## GATE Exam 2020 Mechanical Engineering (ME-1) Question Paper With Answer Key

GATE-2020

ME-1: Mechanical Engineering

GA – General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.

(A)  fox’s

(B)  crocodile’s

(C)  crocodile

(D)  fox

2. Jofra Archer, the England fast bowler, is ____ than accurate.

(A)  more fast

(B)  faster

(C)  less fast

(D)  more faster

3. Select the word that fits the analogy:

Build : Building :: Grow : ______

(A)  Grown

(B)  Grew

(C)  Growth

(D)  Growed

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A)  as opposed to what I have said

(B)  despite what I have said

(C)  in addition to what I have said

(D)  contrary to what I have said

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.

(A)  1

(B)  3

(C)  4

(D)  6

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A)  Funds raised through unwilling contributions on web-based platforms.

(B)  Funds raised through large contributions on web-based platforms.

(C)  Funds raised through coerced contributions on web-based platforms.

(D)  Funds raised through voluntary contributions on web-based platforms.

7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.

(A)  βα and αβ

(B)  ββ and αα

(C)  αβ and ββ

(D)  βα and ββ

8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.

(A)

(B)

(C)

(D)

9. Select the graph that schematically represents BOTH y = xm and y = x1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ________.

(A)  58.5%

(B)  58.8%

(C)  59.0%

(D)  59.3%

ME1: Mechanical Engineering

Q1 – Q25 carry one mark each.

1. Multiplication of real valued square matrices of same dimension is

(A)  associative

(B)  commutative

(C)  always positive definite

(D)  not always possible to compute

2. The value of  is

(A)  c

(B)  c + 1

(C)

(D)

3. The Laplace transform of a function f(t) is  Then, f(t) is

(A)

(B)

(C)

(D)

4. Which of the following function f(z), of the complex variable z, is NOT analytic at all the points of the complex plane?

(A)  f(z) = z2

(B)  f(z) = ez

(C)  f(z) = sin z

(D)  f(z) = log z

5. The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P > 0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are

(A)  BF and DH only

(B)  BF, DH and GC only

(C)  BF, DH, GC, CD and DE only

(D)  BF, DH, GC, FG and GH only

6. A single-degree-freedom oscillator is subjected to harmonic excitation F(t) = F0 cos(ωt) as shown in the figure.

The non-zero value of ω, for which the amplitude of the force transmitted to the ground will be F0, is

7. The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ – τ plane is 1 MPa, the Mohr’s circle representation of the state-of-stress is given by

(A)  a circle with a radius equal to principal stress and its center at the origin of the σ – τ plane

(B)  a point on the σ axis at a distance of 10 units from the origin

(C)  a circle with radius of 10 units of the σ – τ plane

(D)  a point on the τ axis at a distance of 10 units from origin

8. A four bar mechanism is shown below.

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be

(A)  80 mm

(B)  200 mm

(C)  300 mm

(D)  350 mm

9. A helical gear with 20° pressure angle and 30° helix angle mounted at the mid-span of a shaft that is supported between two bearings at the ends. The nature of the stress induced in the shaft is

(A)  normal stress due to bending only

(B)  normal stress due to bending in one plane and axial loading; shear stress due to torsion

(C)  normal stress due to bending in two planes and axial loading; shear stress due to torsion

(D)  normal stress due to bending in two planes; shear stress due to torsion

Answer: (A OR C)

10. The crystal structure of γ iron (austenite phase) is

(A)  BCC

(B)  FCC

(C)  HCP

(D)  BCT

11. Match the following.

(A)  P-2, Q-3, R-4, S-1

(B)  P-1, Q-1, R-3, S-2

(C)  P-3, Q-3, R-1, S-3

(D)  P-4, Q-3, R-2, S-1

12. The base of a brass bracket needs rough grinding. For this purpose, the most suitable grinding wheel grade specification is

(A)  C30Q12V

(B)  A50G8V

(C)  C90J4B

(D)  A30D12V

13. In the Critical Path Method (CPM), the cost-time slope of an activity is given by

14. Froude number is the ratio of

(A)  buoyancy forces to viscous forces

(B)  inertia forces to viscous forces

(C)  buoyancy forces to inertia forces

(D)  inertia forces to gravity forces

15. Match the following non-dimensional numbers with the corresponding definitions:

(A)  P-1, Q-3, R-2, S-4

(B)  P-3, Q-1, R-2, S-4

(C)  P-4, Q-3, R-1, S-2

(D)  P-3, Q-1, R-4, S-2

16. The velocity filed of an incompressible flow in a Cartesian system is represented by  Which one of the following expressions for v is valid?

(A)  −4xz + 6xy

(B)  −4xy − 4xz

(C)  4xz – 6xy

(D)  4xy + 4xz

17. For an ideal gas, the value of the Joule-Thomson coefficient is

(A)  positive

(B)  negative

(C)  zero

(D)  indeterminate

18. For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (T) versus specific entropy (s) diagram. CP is the specific heat at constant pressure and C­V is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is

(A)

(B)  CP/CV

(C)

(D)  CV/CP

19. For three vectors  and  are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of  is _______.

Answer: (6 to 6)

20. A flywheel is attached to an engine to keep its rotational speed between 100 rad/s and 110 rad/s. If the energy fluctuation in the flywheel between these two speeds is 1.05 kJ then the moment of inertia of the flywheel is _______ kg.m2 (round off to 2 decimal places).

Answer: (0.98 to 1.02)

21. A balanced rigid disc mounted on a rigid roto has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure.

The rotor is driven by a motor at uniform angular speed of 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is _______ N (round off to 2 decimal places).

Answer: (0.09 to 0.11)

22. A sheet metal with a stock hardness of 250 HRC has to be sheared using a punch and a die having a clearance of 1 mm between them. If the stock hardness of the sheet metal increases to 400 HRC, the clearance between the punch and the die should be _______mm.

Answer: (1.0 to 1.3)

23. A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is _______ (round off to 2 decimal places).

Answer: (0.90 to 0.95)

24. The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of 6 in two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressors at 300 K and 100 KPa. If the properties of gas are constant, the intercooling pressure for minimum compressor work is ________kPa (round off to 2 decimal places).

25. In a concentric tube counter-flow heat exchanger, hot oil enters at 102°C and leaves at 65° Cold water enters at 25°C and leaves at 42°C. The log mean temperature difference (LMTD) is __________°C (round of to one decimal place)

Answer: (48.8 to 49.8)

Q26 – Q55 carry two marks each.

26. The evaluation of the definite integral  by using Simpson’s 1/3rd (one-third) rule with step size h = 0.6 yields

(A)  0.914

(B)  1.248

(C)  0.581

(D)  0.592

27. A vector field is defined as

where  are unit vectors along the axes of right-handed rectangular /Cartesian coordinate system. The surface integral  is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 1 and 2, respectively, is

(A)  0

(B)  2π

(C)  4π

(D)  8π

28. Bar of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure.

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

(A)  Tensile and compressive load specimens

(B)  Torsional load specimen

(C)  Bending load specimen

(D)  None of the specimens

29. The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to massless elastic cord that has a stiffness 5 N/m.

The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity v of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is

(A)  0.83

(B)  1.07

(C)  1.36

(D)  1.50

30. The truss shown in the figure has four members of length l and flexural rigidity EI, and one member of length l√2 and flexural rigidity 4EI. The truss is loaded by a pair of forces of magnitude P, as shown in the figure.

The smallest value of P, at which any of the truss members will buckle is

31. A rigid mass-less rod of length L is connected to a disc (pulley) of mass m and radius r = L/4 through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness 2k is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness k at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut.

Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is

32. A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively are

(A)  0.45 and 38.84

(B)  0.39 and 38.84

(C)  0.39 and 44.72

(D)  0.45 and 44.72

33. For an assembly line, the production rate was 4 pieces per hour and the average processing time was 60 minutes. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent. As a result of this change in the processing time, the WIP inventory

(A)  decreases by 25%

(B)  increases by 25%

(C)  decreases by 30%

(D)  increases by 30%

34. A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density specific heat of the metal are 8500 kg/m3 and 400 J/kg.K, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in W/m2.K) between the metal bead and the fluid steam is

(A)  283.3

(B)  299.8

(C)  149.9

(D)  449.7

35. Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is ________ (round off to 2 decimal places).

Answer: (-1.00 to -0.98)

36. An analytic function of a complex variable z = x + iy(i = √−1) is defined as f(z) = x2 – y2 + iψ(x, y), where iψ(x, y) is a real function. The value of imaginary part of f(z) at z = (1+ i) is ________( round off to 2 decimal places).

Answer: (1.99 to 2.01)

37. In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force F1 is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F2 when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch, and the coefficient of friction does not change, then the ratio F1/F2 is _______ (round off to 2 decimal places).

Answer: (0.85 to 0.89)

38. A cam with a translating flat-face follower is desired to have the follower motion y(θ) = 4[2πθ – θ2], 0 ≤ θ ≤ 2π. Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radius is _______ mm (round off to one decimal place).

Answer: (47.9 to 48.1)

39. A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown.

For an external load of 10 kN applied at the ip of the steel bar, the resultant shear load on the bolt at B, is _______ kN (round off to one decimal place).

Answer: (15.9 to 16.1)

40. The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modeled as cantilever.

Taking the density of water as 1000 kg/m3, and the acceleration due to gravity as 10 m/s2, the maximum absolute bending moment developed in the cantilever is ______kN∙m (round off to the nearest integer).

Answer: (104 to 106)

41. The magnitude of reaction force at joint C o the hinge-beam shown in the figure is _______ kN (round off to 2 decimal places).

Answer: (19.95 to 20.05)

42. A slot of 25 mm × 25 mm is to be billed in a workpiece of 300 mm length using a side and face milling cutter of diameter 100 mm, width 25 mm and having 20 teeth.

For a depth of cut 5 mm, feed per tooth 0.1 mm, cutting speed 35 m/min and approach and over travel distance of 5 mm each, the time required for milling the slot is _____ minutes (round off to one decimal place).

Answer: (7 to 9)

43. The following data applies to basic shaft system:

tolerance for hole = 0.002 mm,

tolerance for shaft = 0.001 mm,

allowance = 0.003 mm,

basic size = 50 mm.

The maximum hole size is ____ mm (round off to 3 decimal places).

Answer: (50.005 to 50.005)

44. A steel part with surface area of 125 cm2 is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation :

I = 12 + 0.2t

where, I = current (A) and t = time (minutes). The part is a submerged in the plating solution for a duration of 20 minutes for plating purpose. Assuming the cathode efficiency of chromium to be 15% and the plating constant of chromium acid sulphate to be 2.50 × 102 mm3/A∙s, the resulting coating thickness on the part surface is _______ μm (round off to one decimal place).

Answer: (0 to 0)

45. In a turning process using orthogonal tool geometry, a chip length of 100 mm is obtained for an uncut chip length of 250 mm.

The cutting conditions are: cutting speed = 30 m/min, rake angle = 20°.

The shear plane angle is _______ degrees (round off to one decimal place).

Answer: (22 to 25)

46. The thickness of a steel plate with material strength coefficient of 210 MPa, has to be reduced from 20 mm to 15 min in a single pass in two-high rolling mill with a roll radius of 450 mm and rolling velocity of 28 m/min. If the plate has a width of 200 mm and its strain hardening exponent, n is 0.25, the rolling force required for the operation is ______ kN (round off to 2 decimal places).

Answer: (1164 to 1168)

47. Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much as B, and the upper limit for production of B is 10 kg per day, and (ii) the respective state regulations restrict Shveta’s production of A to less than 20 kg per day, and Ashok’s production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold.

The absolute value of the difference in daily (optimal) revenue of Shveta and Ashok is _________ thousand Rupees (round off to 2 decimal places).

Answer: (9.90 to 10.10)

48. Consider two cases as below.

Case 1: A company buys 1000 pieces per year of a certain part from vendor ‘X’. The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is 10% per year.

Case 2: For the same part, another vendor ‘Y’ offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from ‘X’ and 200 pieces per year from ‘Y’.

Assume the cost of downtime as Rs. 200 per hour. The percentage reduction in the annual cost for Case 2, as compared to Case 1 is ______ (round off to 2 decimal places).

Answer: (8.19 to 8.23)

49. Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter D. We know that the velocity profile forms a paraboloid about the pipe centre line, given by:   where C is a constant. The rate of kinetic energy (in J/s) at the control surface A-B, as shown in the figure, is proportional to Dn. The value of n is ______.

Answer: (8 to 8)

50. Air discharges steadily through a horizontal nozzle and impings one a stationary vertical plate as shown in figure.

The inlet and outlet area of the nozzle are 0.1 m2 and 0.02 m2, respectively. Take air density as constant and equal to 1.2 kg/m3. If the inlet gauge pressure of air is 0.36 kPa, the gauge pressure at point O on the plate is ______ kPa (round off to two decimal places)

Answer: (0.37 to 0.45)

51. Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ______ kJ/kg (round off to nearest integer).

Answer: (244 to 246)

52. One kg of air, initially at a temperature of 127°C, expands reversible at a constant pressure until the volume is doubled. If the gas constant of air is 287 J/kg.K, the magnitude of work transfer is ______ kJ (round off to 2 decimal places).

Answer: (114.6 to 115.0)

53. For an ideal Rankine cycle operating between pressures of 30 bar and 0.04 bar, the work output from the turbine is 903 kJ/kg and the work input to the feed pump is 3 kJ/kg. The specific steam consumption is _______ kg/kW.h (round of to 2 decimal places).

Answer: (3.98 to 4.02)

54. For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in figure.

The diameter at this section is 3 m. The hub and tip diameters of the blade are 2 n and 4 m, respectively. The water volume flow rate is 100 m3/s. The rotational speed of the turbine is 300 rpm. The blade outlet angle β is _____ degrees (round off to one decimal place).

Answer: (11.0 to 14.0)

55. The indicated power developed by an engine with compression ratio of 8, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is 10 kW. The ratio of specific heats at constant pressure and constant volume is 1.4. The mechanical efficiency of the engine is 80 percent.

The brake power output of the engine is ______kW (round off to one decimal place).

Answer: (4.4 to 4.6)

## GATE Exam 2020 Mathematics (MA) Question Paper With Answer Key

GATE-2020

MA: Mathematics

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

(C)  on, at

(D)  to, at

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A)  slim

(B)  bright

(C)  obvious

(D)  uncertain

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A)  Unassociate

(B)  Inassociate

(C)  Missassociate

(D)  Dissociate

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.

(C)  Officials feel that the food-grain production target cannot be met due to floods.

(D)  Officials hope that the food-grain production target will be met due to a good rabi produce.

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

(C)  2n2 – n

(D)  2n2 + n

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.

(C)  Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.

(D)  Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

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.

(C)  P is not seated opposite to Q.

(D)  R is the left neighbor of S.

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

(C)  88.2

(D)  116.5

9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.

(A)  0

(B)  6

(C)  12

(D)  16

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

(C)  17 : 15

(D)  17 : 16

MA: Mathematics

Q1 – Q25 carry one mark each.

1. Suppose that ℑ1 and ℑ2 are topologies on X induced by metrics d1 and d2, respectively, such that ℑ1 ⊆ ℑ2. Then which of the following statements is TRUE?

(A)  If a sequence converges in (X, d2) then it converges in (X, d1)

(B)  If a sequence converges in (X, d1) then it converges in (X, d2)

(C)  Every open ball in (X, d1) is an open ball in (X, d2)

(D)  The map x → x from (X, d1) to (X, d2) is continuous

2. Let D = [−1, 1] × [−1, 1]. If the function f : D → ℝ is defined by

then

(A)  f is continuous at (0, 0)

(B)  both the first order partial derivatives of f exist at (0, 0)

(C)  ∬D |f(x, y)|1/2 dx dy is finite

(D)  ∬D |f(x, y)| dx dy is finite

3. The initial value problem y′ = y3/5, y(0) = b has

(A)  a  unique solution if b = 0

(B)  no solution if b = 1

(C)  infinitely many solutions if b = 2

(D)  a unique solution if b = 1

4. Consider the following statements:

I : log(|z|) is harmonic on ℂ\{0}

II: log(|z|) has a harmonic conjugate on ℂ\{0}

Then

(A)  both I and II are true

(B)  I is true but II is false

(C)  I is false but II is true

(D)  both I and II are false

5. Let G and H be defined by

G = ℂ\ {z =  x + iy ∈ ℂ : x ≤ 0, y = 0},

H = ℂ\ {z = x + iy ∈ ℂ : x ∈ ℤ, x ≤ 0, y = 0}.

Suppose  f: G → ℂ and g : H → ℂ are analytic functions. Consider the following statements:

I : ∫γ f dz is independent of pathys γ in G joining –i and i

II : ∫γ g dz is independent of paths γ in H joining –i and i

Then

(A)  both I and II are true

(B)  I is true but II is false

(C)  I is false but II true

(D)  both I and II are false

6. Let f (z) = e1/z, z ∈ ℂ \ {0} and let, for n ∈ ℕ,

If for a subset S of ℂ,  denotes the closure of S in ℂ, then

Answer: (A or D)

7. Suppose that

Then, with respect to the Eclidean metric on ℝ2,

(A)  both U and V are disconnected

(B)  U is disconnected but V is connected

(C)  U is connected but V is disconnected

(D)  both U and V are connected

8. If (D1) and (D2) denote the dual problems of the linear programming problems (P1) and P2), respectively, where

(P1) : minimize x1­ – 2x2 subject to –x1 +x2 = 10, x1, x2 ≥ 0,

(P2) : minimize x1 – 2x2 subject to –x1 + x2 = 10, x1 – x2 = 10, x1, x2 ≥ 0, then

(A)  both (D1) and (D2) are infeasible

(B)  (P2) is infeasible and (D2) is feasible

(C)  (D1) is infeasible and (D2) is feasible but unbounded

(D)  (P1) is feasible but unbounded and (D1) is feasible

9. If (4, 0) and (0, −1/2) are critical points of the function

f(x, y) = 5 – (α + β) x2 + βy2 + (α + 1) y3 + x3,

where α, β ∈ ℝ, then

(A)  (4, −1/2) is a point of local maxima of f

(B)  (4, −1/2) is saddle point of f

(C)  α = 4, β = 2

(D)  (4, −1/2) is a point of local minima of f

10. Consider the iterative scheme

with initial point x0 > 0. Then the sequence {xn}

(A)  converges only if x0 > 1

(B)  converges only if x0 < 3

(C)  converges for any x­0

(D)  does not converge for any x­0

11. Let C[0, 1] denote the space of all real-valued continuous functions on [0, 1] equipped with the supremum norm || ∙ ||. Let T : C[0, 1] → C[0, 1] be the linear operator defined by

Then

(A)  || T || = 1

(B)  I – T is not invertible

(C)  T is surjective

(D)  ||I + T|| = 1+ ||T||

12. Suppose that M is a 5 × 5 matrix with real entries and p(x) = det(xI – M). Then

(A)  p(0) = det(M)

(B)  every eigenvalue of M is real if p(1) + (p)2 = 0 = p(2) + p(3)

(C)  M1 is necessarily a polynomial in M of degree 4 if M is invertible

(D)  M is not invertible if M2 – 2M = 0

13. Let C[0, 1] denote the space of all real-valued continuous functions on [0, 1] equipped with the supremum norm || ∙ ||. Let f ∈[0, 1] be such that

|f(x) – f(y)| ≤ M |x – y|, for all x, y ∈ [0, 1] and for some M  > 0.

