______ rad/s.

(A) 1

(B) 2

(D) 4

Answer: (B)

37. Match the following in the context of biomaterial characterization:

(A) P-L, Q-N, R-K, S-M

(B) P-N, Q-M, R-K, S-L

(D) P-M, Q-K, R-N, S-L

Answer: (B)

38. In comparison to ECG amplifiers, the surface-EMG amplifiers have

(A) A comparable gain and smaller bandwidth

(B) A comparable gain and larger bandwidth

(D) At least 20 dB lower gain and a smaller bandwidth

Answer: (B)

39. Match the following organs with their functions:

(A) P-M, Q-N, R-K, S-L

(B) P-N, Q-M, R-K, S-L

(D) P-L, Q-M, R-K, S-N

Answer: (B)

40. An RF pulse is applied to acquire an axial MR image at the isocenter of a 1.5T MRI scanner with slice thickness of 2.5 mm. Assuming a gradient field strength of 2 Gauss/cm is applied and Gyromagnetic ratio of protons is 42.58 MHz/T, the RF pulse bandwidth required for slice selection is _______ kHz.

(A) 1.06

(B) 2.13

(D) 13.31

Answer: (B)

41. A longitudinal pressure wave travelling inside a muscle tissue is incident at an angle of 60° at the interface between the muscle and kidney. Let the wave impedance be Z_muscle = 1.70 × 10⁵g cm⁻² s⁻¹, Z_kidney = 1.62 × 10⁵g cm⁻² s⁻¹ and wave velocities in muscle and kidney tissues be 1590 and 1560 m/s respectively. The transducer centre frequency is 1.5 MHz. The pressure wave propagation angle in the kidney tissue and intensity transmission coefficient at the tissue interface are ________degrees (rounded off to the nearest integer) and ______ (rounded off to two decimal places), respectively.

(A) 58, 0.24

(B) 30, 0.68

(D) 30, 0.99

Answer: (C)

42. A novel biomaterial was tested for its tensile properties. The experiment was conducted using a cylindrical sample of this material, which was 10 cm long with 1 cm diameter. When a tensile force of 50 kN was applied, this cylindrical sample elongated by 4 mm. Based on the experimental results described above and the tensile moduli of different tissues given in the table below, this biomaterial would be a suitable replacement for __________.

(A) Bone

(B) Tendon

(D) Articular cartilage

Answer: (A)

Q.43 – Q.45 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

43. In the circuit shown below, R₁= 2 Ω, R₂= 1 Ω, L₁= 2 H, and L₂= 0.5 H. Which of the following describe(s) the characteristics of the circuit?

(A) Second order high pass filter

(B) Second order low pass filter

(D) Overdamped system

Answer: (B; D)

44. An inexperienced clinician was measuring the cardiac output of a healthy human by thermo dilution technique. A 2.0 mL of cold saline solution of volume (V_i) at 7 °C was injected at the entrance of the right atrium. The change in blood temperature at the pulmonary artery was measured to be −20 Kelvin. second. The cardiac output F was calculated using the following formula

where Q is the heat content of injectate in Joules, given by V_i∆T_iρ_ic_i and ∆T_i is the temperature difference between the injectate and blood. It was assumed that the density of blood (ρ_b in kg/m³) and the specific heat

capacity of blood (c_b in J/(kg. K)) were respectively equal to that of the injectate ρ_i and c_i.

The clinician realized that there was an error in the measurement of F. Which of the following is TRUE?

(A) Cardiac output is too low because the cold saline volume was too small

(B) Cardiac output is too low because is too large

(D) Cardiac output is too high because is too small

Answer: (A; B)

45. Which of the following statements about smooth muscles are TRUE?

(A) Smooth muscles are found in the walls of hollow organs

(B) Smooth muscles are controlled by the autonomic nervous system

(D) Smooth muscles are made up of striated cells

Answer: (A; B; C)

Q.46 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

46. Consider a unity feedback system with closed loop transfer function

The steady state error with respect to a unit ramp input is ____. (rounded off to one decimal place)

Answer: (0.1 to 0.1)

47. The diameter of a renal artery lumen in humans is 5 mm. If the mean velocity of the blood flowing in the renal artery is 40 cm/s, the density of blood (ρ) is 1060 kg/m3, and the viscosity of blood (μ) is 3 cP, the Reynolds number for the blood flowing in the renal artery is ________ (rounded off to the nearest integer).

Answer: (700 to 710)

48. A drug manufacturer believes that there is a 95% chance that the drug controller will approve a new drug the company plans to distribute if the results of the current testing show that the drug causes no side effects. The manufacturer further believes that there is a 0.50 probability that the drug will be approved even if the test shows side effects. A physician working for the drug manufacturer believes there is a 0.20 probability that tests will show side effects. If the drug is approved by the drug controller, the probability that the drug causes side effects is ______. (rounded off to three decimal places)

Answer: (0.111 to 0.121)

49. In a measurement process, groups A and B recorded 10 and 15 values, respectively. The arithmetic means and standard deviations of group A are μ_A = 35, σ_A = 0.4 and group B are μ_B = 38, σ_B = 0.6, respectively. The standard deviation for the combined set of group A and group B measurements is ____. (rounded off to two decimal places)

Answer: (1.54 to 1.58)

50. In the circuit given below, V_s = 50 V. Let the circuit reach steady state for the SPDT switch at position 1. Once the circuit is switched to position 2, the energy dissipated in the resistors is _______ J. (rounded off to one decimal place)

Answer: (0.2 to 0.2)

51. In the circuit shown below, the output voltage V_OUT is ________ V.

Answer: (-10 to -10)

52. A pacemaker was implanted in a cardiac patient. It has a battery of 2.4 A.h (Ampere.hour). It is designed to deliver a rectangular pulse of amplitude 1.5 V for 1 ms ON time for every one second. The electrode – heart resistance is 150 Ω. Assuming the current drained from the battery is negligible, the lifetime of the pacemaker is _____ years. (rounded off to the nearest integer)

Answer: (27 to 28)

53. A radiographic system is using X-ray tube operating at 80 kVp. In order to filter the low energy X-rays, an aluminum (Al) filter of 2.5 mm thickness is used. The Al filter is replaced with a copper (Cu) filter to have the same energy filtered. The mass attenuation coefficients of Al and Cu at 80 kVp are 0.02015 m²/kg and 0.07519 m²/kg, respectively. The densities of Al and Cu are 2699 kg/m³ and 8960 kg/m³ The thickness of the new Cu filter is ______ mm. (rounded off to two decimal places)

Answer: (0.15 to 0.25)

54. In a radioactive isotope, N nuclei are needed to produce radioactivity level of 2 mCi. Assuming decay constant of 3. 22 × 10⁻⁵ s⁻¹ and atomic weight of 98 g/mol and Avogadro’s number = 6. 02 × 10²³ mol⁻¹, the mass of N radionuclide is __________ picograms. (rounded off to the nearest integer)

Answer: (372 to 376)

55. A PZT crystal of thickness 1 mm and wave velocity 4000 m/s is emitting a longitudinal pressure wave, which is incident on a blood vessel at an angle of 30°. The doppler shift in the ultrasound wave for a blood flow of 10 cm/s and wave velocity in the soft tissue of 1540 m/s is ______ Hz.

Answer: (222 to 228)

GATE Exam 2021 Architecture and Planning (AR) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

AR-Architecture and Planning

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Architecture and Planning (AR)

Q.1 – Q.25 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. As per National Building Code of India, 2016, the function of an Automatic Rescue Device is to

(A) bring a stuck lift to the nearest landing level.

(B) control fire in electrical system at plenum level.

(D) trigger fire sprinkler system.

Answer: (A)

2. Which among the following acronyms represents a thermal comfort index?

(A) PMV

(B) NDVI

(D) PCA

Answer: (A)

3. Indian satellite sensor that can be used for very high resolution mapping of urban areas is

(A) LANDSAT.

(B) CARTOSAT.

(D) MODIS.

Answer: (MTA)

4. What is the smallest entity of raster data used in GIS?

(A) Line

(B) Pixel

(D) Polygon

Answer: (B)

5. The correct sequence of stages during firing/burning of bricks is

(A) Dehydration – Oxidation – Vitrification – Cooling.

(B) Vitrification – Dehydration – Oxidation – Cooling.

(D) Cooling – Oxidation – Vitrification – Dehydration.

Answer: (A)

6. Industry Foundation Classes (IFC) in BIM is

(A) a module used to improve energy savings.

(B) an algorithm related to the precision of the BIM model.

(D) an object oriented data model to facilitate interoperability.

Answer: (D)

7. As per urban design principles proposed by Gordon Cullen, Rashtrapati Bhavan, New Delhi, is an example of

(A) Serial Vision.

(B) Pinpointing.

(D) Here and there.

Answer: (A)

8. A waste water pipe connecting two inspection chambers (IC) is laid at a slope of 1:200. The Invert Level of the starting IC is -450 mm. The Invert level of the second pit at a distance of 40 m from the first IC is

(A) -650 mm.

(B) -200 mm.

(D) -550 mm.

Answer: (A)

9. From the images P, Q and R given below, select the corresponding land use categories according to Alonso’s Bid Rent Theory.

(A) P–Manufacturing; Q–Residential; R–Retail

(B) P–Retail; Q–Residential; R–Manufacturing

(D) P–Retail; Q–Manufacturing; R–Residential

Answer: (D)

10. The urban land use model based on the concept of a polycentric city is known as

(A) Burgess Model.

(B) Harris and Ullman model.

(D) Homer Hoyt’s model.

Answer: (B)

11. The total head or total lift against which a pump works includes suction lift, discharge lift and

(A) cone of depression.

(B) salvage lift.

(D) frictional head loss.

Answer: (D)

12. The two components for measuring time of concentration for storm water are

(A) overland flow time and retention time.

(B) overland flow time and gutter flow time.

(D) retention time and inlet time.

Answer: (B)

13. The traffic assignment technique where the traffic arranges itself in congested networks such that the journey time in all used routes between an Origin-Destination pair are equal and less than those that would be experienced in all unused routes. This is known as

(A) System equilibrium.

(B) All–or–nothing.

(D) Incremental.

Answer: (C)

14. What is the dependent variable in a regression based trip generation model?

(A) Population of Traffic Analysis Zone

(B) Number of trips

(D) Number of households

Answer: (B)

15. The curve traced by a point on a circle rolling inside another circle is known as

(A) hypocycloid.

(B) helix.

(D) hyperbola.

Answer: (A)

16. The law of Primate City was first proposed by

(A) Samuel A. Stouffer.

(B) Colin Clark.

(D) Harold Hotelling.

