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GATE Exam 2022 Mechanical Engineering (ME-2) Question Paper With Answer Key

July 18, 2022 by suresh84

GATE-2022

ME2: Mechanical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Writing too many things on the ________ while teaching could make the students get _________.

(A) bored / board

(B) board / bored

(D) bored / bored

Answer: (B)

2. Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality on the real number line?

Answer: (C)

3. If f(x) = 2 ln (√e^x), what is the area bounded by f(x) for the interval [0, 2]on the x-axis?

(A) 1/2

(B) 1

(D) 4

Answer: (C)

4. A person was born on the fifth Monday of February in a particular year.

Which one of the following statements is correct based on the above information?

(A) The 2nd February of that year is a Tuesday

(B) There will be five Sundays in the month of February in that year

(D) All Mondays of February in that year have even dates

Answer: (A)

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other?(rotation and translation operations may be used).

Answer: (B OR C)

Q.6 – Q. 10 Carry TWO marks each.

6. Fish belonging to species S in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower collagen on their skin, making their skin more fragile.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Having ultra-black skin is only advantageous to species S

(B) Species S with lower collagen in their skin are at an advantage because it helps them avoid predators

(D) Having ultra-black skin is only disadvantageous to species S but advantageous only to their predators

Answer: (C)

7. For the past m days, the average daily production at a company was 100 units per day.

If today’s production of 180 units changes the average to 110 units per day, what is the value of m?

(A) 18

(B) 10

(D) 5

Answer: (C)

8. Consider the following functions for non-zero positive integers, p and q.

Which one of the following options is correct based on the above?

(A) f(2,2) = g(2,2)

(B) f(g(2,2), 2) < f(2, g(2,2)

(D) f(3,2) >g(3,2)

Answer: (A)

9. Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.

If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?

(A) 6 hours 30 minutes

(B) 3 hours 45 minutes

(D) 5 hours 15 minutes

Answer: (A)

10. Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?

(A) 2 : 3

(B) 1 : 1

(D) 2 : 1

Answer: (B)

ME2: Mechanical Engineering

Q.11 – 35 Carry ONE mark each.

11. F(t) is a periodic square wave function as shown. It takes only two values, 4 and 0, and stays at each of these values for 1 second before changing. What is the constant term in the Fourier series expansion of F(t)?

(A) 1

(B) 2

(D) 4

Answer: (B)

12. Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point (1, 2, 3). The surface integral of a vector field over the entire surface A of the cube is ______.

(A) 14

(B) 27

(D) 31

Answer: (A)

13. Consider the definite integral

Let I_e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is I_s. The percentage error is defined as 𝑒 = 100 × (I_e − I_s)/I_e. The value of e is

(A) 2.5

(B) 3.5

(D) 0

Answer: (D)

14. Given

If a and b are positive integers, the value of is ______.

Answer: (B)

15. A polynomial φ(s) = a_nsⁿ + a_{n – 1}sⁿ⁻¹ + … + a₁s + a₀ of degree n> 3 with constant real coefficients a_n, a_n₋₁, … a₀ has triple roots at s = −σ. Which one of the following conditions must be satisfied?

Answer: (B)

16. Which one of the following is the definition of ultimate tensile strength (UTS)obtained from a stress-strain test on a metal specimen?

(A) Stress value where the stress-strain curve transitions from elastic to plastic behavior

(B) The maximum load attained divided by the original cross-sectional area

(D) Stress where the specimen fractures

Answer: (B)

17. A massive uniform rigid circular disc is mounted on a frictionless bearing at the end E of a massive uniform rigid shaft AE which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings AB and CD as shown,where G is the center of mass of the shaft-disc assembly and g is the acceleration due to gravity. The disc is then given a rapid spin ω about its axis in the positive x-axis direction as shown, while the shaft remains at rest. The direction of rotation is defined by using the right-hand thumb rule. If the string AB is suddenly cut,assuming negligible energy dissipation, the shaft AE will

(A) rotate slowly (compared to ω) about the negative z-axis direction

(B) rotate slowly (compared to ω) about the positive z-axis direction

(D) rotate slowly (compared to ω) about the negative y-axis direction

Answer: (A)

18. A structural member under loading has a uniform state of plane stress which in usual notations is given byσ_x = 3P, σ_y = −2P and τ_xy = √2P, where P > 0. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of P at which yielding starts (according to the maximum distortion energy theory) is

(A) 70 MPa

(B) 90MPa

(D) 75MPa

Answer: (A)

19. Fluidity of a molten alloy during sand casting depends on its solidification range.The phase diagram of a hypothetical binary alloy of components A and B is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, including the solidus and liquidus lines, are straight lines. If this binary alloy with 15 weight % of B is poured into a mould at a pouring temperature of 800ºC, then the solidification range is

(A) 400°C

(B) 250°C

(D) 150°C

Answer: (D)

20. A shaft of diameter is assembled in a hole of diameter Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft-hole assembly.

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

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

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

Answer: (A)

21. Match the additive manufacturing technique in Column I with its corresponding input material in Column II.

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

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

(D) P-4, Q-1, R-4

Answer: (A)

22. Which one of the following CANNOT impart linear motion in a CNC machine?

(A) Linear motor

(B) Ball screw

(D) Chain and sprocket

Answer: (D)

23. Which one of the following is an intensive property of a thermodynamic system?

(A) Mass

(B) Density

(D) Volume

Answer: (B)

24. Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right.

Pressure at location B is observed to be higher than that at an upstream location A.Which among the following options can be the reason?

(A) Since volume flow rate is constant, velocity at B is lower than velocity at A

(B) Normal shock

(D) Boundary layer separation

Answer: (B)

25. Which of the following non-dimensional terms is an estimate of Nusselt number?

(A) Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance

(B) Ratio of the rate at which internal energy is advected to the rate of conduction heat transfer

(D) Non-dimensional velocity gradient multiplied by Prandtl number

Answer: (C)

26. A square plate is supported in four different ways (configurations (P) to (S) as shown in the figure). A couple moment C is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to be frictionless. All support links of the plate are identical.

The square plate can remain in equilibrium in its initial state for which one or more of the following support configurations?

(A) Configuration (P)

(B) Configuration (Q)

(D) Configuration (S)

Answer: (B, C, D)

27. Consider sand casting of a cube of edge length a. A cylindrical riser is placed at the top of the casting. Assume solidification time,t_s∝ V/A, where V is the volume and A is the total surface area dissipating heat. If the top of the riser is insulated,which of the following radius/radii of riser is/are acceptable?

(A) a/3

(B) a/2

(D) a/6

Answer: (A,B OR B)

28. Which of these processes involve(s) melting in metallic workpieces?

(A) Electrochemical machining

(B) Electric discharge machining

(D) Electron beam machining

Answer: (B,C,D)

29. The velocity field in a fluid is given to be Which of the following statement(s) is/are correct?

(A) The velocity field is one-dimensional.

(B) The flow is incompressible.

(D) The acceleration experienced by a fluid particle is zero at (x = 0, y = 0).

Answer: (B,C,D)

30. A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of 20 N each can be placed on the platforms. The number of discs placed on the left side plat form is n and that on the right side platform is m.

It is found that for n = 5 and m = 0, a force F = 200 N (refer to part (i) of the figure)is just sufficient to initiate upward motion of the left side platform. If the force F is removed then the minimum value of 𝑚 (refer to part (ii) of the figure) required to prevent downward motion of the left side platform is______ (in integer).

Answer: (3 to 3)

31. For a dynamical system governed by the equation,

the damping ratioζ is equal to The displacement x of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be 4 mm. Neglecting higher powers (>1) of the damping ratio, the displacement at the next peak in the positive direction will be___________ mm (in integer).

Answer: (1.95 to 2.05)

32. An electric car manufacturer underestimated the January sales of car by 20 units,while the actual sales was 120 units. If the manufacturer uses exponential smoothing method with a smoothing constant of α = 0.2, then the sales forecast for the month of February of the same year is ___________units (in integer).

Answer: (104 to 104)

33. The demand of a certain part is 1000 parts/year and its cost is Rs. 1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering isRs. 100/order and the lead time for receiving the orders is 5 days. If the holding cost is Rs. 20/part/year, the inventory level for placing the orders is _________ parts(round off to the nearest integer).

Answer: (13 to 15)

34. Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume c_v is equal to 750 J∙kg⁻¹∙K⁻¹. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be _________ bar (in integer).

Answer: (2 to 2)

35. Wien’s law is stated as follows: λ_mT= C, where C is 2898 μm∙K and λ_m is the wavelength at which the emissive power of a black body is maximum for a given temperature T. The spectral hemispherical emissivity (ε_λ) of a surface is shown in the figure below (1Å = 10^–10m). The temperature at which the total hemispherical emissivity will be highest is __________ K (round off to the nearest integer).

Answer: (4825 to 4835)

Q.36 – 65 Carry TWO marks each.

36. For the exact differential equation,

which one of the following is the solution?

(A) u² + 2x² = constant

(B) xu² + u = constant

(C)

(D)

Answer: (C)

37. A rigid homogeneous uniform block of mass 1 kg, height h = 0.4 m and width b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field(g = 9.81 m/s²), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force F, producing an impulse I_F , is applied at a height of d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of I_F required to topple the block is

(A) 0.953 Ns

(B) 1.403Ns

(D) 1.172Ns

Answer: (A)

38. A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stressσ_xx is _______.

(A) 3σ/2

(B) σ(1 + 1/√2)

(D) σ(1 – 1/√2)

Answer: (A)

39. A rigid body in the X-Y plane consists of two point masses (1 kg each) attached to the ends of two massless rods, each of 1 cm length, as shown in the figure. It rotates at 30 RPM counter-clockwise about the Z-axis passing through point O. A point mass of√2 kg, attached to one end of a third massless rod, is used for balancing the body by attaching the free end of the rod to point O. The length of the third rod is ________ cm.

(A) 1

(B) √2

(D) 1/2√2

Answer: (A)

40. A spring mass damper system (mass m, stiffness k, and damping coefficient c)excited by a force F(t) = B sin ωt, where B, ω and t are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system(marked as (i) to (iv)) are shown just to the right of the system figure. In the figures of the responses, A is the amplitude of response shown in red color and the dashed lines indicate its envelope. The responses represent only the qualitative trend and those are not drawn to any specific scale.

Four different parameter and forcing conditions are mentioned below.

Which one of the following options gives correct match (indicated by arrow →) of the parameter and forcing conditions to the responses?

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

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

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

Answer: (C)

41. Parts P1-P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required for carrying out both the operations for all 7 parts is ________ hours.

(A) 31

(B) 33

(D) 32

Answer: (B)

42. A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is Rs. _______.

(A) 5000

(B) 4000

(D) 6000

Answer: (B)

43. A tube of uniform diameter D is immersed in a steady flowing inviscid liquid stream of velocity V, as shown in the figure. Gravitational acceleration is represented by g.The volume flow rate through the tube is ______.

Answer: (D)

44. The steady velocity field in an inviscid fluid of density 1.5 is given to be Neglecting body forces, the pressure gradient at(x = 1, y = 1) is ________.

Answer: (C)

45. In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg. The exit of the compressor is super heated at condenser pressure with specific enthalpy equal to 300 kJ/kg. At the condenser exit, the refrigerant is throttled to the evaporator pressure. The coefficient of performance (COP) of the cycle is 3. If the specific enthalpy of the saturated liquid at evaporator pressure is 50 kJ/kg, then the dryness fraction of the refrigerant at entry to evaporator is _________.

(A) 0.2

(B) 0.25

(D) 0.35

Answer: (B)

46. A is a 3×5 real matrix of rank 2. For the set of homogeneous equations Ax = 0,where 0 is a zero vector and x is a vector of unknown variables, which of the following is/are true?

(A) The given set of equations will have a unique solution.

(B) The given set of equations will be satisfied by a zero vector of appropriate size.

(D) The given set of equations will have many but a finite number of solutions.

Answer: (B, C)

47. The lengths of members BC and CE in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible.Two forces of magnitude Q> 0 are applied as shown, each at the mid-length of the respective member on which it acts.

Which one or more of the following members do not carry any load (force)?

(A) AB

(B) CD

(D) GH

Answer: (B, D)

48. If the sum and product of eigenvalues of a 2 × 2 real matrix are 4 and −1 respectively, then |p| is ______ (in integer).

Answer: (2 to 2)

49. Given z = x + iy, i = √−1. C is a circle of radius 2 with the centre at the origin.If the contour C is traversed anticlockwise, then the value of the integral is _______ (round off to one decimal place).

Answer: (0.2 to 0.2)

50. A shaft of length L is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is d_o and the external diameter of the rim is d_i, as shown in the figure. The modulus of rigidity of the core and rim materials are G_i and G_o, respectively. It is given that d_o = 2d_i and G_i = 3G_o. When the shaft is twisted by application of a torque along the shaft axis,the maximum shear stress developed in the outer rim and the inner core turn out to be τ_o and τ_i, respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio τ_i/τ_o is ______ (round off to 2 decimal places).

Answer: (1.48 to 1.52)

51. A rigid beam AD of length 3a = 6 m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over two small frictionless pulleys of negligible radius. All the strings are made of the same material and have equal cross-sectional area. A force F = 9 kN is applied at C and the resulting stresses in the strings are within linear elastic limit. The self-weight of the beam is negligible with respect to the applied load. Assuming small deflections, the tension developed in the string at C is _________ kN (round off to 2 decimal places).

Answer: (1.48 to 1.52)

52. In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the 2 cm long link is ω₂ = 5 rad/s. Given the dimensions as shown, the magnitude of the angular velocity ω₄ of the 4 cm long link is given by _____ rad/s (round off to 2 decimal places).

Answer: (1.24 to 1.26)

53. A shaft AC rotating at a constant speed carries a thin pulley of radius r = 0.4 m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque M_zabout the shaft axis without causing any bending moment.The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = L = 0.5 m.The taut and slack side tensions of the belt are T₁ = 300 N 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of π available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is _______ mm (round off to 2 decimal places).

Answer: (23.60 to 24.20)

54. A straight-teeth horizontal slab milling cutter is shown in the figure. It has 4 teeth and diameter (D) of 200 mm. The rotational speed of the cutter is 100 rpm and the linear feed given to the work-piece is 1000 mm/minute. The width of the work-piece(w) is 100 mm, and the entire width is milled in a single pass of the cutter. The cutting force/tooth is given by F = Kt_cw, where specific cutting force K = 10 N/mm², w is the width of cut, and t_c is the uncut chip thickness.

The depth of cut (d) is D/2, and hence the assumption of is invalid. The maximum cutting force required is ________ kN (round off to one decimal place).

Answer: (2.4 to 2.6)

55. In an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is 0.5 mm and the shear angle is 15°. The orthogonal rake angle of the tool is 0° and the width of cut is 2 mm. The work-piece material is perfectly plastic and its yield shear strength is 500 MPa. The cutting force is _________ N (round off to the nearest integer).

Answer: (2700 to 2750)

56. The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch (p) and included angle of the thread are 4 mm and 60º, respectively. The diameter of the best size wire is _________ mm (round off to 2 decimal places).

Answer: (2.29 to 2.33)

57. In a direct current arc welding process, the power source has an open circuit voltage of 100 V and short circuit current of 1000 A. Assume a linear relationship between voltage and current. The arc voltage (V) varies with the arc length (l) asV = 10 + 5l, where V is in volts and l is in mm. The maximum available arc power during the process is _________ kVA (in integer).

Answer: (25 to 25)

58. A cylindrical billet of 100 mm diameter and 100 mm length is extruded by a direct extrusion process to produce a bar of L-section. The cross sectional dimensions of this L-section bar are shown in the figure. The total extrusion pressure (p) in MPa for the above process is related to extrusion ratio (r) as

where σ_m is the mean flow strength of the billet material in MPa, l is the portion of the billet length remaining to be extruded in mm, d₀ is the initial diameter of the billet in mm, and K_s is the die shape factor.If the mean flow strength of the billet material is 50 MPa and the die shape factor is 1.05, then the maximum force required at the start of extrusion is ________ kN (round off to one decimal place).

Answer: (2426.0 to 2432.0)

59. A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor(s) are listed in the table. The expected time of the project completion is __________ weeks (in integer).

Answer: (15 to 15)

60. A rigid tank of volume of 8 m³ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained at 600 kPa and 306 K, respectively. The filling of the tank begins by opening the valve and the process ends when the tank pressure is equal to the pipeline pressure. During the filling process, heat loss to the surrounding is 1000 kJ. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kg.K and 0.718 kJ/kg.K, respectively. Neglect changes in kinetic energy and potential energy.

The final temperature of the tank after the completion of the filling process

is _________ K (round off to the nearest integer).

Answer: (385 to 405)

61. At steady state, 500 kg/s of steam enters a turbine with specific enthalpy equal to 3500 kJ/kg and specific entropy equal to 6.5 kJ∙kg⁻¹∙K⁻¹. It expands reversibly in the turbine to the condenser pressure. Heat loss occurs reversibly in the turbine at a temperature of 500 K. If the exit specific enthalpy and specific entropy are 2500 kJ/kg and 6.3 kJ∙kg⁻¹∙K⁻¹, respectively, the work output from the turbine is ________ MW (in integer).

Answer: (450 to 450)

62. A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm and length = 8 m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = 11.4) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod.

Assume density of water = 103 kg/m³ and π = 3.14.

Radius of the ball is _______ cm (round off to 2 decimal places).

Answer: (3.48 to 3.70)

63. Consider steady state, one-dimensional heat conduction in an infinite slab of thickness 2L (L = 1 m) as shown in the figure. The conductivity (k) of the material varies with temperature as k = CT, where T is the temperature in K, and C is a constant equal to 2 W∙m⁻¹∙K⁻¹. There is a uniform heat generation of 1280 kW/m³in the slab. If both faces of the slab are maintained at 600 K, then the temperature at x = 0 is ________ K (in integer).

Answer: (1000 to 1000)

64. Saturated vapor at 200°C condenses to saturated liquid at the rate of 150 kg/s on the shell side of a heat exchanger (enthalpy of condensation h_fg = 2400 kJ/kg). A fluid with c_p = 4 kJ∙kg⁻¹∙K⁻¹enters at 100°C on the tube side. If the effectiveness of the heat exchanger is 0.9, then the mass flow rate of the fluid in the tube side is ________ kg/s (in integer).