For n ∈ ℕ, let fn(x) = f(x1+1/n). If S = {fn : n ∈ ℕ}, then

(A)  the closure of S is compact

(B)  S is closed and bounded

(C)  S is bounded but not totally bounded

(D)  S is compact

14. Let K : ℝ × (0, ∞) → ℝ be a function such that the solution of the initial value problem  u(x, 0), = f(x), x ∈ ℝ, t > 0, is given by

for all bounded continuous functions f. Then the value of  is ______

Answer: (1 to 1)

15. The number of cyclic subgroups of the quaternion group  is _________

Answer: (5 to 5)

16. The number of elements of order 3 in the symmetric group S6 is _______

Answer: (80 to 80)

17. Let F be the field with 4096 elements. The number of proper subfields of F is ______

Answer: (5 to 5)

18. If (x­1*, x2*) is an optimal solution of the linear programming problem, minimize x1 + 2x2 subject to

4x1 – x2 ≥8

2x1 + x2 ≥ 10

−x1 + x2 ≤ 7

x1, x2 ≥ 0

and (λ1*, λ2*, λ3*) in an optimal solution of its dual problem, then  is equal to ______ (correct up to one decimal place)

Answer: (5.5 to 5.5)

19. Let a, b, c ∈ ℝ be such that the quadrature rule

is exact for al polynomials of degree less than or equal to 2. Then b is equal to ______ (rounded off to two decimal places)

Answer: (1.70 to 1.80)

20. Let f(x) = x4 and let p(x) be the interpolating polynomial of f at nodes 1, 2 and 3. Then p(0) is equal to _______

Answer: (36 to 36)

21. For n ≥ 2, define the sequence {xn} by

Then the sequence {xn} converges to ______ (correct up to two decimal places)

Answer: (0.25 to 0.25)

22. Let

equipped with the norm  and let T be the linear functional on L2[0, 10] given by

Then ||T|| is equal to ______

Answer: (3 to 3)

23. If {x13 x22, x23 = 10, x31, x32, x34} is the set of basic variable of a balanced transportation problem seeking to minimize cost of transportation from origins to destinations, where the cost matrix is,

and λ, μ ∈ ℝ, then x32 is equal to ______

Answer: (5 to 5)

24. Let ℤ225 be the ring of integers modulo 225. If x is the number of prime ideals and y is the number of nontrivial units in ℤ225, then x + y is equal to _______

Answer: (121 to 121)

25. Let u(x, t) be the solution of

where f is a twice continuously differential function. If f(−2) = 4, f(0) = 0, and u(2, 2) = 8, then the value of u(1, 3) is ________

Answer: (10 to 10)

Q26 – Q55 carry two marks each.

26. Let  be an orthonormal basis for a separable Hilbert space H with the inner product  Define

Then

(A)  the closure of the span {fn : n ∈ ℕ} equals H

(B)  f = 0 if  for all n ∈ ℕ

(C)   is an orthogonal subset of H

(D)  there does not exist nonzero f ∈ H such that

27. Suppose V is a finite dimensional non-zero vector space over ℂ and T : V → V is a linear transformation such that Range (T) = Nullspace (T). Then which of the following statements is FALSE ?

(A)  The dimension of V is even

(B)  0 is the only eigenvalue of T

(C)  Both 0 and 1 are eigenvalues of T

(D)  T2 = 0

28. Let P ∈ Mm×n(ℝ). Consider the following statements:

I : If XPY = 0 for all X ∈ M1×m(ℝ), then P = 0.

II : If m = n, P is symmetric and P2 = 0, then P = 0.

Then

(A)  both I and II are true

(B)  I is true but II is false

(C)  I is false but II is true

(D)  both I and II are false

29. For n ∈ ℕ, let Tn : (l1, ||∙||1) → (l, ||∙||) and T : (l1, ||∙||) be the bounded linear operators defined by

and

T(x1, x2, …) = (x1, x2 …).

Then

(A)  ||Tn|| does not converge to ||T|| as n → ∞

(B)  ||Tn – T|| converges to zero as n → ∞

(C)  for all x ∈ l1, ||Tn(x) – T(x)|| converges to zero as n → ∞

(D)  for each non-zero x ∈ l1, there exists a continuous linear functional g on l such that g(Tn(x)) does not converge to g(T(x)) as n → ∞

30. Let P(ℝ) denote the power set of ℝ, equipped with the metric

where χU and χ­V denote the characteristic functions of the subjects U and V, respectively of ℝ. The set {{m} : m ∈ ℤ} in the metric space (P(ℝ), d) is

(A)  bounded but not totally bounded

(B)  totally bounded but not compact

(C)  compact

(D)  not bounded

31. Let f : ℝ → ℝ be defined by

where χ(n n+1] is the characteristic function of the interval (n, n + 1]. for α ∈ ℝ, let Sα  = {x ∈ ℝ : f(x) > α}. Then

(A)  S1/2 is open

(B)  S5/2 is not measurable

(C)  S0 is closed

(D)  S1/3 is measurable

32. For n ∈ ℕ, let fn, gn­ : (0, 1) → ℝ be functions defined by fn(x) = xn and gn(x) = xn (1 – x).

Then

(A)  {fn} converges uniformly but {gn} does not converge uniformly

(B)  {gn} converges uniformly but {fn} does not converge  uniformly

(C)  both {fn} and {gn} converge uniformly

(D)  neither {fn} nor{gn} converge uniformly

33. Let u be a solution of the differential equation y′ + xy = 0 and let ϕ = uψ be a solution of the differential equation y′′ + 2xy′ + (x2 + 2) y = 0 satisfying ϕ(0) = 1 and ϕ′(0) = 0. Then ϕ(x) is

34. For n ∈ ℕ ⋃ {0}, let yn be a solution of the differential equation xy′′ + (1 – x)y′ + ny = 0 satisfying yn(0) = 1. For which of the following functions w(x), the integral  is equal to zero?

35. Suppose that

are metric spaces with metrics induced by the Euclidean metric of ℝ2. Let Band BY be the open unit balls around (0 0) in X and Y, respectively. Consider the following statements:

I : The closure of B­X in X is compact.

II : The closure of BY is compact.

Then

(A)  both I and II are true

(B)  I is true but II is false

(C)  I is false but II is true

(D)  both I and II are false

36. If f : ℂ \ {0} → ℂ is a function such that  and its restriction to the unit circle is continuous, then

(A)  f is continuous but not necessarily analytic

(B)  f is analytic but not necessarily a constant function

(C)  f is a constant function

(D)

37. For a subset S of a topological space, let Int(S) and  denote the interior and closure of S, respectively. Then which of the following statements is TRUE?

(A)  If S is open, then

(B)  If the boundary of S is empty, then S is open

(C)  If the boundary of S is empty, then S is open

(D)  If  is a proper subset of the boundary of S, then S is open

38. Suppose ℑ1, ℑ2, and ℑ3 are the smallest topologies on ℝ containing S1, S2 and S3, respectively, where

Then

(A)  ℑ3 ⊋ ℑ1

(B)  ℑ3 ⊋ ℑ2

(C)  ℑ1 = ℑ2

(D)  ℑ1 ⊋ ℑ2

39. Let  Consider the following statements:

I: There exists a lower triangular matrix L such that M = LLt, where Lt denotes transpose of L.

II : Gauss-Seidel method of Mx = b (b ∈ ℝ3) converges for any initial choice x0 ∈ ℝ3.

Then

(A)  I is not true when α > 9/2, β = 3

(B)  II is not true when α > 9/2, β =−1

(C)  II is not true when α = 4, β = 3/2

(D)  I is true when α = 5, β = 3

40. Let I and J be the ideals generated by {5, √10} and {4, √10} in the ring ℤ[√10] = {a+ b√10|a, b ∈ ℤ}, respectively. Then

(A)  both I and J are maximal ideals

(B)  I is a maximal ideal but J is not a prime ideal

(C)  I is not a maximal ideal but J is a prime ideal

(D)  neither I nor J is a maximal ideal

41. Suppose V is finite dimensional vector space over ℝ. If W1, W2 and W3 are subspaces of V, then which of the following statements is TRUE?

(A)  If W1  + W2 + W3 = V then span (W1 ⋃ W2) ⋃ span(W2 ⋃ W3) ⋃ span(W3 ⋃ W1) = V

(B)  If W1 ⋂ W2 = {0} and W1 ⋂ W3 = {0}, then W1 ⋂ (W2 + W3) = {0}

(C)  If W1 + W2 = W1 + W3, then W2 =  W3

(D)  If W1 ≠ V, then span(V\W1) = V

42. Let α, β ∈ ℝ, α ≠ The system

x1 – 2x2 + αx3 = 8

x1 – x2 + x4 = β

x1, x2, x­3, x4 ≥ 0

has NO basic feasible solution if

(A)  α < 0, β > 8

(B)  α > 0, 0 < β < 8

(C)  α > 0, β < 0

(D)  α < 0, β < 8

43. Let 0 < p < 1 and let

Then

(A)  |∙| defines a norm on X

(B)  |f + g|p ≤ |f|p + |g|p for all f, g ∈ X

(C)  |f +g|pp ≤ |f|pp + |g|pp for all, f, g ∈ X

(D)  if fn converges to f pointwise on ℝ, then

44. Suppose the ϕ1 and ϕ2 are linearly independent solutions of the differential equation 2x2y′′ – (x + x2)y′ + (x2 – 2)y = 0, and ϕ1(0) = 0. Then the smallest positive integer n such that  is _______

Answer: (3 to 3)

45. Suppose that  z ∈ ℂ and γ(t) = e2it, t ∈[0, 2π]. If  then the value of α is equal to ________

Answer: (56 to 56)

46. If  t ∈ [0, 2] and  then β is equal to _______ (correct up to one decimal place)

Answer: (0.5 to 0.5)

47. Let  where ω is a primitive cube root of unity. Then the degree of extension of K over ℚ is _______

Answer: (4 to 4)

48. Let α ∈ ℝ. If (3, 0, 0, β) is an solution of the linear programming problem minimize x1 + x2 + x3 – αx4 subject to

2x1 – x2 + x3 = 6

−x1 + x2 + x4 = 3

x1, x2, x3, x4 ≥ 0

then the maximum value of β – α is _________

Answer: (7 to 7)

49. Suppose that T : ℝ4 → ℝ[x] is a linear transformation over ℝ satisfying T(−1, 1, 1, 1) = x2 + 2x4, T(1, 2, 3, 4) = 1 – x2, T(2, −1, −1, 0) = x3 – x4. Then the coefficient of x4 in T(−3, 5, 6, 6) is ________

Answer: (5 to 5)

50. Let and let S be the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1.If is the unit outward normal to the tetrahedron, then the value of   is _______ (rounded off to two decimal places)

Answer: (1.30 to 1.40)

51. Let  and let S be the surface x2 + y2 + z = 1, z ≥ If  is a unit normal to S and  Then α is equal to _____

Answer: (2 to 2)

52. Let G be a non-cyclic group of order 57. Then the number of elements of order 3 in G is _______

Answer: (38 to 38)

53. The coefficient of (x – 1)5 in the Taylor expansion about x = 1 of the function  is _______ (correct up to two decimal places)

Answer: (0.04 to 0.04)

54. Let u(x, y) be the solution of the initial value problem  u(x, 0) = 1 + x2. Then the value of u(0, 1) is ______ (rounded off to three decimal places

Answer: (1.610 to 1.625)

55. The value of  is _______ (rounded off to three decimal places)

Answer: (2.710 to 2.725)

## GATE Exam 2020 Instrumentation Engineering (IN) Question Paper With Answer Key

GATE-2020

IN: Instrumentation Engineering

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds ______ tears to deceive people.

(A)  fox’s

(B)  crocodile’s

(C)  crocodile

(D)  fox

2. Jofra Archer, the England fast bowler, is _____ than accurate.

(A)  more fast

(B)  faster

(C)  less fast

(D)  more faster

3. Select the word that fits the analogy:

Build : Building :: Grow :______

(A)  Grown

(B)  Grew

(C)  Growth

(D)  Growed

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A)  as opposed to what I have said

(B)  despite what I have said

(C)  in addition to what I have said

(D)  contrary to what I have said

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then are under y for x ∈ [1, 4] is _____.

(A)  1

(B)  3

(C)  4

(D)  6

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A)  Funds raised through unwilling contributions on web-based platforms.

(B)  Funds raised through large contributions on web-based platforms.

(C)  Funds raised through coerced contributions on web-based platforms.

(D)  Funds raised through voluntary contributions on web-based platforms.

7. P, Q, R and S are to the uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as _______.

(A)  βα and αβ

(B)  ββ and αα

(C)  αβ and ββ

(D)  βα and ββ

8. The sum of the first n terms in the sequence, 8, 88, 888, …. is _______.

(A)

(B)

(C)

(D)

9. Select the graph that schematically represents BOTH y = xm and y = x1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. Te average of success rates (in percentage) of these four schools is _______.

(A)  58.5%

(B)  58.8%

(C)  59.0%

(D)  59.3%

IN: Instrumentation Engineering

Q1 – Q25 carry one mark each.

1. The unit vectors along the mutually perpendicular x, y and z axes are,  Consider the plane z = 0 and two vectors  on that plane such that  for any scalar α. A vector perpendicular to both  is ______.

(A)

(B)

(C)

(D)

2. Consider the recursive equation Xn+1 = Xn – h(F(Xn) – Xn), with initial condition X0 = 1 and h > 0 being a very small valued scalar. This recursion numerically solves the ordinary differential equation_____

(A)  Ẋ = −F(X), X(0) = 1

(B)  Ẋ = −F(X) + X, X(0) = 1

(C)  Ẋ = F(X), X(0) =1

(D)  Ẋ = F(X) + X, X(0) = 1

3. A set of linear equations is given in the form Ax = b, where A is a 2 × 4 matrix with real number entries and b ≠ Will it be possible to solve for x and obtain a unique solution by multiplying both left and right sides of the equation by AT (the super script T denotes the transpose) and inverting the matrix ATA? Answer is _______

(A)  Yes, it is always possible to get a unique solution for any 2 × 4 matrix A.

(B)  No, it is not possible to get a unique solution for any 2 × 4 matrix A.

(C)  Yes, can obtain a unique solution provided the matrix ATA is well conditioned

(D)  Yes, can obtain a unique solution provided the matrix A is well conditioned

4. In the circuit shown below, the safe maximum value for the current I is ______

(A)  1.0 A

(B)  0.5 A

(C)  0.1 A

(D)  0.05 A

5. A differentiator has a transfer function whose

(A)  phase increases linearly with frequency

(B)  magnitude remains constant

(C)  magnitude increases linearly with frequency

(D)  magnitude decreases linearly with frequency

6. A phase lead network has the transfer function  The angular frequency at which the maximum phase shift for the network occurs is _____

7. If the diodes in the circuit shown are ideal and the breakdown voltage VZ of the Zener diode is 5 V, the power dissipated in the 100 Ω resistor (in watts) is _______

(A)  0

(B)  1

(C)  25/100

(D)  225/100

8. Given f(A, B, C, D) = ∑m(0, 1, 2, 6, 8, 9, 10, 11) + ∑d(3, 7, 14, 15) is a Boolean function, where m represents min-terms and d represents don’t-cares. The minimal sum of products expression for f is______

(A)

(B)

(C)

(D)

9. A Q meter is best suited for the measurement of the ______

(A)  Quality factor of a capacitance.

(B)  Distributed capacitance of a coil.

(C)  Quality factor of piezoelectric sensor.

(D)  Turns-ratio of a transformer

10. If I is the current flowing through a Hall effect sensor and B is the magnetic flux density perpendicular to the direction of the current (in the plane of the Hall effect sensor), the Hall voltage generated is______

(A)  Directly proportional to I and inversely proportional to B

(B)  Directly proportional to both I and B

(C)  Inversely proportional to both I and B

(D)  Inversely proportional to I and directly proportional to B

11. The Boolean expression for the shaded regions as shown in the figure is _______

(A)

(B)

(C)

(D)

12. The Boolea operation performed by the following circuit at the output O is ______

(A)  O = S1 ⊕ S0

(B)

(C)  O = S1 + S0

(D)

13. Consider the Signal x[n] = sin(2πn) u[n], where  The period of this signal x[n] is _____

(A)  4

(B)  3

(C)  2

(D)  1

14. The closed loop transfer function of a control system is given by  For the input r(t) = sin t, the steady state response c(t) is _____

(A)  1

(B)

(C)

(D)

15. Let  The value of the integral ∮f(z) dz over a circle C with center (−a, 0) and radius R > 0 evaluated in the anti-clockwise direction is ____

(A)  0

(B)  2πi

(C)  −2πi

(D)  4πi

16. A player throws a ball at a basket kept at a distance. The probability that the ball falls into the basket in a single attempt is 0.1. The player attempts to throw the ball twice. Considering each attempt to be independent, the probability that this player puts the ball into the basket only in the second attempt (rounded off to two decimal places) is ____

Answer: (0.09 to 0.09)

17. Assuming ideal opamps, the output voltage at V1 in the figure shown (in volts) is ______

Answer: (7 to 7)

18. Three 400 Ω resistors are connected in delta and powered by a 400 V (rms), 50 Hz, balanced, symmetrical R-Y-B sequence, three-phase three-wire mains. The rms value of the line current (in amperes, rounded off to one decimal place) is _______

Answer: (1.7 to 1.8)

19. Consider the signal x(t) = e|t|. Let  be the Fourier transform of x(t). The value of X(j0) is _____

Answer: (2 to 2)

20. A second order system has closed loop poles located at s = −3 ± The time t at which the maximum value of the step response occurs (in seconds, rounded off to two decimal places)

Answer: (0.78 to 0.79)

21. Assume that the opamp in the circuit shown is ideal.

The value of Vx/Ix (in kΩ) is ____

Answer: (-4 to -4)

22. A sinusoid of 10 kHz is sampled at 15 k samples/s. The resulting signal is passed through an ideal low pass filter (LPF) with cut-off frequency of 25 kHz. The maximum frequency component at the output of the LPF (in kHz) is _____

Answer: (25 to 25)

23. A 200 mV full-scale dual-slope analog to digital converter (DS-ADC) has a reference voltage of 100 mV. The first integration time is set as 100 ms. The DS-ADC is operated in the continuous conversion mode. The conversion time of the DS-ADC for an input voltage of 123.4 mV (in ms, rounded off to one decimal place) is______

Answer: (223.3 to 223.5)

24. The capacitance Cx of a capacitive type sensor is (1000 x) pF, where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage 10 sin (100 πt) V. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected to ground. The cable capacitance is 100 pF. The peak of the voltage V­A at the input of the amplifier when x = 0.1 (in volts) is

Answer: (5 to 5)

25. Two 100 Ω resistors having tolerance 3% and 4% are connected in series. The effective tolerance of the series combination (in n% rounded off to one decimal place) is ______

Answer: (2.5 to 2.5 OR 3.5 to 3.5)

Q26 – Q55 carry two marks each.