Answer: (C)

17. In the European Union which constitutes the cities namely, London, Paris, Brussels, Amsterdam, Cologne, Frankfurt, Munich and Milan, lie within a linear megalopolitan zone known as

(A) Purple Zone.

(B) Golden Polygon.

(D) Yellow Corridor.

Answer: (C)

18. An urban governance tool to mobilize financial resources by permitting additional FAR over and above the prescribed FAR by imposing a charge or fee for the same is known as

(A) Betterment Levy.

(B) Impact Fee.

(D) Floor Area Incentive Tax.

Answer: (MTA)

19. Identify the colour palette that is created using any three equally spaced hues around the colour wheel.

(A) Split – complementary

(B) Analogous

(D) Complementary

Answer: (C)

20. Coefficient of Performance (COP) for heat pump is used to calculate

(A) the number of air changes.

(B) the Energy Efficiency Ratio.

(D) the Indoor Air Quality index.

Answer: (B)

21. Freight flows are converted to truck flows using

(A) Volume factor.

(B) Weight factor.

(D) Distance load factor.

Answer: (C)

22. Rebound hammer test is used to measure

(A) permeability of concrete.

(B) bond stress between rebar and concrete.

(D) tensile strength of concrete.

Answer: (C)

23. Which type of temporary supporting structure can be used in case of rebuilding the lower part of a load bearing wall at ground floor above plinth level?

(A) Dead Shore

(B) Pit Underpinning

(D) Needle Scaffolding

Answer: (A)

24. During earthquake, soft storey failure in a building is due to

(A) shear failure initiated by short column effect.

(B) stress discontinuity initiated by abrupt changes of stiffness.

(D) drift of building storey initiated by pounding effect.

Answer: (B)

25. Following five activities are associated with construction contract management. Choose the option showing the correct progressive sequence of the activities.

(A) R – Q – P – T – S

(B) S – P – R – T – Q

(D) S – T – P – R – Q

Answer: (C)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Match the acronym in Group I with the particulars in Group II.

(A) P–3, Q–5, R–4, S–2

(B) P–4, Q–3, R–1, S–2

(D) P–5, Q–3, R–4, S–1

Answer: (D)

27. Match the buildings in Group I with their corresponding architect in Group II.

(A) P–4, Q–3, R–1, S–2

(B) P–2, Q–4, R–2, S–5

(D) P–2, Q–3, R–4, S–5

Answer: (D)

28. Match the heritage conservation charters in Group I with their focus areas in Group II.

(A) P–3, Q–1, R–4, S–5

(B) P–5, Q–4, R–1, S–2

(D) P–4, Q–1, R–3, S–2

Answer: (C)

29. Match the Buildings (name of architects) in Group I with the abstractions used in Group II.

(A) P–4, Q–2, R–1, S–3

(B) P–5, Q–1, R–4, S–3

(D) P–5, Q–2, R–4, S–1

Answer: (B)

30. Match the names of the gardens in Group I with their type in Group II.

(A) P–3, Q–1, R–2, S–4

(B) P–5, Q–1, R–4, S–3

(D) P–5, Q–4, R–1, S–3

Answer: (B)

31. Match the various types of impurities present in water in Group I with the appropriate water treatment process given in Group II.

(A) P–2, Q–5, R–3, S–4

(B) P–3, Q–4, R–1, S–2

(D) P–3, Q–5, R–1, S–4

Answer: (D)

32. Match the temples in Group I with their style of Architecture in Group II

(A) P–3, Q–1, R–2, S–5

(B) P–3, Q–4, R–2, S–1

(D) P–5, Q–1, R–4, S–2

Answer: (A)

33. Match the urban form/structure in Group I with their respective proponents in Group II.

(A) P–4, Q–1, R–5, S–3

(B) P–5, Q–1, R–4, S–2

(D) P–3, Q–4, R–1, S–2

Answer: (C)

34. Match the elements in Group I to their description in Group II.

(A) P–3, Q–1, R–5, S–4

(B) P–4, Q–3, R–1, S–2

(D) P–5, Q–1, R–2, S–4

Answer: (D)

35. Match the position of feet in Group I to the most appropriate description of stability of human body in Group II.

(A) P–5, Q–5, R–2, S–1

(B) P–5, Q–3, R–1, S–2

(D) P–4, Q–3, R–2, S–1

Answer: (B)

36. Match the buildings in Group I with their corresponding structural systems in Group II.

(A) P–5 , Q–3 , R–4 , S–1

(B) P–3 , Q–5 , R–1 , S–2

(D) P–5 , Q–1 , R–4 , S–2

Answer: (D)

Q.37 – Q.43 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

37. Choose the correct options with respect to cycle track design as per Indian Road Congress guidelines.

(A) The minimum width of cycle track is 3 m if overtaking is to be provided for

(B) Cycle tracks may be provided when peak hour cycle traffic is 400 or more on routes with a traffic of 100 to 200 vehicles/hour

(D) Cyclist should have a clear view of at least 80 m

Answer: (A, B)

38. As per the Right to Fair Compensation and Transparency in Land Acquisition, Rehabilitation and Resettlement Act, 2013, for which purposes can the urgency clause for land acquisition be invoked?

(A) National defence and security purposes

(B) Affordable housing program

(D) Emergency arising out of natural calamities

Answer: (A, D)

39. Which of the following international treaties are related to Climate Change and global warming?

(A) Cartagena protocol, 2000

(B) Copenhagen summit, 2001

(D) Paris Agreement, 2016

Answer: (B, D OR D)

40. Which of the following algorithms are used for finding the shortest path in an urban transportation network?

(A) Logit

(B) Huff

(D) Dijkstra

Answer: (C, D)

41. Which of the following statements are true with respect to surface paint?

(A) Paint is glossy when Pigment Volume Concentration is high

(B) Vehicle is the volatile part of the paint

(D) High VOC content is preferred in paints

Answer: (B, C)

42. As per the Solid Waste Management Rules 2016, which among the following are ‘Duties of waste generators’?

(A) Segregate and store waste generated in four separate streams namely, combustible, non-combustible, organic and domestic hazardous waste

(B) Store construction and demolition waste separately within own premise before disposal

(D) Compost horticulture waste and garden waste separately within own premise

Answer: (B, C)

43. Choose the correct options with regard to activated sludge process.

(A) The activated sludge process is an aerobic process

(B) The entire settled sludge is sent back to the aeration tank

(D) In aeration tanks, sewage is aerated and agitated for a few hours

Answer: (A, D)

44. A rectangular hall having dimension of 8.0 m × 14.0 m × 4.0 m has total 4 windows (1.5 m ×0 m each) and 2 doors (1.0 m × 2.0 m each).

The coefficients of absorption are given below. Considering all windows open and doors closed, the reverberation time in seconds is _______.

[round off to 2 decimal places]

Answer: (0.82 to 0.86)

45. If surface conductance of external surface is 20 W/m²°C, absorbance of the surface is 0.66 and U value of the wall is 1.2 W/m²°C, the solar gain factor of a wall is ______. [round off to 2 decimal places]

Answer: (0.03 to 0.05)

46. The initial cost of a property is INR 4,00,000 and its future life is 30 years. Considering the scrap value as 10% of its initial cost and rate of interest as 5%, the sinking fund (deposited at the end of year) for the property is INR _______.

[round off to 2 decimal places]

Answer: (5405.00 to 5422.00)

47. Reading in the staff stationed at P measured by a dumpy level is 3.5 m. The dumpy level is stationed at Q. The Reference Level (RL) at point P is 96.5 m and the height of the dumpy level is 1.25 m. The RL at point Q is _______ m.

[round off to 2 decimal places]

Answer: (98.75 to 98.75)

48. A circular cricket field of 180 m diameter is illuminated by four floodlight towers. The floodlight towers are equally spaced along the perimeter of the field. The height of the floodlight tower is 48 m. Using ‘Inverse Square Law’, the illumination level at the center of the field is found as 750 Lux. Each tower is consisting of 50 lamps. The rating of each lamp is 700 Watt. The efficacy of each lamp is _______ Lumen /Watt. [round off to 2 decimal places]

Answer: (117.00 to 119.00 OR 1483.00 to 1496.00)

49. A building is constructed on a plot measuring 70 m × 40 m. The utilized FAR of the building is 1.5. An energy audit team found that the average monthly electricity bill of the building is INR 2,94,000. The unit cost of the electricity is INR 7. The Building Energy Index is __________ kW-hr/m²/year. [in integer]

Answer: (120 to 120)

50. A simply-supported steel beam made of an I-section has a span of 8 m. The beam is carrying a uniformly distributed load of 15 kN/m. The overall depth of the beam is 450 mm. The moment of inertia of the beam section is 18000 cm⁴. The maximum bending stress in the beam will be _________ N/mm². [in integer]

Answer: (150 to 150)

51. The slenderness ratio of a circular column of diameter 300 mm and effective height 3 m is __________. [in integer]

Answer: (40 to 40)

52. A construction project consists of following five activities. The immediate successor activity relationship and duration of each activity are mentioned in the table below.

The total duration of the project is _______ weeks. [in integer]

Answer: (12 to 12)

53. It is proposed to have ceramic tile flooring in a room having internal clear dimension of 1.8 m × 2.4 m. Tile sizes are 300 mm × 300 mm. The door opening is 900 mm and the door is flushed with the internal face of the wall. The height of skirting is 600 mm. The number of ceramic tiles required for internal flooring and skirting is _______.[in integer]

Answer: (98 to 98)

54. In a housing project, 75% of the permissible FAR was utilised after constructing four numbers eight storey MIG towers with identical floor area of 400 sqm. If three numbers seven storey LIG towers with identical floor area are built utilising the remaining FAR, the floor area of each LIG tower is _______ sqm.

[round off to 2 decimal places]

Answer: (MTA)

55. Using the following values of thermal conductance, surface conductance and thermal resistance, the U value across the given wall cross-section is _______W/m²° [round off to 2 decimal places]

Answer: (MTA)

GATE Exam 2021 Agricultural Engineering (AG) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

AG : Agricultural Engineering

General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A) whose

(B) which

(D) whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A) 396

(B) 324

(D) 144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (11¹³ +1) ?

(A) 11²⁶ + 1

(B) 11³³ + 1

(D) 11⁵² – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Stone

(B) Land

(D) Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

Which one of the following statements is the CORRECT inference from the above passage?

(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.

(D) To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

7. In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm² is:

(A) 12.50

(B) 6.25

(D) 1.5625

Answer: (C)

The mean of X is _____

(A) 2.5

(B) 5.0

(D) 50.0

Answer: (D)

9. The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A) 65 and 53

(B) 60 and 50

(D) 55 and 48

Answer: (D)

Based on the above statements, the only INCORRECT option given below is:

(A) There are two cars parked in between Q and V.