Answer: (1000 to 1000)

65. Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. Aconstant heat flux of magnitude 15000 W/m² is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200°The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 W∙m⁻¹∙K⁻¹and 2600 J∙kg⁻¹∙K⁻¹, respectively. The correlation Nu = 0.023 Re^0.8Pr^0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ °C (round off to the nearest integer).

Answer: (317 to 324)

GATE Exam 2022 Mechanical Engineering (ME-1) Question Paper With Answer Key

July 17, 2022 by suresh84

GATE-2022

ME1: Mechanical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. After playing _________ hours of tennis, I am feeling _________ tired to walk back.

(A) too / too

(B) too / two

(D) two / too

Answer: (D)

2. The average of the monthly salaries of M, N and S is Rs. 4000. The average of the monthly salaries of N, S and P is Rs. 5000. The monthly salary of P is Rs. 6000.

What is the monthly salary of M as a percentage of the monthly salary of P?

(A) 50%

(B) 75%

(D) 125%

Answer: (A)

3. A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph.

What percentage of the total distance is travelled at a uniform speed of 10 kmph?

(A) 28.25

(B) 37.25

(D) 50.00

Answer: (C)

4. Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning Dutch and Japanese.

Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch is easier than Japanese, and Spanish is easier than French.

Based on the above information, which girl is learning the most difficult pair of languages?

(A) P

(B) Q

(D) S

Answer: (B)

A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above.

Which one of the following is the correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow in the above figure?

Answer: (A)

6. Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear “lost”, it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets that had a key and money are more likely to be returned than wallets with the same amount of money alone. This suggests that the primary reason for this behavior is compassion and empathy.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Wallets with a key are more likely to be returned because people do not care about money

(B) Wallets with a key are more likely to be returned because people relate to suffering of others

(D) Money is always more important than keys

Answer: (B)

7. A rhombus is formed by joining the midpoints of the sides of a unit square.

What is the diameter of the largest circle that can be inscribed within the rhombus?

(A) 1/√2

(B) 1/2√2

(D) 2√2

Answer: (A)

8. An equilateral triangle, a square and a circle have equal areas.

What is the ratio of the perimeters of the equilateral triangle to square to circle?

Answer: (B)

9. Given below are three conclusions drawn based on the following three statements.

Statement 1: All teachers are professors.

Statement 2: No professor is a male.

Statement 3: Some males are engineers.

Conclusion I: No engineer is a professor.

Conclusion II: Some engineers are professors.

Conclusion III: No male is a teacher.

Which one of the following options can be logically inferred?

(A) Only conclusion III is correct

(B) Only conclusion I and conclusion II are correct

(D) Only conclusion I and conclusion III are correct

Answer: (A)

10. In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?

(A) 11

(B) 12

(D) 2

Answer: (MTA)

ME1: Mechanical Engineering

Q.11 – 35 Carry ONE mark each.

11. The limit has a finite value for a real α. The value of 𝛼 and the corresponding limit p are

(A) α = −3π, and p = π

(B) α = −2π, and p = 2π

(D) α = 2π, and p = 3π

Answer: (B)

12. Solution of ∇²T = 0 in a square domain (0 <x< 1 and 0 <y< 1) with boundary conditions:

T(x, 0) = x; T(0, y) = y; T(x, 1) = 1 + x; T(1, y) = 1 + y is

(A) T(x, y) = x – xy + y

(B) T(x, y) = x + y

(D) T(x, y) = x + xy + y

Answer: (A)

13. Given a function in three-dimensional Cartesian space, the value of the surface integral where S is the surface of a sphere of unit radius and is the outward unit normal vector on S, is

(A) 4π

(B) 3π

(D) 0

Answer: (A)

14. The Fourier series expansion of x³ in the interval −1 ≤ x< 1 with periodic continuation has

(A) only sine terms

(B) only cosine terms

(D) only sine terms and a non-zero constant

Answer: (A)

15. If is a symmetric matrix, the value of k is ___________.

(A) 8

(B) 5

(D)

Answer: (A)

16. A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight W as shown. If the maximum value of W to avoid buckling of the beam AB is obtained as βπ²EI, where π is the ratio of circumference to diameter of a circle, then the value of β is

(A) 0.0924 m⁻²

(B) 0.0713 m⁻²

(D) 0.1417 m⁻²

Answer: (A)

17. The figure shows a schematic of a simple Watt governor mechanism with the spindle O₁O₂ rotating at an angular velocity ω about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot O₁ is denoted by h. The value of h = 400 mm at a certain ω. If ω is doubled, the value of h will be _________ mm.

(A) 50

(B) 100

(D) 200

Answer: (B)

18. A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed as

(A) The ratio of work done by W per revolution to work done by F per revolution

(B) W/F

(D) The ratio of work done by F per revolution to work done by W per revolution

Answer: (A)

19. 1A CNC worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is 5 mm. The stepper motor completes one full revolution upon receiving 600 pulses. If the worktable speed is 5 m/minute and there is no missed pulse, then the pulse rate being received by the stepper motor is

(A) 20 kHz

(B) 10kHz

(D) 15kHz

Answer: (B)

20. The type of fit between a mating shaft of diameter and a hole of diameter is _______.

(A) Clearance

(B) Transition

(D) Linear

Answer: (B)

21. In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is

(A) positive

(B) negative

(D) infinity

Answer: (C)

22. Which one of the following is NOT a form of inventory?

(A) Raw materials

(B) Work-in-process materials

(D) CNC Milling Machines

Answer: (D)

23. The Clausius inequality holds good for

(A) any process

(B) any cycle

(D) only reversible cycle

Answer: (B)

24. A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is and the temperature field in the fluid is T = 2x² + xy + 4t, where x and y are the spatial coordinates, and t is the time. The time rate of change of temperature recorded by the probe at (x = 1, y = 1, t = 1) is _______.

(A) 4

(B) 0

(D) 14

Answer: (C)

25. In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature T_∞ (g is the gravitational acceleration, β is the volumetric thermal expansion coefficient, v is the kinematic viscosity, u and v are the velocities in x and y directions, respectively, and T is the temperature)

the term gβ(T – T_∞) represents

(A) Ratio of inertial force to viscous force.

(B) Ratio of buoyancy force to viscous force.

(D) Buoyancy force per unit mass.

Answer: (D)

26. Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE?

(A) A body subjected to hydrostatic pressure has no shear stress.

(B) If a long solid steel rod is subjected to tensile load, then its volume increases.

(D) If a portion of a beam has zero shear force, then the corresponding portion of theelastic curve of the beam is always straight.

Answer: (A, B)

27. Which of the following heat treatment processes is/are used for surface hardening of steels?

(A) Carburizing

(B) Cyaniding

(D) Carbonitriding

Answer: (A, B, D)

28. Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?

(A) Stereolithography

(B) Fused deposition modeling

(D) Directed energy deposition processes

Answer: (B, D)

29. Which of the following methods can improve the fatigue strength of a circular mild steel (MS) shaft?

(A) Enhancing surface finish

(B) Shot peening of the shaft

(D) Reducing relative humidity

Answer: (A,B,D OR A, B)

30. The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure (P₀) is increased while keeping the back pressure (P_back) unchanged, which of the following statements is/are true?

(A) Mass flow rate through the nozzle will remain unchanged.

(B) Mach number at the exit plane of the nozzle will remain unchanged at unity.

(D) Mach number at the exit plane of the nozzle will become more than unity.

Answer: (B, C)

31. The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through O. Its mass moment of inertia is equal to 0.1 kg∙cm² about O. A point mass of 0.001 kg hits it normally at 200 cm/s at the location shown, and sticks to it. Immediately after the impact, the angular velocity of the rod is ___________ rad/s (in integer).

Answer: (10 to 10)

32. A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius r and outer radius R are such that r² = R²/2 and the acceleration due to gravity is g. If the time period of small amplitude simple harmonic motion is given by where π is the ratio of circumference to diameter of a circle, then β = ________ (round off to 2 decimal places).

Answer: (2.62 to 2.70)

33. Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below.

Ignore over potentials, and assume that current efficiency is 100% for both the workpiece materials. Under identical conditions, if the material removal rate (MRR)of copper is 100 mg/s, the MRR of aluminum will be ________________ mg/s(round-off to two decimal places).

Answer: (27.00 to 30.00)

34. A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m³ to a final volume of 2.5 m³. The polytropic index is given by n = 1.2. The absolute value of the work done during the process is _______ kJ (round off to 2 decimal places).

Answer: (404.00 to 414.00)

35. A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 25 ° Assume that the entire solar flux is absorbed by the plate.

Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 × 10⁻⁸ W/m²-K⁴. Neglect all other modes of heat transfer except radiation.

Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ °C (round off to the nearest integer)

Answer: (210 to 225)

Q.36 – Q.65 Carry TWO marks Each

36. The value of the integral

evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where 𝑖 is the imaginary unit, is

(A) (−1 + i)π

(B) (1 + i)π

(D) (2 + i)π

Answer: (A)

37. An L-shaped elastic member ABC with slender arms AB and BC of uniform cross-section is clamped at end A and connected to a pin at end C. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force 𝑃 and all the deflections are in the plane of the figure. Given the length AB is 4a and length BC is 𝑎, the magnitude and direction of the normal force on the pin from the slot, respectively, are

(A) 3P/8, and downwards

(B) 5P/8, and upwards

(D) 3P/4, and upwards

Answer: (A)

38. A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB ⊥ CE and FD ⊥ The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is

(A) a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG

(B) a non-Grashof chain with all oscillating links

(D) on the border of Grashof and non-Grashof chains with uncertain configuration(s)

Answer: (A)

39. Consider a forced single degree-of-freedom system governed by where ζ and ω_n are the damping ratio and undamped natural frequency of the system, respectively, while ω is the forcing frequency. The amplitude of the forced steady state response of this system is given by [(1 – r²)² + (2ζr)²]^−1/2, where r = ω/ω_n. The peak amplitude of this response occurs at a frequency ω = ω_p. If ω_d denotes the damped natural frequency of this system, which one of the following options is true?

(A) ω_p<ω_d<ω_n

(B) ω_p = ω_d<ω_n

(D) ω_d<ω_n<ω_p

Answer: (A)

40. A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of 2a = 100 mm, as shown in the figure. The permissible shear stress of the rivet material is 50 MPa. If a load P = 10 kN is applied at an eccentricity e = 3√7 a, the minimum cross-sectional area of each of the rivets to avoid failure is ___________ mm².

(A) 800

(B) 25

(D) 200

Answer: (A)

41. In Fe-Fe₃C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel sample, having no other alloying element except 0.5 weight % of carbon, is slowly cooled from 1000 ºC to room temperature. The fraction of pro-eutectoid α-ferrite in the above steel sample at room temperature is

(A) 0.387

(B) 0.864

(D) 0.775

Answer: (A)

42. Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ________ hours.

(A) 5

(B) 10

(D) 9

Answer: (B)

43. A solid spherical bead of lead (uniform density = 11000 kg/m³) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 10⁻³ kg∙m⁻¹∙s⁻¹). The coefficient of drag is given by C_D = 24/Re, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as D = (C_D) (0.5ρV²) (πd²/4), where ρ is the density of the liquid. Neglect the buoyancy force. Using g = 10 m/s², the velocity V is __________ m/s.

(A) 1/24

(B) 1/6

(D) 1/12

Answer: (C)

44. Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ________ N.

(A) 350π²

(B) 750π

(D) 3000

Answer: (B)

45. Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T_∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as

The steady state temperature at the mid-location of the rod is given as TA. What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h?

(A)

(B) 2T_A

(D)

Answer: (C)

46. The system of linear equations in real (x, y) given by

involves a real parameter 𝛼 and has infinitely many non-trivial solutions for special value(s) of α. Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α?

(A) x = 2, x = −2

(B) x = −1, y = 4

(D) x = 4, y = 2

Answer: (A, B)

47. Let a random variable X follow Poisson distribution such that

Prob(X = 1) = Prob(X = 2).

The value of Prob(X = 3) is __________ (round off to 2 decimal places).

Answer: (0.17 to 0.19)

48. Consider two vectors:

Magnitude of the component of orthogonal to in the plane containing the vectors is ________ (round off to 2 decimal places).

Answer: (7.90 to 8.70)

49. A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. AE is a single member that contains pin C. Likewise, BE is a single member that contains pin D. Members GI and FH are overlapping rigid members. The magnitude of the force carried by member CI is ________ kN (in integer).

Answer: (18 to 18)

50. Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively, as shown in the figure. A vertical force F acts on the pin R as shown. When the included angle θ< 90°, the rods remain in static equilibrium due to Coulomb friction between the rods and ground at locations P and Q. At θ = 90°, impending slip occurs simultaneously at points P and Q. Then the ratio of the coefficient of friction at Q to that at P(μ_Q/μ_P) is _________ (round off to two decimal places).

Answer: (5.70 to 5.80)

51. A cylindrical disc of mass 𝑚 = 1 kg and radius r = 0.15 m was spinning at ω = 5 rad/s when it was placed on a flat horizontal surface and released (refer to the figure). Gravity g acts vertically downwards as shown in the figure. The coefficient of friction between the disc and the surface is finite and positive. Disregarding any other dissipation except that due to friction between the disc and the surface, the horizontal velocity of the center of the disc, when it starts rolling without slipping, will be _________ m/s (round off to 2 decimal places).

Answer: (0.24 to 0.26)

52. A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became The corresponding change in the wall thickness of the cylindrical portion, i.e. is ________% (round off to 3 decimal places).

Answer: (-0.062 to -0.058)

53. A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3 has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter clockwise (ccw), the magnitude of angular velocity of arm OP is __________rpm (in integer).

Answer: (600 to 600)

54. Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m/s. The orthogonal rake angle of the cutting tool is 5º. The uncut chip thickness and width of cut are 0.2 mm and 3 mm, respectively. In this turning operation, the resulting friction angle and shear angle are 45º and 25º, respectively. If the dynamic yield shear strength of the workpiece material under this cutting condition is 1000 MPa, then the cutting force is ________ N (round off to one decimal place).

Answer: (2570.0 to 2576.0)

55. A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is 1 m/minute and the specific cutting energy (u) of the tube material is 6J/mm³. Neglect contribution of feed force towards power. The power required to carry out this operation is _________ kW (round off to one decimal place).

Answer: (30.0 to 32.0)

56. A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece is lubricated with a mineral oil, which gives a coefficient of friction, μ = 0.1. The flow stress (σ) of the material in MPa is σ = 207 + 414 ε, where ε is the true strain. Assuming rolling to be a plane strain deformation process, the roll separation force (F) for maximum permissible draft (thickness reduction) is _________ kN (round off to the nearest integer).

Use:

is average flow stress, L is roll-workpiece contact length, and is the average sheet thickness.

Answer: (340 to 360)

57. Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters.

A filler wire of the same mild steel material having 3 mm diameter is used in this welding process. The filler wire feed rate is selected such that the final weld bead is composed of 60% volume of filler and 40% volume of plate material. The heat required to melt the mild steel material is 10 J/mm³. The heat transfer factor is 0.7 and melting factor is 0.6. The feed rate of the filler wire is __________ mm/s (round off to one decimal place).

Answer: (10.5 to 10.9)

58. An assignment problem is solved to minimize the total processing time of four jobs(1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _________ minutes (in integer).

Answer: (520 to 520)

59. The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units of on handinventory of component A, the number of additional units of component A needed to produce 10 units of product P is _________ (in integer).

Answer: (110 to 110)

60. Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperature side A has a surface temperature of 80 °C,and the heat transfer rate per unit area to low temperature side B is 4.5 kW/m². The thermal conductivity of the slab is 15 W/m.K. The rate of entropy generation per unit area during the heat transfer process is ________ W/m2.K (round off to 2

decimal places).

Answer: (1.12 to 1.24)

61. In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________ kJ/kg (round off to 2 decimal places).

Answer: (2620.00 to 2630.00)

62. An engine running on an air standard Otto cycle has a displacement volume 250 cm³ and a clearance volume 35.7 cm³. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).

Answer: (4780 to 4825)

63. A steady two-dimensional flow field is specified by the stream function ψ = kx³y,

wherex and y are in meter and the constant k = 1 m⁻²s⁻¹. The magnitude of acceleration at a point (x, y) = (1 m, 1 m) is ________ m/s2 (round off to 2 decimal places).

Answer: (4.20 to 4.28)

64. Consider a solid slab (thermal conductivity, k = 10 W∙m⁻¹∙K⁻¹) with thickness 0.2 m and of infinite extent in the other two directions as shown in the figure.Surface 2, at 300 K, is exposed to a fluid flow at a free stream temperature (T_∞) of 293 K, with a convective heat transfer coefficient (h) of 100 W∙m⁻²∙K⁻¹. Surface 2 is opaque, diffuse and gray with an emissivity (ε) of 0.5 and exchanges heat by radiation with very large surroundings at 0 K. Radiative heat transfer inside the solid slab is neglected. The Stefan-Boltzmann constant is 5.67×10⁻⁸ W∙m⁻²∙K⁻⁴. The temperature T₁ of Surface 1 of the slab, under steady-state conditions,is _________ K (round off to the nearest integer).

Answer: (315 to 323)

65. During open-heart surgery, a patient’s blood is cooled down to 25°C from 37 °Cusing a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at 4°C and leaves at 18° Blood flow rate during the surgery is 5 L/minute.

Use the following fluid properties:

Effectiveness of the heat exchanger is _______ (round off to 2 decimal places).

Answer: (0.40 to 0.44)

GATE Exam 2022 Mathematics (MA) Question Paper With Answer Key

July 17, 2022 by suresh84

GATE-2022

MA: Mathematics

General Aptitude

1. As you grow older, an injury to your _________ may take longer to _________.

(A) heel / heel

(B) heal / heel

(D) heel / heal

Answer: (D)

2. In a 500 m race, P and Q have speeds in the ratio of 3 ∶ Q starts the race when P has already covered 140 m.

What is the distance between P and Q (in m) when P wins the race?

(A) 20

(B) 40

(D) 140

Answer: (A)

3. Three bells P, Q, and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.

If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?

(A) 5:00 PM

(B) 5:30 PM

(D) 6:30 PM

Answer: (A)

4. Given below are two statements and four conclusions drawn based on the statements.

Statement 1: Some bottles are cups.

Statement 2: All cups are knives.

Conclusion I: Some bottles are knives.

Conclusion II: Some knives are cups.

Conclusion III: All cups are bottles.

Conclusion IV: All knives are cups.

Which one of the following options can be logically inferred?