26. Consider the matrix  One of the eigenvectors of M is

(A)

(B)

(C)

(D)

27. Consider the differential equation  with the initial condition x(0) = 0. The solution to this ordinary differential equation is _______

(A)  x(t) = 0

(B)  x(t) = sin(t)

(C)  x(t) = cos(t)

(D)  x(t) = sin(t) – cos(t)

28. A straight line drawn on an x-y plane intercepts the x-axis at −5 and the y-axis at 1. The equation that describes this line is _____

(A)  y = −0.5x + 1

(B)  y = x – 0.5

(C)  y = 0.5x – 1

(D)  y = 2x + 1

29. The loop transfer function of a negative feedback system is  The Nyquist plot for the above system____

(A)  encircles (−1 + j0) point once in the clockwise direction

(B)  encircles (−1 + j0) point once in the counterclockwise direction

(C)  does not encircle (−1 +  j0) point

(D)  encircles (−1 + j0) point twice in the counterclockwise direction

30. I1, I2, I3 in the figure below are mesh currents. The correct set of mesh equations for these currents, in matrix form, is ______

31. Consider the function f(x, y) = x2 + y2. The minimum value the function attains on the line x + y = 1 (rounded off to one decimal place) is ______

Answer: (0.5 to 0.5)

32. Consider two identical gas B1 and B2 each containing 10 balls o identical shapes and sizes. Bag B1 contains 7 Red and 3 Green balls, while bag B2 contains 3 Red and 7 Green balls. A bag is picked at random and a ball is drawn from it, which was found to be Red. The probability that the Red ball came from bag B1 (rounded off to ne decimal place) is ______

Answer: (0.7 to 0.7)

33. The rms of the phasor current I in the circuit shown (in amperes) is ______

Answer: (1 to 1)

34. In the circuit shown, the rms value of the voltage across the 100 Ω resistor (in volts) is _____

Answer: (115 to 116)

35. Let  and   Consider y[n] = h[n] ⊗ g[n], where ⊗ denotes the convolution operator. The value of y[2] is ______

Answer: (0 to 0)

36. The loop transfer function of a negative feedback system is given by  where K > 0. The value of K at the breakaway point of the root locus for the above system (rounded off to one decimal place) is ______

Answer: (5.0 to 5.1)

37. The system shown in Fig. (a) has a time response y(t) to an input r(t) = 10 u(t) as shown in Fig. (b), u(t) being the unit step input. Both K, τ are positive. The gain K of the system is ________

Answer: (4 to 4)

38. Assuming that the opamp used in the circuit shown in ideal, the reading of the 1 Hz bandwidth, permanent magnet moving coil (PMMC) type voltmeter (in volts) is ______

Answer: (1 to 1)

39. If the opamps in the circuit shown are ideal and Vx = 0.5 mV, the steady state value of VO (in volts, rounded off to two decimal places) is _____

Answer: (0.45 to 0.55)

40. Two T-flip flops are interconnected as shown in the figure. The present state of the flip flops are: A = 1, B = 1. The input x is given as 1, 0, 1 in the next three clock cycles. The decimal equivalent of (ABy)2 with A being the MSB and y being the LSB, after the 3rd clock cycle is ________

Answer: (7 to 7)

41. The address lines A9 …. A2 of a 10 bit, 1.023 V full-scale digital to analog converter (DAC) is connected to the data lines D7 to D0 of an 8-bit microprocessor, with A1 and A0 of the DAC grounded. Now, D7 … D0 is changed from 1010 1010 to 1010 1011. The corresponding change in the output of the DAC (in mV, rounded off to one decimal place) is _____

Answer: (3.5 to 4.5)

42. The real power drawn by a balanced load connected a 400 V, 50 Hz balanced, symmetrical 3-phase, 3-wire, RYB sequence mains is measured using the two-wattmeter method. Wattmeter W­1 is connected in the R line and wattmeter W2 is connected in the B line. The line current is measured as 1/√3 A. If the wattmeter W1 reads zero, the reading on W2(in watt) is ____

Answer: (199 to 201)

43. A 6½ digit timer-counter is set in the ‘time period’ mode of operation and the range is set as ‘ns’. For an input signal, the timer-counter displays 1000000. With the same input signal, the timer-counter is changed to ‘frequency’ mode of operation and the range is et as ‘Hz’. The display will show the number_____

Answer: (999 to 1001)

44. The circuit shown uses ideals opamp powered from a supply VCC = 5 V. If the charge qp generated by the piezoelectric sensor is o the form qp = 0.1 sin(10000πt) μC, the peak detector output after 10 cycles of qp (in volts, rounded off to one decimal place) is _____

Answer: (3.4 to 3.6)

45. A metallic strain gauge of resistance Rx with a gauge factor is 2 is bonded to a structure made of a metal with modulus of elasticity of 200 GN/m2. The value of R­x is 1 kΩ when no stress is applied. Rx is a part of quarter bridge with three identical fixed resistors of 1 kΩ The bridge is excited from a DC voltage of 4 V. The structure is subjected to a stress of 100 MN/m2. Magnitude of the output of the bridge (in mV, rounded off to two decimal places is _____

Answer: (0.95 to 1.05)

46. A laser beam of 10 mm beam diameter is focused onto an optical fibre using a thin biconvex lens as shown in the figure. The refractive index of the lens is 1.5. The refractive indices of the core and cladding of the fibre are 1.55 and 1.54 respectively. The minimum value of the focal length of the lens to attain the maximum coupling to the fibre (in mm, rounded off to one decimal place) is ______

Answer: (27.5 to 28.5)

47. As shown in the figure, a slab of finite thickness t with refractive index n2 = 1 .5, has air (n1 = 1) above and below it. Light of free space wavelength 600 nm is incident normally from air as shown. For a destructive interference to be observed at R, the minimum value of thickness of the slab t (in mm) is _____

Answer: (200 to 200)

48. Consider the finite sequence X = (1, 1, 1). The Inverse Discrete Fourier Transform (IDFT) of X is given as (x90), x(1), x(2)). The value of x(2) is ______

Answer: (0 to 0)

49. A circuit consisting of capacitors, DC voltage source and an amplifier having a voltage gain G = −5 is shown in the figure. The effective capacitance across the nodes A and B (in μF, rounded off to one decimal place) is _____

Answer: (14.5 to 15.0)

50. Consider the following state variable equations:

The initial conditions are x1(0) = 0 and x2(0) = 1. At t = 1 second, the value of x2(1) (rounded off to two decimal places) is ______

Answer: (-0.13 to -0.11)

51. Assume the diodes in the circuit shown are ideal. The current Ix flowing through the 3 kΩ resistor (in mA, rounded off to one decimal place) is ____

Answer: (1.8 to 1.8)

52. A 1000/1 A, 5VA, UPF bar-primary measuring current transformer has 1000 secondary turns. The current transformer exhibits a ratio error of −1% and a phase error of 3.438 minutes when the primary current is 1000 A. At this operating condition, the rms value of the magnetization current of the current transformer (in amperes, rounded off to two decimal places) is ____

Answer: (0.95 to 1.05)

53. The mutual inductances between the primary coil and the secondary coils of a linear variable differential transformer (LVDT) shown in the figure are M1 and M2. Assume that the self-inductances LS1 and LS2 remain constant and are independent of x. When x = 0, M1 = M2 = M0. When x is in the range ±10 mm, M1 and M2 change linearly with x. At x = +10 mm or −10 mm, the change in the magnitudes of M1 and M2 is 0.25 M0. For a particular displacement x =  D, the voltage across the detector becomes zero when |V2| = 1.25|V1|. The value of D (in mm, rounded off to one decimal place) is _____

Answer: (4.3 to 4.6)

54. In the Maxwell-Wien bridge shown, the detector D reads zero when C1 = 100 nF and R1 = 100 kΩ. The Q factor of the coil is____

Answer: (10 to 10)

55. The loop transfer function of a negative feedback system is  The phase margin of the system (in degrees, rounded off to one decimal place) is ____

Answer: (65.4 to 65.6)

## GATE Exam 2020 Geology and Geophysics (GG) Question Paper With Answer Key

GATE-2020

GG-Geology  & Geophysics

GA: General Aptitude

Q 1 – Q5 Carry one mark each.

1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.

(A)    in, of

(B)    from, of

(C)    during, from

(D)    from, from

2. He was not only accused of theft ______ of conspiracy.

(A)    rather

(B)    but also

(C)    but even

(D)    rather than

3. Select the word that fits the analogy:

Explicit : Implicit : : Express: _______

(A)    Impress

(B)    Repress

(C)    Compress

(D)    Suppress

4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.

The French-speaking couple were  upset at ______.

(A)    the in-flight announcements being made in English.

(B)    the English announcements being clearer than the French ones.

(C)    the English announcements being longer than the French ones.

(D)    equal importance being given to English and French.

5. A superadditive function f (∙) satisfies the following property

f(x1 + x2) ≥ f(x1) + f(x2)

Which of the following functions is a superadditive function for x > 1?

(A)    ex

(B)    √x

(C)    1/x

(D)    ex

Q6 – Q10 carry two marks each.

6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.

Which one of the following sequences shows the correct precedence as per the given passage?

(A)    East Asian crisis → subprime lending crisis → banking crisis global financial crisis.

(B)    Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.

(C)    Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.

(D)    Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.

7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

(A)    0°

(B)    7.5°

(C)    15°

(D)    22.5°

8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.

(A)    πa2 – a2

(B)    πa2 – √2a2

(C)    πa2 – 2a2

(D)    πa2 – 3a2

9. a, b, c are real numbers. The quadratic equation ax2 – bx + c = 0 has equal roots, which is β, then

(A)    β = b/a

(B)    β2 = ac

(C)    β3 = bc/(2a2)

(D)    b2 ≠ 4ac

10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .

(A)    8 : 23

(B)    23 : 8

(C)    23 : 31

(D)    31 : 23

Part A- Compulsory Section For All Candidates

Q1 – Q25 carry cone mark each.

1. A plagioclase with  is

(A)  albite

(B)  anorthite

(C)  oligoclase

(D)  bytownite

2. Tillite is an important constituent of the

(A)  Talchir Formation

(B)  Barakar Formation

(C)  Pachmarhi Formation

(D)  Lameta Formation

3. If the ratio of gravity to total magnetic field at the equator of t he Earth is X, then the ratio of gravity to total magnetic field at the pole of the Earth will be close to

(A)  2X

(B)  X/2

(C)  4X

(D)  X/8

4. Which of the following is NOT a point group?

(A)  222

(B)  422

(C)  432

(D)  632

5. Mississippian is an Epoch within the

(A)  Permian Period

(B)  Carboniferous Period

(C)  Triassic Period

(D)  Jurassic Period

6. The given stereoplot of the axial plane and the axis of a fold represents an/a

(A)  upright fold

(B)  vertical fold

(C)  reclined fold

(D)  recumbent fold

7. A siliciclastic sedimentary rock with <5% matrix and QFL composition of 60% quartz, 30% rock fragments and 10% feldspar, is called

(A)  quartz wacke

(B)  lithic arenite

(C)  quartz arenite

(D)  feldspathic wacke

8. Which one of the following pairs of geophysical methods is most suitable to delineate chromite ore deposits occurring at a shallow depth in a granitic terrain?

(A)  Gravity and Electrical methods

(B)  Electrical and Electromagnetic methods

(C)  Seismic and Gravity methods

(D)  Seismic and Magnetic methods

9. The ratio of bridging to non-bridging oxygen atoms is zero in case of

(A)  nesosilicates

(B)  inosilicates

(C)  phyllosilicates

(D)  tectosilicates

10. Lahar is geomorphic feature associated with

(A)  wind activity

(B)  river activity

(C)  glacial activity

(D)  volcanic activity

11. Kepler’s second law of planetary motion follows the principle of conservation of

(A)  energy

(B)  momentum

(C)  angular momentum

(D)  moment of inertia

12. Which one of the following options shows the internal structural units of the Earth arranged in the CORRECT sequence of increasing volume?

(A)  Outer core < Inner core < Upper mantle < Lower mantle

(B)  Outer core < Inner core < lower mantle < Upper mantle

(C)  Inner core < Outer core < Upper mantle < Lower mantle

(D)  Inner core < Outer core < Lower mantle < Upper mantle

13. Which one of the following is NOT an earthquake intensity scale?

(A)  Richter scale

(B)  JMA scale

(C)  Modified Mercalli scale

(D)  Rossi-Forel scale

14. The dimension of transmissivity of an aquifer is

(A)  M0L1T1

(B)  M0L0T0

(C)  M1L1T2

(D)  M0L2T1

15. During ‘K-capture’ nuclear transmutation process

(A)  both atomic number atomic mass increase

(B)  atomic number decreases but atomic mass remains the same

(C)  atomic number increases but atomic mass remains the same

(D)  both atomic number and atomic mass decrease

16. Which one amongst the following logs has the maximum depth of investigation?

(A)  Neutron log

(B)  Natural Gamma-ray log

(C)  Lateral log

(D)  Density log

17. The scale factor of an aerial photo of a planar ground surface, taken vertically downwards by a camera with a focal length of 300 mm, from a flying height of 3000 m is ______.

Answer: (10000 to 10000 OR 0.0001 to 0.0001)

18. In a soil sample, specific gravity of soil particles is 2.5 and the void ratio is 0.5. The density of the soil sample when it is fully saturated with water is _______ kg/m3. (Assume density of water = 1000 kg/m3, and no volume change of the soil sample with saturation)

Answer: (2000 to 2000)

19. Nuclide A decays to nuclide B exclusively through α and β decay, such that the mass number is reduced by 32 and the atomic number is reduced by 10. The number of β particles emitted during the decay of nuclide A to nuclide B is ________.

Answer: (6 to 6)

20. A cylindrical specimen (diameter = 54.7 mm; length = 110 mm) of basalt shows linear elastic behavior under uniaxial compression. At an axial stress of 100 Mega-Pascal (MPa), the absolute value of the measured axial strain is 0.2%. The Young’s modulus is calculated to be __________ Giga-Pascal (GPa).

Answer: (50 to 50)

21. A Mid-Oceanic-Ridge has symmetric magnetic anomalies about the ridge axis as shown below. Using the information given in the figure, the average relative velocity between the Plates A and B is calculated to be _______ cm/year.

Answer: (10 to 10)

22. The transmission coefficient for the vertically incident seismic wave at the interface between Layer and Layer 2 given in the figure is __________. (Round off to 2 decimal places)

Answer: (0.71 to 0.81)

23. The ‘geometrical factor’ for the electrode configuration given below will be ________ m. (Round off to 2 decimal places) (Use π = 3.14)

(C1 and C2 are current electrodes; P1 and P2 are potential electrodes)

Answer: (186.00 to 192.00)

24. In an electromagnetic measurement, the resultant field shows a phase lag of 30° with respect to the primary field at the receiver coil. The ratio of Inphase to Quadrature component of the resultant field is _________. (Round off to 2 decimal places)

Answer: (1.70 to 1.75)

25. A 4 km-high plateau is isostatically compensated as shown in the figure. Assuming Pratt’s hypothesis of isostasy, the calculated density of the plateau is ________ kg/m3.

Answer: (2450 to 2450)

Part B (Section 1): For Geology Candidates Only

Q1 – Q30 carry two marks each.

1. “Point Group” in crystallography is characterized by a set of symmetry operations such that

(A)  all points in a crystal are affected by it

(B)  no point in a crystal is affected by bit

(C)  at least one point in a crystal is affected by it

(D)  at least one point in a crystal is unaffected by it

2. What are the Miller indices of a plane that intercepts each of the crystallographic axes X, Y and Z at 20 Å? (Assume a primitive unit-cell with the dimensions a = 5 Å, b = 2 Å and c = Å.)

(A)  (111)

(B)  (524)

(C)  (425)

(D)  (542)

3. Which one of the following processes is associated with the emission of X-rays?

(A)  alpha decay

(B)  beta decay

(C)  electron capture decay

(D)  positron decay

4. Which one of the following radioisotopes has the longest half-life?

(A)  87Rb

(B)  147Sm

(C)  232Th

(D)  238U

5. The given geological map represents

(A)  culmination of an antiformal anticline

(B)  culmination of an antiformal syncline

(C)  depression of a synformal anticline

(D)  culmination of a synformal syncline

6. On a fault plane, the net slip is parallel to the bedding trace. Then, the apparent movement will be recognizable

(A)  both in horizontal and vertical sections

(B)  in horizontal, but not in vertical section

(C)  in vertical, but not in horizontal section

(D)  neither in horizontal nor in vertical section

7. The CORRECT sequence of the given electromagnetic radiations in order of increasing wavelength is

(A)  Ultraviolet < Gamma Rays < Radiowave < Near-Infrared

(B)  Gamma Rays < Ultraviolet < Near-Infrared < Radiowave

(C)  Gamma Rays < Radiowave < Ultraviolet < Near-Infrared

(D)  Ultraviolet < Radiowave < Near-Infrared < Gamma Rays

8. Choose the CORRECT combination of foraminiferal tests and types of coiling.

(A)  Test 1 – Trochospiral, Test 2 – Planispiral, Test 3 – Milioline

(B)  Test 1 – Milioline, Test 2 – Planispiral, Test 3 – Trochospiral

(C)  Test 1 – Milioline, Test 2 – Trochospiral, Test 3 – Planispiral

(D)  Test 1 – Trochospiral, Test 2 – Milioline, Test 3 – Planispiral

9. The figure below represents an isobaric binary liquidus phase diagram, with the solid phases A, B and C. What are the degrees of freedom associated with equilibrium phase assemblages represented by the bulk compositions w, x, y and z, in the fields indicated in the figure?