(B) Q and R are not parked together.

(D) Car P is parked at the extreme end.

Answer: (A)

Agricultural Engineering (AG)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE marks each (for each wrong answer: – 1/3).

1. Let the vector be a differentiable vector function of Cartesian coordinates x, y and z. The curl of the vector is given by curl =

Answer: (C)

2. If x is an integer with x > 1, the solution of is

(A) Zero

(B) 0.5

(D) ∞

Answer: (B)

3. In a tyre axis system as defined by Society of Automotive Engineers, the moment acting about z-axis is called

(A) aligning torque

(B) over turning torque

(D) lateral moment

Answer: (A)

4. Pitting is a process of

(A) mixing of pulses with red earth

(B) mixing of pulses with edible oil

(D) beating of oil seeds for oil extraction

Answer: (C)

5. During ploughing with a tractor mounted mould board plough, the mast of three point hitch system would be

(A) inclined 5 to 20° with horizontal

(B) nearly vertical

(D) parallel to the rear axle of the tractor

Answer: (B)

6. The hydrologic reservoir routing methods use

(A) Bernoulli’s equation only

(B) hydrologic continuity equation only

(D) both the hydraulic momentum and hydrologic continuity equations

Answer: (B)

7. While assessing the intensity of agricultural drought, a negative value of aridity index indicates that the area is classified as

(A) severely arid

(B) moderately arid

(D) non-arid

Answer: (B)

8. The approximate relationship between Sediment Delivery Ratio (SDR) and drainage area (A) shows that SDR varies

(A) directly with A^0.2

(B) inversely with A^0.2

(D) inversely with A

Answer: (B)

9. One-dimensional generalized heat conduction equation representing temperature distribution in a sphere, based on thermal conductivity k, specific heat capacity C_p, density ρ, and energy generation E, can be written as where the value of n is

(A) 1

(B) 2

(D) 4

Answer: (B)

10. In butter, the fishy flavor defect is due to the decomposition of

(A) α-lactalbumin

(B) β-lactoglobulin

(D) lecithin

Answer: (D)

11. In a field test of drip irrigation system having an application efficiency of 90%, the minimum, maximum and average flow rates are found to be 45 L∙h⁻¹, 65 L∙h⁻¹ and 50 L∙h⁻¹, respectively. The manufacturer’s coefficient of variation of the emitter is 0.07. If there is one emitter per plant, the drip irrigation efficiency in percent is ________. [round off to 2 decimal places]

Answer: (73.70 to 73.85)

12. Trace of the matrix is _______. [in integer]

Answer: (18 to 18)

13. The probabilities of A and B are given by P(A) = 0.35 and P(B) = 0.25, respectively. If A and B are mutually exclusive so that P(A⋃B) = P(A) + P(B), then the value of P(A/A⋃B) is _________. [round off to 3 decimal places]

Answer: (0.583 to 0.584)

14. Stoichiometric air-fuel ratio of an SI engine is 14.7:1. If equivalence ratio (λ) is 0.92, the actual air-fuel ratio maintained during the engine operation is ______. [round off to 2 decimal places]

Answer: (13.47 to 13.57 OR 15.93 to 16.03)

15. While harvesting paddy with a self-propelled vertical conveyor reaper with a cutter bar of width 60 cm, the power required for cutting and propelling are measured to be 300 W and 350 W, respectively. If the power required for conveying the cut crop is 50% of the power required for cutting, the power required by the header unit of the vertical conveyor reaper in W will be ________. [answer in integer]

Answer: (450 to 450)

16. A gear pump has a displacement of 120 cm³ rev^-1 and it runs at 1500 rpm against a system pressure of 18 MPa. If the torque efficiency of the pump is 90%, actual torque required to run the pump in N∙m is _______. [round off to 2 decimal places]

(Take π = 3.14)

Answer: (380.00 to 383.00)

17. Useful soil reaction forces acting on a tractor drawn mould board plough during operation are 2.0 kN, 0.9 kN and 0.6 kN along longitudinal, transverse and vertical directions, respectively. The soil-metal friction angle is 25°. Neglecting the effects of weight of the implement and the vertical soil reaction, the estimated draft in N is _______. [round off to one decimal place]

Answer: (2400.0 to 2440.0)

18. Cohesionless soil is naturally deposited and makes a slope of infinite extent having slope angle of 25°. If the effective angle of internal friction of this soil is 30°, the factor of safety of slope is _______. [round off to 2 decimal places]

Answer: (1.22 to 1.25)

19. A pump, discharging water at a rate of 80 L∙s⁻¹, is used to irrigate 2 ha of land in 10 h. On irrigation, moisture content of the soil (on weight basis) in the root zone depth of 50 cm is increased from 18% to 30%. If bulk density of the soil is 1500 kg∙m⁻³, water application efficiency in per cent is _______.

[round off to 2 decimal places]

Answer: (62.25 to 62.75)

20. Pumping test is carried out at a constant discharge of 5400 L∙min⁻¹ for 24 h in a main well of 30 cm diameter penetrated 25 m below the static water table. The water level in observation wells located at 30 m and 90 m away from the main well are lowered by 1.11 m and 0.53 m, respectively. Considering steady state flow condition, drawdown estimated in the main well in m is _______.

[round off to 2 decimal places] (Take π = 3.14)

Answer: (4.00 to 4.25)

21. The observed concentrations of magnesium (Mg²⁺), sodium (Na⁺), and bicarbonate (HCO₃⁻) in saturated extract of a soil sample taken from the root zone are 5.68 meq∙L⁻¹, 9.90 meq∙L⁻¹, and 11.20 meq∙L⁻¹, respectively. If the concentration ratio of HCO₃⁻/Ca²⁺ is 2.8, the sodium adsorption ratio is ________. [round off to 2 decimal places]

Answer: (4.50 to 4.50)

22. Fresh potatoes of mass 1000 kg are dried from 14% to 93% total solids. If 7% of original potatoes is lost in peeling, the product yield from fresh potatoes in percent is ________. [answer in integer]

Answer: (14.0 to 14.0)

23. In an ordinary chimney, the draught is 12 mm of water column. Assuming density of water to be 1000 kg∙m⁻³, the pressure difference between the outside air and gas at the base of the chimney in Pa is ________. [round off to one decimal place]

Answer: (117.1 to 118.1)

24. A ball mill of 200 cm diameter grinds solid materials while operating with 10 cm size balls. If the same ball mill is used for wet grinding, charged with 20 cm diameter balls, the change in the operating speed in rpm is _______. [round off to 2 decimal places] (Take π = 3.14 and g = 9.81 m∙s⁻²)

Answer: (3.60 to 4.20)

25. Rushton turbine having an impeller diameter of 20 cm and operating at a stirrer speed of 200 rpm is used in a mixing tank. If the tank receives air at a volumetric flow rate of 0.2 m³∙min⁻¹, the non-dimensional Froude number, N_Fr is ______. [round off to 2 decimal places]

Answer: (0.21 to 0.31)

Q.26 – Q.38 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. Solution of the differential equation y′′ + y′ + 0. 25y = 0 with the initial values y(0) = 3. 0 and y′(0) = −3. 5 is

(A) y = (3 − 2x) e^0.5x

(B) y = (3 − 2x) e^−0.25x

(D) y = (2 − 3x) e^−0.5x

Answer: (C)

27. A shear annulus with inner and outer diameters of 240 mm and 300 mm, respectively is used to measure shear strength of soil in the field. When it is inserted into the soil and rotated, the torque measured at the soil failure is 50 N∙ Shear strength of the soil in kPa is

(Take π = 3.14)

(A) 14.49

(B) 18.94

(D) 28.98

Answer: (A)

28. A bushy crop with stem cross-sectional diameter 6 mm is to be cut by impact force at a height of 50 mm above the soil surface. Based on the entire stem cross-section, the modulus of elasticity is 1500 N∙mm⁻² and ultimate tensile strength is 35 N∙mm⁻². The force in N that would cause failure of the stem due to bending is

(Take π = 3.14)

(A) 14.84

(B) 23.52

(D) 44.53

Answer: (A)

29. A solar panel has length of 1.3 m and width of 0.65 m. The solar cells cover 90% of the panel area and its conversion efficiency is 13.7%. For a total solar radiation of 750 W∙m⁻², the panel output voltage is 18 V at its maximum power output. If two such panels are connected in series to supply power to run a thresher, the current in A that can be supplied by the two panels at the maximum power output is

(A) 2.17

(B) 3.01

(D) 8.68

Answer: (C)

30. A fertilizer drill with a row to row spacing of 40 cm, discharges 38 g of fertilizer per row per revolution of the metering wheel. The metering wheel is driven through a chain transmission system by ground wheel having 60 cm diameter. Neglecting skid of the ground wheel, for an application rate of 200 kg∙ha⁻¹, the speed ratio of ground wheel to metering wheel will be

(Take π = 3.14)

(A) 1.40 : 1

(B) 2.52 : 1

(D) 4.76 : 1

Answer: (B)

31. A sample of wet sandy-clay loam soil of mass 135 kg is collected for laboratory tests. The wet density, water content (weight basis) and specific gravity of solids of this soil sample are 1.8 g∙cm⁻³, 18%, and 2.7, respectively. The dry density (in g∙cm⁻³) and porosity (in per cent) of the soil sample, respectively, are

(A) 1.53 and 43.50

(B) 1.53 and 77.00

(D) 1.65 and 77.00

Answer: (A)

32. It is proposed to develop bench terraces in an area having land slope of 10%. If the vertical interval between the bench terraces is 2.5 m and the batter slope is 100%, working width (in m) and the area lost for cultivation (in per cent), respectively will be

(A) 22.50 and 0.05

(B) 25.00 and 0.50

(D) 25.00 and 10.45

Answer: (C)

33. While carrying out a traverse survey ABCDA′ using a theodolite with the originating station A, the departures and latitudes of the lines, as obtained, are shown in the following figure (not drawn to scale). It is seen that, due to the observational errors, the originating station A and its computed station A′ are not the same. For this survey, the ‘closing error’ in m is

(A) 6.33

(B) 7.62

(D) 35.21

Answer: (B)

34. The shape of the Instantaneous Unit Hydrograph (IUH) of a catchment is an isosceles triangle with a peak of 60 m³∙s⁻¹ and time to peak of 3 h. If the constant base flow is 7.5 m³∙s⁻¹, the peak of the 3 h Unit Hydrograph (UH) in m³∙s⁻¹ is

(A) 43.33

(B) 50.83

(D) 60.00

Answer: (A)

35. Match the following hulling mechanism in column 1 with the corresponding machine in column 2

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

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

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

Answer: (A)

36. Match the correct items in column 1 with column 2

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

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

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

Answer: (D)

37. A 30 μm thick membrane having 3 m² surface area is used to separate NaCl from a solution at steady state condition. The mass transfer coefficient of NaCl at the solution side is 1×10⁻⁶ m∙s⁻¹ and that at the other side of the membrane is 3×10⁻⁷ m∙s⁻¹. Concentration of NaCl in the solution is 0.03 g∙(100 mL)⁻¹ and, that on the other side of the membrane is assumed to be zero. Permeability of the membrane is 9×10-6 m∙s⁻¹. The rate of removal of the NaCl by the membrane in g∙h⁻¹ is

(A) 0.73

(B) 0.81

(D) 0.93

Answer: (A)

38. In a size reduction operation, the power required to crush 2 ton of feed material per hour is 7.2 kW. Eighty per cent of the feed and product material pass through 4.75 mm and 0.5 mm sieve openings, respectively. The work index of the material is

(A) 6.5

(B) 7.4

(D) 14.8

Answer: (C)

Q.39 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

39. A nine-member committee of an Agricultural University consists of 4 B. Tech., 3 M. Tech., and 2 Ph. D. students. It is decided to remove three students from the committee at random. The probability of removing 2 students from the same category and the third one from any other category is__________.