(A) Only conclusion I and conclusion II are correct

(B) Only conclusion II and conclusion III are correct

(D) Only conclusion III and conclusion IV are correct

Answer: (A)

5. The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2 or 3-3 chosen uniformly at random.

What is the probability that the disc DOES NOT retain the same front and rearviews after the flipping operation?

(A) 0

(B) 1/3

(D) 1

Answer: (A)

6. Altruism is the human concern for the well being of others. Altruism has been shown to be motivated more by social bonding, familiarity and identification of belongingness to a group. The notion that altruism may be attributed to empathy or guilt has now been rejected.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Humans engage in altruism due to guilt but not empathy

(B) Humans engage in altruism due to empathy but not guilt

(D) Humans engage in altruism due to empathy but not familiarity

Answer: (C)

7. There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U and V?

(A) 1/4

(B) 3/4

(D) 5/36

Answer: (A)

8. The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges Rs. 150 for delivery. There are no delivery charges for orders from the store M. A person bought the item from the store S and saved Rs. 100.

What is the price of the item at the online store S (in Rs.) if there are no other charges than what is described above?

(A) 2500

(B) 2250

(D) 1500

Answer: (B)

9. The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements:

• The line segment joining R and S is longer than the line segment joining P and Q.

• The line segment joining R and S is perpendicular to the line segment joining P and Q.

• The line segment joining R and U is parallel to the line segment joining T and Q.

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

(A) The line segment joining R and T is parallel to the line segment joining Q and S

(B) The line segment joining T and Q is parallel to the line joining P and U

(D) The line segment joining Q and S is perpendicular to the line segment joining Rand P

Answer: (A)

10.

An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.

Which one of the following is a part of a possible trajectory of the ant during the movement?

Answer: (C)

Mathematics

Q.1 – Q.5 Carry ONE mark each.

11. Suppose that the characteristic equation of M ∈ ℂ³^×³ is

λ³ + αλ² + βλ – 1 = 0,

where α, β ∈ ℂ with α + β ≠ 0.

Which of the following statements is TRUE?

(A) M(I – βM) = M⁻¹(M + αI)

(B) M(I + βM) = M⁻¹(M – αI)

(D) M⁻¹(M⁻¹ – βI) = M + αI

Answer: (D)

12. Consider

P: Let M ∈ ℝ^m^×ⁿ with m > n ≥ 2. If rank (M) = n, then the system of linear equations M_x = 0 has x = 0 as the only solution.

Q: Let E ∈ ℝⁿ^×ⁿ, n ≥ 2 be a non-zero matrix such that E³ = 0. Then I + E² is a singular matrix.

Which of the following statements is TRUE?

(A) Both P and Q are TRUE

(B) Both P and Q are FALSE

(D) P is FALSE and Q is TRUE

Answer: (C)

13. Consider the real function of two real variables given by

u(x, y) = e^2x[sin 3x cos 2y cosh 3y − cos 3x sin 2y sinh 3y].

Let v(x, y) be the harmonic conjugate of u(x, y) such that v(0, 0) = 2. Let z = x + iy and f(z) = u(x, y) + iv(x, y), then the value of 4 + 2if (iπ) is

(A) e³^π + e⁻³^π

(B) e³^π – e⁻³^π

(D) −e³^π – e⁻³^π

Answer: (C)

14. The value of the integral

where C is the circle of radius 2 centred at the origin taken in the anti-clockwise direction is

(A) −2πi

(B) 2π

(D) 2πi

Answer: (D)

15. Let X be a real normed linear space. Let X₀ = {x ∈ X : ∥x∥ = 1}. If X₀ contains two distinct points x and y and the line segment joining them, then, which of the following statements is TRUE?

(A) ∥x + y∥ = ∥x∥ + ∥y∥ and x, y are linearly independent

(B) ∥x + y∥ = ∥x∥ + ∥y∥ and x, y are linearly dependent

(D) ∥x + y∥ = 2∥x∥∥y∥ and x, y are linearly dependent

Answer: (A)

16. Let {e_k : k ∈ ℕ} be an orthonormal basis for a Hilbert space H.

Define f_k = e_k + e_k+1, k ∈ ℕ and

Then

(A) 0

(B) j²

(D) 1

Answer: (D)

17. Consider ℝ² with the usual metric. Let A = {(x, y) ∈ ℝ² : x² + y² ≤ 1} and B = {(x, y) ∈ ℝ² : (x−2)²+ y² ≤ 1}. Let M = A ⋃ B and N = interior(A) ⋃ interior(B). Then, which of the following statements is TRUE?

(A) M and N are connected

(B) Neither M nor N is connected

(D) M is not connected and N is connected

Answer: (C)

18. The real sequence generated by the iterative scheme

(A) converges to √2, for all x₀ ∈ ℝ\{0}

(B) converges to √2, whenever

(D) diverges for any x₀ ≠ 0

Answer: (B)

19. The initial value problem where y₀ is a real constant, has

(A) a unique solution

(B) exactly two solutions

(D) no solution

Answer: (A)

20. If eigenfunctions corresponding to distinct eigenvalues λ of the Sturm-Liouville problem

are orthogonal with respect to the weight function w(x), then w(x) is

(A) e⁻^3x

(B) e⁻^2x

(D) e^3x

Answer: (A)

21. The steady state solution for the heat equation

with the initial condition u(x, 0) = 0, 0 < x < 2 and the boundary conditions u(0, t) = 1 and u(2, t) = 3, t > 0, at x = 1 is

(A) 1

(B) 2

(D) 4

Answer: (B)

22. Consider ([0, 1], T₁), where T₁ is the subspace topology induced by the Euclidean topology on ℝ, and let T₂ be any topology on [0, 1]. Consider the following statements:

P : If T₁ is a proper subset of T₂, then ([0, 1], T₂) is not compact.

Q : If T₂ is a proper subset of T₁, then ([0, 1], T₂) is not Hausdorff.

Then

(A) P is TRUE and Q is FALSE

(B) Both P and Q are TRUE

(D) P is FALSE and Q is TRUE

Answer: (B)

23. Let p : ([0, 1], T₁) → ({0, 1}, T₂) be the quotient map, arising from the characteristic function on [1/2, 1], where T₁ is the subspace topology induced by the Euclidean topology on ℝ. Which of the following statements is TRUE?

(A) p is an open map but not a closed map

(B) p is a closed map but not an open map

(D) p is neither an open map nor a closed map

Answer: (D)

24. Set X_n = ℝ for each n ∈ ℕ. Define Endow Y with the product topology, where the topology on each X_n is the Euclidean topology. Consider the set

∆ = {(x, x, x, …) | x ∈ ℝ}

with the subspace topology induced from Y . Which of the following statements is TRUE?

(A) Δ is open in Y

(B) Δ is locally compact

(D) Δ is disconnected

Answer: (B)

25. Consider the linear system of equations Ax = b with

Which of the following statements are TRUE?

(A) The Jacobi iterative matrix is

(B) The Jacobi iterative method converges for any initial vector

(D) The spectral radius of the Jacobi iterative matrix is less than 1

Answer: (B, C, D)

26. The number of non-isomorphic abelian groups of order 2².3³.5⁴ is ______.

Answer: (30 to 30)

27. The number of subgroups of a cyclic group of order 12 is _____.

Answer: (6 to 6)

28. The radius of convergence of the series

is ______ (round off to TWO decimal places).

Answer: (0.55 to 0.59)

29. The number of zeros of the polynomial 2z⁷ – 7z⁵ + 2z³ – z + 1

in the unit disc {z ∈ ℂ : |z| < 1} is _______.

Answer: (5 to 5)

30. If P(x) is a polynomial of degree 5 and

where x₀, x₁, · · · , x₆ are distinct points in the interval [2, 3], then the value of α² − α + 1 is ______.

Answer: (1 to 1)

31. The maximum value of f(x, y) = 49 − x² − y² on the line x + 3y = 10 is _____.

Answer: (39 to 39)

32. If the function x ≠ 0, y ≠ 0 attains its local minimum value at the point (a, b), then the value of a³ + b³ is _________ (round off to TWO decimal places).

Answer: (0.65 to 0.68)

33. If the ordinary differential equation

has a solution of the form where a_n’s are constants and a₀ ≠ 0, then the value of r² + 1 is ________.

Answer: (1 to 1)

34. The Bessel functions J_α(x), x > 0, α ∈ ℝ satisfy Then, the value of (πJ_3/2(π))² is ______.

Answer: (2 to 2)

35. The partial differential equation

is transformed to

using ξ = y − 2x and η = 7y − 2x.

Then, the value of is _______.

Answer: (12 to 12)

Q.36 – Q.65 Carry TWO marks each.

36. Let ℝ[X] denote the ring of polynomials in X with real coefficients. Then, the quotient ring ℝ[X]/(X⁴ + 4) is

(A) a field

(B) an integral domain, but not a field

(D) a ring which contains non-zero nilpotent elements

Answer: (C)

37. Consider the following conditions on two proper non-zero ideals J₁ and J₂ of a non-zero commutative ring R.

P: For any r₁, r₂ ∈ R, there exists a unique r ∈ R such that r − r₁ ∈ J₁

and r − r₂ ∈ J₂.

Q: J₁ + J₂ = R

Then, which of the following statements is TRUE?

(A) P implies Q but Q does not imply P

(B) Q implies P but P does not imply Q

(D) P does not imply Q and Q does not imply P

Answer: (A)

38. Let f : [−π, π] → ℝ be a continuous function such that for some δ satisfying 0 < δ < π. Define P_n,δ(x) = (1+cos x−cos δ)ⁿ, for n = 1, 2, 3, · · · . Then, which of the following statements is TRUE?

Answer: (D)

39. P : Suppose that converges at x = −3 and diverges at x = 6. Then converges.

Q: The interval of convergence of the series is [−4, 4].

Which of the following statements is TRUE?

(A) P is true and Q is true

(B) P is false and Q is false

(D) P is false and Q is true

Answer: (C)

40. Let x ∈ [0, 1], n = 1, 2, 3, · · · .

Then, which of the following statements is TRUE?

(A) {f_n} is not equicontinuous on [0, 1]

(B) {f_n} is uniformly convergent on [0, 1]

(D) {f_n} is uniformly bounded and has a subsequence converging uniformly on [0, 1]

Answer: (A)

41. Let (ℚ, d) be the metric space with d(x, y) = |x − y|. Let E = {p ∈ ℚ : 2 < p² < 3}. Then, the set E is

(A) closed but not compact

(B) not closed but compact

(D) neither closed nor compact

Answer: (A)

42. Let T : L²[−1, 1] → L²[−1, 1] be defined by where almost everywhere. If M is the kernel of I − T, then the distance between the function ϕ(t) = e^t and M is

Answer: (D)

43. Let X, Y and Z be Banach spaces. Suppose that T : X → Y is linear and S : Y → Z is linear, bounded and injective. In addition, if S ∘ T : X → Z is bounded, then, which of the following statements is TRUE?

(A) T is surjective

(B) T is bounded but not continuous

(D) T is not bounded

Answer: (C)

44. The first derivative of a function f ∈ C^∞(−3, 3) is approximated by an interpolating polynomial of degree 2, using the data

(−1, f(−1)), (0, f(0)) and (2, f(2)).

It is found that

Then, the value of 1/αβ is

(A) 3

(B) 6

(D) 12

Answer: (D)

45. The work done by the force where are unit vectors in directions, respectively, along the upper half of the circle x² + y² = 1 from (1, 0) to (−1, 0) in the xy-plane is

(A) −π

(B) –π/2

(D) π

Answer: (B)

46. Let u(x, t) be the solution of the wave equation

0 < x < π, t > 0,

with the initial conditions

u(x, 0) = sin x + sin 2x + sin 3x,

and the boundary conditions u(0, t) = u(π, t) = 0, t ≥ 0. Then, the value of is

(A) −1/2

(B) 0

(D) 1

Answer: (B)

47. Let T : ℝ² → ℝ² be a linear transformation defined by

T((1, 2)) = (1, 0) and T((2, 1)) = (1, 1).

For p, q ∈ R, let T⁻¹((p, q)) = (x, y).

Which of the following statements is TRUE?

(A) x = p − q; y = 2p − q

(B) x = p + q; y = 2p − q

(D) x = p − q; y = 2p + q

Answer: (B)

48. Let y = (α,−1)^T , α ∈ ℝ be a feasible solution for the dual problem of the linear programming problem

Maximize: 5x₁ + 12x₂

subject to: x₁ + 2x₂ + x₃ ≤ 10

2x₁ − x₂ + 3x₃ = 8

x₁, x₂, x₃ ≥ 0.

Which of the following statements is TRUE?

(A) α < 3

(B) 3 ≤ α < 5.5

(D) α ≥ 7

Answer: (D)

49. Let K denote the subset of ℂ consisting of elements algebraic over ℚ. Then, which of the following statements are TRUE?

(A) No element of ℂ \K is algebraic over ℚ

(B) K is an algebraically closed field

(D) There is no bijection between K and ℚ

Answer: (A, B, C)

50. Let T be a M¨obius transformation such that T(0) = α, T(α) = 0 and T(∞) = −α, where α = (−1 + i)/√2. Let L denote the straight line passing through the origin with slope −1, and let C denote the circle of unit radius centred at the origin. Then, which of the following statements are TRUE?

(A) T maps L to a straight line

(B) T maps L to a circle

(D) T⁻¹ maps C to a circle

Answer: (A, C)

51. Let a > 0. Define D_a : L²(ℝ) → L²(ℝ) by almost everywhere, for f ∈ L²(ℝ). Then, which of the following statements are TRUE?

(A) D_a is a linear isometry

(B) D_a is a bijection

(D) D_a is bounded from below

Answer: (A, B, D)

52. Let {ϕ₀, ϕ₁, ϕ₂, · · · } be an orthonormal set in L²[−1, 1] such that ϕ_n = C_nP_n, where C_n is a constant and Pn is the Legendre polynomial of degree n, for each n ∈ ℕ ⋃{0}. Then, which of the following statements are TRUE?

(A) ϕ₆(1) = 1

(B) ϕ₇(−1) = 1

(C)

(D)

Answer: (C, D)

53. Let X = (ℝ, T), where T is the smallest topology on ℝ in which all the singleton sets are closed. Then, which of the following statements are TRUE?

(A) [0, 1) is compact in X

(B) X is not first countable

(D) X is first countable

Answer: (A, B)

54. Consider (ℤ, T), where T is the topology generated by sets of the form

A_{m, n} = {m + nk | k ∈ ℤ},

for m, n ∈ ℤ and n ≠ 0. Then, which of the following statements are TRUE?

(A) (ℤ, T) is connected

(B) Each A_{m, n} is a closed subset of (ℤ, T)

(D) (ℤ, T) is metrizable

Answer: (B, C, D)

55. Let A ∈ ℝ^m^×ⁿ, c ∈ ℝⁿ and b ∈ ℝ^m. Consider the linear programming primal problem

Minimize: c^Tx

subject to : Ax = b

x ≥ 0.

Let x⁰ and y⁰ be feasible solutions of the primal and its dual, respectively. Which of the following statements are TRUE?

(A) c^T x⁰ ≥ b^T y⁰

(B) c^T x₀ = bT y⁰

(D) If c^T x⁰ = b^T y⁰, then y0 is optimal for the dual

Answer: (A, C, D)

56. Consider ℝ³ as a vector space with the usual operations of vector addition and scalar multiplication. Let x ∈ ℝ³ be denoted by x = (x₁, x₂, x₃). Define subspaces W₁ and W₂ by

W₁ := {x ∈ ℝ³ : x₁ + 2x₂ − x₃ = 0}

and

W₂ := {x ∈ ℝ³ : 2x₁ + 3x₃ = 0}.

Let dim(U) denote the dimension of the subspace U.

Which of the following statements are TRUE?

(A) dim(W₁) = dim(W₂)

(B) dim(W₁) + dim(W₂) − dim(ℝ³) = 1

(D) dim(W₁ ⋂ W₂) = 1

Answer: (A, B, D)

57. Three companies C₁, C₂ and C₃ submit bids for three jobs J₁, J₂ and J₃. The costs involved per unit are given in the table below:

Then, the cost of the optimal assignment is ________.

Answer: (27 to 27)

58. The initial value problem is solved by using the following second order Runge-Kutta method:

K₁ = hf(x_i, y_i)

K₂ = hf(x_i + αh, y_i + βK₁)

where h is the uniform step length between the points x₀, x₁, · · · , x_n and y_i = y(x_i). The value of the product αβ is _____ (round off to TWO decimal places).

Answer: (0.43 to 0.45)

59. The surface area of the paraboloid z = x² + y² between the planes z = 0 and z = 1 is ______ (round off to ONE decimal place).

Answer: (5.1 to 5.5)

60. The rate of change of f(x, y, z) = x + x cos z − y sin z + y at P₀ in the direction from P₀(2,−1, 0) to P₁(0, 1, 2) is ______.

Answer: (0 to 0)

61. If the Laplace equation

with the boundary conditions

and

has a solution, then the constant α is ______.

Answer: (15 to 15)

62. Let u(x, y) be the solution of the first order partial differential equation _____

satisfying u(2, y) = y − 4, y ∈ ℝ. Then, the value of u(1, 2) is _____.

Answer: (1 to 1)

63. The optimal value for the linear programming problem

Maximize: 6x₁ + 5x₂

subject to: 3x₁ + 2x₂ ≤ 12

−x₁ + x₂ ≤ 1

x₁, x₂ ≥ 0

is _______.

Answer: (27 to 27)

64. A certain product is manufactured by plants P₁, P₂ and P₃ whose capacities are 15, 25 and 10 units, respectively. The product is shipped to markets M₁, M₂, M₃ and M₄, whose requirements are 10, 10, 10 and 20, respectively. The transportation costs per unit are given in the table below.

Then the cost corresponding to the starting basic solution by the Northwest-corner method is _______.

Answer: (105 to 105)

65. Let M be a 3 × 3 real matrix such that M² = 2M + 3I. If the determinant of M is −9, then the trace of M equals _______.

Answer: (5 to 5)

GATE Exam 2022 Instrumentation Engineering (IN) Question Paper With Answer Key

July 16, 2022 by suresh84

GATE-2022

IN: Instrumentation Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Inhaling the smoke from a burning _________ could _________ you quickly.

(A) tire / tier

(B) tire / tyre

(D) tyre / tier

Answer: (C)

2. A sphere of radius r cm is packed in a box of cubical shape.

What should be the minimum volume (in cm³) of the box that can enclose the sphere?