(A)  w  = 2, x = 1, y = 1, z = 1

(B)  w = 2, x = 1, y = 0, z = 2

(C)  w = 1, x = 1, y = 0, z = 1

(D)  w = 1, x = 1, y = 1, z = 2

10. Match the basins (Group I) with the corresponding stratigraphic units (Group II).

(A)  P-3, Q-4, R-1, S-2

(B)  P-2, Q-4, R-1, S-3

(C)  P-3, Q-1, R-4, S-2

(D)  P-2, Q-3, R-4, S-1

11. In the metamorphic reaction Quartz + Muscovite = X + Sillimanite + Water, ‘X’ represents

(A)  Garnet

(B)  Staurolite

(C)  Orthoclase

(D)  Cordierite

12. The talc-kyanite assemblage can stabilize in

(A)  greenschist facies marly rocks

(B)  amphibolites facies mafic rocks

(C)  eclogite facies politic rocks

(D)  sanidinite facies ultramafic rocks

13. Which one of the following statements about igneous rocks is CORRECT ?

(A)  Tholeiitic and calc-alkaline rocks are both alkaline in nature.

(B)  Tholeiitic rocks are subalkline, but calc-alkaline rocks are alkaline in nature.

(C)  Tholeiitic rocks are subalkaline, but calc-alkaline rocks are alkaline in nature.

(D)  Tholeiitic and calc-alkaline rocks are both subalkaline in nature.

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

Statement I: Barchans are crescent-shaped dunes that close in the downwind direction.

Statement II : Parabolic dunes are U-shaped dunes that close in the downwind direction.

Statement III: Barchanoid dunes are sinuous transverse ridges, the crestline sinuousity of successive bed forms are either in-phase or out-phase.

(A)  All the statements are correct

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

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

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

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

Statement I: Barapasaurus is  known from the Jurassic Kota Formation.

Statement II: Morganucodon is known from the Tatrot Formation.

Statement III: Lystrosaurus is known from the Lameta Formation.

(A)  All the three statements are correct

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

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

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

16. Which one of the following assemblages of plant fossils is known from the Barakar Formation?

(A)  Glossopteris, Gangamopteris, Dicroidium

(B)  Glossopteris, Gangamopteris, Noeggerathiopsis

(C)  Glossopteris, Gangamopteris, Ptilophyllum

(D)  Schizoneura, Noeggerathiopsis, Ptilophyllum

17. Match the features (Group I) with the corresponding invertebrate genera (Group II).

(A)  P-3, Q-4, R-1, S-2

(B)  P-3, Q-4, R-2, S-1

(C)  P-4, Q-3, R-2, S-1

(D)  P-2, Q-1, R-4, S-3

18. If the orthogonal thickness is constant along a folded layer, as per Ramsay’s morphological classification of folds, it is a

(A)  Class IA fold

(B)  Class IB fold

(C)  Class 2 fold

(D)  Class 3 fold

19. If density of quartz is 2650 kg/m3 and that of orthoclase is 2550 kg/m3, the lithostatic pressure due to granite with 68 modal % orthoclase at a depth of 10 km will be _______ kbar. (Round off to 2 decimal places) (Acceleration due to gravity g = 9.8 m/s2

Answer: (2.56 to 2.58)

20. The unit-cell of an orthorhombic mineral was compressed during deformation from 5 Å to 4.5 Å along the c-axis, with the other two dimensions remaining unaffected. The absolute value of the shift in the position of the (001) peak in its XRD pattern is _______ °2θ. (Round off to 3 decimal places) (Wavelength of X-ray used = 1.5418 Å. For orthorhombic system: 1/d2 = h2/a2 + k2/b2 + l2/c2).

Answer: (1.98 to 2.00)

21. The grade of iron in an ore body containing 80 wt. % hematite and 20 wt. % gangue is _______ %. (Round off to 2 decimal places) (Atomic wt. of Fe = 55.85, atomic weight of O = 16)

Answer: (55.90 to 55.97)

22. The abundances of the isotopes 35C­l (atomic mass = 34.96885 amu) and 37Cl (atomic mass = 36.96590 amu) are 75.77% and 24.23%, respectively. The calculated atomic weight of Cl is ______ amu. (Round off to 3 decimal places)

Answer: (35.451 to 35.454)

23. A vertical profile perpendicular to the rest line of an asymmetrical ripple is given in the figure. The calculated Ripple Index is ________.

Answer: (4 to 4)

24. A source rock undergoes melting. Assuming batch melting, 5% partial melting and bulk distribution coefficient of 0.045, the enrichment factor (C1/C0) of Rb in the melt will be _______. (Round off to 2 decimal places)

Answer: (10.75 to 10.87)

25. If the ∆H of formation of CaSiO3, SiO and CaO from Ca, Si and O are respectively −1635, −911 and −635 kJ/mol, the enthalpy of formation of CaSiO3 from CaO and SiO­2 is ________ kJ/mol.

Answer: (-89 to -89)

26. The tip-line of an actively propagating thrust fault is located at a depth of 1 km from the horizontal ground surface. The average density of the material from the ground surface to this depth is assumed to be uniform and can be taken as 2700 kg/m3. The rock at this depth follows the failure criterion given by the equation: σ1 = 10 MPa + 3σ­3, where σ1 and σ3 are the maximum and minimum principal stresses. Considering Anderson’s theory of faulting, the calculated maximum principal stress at this depth is _______ Mega-Pascal (MPa). (Assume the acceleration due to gravity (g) to be 10 m/s2.)

Answer: (91 to 91)

27. During a rockslide, a 20 kg granite block gets dislodged from the top of a planar hill slope and starts sliding down the slope as shown in the figure. The slope angle is 30° with the horizontal. After travelling a distance of 40 m in the same direction on the slope, the block hits the road. Assuming zero cohesion and zero friction, and considering acceleration due to gravity (g) as 10 m/s2, the velocity with which the block hits the road is ________ m/s.

Answer: (20 to 20)

28. Liquid limit and plastic limit of a soil are 40% and 20%, respectively. If the natural (i.e. in situ) water content of the soil is 30%. the liquidity index is ___________.

Answer: (0.5 to 0.5)

29. A confined aquifer has a uniform area (‘A’) perpendicular to the water flow. The hydraulic gradient and coefficient of permeability are given as 0.005 and 2 m/day, respectively. The total daily flow of water is 250 m3. Using Darcy’s law, the calculated value of ‘A’ is ________m2.

Answer: (25000 to 25000)

30. The apparent dip amount of a sandstone bed is 45°. The angle between the true dip direction and the apparent dip direction is 60°. The true dip amount of the bed is ________ degree (°). (Round off to 2 decimal places)

Answer: (63.42 to 63.44)

PART B (Section 2): Fro Geophysics Candidates only)

Q1 – Q30 carry two marks each.

1. International gravity formula is based on which one of the following models?

(A)  Non-rotating homogeneous spherical Earth model

(B)  Non-rotating homogenous oblate spheroidal Earth model

(C)  Rotating homogeneous oblate spheroidal Earth model

(D)  Rotating inhomogeneous spherical Earth model

2. Heat flow equation  is valid when

[T = Temperature, z is coordinate along z-axis]

(A)  steady state heat conduction is considered in an isotropic medium without heat source

(B)  steady state heat conduction is considered in an isotropic medium with heat source

(C)  steady state heat convection is considered in an isotropic medium without heat source

(D)  steady state heat convection is considered in an isotropic medium with heat source

3. Assuming the inner core of the Earth to be one-third of its present size, which one of the following statements is CORRECT? (Radius of the Earth and outer core remain unchanged)

(A)  Shadow zone of P-wave increases but that of S-wave decreases

(B)  Shadow zone of P-wave increases and that S-wave remains unchanged

(C)  Shadow zone of P-wave increases and that S-wave increases

(D)  Shadow zone of P-wave decreases but that of S-wave remains unchanged

4. Match the following instruments (Group I) with their corresponding physical principle (Group II)

(A)  P-4, Q-1, R-2, S-3

(B)  P-4, Q-3, R-2, S-1

(C)  P-3, Q-1, R-4, S-2

(D)  P-3, Q-2, R-4, S-1

5. The sensitivity of LaCoste-Romberg gravimeter is proportional to the line period (T) of the spring as

(A)  T2

(B)  1/T2

(C)  √T

(D)  1/√T

6. Match the following gravity/magnetic data interpretation techniques (Group I) with the corresponding terms (Group II)

(A)  P-4, Q-1, R-2, S-3

(B)  P-3, Q-4, R-1, S-2

(C)  P-4, Q-2, R-1, S-3

(D)  P-3, Q-1, R-4, S-2

7. Assuming uncorrelated noise, the improvement in the signal to noise ratio in a reflection seismic survey with ‘n’ geophones spaced equally along the profile is proportional to

(A)  n

(B)  1/n

(C)  √n

(D)  1/√n

8. A waveform with amplitude spectrum A(ω) and phase spectrum ϕ(ω) is auto-correlated. Which one of the options given below correctly represents the information about t he original waveform that can be retrieved from the autocorrelated waveform?

(A)  A(ω) can be retrieved but not ϕ(ω)

(B)  ϕ(ω) can be retrieved but not A(ω)

(C)  Both A(ω) and ϕ(ω) can be retrieved

(D)  Both A(ω) and ϕ(ω) cannot retrieved

9. The convolution A(4, 2, −1, 2) with B(1, 0, −1) gives

(A)  {−4, 2, −5, 0, 1 2}

(B)  {4, 2, −5, 0, 1, −2}

(C)  {−4, −2, 5, 0, −1, −2}

(D)  4, 2, 5, 0, −1, 2}

10. Which one of the following does NOT contribute to the suppression of SP log response for a thin, shaly, gas-bearing sandstone formation? (Resistivity of mud filtrate > resistivity of formation water)

(A)  Increase in shale content

(B)  Increase in hydrocarbon content

(C)  Decrease in the thickness of the bed

(D)  Increase in the salinity of formation water

11. The crossover observed for a hydrocarbon-bearing sandstone formation in the plot of Neutron and Density porosity logs (∅n – Neutron Density porosity is due to

(A)  increase in ∅d and decrease in ∅n

(B)  decrease in ∅d and increase in ∅n

(C)  increase in both ∅d and ∅n

(D)  decrease in both ∅d and ∅n

12. In which one of the following electromagnetic methods are the amplitude ratio and relative phase difference measured between two receiver coils?

(A)  Fixed vertical loop method

(B)  Compensator method

(C)  TURAM method

(D)  Slingram method

13. If four impedance tensors Zxx, Zyy, Zxy and Zyx are computed for a 2D body in magneto-telluric method (x is the strike direction), then

(A)  Zxx = 0, Zyy ≠ 0, Zxy = Zyx

(B)  Zxx ≠ 0, Zyy ≠ 0, Zxy = Zyx

(C)  Zxx ≠ 0, Zyy ≠ 0, Zxy ≠ Zyx

(D)  Zxx = 0, Zyy = 0, Zxy ≠ Zyx

14. Match the inversion methods (Group I) with the associated terms (Group II)

(A)  P-3, Q-2, R-1, S-4

(B)  P-4, Q-3, R-1, S-2

(C)  P-2, Q-1, R-4, S-3

(D)  P-2, Q-3, R-4, S-1

15. Ten equispaced metal electrodes are arranged along a profile for multi-electrode 2D resistivity imaging survey. If Wenner array is used for data recording, the maximum number of observations will be

(A)  7

(B)  11

(C)  12

(D)  13

16. P and R are Jacobian matrices for two different geophysical inverse problems. If their generalized inverses are written as P1 = (PTP)1PT and R1 = RT(RRT)1, then

(A)  both P and R deal with over-determined problems

(B)  both P and R deal with under-determined problems

(C)  P deals with over-determined and R deals with under-determined problem

(D)  P deals with under-determined and R deals with over-determined problem

17. In a 3D seismic survey, there are 512 groups of receivers in one line of a patch. Eight groups are moved per line from one patch to the next along the swath. What is the inline fold?

(A)  32

(B)  16

(C)  8

(D)  4

18. The magnetic potential of a uniform vertically magnetized buried spherical body with uniform density is given as   Then, the vertical magnetic field Bz is proportional to

[I = intensity of magnetization, ρ = density, gz = vertical component of gravity field, G = Universal gravitational constant, μ0  = magnetic permeability of three space, coordinate of the center of the body is (0, z) and that of the observation point is (x, 0)]

(A)

(B)

(C)

(D)

19. A sample of granite is observed to have a P-wave velocity of 5 km/s and density of 2600 kg/m3. The bulk modulus of the granite, assuming it to be a Poisson’s solid, is ________kilo-Pascal (kPa). (Round off to 2 decimal places)

Answer: (35000000 to 37000000)

20. The half-life of a parent radionuclide is 100 yrs. If the parent radionuclide decays to a daughter radionuclide which itself decays with a decay constant of 1/4th that of the parent radionuclide, then radioactive equilibrium will be reached after ______ (Round of to 2 decimal places) (Assume at time t = 0 the number of daughter radionuclide is zero)

Answer: (265.00 to 270.00)

21. Current and potential electrodes in resistivity survey over an inhomogeneous ground is shown in the figure below. If 100 mA current flow between C1 and C2 generates 50 mV potential difference between P1 and P2, then the apparent resistivity of the medium will be _______Ω (Round off to 2 decimal places) (Use π = 3.14)

Answer: (37.00 to 41.00)

22. Skin depths in homogeneous media of resistivity ρ1 and ρ2 are 100 m and 200 m, respectively, at 1000 Hz frequency. The ratio ρ12 will be _______.(Round of to 2 decimal places)

Answer: (0.23 to 0.27)

23. The mean resistivity of a horizontally stratified cuboid rock sample is 100 Ωm and coefficient of electrical anisotropy is 1.15. The transverse resistivity of the rock sample is _______ Ω (Round off to 2 decimal places)

Answer: (113.00 to 117.00)

24. A seismic reflection survey is carried out over a 1500 m thick horizontal layer with a P-wave velocity of 2000 m/s. The travel time of a reflected wave at a surface detector placed 1000 m from a surface source is ________ milliseconds.

Answer: (1576 to 1586)

25. A seismic reflection survey is carried out using a 10 milliseconds seismic wavelet over a subsurface medium having an average P-wave velocity of 1600 m/s. The best resolution which is obtained on the basis of Rayleigh criteria is _______ m. (Assume seismic wavelet contains one cycle)

Answer: (4 to 4)

26. To detect a 0.01 nT change in magnetic field using a proton precession magnetometer, the sensitivity required in the frequency measurement of the instrument is ______ × 104 (Round off to 2 decimal places) (Assume gyromagnetic ratio of proton as 2.67515 × 108 s1T1)

Answer: (4.24 to 4.28)

27. A micro-gravity survey with appropriate station spacing is performed to detect a subsurface spherical cavity in a bedrock of density 2500 kg/m3. The depth to the center of the cavity is 4 m from the surface and the elevation measurement accuracy of the surveying instrument is 0.1 m. The smallest cavity that can be detected by the survey must have a radius greater than _______m. (Round of to 1 decimal place) (Assume G = 6.673 × 1011 m3kg1s2)

Answer: (1.6 to 2.1)

28. The gravity anomaly over a spherical ore body is shown in the figure below. The calculated excess mass due to the ore body will be ________ × 1010 (Round off to 1 decimal place) (Assume z = 1.3 × x1/2; G = 6.673 × 1011 m3kg1s2)

Answer: (2.1 to 2.5)

29. A scalar potential field in 3D space is expressed as U(x, y, z) = x2 + yz2. The magnitude of the maximum rate of change in U(x, y, z) at a point (1, 1, 2) is ________.

Answer: (6 to 6)

30. A 10 Hz seismic wave propagates for 40 km through a material with a P-wave velocity of 5 km/s and quality factor (Q) of 100. The percentage of the initial amplitude retained in the attenuated wave is _______. (Round off to 1 decimal place) (Use π = 3.14)

Answer: (7.9 to 8.3)

## GATE Exam 2020 Ecology and Evolution (EY) Question Paper With Answer Key

GATE-2020

EY-Ecology and Evolution

GA- General Aptitude

Q1 – Q5 carry one mark each.

1. This book, including all its chapters, ______ interesting. The students as well as the instructor ______ in agreement about it.

(A)  is, was

(B)  are, are

(C)  is, are

(D)  were, was

2. People were prohibited ______ their vehicles near the entrance of the main administrative building.

(A)  to park

(B)  from parking

(C)  parking

(D)  to have parked

3. Select the word that fits the analogy:

Do : Undo :: Trust : ________

(A)  Entrust

(B)  Intrust

(C)  Distrust

(D)  Untrust

4. Stock markets ________ at the news of the coup.

(A)  poised

(B)  plunged

(C)  plugged

(D)  probed

5. If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed, with Q as a member ?

(A)  5

(B)  6

(C)  7

(D)  8

Q6 – Q10 carry two marks each.

6. Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).

Based on the above paragraph, the holding period of loans in 2004 after the third revision was ______ days.

(A)  45

(B)  90

(C)  135

(D)  180

7. Select the next element of the series: Z, WV, RQP, ______

(A)  LKJI

(B)  JIHG

(C)  KJIH

(D)  NMLK

8. In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ______ times.

(A)  270

(B)  279

(C)  280

(D)  299

9. Given a semicircle with O as the centre, as shown in the figure, the ratio is ______. where  are chords.

(A)  √2

(B)  √3

(C)  2

(D)  3

10. The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______.

(A)  32.7

(B)  33.7

(C)  34.1

(D)  35.1

EY: Ecology and Evolution

Q1 – Q25 carry one mark each.

1. Who among the following was a strong public supporter of Darwin’s theory of evolution by natural selection?

(A)  Jean-Baptiste Lamarck

(B)  Carl Linnaeus

(C)  Thomas Huxley

(D)  Gregor Mendel

2. Analysis of variance (ANOVA) can be used to compare multiple groups of samples. Select the correct option that reflects the principle behind ANOVA.

(A)  The sum of the squares of the variances is calculated for the groups being compared.

(B)  The variance ratio is calculated by subtracting each value from the overall mean, squaring the difference, and summing the resulting squared deviations.

(C)  The variation between groups is compared with the variation within groups.

(D)  The F value I statistically significant if the mean values between the groups are the same.

3. Which of the following information is provided by phylogenetic tree?

(A)  The topology and the branch lengths of the related taxa.

(B)  The topology and sequence length of the gene.

(C)  The sequence length of the gene and tree length.

(D)  The sequence type ad sequence variations within each taxa.