[round off to 3 decimal places]

Answer: (0.654 to 0.656)

40. Summation of eigenvalues of a matrix is _______.

Answer: (10 to 10)

41. During operation of a two-wheel drive tractor with a total weight of 20 kN in pure sandy soil (angle of internal friction is 26.5°), the weight distribution at the front and rear axles are found to be 35% and 65%, respectively. If extra weight of 2.5 kN is added to each of the rear wheels, the change in maximum thrust developed by the tractor in per cent will be ________. [round off to 2 decimal places]

Answer: (38.20 to 38.60)

42. A tractor PTO driven rotavator with a rotor radius 30 cm has 20 L-shaped blades each of width 12 cm. These blades are fixed at a radial distance of 7 cm from the center of the rotor shaft to the brackets attached to the rotor shaft. When this rotavator is operated at a forward speed of 4.5 km∙h⁻¹ and at a depth of 12 cm, the resultant soil force of 150 N tangential to the rotor circumference acts at the middle of the blade width. The torsional moment acting on the blade in N∙m is _______. [round off to one decimal place]

Answer: (8.90 to 9.10)

43. Fixed cost per year and variable cost per hour of a tractor were estimated based on its annual usage of 800 h. The total cost of operation was found to be Rs. 540 per hour. It was later re-estimated and found that total cost of operation would be Rs. 510 per hour, if the annual hours of use were increased to 1000 h. Considering all the components of annual usage cost to be the same, the variable cost in Rs. per hour would be ___________. [answer in integer]

Answer: (395.0 to 395.0)

44. Two meshed involute gears transmit 1.0 kW power. The pressure angle is 200 and the pitch circle diameter of the large gear rotating at a speed of 600 rpm is 20 cm. If only a pair of teeth meshes at a time, the normal force acting between the meshed teeth in N will be _______. [round off to one decimal place]

(Take π = 3.14)

Answer: (165.0 to 176.0)

45. A horizontal axis lift type wind rotor of diameter 4 m is used to run a pump at a wind velocity of 15 km∙h⁻¹ at standard atmospheric pressure and temperature (density of air is 1.23 kg∙m⁻³). If velocity of wind leaving the rotor blade is reduced to one-third of the approaching wind velocity, the thrust acting on the blade of the wind rotor in N is ____________. [round off to 2 decimal places]

Answer: (118.90 to 119.60)

46. A small watershed receives rainfall of 90 mm in a day. For this watershed, irrespective of the land use, the amount of initial abstraction can be considered as 25% of the potential maximum retention (S) of soil. Initially, the entire watershed was under forest with S = 136 mm, which was converted into cultivated land with S = 64 mm. The change in the daily runoff volume due to this land use alteration for this specific rainfall event in percent is __________.

[round off to one decimal place]

Answer: (142.9 to 143.6)

47. The most economical trapezoidal channel section with 1:1 (horizontal : vertical) side slope is designed to carry a maximum of 40 cm depth of water at its full capacity. If the bed slope of the channel is 1:2500 and the Manning’s roughness coefficient of channel section is 0.01, the estimated discharge capacity of the channel in m³∙s⁻¹is ________. [round off to 2 decimal places]

Answer: (0.18 to 0.22)

48. A windbreak, 15 m in height and 200 m in length, is established to protect the land from wind erosion in an arid area. The minimum wind velocity at the height of 15 m above the ground required to move the most erodible soil fraction is 9.6 m∙s⁻¹. If 5-year return period wind velocity at 15 m height is 16 m∙s⁻¹ and the wind direction deviates 20° from the line perpendicular to the windbreak, the area protected by the windbreak in ha is _________.

[round off to 2 decimal places]

Answer: (2.70 to 3.00)

49. Water is discharged from a tank through a rectangular orifice of width 1.5 m and height 1.2 m. The water level in the tank is 3.5 m above the top edge of the orifice. If the coefficient of discharge of this orifice is 0.62, the discharge through the orifice in m³∙s⁻¹ is ____________. [round off to 2 decimal places]

(Take acceleration due to gravity, g = 9.81 m∙s⁻²)

Answer: (9.90 to 10.10)

50. Two fully penetrating wells are dug 1.4 km apart in a homogenous confined aquifer. The difference in their piezometric levels is 4.0 m. The groundwater flow is steady and unidirectional. If the aquifer has a hydraulic conductivity of 3.5 m∙day⁻¹ and effective porosity of 40%, the time taken for water to move from one well to the other in days is __________. [in integer]

Answer: (56000 to 56000)

51. Food cans are sterilized in a retort to inactivate Clostridium botulinum. Process time (F_o) of this food material is 150 s and the z value is 10°C. Temperatures at the slowest heating region of the food can are measured and the average temperature during time periods 0 to 20 min, 20 to 40 min and 40 to 70 min are 71.1°C, 98.9°C and 110°C, respectively. The actual process time in minutes that is required for equivalent sterilization at 121.1 °C is _________.

[round off to 2 decimal places]

Answer: (2.01 to 3.01)

52. Molecular masses of water and air are 18.02 and 28.97 kg∙(kg mol)⁻¹, respectively. Air in a room is at 40°C under a total pressure of 101.3 kPa absolute and contains water vapour at a partial pressure of 4.0 kPa. If saturated vapour pressure of water at 40 °C is 7.37 kPa, the relative humidity of this air in per cent is ________. [round off to 2 decimal places]

Answer: (52.00 to 54.50)

53. A cylindrical storage bin with an internal diameter of 4 m and a height of 16 m is completely filled with paddy having bulk density of 640 kg∙m⁻³. The angle of internal friction between grain and bin wall is 30° and the ratio of horizontal to vertical pressures is 0.4. When the grain filling rises from 4 m to 16 m in height, the lateral pressure increases by a multiple of__________.

[round off to 2 decimal places]

Answer: (1.60 to 1.70)

54. An air screen grain cleaner unit of capacity one ton∙h⁻¹ with two screens was evaluated with a feed containing 8.5% impurities. During the operation, the clean grain at blower outlet, overflow of 1st screen and underflow of second screen were found to be 0.3%, 1.2% and 0.8%, respectively. If the clean grain contains 0.6% of impurities, the cleaning efficiency of the cleaner unit in per cent would be ________. [round off to one decimal place]

Answer: (93.0 to 94.0)

55. One side of a solid food block of 10 cm thickness is subjected to a heating medium having a film heat transfer coefficient of 70 W∙(m²∙°C)⁻¹. The other side of the food block is being cooled by a medium having a film heat transfer coefficient of 100 W∙(m²∙°C)⁻¹. The food block is having a thermal conductivity of 0.2 W∙(m²∙°C)⁻¹ and the contact area of the block available for heat transfer is 1 m². Heat transfer rate in the block at steady state is 100 J∙s⁻¹. The temperature difference between the two sides of the block in °C is ________.

[round off to 2 decimal places]

Answer: (52.11 to 52.56)

GATE Exam 2021 Aerospace Engineering (AE) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

AE : Aerospace Engineering

General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Aerospace Engineering (AE)

Q.1 – Q.13 carry One marks each (for each wrong answer: -1/3).

1. Consider the differential equation and the boundary conditions y(0) = 1 and The solution to this equation is:

(A) y = (1 + 2x)e⁻^4x

(B) y = (1 – 4x)e⁻^4x

(D) y = (1+4x) e⁻^4x

Answer: (D)

2. u(x, y) is governed by the following equation The nature of this equation is:

(A) linear

(B) elliptic

(D) parabolic

Answer: (B)

3. Consider the velocity field The field is

(A) divergence-free and curl-free

(B) curl-free but not divergence-free

(D) neither divergence-free nor curl-free

Answer: (B)

4. The figures shows schematics of wave patterns at the exit of nozzles A and B operating at different pressure ratios.

Nozzles A and B, respectively, are said to be operating in:

(A) over-expanded mode and under-expanded mode

(B) under-expanded mode and perfectly expanded mode

(D) under-expanded mode and over-expanded mode

Answer: (A)

5. The combustion process in a turbo-shaft engine during ideal operation is:

(A) isentropic

(B) isobaric

(D) isothermal

Answer: (B)

6. How does the specific thrust of a turbojet engine change for a given flight speed with increase in flight altitude?

(A) Increases monotonically

(B) Decreases monotonically

(D) First increases and then decreases

Answer: (A)

7. How does the propulsion efficiency of a turbofan engine, operating at a given Mach number and a given altitude, change with increase in compressor pressure ratio?

(A) Remains constant

(B) Increases monotonically

(D) First decreases and then increases

Answer: (D)

8. A solid propellant rocket producing 25 MN thrust is fired for 150 seconds. The specific impulse of the rocket is 2980 Ns/kg. How much propellant is burned during the rocket operation?

(A) 8390 kg

(B) 82300 kg

(D) 11.2 × 10⁶ kg

Answer: (C)

9. The shape of a supersonic diffuser that slows down an supersonic flow to subsonic flow is

(A) converging

(B) diverging

(D) converging-diverging

Answer: (D)

10. Uniaxial tension test (see the figure) is conducted on two different samples prepared with homogeneous, isotropic materials. One of the materials is brittle, whereas the other is ductile.

Assuming that there is no stress concentration at loading points, the failure would initiate.

(A) along x-x in both materials

(B) along x-x in brittle material and along y-y in ductile material

(D) along y-y in both materials

Answer: (B)

11. For the state of stress as shown in the figure, what is the orientation of the plane with maximum shear stress with respect to the x-axis?