(A) r³/8

(B) r³

(D) 8r³

Answer: (D)

3. Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

(A) 26.8

(B) 60.0

(D) 127.5

Answer: (C)

4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

• P sits next to S and T.

• Q sits diametrically opposite to P.

• The shortest distance between S and R is equal to the shortest distance between T and U.

Based on the above statements, Q is a neighbor of

(A) U and S

(B) R and T

(D) P and S

Answer: (C)

5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

(A) 4

(B) 3

(D) 1

Answer: (C)

Q.6 – Q. 10 Carry TWO marks each.

6. Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientists are working on developing Green Super Rice (GSR), which is resilient under extreme weather conditions yet gives higher yields sustainably.

Which one of the following is the CORRECT logical inference based on the information given in the above passage?

(A) GSR is an alternative to regular rice, but it grows only in an extreme weather

(B) GSR may be used in future in response to adverse effects of climate change

(D) Regular rice will continue to provide good yields even in extreme weather

Answer: (B)

7. A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown. Two such disks are used in a game where their arrows are independently spun. What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?

(A) 1/16

(B) 5/64

(D) 7/64

Answer: (D)

8. Consider the following inequalities.

(i) 3p − q< 4

(ii) 3q − p< 12

Which one of the following expressions below satisfies the above two inequalities?

(A) p + q < 8

(B) p + q = 8

(D) p + q ≥ 16

Answer: (A)

9. Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.

Conclusion II: All engineers are actors.

Conclusion III: No actor is a writer.

Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Only conclusion II and conclusion III are correct

(D) Either conclusion III or conclusion IV is correct

Answer: (C)

10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

Answer: (C)

Instrumentation Engineering (IN)

Q.11 – Q.35 Carry ONE mark Each

11. The input x(t) to a system is related to its output y(t) as

Here u(t) represents a unit-step function.

The transfer function of this system is ________

Answer: (B)

12. A pneumatic nozzle-flapper system is conventionally used to convert ________

(A) Small changes in flapper’s velocity to large changes in output temperature

(B) Small changes in flapper’s displacement to large changes in output temperature

(D) Small changes in flapper’s displacement to large changes in output pressure

Answer: (D)

13. A periodic function f(x), with period 2, is defined as

The Fourier series of this function contains ________

(A) Both cos (nπx) and sin (𝑛𝜋𝑥) where n = 1, 2, 3, …

(B) Only sin (nπx) where n = 1, 2, 3, …

(D) Only cos (2nπx) where n = 1, 2, 3, …

Answer: (B)

14. The output of a system y(t) is related to its input x(t) according to the relation y(t) = x(t) sin(2πt). This system is ________

(A) Linear and time-variant

(B) Non-linear and time-invariant

(D) Non-linear and time-variant

Answer: (A)

15. A unity-gain negative-feedback control system has a loop-gain L(s) given by

The closed-loop system is ____

(A) Causal and stable

(B) Causal and unstable

(D) Non-causal and unstable

Answer: (B)

16. A sinusoidal carrier wave with amplitude A_c and frequency f_c is amplitude modulated with a message signal m(t) having frequency 0 <f_m<< f_c to generate the modulated wave s(t) given by

s(t) = A_c[1 + m(t)]cos (2πf_ct)

The message signal that can be retrieved completely usingenvelope detection is ________

(A) m(t) = 0.5 cos(2πf_mt)

(B) m(t) = 1.5 sin(2πf_mt)

(D) m(t) = 2 cos(4πf_mt)

Answer: (A)

17. A Hall sensor is based on the principle of _____

(A) Photoelectric effect

(B) Seebeck effect

(D) Lorentz force

Answer: (D)

18. A signal x(t) is band-limited between 100 Hz and 200 Hz.

A signal y(t) is related to x(t) as follows:

y(t) = x(2t – 5)

The statement that is always true is________

(A) y(t) is band-limited between 50 Hz and 100 Hz

(B) y(t) is band-limited between 100 Hz and 200 Hz

(D) y(t) is not band-limited

Answer: (C)

19. The figure shows a Chromel-Alumel thermocouple, where the junction A is held at temperature T_A, and a thermal emfE₁ is measured using an ideal voltmeter between the open ends B1 and B2, both held at temperature T_B. Two identical copper wires are introduced between B1-C1 and B2-C2 as shown in the figure. When C1 and C2 are held at temperature T_C, the voltmeter reads a thermal emf E₂. Then, ________

(A) E₁< E₂

(B) E₁> E₂

(D) E₁ = E₂

Answer: (D)

20. The resistance of a pure copper wire of length 10 cm and diameter 1 mm is to be measured. The most suitable method from amongst the choices given below is ________

(A) Two wire method

(B) Three wire method

(D) Ellipsometry

Answer: (C)

21. The logic block shown has an output F given by ________

(A) A + B

(B)

(C)

(D)

Answer: (D)

22. In which of the following bridge(s) is the balancing condition frequency-independent?

(A) Maxwell bridge

(B) Wien bridge

(D) Wheatstone bridge

Answer: (A, C, D)

23. The output F of the digital circuit shown can be written in the form(s) ________

Answer: (A, B)

24. Given which of the following statement(s) is/are correct?

(A) The rank of M is 2

(B) The rank of M is 3

(D) The determinant of M is 0

Answer: (A, D)

25. An analog-to-digital converter with resolution 0.01 V converts analog signals between 0 V to +10 V to an unsigned binary output. The minimum number of bits (in integer) in the output is ________

Answer: (10 to 10)

26. Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by an 8-bit word, the bit-duration (in microseconds) is ________ (round off to two decimal places)

Answer: (0.42 to 0.44)

27. A photodiode is made of a semiconductor with a band gap of 1.42 eV. Given that Planck’s constant is 6.626 × 10⁻³⁴Js, the speed of light in vacuum is 3 × 10⁸ m/s, and 1 eV = 1.6 × 10⁻¹⁹ J, the cut-off wavelength (in nanometers) of the photodiode is ________ (round off to one decimal place)

Answer: (870.0 to 880.0)

28. The global minimum of x³ e⁻^|x| for x ∈ (−∞, ∞) occurs at x = _____ (round off to one decimal place)

Answer: (-3.0 to -3.0)

29. A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is _________ (round off to one decimal place)

Answer: (1440.0 to 1440.0)

30. The transfer function of a system is:

In the state-space representation of the system, the minimum number of statevariables (in integer) necessary is ________

Answer: (3 to 3)

31. A Zener diode is used as a 4 V voltage regulator in the circuit shown. Given that

the diode requires a minimum current of 4 mA for voltage regulation, the maximum current (in milli amperes) permitted to flow through the load R_Lis ________ (round off to one decimal place)

Answer: (6.0 to 6.0)

32. A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is ________ (round off to two decimal places)

Answer: (0.32 to 0.34)

33. In the band pass filter circuit shown, R₀ = 50 Ω, L₀ = 1 mH, C₀ = 10 nF. The Q factor of the filter is ________ (round off to two decimal places)

Answer: (6.22 to 6.42)

34. The Newton-Raphson method is applied to determine the solution of f(x) = 0 where f(x) = x – cos(x). If the initial guess of the solution is x₀ = 0, the value of the next approximation x₁ is ______ (round off to two decimal places)

Answer: (0.99 to 1.01)

35. An OPAMP has a gain of 10⁴, an input impedance of 10 MΩ and an output impedance of 100Ω. The OPAMP is used in unity-gain feedback configuration in a voltage buffer circuit. The closed-loop output impedance of the OPAMP (in milliohms) in the circuit is ________ (round off to one decimal place)

Answer: (9.9 to 10.0)

Q.36 – Q.65 Carry TWO marks Each

36. A signal V_in (t) shown is applied from t = 0 ms to t = 6 ms to the circuit shown. Given the initial voltage across the capacitor is 0.3 V, and that the diode is ideal, the open circuit voltage V_out (t) at t = 5 ms is ______

(A) 0.3 V

(B) 0.6 V

(D) 1.0 V

Answer: (D)

37. The signal flow graph of a system is shown.

The expression for Y(s)/X(s) is ______

Answer: (A)

38. Consider the transfer function

Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function H_d(z). Then H_d(z) is _________

Answer: (C)

39. A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at t = 0 s is received back by the transceiver 100 ns (nanoseconds) later after reflection from the car. A second pulse emitted at t = 0.1 s is received back 90 ns later. Given the speed of light is 3 × 10⁸ m/s, the average speed of the car in this interval is ______

(A) 54 kmph, moving towards the transceiver

(B) 108 kmph, moving towards the transceiver

(D) 108 kmph, moving away from the transceiver

Answer: (A)

40. The signal x(t) = (t – 1)² u(t – 1), where u(t) is the unit-step function, has the Laplace transform X(s). The value of X(1) is _______

(A) 1/e

(B) 2/e

(D) e²

Answer: (B)

41. A proportional-integral-derivative (PID) controller is employed to stably control a plant with transfer function

Now, the proportional gain is increased by a factor of 2, the integral gain is increased by a factor of 3, and the derivative gain is left unchanged. Given that the closed-loop system continues to remain stable with the new gains, the steady-state error in tracking a ramp reference signal ________

(A) Remains unchanged

(B) Decreases by a factor of 2

(D) Decreases by a factor of 5

Answer: (C)

42. A resistor ladder digital-to-analog converter (DAC) receives a digital input that results in the circuit having the state as shown in the figure. For this digital input, the Thevenin voltage, V_th, and Thevenin resistance, R_th, as seen at the output node are ________

(A) V_th = 0.5 V, R_th = 1 kΩ

(B) V_th = 0.5 V, R_th = 2 kΩ

(D) V_th = 1 V, R_th = 2 kΩ

Answer: (C)

43. The Nyquist plot of a stable open-loop system G(jω) is plotted in the frequency range 0 ≤ω<∞ as shown. It is found to intersect a unit circle with center at the origin at the point P = −77 – 0.64j. The points Q and R lie on G(jω) and assume values Q = 14.40 + 0.00j and R = −0.21 + 0.00j. The phase margin (PM) and the gain margin (GM) of the system are ________

(A) PM = 39.7° and GM = 4.76

(B) PM = 39.7° and GM = 0.07

(D) PM = ‒39.7° and GM = 0.07

Answer: (A)

44. In the small signal circuit shown, the enhancement mode n-channel MOSFET is biased in saturation with transconductance g_m. If channel length modulation is ignored, the small signal impedance looking into the node P is given by ______

Answer: (B)

45. Consider the differential equation

If y(0) = e, then y(1) is _______

(A) e^e

(B) e⁻^e

(D) e⁽⁻^1/e)

Answer: (C)

46. The digital circuit shown ________

(A) is a divide-by-5 counter

(B) is a divide-by-7 counter

(D) does not function as a counter due to disjoint cycles of states

Answer: (A)

47. In the small signal circuit shown, the enhancement mode n-channel MOSFET is biased in saturation with a transconductance g_m. A small signal low-frequency voltage v_d injected at the supply terminal results in a small signal voltage fluctuation v₀ at the output. If the channel length modulation of the MOSFET is ignored, the small signal gain v₀/v_d is given by _____

Answer: (D)

48. A = a₁a₀ and B = b₁b₀ are two 2-bit unsigned binary numbers. If F(a_1,a₀, b₁, b₀) is a Boolean function such that F = 1 only when A > B, and F = 0 otherwise, then F can be minimized to the form ______

Answer: (B)

49. The matrix has eigenvalues −5 and 7.

The eigenvector(s) is/are ________

Answer: (A, C)

50. For the complex number where a > 0 and b > 0.

Which of the following statement(s) is/are true?

(A) The phase is

(B) The phase is

(D) The magnitude is

Answer: (A, C)

51. Monochromatic light of wavelength 532 nm is used to measure the absorption coefficient of a material in a UV-Visible Spectrophotometer. The measured light intensity after transmission through a 1 cm thick sample of the material is 0.414 mW/cm². For a sample of thickness 2 cm, the measured light intensity is 0.186 mW/cm². The absorption coefficient (in cm⁻¹) of the material is ________ (round off to two decimal places)

Answer: (0.75 to 0.85)

52. In the circuit shown, the load is driven by a sinusoidal ac voltage source V₁ = 100 ∠0° V at 50 Hz. Given R₁ = 20 Ω, and R₂ = 4 Ω, the power factor is _____ (round off to one decimal place)

Answer: (0.8 to 0.8)

53. In a unity-gain feedback control system, the plant

is controlled by a lag compensator

The slope (in dB/decade) of the asymptotic Bode magnitude plot of the loop gain

atω = 3 rad/s is ________ (in integer)

Answer: (-60 to -60)

54. Given Circuit A with currents I₁ and I₂ as shown, the current I₃ in Circuit B in amperes), is ______ (round off to one decimal place)

Answer: (0.0 to 0.0)

55. In the balanced three-phase circuit shown, C₀ = 8.2 μF and the line-to-line r.m.s. voltage is 440 V at 50 Hz. The reading on the wattmeter (in watts) is _______ (round off to two decimal places)

Answer: (141.80 to 146.20)

56. The circuit shown is driven by a sinusoidal input voltage, V_in, resulting in the output voltage, V_out. The frequency (in kilohertz) at which the voltage gain is 0 dB is ________ (round off to two decimal places)

Answer: (15.80 to 16.00)

57. A conducting semi-circular loop of radius R = 0.1 m, with its diameter centered at the origin, rotates in the x-y plane about the origin with a constant angular velocity, ω = 20 rad/s, as shown. A magnetic field of magnitude B = 2T and normal to x-y plane exists in the region x ≥ 0 as shown. If the loop has a resistance of 2Ω, and negligible inductance, the peak-to-peak current(in milli amperes) in the loop is __________ (round off to one decimal place)

Answer: (200.0 to 200.0)

58. In the circuit shown, R₁ = 100 kΩ and R₂ = 1 kΩ. If the base-to-emitter voltage of the npn BJT is 0.7 V and the collector-to-emitter voltage is 5.2 V, the β (current gain) of the BJT is ________ (round off to two decimal places)

Answer: (148.00 to 152.00)

59. A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air = 8.854 × 10⁻¹² F/m). . The radii of the inner and outer spheres are a =10 cm and b =15 cm, respectively. The capacitance (in picofarads) is ________ (round off to 2 decimal places)

Answer: (32.8 to 33.9)

60. A 1 kHz sine-wave generator having an internal resistance of 50 Ω generates an open-circuit voltage of 10 V_p-p. When a capacitor is connected across the output terminals, the voltage drops to 8 V_p-p. The capacitance of the capacitor (in microfarads) is _______ (round off to two decimal places)

Answer: (2.35 to 2.43)

61. Consider the function The residue of f(z) at z = −1, is _____

Answer: (0.49 to 0.51)

62. In the circuit shown, the capacitance C₀ = 10 μF and inductance L₀ = 1 mH and the diode is ideal. The capacitor is initially charged to 10 V and the current in the inductor is initially zero. If the switch is closed at t = 0 s, the voltage V_c(t) (involts) across the capacitor at t = 0.5 s is ______ (round off to one decimal place)

Answer: (-10.1 to -9.9)

63. The bridge shown is balanced when R₁ = 100 Ω, R₂ = 210 Ω, C₂ = 2.9 μF, and R₄ = 50 Ω. The 2 kHz sine-wave generator supplies a voltage of 10 V_p-p.The value of L₃ (in milli henry) is _______ (round off to two decimal places)

Answer: (14.40 to 14.60)

64. In the circuit shown, the switch is initially closed. It is opened at t = 0 s and remains open thereafter. The time (in milliseconds) at which the output voltage V_out becomes LOW is ________ (round off to three decimal places)

Answer: (0.365 to 0.369)

65. In the Wheatstone bridge circuit shown, R₁ = 1.5 kΩ and R₂ = R₃ = R₄ = 1 kΩ. The switch is initially open and the voltage between the points C and D is V_CD. Upon closing the switch at t = 0, the resistance in the arm AD changes by an amount δR₁, and the voltage between C and D changes by δV_CD. The sensitivity of the bridge (in volt/kiloohm), defined as is ________ (round off to two decimal places)

Answer: (1.62 to 1.72)

GATE Exam 2022 Geology and Geophysics (GG) Question Paper With Answer Key

July 15, 2022 by suresh84

GATE-2022

GG: Geology and Geophysics

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Inhaling the smoke from a burning _________ could _________ you quickly.

(A) tire / tier

(B) tire / tyre

(D) tyre / tier

Answer: (C)

2. A sphere of radius r cm is packed in a box of cubical shape.

What should be the minimum volume (in cm³) of the box that can enclose the sphere?

(A) r³/8

(B) r³

(D) 8r³

Answer: (D)

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

(A) 26.8

(B) 60.0

(D) 127.5

Answer: (C)

4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

• P sits next to S and T.

• Q sits diametrically opposite to P.

• The shortest distance between S and R is equal to the shortest distance between T and U.

Based on the above statements, Q is a neighbor of

(A) U and S

(B) R and T

(D) P and S

Answer: (C)

5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

(A) 4

(B) 3

(D) 1

Answer: (C)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information given in the above passage?

(A) GSR is an alternative to regular rice, but it grows only in an extreme weather

(B) GSR may be used in future in response to adverse effects of climate change

(D) Regular rice will continue to provide good yields even in extreme weather

Answer: (B)

(A) 1/16

(B) 5/64

(D) 7/64

Answer: (D)

8. Consider the following inequalities.

(i) 3p − q< 4

(ii) 3q − p< 12

Which one of the following expressions below satisfies the above two inequalities?

(A) p + q < 8

(B) p + q = 8

(D) p + q ≥ 16

Answer: (A)

9. Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.

Conclusion II: All engineers are actors.

Conclusion III: No actor is a writer.

Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Only conclusion II and conclusion III are correct

(D) Either conclusion III or conclusion IV is correct

Answer: (C)

10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

Answer: (C)

PART A: COMPULSORY SECTION FOR ALL CANDIDATES

Q.11 – Q .17 Carry ONE mark each

11. Which one of the following is the typical product of ductile deformation?

(A) Gouge

(B) Breccia

(D) Mylonite

Answer: (D)

12. Which one among the following coastal erosional land forms is caused by the action of sea waves?

(A) Ventifact

(B) Kettle

(D) Cliff

Answer: (D)

13. In which one of the following regions of the electromagnetic spectrum does the maximum atmospheric scattering occur?

(A) UV

(B) IR

(D) Microwave

Answer: (A)

14. Which one of the following is the Poisson’s ratio for an incompressible fluid?

(A) 0

(B) 0.25

(D) 0.5

Answer: (D)

15. Which among the following Period(s) belong(s) to the Paleozoic Era?

(A) Carboniferous

(B) Paleogene

(D) Cretaceous

Answer: (A, C)

16. The average bulk density of a fully saturated sandstone reservoir with a fractional porosity of 0.23 is ______ g/cc. [round off to 2 decimal places]

[Assume matrix density for sandstone = 2.63 g/cc and fluid density = 1.05 g/cc]

Answer: (2.24 to 2.30)

17. For a productive alluvial aquifer with hydraulic conductivity = 105 m/day and hydraulic gradient = 0.01, the flow rate is _________ m/day. [round off to 2 decimal places]

Answer: (1.00 to 1.10)

Q.18 – Q .26 Carry TWO marks each

18. The relationship between conjugate shear fractures and the principal stresses in a homogenous, isotropic, deformed body is shown in the stereoplot given below (σ₁, σ₂ and σ₃ are compressive stresses). Which one of the given fault regimes is indicated according to the Anderson’s theory of faulting for the formation of conjugate shear fractures under plane strain?

(A) Dextral strike-slip

(B) Sinistral strike-slip

(D) Normal

Answer: (C)

19. How many independent elastic parameters are needed to describe a homogenous isotropic material?

(A) 21

(B) 2

(D) 3

Answer: (B)

20. Which one of the following is a mafic volcanic rock?

(A) Dacite

(B) Trachyte

(D) Basalt

Answer: (D)

21. The intercepts of a crystal face on the crystallographic axes are ∞a, 2b, 3c. Which one of the following is its Miller Index?

(A) (032)

(B) (023)

(D) (320)

Answer: (A)

22. Match the locations in Group I with the corresponding economic deposits in Group II.

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

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

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

Answer: (C)

23. Choose the CORRECT statement(s) on seismic wave propagation in an elastic isotropic medium.

(A) P-waves are polarized in the direction of propagation.

(B) S-waves are polarized in the direction of propagation.

(D) Love waves are elliptically polarized

Answer: (A, C)

24. The difference in arrival times of P- and S-waves generated by an earthquake and recorded at a seismological station is one second. Assuming a homogeneous and isotropic Earth, a P-wave velocity (V_P) of 3 km/s, the ratio of P- to S-wave velocities (V_P/V_S) of 2.0, the distance between the station and the hypocenter is _______ km. [round off to 1 decimal place]

Answer: (3.0 to 3.0)

25. Assuming the rate of rotation of the Earth is 7.27 × 10⁻⁵ radians/s and the radius of Earth is 6371 km, the centrifugal acceleration at 60o latitude for a spherically rotating Earth is ______ × 10⁻³ m/s². [round off to 1 decimal place]

Answer: (16.3 to 17.3)

26. The angle of inclination of the remanent magnetization of a volcanic rock measured at a location is 45°. The magnetic latitude of the location of the volcanic rock at the time of its magnetization is _________ °N. [round off to 1 decimal place]

Answer: (26.2 to 27.0)

PART B (SECTION 1): FOR GEOLOGY CANDIDATES ONLY

Q.27 – Q.44 Carry ONE mark Each

27. A coarse-grained igneous rock consists of 55% olivine, 25% augite and 20% enstatite. According to the IUGS classification, the rock is

(A) websterite

(B) lherzolite

(D) harzburgite

Answer: (B)

28. The rock-type used to build the walls of the Red Fort in Delhi is

(A) sandstone

(B) marble

(D) basalt

Answer: (A)

29. During crystallization of a magma, which one of the following schematic paths (I, II, III and IV) describes the behavior of compatible elements in the residual melt?

(A) II

(B) IV

(D) III

Answer: (B)

30. In the geological map of India, which one of the following geological units has the largest area?

(A) Vindhyan Super group

(B) Deccan Volcanic Province

(D) Mesozoic rocks of Kutch

Answer: (B)

31. Which one of the following cross-stratifications provides the paleocurrent direction on the truncated bedding surface of an undeformed cross-stratified sedimentary strata?

(A) Tabular

(B) Hummocky

(D) Herringbone

Answer: (C)

32. Which one of the following is a dinosaur?

(A) Stegodon

(B) Stegosaurus

(D) Otoceras

Answer: (B)

33. The Hoek-Brown failure envelope is typically the segment of which one of the following?

(A) Straight line

(B) Ellipse

(D) Hyperbola

Answer: (C)

34. Which one of the following is the optical spectral window suitable for remote sensing?

(A) 0.02 – 0.2 µm

(B) 0.4 – 14 µm

(D) 0.01 – 1 m

Answer: (B)

35. A radioactive nucleus The number of α and β particles emitted during this decay are

(A) 12α and 1β⁺

(B) 6α and 1β⁻

(D) 3α and 1β⁻

Answer: (D)

36. The silicate mineral(s) that commonly occur(s) in regionally metamorphosed siliceous dolomitic limestone is/are

(A) diopside

(B) cordierite

(D) wollastonite

Answer: (A, C, D OR A, C)

37. Which of the natural hazard(s) listed below can be caused by Earthquakes?

(A) Tsunamis

(B) Landslides

(D) Lightning

Answer: (A, B)

38. Which of the following is/are the driving force(s) behind plate motion?

(A) Slab-Pull

(B) Ridge-Push

(D) Advection

Answer: (A, B, C)

39. Which of the following is/are copper ore mineral(s)?

(A) Bornite

(B) Pentlandite

(D) Covellite

Answer: (A, D)

40. Which of the following stratigraphic unit(s) of the Vindhyan Super group contain(s) commercially significant limestone deposit(s)?

(A) Bhander Formation

(B) Rewa Formation

(D) Rohtas Formation

Answer: (A, D)

41. The strike and dip of the axial plane of a reclined fold is 022° and 28° SE, respectively. The plunge direction (in whole circle bearing) of the axis of the reclined fold is ______ degrees. [in integer]

Answer: (112 to 112)

42. If the shrinkage factor of a crude oil is 0.7, its formation volume factor is _____. [round off to 1 decimal place]

Answer: (1.4 to 1.5)

43. The cross section of a river channel is approximated by a trapezium. The river has an average channel width of 40 m and average depth of 3 m. If the average flow speed is 2 m/s, the discharge rate is _________ m³/s. [in integer]

Answer: (240 to 240)

44. A mineral of uniform composition is cut into a wedge shape. The birefringence of the wedge section is 0.012. The retardation at 40 µm thickness of the wedge is _______ nm. [in integer]

Answer: (480 to 480)

Q.45 – Q.65 Carry TWO marks Each

45. The sand supply and the variability of wind direction results in different dune types. In the options below, choose the CORRECT pair of dune types marked I and II in the figure.

(A) I – Transverse dune; II – Barchan dune

(B) I – Star dune; II – Barchan dune

(D) I – Barchan dune; II – Star dune

Answer: (B)

46. Which one of the following statements is CORRECT?

(A) Salt dome traps are abundant in the Upper Assam Basin

(B) Fold and thrust related traps are common in the Mumbai Offshore Basin

(D) Sandstone is the reservoir rock in the Krishna-Godavari Basin

Answer: (D)

47. Identify the common metamorphic minerals labelled X and Y in the ACF diagram.

(A) X – Anorthite; Y – Actinolite

(B) X – Grossular; Y – Diopside

(D) X – Ferrosilite; Y – Andradite

Answer: (B)

48. Which one of the following schematic P-T paths is characteristic for a rock metamorphosed in a subduction zone?

Answer: (B)

49. Which one of the following is the CORRECT statement regarding the ecology of bivalves?

(A) Pholas is a swimming form

(B) Venus is a shallow burrower

(D) Spondylus is a deep burrower

Answer: (B)

50. On a fault surface with strike and dip 320° and 55° NE, respectively, four sets of slickenlines were measured by a geologist. Given that the fault surface was measured correctly, the plunge and plunge direction of the lineation on the fault surface is

(A) 55° → 050°

(B) 20° → 320°

(D) 60° → 090°

Answer: (A)

51. Match the following tectonic settings in Group-I with the corresponding examples in Group-II.

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

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

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

Answer: (A)

52. Match the following igneous textures in Group-I with their definitions in Group-II.

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

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

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

Answer: (C)

53. Match the Volcanogenic Massive Sulfide (VMS)-type deposits in Group-I with the dominant mineralized host rocks in Group-II.

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

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

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

Answer: (B)

54. The following diagram shows phase relations in a system consisting of components A and B at 1 bar pressure. If the initial composition of liquid is R, during cooling and crystallization of magma, which of the following statement(s) is/are CORRECT?

(A) On complete crystallization of magma, the final composition (in wt.%) of rock consists of 25 of mineral A and 75 of mineral B.

(B) On cooling of magma, mineral A is the first mineral to crystallize.

(D) The composition (in wt.%) of liquid at point E is 40 A and 60 B.

Answer: (A, C)

55. Which of the following systems tract(s) indicate regression?

(A) Transgressive systems tract

(B) Falling stage systems tract

(D) Low stand systems tract

Answer: (B, C, D)

56. Which of the following sedimentary feature(s) indicate(s) sub-aerial exposure of the depositional surface?

(A) Groove cast

(B) Double mud drape

(D) Adhesion ripple

Answer: (C, D)

57. Which of the following statement(s) is/are correct?

(A) Diatoms are algal forms.

(B) Dinoflagellates are unicellular algae.

(D) Radiolarians are organic-walled microfossils.

Answer: (A, B, C OR A,B)

58. Which among the following space groups is/are non-compatible with glide plane?

(A) Pab2₁

(B) Pnma

(D)

Answer: (A, C)

59. Which type of porphyroclast(s) listed below is/are suitable as kinematic indicators in ductile shear zones?

(A) σ – type

(B) Θ-type

(D) φ-type

Answer: (A, C)

60. Which of the following parameter(s) is/are Rock Mass Rating (RMR) based on?

(A) Rock Quality Designation

(B) Uniaxial compressive strength of intact rock

(D) Rock composition

Answer: (A, B, C)

61. A sample of 10 g coal yields 1 g of moisture, 2 g of ash and 5.6 g of volatile matter. The percentage of volatile matter content of the coal on dry ash-free basis is ________. [round off to 1 decimal place]

Answer: (80.0 to 80.0)

62. A soil sample shows an average beta count of 6.8 counts per minute (cpm) per gram of organic carbon. The ¹⁴C count rate from organic carbon of present day vegetation is 15.26 cpm/g. The age of the sample is _________ years. [round off to 1 decimal place] (Half-life of ¹⁴C = 5370 years)

Answer: (6261.0 to 6266.0)

63. A digital camera with a focal length of 150 mm is flown at a height of 3000 m over a flat terrain for taking aerial photographs. The scale of the aerial photograph is1: ________. [in integer]

Answer: (20000 to 20000)

64. The following reaction occurs at 1 bar and 823 K.

Using the above molar thermodynamic data, the calculated slope of the above reaction is ________bar K⁻¹. [round off to 2 decimal places]

Answer: (20.00 to 21.00)

65. Operating costs of an open cast gold mine are Rs. 4000/tonne. The recovery at the mill is 90%. At a gold price of Rs. 4550/g, the cutoff grade of gold calculated on the basis of operating cost is _________ g/tonne. [round off to 2 decimal places]

Answer: (0.96 to 1.00)

PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY

Q.27 – Q.47 Carry ONE mark Each

27. In 2D stacked seismic sections, the vertical axis corresponds to two-way travel time and the horizontal axis corresponds to _____.

(A) receiver locations

(B) source locations

(D) common midpoint (CMP) locations

Answer: (D)

28. In a 2D seismic survey acquired on land, head waves were recorded at the surface. Assuming that the subsurface consisted of horizontal, isotropic and homogeneous layers, the move out of the head wave event(s) would be _____.

(A) linear

(B) parabolic

(D) elliptical

Answer: (A)

29. An accurate depth migration of seismic data requires the knowledge of ________

(A) interval velocities

(B) root mean squared (RMS) velocities

(D) normal move out (NMO) velocities

Answer: (A)

30. The dimension of bulk modulus is ______.

(A) [ML⁻¹T⁻²]

(B) [MLT⁻¹]

(D) [ML²T⁻²]

Answer: (A)

31. A current flows from a medium with resistivity ρ₁ to a medium with resistivity ρ₂.A planar interface separates the two media. The angle of incidence and refraction with respect to the normal to the interface are θ₁ and θ₂, respectively. If the components of the current density perpendicular to the interface and the components of the electric field horizontal to the interface are continuous, the electrical law of refraction can be expressed as ____.

(A) ρ₁ tan θ₁ = ρ₂ tan θ₂

(B) ρ₁ sin θ₁ = ρ₂ sin θ₂

(D) ρ₁ tan θ₂ = ρ₂ tan θ₁

Answer: (A)

32. The convolution of two box-car pulses of positive amplitudes, with unequal and finite durations yields a ______ pulse.

(A) triangular

(B) trapezoidal

(D) sinusoidal

Answer: (B)

33. Which ONE of the following P-phases represents a reflection from the Moho?

(A) Pn

(B) Pg

(D) PmP

Answer: (D)

34. The remanent, induced and total magnetizations of a rock sample are denoted by The Königs berger ratio is

Answer: (C)

35. Which among the following is/are CORRECT statement(s) about the Van Allen radiation belts?

(A) The inner belt consists mainly of protons and the belt extends to about 1000-3000 km from the Earth’s surface.

(B) The belts are doughnut-shaped regions coaxial with the geomagnetic field lines of the Earth.

(C) The pitch of the helical motion of the charged particles increases as the particles approach the surface of the Earth.

(D) The outer belt occupies regions between 3 to 4 Earth radii and consists primarily of electrons.

Answer: (A, B, D)

36. Which of the following logging methods can be used to measure the resistivity of the flushed zone?

(A) Lateral log

(B) Long normal log

(D) Microspherically focused log

Answer: (C, D)

37. Which of the following statement(s) is/are CORRECT about the continuation of the gravity field?

(A) Continuation of the gravity field from one surface to another is permissible only when there are no masses present between the two surfaces.

(B) In upward continuation, the longer wavelength anomalies are attenuated more than the shorter wavelength anomalies.

(D) Upward continuation is a smoothing process.

Answer: (A, C, D)

38. An oceanic plate formed at a mid-oceanic ridge 27 million years ago. The plate has been moving with a uniform half-spreading rate of 4 cm/year ever since its formation. The current distance between the edge of this plate and the centre of the ridge is ________ km. [round off to 1 decimal place]

Answer: (1080.0 to 1080.0)

39. An artificial neural network (ANN) is trained to classify between shale and sand formations. The final layer of the ANN consists of a single neuron with a sigmoid activation function given by If the input to the final neuron is 0, then the output is __________. [round off to 1 decimal place]

Answer: (0.5 to 0.5)

40. A current electrode introduces a 2 Ampere current at a point (P) on the surface of a uniform half space. If the resistivity of the half space is 5 Ω-m, the magnitude of the electric field (due to the current) in the half space at a distance of 1 m from P is ________ V/m. [round off to 2 decimal places]

Answer: (1.55 to 1.65)

41. The relative dielectric permittivity of a homogeneous isotropic medium is 10 and the relative magnetic permeability of the same medium is 1. If the velocity of the electromagnetic wave propagating through this medium is v and the velocity of light in vacuum is c, then the ratio v/c is ________. [round off to 2 decimal places]

Answer: (0.29 to 0.35)

42. A mountain of height 8 km above mean sea level is in isostatic equilibrium with a 42 km thick continental crust. As predicted by Airy’s hypothesis, the root beneath this mountain is ________ km. [round off to 1 decimal place]

[Assume, density of mantle = 3.7 ×10³

kg m⁻³ and density of crust = 2.7 ×10³

kg m⁻³]

Answer: (21.0 to 22.0)

43. In wet soil of resistivity 100 Ωm, the skin depth of a GPR signal of 100 MHz is _________ m. [round off to 2 decimal places]

[Assume: μ₀ = 4𝜋 × 10⁻⁷ H/m]

Answer: (0.46 to 0.54)

44. A Wadati diagram was prepared for a local earthquake occurring in a homogeneous crust. If the crust is assumed to be a Poisson solid, the slope of the straight line in the Wadati diagram is ________. [round off to 2 decimal places]

Answer: (0.71 to 0.75)

Q.45 – Q.65 Carry TWO marks Each

45. The gravitational potential of the spheroidal Earth can be expressed as where G is the gravitation constant, E is the mass of the Earth, r is the radial distance from the centre of the Earth, R is the radius of Earth, J_n are the coefficients obtained from satellite geodesy, P_n represents the Legendre polynomial of order n, and θ is the colatitude. Which among the following is described by the term corresponding to n = 2?

(A) Gravitational potential due to a spherical Earth

(B) Deviations from the ellipsoid that correspond to a pear-shaped Earth

(D) The gravitational potential of the Earth-Moon system

Answer: (C)

46. The magnetic potential of a dipole at any external point (P) can be expressed as is the dipole moment, is a unit normal along the vector directed from the centre of the dipole to the external point (P) and C_m is a constant. If θ is the angle between , the radial component of is:

Answer: (A)

47. The functions g(t) and G(ω) constitute a Fourier Transform pair [g(t) ↔ G(ω)] as per the convention:

Which ONE among the following is the correct Fourier transform pair?

Answer: (B)

48. Gauss’ divergence theorem is given by

where is a vector field and V is the volume enclosed by the surface S. If then the application of divergence theorem to yields:

Answer: (A)

49. The angular frequency (ω) and wave number (k) for an electromagnetic wave is related by the expressionω² = αk + βk³, where α and β are constants. The wave number k₀ for which the group velocity equals the phase velocity is _____.

Answer: (C)

50. The schematic represents P-wave arrivals from a zero-offset Vertical Seismic Profiling (VSP) experiment conducted over a horizontally layered and isotropic Earth. Match the four events labelled in the schematic and their listed descriptions.

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

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

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

Answer: (A)

51. The transfer function of a linear system is given as The poles of this function are _______.

(A) –3 and –2

(B) –3 and 2

(D) 3 and 2

Answer: (A)

52. The eigenvalues of the given matrix A are _________.

(A) –1, 2 and 3

(B) 1, 2 and 3

(D) 0, 2 and 2

Answer: (A)

53. The apparent resistivity values obtained from a vertical electrical sounding (VES)survey over a horizontally layered 1-D Earth are indicated by ρ₁, ρ₂, ρ₃, ρ₄, where the subscript refers to the nth layer from the surface. Match the VES curve types listed in Group-I with the corresponding ordering of resistivity values listed in Group-II.