4. Myrmecochory refers to seed dispersal by which of the following agents?

(A)  Bats

(B)  Ants

(C)  Lizards

(D)  Birds

5. Which of the following is NOT capable of photosynthesis ?

(A)  Diatoms

(B)  Phytoplankton

(C)  Pteridophytes

(D)  Ascomycetes

6. Which of the following sensory mechanisms do most frugivorous bats primarily use while foraging?

(A)  Olfaction

(B)  Electromagnetism

(C)  Vibration

(D)  Echolocation

7. What direct effect does Follicle Stimulating Hormone (FSH) have in vertebrates?

(A)  It causes follicles of the duodenum to contract.

(B)  It causes follicles o the ovaries to grow.

(C)  It causes follicles of the liver to enlarge.

(D)  It causes follicles of muscles to contract.

8. Juvenile rhesus macaques, who have never seen a leopard before, can learn to show fear response if they see an adult react fearfully to a leopard. What kind of behavioural response is this?

(A)  Imprinting

(B)  Instinct

(C)  Cultural transmission

(D)  Mimicry transmission

9. In a tropical rainforest during the day, which of the following factors does NOT affect the spectral irradiance at the forest floor?

(A)  Angle of the sun on the horizon.

(B)  Weather conditions of the atmosphere.

(C)  Structure of the canopy vegetation.

(D)  Spectral reflectance of the leaf litter.

10. What would evolutionary biologist hypothesize as the ultimate cause for the presence of colouful dewlaps in lizards?

(A)  Colour of dewlaps are formed by pigments in the skin.

(B)  Colourful dewlaps are formed by folds in the skin.

(C)  Colourful dewlaps increase mating success.

(D)  Colourful dewlaps are regions where motor neurons control head movement.

11. Which of the following is true about comparisons between herbivorous and carnivorous mammals?

(A)  Herbivores have longer digestive tracts and smaller caecum for the given body size than carnivores.

(B)  Carnivores have longer digestive tracts and smaller caecum for a given body size than herbivores.

(C)  Herbivores have shorter digestive tracts and smaller caecum for a given body size than carnivores.

(D)  Carnivores have shorter digestive tracts and smaller caecum for a given body size than herbivores.

12. Two isolated populations X and Y have 100 ad 10000 individuals respectively. Both populations have the same starting allele frequencies of p = 0.5 and q = 0.5. After 1000 generations of genetic drift, which of the following statements is true about the heterozygosity at this locus in these two populations?

(A)  The heterozygosity of population X will be more than population Y.

(B)  The heterozygosity of  population Y will be more than in population X.

(C)  The heterozygosity of both the populations will be identical.

(D)  The heterozygosity of these populations will not depend on their population sizes.

13. Which of the following criteria is used to define species under the biological species concept?

(A)  Niche partitioning

(B)  Reproductive isolation

(C)  Morphological divergence

(D)  Genetic distance

14. The abundances of three species (P, Q and R) were measured along a resource gradient. The resultant pattern in summarized in the figure. Which of the following statements can be inferred from niche theory?

(A)  P is generalist; Q and R are specialists.

(B)  Q is a generalist; P and R specialists.

(C)  P and Q are generalists; R is a specialist.

(D)  P and R are generalists; Q is a specialist.

15. In the last 3 to 4 decades, the average CO2 concentration in the Earth’s atmosphere has increased from_______.

(A)  3 ppm to 4 ppm

(B)  30 ppm to 40 ppm

(C)  300 ppm to 400 ppm

(D)  3000 ppm to 4000 ppm

16. What effect does myelination have on neurons?

(A)  It increases the transmembrane resistance.

(B)  It increases the membrane capacitance.

(C)  It changes the direction of signal propagation.

(D)  It protects synapse from damage.

17. Which of the following processes contributes to an increase in genetic variation?

(A)  Genetic drift

(B)  Directional selection

(C)  Inbreeding

(D)  Immigration

18. What characteristic do the plant species, sundew (Drosera capensis) and Venus fly trap (Dionaea muscipla), share?

(A)  They are thigmonastic.

(B)  They are nyctinastic.

(C)  They are epiphytic.

(D)  They are endophytic.

19. What is the study of fish known as?

(A)  Malacology

(B)  Herpetology

(C)  Physiology

(D)  Ichthyology

20. On one side of a house, a 50 watt bulb attracts moths at a rate of 30 individuals/minute. On the other side of the house, a 15 watt bulb attracts moths at a rate of 10 individuals/minute. There are 20 bats in the area who are foraging for these moths. According to Ideal Free Distribution, the number of bats near the 15 watt bulb should be _______.

Answer: (5 to 5)

21. The Simpson’s index of diversity is expressed as:

Where pi is the proportion of the ith species, and n is the total number of species.

The Simpson’s index of diversity for this dataset is ____ (round off to three decimal places).

Answer: (0.440 to 0.454)

22. In a botanical garden, tree species P had an average height of 1.5 m, while tree species Q had n average height of 1.8 m Pooled together, these two tree species had an average height of 1.7 m. From this, one can infer that the number of trees of species Q in the garden was _______ times the number of trees of species P.

Answer: (2 to 2)

23. A fragment of double stranded DNA has 30% Adenine. The % GC content in this fragment is _______.

Answer: (40 to 40)

24. A researcher traps rodents in a small, isolated forest patch. In the first trapping session she captures 24 mice ad marks them by notching their ears. In the second trapping session she captures 16 mice, of which 8 are already marked. Assuming that the population is closed (no immigration, emigration, birth, or death), the estimated number mice in the patch is_______.

Answer: (48 to 48)

25. A raptor sitting on a tree sees a rodent on the ground below as shown in the figure (not to scale). If the raptor views the rodent from a height of 10 metres, and the rodent subtends a visual angle of 45° on the raptor’s eye, the straight line distance from the raptor to the rodent in metres is ______ (round off to two decimal places).

Answer: (14.00 to 14.28)

Q26 – Q55 carry two marks each.

26. Beetles of one species have the option of eating plant species X or Y in their environment. Plant species X and Y have the same nutritional quality. When beetle diets comprise a greater proportion of a plant X, the population size of beetles increase faster than when beetle diets are dominated by plant Y. Which of the following is NOT a probable explanation for this outcome?

(A)  Xenobiotics in X are physiologically easier for the beetles to detoxify than t hose in Y.

(B)  Sequestration of xenobiotics from Y by the beetles confers greater protection from bird predators than those from Y.

(C)  X attracts parasites of the beetles while Y does not.

(D)  X provides greater protection from bird predators during foraging than does Y.

27. A researcher was documenting the number of tree species in landscape. Within each of three forest types (P, Q and R), she laid 100 quadrats and documented all the species found in each quadrat. She then plotted the cumulative species richness for these forest types as shown in the figure. Which of the following statements is FALSE?

(A)  There are more species of trees in P than in R.

(B)  There are more species of trees in Q than in R.

(C)  More quadrats are required to estimate species richness in P than in Q.

(D)  More quadrats are required to estimate species richness in Q than in R.

28. Which of the following ha an endemic species represented in the Andaman and Nicobar Islands for all taxonomic groups in that column?

(A)  Column P

(B)  Column Q

(C)  Column R

(D)  Column S

29. The theory of island biogeography predicts that the number of species o islands is determined by: (i) the rate of colonization, which depends on the distance of the island from the mainland and (ii) the rate of extinction which depends on the size of the island. A researcher surveyed two islands with similar habitats and geological history, and found that both islands have the same number of species. Which of the following statement(s) can explain this observation?

(P) The islands are of the same size and are at the same distance from the mainland.

(Q) The islands are of different sizes and are at the same distance from the mainland.

(R) The islands are of the same size and are at different distance from the mainland.

(S) The  islands are of different sizes and are of different distances from t he mainland.

(A)  Only P.

(B)  Only Q.

(C)  Both P and S.

(D)  Both Q and R.

30. In marine fauna, Pelagic Larval Duration (PLD) or the amount of time that larvae spend swimming or drifting in the water column affects their dispersal distance. Successful establishment of the larvae on a substrate also depends on finding a suitable habitat after dispersal, which is influenced by whether that habitat is patchy or continuous. Which of the following species will have the lowest population genetic structure (FST) across the same spatial scale?

(A)  Species with high PLD inn patchy habitats.

(B)  Species with high PLD in continuous habitats.

(C)  Species with low PLD in patchy habitats.

(D)  Species with low PLD in continuous habitats.

31. Every lake in Wakanda has three species of fish: P, Q and R. Species P is a bottom dweller and substrate feeder, species Q is a mid-column dweller and herbivore, and species R is a surface dweller and piscivore. Which of the following processes best explains this distribution pattern?

(A)  Speciation within one lake followed by dispersal to other lakes.

(B)  Dispersal between lakes followed by speciation within lakes.

(C)  Independent speciation events within all the takes.

(D)  Speciation within a lake with no dispersal between lakes.

32. Group living can have both benefits (such as protection from predators) and costs (such as competition for resources). The figure depicts net benefit to individuals as a function of group size. Consider a population with more than hundred individuals, where groups do not split, and individuals can choose to either join a group or remain solitary. Given this information, what is the typical group size predicted?

(A)  Less than 6

(B)  Equal to 6

(C)  Between 6 and 12

(D)  Greater than 12

33. Two species of snails, P and Q, are found in rivers across a range of temperatures that vary from upstream a downstream. An experiment was conducted in which P was removed from a river and the distribution of Q was measured after a few weeks. In another similar river, the reciprocal experiment was conducted I which Q was removed, and the distribution of P was measured after a few weeks. In the graph below, the filled bars plot the distribution of P and Q when both species are present in a river. The open bars plot the distribution of P when Q is removed, and Q when P is removed. Which of the following statements is true?

(A)  The realized niche of P is smaller than its fundamental niche.

(B)  The realized niche of Q is smaller than its fundamental niche.

(C)  The realized niche is smaller than the fundamental niche for both species.

(D)  The realized niches of both species are equal.

34. In plants with bisexual flowers (hermaphrodites), mate-choice by females is expected to be important under which of the following cases?

(i) Seed set is pollen-limited rather than resource-limited.

(ii) Obligate self-pollination is present.

(iii) Seed set is resource-limited rather than pollen-limited.

(iv) Obligate cross-pollination is present.

(A)  (i) and (ii)

(B)  (ii) and (iii)

(C)  (iii) and (iv)

(D)  (i) and (iv)

35. Match the breeding system of the plants with their pollen : ovule ratio.

(A)  P-i, Q-iii, R-ii, S-iv

(B)  P-ii, Q-i, R-iv, S-iii

(C)  P-iv, Q-iii, R-i, S-ii

(D)  P-iii, Q-iv, R-i, S-ii

36. A particular gene sequence from two different species shows molecular clock-like evolution. Which of the following statements is consistent with this observation?

(A)  The two sequences will show a linear decrease in their genetic distance with time.

(B)  The genetic distance between the two sequences remains constant over time.

(C)  The rate of evolution for this gene sequence is not constant over time.

(D)  The two sequences will show a linear increase in their genetic distance with time.

37. An internal parasite of a mammal does not generate its own heat and yet it can maintain a constant body temperature. Which characteristics describe this parasite?

(A)  Homeothermic ectotherm

(B)  Homeothermic endotherm

(C)  Poikilothermic ectotherm

(D)  Poikilothermic endotherm

38. In a population of infinite size, the frequency of two alleles. A1 and A2 at a neutral locus are the same. What are the expected genotype frequencies (A1A1, A1A2, A2A2) after 100 generations of random mating?

(A)  0.25, 0.5, 0.25

(B)  0.5, 0.25, 0.25

(C)  0.25, 0.25, 0.5

(D)  0.05, 0.5, 0.45

39. A certain rodent species shows territoriality, competes for space and food, and their population is at carrying capacity. In the figures, the area within the rectangle (i) to (iv) represents a completely homogenous habitat where resources are distributed throughout, and the grey polygons represent rodent home ranges. Which of the following patterns best represents the expected distribution of home ranges of the rodent species if individuals vary in competitive ability?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

40. For a given gene there is 5% DNA sequence divergence between two species, however the protein coded by this gene has identical sequences in the two species. Which of the following types of mutations best explains this pattern in the DNA sequence?

(A)  Nonsense mutation

(B)  Synonymous substitution

(C)  Non-synonymous substitution

(D)  Frame-shift mutation

41. A researcher collects data on plant species composition in two habitats (P and Q) by using 10 quadrats each in both habitats. She calculates the average α-diversity and the β-diversity of each habitat from this data (shown below). Which of the following can be inferred about these habitats?

(A)  p and Q have the same total diversity (γ) and P is more heterogeneous than Q.

(B)  Q has lower total diversity (γ) and is more heterogeneous than P.

(C)  P has greater total diversity (γ) and is more heterogeneous than Q.

(D)  Q has greater total diversity (γ) and is more heterogeneous than P.

42. Among four related bird species P, Q, R and S, species P and Q are nectar feeding with long thin beaks, whereas species R and S are seed eaters with short thick beaks. Which o the following phylogenies unambiguously suggests that seed eating habit was the ancestral state?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

43. A population of unicorns is growing over time, but its rate of growth is declining. Which of the following graphs best represents this pattern of growth?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

44. In a polyploidization event, tetraploid progeny were formed by diploid parents. Hybridization between the tetraploid and diploid parent gave rise to sterile triploids. Which of the following best explains why these triploids were sterile?

(A)  Many mutations during polyploidization have no phenotypic effect.

(B)  Some chromosomes are without homologs during meiosis.

(C)  Some chromosomes are without homologs during mitosis.

(D)  All chromosomes have homologs during mitosis.

45. Blood tests are often used to screen for potential diseases. For a particular disease:

(i) Of 1000 persons who tested negative (T’), 1 person had the disease (D); Pr(D|T’).

(ii) of 10 persons who tested positive (T’), 1 person had the disease (D); Pr(D|T’).

From this we can calculate

What can be inferred from t his value ?

(A)  100 people have the disease but they will not test positive.

(B)  1 in 100 people have the disease and they will test positive.

(C)  100 in 1000 people have the disease and their blood tests will be inconclusive.

(D)  People with positive tests are 100 time more likely t have the disease than people with negative tests.

46. The relative frequency distributions of vales of a trait in two samples, P and Q, are shown in figure. Which of the following statements is consistent with the figure?

(A)  P has higher mean than Q; Q has higher variance than P.

(B)  P has a higher mean than Q: P has a higher variance than Q.

(C)  P and Q have the same mean; Q has higher variance than P.

(D)  P and Q  have the same mean; P has higher variance than Q.

47. Consider the function f(x) = |(eβx)/(β)|

Which of the following graphs represents the relationship between x and f(x)?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

48. In a nocturnal moth species (X), individuals with longer antennae have smaller eyes. This indicates a sensory trade-off. In a closely related but diurnal moth species (Y), individuals exhibit the same obligate sensory trade-off. Which of the following figures describes the relationship between these two traits in moth species Y, if it relies more on vision than olfaction?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

49. A researcher compared grass species richness in a 10 m × 10 m plot immediately before (T0) and 100 days after (T100) a fire. She observed that species richness was higher at T100 than at T­0. Which of the following data is required for her to conclude that species richness increased because of the fire?

(A)  Grass species richness of a 10 m × 10 m plot in a nearby area that also burned.

(B)  Grass species richness of a 10 m × 10 m plot only at T100 in nearby area that did not burn.

(C)  Grass species richness of a 10 m × 10 m plot at both T0 and T100 in a nearby area that did not burn.

(D)  Grass species richness of the same 10 m × 10 m  plot every 10 days after the fire until T100.

50. Following a gene duplication event, the duplicated copy often loses function and is called a pseudogene. In the absence of positive selection, which of the following is true about these genes?

(A)  The functional gene will accumulate mutations more rapidly than the pseudogene.

(B)  The pseudogene will accumulate mutations more rapidly than the functional gene.

(C)  Both the functional gene and pseudogene will accumulate mutations at the same rate.

(D)  The pseudogene will not accumulate mutations.

51. Which of the figures represents the expected relationship between parental care and the number of offspring produced across taxa?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

52. Match the following plant traits with the correct plant group/family:

(A)  P-iv, Q-v, R-i, S-ii

(B)  P-ii, Q-iv, R-iii, S-i

(C)  P-i, Q-ii, R-iii, S-iv

(D)  P-iii, Q-v, R-i, S-ii

53. In a population of 100 individuals of a diploid organism with 1:1 sex ratio, the probability of fixation of a new neutral mutation is ______ (round off to three decimal places).

Answer: (0.005 to 0.005)

54. The binomial probability of obtaining exactly k successes in n trials, where the probability of success in a single trial is p, is given by :

Here,  rotation refers to number of combinations for k successes among n trials. With a fair and unbiased coin, the probability of getting 2 HEADS in a trial with 5 tosses is __________ (round off to two decimal places).

Answer: (0.30 to 0.35)

55. The petrified wood fossil was discovered with 8 g of 14 The decay of 14C over time is given by:

NT = N0e0.0001216T

I the half-life of 14C is 5700 years, and the fossil initially had 2 g of 14C, the age of the fossil in  years is ________.

Answer: (11300 to 11500)

## GATE Exam 2020 Electrical Engineering (EE) Question Paper With Answer Key

GATE-2020

EE: Electrical Engineering

GA- General Aptitude

Q1 – Q5 carry one mark each.

1. This book, including all its chapters, ______ interesting. The students as well as the instructor ______ in agreement about it.

(A)  is, was

(B)  are, are

(C)  is, are

(D)  were, was

2. People were prohibited ______ their vehicles near the entrance of the main administrative building.

(A)  to park

(B)  from parking

(C)  parking

(D)  to have parked

3. Select the word that fits the analogy:

Do : Undo :: Trust : ________

(A)  Entrust

(B)  Intrust

(C)  Distrust

(D)  Untrust

4. Stock markets ________ at the news of the coup.

(A)  poised

(B)  plunged

(C)  plugged

(D)  probed

5. If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed, with Q as a member ?

(A)  5

(B)  6

(C)  7

(D)  8

Q6 – Q10 carry two marks each.

6. Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).

Based on the above paragraph, the holding period of loans in 2004 after the third revision was ______ days.

(A)  45

(B)  90

(C)  135

(D)  180

7. Select the next element of the series: Z, WV, RQP, ______

(A)  LKJI

(B)  JIHG

(C)  KJIH

(D)  NMLK

8. In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ______ times.

(A)  270

(B)  279

(C)  280

(D)  299

9. Given a semicircle with O as the centre, as shown in the figure, the ratio  is ______. where  are chords.

(A)  √2

(B)  √3

(C)  2

(D)  3

10. The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______.

(A)  32.7

(B)  33.7

(C)  34.1

(D)  35.1

EE: Electrical Engineering

Q1 – Q25 carry one mark each.

1. ax3 + bx2 + cx + d is a polynomial on real x over real coefficients a, b, c, d wherein a ≠ Which of the following statements is true?