(A) 45°

(B) -45°

(D) -22.5°

Answer: (D)

12. Let V_TAS be the true airspeed of an aircraft flying at a certain altitude where the density of air is ρ, and V_EAS be the equivalent air speed. If ρ₀ is the density of air at sea-level, what is the ratio equal to ?

(A) ρ/ρ₀

(B) ρ₀/ρ

(C)

(D)

Answer: (C)

13. C_m – α variation for a certain aircraft is shown in the figure. Which one of the following statements is true for this aircraft?

(A) The aircraft can trim at a positive α and it is stable.

(B) The aircraft can trim at a positive, α but it is unstable

(D) The aircraft can trim at a negative α, but it is unstable

Answer: (B)

14. Which of the following statement(s) is/are true across an oblique shock (in adiabatic conditions) over a wedge shown below?

(A) Total pressure decreases

(B) Mach number based on velocity tangential to the shock decreases

(D) Mach number based on velocity tangential to the shock remains the same and that based on velocity normal to the shock decreases

Answer: (A, B, C)

15. Which of the following statement(s) is/are true with regards to Kutta condition for flow past airfoils?

(A) It is utilized to determine the circulation on an airfoil.

(B) It is applicable only to airfoils with sharp trailing edge.

(D) The flow leaves the trailing edge smoothly

Answer: (A, B, D)

16. According to the thin airfoil theory, which of the following statement(s) is/are true for a cambered airfoil?

(A) The lift coefficient for an airfoil is directly proportional to the absolute angle of attack.

(B) The aerodynamic center lies at quarter chord point.

(D) Drag coefficient is proportional to the square of lift coefficient.

Answer: (A, B)

17. (round off to nearest integer).

Answer: (0 to 0)

18. Given that ζ is the unit circle in the counter-clockwise direction with its center at origin, the integral (round of to three decimal place).

Answer: (0.02 to 0.03)

19. A single degree of freedom spring-mass-damper system is designed to ensure that the system returns to its original undisturbed position in minimum possible time without overshooting. If the mass of the system is 10 kg, spring stiffness is 17400 N/m and the natural frequency is 13.2 rad/s, the coefficient of damping of the system in Ns/m is _____ (round off to nearest integer).

Answer: (264 to 264 OR 833 to 835)

20. Two cantilever beams (Beam 1 and Beam 2) are made of same homogenous material and have identical cross sections, Beam 1 has length l and Beam 2 has length 2l. Ratio of the first natural frequency of Beam 1 to that of Beam 2 is ______(round off to nearest integer.

Answer: (4 to 4)

21. A free vortex filament (oriented along Z-axis) of strength K= 5 m²/s is placed at the origin as shown in the figure. The circulation around the closed loop ABCDEFA for this flow is ______.

Answer: (0 to 0)

22. A thin-walled cylindrical tank with closed ends, made of homogenous and isotropic material, is pressurized internally. If the hoop (circumferential strain developed in the material is thrice the value of the axial strain then the Poisson’s ratio of the material is ______ (correct up to one decimal place).

Answer: (0.2 to 0.2)

23. A jet aircraft has the following specifications: wing loading = 1800 N/m², wing area = 30 m², drag polar C_D = 0.02 + 0.04C_L² , and C_{L, max} = 1.6. Take density of air at sea level as 1.225 kg/m³.

The speed at which the aircraft achieves maximum endurance in a steady and level flight at sea level is ______ m/s (round off to two decimal places).

Answer: (64.30 to 64.60)

24. An aircraft with twin jet engines has the following specifications:

Thrust produced (per engine) = 8000 N

Spanwise distance between the two engines = 10 m

Wing area = 50 m², Wing span = 10 m

Rudder effectiveness C_nδr = −0.002/deg

Density of air at sea level = 1.225 kg/m³

The rudder deflection, in degrees, required to maintain zero sideslip at 100 m/s in steady and level flight at sea level with a non-functional right engine is ______ (round off to two decimal places).

Answer: (6.50 to 6.60)

25. The velocity required to launch a space shuttle from the surface of the earth to achieve a circular orbit of 250 km altitude is ______ (round off to two decimal places).

For earth, Gm_e = 398,600.4 km³/s² and surface radius R₀ = 6378.14 km.

Answer: (7.75 to 7.77 OR 7750.00 to 7770.00)

Q.26 – Q.30 carry TWO marks each (for each wrong answer: – 2/3).

26. A rigid massless rod pinned at one end has a mass m attached to its other end. The rod is supported by a linear spring of stiffness k as shown in the figure.

The natural frequency of this system is:

(A)

(B)

(C)

(D)

Answer: (A)

27. The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:

(A) remains same, increases, and decreases

(B) increases, decreases, and increases

(D) remains same, decreases, and increases

Answer: (C)

28. To estimate aerodynamic loads on an aircraft flying at 100 km/h at standard sea-level conditions, a one-fifth scale model is tested in a variable-density wind tunnel ensuring similarity of inertial and viscous forces. The pressure used in the wind tunnel is 10 times the atmospheric pressure. Assuming ideal gas law to hold and the same temperature conditions in model and prototype, the velocity needed in the wind tunnel test-section is _______.

(A) 25 km/h

(B) 50 km/h

(D) 20 km/h

Answer: (B)

29. The figure shows schematic of a set-up for visualization of non-uniform density field in the test section of a supersonic wind tunnel. This technique of visualization of high speed flows is known as:

(A) schlieren

(B) interferometry

(D) holography

Answer: (C)

30. For a conventional fixed-wing aircraft in a 360° inverted vertical loop maneuver, what is the load factor (n) at the topmost point of the loop? Assume the flight to be steady at the topmost point.

(A) n = 1

(B) n < 1

(D) n > −1

Answer: (D)

31. Which of the following statement(s) is/are true about the function defined as f(x) = e⁻^x |cos x| for x > 0 ?

(A) Differentiable at x = π/2

(B) Differentiable at x = π

(D) Continuous at x = 2π

Answer: (B, D)

32. A two degree of freedom spring-mass system undergoing free vibration with generalized coordinates x₁ and x₂ has natural frequencies ω₁ = 233.9 rad/s and ω₂ = 324.5 rad/s, respectively. The corresponding mode shapes are If the system is disturbed with certain deflections and zero initial velocities, then which of the following statement(s) is/are true?

(A) An initial deflection of x₁ (0) = 6.32 cm and x₂ (0) = −3.16 cm would make the system oscillate with only the second natural frequency.

(B) An initial deflection of x₁ (0) = 2 cm and x₂ = −6.32 cm would make the system oscillate with only the first natural frequency.

(C) An initial deflection of x₁ (0) = 2 cm and x₂ = −2 cm would make the system oscillate with a linear combination of first and second natural frequencies.

(D) An initial deflection of x₁ (0) = 1 cm and x₂ = −6.32 cm cm would make the system oscillate with only the first natural frequency.

Answer: (B, C)

33. A shock moving into a stationary gas can be transformed to a stationary shock by a change in reference frame, as shown in the figure. Which of the following is/are true relating the flow properties in the two reference frames?

Answer: (D)

34. For a conventional fixed-wing aircraft, which of the following statements are true?

(A) Making C_m_α more negative leads to an increase in the frequency of its short-period mode.

(B) Making C_mqmore negative leads to a decreased damping of the short-period mode.

(D) Increasing the size of the vertical fin leads to a higher yaw damping.

Answer: (A, C, D)

35. Which of the following statement(s) is/are true?

(A) Service ceiling is higher than absolute ceiling for a piston-propeller aircraft.

(B) For a given aircraft, the stall speed increases with increase in altitude.

(D) For a jet aircraft constrained to fly at constant altitude, there exists an altitude where its range is maximum.

Answer: (B, C, D)

36. A conventional fixed-wing aircraft, with a horizontal tail and vertical fin, in steady and level flight is subjected to small perturbations. Which of the following statement(s) is/are true?

(A) Vertical fin has a stabilizing effect on the lateral stability of the aircraft.

(B) Vertical fin has a destabilizing effect on the directional stability of the aircraft.

(D) Horizontal tail has a stabilizing effect on the longitudinal static stability of the aircraft.

Answer: (A, D)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

37. The ratio of the product of eigenvalues to the sum of the eigenvalues of the given matrix is _______ (round off to nearest integer).

Answer: (8 to 8)

38. The definite integral is evaluated using four equal intervals by two methods – first by the trapezoidal rule and then by the Simpson’s one- third rule. The absolute value of the difference between the two calculations is _______ (round off to two decimal places).

Answer: (0.66 to 0.68)

39. The deflection y of a certain beam of length l and uniform weight per unit length w, is given as where x is the distance from the point of support and EI is a constant. The non-dimensional location x/l, where the deflection of the beam is maximum, is _____ (round off to two decimal places).

Answer: (0.41 to 0.43)

40. A large water tank is fixed on a cart with wheels and a vane (see figure). The wheels of the cart provide negligible resistance for rolling on the fixed support. The cart is tied to the fixed support with a thin horizontal rope. There is a hole of diameter 5 cm on the side of the tank through which a jet of constant velocity of 10 m/s emerges. The jet of water is deflected by the attached vane by 60° (see figure). Assume that the jet velocity remains constant at 10 m/s after emerging from the vane. Take density of water to be 1000 kg/m³. The tension in the connecting rope is _____ N (round off to one decimal place).

Answer: (98.0 to 98.5)

41. A finite wing of elliptic planform with aspect ratio 10, whose section is a symmetric airfoil, is placed in a uniform flow at 5 degrees angle of attack. The induced drag coefficient for the wing is ______ (round off to three decimal places).

Answer: (0.005 to 0.009)

42. Consider a model of a boundary layer with the following velocity profile:

The shape factor, defined as the ratio of the displacement thickness to momentum thickness, for this profile is _____ (round off to 2 decimal places).

Answer: (4.8 to 5.2)

43. An aircraft with a turbojet engine is flying at 270 m/s. The enthalpy of the incoming air at the intake is 260 kJ/kg and the enthalpy of the exhaust gases at the nozzle exit is 912 kJ/kg. The ratio of mass flow rates of fuel and air is equal to 0.019. The chemical energy (heating value) of fuel is 44.5 MJ/kg and the combustion process is ideal. The total loss of heat from the engine to the ambient is 25 kJ per kg of air. The velocity of the exhaust jet is __________m/s (round off to two decimal places).

Answer: (605 to 607)

44. Hot gases are generated at a temperature of 2100 K and a pressure of 14 MPa in a rocket chamber. The hot gases are expanded ideally to the ambient pressure of 0.1 MPa in a convergent-divergent nozzle having a throat area of 0.1 m². The molecular mass of the gas is 22 kg/kmol. The ratio of specific heats (γ) of the gas is 1.32. The value of the universal gas constant (R₀) is 8314 J/kmol-K. The acceleration due to gravity, g, is 9.8 m/s². The specific impulse of the rocket is _______ seconds (round off to two decimal places).