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

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

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

Answer: (B)

54. Choose the CORRECT statement(s) from the following on the solution of systems of linear equations without the application of regularization.

(A) An under-determined system of linearly independent equations has either a trivial solution or an infinite number of solutions.

(B) An ill-conditioned system of linear equations can yield stable solutions in the presence of noise.

(D) A system of linearly independent equations with the number of equations equal to the number of unknowns is a mixed-determined system

Answer: (A, C)

55. In seismic spiking deconvolution with an unknown source wavelet, the wavelet can be deconvolved most effectively under which of the following condition(s)?

(A) The source wavelet is minimum phase.

(B) The source wavelet is zero phase.

(D) The autocorrelation of the reflectivity series in time domain can be approximated to be identically zero.

Answer: (A, C)

56. The stacking chart for an end-on 2D seismic survey is shown in the figure. The shot, receiver, mid-point and offset coordinate axes are as indicated in the figure,while each star represents a unique seismic trace. With reference to the stacking chart, which of the following is/are CORRECT statement(s)?

(A) The traces along LL constitute a common mid-point (CMP) gather.

(B) The traces along LL constitute a common shot gather.

(D) The traces along NN constitute a common receiver gather.

Answer: (A, C)

57. Suppose x_1/5defines the half-width at 1/5th of the maximum gravity value measured over a buried sphere of uniform density. If d is the distance from the surface to the centre of the sphere, the value of x_1/5/d is _____. [round off to 2 decimal places]

Answer: (1.34 to 1.44)

58. In a reservoir zone, the deep induction log reads 3 Ωm for a formation whose

porosity is 19%. The hydrocarbon saturation of that formation as estimated from Archie’s equation is ______%. [round off to 1 decimal place]

[Assume: a=1, n=2, m=1.5, formation water resistivity = 0.04 Ωm]

Answer: (57.0 to 63.0)

59. The heat flow q (mW/m²) is related to the age t (My) of the ocean floor as

t = (510/q)². Assuming the temperature gradient and the thermal conductivity at a site in the Indian ocean to be 55 °C /km and 2.3 W/m °C, respectively, the age of the site is_______ My. [round off to 2 decimal places]

[Use the magnitude of the calculated value of q]

Answer: (16.00 to 16.50)

60. The radioactive isotopes ^AX and ^BX of an element X at the time of formation of a rock sample were in equal proportions. Subsequently, in a closed system, it was found that the abundances of the isotopes were in the ratio ^BX/^AX = 128.55. The elapsed time since the formation of the sample is ______ years. [round off to 1 decimal place]

[Assume: decay rate of λ_A = 9.85 × 10⁻³ y⁻¹, λ_B = 1.55 × 10⁻³ y⁻¹].

Answer: (580.0 to 590.0)

61. A two-layered planet consists of a core and a mantle of uniform but unequaldensities. The density of the core is 7150 kg m⁻³ and the mean density of the planet is 5620 kg m⁻³. If the mantle enclosing the core occupies 2/3rd of the radius of the planet from the surface, then the density of the mantle is ______ kg m⁻³. [round off to 1 decimal place]

Answer: (5556.1 to 5566.1)

62. A reflection seismic survey is conducted over a two-layered medium with a single horizontal, homogeneous, isotropic layer underlain by a homogenous, isotropichalf-space. The Shuey two-term approximation for the P-wave reflection coefficient for the interface separating the media is given by:

R(θ) = 0.025 – 0.1 sin²θ,

whereθ is the angle of incidence of the P-wave with respect to the normal to the interface. Assuming the validity of the approximation, the offset-to-depth ratio(offset/depth) at which a polarity reversal can be observed in a CMP gather from the survey is _______. [round off to two decimal places]

[Hint: A change in the sign of the reflection coefficient leads to polarity reversal]

Answer: (1.10 to 1.20)

63. The given figure shows the rupture of a unilateral fault with the rupture velocity(V_r) of 2 km/s. According to the simple Haskell source model, the rupture time associated with the entire length of the fault as estimated at the station is ________sec. [round off to 2 decimal places]

[Assume: Shear wave speed = 3.5 km/s]

Answer: (1.69 to 1.89)

64. The given figure shows ray paths for direct P and P-to-S converted phases recorded at a station on the surface (R) for a teleseismic event. Given that the ray parameter(p) is 0.1 s/km, the arrival time difference between the P-to-S converted phase and the direct P-phase at the receiver R is _____sec. [round off to 2 decimal places]

Answer: (4.00 to 4.50)

65. A land seismic survey is conducted over a horizontally layered and isotropic Earth.The thickness and the P-wave velocity of the homogeneous weathered layer are 5 m and 800 m/s, respectively. The shots are fired at a depth of 5 m below the surface and the receivers are placed on the surface at mean sea level (MSL). If the datum plane is defined to be 5 m below the MSL, the magnitude of the P-wave static correction to be applied to the data is ________ milliseconds. [round off to 2 decimal places]

Answer: (6.20 to 6.30)

GATE Exam 2022 Geomatics Engineering (GE) Question Paper With Answer Key

July 15, 2022 by suresh84

GATE-2021

GE: Geomatics Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Writing too many things on the ________ while teaching could make the students get _________.

(A) bored / board

(B) board / bored

(D) bored / bored

Answer: (B)

2. Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality on the real number line?

Answer: (C)

3. If f(x) = 2 ln (√e^x), what is the area bounded by f(x) for the interval [0, 2]on the x-axis?

(A) 1/2

(B) 1

(D) 4

Answer: (C)

4. A person was born on the fifth Monday of February in a particular year.

Which one of the following statements is correct based on the above information?

(A) The 2nd February of that year is a Tuesday

(B) There will be five Sundays in the month of February in that year

(D) All Mondays of February in that year have even dates

Answer: (A)

Answer: (B OR C)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Having ultra-black skin is only advantageous to species S

(B) Species S with lower collagen in their skin are at an advantage because it helps them avoid predators

(D) Having ultra-black skin is only disadvantageous to species S but advantageous only to their predators

Answer: (C)

7. For the past m days, the average daily production at a company was 100 units per day.

If today’s production of 180 units changes the average to 110 units per day,what is the value of m?

(A) 18

(B) 10

(D) 5

Answer: (C)

8. Consider the following functions for non-zero positive integers, p and q.

Which one of the following options is correct based on the above?

(A) f(2,2) = g(2,2)

(B) f(g(2,2), 2) < f(2, g(2,2)

(D) f(3,2) >g(3,2)

Answer: (A)

If the person starts from R at 7 AM and is required to visit S and return to R,what is the minimum time required?

(A) 6 hours 30 minutes

(B) 3 hours 45 minutes

(D) 5 hours 15 minutes

Answer: (A)

What is the ratio of the areas of unshaded regions of case M to that of case N?

(A) 2 : 3

(B) 1 : 1

(D) 2 : 1

Answer: (B)

Geomatics Engineering

PART A: Common FOR ALL CANDIDATES

Q.11 – Q.35 Carry ONE mark Each

11. Most probable value of a quantity

(A) always increases with increase in True value

(B) always decreases with decrease in True value

(D) is nearest to True value

Answer: (D)

12. Two surveyors, P and Q measured a 20 m distance six times each, as given below (in m):

Surveyor P: 19.97, 20.02, 20.04, 19.98, 19.96, 20.03

Surveyor Q: 20.05, 20.07, 20.05, 20.06, 20.07, 20.07

On the basis of accuracy and precision of the measured values, choose the CORRECT statement.

(A) Observed values of Surveyor P are less precise and observed values of Surveyor Q are more accurate.

(B) Observed values of Surveyor P are more precise and observed values of Surveyor Q are less accurate.

(D) Observed values of Surveyor P are less accurate and observed values of Surveyor Q are less precise.

Answer: (C)

13. Identify the error, which has all the following characteristics:

(i) Caused by observer’s misunderstanding and carelessness

(ii) Reading an angle counter-clockwise, but recording it as clockwise angle

(iii) Sighting the wrong target

(iv) Poor judgment by the observer

(A) Mistake

(B) Cumulative error

(D) Accidental error

Answer: (A)

14. Electromagnetic Spectrum can be broadly divided as (in order of increasing wavelength)

(A) X-rays, Gamma rays, Infrared, Ultraviolet, Visible, Radiowave, Microwave

(B) Gamma rays, X-rays, Radiowave, Microwave, Ultraviolet, Infrared, Visible

(D) Gamma rays, X-rays, Ultraviolet, Visible, Infrared, Microwave, Radiowave

Answer: (D)

15. The relationship between wavelength (λ), frequency (ν), and velocity (c) of electromagnetic wave is

(A) c = ν² / λ

(B) c = ν / λ

(D) c = ν λ²

Answer: (C)

16. Spectral signature of an object in a satellite image does NOT depend on the

(A) season of the year

(B) wavelength of electromagnetic spectrum

(D) reflectance value from the object

Answer: (C)

17. Component of GPS signal that gets deciphered by all types of GPS receivers is

(A) Coarse-Acquisition code

(B) Precision code

(D) Link-2C frequency

Answer: (A)

18. For 3D-positioning, Global Navigational Satellite System (GNSS) requires a minimum of ______ satellites.

(A) 3

(B) 4

(D) 2

Answer: (B)

19. Basic objective of NAVSTAR GPS is to provide services for

(A) Positioning, Velocity and Timing

(B) Positioning, Navigation and Timing

(D) Positioning, Velocity and Navigation

Answer: (B)

20. A satellite image with 6-bit radiometric resolution has ______ gray levels.

(A) 16

(B) 32

(D) 128

Answer: (C)

21. Thermal Infrared images are provided by

(A) LANDSAT MSS and IRS LISS-II sensors

(B) SPOT and CARTOSAT

(D) LANDSAT TM and NOAA AVHRR sensors

Answer: (D)

22. Which of the following gets mitigated in DGPS positioning?

(A) Atmospheric error

(B) Multi-path error

(D) Topographic error

Answer: (A)

23. In GIS database, which type of attribute may be used to represent area?

(A) Nominal

(B) Interval

(D) Ordinal

Answer: (C)

24. What is attribute uncertainty?

(A) Error due to imprecision in coordinate registration

(B) Error due to incorrect labelling or quantification of features

(D) Error associated with displacement of the object from its true location

Answer: (B)

25. In GIS, ______ triangulation is a proximal method that satisfies the requirement that a circle drawn through the three nodes of a triangle contains no other node.

(A) Dalhousie

(B) Delaunay

(D) Davenport

Answer: (B)

26. In GIS, reclassification is performed to

(A) group ranges of values into a single value within a data layer

(B) segment a data layer into multiple data layers

(D) classify a data layer using many attributes

Answer: (A)

27. For the following observation equation

2𝛼 = 124° 52ʹ 22ʺ weight 4,

the weight of (α/3) is _____ (in integer).

Answer: (144 to 144)

Q.28 – Q .46 Carry TWO marks each

28. Following observation equations are obtained in a survey task.

x + y = 3

2x + y = 6

x + 2y = 4

Using least square method, the most probable values of x and y will be

(A) x = 2.10, y = 0.90

(B) x = 2.64, y = 0.64

(D) x = 2.75, y = 0.75

Answer: (B)

29. The internal angles P, Q, R of a triangle are observed in degree minute second (° ʹ ʺ) using a Total Station. The angles along with their probable errors are given below.

P = 40° 30ʹ 01ʺ ± 02ʺ

Q = 60° 00ʹ 02ʺ ± 03ʺ

R = 79° 30ʹ 05ʺ ± 04ʺ

The corrected values of the angles P, Q and R are

(A) P = 40° 30ʹ 01ʺ, Q = 60° 00ʹ 02ʺ, R = 79° 30ʹ 05ʺ

(B) P = 40° 29ʹ 59.6ʺ, Q = 59° 59ʹ 59.5ʺ, R = 79° 30ʹ 0.9ʺ

(D) P = 40° 29ʹ 59ʺ, Q = 59° 59ʹ 59ʺ, R = 79° 30ʹ 02ʺ

Answer: (C)

30. How many number of cells of a 30 m spatial resolution DEM would be required to cover a 1:50,000 topographic map of Survey of India, assuming that 1 minute = 1.85 km?

(A) 855,625

(B) 855,525

(D) 855,325

Answer: (A)

31. Choose the CORRECT statement(s)

(A) True Color Composite is produced by superimposing Red band in Red, Green band in Green, and Blue band in Blue color.

(B) True Color Composite is produced by superimposing Blue band in Red, Green band in Green, and Red band in Blue color.

(C) Standard False Color Composite is produced by superimposing Near Infrared band in Red, Red band in Green, and Green band in Blue color.

(D) Standard False Color Composite is produced by superimposing Green band in Red, Green band in Green, and Near Infrared band in Blue color.

Answer: (A, C)

32. Choose the CORRECT statement(s) in case of visual image interpretation.

(A) Tone/Color is a primary element while Size, Shape and Texture are secondary elements.

(B) Size, Shape and Texture are primary elements while Tone/Color is a secondary element.

(D) Tone/Color is a primary element while Pattern and Association are secondary elements.

Answer: (A, C)

33. The spatial resolution of a satellite image P is 80 m and another satellite image Q is 20 m; each of 512 × 512 pixel size. Choose the CORRECT option(s).

(A) Image P will cover four times the area of image Q.

(B) Image P will cover sixteen times the area of image Q.

(D) Image P is higher resolution and image Q is lower resolution.

Answer: (B, C)

34. Which statement(s) is/are CORRECT for Hyperspectral images?

(A) Bandwidth is large.

(B) Bandwidth is narrow.

(D) Bands are contiguous.

Answer: (B, C, D)

35. Satellite-Based NAVSTAR GPS Augmentation System(s) is/are

(A) EGNOS

(B) WAAS

(D) DGPS

Answer: (A, B, C)

36. Identify the CORRECT statement(s)

(A) NAVSTAR GPS consists of minimum 24 satellites.

(B) Precision of GPS positioning is being defined by its standard deviation.

(D) GPS observations from geodetic GPS receiver provide less accurate position than

GPS code receiver.

Answer: (A, B)

37. Identify the CORRECT statement(s).

(A) For accurate GPS positioning, Geometric Dilution of Precision should be as large as possible.

(B) Integer ambiguity is associated with carrier frequency observation of GPS signal.

(D) GPS is two way ranging system for user.

Answer: (B, C)

38. During GPS Surveying, initialization of rover receiver is required for

(A) Relative Static method

(B) Relative Kinematic method

(D) Kinematic On Fly method

Answer: (B, C)

39. Centroid of a polygon is

(A) geometric center of the polygon.

(B) arithmetic mean position of all its vertices in two coordinate directions.

(D) center of polyline.

Answer: (A, B, C)

40. The area of a buffer of 50 m around a proposed 1 km straight road segment to restrict any future construction is ______ sq. m. (in integer).

(Take the value of π = 3.14)

Answer: (107850 to 107850)

41. The Degree of Accuracy of a traverse having error of closure of 0.5 m and perimeter of 100 m is ______ (round off to 3 decimal places).

Answer: (0.004 to 0.006)

42. Using the following regression equations, the correlation coefficient between two survey quantities x and y will be ______ (round off to 2 decimal places).

2x – 5y + 98 = 0

6x – 7y + 114 = 0

Answer: (0.68 to 0.69)

43. If population variance is 14.8, sample variance is 15.4 and the number of degrees of freedom is 10, then Chi-square value is ______ (round off to 2 decimal places).

Answer: (10.38 to 10.44)

44. Height of a station determined by Global Navigational Satellite System (GNSS) is 284.097 m and the geoid height of the station is –30.052 m. The elevation of the station is ______ m (round off to 3 decimal places).

Answer: (314.000 to 314.500)

45. Number of cells required to cover an area of 9 sq. km of ASTER-GDEM are ______ (in integer).

Answer: (10000 to 10000)

46. If a 1:50,000 scale map is digitized to an accuracy of ± 0.5 mm, the level of error that might be expected in ground is ± ______ m (in integer).

Answer: (25 to 25)

PART B: FOR Section I CANDIDATES ONLY

47. The main principle of Surveying is to work from

(A) whole to part

(B) part to whole

(D) lower elevation to higher elevation

Answer: (A)

48. The type of survey carried out to define the property boundaries for transfer of land property is called

(A) city survey

(B) cadastral survey

(D) geodetic survey

Answer: (B)

49. Departure of a line of a traverse is obtained by multiplying its length by the ______ of the reduced bearing of the line.

(A) Sine

(B) Cosine

(D) Cotangent

Answer: (A)

50. The multiplying constant of a Tacheometer, where f is the focal length and i is the distance between the stadia hairs, is

(A) i/f

(B) f²/i

(D) f × i

Answer: (C)

51. The camera axis of an aerial camera is defined as

(A) the line joining the optical centres of the objective and eyepiece lens.

(B) the perpendicular line between the photographic centre and optical centre of the objective lens.

(D) the line perpendicular to the plumb line

Answer: (B)

52. Bowditch rule for adjusting a closed traverse of perimeter ‘l’ is based on the assumption that the probable error is proportional to

(A) l

(B) √l

(D) 1/√l

Answer: (B)

53. Select the INCORRECT statement:

(A) Scale of a tilted photograph is uniform throughout its extent.

(B) The relief displacement of any point will be radial from nadir point of the tilted photograph.

(D) A line perpendicular to the principal line and passing through the isocentre is known as the axis of tilt.

Answer: (A)

54. A topographic map prepared by Survey of India covers 1 degree by 1 degree area on a single map. The minimum ground distance which can be represented on this map is ______ m (round off to 2 decimal places).

Answer: (62.5 to 62.5)

Q.55 – Q .65 Carry TWO marks Each

55. In a closed traverse, the sum of the latitudes is 1.39 m and the sum of the departures is 2.17 m. The Length and Whole Circle Bearing of the closing error are

(A) Length = 2.57 m, Whole Circle Bearing = 58°

(B) Length = 2.57 m, Whole Circle Bearing = 57°

(D) Length = 2.67 m, Whole Circle Bearing = 57°

Answer: (B)

56. In surveying, an odometer is used for measuring

(A) azimuth

(B) horizontal angle

(D) distance

Answer: (D)

57. Choose the CORRECT statements(s).

(A) The spheroid is a mathematical surface of the Earth.