(A)  d can be chosen to ensure that x = 0 is a root for any given set a, b, c.

(B)  no choice of coefficients can make all roots identical.

(C)  a, b, c, d can be chosen to ensure that all roots are complex.

(D)  c alone cannot ensure that all roots are real.

Answer: (A OR D)

2. Which of the following is true for all possible non-zero choices of integers m, n; m ≠ n, or all possible non-zero choices of real numbers p, q; p ≠ q, as applicable?

(A)

(B)

(C)

(D)

3. Which of the following statements is true about the two sided Laplace transform?

(A)  It exists for every signal that may or may not have a Fourier transform.

(B)  It has no poles for any bounded signal that is non-zero only inside a finite time interval.

(C)  The number of finite poles and finite zeroes must be equal.

(D)  If a signal can be expressed as a weighted sum of shifted one sided exponentials, then its Laplace Transform will have no poles.

4. Consider a signal  where 1[n] = 0 if n < 0, and 1 [n] = 1 if n ≥ The z-transform of x[n – k], k > 0 is   with region of convergence being

(A)  |z| < 2

(B)  |z| > 2

(C)  |z| < 1/2

(D)  |z| > 1/2

5. The value of the following complex integral, with C representing the unit circle centered at origin in the counterclockwise sense, is:

(A)  8πi

(B)  −8πi

(C)  −πi

(D)  πi

6. xR and xA are, respectively, the rms and average values of x(t) = x(t – T), and similarly, yR and yA are, respectively, the rms and average values of y(t) = kx(t). k, T are independent of t. Which of the following is true?

(A)  yA = kxA; yR = kxR

(B)  yA = kxA; yR ≠ kxR

(C)  yA ≠ kxA; yR = kxR

(D)  yA ≠ kxA; yR ≠ kxR

7. A three-phase cylindrical rotor synchronous generator has a synchronous reactance Xs and a negligible armature resistance. The magnitude of per phase terminal voltage is VA and the magnitude of per phase induced emf is E­A. Considering the following two statements, P and Q.

P: For any three-phase balanced leading load connected across the terminals of this synchronous generator, V­A is always more than EA

Q: For any three-phase balanced lagging load connected across the terminals of this synchronous generator, VA is always less than EA

Which of the following options is correct?

(A)  P is false Q is true.

(B)  P is true and Q is false.

(C)  P is false and Q is false.

(D)  P is true and Q is true.

8. A lossless transmission line with 0.2 pu reactance per phase uniformly distributed along the length of the line, connecting a generator bus to a load bus, is protected up to 80% of its length by a distance relay placed at the generator bus. The generator terminal voltage is 1 pu. There is no generation at the load bus. The threshold pu current for operation of the distance relay for a solid three phase-to-ground fault on the transmission line is closest to:

(A)  1.00

(B)  3.61

(C)  5.00

(D)  6.25

9. Out of the following options, the most relevant information needed to specify the real power (P) at the PV buses in a load flow analysis is

(A)  solution of economic load dispatch

(B)  rated power output of the generator

(C)  rated voltage of the generator

(D)  base power of the generator

10. Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:

The poles of this system are at

(A)  +2j, −2j

(B)  +2, −2

(C)  +4, −4

(D)  +4j, −4j

11. A single-phase, full-bridge diode rectifier fed from a 230 V, 50 Hz sinusoidal source supplies a series combination of finite resistance, R, and a very large inductance, L. The two most dominant frequency components in the source current are:

(A)  50 Hz, 0 Hz

(B)  50 Hz, 100 Hz

(C)  50 Hz, 150 Hz

(D)  150 Hz, 250 Hz

12. Thyristor T1 is triggered at an angle α (in degree), and T2 at angle 180° + α, in each cycle of the sinusoidal input voltage. Assume both thyristors to be ideal. To control the load power over the range 0 to 2 kW, the minimum range of variation in α is:

(A)  0° to 60°

(B)  0° to 120°

(C)  60° to 120°

(D)  60° to 180°

13. Which of the options is an equivalent representation of the signal flow graph shown here?

14. A common-source amplifier with a drain resistance, RD = 4.7 kΩ, is powered using a 10 V power supply. Assuming that the transconductance, gm, is 520 μA/V, the voltage gain of the amplifier is closest to:

(A)  −2.44

(B)  −1.22

(C)  1.22

(D)  2.44

15. A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequences detectable. For the sequence (1, 0, 1) and input data (1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0)

(A)  1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0

(B)  0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0

(C)  0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0

(D)  0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0

16. Consider the initial value problem below. The value of y at x = ln 2, (rounded off to 3 decimal places) is ______.

Answer: (0.8774 to 0.8952)

17. A three-phase, 50 Hz, 4-pole induction motor runs at no-load with a slip of 1%. With full load, the slip increases to 5%. The % speed regulation of the motor (rounded off to 2 decimal places) is _______.

Answer: (4.10 to 4.40)

18. Currents through ammeters A2 and A3 in the figure are 1∠10° and 1∠70°, respectively. The reading of the ammeter A1(rounded off to 3 decimal places) is _______A.

Answer: (1.700 to 1.750)

19. The Thevenin equivalent voltage, VTH, in V (rounded off to 2 decimal places) of the network shown below, is ________

Answer: (13.80 to 14.20)

20. A double pulse measurement for an inductively loaded circuit controlled by the IGBT switch is carried out to evaluate the reverse recovery characteristics of the diode, D, represented approximately as a piecewise linear plot of current vs time at diode turn-off. Lpar is a parasitic inductance due to the wiring of the circuit, and in series with the diode. The point on the plot (indicate your choice by entering 1, 2, 3 or 4) at which the IGBT experiences the highest current stress is ________.

Answer: (3 to 3)

21. A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac source, the no-load losses will be _________ W (rounded off to 2 decimal places).

Answer: (162.41 to 162.59)

22. A single-phase inverter is fed from a 100 V dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform. v(t), as shown. The angle σ is adjusted to entirely eliminate the 3rd harmonic component from the output voltage. Under this condition, for v(t), the magnitude of the 5th harmonic component as a percentage of the magnitude of the fundamental component is ________ (rounded off to 2 decimal places).

Answer: (19.90 to 20.20)

23. A single 50 Hz synchronous generator on droop control was delivering 100 MW power to a system. Due to increase in load, generator power had to be increased by 10 MW, as a result of which, system frequency dropped to 49.75 Hz. Further increase in load in the system resulted in a frequency of 49.25 Hz. At this condition, the power in MW supplied by the generator is ________ (rounded off to 2 decimal places).

Answer: (123.00 to 135.00)

24. Consider a negative unity feedback system with forward path transfer function  where K, a, b, c are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the s-plane in the clockwise direction, the Nyquist plot of (1+ G(s)), encircles the origin of (1+G(s)-plane) once in the clockwise direction and never passes through this origin for a certain value of K. Then, the number of poles of  lying in the open right half of the s-plane is ________.

Answer: (2 to 2)

25. The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of +3 V is applied to the gate contact with respect to the body contact. The charge inside the silicon dioxide layer is then measured to be +Q. The total charge contained within the dashed box shown, upon application of bias, expressed as a multiple of Q (absolute value in Coulombs, rounded off to nearest integer( is __________.

Answer: (0 to 0)

Q26 – Q55 carry two marks each.

26. For real numbers, x and y, with y = 3x2 + 3x + 1, the maximum and minimum value of y for x ∈ [−2, 0] are respectively_______.

(A)  7 and 1/4.

(B)  7 and 1.

(C)  −2 and −1/2.

(D)  1 and 1/4.

27. The vector function expressed by F = ax (5y – k1z) + ay (3z + k2x) + az (k3y – 4x) represents a conservative field, where ax, ay, az are unit vectors along x, y and z directions, respectively. The values of constants k1, k2, k3 are given by:

(A)  k1 = 3, k2 = 3, k3 = 7

(B)  k1 = 3, k2 = 8, k3 = 5

(C)  k1 = 4, k2 = 5, k3 = 3

(D)  k1 = 0, k2 = 0, k3 = 0

28. A 250 V dc shunt motor has an armature resistance of 0.2 Ω and a field resistance of 100 Ω. When the motor is operated on no-load at rated voltage, it draws an armature current of 5 A and runs at 1200 rpm. When a load is coupled to the motor, it draws total line current of 50 A at rated voltage, with a 5% reduction in the air-gap flux due to armature reaction. Voltage drop across the brushes can be taken as 1 V per brush under all operating conditions. The speed of the motor, in rpm, under this loaded condition, is closest to:

(A)  1200

(B)  1000

(C)  1220

(D)  900

29. Two buses, i and j, are connected with a transmission line of admittance Y, at the two ends of which there are ideal transformers with turns ratios as shown. Bus admittance matrix for the system is:

30. Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic  where n > 1, VT > 0, VD is the voltage across the diode and ID is the current through it. The circuit is biased so that voltage, V > 0 and current, I < 0. If you had to design this circuit to transfer maximum power from the current source (I­1) to a resistive  load (not shown) at the output, what values of R1 and R2 would you choose?

(A)  Large R1 and large R2.

(B)  Small R1 and small R2.

(C)  Large R1 and small R2.

(D)  Small R1 and large R2.

31. A non-ideal diode is biased with a voltage of −03 V, and a diode current of I1 is measured. The thermal voltage is 26 m V and the ideality factor for the diode is 15/13. The voltage, in V, at which the measured current increases to 1.5I1 is closest to:

(A)  −0.02

(B)  −0.09

(C)  −1.50

(D)  −4.50

32. A benchtop dc power supply acts as an ideal 4 A current source as long as its terminal voltage is below 10 V. Beyond this point, it begins to behave as an ideal 10 V voltage source for all load currents going down to 0 A. When connected to an ideal rheostat, find the load resistance value at which maximum power is transferred, and the corresponding load voltage and current.

(A)  Short, ∞ A, 10 V

(B)  Open, 4 A, 0 V

(C)  2.5 Ω, 4 A, 10 V

(D)  2.5 Ω, 4 A, 5 V

33. The static electric field inside a dielectric medium with relative permittivity, εr = 2.25, expressed in cylindrical coordinate system is given by the following expression  where ar, aφ, az are unit vectors along r, φ and z directions, respectively. If the above expression represents a valid electrostatic field inside the medium, then the volume charge density associated with this field in terms of free space permittivity, ε0, in SI units is given by:

(A)  3ε0

(B)  4ε0

(C)  5ε0

(D)  9ε0

34. Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t = 0, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is

35. Which of the following options is correct for the system shown below?

(A)  4th order and stable

(B)  3rd order and stable

(C)  4th order and unstable

(D)  3rd order and unstable

36. Consider a negative unity feedback system with the forward path transfer function  where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is_______.

(A)  9

(B)  8

(C)  7

(D)  6

37. Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) * h (t) = y(t). Further, if |x(t)| * |h(t)| = z(t), which of the following statements is true?

(A)  For all t ∈ (−∞, ∞) z(t) ≤ y(t)

(B)  For some but not all t ∈ (−∞, ∞), z(t) ≤ y(t)

(C)  For all t ∈ (−∞, ∞), z(t) ≥ y(t)

(D)  For some but not all t ∈ (−∞, ∞), z(t) ≥ y(t)

38. The casual realization of a system transfer function H(s) having poles at (2, −1), (−2, 1) and zeroes at (2, 1) (−2, −1) will be

(A)  stable, real, allpass

(B)  unstable, complex, allpass

(C)  unstable, real, highpass

(D)  stable, complex, lowpass

39. Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:

y[n] – ay[n – 1] = b0x[n] – b1x[n – 1]

(A)  y[n] is unaffected by the values of x[n – k]; k > 2.

(B)  The system is necessarily casual.

(C)  The system impulse response is non-zero at infinitely many instants.

(D)  When x[n] = 0, n < 0, the function y[n]; n > 0 is solely determined by the function x[n].

40. Let ar, aϕ and az be unit vectors along, r, ϕ and z directions, respectively in the cylindrical coordinate system. For the electric flux density given b y D = (ar15 + aϕ2r – az3rz) Coulomb/m2, the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius 3 m and height 5 m oriented along the z-axis with its base at the origin is:

(A)  54 π

(B)  90 π

(C)  108 π

(D)  180 π

41. A stable real linear time-invariant system with single pole at p, has a transfer function  with a dc gain of 5. The smallest positive frequency, in rad/s, at unity gain is closest to:

(A)  8.84

(B)  11.08

(C)  78.13

(D)  122.87

42. The number of purely real elements in a lower triangular representation of the given 3 × 3 matrix, obtained through the given decomposition is _______.

(A)  5

(B)  6

(C)  8

(D)  9

43. The figure below shows the per-phase Open Circuit Characteristics (measured in V) and Short Circuit Characteristics (measured in A) of a 14 kVA, 400 V, 50 Hz, 4-pole, 3-phase, delta connected alternator, driven at 1500 rpm. The field current, If is measured in A. Readings taken are marked as respective (x, y) coordinates in the figure. Ratio of the unsaturated synchronous impedances (Zs(unsat)/Zs(sat)) of the alternator is closest to:

(A)  2.100

(B)  2.025

(C)  2.000

(D)  1.000

44. Let ax and ay be unit vectors along x and y directions, respectively. A vector function is given by

F = axy – ayx

The line integral of the above function

along the curve C, which follows the parabola y = x2 as shown below is _______ (rounded off to 2 decimal places).

Answer: (-3.05 to -2.95)

45. A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ is the circuit time constant The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2τ is ________(rounded off to 2 decimal places).

Answer: (54.00 to 56.00)

46. A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now ________ A (rounded off to 2 decimal places).

Answer: (123.00 to 127.00)

47. Bus 1 with voltage magnitude V1 = 1.1 pu is sending reactive power Q12 towards bus 2 with voltage magnitude V2 = 1 pu through a lossless transmission line of reactance X. Keeping the voltage at bus 2 fixed at 1 pu, magnitude of voltage at bus 1 is changed, so that the reactive power Q12 sent from bus 1 is increased by 20%. Real power flow through the line number both the conditions is zero. The new value of the voltage magnitude V1, in pu (rounded off to 2 decimal places),at bus 1 is _______.

Answer: (1.11 to 1.13)

48. Windings ‘A’, ‘B’ and ‘C’ have 20 turns each and are wound on the same iron core as shown, along with winding ‘X’ which has 2 turns. The figure shows the sense (clockwise/anti-clockwise) of each of the windings only and does not reflect the exact number of turns. If windings ‘A’, ‘B’ and ‘C’ are supplied with balanced 2-phase voltages at 50 Hz and there is no core saturation, the no-load RMS voltage (in V, rounded off to 2 decimal places) across winding ‘X’ is ________.

49. A cylindrical rotor synchronous generator has steady state synchronous reactance of 0.7 pu and subtransient reactance of 0.2 pu. It is operating at (1 + j0) pu terminal voltage with an internal emf of (1 + j0.7) pu. Following a three-phase solid short circuit fault at the terminal of the generator, the magnitude of the subtransient internal emf (rounded off to 2 decimal places) is _______pu.

Answer: (1.01 to 1.03)

50. In the dc-dc converter circuit shown, switch Q is switched at a frequency of 10 kHz with a duty ratio of 0.6. All components of the circuit are ideal, and the initial current in the inductor is zero. Energy stored in the inductor in mJ (rounded off to 2 decimal places) at the end of 10 complete switching cycles is ________.

Answer: (4.95 to 5.05)

51. A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a 10 Ω resistance in series with a very large inductance. The rectifier is fed from an ideal 230 V, 50 Hz sinusoidal source through cables which have negligible internal resistance and a total inductance of 2.28 mH. If the thyristors are triggered at an angle α = 45°, the commutation overlap angle in degree (rounded off to 2 decimal p laces) is _______.

Answer: (4.51 to 5.10)

52. A non-ideal Si-based pn junction diode is tested by sweeping the bias applied across its terminals from −5 V to + 5 V. The effective thermal voltage, VT, for the diode is measured to be (29 ± 2) mV. The resolution of the voltage source in the measurement range is 1 mV. The percentage uncertainty (rounded off to 2 decimal places) in the measured current at a bias voltage of 0.02 V is ______.

Answer: (11.50 to 12.00)

53. The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, Rthermistor = 2(1 + αT) kΩ, where T is the temperature in ° The temperature coefficient, α, is –(4 ± 0.25)%/°C. Circuit parameters; R1 = 1 kΩ, R2 = 1.3 kΩ, R3 = 2.6 kΩ. The error in the output signal (in V, rounded off to 2 decimal places) at 150°C is _______.

54. An 8085 microprocessor accesses two memory locations (2001 H) and (2002 H), that contain 8-bit numbers 98H and B1H, respectively. The following program is executed:

LXIH,2001H

MVI A, 21H

INX H

INX H

MOV M, A

HLT

At the end of this program, the memory location 2003H contains the number in decimal (base 10) form _______.

Answer: (210 to 210)

55. A conducting square loop of side length 1 m is placed at a distance of 1 m from a long straight wire carrying a current I = 2 A as shown below. The mutual inductance, in nH (rounded off to 2 decimal places), between the conducting loop and the long wire is _______.

Answer: (138.10 to 139.20)

## GATE Exam 2020 Electronics and Communication Engineering (EC) Question Paper With Answer Key

GATE-2020

EC: Electronics and Communication Engineering

GA: General Aptitude

Q 1 – Q5 Carry one mark each.

1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.

(A)    in, of

(B)    from, of

(C)    during, from

(D)    from, from

2. He was not only accused of theft ______ of conspiracy.

(A)    rather

(B)    but also

(C)    but even

(D)    rather than

3. Select the word that fits the analogy:

Explicit : Implicit : : Express: _______

(A)    Impress

(B)    Repress

(C)    Compress

(D)    Suppress

4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.

The French-speaking couple were  upset at ______.

(A)    the in-flight announcements being made in English.

(B)    the English announcements being clearer than the French ones.

(C)    the English announcements being longer than the French ones.

(D)    equal importance being given to English and French.

5. A superadditive function f (∙) satisfies the following property

f(x1 + x2) ≥ f(x1) + f(x2)

Which of the following functions is a superadditive function for x > 1?

(A)    ex

(B)    √x

(C)    1/x

(D)    ex

Q6 – Q10 carry two marks each.

6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.

Which one of the following sequences shows the correct precedence as per the given passage?

(A)    East Asian crisis → subprime lending crisis → banking crisis global financial crisis.

(B)    Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.

(C)    Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.

(D)    Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.

7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

(A)    0°

(B)    7.5°

(C)    15°

(D)    22.5°

8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.