Answer: (216 to 220)

45. A twin-spool turbofan engine is operated at sea level (P_a = 1 bar, T_a = 288 K). The engine has separate cold and hot nozzles. During static thrust test at sea level, the overall mass flow rate of air through the engine and the cold exhaust temperature are measured to be 100 kg/s and 288 K, respectively. The parameters for the engine are:

Fan pressure ratio = 1.6

Overall pressure ratio = 20

Bypass ratio = 3.0

Turbine entry temperature = 1800 K.

The specific heat at constant pressure (Cp) is 1.005 kJ/kg-K and the ratio of specific heats (γ) is 1.4 for air.

Assuming ideal fan and ideal expansion in the nozzle, the sea-level static thrust from the cold nozzle is _____________ kN (round off to two decimal places).

Answer: (20 to 22)

46. At the design conditions, the velocity triangle at the mean radius of a single stage axial compressor is such that the blade angle at the rotor exit is equal to 30°. The absolute velocities at the rotor inlet and exit are equal to 140 m/s and 240 m/s, respectively. The flow velocities relative to the rotor at inlet and exit of the rotor are equal to 240 m/s and 140 m/s, respectively.

The blade speed (U) at the mean radius of the rotor is __________ m/s (round off to two decimal places).

Answer: (274 to 282)

47. A single stage axial turbine has a mean blade speed of 340 m/s at design condition with blade angles at inlet and exit of the rotor being 21° and 55°, respectively. The degree of reaction at the mean radius of the rotor is equal to 0.4. The annulus area at the rotor inlet is 0.08 m² and the density of gas at the rotor inlet is 0.9 kg/m³. The flow rate through the turbine at these conditions is __________ kg/s (round off to two decimal places).

Answer: (18.0 to 19.5)

48. The air flow rate through the gas generator of a turboprop engine is 100 kg/s. The stagnation temperatures at inlet and exit of the combustor are 600 K and 1200 K, respectively. The burner efficiency is 90% and the heating value of the fuel is 40 MJ/kg. The specific heats at constant pressure (Cp) for air and burned gases are 1000 J/kg-K and 1200 J/kg-K, respectively. The flow rate of the fuel being used is _____________ kg/s (round off to two decimal places)..

(Note: Do not neglect the fuel flow rate with respect to the air flow rate)

Answer: (2.35 to 2.50)

49. A rigid horizontal bar ABC, with roller support at A, is pinned to the columns BD and CE at points B and C, respectively as shown in figure. The other end of the column BD is fixed at D, whereas the column CE is pinned at E. A vertical load P is applied on the bar at a distance ‘a’ from point B.

The two columns are made of steel with elastic modulus 200 GPa and have a cross section of 1.5 cm x 1.5 cm. The value of ‘a’ for which both columns buckle simultaneously, is ____________ cm (round off to one decimal place).

Answer: (14.0 to 16.0)

50. A two-cell wing box is shown in the figure. The cell walls are 1.5 mm thick and the shear modulus G = 27 GPa. If the structure is subjected to a torque of 12 kNm, then the wall AD will experience a shear stress of magnitude _________ MPa (round off to one decimal place).

Answer: (2.1 to 2.5)

51. Two cantilever beams AB and DC are in contact with each other at their free ends through a roller as shown in the figure. Both beams have a square cross section of 50 mm x 50 mm, and the elastic modulus E = 70 GPa. If beam AB is subjected to a uniformly distributed load of 20 kN/m, then the compressive force experienced by the roller is ___________ kN (round off to one decimal place).

Answer: (2.2 to 2.6)

52. A 3 m x 1 m signboard is supported by a vertical hollow pole that is fixed to the ground. The pole has a square cross section with outer dimension 250 mm. The yield strength of the pole material is 240 MPa. To sustain a wind pressure of 7.5 kPa, the dimension d of the pole is _________ mm (round off to nearest integer).

Answer: (232 to 238)

53. An airplane weighing 5500 kg is in a steady level flight with a speed of 225 m/s. The pilot initiates a steady pull-up maneuver with a radius of curvature of 775 m. The location of center of gravity (CG), center of pressure on wing (CP) and point of action (T) of tail force are marked in the figure. Use g = 9.81 m/s². Neglect drag on the tail and assume that tail force is vertical. Assuming the engine thrust and drag to be equal, opposite and collinear, the tail force is_____________ kN (round off to one decimal place).

Answer: (14.8 to 15.2)

54. A jet aircraft weighing 10,000 kg has an elliptic wing with a span of 10 m and area 30 m². The C_D0 for the aircraft is 0.025. The maximum speed of the aircraft in steady and level flight at sea level is 100 m/s. The density of air at sea level is 1.225 kg/m³, and take g = 10 m/s². The maximum thrust developed by the engine at sea level is ______ N (round off to two decimal places).

Answer: (9735 to 9797)

55. Consider a jet transport airplane with the following specifications:

Lift curve slope for wing-body

Lift curve slope for tail

Tail area S_t = 80 m²

Wing area S = 350 m²

Distance between mean aerodynamic centers of tail and wing-body

Mean aerodynamic chord

Downwash ε = 0. 4α

Axial location of the wing-body mean aerodynamic center

Axial location of the center of gravity

All axial locations are with respect to the leading edge of the root chord

and along the body x-axis. Ignore propulsive effects.

The pitching-moment-coefficient curve slope (C_mα) is ________ /deg (round off to three decimal places).

Answer: (-0.025 to -0.023)

GATE Exam 2020 Life Sciences (XL) Question Paper With Answer Key

June 8, 2023May 6, 2022 by suresh84

GATE-2020

XL: Life Sciences

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.

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

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

Which of the following statements can be inferred from the above passage?

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

XL: Life Sciences – P : Chemistry (Compulsory)

Q1 – Q5 carry one mark each.

1. An aqueous solution contains a mixture of 10⁻⁸ M NaCl and 10⁻⁸ M HCl.

Choose the correct statement about this solution.

(A) The solution is a buffer with pH less than 7.00

(B) The solution is a buffer with pH greater than 7.00

(D) The solution is not a buffer but has its pH greater than 7.00

Answer: (C)

2. The coordination complex which has a distorted octahedral structure is

(Given: Atomic numbers of V: 23; Mn: 25; Ni: 28; Cu: 29)

(A) [Ni(H₂O)₆]²⁺

(B) [Mn(H₂O)₆]²⁺

(D) [Cu(H₂O)₆]²⁺

Answer: (D)

3. In naphthalene, the value of the integer “n” according to Huckel’s rule of aromaticity is ______.

Answer: (2 to 2)

4. The azimuthal quantum number (l) of an electron in the orbital of a copper atom (atomic number: 29) is ______.

Answer: (2 to 2)

5. The standard enthalpy of reaction (in kJ mol⁻¹) for obtaining three moles of H₂(g) from atomic hydrogen in gas phase is ______. (Given: Standard enthalpy of formation of atomic hydrogen is gas phase is 218 kJ mol⁻¹)

Answer: (-1308 to -1308)

Q6 – Q15 carry two marks each.

6. The correct order of the first ionization energies of He, B, N and O in their corresponding ground state is

(A) He > N > O > B

(B) O > N > B > He

(D) N > O > B > He

Answer: (A)

7. Based on the molecular orbital theory, which one of the following statements with respect to N₂, N₂⁺, O₂ and O₂⁺ is correct?

(A) Bond orders of N₂ and O₂ are higher than their corresponding cations.

(B) Bond energy of N₂⁺ is higher than that of N₂, whereas bond energy of O₂⁺ is lower than that of O₂.

(D) The bond in N₂⁺ is shorter than that is N₂, whereas bond in O₂ is shorter than that in O₂⁺.

Answer: (C)

8. Which one of the following statements is incorrect about the diborane molecule?

(A) B-H^t bond is 2-centre-2-electron bond (H^t : terminal hydrogen).

(B) BH^bB bond is a 3-centre-2-electron bond (H^b: bridged hydrogen).

(D) The B-H^t bond distance is longer than B-H^b bond distance (H^t : terminal hydrogen, H^b: bridged hydrogen).

Answer: (D)

9. Given below are Newman projections of ethylene glycol and 1, 2-difluoroethane about their respective C-C bonds. The most stable conformations (lowest energy) of ethylene glycol and 1, 2-difluoroethane are

(A) I and III respectively.

(B) I and IV respectively.

(D) II and IV respectively.

Answer: (A)

10. In the reaction given below, choose the condition that gives an anti-Markovnikov’s product.

(A) Peroxide/HCl

(B) Aqueous mercuric acetate treatment

(D) Sulfuric acid addition

Answer: (C)

11. Which one of the following hexoses will give an osazone that has a different melting point from that of the osazone obtained from D (+) glucose?

Answer: (C)

12. A molecule in solution crystallizes into two different crystal forms with rate constants of 0.02 s⁻¹ and 0.13 s⁻¹. If the crystallization is assumed to be under kinetic control, then the half-life (in seconds, rounded off to one decimal place) of the molecular is ________.

Answer: (4.5 to 4.7)

13. The standard potential (E^θ_cell) for a cell reaction given below is +0.7 V. The standard reactions free energy (∆_rG^θ) for this cell is _____ kJ mol⁻¹ (correct up to two decimal places). (Given: Faraday constant, F = 96500 C mol⁻¹)

Au³⁺ (aq) + 3 Ag(s) → Au(s) + 3Ag⁺ (aq)

Answer: (-202.66 to -202.64)

14. The activation energy (E_a) estimated for a reaction from the Arrhenius equation is 21 kJ mol⁻¹. If the frequency factor is assumed to be independent of temperature, then the ratio of the rate constants determined at 298 K and 260 K is ______ (rounded off to two decimal places). (Given: Gas constant, R = 8.315 J K⁻¹ mol⁻¹)

Answer: (3.44 to 3.46)

15. At a given pressure, a substance is heated from 2000 K to 2600 K. If the entropy of the substance is 60 J K⁻¹ mol⁻¹, and is assumed to be constant over the given temperature range, then the change in the chemical potential (in kJ mol⁻¹) of the substance is _________.

Answer: (-36 to -36)

XL: Life Sciences – Q : Biochemistry

Q1 – Q10 carry one mark each.