(B) Geoid is an equipotential reference surface of the Earth.

(D) The WGS-84 datum varies from country to country.

Answer: (A, B)

58. Choose the CORRECT statement(s).

(A) Latitude of a place varies from 0 degree to 90 degree North or South, and Longitude varies from 0 degree to 180 degree East or West of Greenwich Meridian.

(B) Latitude of a place varies from 0 degree to 180 degree East or West of Greenwich Meridian, and Longitude varies from 0 degree to 90 degree North or South.

(D) Latitude and Longitude of a place are subject to change with time.

Answer: (A, C)

59. A map projection is

(A) a systematic representation of latitude and longitude lines on a plane (paper) map.

(B) a representation of 3D shape of Earth on 2D plane.

(D) required for taking theodolite observations of horizontal angles.

Answer: (A, B, C)

60. Face Left and Face Right observations using a vernier theodolite will eliminate

(A) index error

(B) graduation error

(D) atmospheric error

Answer: (A, B)

61. The parallax of a point ‘a’ on a pair of successive overlapping photographs is 73.22 mm and the micrometer reading of a parallax bar of point ‘a’ is 12.10 mm. Similarly, the micrometer reading of the parallax bar of point ‘b’ is 9.65 mm, then the parallax of the point ‘b’ is ______ mm (round off to 2 decimal places).

Answer: (70.00 to 71.00)

62. The scale of an aerial photograph is 5 mm = 100 m. The size of the photograph is 23 cm × 23 cm. If the longitudinal overlap is 65% and sidelap is 20%, the number of photographs required to cover an area of 12.5 km × 8 km is ______ (in integer).

Given that the flight line is along the longer dimension.

Answer: (36 to 36)

63. An instrument is set up at a station P and the angle of depression to a vane, 1.20 m above the foot of the staff held at Q is 5°. The horizontal distance PQ is observed to be 300 m. The R.L. of point Q is ______ m (round off to 3 decimal places).

Given that the staff reading at a BM (Elevation 436.050 m) is 2.865 m.

Answer: (411 to 412)

64. A staff is held vertical at a distance of 100 m and 300 m, respectively. Observations are taken with a Tacheometer and staff intercepts, with the telescope kept horizontal, are 0.990 m and 3.000 m, respectively. The theodolite is set over a station having a RL of 950.500 m and the height of instrument is 1.425 m. The multiplicative constant of the Tacheometer is ______ (round off to 2 decimal places).

Answer: (99.10 to 99.99)

65. Survey of India topographic sheet is 53G/12. At this scale, the numbers of toposheets that would cover a land area equivalent to 4 degree by 4 degree is ______ (in integer).

Answer: (256 to 256)

PART B: FOR Section II CANDIDATES ONLY

Q.66 – Q.73 Carry ONE mark Each

66. The correlation coefficient between two bands of remote sensing data that would yield good classification is

(A) close to one

(B) close to zero

(D) between one to ten

Answer: (B)

67. In a covariance matrix, the main diagonal shows the ______ of each band.

(A) standard deviation

(B) variance

(D) median

Answer: (B)

68. Choose the INCORRECT statement about image segmentation in digital image processing.

(A) Segmentation divides an image into different regions.

(B) Image segmentation does not help in image classification.

(D) Segmentation is a process of partitioning an image into multiple sets of similar pixels.

Answer: (B)

69. When the histogram of an image is non-Gaussian in nature, the type of linear contrast enhancement preferred to be used is

(A) Piece-wise Linear Contrast Stretching

(B) Min-max Linear Contrast Stretching

(D) Standard Deviation Contrast Stretching

Answer: (A)

70. Spinning of the Earth, as viewed from the North pole, appears to be from

(A) West to East in anti-clockwise direction

(B) West to East in clockwise direction

(D) East to West in clockwise direction

Answer: (A)

71. In case of Principal Component Analysis (PCA), the variance of a single variable expresses the spread of its values about the

(A) Mode

(B) Median

(D) Standard Deviation

Answer: (C)

72. Select the CORRECT sequence for supervised classification of satellite image

(i) Classification

(ii) Training

(iii) Accuracy assessment

(iv) Radiometric/geometric correction

(A) (i), (ii), (iii), (iv)

(B) (iv), (ii), (i), (iii)

(D) (i), (iv), (ii), (iii)

Answer: (B)

73. The sum of all the values of a normalized histogram is equal to _________ (in integer).

Answer: (1 to 1)

Q.74 – Q.84 Carry TWO marks Each

74. In a Landsat-8 scene, digital number (DN) values of a pixel in band-4, band-5 and band-10 are 80, 100 and 30, respectively. What would be the NDVI value for the same pixel (round off to 3 decimal places)?

(A) 0.111

(B) 0.222

(D) 0.889

Answer: (A)

75. For a given set of radiance values, which amongst the following is/are unit less?

(A) Skewness

(B) Kurtosis

(D) Standard Deviation

Answer: (A, B)

76. Identify the CORRECT statement(s).

(A) External geometric errors in satellite images can be corrected using GCPs and an appropriate mathematical model.

(B) During rectification, transformation coefficients are used to rectify remote sensing images to a standard datum and map projection.

(D) Registration is done between a satellite image and field data.

Answer: (A, B)

77. Choose the CORRECT statement(s).

(A) Higher frequencies in an original image predominantly appear around the center of its Fourier Spectrum.

(B) Higher frequencies in an original image predominantly appear progressively along the outer edge of its Fourier Spectrum.

(D) Vertical features in an original image appear as vertical components in its Fourier Spectrum.

Answer: (B, C)

78. Match the CORRECT option(s) for the types of filters given in (I), (II), (III), and (IV) with their kernels given in (P), (Q), (R) and (S).

(A) I – P and II – Q

(B) III – R and IV – S

(D) II – R and III – S

Answer: (C, D)

79. Band ratio in satellite images interpretation is applied to

(A) enhance the spectral separation

(B) reduce the effects of topography

(D) increase spatial differences between bands

Answer: (A, B)

80. The decorrelation stretch enhances colour differences and removes inter-band ______.

(A) decorrelation

(B) contradiction

(D) relationship

Answer: (C, D)

81. The overall image classification accuracy (in percentage) calculated from the following error matrix is ______ (in integer).

Answer: (82 to 82)

82. Number of bytes required to store an 8-bit uncompressed image of size 512 × 512 pixels is _______ (in integer).

Answer: (262144 to 262144)

83. The minimum and maximum Digital Number (DN) values of an image are 30 and 55, respectively. If the input DN value of a pixel is 35, the output DN value after linear contrast stretch of an 8-bit data is ______ (in integer).

Answer: (51 to 51)

84. The FOV of a sensor (for a scene) placed at a nadir height of 6 km is 90 degree. The ground swath width of the scene is ______ km (in integer).

Answer: (12 to 12)

GATE Exam 2022 Ecology and Evolution (EY) Question Paper With Answer Key

July 15, 2022 by suresh84

GATE-2022

EY: Ecology and Evolution

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. You should _________ when to say _________.

(A) no / no

(B) no / know

(D) know / no

Answer: (D)

2. Two straight lines pass through the origin (x₀, y₀) = (0,0). One of them passes through the point (x₁, y₁) = (1,3) and the other passes through the point (x₂, y₂) = (1, 2).

What is the area enclosed between the straight lines in the interval [0, 1] on the 𝑥-axis?

(A) 0.5

(B) 1.0

(D) 2.0

Answer: (A)

3. If

p ∶ q = 1 ∶ 2

q ∶ r = 4 ∶ 3

r ∶ s = 4 ∶ 5

and u is 50% more than s, what is the ratio p ∶ u?

(A) 2 : 15

(B) 16 :15

(D) 16 : 45

Answer: (D)

4. Given the statements:

• P is the sister of Q.

• Q is the husband of R.

• R is the mother of S.

• T is the husband of P.

Based on the above information, T is ______ of S.

(A) the grandfather

(B) an uncle

(D) a brother

Answer: (B)

5. In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

(A) Area of SPQT = Area of RUVZ = Area of PXWR

(B) Area of SPQT = Area of PXWR  Area of RUVZ

(D) Area of PXWR = Area of RUVZ  Area of SPQT

Answer: (B)

Q.6 – Q. 10 Carry TWO marks each.

6. Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy in the first year are more likely to have better overall health as they get older.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Healthy eating is important for those with good health conditions, but not for others

(B) Eating healthy can be started at any age, earlier the better

(D) Healthy eating is more important for adults than kids

Answer: (B)

7. P invested Rs. 5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.

If at the end of that investment year, Q receives 4/9 of the total profit, what is the value of x (in Rs.) ?

(A) 2500

(B) 3000

(D) 8437

Answer: (B)

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.

From the data presented above, which one of the following is CORRECT?

(A) mean > mode > median

(B) mode > median > mean

(D) median > mode > mean

Answer: (B)

9. In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.

The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.

For example, a person at a given position Y can move only to the positions marked X on the right.

Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is

(A) 4

(B) 5

(D) 7

Answer: (B)

10.

Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank.

Which one of the following represents a possible unfolding of the cube?

Answer: (MTA)

ECOLOGY AND EVOLUTION

Q.11 – Q.35 Carry ONE mark Each

11. Which one of the following options denotes the time when the majority of animal phyla first appeared in the fossil record? (MYA = Million Years Ago)

(A) 65 MYA

(B) 250 MYA

(D) 700 MYA

Answer: (C)

12. Consider the following strains of an influenza virus and their basic reproduction numbers (R₀). Assuming that they are all equally virulent, which one of the following strains would be most concerning for a completely vulnerable population of humans?

(A) α-strain with R₀ = 4.0

(B) β-strain with R₀ = 1.0

(D) δ-strain with R₀ = 0.2

Answer: (A)

13. Which one of the following statements is true with respect to energy requirements of photosynthesis in C3 and C4 biochemical cycles?

(A) C3 > C4

(B) C4 > C3

(D) Energy requirement is unrelated to C3 or C4 cycle

Answer: (B)

14. Which one of the following is a proximate explanation for grouping in animals?

(A) Animals in groups face a lower risk of predation.

(B) Animals form groups to forage efficiently.

(D) Groups form when individuals show attraction to others.

Answer: (D)

15. The ethologist Konrad Lorenz is known for his discovery of which one of the following processes?

(A) Habituation

(B) Sensitization

(D) Imprinting

Answer: (D)

16. Male stickleback fish develop red colour on their ventral side in the breeding season and maintain territories. When a conspecific male intruder enters their territory, resident males perform an aggressive display. The ethologist Niko Tinbergen presented models of different shapes to territorial male stickleback fish. He found that models of any shape elicited aggressive displays, provided the ventral part of the models was coloured red. This observation led to the development of which one of the following concepts?

(A) Supernormal stimuli

(B) Sign stimuli

(D) Internal stimuli

Answer: (B)

17. Neuronal circuits that mediate escape responses in animals would perform best if they had which one of the following combination of properties?

(A) Large diameter axons and electrical synapses

(B) Small diameter axons and electrical synapses

(D) Small diameter axons and chemical synapses

Answer: (A)

18. Moth caterpillars that mimic bird droppings are an example of which one of the following phenomena?

(A) Aposematism

(B) Batesian mimicry

(D) Müllerian mimicry

Answer: (C)

19. Which one of the following processes is not likely to lead to the stable coexistence of two species at the same trophic level within an ecological community?

(A) Density-dependent predation

(B) Facilitation

(D) Niche differentiation

Answer: (C)

20. Which one of the following organisms is a cytoplasmically inherited symbiotic bacterium that can cause extreme female-biased sex ratios in many insects?

(A) Clostridium

(B) Escherichia

(D) Wolbachia

Answer: (D)

21. A cross between a pure-bred plant with red flowers and a pure-bred plant with white flowers produced F1 generation with pink flowers. If the plants with pink flowers are selfed, what is the proportion of white : pink : red flowers expected in the next generation?

(A) 1 : 1 : 1

(B) 1 : 2 : 1

(D) 2 : 2 : 1

Answer: (B)

22. A gene coding for a particular protein exhibits 2% DNA sequence divergence between humans and chimpanzees. However, protein sequences encoded by them are identical. Which one of the following processes explains this?

(A) Non synonymous changes in the gene sequences

(B) Synonymous changes in the gene sequences

(D) Frame shift mutations in the gene sequences

Answer: (B)

23. Which one of the following sets of characteristics is most likely to cause population extinction via demographic stochasticity?

(A) Small geographical range and low population density

(B) Large geographical range and low population density

(D) Large geographical range and high population density

Answer: (A)

24. Which one of the following is not an expected impact of global warming?

(A) Birds shifting their distributions to higher elevations

(B) Fish shifting their distributions to deeper waters

(D) Mammals shifting their distributions towards higher latitudes

Answer: (C)

25. Which one of the following represents the chemical energy available to herbivores in an ecosystem?

(A) Net Secondary Productivity

(B) Gross Primary Productivity

(D) Net Primary Productivity

Answer: (D)

26. Which one of the following major mass extinctions is the most recent?

(A) Cretaceous-Paleogene

(B) Late Devonian

(D) Triassic-Jurassic

Answer: (A)

27. Which one of the following does not help maintain genetic diversity at a given locus?

(A) Heterozygote advantage

(B) Genetic drift

(D) Mutation-Selection balance

Answer: (B)

28. Which one of the following is potentially explained by the mid-domain effect?

(A) Increase in body size of mammals at high latitudes

(B) Species richness along an elevational gradient

(D) Species richness along a disturbance gradient

Answer: (B)

29. The graph shows the yield of coffee plantations located at different distances from a patch of primary forest.

Which one of the following options best explains this pattern?

(A) Carbon sequestration

(B) Seed predation by forest-dwelling insects

(D) Seed dispersal by forest-dwelling birds and mammals

Answer: (C)

30. Which one or more of the following bird species is/are the focus of conservation-oriented captive breeding efforts in India?

(A) Great Indian Bustard

(B) Himalayan Quail

(D) White-winged Wood Duck

Answer: (A)

Which one or more of the following is/are not an example of a zoonotic disease(s)?

(A) Ebola

(B) HIV-AIDS

(D) Poliomyelitis

Answer: (D)

32. Small islands tend to have fewer species than nearby large islands. Which one or more of the following reasons explain(s) this outcome?

(A) Smaller areas have higher extinction rates.

(B) Smaller areas have low environmental heterogeneity.

(D) Smaller areas have higher speciation rates.

Answer: (A, B, C)

33. The term “living fossil” applies to which one or more of the following organisms?

(A) Coelacanth

(B) Echidna

(D) Rhinoceros viper

Answer: (A, B, C)

34. Which one or more of the following reasons has/have been invoked to explain island gigantism?

(A) Absence of inter specific competitors

(B) Absence of predators

(D) Limited prey base

Answer: (A, B)

35. Which one or more of the following options represent(s) life history trade-offs?

(A) Egg size versus clutch size

(B) Growth versus age at sexual maturation

(D) Survival versus reproduction

Answer: (A, B, D)

Q.36 – Q.65 Carry TWO marks Each

36. Certain plants and animals rely on toxins such as cardiac glycosides for self-defense. Digitoxin and bufalin, structurally similar toxins produced by foxglove plants and bufonid toads, respectively, are one such example. Which one of the following statements about these toxins is correct?

(A) They are structural and functional analogs.

(B) They are structural and functional homologs.

(D) They are structural homologs and functional analogs.

Answer: (A)

37. A behavioural ecologist records the number of times a kingfisher succeeds in catching fish over multiple five-minute intervals. Which one of the following distributions best describes these data?

(A) Chi-squared

(B) Normal

(D) Student’s-t

Answer: (C)

38. Excess fertilizers used in agriculture commonly end up as runoff and cause phytoplankton blooms in rivers. To figure out whether these blooms were driven by ammonium or phosphate fertilizers, researchers cultured a phytoplankton species in multiple samples of unpolluted river water. The samples were divided equally among three treatments: ammonium fertilizer added, phosphate fertilizer added and no fertilizer added. They then measured phytoplankton density in each of the samples after a week. Phytoplankton densities (in thousands of cells/ml) are reported in the table shown.

Which one of the following inferences is correct?

(A) Nitrogen is the limiting nutrient for phytoplankton growth.

(B) Phosphorus is the limiting nutrient for phytoplankton growth.

(D) Neither nitrogen nor phosphorus limits phytoplankton growth.

Answer: (A)

39. S1 and S2 are two strains of bacteria. The results of a bacterial growth experiment on these strains measured after 24 hours are shown. Black and white bars represent S1 and S2, respectively.

Which one of the following best describes the interaction between S1 and S2?

(A) Amensalism

(B) Commensalism

(D) Mutualism

Answer: (C)

40. Habitat P has twice the density of resources as habitat Q. Assume that individuals are identical, can move freely, have perfect information about the environment, and compete for resources when they are in a habitat. At equilibrium, which one of the following represents the predicted outcome?

(A) The number of individuals present and the profitability per individual will be higher in P than in Q.

(B) The number of individuals present and the profitability per individual will be the same in P and in Q.

(C) The number of individuals present will be higher in P than in Q and the profitability per individual will be the same in P and in Q.

(D) The number of individuals present will be higher in Q than in P and the profitability per individual will be higher in P than in Q.

Answer: (C)

41. Consider Holling’s Type-III functional response, as shown.

Which one of the marked points has the highest rate-of-change of prey-capture-rate?

(A) P

(B) Q

(D) S

Answer: (B)

42. In a population of birds on an island, the average beak size reduced over one generation. A researcher estimated the association between beak size and relative fitness, shown in the graph. The estimated slope was −0.05 with a 95% confidence interval of −0.15 to 0.09.

Which one of the following evolutionary processes acting on beak size is the most

likely reason for the observed reduction in beak size?

(A) Genetic drift

(B) Group selection

(D) Natural selection

Answer: (A)

43. The Bateman gradient is a popular explanation for why the strength of sexual selection is typically stronger on males than on females. Which one of the following figures is the correct representation of the Bate man gradient? In all figures, the dotted line represents males and the solid line females.

(A) A

(B) B

(D) D

Answer: (A)

44. Sparrows use two foraging tactics to obtain food. They either search for grains themselves (Producer tactic P) or follow other individuals and steal grains from them(Scrounger tactic S). The following graphs show how the fitness of each tactic(P : dashed line and S : solid line) varies as a function of the relative frequency of S.Which one of the graphs shows the correct representation of these tactics if they were maintained through negative frequency dependence?