(A)    πa2 – a2

(B)    πa2 – √2a2

(C)    πa2 – 2a2

(D)    πa2 – 3a2

9. a, b, c are real numbers. The quadratic equation ax2 – bx + c = 0 has equal roots, which is β, then

(A)    β = b/a

(B)    β2 = ac

(C)    β3 = bc/(2a2)

(D)    b2 ≠ 4ac

10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .

(A)    8 : 23

(B)    23 : 8

(C)    23 : 31

(D)    31 : 23

EC: Electronics and Communication Engineering

Q1- Q25 carry one mark each.

1. If v1, v2,….,v6 are six vectors in R4, which one of the following statements is FALSE

(A)  It is not necessary that these vectors span R4.

(B)  These vectors are not linearly independent.

(C)  Any four of these vectors form a basis for R4.

(D)  If {v1, v3, v5, v6} spans R4, then it forms a basis for R4

2. For a vector field , which one of the following is FALSE?

(A)  is solenoidal if

(B)   is another vector field.

(C)  is irrotational if

(D)

3. The partial derivative of the function f(x, y, z)  with respect to x at the point (1, 0, e) is

(A)  −1

(B)  0

(C)  1

(D)  1/e

4. The general solution of  is

(A)  y = C1e3x + C2e3x

(B)  y = (C1 + C2x) e3x

(C)  y = (C1 + C2x)e3x

(D)  y = C1e3x

5. The output y[n] of a discrete-time system for an input x[n] is  The unit impulse response of the system is

(A)  0 for all n.

(B)  1 for all n.

(C)  unit step signal u[n].

(D)  unit impulse signal δ[n].

6. A single crystal intrinsic semiconductor is at a temperature of 300 K with effective density of states for holes twice that of electrons. The thermal voltage is 26 mV. The intrinsic Fermi level is shifted from mid-bandgap energy level by

(A)  18.02 meV.

(B)  9.01 meV.

(C)  13.45 meV.

(D)  26.90 meV.

7. Consider the recombination process via bulk traps in a forward biased pn homojunction diode. The maximum recombination rate is Umax. If the electron and the hole capture cross-sections are equal, which one of the following is FALSE?

(A)  With all other parameters unchanged, Umax decreases if the intrinsic carrier density is reduced.

(B)  Umax occurs at the edges of the depletion region in t he device.

(C)  Umax depends exponentially on the applied bias.

(D)  With all other parameters unchanged, Umax increases if the thermal velocity of the carriers increases.

8. The components in the circuit shown below are ideal. If the op-amp is in positive feedback and the input voltage Vi is a since wave of amplitude 1 V, the output voltage Vo is

(A)  a non-inverted sine wave of 2 V amplitude.

(B)  an inverted sine wave of 1 V amplitude.

(C)  a square wave of 5 V amplitude.

(D)  a constant of either +5V or −5V.

9. In the circuit shown below, the Thevenin voltage VTH is

(A)  2.4 V

(B)  2.8 V

(C)  3.6 V

(D)  4.5 V

10. The figure below shows a multiplexer where S1 and S0 are the select lines, I0 to I3 are the input data lines, EN is the enable line, and F(P, Q, R) is the output. F is

(A)

(B)

(C)

(D)

11. The pole-zero map of a rational function G(s) shown below. When the closed contour Γ is mapped into the G(s)-plane, then the mapping encircles

(A)  the origin of the G(s)-plane once in the counter-clockwise direction.

(B)  the origin of the G(s)-plane once in the clockwise direction.

(C)  the point −1 + j0 of the G(s)-plane once in the counter-clockwise direction.

(D)  the point −1 + j0 of the G(s)-plane once in the clockwise direction.

12. A digital communication system transmits a block of N bits. The probability of error in decoding a bit is α. The error event of each bit is independent of the error events of the other bits. The received block is erroneous if at least one of its bits is decoded wrongly. The probability that the received block is erroneous is

(A)  N(1 – α)

(B)  αN

(C)  1 – αN

(D)  1 – (1 – α)N

13. The impedances Z = jX, for all X in the range (−∞, ∞), map to the Smith chart as

(A)  a circle of radius 1 with centre at (0, 0).

(B)  a point at the centre of the chart.

(C)  a line passing through the centre of the chart.

(D)  a circle of radius 0.5 with centre at (0.5, 0).

14. Which one of the following pole-zero plots corresponds to the transfer function of an LTI system characterized by the input-output difference equation given below?

15. In the given circuit, the two-port network has the impedance matrix  The value of ZL for which maximum power is transferred to the load is ________ Ω.

Answer: (48 to 48)

16. The current in the RL-circuit shown below is i(t) = 10 cos(5t – π/4) A. The value of the inductor (rounded off to two decimal places) is _______ H.

Answer: (2.80 to 2.85)

17. In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output V0(rounded off to two decimal places) is _______ V.

Answer: (644 to 657)

18. In the circuit shown below, all the components are ideal. If Vi is +2V, the current Io sourced by the op-amp is _______mA.

Answer: (6 to 6)

19. In an 8085 microprocessor, the number of address lines required to access a 16 K byte memory bank is _________.

Answer: (14 to 14)

20. A 10-bit D/A converter is calibrated over the full range from 0 to 10 V. If the input to the D/A converter is 13A (in hex), the output (rounded off to three decimal places) is _______V.

Answer: (3.050 to 3.080)

21. A transmission line of length 3λ/4 and having a characteristic impedance of 50 Ω is terminated with a load of 400 Ω. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is _______ Ω.

Answer: (6.25 to 6.25)

22. A binary random variable X takes the value +2 or − The probability P(X = +2) = α. The value of α (rounded off to one decimal place), for which the entropy of X is maximum, is _______.

Answer: (0.5 to 0.5)

23. The loop transfer function of a negative feedback system is  The value of K, for which the system is marginally stable, is ________.

Answer: (160 to 160)

24. The random variable  where  and W(t) is a real white Gaussian noise process with two-sided power spectral density SW(f) = 3 W/Hz, for all f. The variance of Y is _______.

Answer: (6 to 6)

25. The two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote the labels corresponding to the outcomes of those tosses. For a random variable X, defined as X = min(M, N), the expected value E(X) (rounded off to two decimal places) is _______.

Answer: (0.25 to 0.25)

Q26 – Q55 carry two marks each.

26. Consider the following system of linear equations.

x1 + 2x2 = b1;      2x1 + 4x2 = b2;             3x1 + 7x2 = b3;             3x1 + 9x2 = b4

Which one of the following conditions ensures that a solution exists for the above system?

(A)  b2 = 2b1 and 6b1 – 3b3 + b4 = 0

(B)  b3 = 2b1 and 6b1 – 3b3 + b4 = 0

(C)  b2 = 2b1 and 3b1 – 6b3 + b4 = 0

(D)  b3 = 2b1 and 3b1 – 6b3 + b4 = 0

27. Which one of the following options contains two solutions of the differential equation

(A)  ln|y – 1| = 0.5x2 + C and y = 1

(B)  ln|y – 1| = 2x2 + C and y = 1

(C)  ln|y – 1| = 0.5x2 + C and y = −1

(D)  ln|y – 1| = 2x2 + C and y = −1

28. The current I in the given network is

(A)  0 A.

(B)  2.38 ∠−96.37° A.

(C)  2.38 ∠143.63° A.

(D)  2.38 ∠−23.63° A.

29. A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) = cos (200 πt) at sampling instants t = n/400, n = 0, 1, …. , 7. The 8-point discrete Fourier transform (DFT) of x[n] is defined as

Which one of the following statements is TRUE?

(A)  All X[k] are non-zero.

(B)  Only X[4] is non-zero.

(C)  Only X[2] and X[6] are non-zero.

(D)  Only X[3] and X[5] are non-zero.

30. For the given circuit, which one of the following is the correct state equation?

31. A one-sided abrupt pn junction diode has a depletion capacitance CD of 50 pF at a reverse bias of 0.2 V. The plot of 1/CD2 versus the applied voltage V for this diode is a straight line as shown in the figure below. The slope of the plot is ________× 1020 F2 V1.

(A)  −5.7

(B)  −3.8

(C)  −1.2

(D)  −0.4

32. The band diagram of a p-type semiconductor with a band-gap of 1 eV is shown. Using this semiconductor, a MOS capacitor having VTH of −16 V C′ox of 100 nF/cm2 and a metal work function of 3.87 eV is fabricated. There is no charge within the oxide. If the voltage across the capacitor is VTH, the magnitude of depletion charge per unit area (in C/cm2) is

(A)  1.70 × 108

(B)  0.52 × 108

(C)  1.41 × 108

(D)  0.93 × 108

33. The base of an npn BJT T1 has a linear doping profile NB(x) as shown below. The base of another npn BJT T2 has a uniform doping NB of 1017 cm3. All other parameters are identical for both the devices. Assuming that the hole density profile is the same as that of doping, the common-emitter current gain of T2 is

(A)  approximately 2.0 times that of T1.

(B)  approximately 0.3 times that of T1.

(C)  approximately 2.5 times that of T1.

(D)  approximately 0.7 times that of T1.

34. A pn junction solar cell of area 1.0 cm2, illuminated uniformly with 100 nW cm2, has the following parameters: Efficiency = 15%, open circuit voltage = 0.7 V, fill factor = 0.8, and thickness = 200 μ The charge of an electron is 1.6 × 1019 C. The average optical generation rate (in cm3 s1) is

(A)  0.84 × 1019.

(B)  5.57 × 1019.

(C)  1.04 × 1019.

(D)  83.60 × 1019.

35. For the BJT in the amplifier shown below, VBE = 0.7 V, kT/q = 26 mV. Assume that BJT output resistance (r0) is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input vi is direct coupled. The low frequency voltage gain v0/vi of the amplifier is

(A)  −89.42

(B)  −128.21

(C)  −178.85

(D)  −256.42

36. An enhancement MOSFET of threshold voltage 3 V is being used in the sample and hold circuit given below. Assume that the substrate of the MOS device is connected to −10 V. If the input voltage v1 lies between ±10 V, the minimum and the maximum values of vG required for proper sampling and holding respectively, are

(A)  3 V and −3 V.

(B)  10 V and −10 V.

(C)  13 V and −7 V.

(D)  10 V and −13 V.

37. Using the incremental low frequency small-signal model of the MOS device, the Norton equivalent resistance of the following circuit is

(A)  rds + R + gmrdsR

(B)

(C)

(D)  rds + R

38. P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is

(A)  110101

(B)  110010

(C)  111101

(D)  111001

39. The state diagram of a sequence detector is shown below. State S0 is the initial state of the sequence detector. If the output is 1, then

(A)  the sequence 01010 is detected.

(B)  the sequence 01011 is detected.

(C)  the sequence 01110 is detected.

(D)  the sequence 01001 is detected.

40. The characteristic equation of a system is s3 + 3s2 + (K + 2)s + 3K = 0. In the root locus plot for the given system, as K varies from 0 to ∞, the break-way or break-in point(s) lie within

(A)  (−1, 0).

(B)  (−2, −1).

(C)  (−3, −2).

(D)  (−∞,−3).

41. The components in the circuit given below are ideal. If R = 2 kΩ and C = 1 μF, the –dB cutt-off frequency of the circuit in Hz is

(A)  14.92

(B)  34.46

(C)  59.68

(D)  79.58

42. For the modulated signal x(t) = m(t) cos (2πfct), the message signal m(t) = 4 cos(1000 πt) and the carrier frequency f­c is 1 MHz. The signal x(t) is passed through a demodulator, as shown in the figure below. The output y(t) of the demodulator is

(A)  cos(460 πt).

(B)  cos(920 πt).

(C)  cos(1000 πt).

(D)  cos(540 πt).

43. For an infinitesimally small dipole in free space, the electric field Eθ in the far field is proportional to (ejkr/r) sin θ, where k = 2π/λ. A vertical infinitesimally electric dipole (δl << λ) is placed at a distance h(h > 0) above an infinite ideal conducting plane, as shown in the figure. The minimum value of h, for which one of the maxima in the far field radiation pattern occurs at θ = 60°, is

(A)  λ

(B)  0.5λ

(C)  0.25λ

(D)  0.75λ

44. In the voltage regulator shown below, V1 is the unregulated input at 15 V. Assume VBE = 0.7 V and the base current in negligible for both the BJTs. If the regulated output VO is 9 V, the value of R­2 is ________ Ω.

Answer: (800 to 800)

45. The magnetic field of a uniform plane wave in vacuum is given by  cos(ωt + 3x – y – z). The value of b is _______.

Answer: (1 to 1)

46. For a 2-port network consisting of an ideal lossless transformer, the parameter S21 (rounded off to two decimal places) for a reference impedance of 10 Ω, is _______.

Answer: (0.8 to 0.8)

47. SPM(t) and S­FM(t) as defined below, are the phase modulated and the frequency modulated waveforms, respectively, corresponding to the message signal m(t) shown in the figure.

SPM(t) = cos(1000πt + Kpm(t))

where Kp is the phase deviation constant in radians/volt and Kf is the frequency deviation constant in radians/second/volt. If the highest instantaneous frequencies of SPM(t) and SFM(t) are same, then the value of the ratio kp/kff is _______ seconds.

Answer: (2 to 2)

48. In a digital communication system, a symbol S randomly chosen from the set {s1, s2, s3, s4} is transmitted. It is given that s1 = −3, s2 = −1, s3 = +1 and s4 = +2. The received symbol is Y = S + W. W is a zero-mean unit-variance Gaussian random variable and is independent of S. Pi­ is the conditional probability of symbol error for the maximum likelihood (ML) decoding when the transmitted symbol S = si. The index i for which the conditional symbol error probability Pi is the highest is _________.

Answer: (3 to 3)

49. A system with transfer function  is subjected to an input 5 cos 3t. The steady state output of the system is  The value of a is _______.

Answer: (3.95 to 4.05)

50. For the components in the sequential circuit shown below, tpd is the propagation delay, tsetup is the setup time, and thold is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is _________ MHz.

Answer: (76 to 77)

51. For the solid S shown below, the value of  (rounded off to two decimal places) is ___________

Answer: (2.25 to 2.25)

52. X(ω) is the Fourier transform of x(t) shown below. The value of  (rounded off to two decimal places) is _________.

Answer: (58.50 to 58.80)

53. The transfer function of a stable discrete-time LTI system is  where K and α are real numbers. The value of α (rounded off to one decimal place) with |α| > 1, for which the magnitude response of the system is constant over all frequencies, is _______.

Answer: (-2 to -2)

54. X is a random variable with uniform probability density function in the interval [−2, 10]. For Y = 2X – 6, the conditional probability P(Y ≤ 7\X ≥ 5) (rounded off to three decimal places) is ________.

Answer: (0.299 to 0.301)

55. Consider the following closed loop control system

where  If the steady state error for a unit ramp input is 0.1, then the value of K is _________.

Answer: (30 to 30)

## GATE Exam 2020 Chemistry (CY) Question Paper With Answer Key

GATE-2020

CY: Chemistry

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. While I agree _____ his proposal this time, I do not often agree _____ him.

(A)  to, with

(B)  with, to

(C)  with, with

(D)  to, to

2. The recent measures to improve the output would _______ the level of production to our satisfaction.

(A)  increase

(B)  decrease

(C)  speed

(D)  equalise

3. Select the word that fits the analogy:

White : Whitening : Light: ______

(A)  Lightning

(B)  Lightening

(C)  Lighting

(D)  Enlightening

4. In one of the greatest innings ever seen in 142 years of Test history, Ben Stokes upped the tempo in a five-and-a-half hour long stay of 219 balls including 11 fours and 8 sixes that saw him finish on a 135 not out as England squared the five-match series.

Based on their connotations in the given passage, which one of the following meanings DOES NOT match?

(A)  upped = increased

(B)  squared = lost

(C)  tempo = enthusiasm

(D)  saw = resulted in

5. There are five levels {P, Q, R, S, T} in a linear supply chain before a product reaches customers, as shown in the figure.

At each of the five levels, the price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid (in rupees) by the customers?

(A)  187.50

(B)  234.38

(C)  292.26

(D)  366.21

Q6 – Q10 carry two marks each.

6. Climate change and resilience deal with two aspects – reduction of sources of non-renewable energy resources and reducing vulnerability of climate change aspects. The terms ‘mitigation’ and ‘adaptation’ are used to refer to these aspects, respectively.

Which of the following assertions is best supported by the above in information?

(A)  Mitigation deals with consequences of climate change.

(B)  Adaptation deals with causes of climate change.

(C)  Mitigation deals with actions taken to reduce the use of fossil fuels.

(D)  Adaptation deals with actions taken to combat gree-house gas emissions.

7. Find the missing element in the following figure.

(A)  d

(B)  e

(C)  w

(D)  y

8. It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

(A)  3 days

(B)  5 days

(C)  10 days

(D)  13 days

9. An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below : (the product of X and Y linearly varies with Z)

Then, which of the following statements is FALSE?

(A)  For fixed Z; X is proportional to Y

(B)  For fixed Y; X is proportional to Z

(C)  For fixed X; Z is proportional to Y

(D)  XY/Z is constant

10. The two pie-charts given below show the data of total students and only girls registered in different streams in a university. If the total number of students registered in the university is 5000, and the total number of the registered girls is 1500; then, the ratio of boys enrolled in Arts to the girls enrolled in Management is ______.

(A)  2:1

(B)  9:22

(C)  11:9

(D)  22:9

CY: Chemistry

Q1 – Q25 carry one mark each.

1. Among the following, the suitable reagents for the given transformation is:

(A)  H2, Pd/C

(B)  H2N-NH2/KOH, ∆

(C)  NaBH4/CeCl3∙7H2O

(D)  Li/Liq. NH3

2. Major product formed in the following reaction sequence is:

3. Major product formed in the following reaction is:

4. Major product formed in the following transformation is:

5. Absolute stereochemistry of the given compound is:

(A)  4aR, 8aS

(B)  4aR, 8aR

(C)  4aS, 8aS

(D)  4aS, 8aR

6. In the following reaction sequence,

the major product P and Q are :

7. Major product formed in the given reaction is:

8. The CORRECT statement regarding the substitution of coordinated ligands in Ni(CO)4 and CO(NO)(CO)3 is:

(Given Co―N―O bond is nearly linear; atomic numbers of Co and Ni are 27 and 28, respectively)

(A)  Ni(CO)4 and Co(NO)(CO)3 follow associative and dissociative pathways, respectively.

(B)  Ni(CO)4 and Co(NO)(CO)3 follow dissociative and associative pathways, respectively.

(C)  Both Ni(CO)4 and Co(NO)(CO)3 follow associative pathway.

(D)  Both Ni(CO)4 and Co(NO)(CO)3 follow dissociative pathway.

9. The CORRECT statement about hexagonal boron nitride is :

(A)  It is a good electrical conductor.

(B)  It has same layer stacking as that of graphite.