1. Which one of the following hormones initiates a signaling cascade by directly binding to an intra-cellular receptor?

(A) Insulin

(B) Gonadotropin

(D) Epinephrine

Answer: (C)

2. Which one of the following bonds is NOT present in ATP ?

(A) Phosphoester

(B) Phosphoanhydride

(D) α-Glycosidic

Answer: (D)

3. The reaction involved in the direct conversion of L-phenylalanine of L-tyrosine is

(A) Hydroxylation

(B) Decarboxylation

(D) Reduction

Answer: (A)

4. The humn major histocompatibility complex (MHC) is

(A) Polygenic and monomorphic

(B) Polygenic and polymorphic

(D) Monogenic and monomorphic

Answer: (B)

5. Har Gobind Khorana and Marshall Nirenberg elucidated the genetic code by using a cell-free protein synthesizing system. It was found that poly(U) and poly(C) result in the synthesis of poly(L-Phe) and poly(L-pro), respectively. Based on these observations, which one of the following conclusions is correct?

(A) Codon GGG specifies L-Phe and codon AAA specifies L-Pro

(B) Codon CCC specifies L-Phe and codon UUU specifies L-pro

(D) Codon UUU specifies L-Phe and codon CCC specifies L-Pro

Answer: (D)

6. Binding of an antibody to its cognate antigen does NOT involve

(A) Covalent bonds

(B) Electrostatic foces

(D) Hydrogen bonds

Answer: (A)

7. A globular protein of molecular weight 50 kDa exists as a mixture of monomers and dimmers in solution. The most appropriate technique for the separation of these two forms of the protein is

(A) Thin layer chromatography

(B) Ion exchange chromatography

(D) Paper chromatography

Answer: (C)

8. Choose the correct order of molecules according to their ability to diffuse across as lipid bilayer.

(A) CO₂ > H₂O > Glucose > RNA

(B) CO₂ > Glucose > H₂O > RNA

(D) H₂O > CO₂ > RNA > Glucose

Answer: (A)

9. When one glucose unit from glycogen gets converted to lactate in the muscle, the ne number of ATP molecules produced is _______.

Answer: (3 to 3)

10. Considering that the three pK_as of histidine are pK₁ = 1.8, pK₂ = 9.2 and pK_R = 6.0, its isoelectric point will be ______ (rounded off to one decimal place).

Answer: (7.5 to 7.7)

Q11- Q20 carry two marks each.

11. One mole of a native protein upon N-terminal analysis yielded one mole each of Asp and Val. Therefore, the protein in its native state exists as a

(A) Monomer

(B) Homo-dimer

(D) Tetramer

Answer: (C)

12. The prosthetic groups/cofactors involved in both 1e⁻ and 2e⁻ transfer in the mitochondrial electron transport chain are

(A) NAD and NADP

(B) NAD and FAD

(D) Coenzyme Q and FMN

Answer: (D)

13. Match the items in Group I with the most appropriate items in Group II and choose the correct option.

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

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

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

Answer: (B)

14. The correct combination of glycosidic linkages present in glycogen is

(A) α 1 → 4 and α 1 → 6

(B) α 1 → 4 and β 1 → 6

(D) α 1 → 6 and β 1 → 6

Answer: (A)

15. Polypeptides are either biosynthesized on the ribosomes using an mRNA template or chemically synthesized by the Merrifield’s solid phase method. The correct directions of peptide synthesis are

(A) C→ N direction on the ribosomes and N → C direction on the solid phase

(B) N → C direction on the ribosomes and C → N direction on the solid phase

(D) C → N direction in both cases

Answer: (B)

16. A solution absorbs 20% of the incident light in a cuvette of path length 1.0 cm. The amount of light transmitted by the same solution in a curvette of 3.0 cm path length is _______% (rounded off to one decimal place).

Answer: (51.1 to 51.3)

17. The second pKa of phosphoric acid is 6.8. The ratio of Na₂HPO₄ to NaH₂PO₄ required to obtain a buffer of pH 7.0 is _______ (rounded off to two decimal places).

Answer: (1.58 to 1.60)

18. A PCR in a 100 μL reaction volume, containing two primers at a concentration of 0.2 μM each, is set up to amplify a 250 base pair DNA fragment. Consider the average molecular weight of one base pair as 660 Da. If the primers are fully consumed by the end of the reaction, the amount of the final PCR product formed is ________μg (rounded off to one decimal place).

Answer: (3.2 to 3.4)

19. An enzyme obeying Michaelis-Menten kinetics shows as reaction velocity (v) of 10 μmol/min when the substrate concentration [S] equals its K_M. The maximal velocity V_max for this enzyme is _______ μmol/min (correct to integer number). (K_M is Michaelis-Menten constant)

Answer: (20 to 20)

20. The enzyme glucose isomerase catalyzes the inter-conversion of glucose and fructose as shown.

The ∆G’₀ for this reaction is zero kcal/mol. After adding glucose isomerase to a 0.12 M glucose solution and allowing the reaction to attain equilibrium, the final concentration of fructose in the reaction mixture will be _____ mM.

Answer: (60 to 60)

XL: Life Sciences – R: Botany

Q1 – Q10 carry one mark each.

1. Indefinite stamen is a characteristic feature of which of the following plant families?

(A) Malvaceae

(B) Apocynaceae

(D) Brassicaceae

Answer: (A)

2. In natural condition, which of the following plants DOES NOT exhibit anomalous secondary growth?

(A) Rice

(B) Aloe

(D) Dracaena

Answer: (A)

3. In a typical angiosperm under natural condition, primary meristems are usually established during

(A) Gametogenesis

(B) Embryogenesis

(D) Secondary growth

Answer: (B)

4. 2-Methoxy-3, 6-dichlorobenzoic acid belongs to which class of plant growth regulators?

(A) Synthetic auxin

(B) Synthetic cytokinin

(D) Brassinosteroid

Answer: (A)

5. In a typical green plant, the first product of Calvin cycle is

(A) Oxaloacetic acid

(B) Succinic acid

(D) 3-Phosphoglyceric acid

Answer: (D)

6. Among the following, which best describes an organism that lives at the expense of other organisms, harmful but usually not killing?

(A) Predator

(B) Symbiotic

(D) Parasite

Answer: (D)

7. The oleo-gum resin asafoetida (hing) is obtained from the cut surface of

(A) Stem

(B) Root

(D) Fruit

Answer: (B)

8. ‘Bakanae’ disease or ‘foolish seedling’ disease is caused by

(A) Fungus

(B) Bacterium

(D) Mycoplasma

Answer: (A)

9. Which of the following chemicals is used for doubling of chromosome numbers during production of ‘doubled haploids’ in crop plants?

(A) Hygromycin

(B) Kanamycin

(D) Glufosinate

Answer: (C)

10. An mRNA of a nuclear encoded plant gene, DSH20 has an ORF of 1353 nucleotides. Provided that average molecular weight of amino acid is 110 Dalton (Da) calculated molecular weight of DSH20 protein in kDa (round off to 1 decimal place) is ______

Answer: (49.5 to 49.5)

Q11 – Q20 carry two marks each.

11. Group I, Group II and Group III represent enzyme, product of the enzymatic reaction, and metabolic process, respectively.

The CORRECT combination fro Group I, Group II and Group III is

(A) P-ii-1, Q-iv-3, R-v-2, S-iii-4

(B) P-ii-1, Q-i-3, R-v-4, S-iii-2

(D) P-iii-1, Q-i-3, R-iv-4, S-ii-2

Answer: (B)

12. Match the following in CORRECT combination between Group I and Group II with reference to the agents that interfere with oxidative phosphorylation

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

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

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

Answer: (A)

13. In relation to Agrobacterium mediated genetic engineering in plants, match the following in CORRECT combination

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

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

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

Answer: (C)

14. Match the plant part (Group I) with the product obtained (Group II) and the representative plant species (Group III) in CORRECT combination

(A) P-ii-1, Q-i-3, R-iv-2, S-iii-4

(B) P-ii-1, Q-i-2, R-iv-4, S-iii-3

(D) P-iv-3, Q-i-2, R-ii-4, S-iii-1

Answer: (D)

15. Select the CORRECT combination by matching the disease, causal organism and the affected

(A) P-iv-1, Q-iii-3, R-i-2, S-ii-4

(B) P-ii-1, Q-i-6, R-iv-4, S-iii-2

(D) P-iv-1, Q-ii-3, R-iii-2, S-i-5

Answer: (A)

16. Match the following alkaloids with their uses and source plants in CORRECT combination

(A) P-ii-3, Q-iv-1, R-iii-4, S-i-2

(B) P-ii-1, Q-i-3, R-iv-4, S-iii-2

(D) P-iii-4, Q-ii-1, R-iv-3, S-i-2

Answer: (A)

17. Match the following ecological terms with their appropriate definitions

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

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

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

Answer: (B)

18. Arrange the following ‘water reservoirs of earth’ in decreasing order of water volume

P-Streams

Q-Groundwater

R-Glaciers

S-Lakes and inland seas

(A) R-Q-S-P

(B) P-Q-R-S

(D) R-P-Q-S

Answer: (A)

19. Selection markers and the corresponding genes used in plant genetic engineering are given below

Choose the CORRECT combination

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

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

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

Answer: (C)

20. A double homozygous mutant develops green and wrinkled seeds. When it was crossed with true-breeding plant having yellow and round seeds, all the F1 plants developed yellow and round seeds. After self-fertilization of F1, the calculated percentage probability of plants with green and wrinkled seeds in the F2 population (round off to 2 decimal places) is ________

Answer: (6.25 to 6.25)

XL: Life Sciences – S: Microbiology

Q1 – Q10 carry one mark each.

1. The technique of microbial “pure culture” was pioneered by

(A) Edward Jenner

(B) Louis Pasteur

(D) Robert Koch

Answer: (D)

2. The antibacterial trimethoprim is an inhibitor of

(A) dihydrofolate reductase

(B) dihydropteroate synthetase

(D) serine hydroxymethyl transferase

Answer: (A)

3. Choose the correct taxonomical hierarchy among the following:

(A) Species, Genus, Family, Order, Class, Phylum, Domain

(B) Species, Genus, Order, Class, Family, Phylum, Domain

(D) Species, Genus, Family, Class, Order, Phylum, Domain

Answer: (A)

4. Shifting a Sacharomyces cerevisiae culture from fermentative to aerobic respiratory mode will

(A) decrease carbon dioxide production

(B) increase alcohol production

(D) decrease ATP generation per mole of glucose

Answer: (A)

5. Which one of the following diseases is treated by a neuraminidase inhibitor?

(A) Chickenpox

(B) Polio

(D) Japanese encephalitis

Answer: (C)

6. Which one of the following does NOT provide three-dimensional images?

(A) Atomic force microscopy

(B) Confocal scanning laser microscopy

(D) Phase-contrast microscopy

Answer: (D)

7. Which one of the following will increase the resolution of a light microscope ?

(A) Decreasing the numerical aperture of the objective lens

(B) Using an objective lens with a longer working distance

(D) Increasing the wavelength of light

Answer: (C)

8. Which one of the following conditions favors maximum expression of lac operon genes in coli?

(A) Glucose-low, lactose-law, cAMP-high

(B) Glucose-high, lactose-low, cAMP-high

(D) Glucose-high, lactose-high, cAMP-low

Answer: (C)

9. Match the cellular organelle in Group I with its function in Group II

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

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

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

Answer: (B)

10. A 250 μl of bacteriophage stock containing 8 × 10⁸ phages/ml is added to 500 μl of coli culture containing 4 × 10⁸ cells/ml. The multiplicity of infection is _______.

Answer: (1 to 1)

Q11 – Q20 carry two marks each.

11. Digestion of an immunoglobulin G (IgG) molecule with pepsin will NOT

(A) generate a bivalent antigen binding fragment

(B) generate monovalent antigen binding fragments

(D) cleave the heavy chain of IgG molecule

Answer: (B)

12. Match the process involved in nitrogen or sulfur cycle in Group I with the corresponding microbe in Group II.

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

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

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

Answer: (D)

13. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

Assertion [a]: Diphtheria exotoxin is an example of A-B type toxin.

Reason [r]: The A component of the toxin is released from the host cell while the B component inhibits protein synthesis and kills the host cell.

(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)

14. Which one of the following statements about control of microbial growth is NOT correct?

(A) Nonionizing radiation leads to thymine dimmers formation in DNA

(B) Spirochetes and mycoplasma can pass through membrane filters (0.22-0.45 μm)

(D) Thermoduric bacteria can survive pasteurization

Answer: (C)

15. An example of a differential and selective medium in which colonies of Gram-negative bacteria produce large amounts of acidic products and appear green with a metallic sheen is

(A) Blood agar

(B) EMB agar

(D) Mannitol salt agar

Answer: (B)

16. Which one of the following is an example of substrate level phosphorylation?

(A) Glucose to Glucose 6-phosphate

(B) Fructose 6-phosphate to Fructose 1, 6-biphosphate

(D) 2-phosphoglycerate to Phosphoenolpyruvate

Answer: (C)

17. A bacterial culture containing 3 × 10⁵ live cells was exposed to a newly developed sterilizing agent. After 30 minutes of exposure, 3 live cells remained in culture. The decimal reduction time (in minutes) for the new agent is ______.

Answer: (6 to 6)

18. A bacterial culture has a generation time of 34 minutes. The time taken (in minutes, rounded off to two decimal places) for the OD₅₅₀ of this exponentially growing culture to increase from 0.25 to 0.85 is ______.

Assume that OD₅₅₀ has a linear relationship with the cell density.

Answer: (58.50 to 61.50)

19. A 100 μl aliquot (10⁻⁴ dilution) of the bacterial culture plated on the nutrient agar gave 4 colonies. The bacterial stock concentration (in million cells/ml, rounded off to one decimal place) is _____.

Answer: (0.4 to 0.4)

20. A continuous bacterial culture carried out in a chemostat is set to a flow rate of 40 ml/hr. The culture volume is equivalent to that of a cubical container having 10 cm sides. The dilution rate (in hr⁻¹, rounded off to two decimal places) of this system is ________.

Answer: (0.04 to 0.04)

XL: Life Sciences – T: Zoology

Q1 – Q10 carry one mark each.

1. Which ONE of following leucocytes is phagocytic and has clear cytoplasm?

(A) Eosinophil

(B) Monocyte

(D) Basophil

Answer: (B)

2. Which ONE of the following techniques can be used for detecting the subcellular localization of serotonin receptor in intact cells?

(A) Immunoelectron microscopy

(B) SDS-PAGE

(D) Differential centrifugation

Answer: (A)

3. Which ONE of the following is NOT a site for in situ conservation?

(A) Biosphere reserve

(B) Wild life sanctuary

(D) Biodiversity hotspot

Answer: (C)

4. Which ONE of the following is the precursor molecule for corticosteroids?

(A) Androgen

(B) Estrogen

(D) Mineralocorticoids

Answer: (C)

5. Transitional epithelia is found in which ONE of the following organs?

(A) Liver

(B) Lung

(D) Urinary bladder

Answer: (D)

6. Visual signal transduction cascade is activated by rhodopsin and involves degradation rather than synthesis of which ONE of the following second messenger molecules?

(A) cAMP

(B) IP3

(D) DAG

Answer: (C)

7. The genomes of both human and Drosophila code for an amylase that acts on the same substrate. However, the sequence of nucleotides in the genes encoding the two is dissimilar. This is an example of which ONE of the following types of evolution?

(A) Neutral

(B) Directional

(D) Divergent

Answer: (C)

8. “Round dance” is performed by forager bees to indicate the distance between a food source and their colony. Which ONE of the following best represents this distance?

(A) 45 meters

(B) 450 meters

(D) More than 2000 meters

Answer: (A)

9. Which ONE of the following phyla have choanocytes?

(A) Ctenophora

(B) Nematoda

(D) Porifera

Answer: (D)

10. Which ONE of the following glial cells is NOT derived from the ectoderm?

(A) Astrocytes

(B) Microglial cells

(D) Ependyma

Answer: (B)

Q11 – Q20 carry two marks each.

11. Tarantulas and mosquitoes both belong to the phylum Arthropoda. Which ONE of the following represents the correct number of legs in them respectively?

(A) 6 and 6

(B) 6 and 8

(D) 8 and 6

Answer: (D)

12. Match the following subcellular organelles in Column I with associated functions in Column II

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

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

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

Answer: (C)

13. Match the following genetic disorders in Column I with associated typical chromosomal changes mentioned in Column II

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

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

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

Answer: (D)

14. Match the following components listed in Column I with their respective organs in Column II

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

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

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

Answer: (A)

15. Match the following digestive enzymes in Column I with their respective functions in Column II.

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

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

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

Answer: (B)

16. Which ONE of the following graphs represents the relationship between ventricular end-diastolic volume and cardiac output in a healthy adult individual at rest (solid line) and upon exercise (dotted line)?

Answer: (A)

17. Match the household insect vectors in Column I with their associated diseases in Column II.

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

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

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

Answer: (D)

18. Match the proteins in Column I with the organs in which they are maximally expressed in Column II.

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

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

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

Answer: (C)

19. The graph below shows the activity of enzyme pepsin in the presence of inhibitors aliphatic alcohols (P) or N-acetyl-1-phenylalanine (Q). Which ONE of the following represents the nature of inhibition by P and Q, respectively?

(A) Non-competitive and competitive

(B) Competitive and non-competitive

(D) Competitive and uncompetitive

Answer: (B)

20. In Drosophila, the red eye phenotype (W) is dominant over the recessive white eye mutant (w). In a mixed population of red and white eye flies of 10,000 individuals, 3,600 flies were white eyed. The percentage of the heterozygous red eye flies in this population is ________.

Answer: (48 to 48)

XL: Life Sciences – U : Food Technology

Q1 – Q10 carry one mark each.

1. The enzyme majorly involved in postmortem degradation of muscle proteins is

(A) Trypsin

(B) Calpin

(D) Pepsin

Answer: (B)

2. Which of the following is the correct pair of essential fatty acid?

(A) Oleic acid and Lenoleic acid

(B) Lenoleic acid and Linolenic acid

(D) Linolenic acid and Oleic acid

Answer: (B)

3. Nisin A is produced by

(A) Aspergillus niger

(B) Acttobacter aceti

(D) Clostridium perfringens

Answer: (C)

4. Which of the following bacteria will stain purple color after Gram staining?

(A) Bacillus subtilis

(B) Escherichia coli

(D) Yersinia pestis

Answer: (A)

5. The enzyme system used for removal of glucose from egg white prior to its drying consists of

(A) Glucose oxidase and Catalase

(B) Glucosidase and Glucoisomerase

(D) Gluccoamylase and Glucose oxidase

Answer: (A)

6. The INCORRECT pair of food borne illness and its causative microorganism is

(A) Brucellosis-Brucella Sp.

(B) Peptic ulcers-Bacillus subtilis

(D) Q fever-Coxiella burnatii

Answer: (B)

7. Which of the following is commonly used as preservative in the tomato sauce?

(A) Sodium sulphite

(B) Potassium sorbate

(D) Sodium benzoate

Answer: (D)

8. A fluid with flow behvaviour index less than one (n < 1) is

(A) Dilatant

(B) Pseudoplastic

(D) Newtonian

Answer: (B)

9. The velocity of 2.2 μm diameter fat particles inside a cetribfuge, running at 6000 rpm and 20°C, is 0.25 mm s⁻¹. The velocity of 1.5 μm diameter fat particles inside the same centrifuge running at 7500 rpm and same temperature (round off to 2 decimal places) will be ____ mm s⁻¹.

Answer: (0.15 to 0.21)

10. The initial population of a bacterial strain increases from 1 × 10⁴ cells per mL to 1 × 10⁶ cells per mL in 120 minutes. The generation time for this strain (round off to 2 decimal places) is ______ minutes.

Answer: (17.00 to 19.00)

Q11 – Q20 carry two marks each.

11. Match the protein in Column I with its food source in Column II.

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

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

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

Answer: (D)

12. Match the carbohydrate in Column I with corresponding enzyme used for its hydrolysis in Column II.

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

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

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

Answer: (A)

13. Match the edible oil refining stage in Column I with its purpose in Column II.

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

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

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

Answer: (D)

14. Match the food material in Column I with its related term in Column II.

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

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

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

Answer: (B)

15. Match the components/system in Column I with the peeling method for fruits and vegetables in Column II.

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

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

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

Answer: (C)

16. Which among the given options correctly explains the nature of the microbial culture represented by lines 1, 2 and 3 in the following figure?

Answer: (B)

17. Match the equation/law in Column I with its application in Column II.

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

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

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

Answer: (C)

18. Match the absorber used in modified atmosphere packaging and storage in Column I with the scavenger in Column II.

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

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

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

Answer: (A)

19. During extrusion cooking, food materials are generally subjected to a combination of

(A) high shear and low pressure

(B) high temperature and high shear

(D) low shear and low pressure

Answer: (B)

20. An orange juice flowing at 0.80 kg s⁻¹ enters a counter current double pipe heat exchanger at 20°C and leaves at 72° Inlet and outlet temperatures of the hot water used as heating medium in the exchanger are 81°C and 74°C, respectively. The specific heat of the orange juice is 3.74 kJ kg⁻¹ K⁻¹ and overall heat transfer coefficient is 492 W m⁻² K⁻¹. The heat transfer surface area (round off to 2 decimal places) will be ______ m².

Answer: (11.00 to 14.00)