(C)  It is reactive towards fluorine.

(D)  It has lower thermal stability in air compared to that of graphite.

10. In oxyhemocyanin, the coordination number, mode of oxygen binding, color and the net magnetic behavior of copper ions, respectively are:

(Given: atomic number of Cu is 29)

(A)  Four, μ-η11-O2, colorless and paramagnetic.

(B)  Five, μ-η22-O2, colorless and paramagnetic.

(C)  Five, μ-η22-O22, blue and diamagnetic.

(D)  Four, μ-η11-O22, blue and diamagnetic.

11. Among the following species, the one that has pentagonal shape is:

(Given: atomic numbers of O, F, S, I and Xe are 8, 9, 16, 53 and 54, respectively)

(A)  XeOF4

(B)  IF5

(C)  [SF5]

(D)  [XeF5]

12. A solution containing a metal complex absorbs at 480 mm with molar extinction coefficient of 15,000 L mol1 cm1. If the path length of the cell is 1.0 cm and transmittance is 20.5%, the concentration (in mol L1) of the metal complex is:

(A)  1.37 × 105

(B)  2.29 × 105

(C)  4.59 × 105

(D)  8.75 × 105

13. Among the following linear combination of atomic orbitals, the CORRECT representation of the lowest unoccupied π-molecular orbital of butadiene is:

(A)  Ψ = −0.372 ϕ1 + 0.602 ϕ2 – 0.602 ϕ3 + 0..372 ϕ4

(B)  Ψ = 0.602 ϕ1 – 0.372 ϕ2 – 0.372 ϕ3 + 0.602 ϕ4

(C)  Ψ = 0.602 ϕ1 + 0.372 ϕ2 – 0.372 ϕ3 – 0.602 ϕ4

(D)  Ψ = 0.372 ϕ1 + 0.602 ϕ2 + 0.602 ϕ3 + 0.372 ϕ4

14. The activity of ‘m’ molal CuSO­4 solution can be expressed in terms of its mean activity coefficient (γ±) as:

(A)  m2γ±2

(B)  4m3γ±3

(C)  16m4γ±4

(D)  108 m5γ±5

15. The character table for a pyramidal AB3 molecule of C3v point group is given below:

The reducible representation of pyramidal AB3 is

The CORRECT option representing all the normal Raman active modes of pyramidal AB3 is :

(A)  A1 + A2 + 2E

(B)  3E

(C)  3A1 + A2 + E

(D)  2A1 + 2E

16. In the following reaction,

the number of peaks exhibited by the major product P in its broadband proton decoupled 13C NMR spectrum is_______

Answer: (8.0 to 8.0)

17. Among the following,

the total number of aromatic species is________

Answer: (4.0 to 4.0)

18. The maximum number of microstates of d2 electronic configuration is_________

Answer: (45 to 45)

19. In a uranium recovery process, an aqueous solution of uranyl ion is evaporated, dried in air at 400°C and subsequently reduced with hydrogen at 700°C to obtain a uranium compound (X). The oxidation state of uranium in X is __________

(Given : atomic number of U is 92)

Answer: (4 to 4)

20. For a cubic crystal system, the powder X-ray diffraction pattern recorded using Cu Kα source (λ = 1.54 Å) shows a peak at 33.60° (2θ) for (111) plane. The lattice parameter ‘a’ (in Å, rounded off to two decimal places) is _________

Answer: (4.60 to 4.64)

21. In an NMR spectrometer operating at a magnetic field strength of 16.45 T, the resonance frequency (in MHz, rounded off to one decimal place) of 19F nucleus is ________

(Given : g factor of 19F = 5.255; βN = 5.05 × 1027 J T1; h = 6.626 × 1034 J s)

Answer: (658 to 659)

22. When three moles of helium is mixed with one mole of neon at constant temperature and pressure (25 °C, 1 atm), the entropy of mixing (in J K1, rounded off to two decimal places) is ________

(Given : R = 8.314 J K1 mol1)

Answer: (18.60 to 18.80)

23. At 25°C, the emf(in volts, rounded off to three decimal places) of the cell, Ag | AgBr(s) | Br (a = 0.20), Cu2+ (a = 0.48), Cu+(a = 0.24) | Pt is _______

(Given : The standard emf of the cell is 0.082 V; R = 8.314 J K1 mol1; F = 96500 C mol1)

Answer: (0.058 to 0.060)

24. For an enzyme catalyzed reaction, the plot of inverse of initial rate against inverse of initial substrate concentration is linear with slope 0.16 s and intercept 2.12 mol1 L s. The estimated value of Michaelis constant (in mol L1, rounded off to two decimal places is ________

Answer: (0.07 to 0.08)

25. Fluorescence quantum yield and fluorescence lifetime of a molecule are 0.4 and 5 × 109 s, respectively. If the fluorescence decay rate constant is Y × 107 s1, t he value of Y (rounded off to nearest integer) is _________

Answer: (8 to 8)

Q26 – Q55 carry two marks each.

26. Major product formed in the following reaction sequence is:

27. Major products P and Q, in the given reaction sequence, are:

28. Major products P and Q, formed in the reactions given below, are:

29. A compound with molecular formula C10H12O12 showed a strong IR band at ~ 720 cm1 a peak at m/z 122 in the mass spectrum and the following 1H NMR signals: δ1 – 8.0 (2H, m), 7.6 – 7.5(1H, m), 7.5 – 7.3 (2H, m), 4.3(2H, t), 1.8 (2H sextet) and 1.0 (3H, t). The structure of the compound is:

30. Major product formed in the following synthetic sequence is:

31. The CORRECT statement with respect to the stereochemistry of α-hydroxy acids P and Q formed in the following reactions is:

(A)  Both P and Q are formed with retention of configuration.

(B)  Both P and Q are formed with inversion of configuration.

(C)  P is formed with retention of configuration and Q with inversion of configuration.

(D)  P is formed with inversion of configuration and Q with retention of configuration.

32. The rate of solvolysis of the given compounds is in the order

(A)  T > R > Q > S > P

(B)  Q > T > R > P > S

(C)  R > T > Q > S > P

(D)  T > Q > R > P > S

33. In the following reaction sequence, the major products Q and R are:

34. In the electronic absorption spectrum of an aqueous solution of [Ni(NH3)6]2+, a very weak band is observed between the bands due to the transitions 3A2g3T2g and 3A2g3T1g(F). The transition responsible for the very weak band is

(Given: atomic number of Ni is 28)

(A)  3A2g1T1g

(B)  3A2g1T2g

(C)  3A2g1Eg

(D)  3A2g1A2g

35. The experimental magnetic moment (3.4 BM) of a hydrated salt of Eu3+ at 27°C is significantly different from the calculated value. The difference is due to

(Given: atomic number of Eu is 63)

(A)  population of electrons at higher J level(s) via thermal excitation.

(B)  strong ligand field splitting of f-orbitals.

(C)  strong spin-orbit coupling.

(D)  pairing of electrons in f-orbitals.

36. The CORRECT combination of L1 and L2 among H, NO, MeCH2 and CO, that will satisfy the 18 electron rule for both metal centers in the following neutral molecule, is

(Given: atomic number of Ru is 44)

(A)  H, NO

(B)  MeCH2, NO

(C)  MeCH2, CO

(D)  H, CO

37. In the following reaction sequence,

the structure of B is

(Given: atomic number of Mo is 42)

38. The following table lists the reaction/conversion catalyzed by metalloenzymes.

The correct combination is

(A)  P-II; Q-I; R-III; S-IV

(B)  P-IV; Q-III; R-II; S-I

(C)  P-II; Q-III; R-IV; S-I

(D)  P-I; Q-IV; R-III; S-II

39. The fission of  with thermal neutron is represented below.

are the primary fission fragment pair, which undergo series of radioactive decay to form stable nuclei X3 and X4 (chain enders). The X3 and Y4, respectively are:

(A)

(B)

(C)

(D)

40. The CORRECT ‘voltage (E) versus time’ excitation signal used in cyclic voltammetry is

41. The hydrogen-like radial wave function of the 3s orbital is given as

where ρ = 2Zr/a0; Z = atomic number, r = distance from the nucleus and a0 = Bohr radius. Positions of the radial nodes (in  units of a0) of the 3s orbital are at

(A)

(B)

(C)

(D)

42. ∆Gf0 and ∆Hf0 for Fe(g) are 370.7 kJ mol1 and 416.3 kJ mol1 at 298 K, respectively. Assuming ∆Hf0 is constant in the interval 250 K to 375 K, ∆Gf0 (rounded off to the nearest integer) for Fe(g) at 375 K is:

(A)  359 kJ mol1

(B)  338 kJ mol1

(C)  325 kJ mol1

(D)  310 kJ mol1

43. Adsorption of N2 on TiO2 was carried out at 75 K. A plot of  gives a straight line with an intercept, 4.0 × 106 mm3 and slope, 1.0 × 103 mm3. The volume (rounded off to the nearest integer) corresponding to the monolayer coverage is:

(A)  996 mm3

(B)  785 mm3

(C)  690 mm3

(D)  555 mm3

44. Among the following sets,

the total number of set(s) of diastereomeric pair(s) is _______

Answer: (4.0 to 4.0)

45. Among the following.

the total number of compounds showing characteristic carbonyl stretching frequency less than 1700 cm1 in their IR spectra is _______

Answer: (3.0 to 3.0)

46. Consider the AgX crystallizes in rock salt structure. The density of AgX is 6477 kg/m3 and unit cell length is 577.5 pm. Atomic weight of Ag is 107.87 g mol1. The atomic weight of X (in g mol1, rounded off to two decimal places) is _______

Answer: (79.00 to 81.00)

47. The total number of g|| lines expected in the EPR spectrum of a solution of bis(salicylaldimine) copper(II) having pure 63Cu and 14N at 77 K is ________

(Given: I values of 63Cu, 14N and 1H are 3/2, 1 and 1/2, respectively)

Answer: (60 to 60)

48. Among the following,

[B12H12]2, [Ni5(CO)­12]2, [C2B9H11]2, Rh6(CO)16, Os6(CO)20, B5H11, B6H10 the total number of species having nido structure is________

(Given : atomic numbers of H, B, C, O, Ni, Rh and Os are 1, 5, 6, 8, 28, 45 and 76, respectively)

Answer: (3 to 3)

49. The frequency (in cm1, rounded off to two decimal places) for pure rotational line in the spectrum of NO molecule due to change in the quantum number from J = 1 to J = 2 is _______

(Given: Moment of inertia of NO = 1.6427 × 1046 kg m2; h = 6.626 × 1034 J s; c = 3 × 108 m/s)

Answer: (6.80 to 6.82)

50. The % error (rounded off to two decimal places) in the ground state energy of a particle in a one dimensional box of length ‘a’ described by a trial variation function φ = x(a – x), where 0 ≤ x ≤ a, is ________

(Given: The true ground state energy of the above system is h2/8ma2

Answer: (1.22 to 1.44)

51. Assuming no interaction between vibrational and rotational energy levels in HF, the frequency (in cm1, rounded off to the nearest integer) of the R branch line originating from J = 4 in its IR spectrum is ________

(Given: Rotational constant of HF = 19.35 cm1

Answer: (4332 to 4332)

52. The van der Waals constants a and b for gaseous CO are given as 1.49 L2 atm mol2 and 0.0399 L mol1, respectively. The fugacity (in atm, rounded off to two decimal places) of CO at 35°C and 95 atm is ______

(Given: R = 0.082 L atm K−1 mol−1)

Answer: (88.11 to 88.60)

53. At 30°C, the vapor pressure and density of a 1.0 M aqueous solution of sucrose are 31.207 mm Hg and 1.1256 g/mL, respectively. If the vapor pressure of pure water at 30°C is 31.824 mm Hg, the activity coefficient (rounded off to three decimal places) of water in the given solution is _______

(Given: The molar mass of sucrose = 342.3 g mol1)

Answer: (1.002 to 1.004)

54. For the ring opening reaction of cyclopropane to propene at 25°C, the pre-exponential factor is 4.3 × 1015 s1. The entropy of activation (in J K1 mol1, rounded off to two decimal places) is _______.

(Given: h = 6.626 × 1034 J s; kB = 1.38 × 1023 J K1; R = 8.314 J K1 mol1)

Answer: (46.00 to 46.10)

55. In a reaction, reactant X is converted to products Y and Z consecutively with rate constants 6.0 × 102 min1 and 9.0 × 103 min1, respectively. If the initial amount of X is 12.5 moles, the number of moles (rounded off to one decimal place) of Y formed after 10 minutes is ________

Answer: (5.3 to 5.5)

## GATE Exam 2020 Computer Science and Information Technology (CS) Question Paper With Answer Key

GATE-2020

CS: Computer Science and Information Technology

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Raman is confident of speaking English ______ six months as he has been practicing regularly ________ the last three weeks.

(A)  during, for

(B)  for, since

(C)  for, in

(D)  within, for

2. His knowledge of the subject was excellent but his classroom performance was _______.

(A)  extremely poor

(B)  good

(C)  desirable

(D)  praiseworthy

3. Select the word that fits the analogy:

Cook : Cook :: Fly :_____

(A)  Flyer

(B)  Flying

(C)  Flew

(D)  Flighter

4. The drawn of the 21st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to man-made emissions, at least 30% of the northern hemisphere’s surface permafrost could melt by the end of the century. Given this situation of imminent global exodus of billions of people displaced by rising seas, nation-states need to rethink their carbon footprint for political concerns, if not for environmental ones.

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

(A)  Nation-states do not have environmental concerns.

(B)  Nation-states are responsible for providing fresh water to billions of people.

(C)  Billions of people are responsible of man-made emissions.

(D)  Billions of people are affected by melting glaciers.

5. There are multiple routes to reach from node 1 to node 2, as shown in the network.

The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs. 200, and is Rs.100 for the other toll booths. Which is the cheapest route from node 1 to node 2?

(A)  1-a-c-2

(B)  1-f-b-2

(C)  1-b-2

(D)  1-f-e-2

Q6 – Q10 carry two marks each.

6. Goods and Services Tax (GST) is an indirect tax introduced in India in 2017 that is imposed on the supply of goods and services, and it subsumes all indirect taxes except few. It is a destination-based tax imposed on goods and services used, and it is not imposed at the point of origin from where goods come. GST also has a few components specific to state governments, central government and Union Territories (UTs).

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

(A)  GST is imposed on the production of goods and services.

(B)  GST includes all indirect taxes.

(C)  GST does not have a component specific to UT.

(D)  GST is imposed at the point of usage of goods and services.

7. If P = 3, R = 27, T = 243, then Q + S = _____.

(A)  40

(B)  80

(C)  90

(D)  110

8. The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is ________.

(A)

(B)  π[(b2 – a2) – n(b – a)2]

(C)

(D)  π[(b2 – a2) + n(b – a)2]

9. Two straight lines are drawn perpendicular to each other in X-Y plane. If α and β are the acute angles the straight lines make with t he X-axis, then α + β is _______.

(A)  60°

(B)  90°

(C)  120°

(D)  180°

10. The total revenue of a company during 2014-2018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during 2014-2018 is ______.

(A)  16.67% profit

(B)  16.67% loss

(C)  20% profit

(D)  20% loss

CS: Computer Science and Information Technology

Q1 – Q25 carry one mark each.

1. Consider the functions

(I) ex

(II) x2 – sin x

(III)

Which of the above functions is/are increasing everywhere in [0, 1]?

(A)  III only

(B)  II only

(C)  II and III only

(D)  I and III only

2. For parameters a and b, both of which are ω(1), T(n) = T(n1/a) + 1, and T(b) = 1.

Then T(n) is

(A)  Θ(loga logb n)

(B)  Θ(logab n)

(C)  Θ(logb loga n)

(D)  Θ(log2 log2 n)

3. Consider the following statements.

(I) Daisy chaining is used to assign priorities in attending interrupts.

(II) When a device raises a vectored interrupt, the CPU does polling to identify the source of interrupt.

(III) In polling, the CPU periodically checks the status bits to know if any device needs its attention.

(IV) During DMA, both the CPU and DMA controller can be bus masters at the same time.

Which of the above statements is/are TRUE?

(A)  I and II only

(B)  I and IV only

(C)  I and III only

(D)  III only

4. Consider the following data path diagram.

Consider an instruction: R0 ← R1 + R2. The following steps are used to execute it over the given data path. Assume that PC is incremented appropriately. The subscripts r and w indicated read and write operations, respectively.

(1) R2r, TEMP1r, ALUadd, TEMP2w

(2) R1r, TEMP1w

(3) PCr, MARw, MEMr

(4) TEMP2r, R0w

(5) MIDR­r­, IRw

which one of the following is the correct order of execution of the above steps?

(A)  2, 1, 4, 5, 3

(B)  1, 2, 3, 4, 5

(C)  3, 5, 2, 1, 4

(D)  3, 5, 1, 2, 4

5. The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19.

Which one of the following is the postorder traversal of the tree?

(A)  10, 11, 12, 15, 16, 18, 19, 20

(B)  11, 12, 10, 16, 19, 18, 20, 15

(C)  20, 19, 18, 16, 15, 12, 11, 10

(D)  19, 16, 18, 20, 11, 12, 10, 15

6. What is the worst case time complexity of inserting n2 elements into an AVL-tree with n elements initially?

(A)  Θ(n4)

(B)  Θ(n2)

(C)  Θ(n2 log n)

(D)  Θ(n3)

7. Which one of the following regular expressions represents at set of all binary strings with an odd number of 1’s?

(A)  ((0 + 1)*1(0 + 1)*1)*10*

(B)  (0*10*10*)*0*1

(C)  10*(0*10*10*)*

(D)  (0*10*10*)*10*

8. Consider the following statements.

(I) If L1 ⋃ L2 is regular, then both L1 and L2 must be regular.

(II) The class of regular languages is closed under infinite union.

Which of the above statement is/are TRUE?

(A)  I only

(B)  II only

(C)  Both I and II

(D)  Neither I nor II

9. Consider the following statements.

(I) Symbol table is accessed only during lexical analysis and syntax analysis.

(II) Compilers for programming languages that support recursion necessarily need heap storage for memory allocation in the run-time environment.

(III) Errors violating the condition ‘any variable must be declared before its use’ are detected during syntax analysis.

Which of the above statements is/are TRUE?

(A)  I Only

(B)  I and III only

(C)  II only

(D)  None of I, II and III

10. Consider the language L = {an | n ≥ 0} ⋃ {anbn | n ≥ 0} and the following statements.

(I) L is deterministic context-free.

(II) L is context-free but not deterministic context-free.

(III) L is not LL(k) for any k.

Which of the above statements is/are TRUE?

(A)  I only

(B)  II only

(C)  I and III only

(D)  III only