(A) A

(B) B

(D) D

Answer: (C)

45. Some lizard species show positive allometry in head width, with larger individuals investing disproportionately more in musculature leading to wider heads. To test for positive allometry in a study population, a researcher measures body size and head width for 100 individuals and fits a straight line to a log-log plot of these two traits.Which one of the following estimated values of the slope indicates support for positive allometry?

(A) 0

(B) 0.5

(D) 1.5

Answer: (D)

46. A team of ecologists laid 100 plots of 50 m × 50 m in a forest and counted the number of individuals of a tree species in each plot. They then calculated the mean and variance of the number of individuals per plot. If trees are randomly distributed, then which one of the following relationships between the variance and mean is expected?

(A) Variance > mean

(B) Variance < mean

(D) Variance is independent of the mean

Answer: (C)

47. The following graphs show rank abundance data for species in three different communities P, Q and R. Based on both species richness and relative abundance,which one of the following options correctly represents the ordering of communities according to their species diversity?

(A) P > Q > R

(B) Q > P > R

(D) R > Q > P

Answer: (D)

48. Which one of the following cladograms represents the correct phylogenetic relationships in the Kingdom Animalia?

Answer: (A)

49. β-diversity quantifies the difference in species composition between two ecological communities. Which one of the following statements is correct about β-diversity?

(A) Only nestedness affects β-diversity.

(B) Only species turnover affects β-diversity.

(D) Neither nestedness nor species turnover affects β-diversity.

Answer: (C)

50. Consider the logistic population growth model, given by

where r is the intrinsic growth rate, n is the population size and k is the carrying capacity. Which one or more of the following is/are assumption(s) of the model?

(A) Carrying capacity is constant

(B) Density dependence is quadratic

(D) No genetic, age or size structure

Answer: (A, C, D)

51. Which one or more of the following genes/markers is/are typically used for species identification?

(A) 16S rRNA

(B) Cytochrome Oxidase I

(D) Microsatellites

Answer: (A, B)

52. A bee species forages for nectar on a plant species which has yellow flowers. To find out what cues the bees use to recognize the flowers, researchers performed the following experiment. They presented individual bees with the stimuli given below and examined the proportion of bees that approached and landed on the stimuli.The results are shown below.

Which one or more of the following interpretation(s) of the experiment is/are correct?

(A) All flower colours other than yellow are ineffective at eliciting approach responses.

(B) Olfactory cues are sufficient to elicit approach responses.

(D) Visual cues are sufficient to elicit approach responses.

Answer: (C, D)

53. Which one or more of the following reason(s) explain(s) why whales use low frequencies (infrasound) for mate-finding and high frequencies (ultrasound)for hunting prey?

(A) High frequencies transmit further without distortion than low frequencies.

(B) High frequencies scatter more and allow for high-resolution information.

(D) Low frequencies scatter more and allow for high-resolution information.

Answer: (B, C)

54. The table shows the relative abundance of three potential prey species in the environment and in the diet of a bat predator.

Which one or more of the following is/are possible interpretations based on the data?

(A) The predator shows a preference for prey species Z.

(B) The predator shows no preference for any of the three prey species.

(D) The predator shows a preference for prey species Y.

Answer: (A, C)

55. Which one or more of the following options represent(s) an evolutionary arms race?

(A) Snake venom toxin specificity and prey receptor modification

(B) Egg discrimination by hosts and brood parasite egg colouration

(D) Crypsis in prey and visual acuity in predator

Answer: (A, B, D)

56. The figure shows an F probability density function. The two dotted lines represent critical values corresponding to a two-tailed F-test at a level of significance of 0.05.The observed F-statistic for two samples is indicated by the solid line.

Which one or more of the following inferences is/are correct?

(A) The null hypothesis cannot be rejected.

(B) The null hypothesis is true.

(D) The ratio of the skewness of the two samples is not statistically significantly different from 1.

Answer: (A, C)

57. Which one or more of the following conditions can lead to an increase in tree densities in tropical savannas?

(A) Fire suppression

(B) Increase in mean annual rainfall

(D) Increased atmospheric CO₂

Answer: (A, B, D)

58. Gene conversion can lead to which one or more of the following evolutionary outcomes?

(A) Concerted evolution

(B) Increased expression

(D) Increased sequence similarity

Answer: (A, B, D)

59. If the observed heterozygosity at a locus is 0.6, which one or more of the following could produce this outcome?

(A) A neutral locus with three alleles

(B) A locus under selection with two alleles

(D) A locus under selection with one allele

Answer: (A, B)

60. Which one or more of the following reasons has/have been invoked to explain highspecies diversity in the tropics?

(A) Greater area in the tropics

(B) Higher speciation rates in the tropics

(D) The tropics are closer to the sun

Answer: (A, B, C)

61. In a linear regression with a single continuous predictor and 100 data points, theresidual degrees of freedom are _______. (Answer in integer)

Answer: (98 to 98)

62. The genome of an organism has 60% GC (Guanine-Cytosine) content.The Adenine in this genome is _____%. (Answer in integer)

Answer: (20 to 20)

63. The prevalence of flu in a population is 1%. A diagnostic test has a false positive rateof 10% and a false negative rate of 10%. The probability that a randomly chosenperson tests positive is ______. (Round off to three decimal places)

Answer: (0.107 to 0.109)

64. In a deer population, the male-to-female ratio is 1 : 2. The probability that a randomlyformed group of size three has 2 males and 1 female is ______.(Round off to two decimal places)

Answer: (0.21 to 0.23)

65. The fitness f(n) of an individual in a group of size n is given by

f(n) = n(10 – n)

At evolutionary equilibrium, groups are found in two different sizes. If one group sizeis 6, the other group size must be _______.(Answer in integer)

Answer: (4 to 4)

GATE Exam 2022 Environmental Science and Engineering (ES) Question Paper With Answer Key

July 15, 2022 by suresh84

GATE-2022

ES: Environmental Science and Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. X speaks _________ Japanese _________ Chinese.

(A) neither / or

(B) either / nor

(D) also / but

Answer: (C)

2. A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.

If R gets Rs. 1000 more than S, what is the share of Q (in Rs.)?

(A) 500

(B) 1000

(D) 2000

Answer: (D)

3. A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.

Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.

What is the shortest distance between PQ and SR (in cm)?

(A) 1.80

(B) 2.40

(D) 5.76

Answer: (B)

4. The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?

(A) 15

(B) 20

(D) 26

Answer: (B)

5. An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.

If the security guard does not move around the posted location and has a 360° view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.

(A) P and Q

(B) Q

(D) R and S

Answer: (C)

Q.6 – Q. 10 Carry TWO marks each.

6. Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.

Which one of the following is the correct logical inference based on the information in the above passage?

(A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous

(B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects

(D) Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative

consequence

Answer: (D)

7. Consider the following inequalities.

(i) 2x − 1 > 7

(ii) 2x − 9 < 1

Which one of the following expressions below satisfies the above two

inequalities?

(A) x ≤ −4

(B) −4 < x ≤ 4

(D) x ≥ 5

Answer: (C)

8. Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.

What is the area enclosed by the quadrilateral?

(A) 4

(B) 4√2

(D) 8√2

Answer: (C)

9. In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.

Statement of P: R has copied in the exam.

Statement of Q: S has copied in the exam.

Statement of R: P did not copy in the exam.

Statement of S: Only one of us is telling the truth.

Statement of T: R is telling the truth.

The investigating team had authentic information that S never lies.

Based on the information given above, the person who has copied in the exam is

(A) R

(B) P

(D) T

Answer: (B)

10. Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.

Let X, Y and Z represent the following operations:

X: rotation of the square by 180 degree with respect to the S-Q axis.

Y: rotation of the square by 180 degree with respect to the P-R axis.

Z: rotation of the square by 90 degree clockwise with respect to the axis

perpendicular, going into the screen and passing through the point T.

Consider the following three distinct sequences of operation (which are applied in the left to right order).

(1) XYZZ

(2) XY

(3) ZZZZ

Which one of the following statements is correct as per the information provided above?

(A) The sequence of operations (1) and (2) are equivalent

(B) The sequence of operations (1) and (3) are equivalent

(D) The sequence of operations (1), (2) and (3) are equivalent

Answer: (B)

Environmental Science and Engineering

Q.11 – Q.35 Carry ONE mark Each

11. A student reported following arsenic concentrations in water samples:

Which one of the following is a correct statement about arsenic concentration distribution?

(A) Arsenic concentration distribution is symmetric

(B) Arsenic concentration distribution is positively skewed

(D) Arsenic concentration is following Weibull distribution

Answer: (B)

12. X is normally distributed with following data (25.8, 36.6, 26.3, 21.8, 27.2). Select

the correct statement about X (t_{crit, α=0.05,4} = 2.132):

(A) Population mean < 25 with 95% confidence

(B) Population mean < 25 with 100% confidence

(D) Population mean > 25 with 100% confidence

Answer: (A)

13. Assuming s > 0; Laplace transform for f(x) = sin ax is

Answer: (A)

14. Given P is m × n matrix, Q is n × l matrix, R and S are n × n matrices, and superscript T denotes transpose. Consider

Relationship 1: (PQ)^T = Q^TP^T

Relationship 2: (RS)⁻¹ = S⁻¹R⁻¹

Which one of the following is correct?

(A) Relationship 1 is false; Relationship 2 is false

(B) Relationship 1 is true; Relationship 2 is false

(D) Relationship 1 is false; Relationship 2 is true

Answer: (C)

15. Specific conductance is used in water analysis to indirectly estimate dissolved solids. The measurements used in the method accounts for

(A) Cations only

(B) All ions

(D) Un-ionized species

Answer: (B)

16. Ten litres of the sample was filtered through a membrane filter and the filter was transferred to solid agar media which supports growth of coliform organisms. After incubation at 37°C for 48 hours, the agar plates showed an average of 64 colonies per plate. What was the average concentration of coliform organisms (in Colony Forming Units per unit volume) in the original water sample?

(A) 64 CFU/ml

(B) 640 CFU/ml

(D) 64 × 10⁻³ CFU/ml

Answer: (C)

17. Reverse Transcriptase Polymerase Chain Reaction is an analytical procedure used in detection of pathogenic microorganisms. Which one of the following statements is NOT correct in this context?

(A) It is used for identifying presence or absence of specific RNA in samples.

(B) It is used only for identifying Corona Viruses, including SARS CoV2 in samples.

(D) It is based on conversion of RNA to DNA followed by DNA amplification

Answer: (B)

18. Consider the following statements

Statement 1: Goodrich method for reservoir routing is based on hydrologic flood routing method.

Statement 2: Muskingum method for channel routing is based on hydraulic flood routing method.

Which one of the following is correct?

(A) Statement 1 is false; Statement 2 is false

(B) Statement 1 is true; Statement 2 is false

(D) Statement 1 is false; Statement 2 is true

Answer: (B)

19. The correct order of hydraulic conductivity for the geologic formations is

(A) Aquifer > Aquitard > Aquiclude > Aquifuge

(B) Aquifer < Aquitard < Aquiclude < Aquifuge

(D) Aquifer > Aquiclude >Aquitard > Aquifuge

Answer: (A)

20. Centrifugal pumps with suction pipe (shown by solid arrow) and delivery pipe (shown by dotted arrow) are shown in the figures. Choose the option that gives the correct connection

Answer: (A)

21. Carbon dioxide is used in recarbonation process. A solution has 1 mole/L supersaturated calcium carbonate. Estimated amount of carbon dioxide (in grams) needed to completely convert calcium carbonate to calcium ions in 1 litre solution is

(A) 44.000 gram

(B) 0.044 gram

(D) 0.040 gram

Answer: (A)

22. A river water sample has pH of 4 and suspended solids concentration of 100 mg/L. If, alum is chosen as a coagulant, what will be the coagulation mechanism?

(A) Ionic layer compression only

(B) Sweep coagulation and Polymer bridging

(D) Charge neutralization, surface adsorption, ionic layer compression

Answer: (D)

23. Which one of the following is most commonly used raw material in flue gas desulfurization units?

(A) Limestone

(B) Titanium Oxide

(D) Beryllium Oxide

Answer: (A)

24. Leachate generated from a legacy municipal solid waste dumping site has to be collected and managed carefully. Which one of the following statements is correct in the context of treatment of leachate from such a site?

(A) Settling chamber followed by micro-filtration units are required.

(B) Modular treatment units targeting dissolved organic matter and salts are required.

(D) Only a combination of anaerobic-aerobic treatment units is required

Answer: (B)

25. Which one of the following statements is correct regarding Global warming?

(A) Water vapour does not contribute to global warming.

(B) Global warming is likely to increase the productivity of plants due to CO₂

fertilization.

(D) HFCs and HCFCs are good substitutes for the ozone depleting substances as they cause neither global warming nor ozone layer depletion

Answer: (B)

26. In context of ecosystems, which one of the following is NOT a correct statement?

(A) The growth of an organism such as a plant may be dependent on a number of different factors such as sunlight, mineral nutrients (nitrates, phosphates, etc.), etc. Liegib’s law states that, growth occurs at the rate permitted by the most limiting factor.

(B) The carrying capacity of a population is determined by its limiting resources. Carrying capacity is the upper limit of an ecosystem up to which it can provide the basic needs to the population under given circumstances.

(C) The Ramsar convention on lakes and backwater systems of International importance is an international treaty for the conservation and sustainable use of lakes and backwater systems. The treaty was signed in 1981 and became effective in 1985.

(D) A Red Data Book contains lists of species whose continued existence is threatened. Species are classified into different categories of perceived risk. Each Red Data Book usually deals with a specific group of animals or plants and fungi.

Answer: (C)

27. Which one of the following statements correctly defines the concept of ‘Extended Producer’s Responsibility’?

(A) The responsibility of a producer for environmentally sound disposal of the product after the end of its life

(B) The responsibility of a producer for environmentally sound manufacturing process for the product

(C) The responsibility of a producer for environmentally sound management of the product from manufacturing stage until it is sold in the market

(D) The responsibility of a producer for environmentally sound management of the product until the end of its life

Answer: (A OR D)

28. If G represents Gibbs free energy, select the correct statement(s)

(A) If ΔG = 0, reaction will proceed only in one direction

(B) If ΔG = 0, reaction will be in equilibrium

(D) If ΔG > 0, reaction will not proceed forward

Answer: (B, C, D)

29. For effluents generated by a molasses based distillery and wood based pulp and paper industry, which of the following statement(s) is/are NOT correct?

(A) Both the effluents have dark colour.

(B) Both the effluents have high toxicity.

(D) Both the effluents have high pH.

Answer: (B, C, D)

PM₅ concentrations in ambient air can be measured using

(A) Beta attenuation method

(B) Chemiluminescence method

(D) Non dispersive infrared spectroscopy method

Answer: (A, C)

31. Biodegradable wastes like vegetable peelings from kitchen are usually processed by composting techniques. Which of the following option(s) regarding the processing of biodegradable wastes is/are correct?

(A) Vermi-composting is relatively faster than windrow composting, however vermi-composting is not frequently used on large commercial scale.

(B) The windrow height should be as short as possible as large windrow height may cause compaction due to the self-weight.

(C) The windrow height should be as large as possible as that will help to ensure appropriate temperature within the windrow.

(D) Earthworms facilitate the growth of microorganisms and break down complex organic molecules to simpler ones using enzymatic secretions.

Answer: (A, D)

32. As per ‘Hazardous and Other Wastes (Management and Transboundary Movement) Rules, 2016 of Govt. of India, the import of hazardous and other wastes from any country shall NOT be permitted for which of the following option(s)?

(A) Recovery, reuse and recycle

(B) Disposal in abandoned mines

(D) Utilization, including co-processing

Answer: (B, C)

33. The Ministry of Environment, Forest and Climate Change (MoEF&CC), Govt. of India has published the Environment Impact Assessment (EIA) draft Notification 2020, intended to replace the existing EIA Notification, 2006 under the Environment (Protection) Act, 1986. Which of the following is/are the key change(s) from existing regulation?

(A) Removal of several project/ activities from the purview of public consultation.

(B) A list of projects has been included under Category B2, expressly exempted from the requirement of an EIA.

(D) A list of projects has been included under Category B2, bringing them under the requirement of detailed EIA.

Answer: (A, B)

34. is _________(rounded off to one decimal place)

Answer: (0.5 to 0.5)

35. The following figure shows a 2-hour unit hydrograph (1 cm rainfall excess) for a catchment area of 540 hectare.

The peak discharge (in m³/s, rounded off to one decimal place) of the above unit hydrograph is __________

Answer: (10.0 to 10.0)

Q.36 – Q.65 Carry TWO marks Each

36. Given, The problem is a/an

(A) initial value problem having solution y = x

(B) boundary value problem having solution y = x

(D) boundary value problem having solution

Answer: (C)

37. Eigen values of the matrix are

(A) 1 and 2

(B) 1 and 3

(D) 0 and 3

Answer: (A)

38. For an exponentially growing microbial culture, the specific growth rate (µ) is related to its doubling time (t_d) by which one of the following relations?

(A) t_d = µ

(B) t_d = µ²

(C)

(D)

Answer: (C)

39. A microbial culture, with a specific growth rate of µ₁ (per hour), is being grown in a continuous reactor at steady state with hydraulic retention time (HRT) of 24 hours. This reactor is subjected to a perturbation by reducing the HRT to 12 hours. The reactor recovers from the perturbation and comes to a new steady state with a new specific growth rate of µ₂ (per hour). Which one of the following statements is correct?

(A) µ₁ = µ₂

(B) µ₁ = 0.5 µ₂

(D) µ₂ = e^0.5 µ₁

Answer: (B)

40. Which one of the following statements is NOT correct with respect to a batch reactor?

(A) No reactant is added after the reactor has started operation.

(B) No product is withdrawn during the course of the reactor operation.

(D) The reactor operation is carried out for a pre-specified duration.

Answer: (C)

41. A bag filter is used for removal of particulate matter having a range of sizes. The correct sequence of air filtration mechanisms for their removal, in order of decreasing size, is

(A) Diffusion, Impaction, Disintegration

(B) Disintegration, Impaction, Interception

(D) Impaction, Interception, Diffusion

Answer: (D)

42. A relatively calm room has background sound power level (SPL) of 30 decibels (dB). A television and a radio with SPL of 80 dB and 70 dB, respectively, started operating simultaneously in this room. Given the reference sound power is 10-12 Watts, what will be the resulting SPL in the room, assuming all the sources operate independently?

(A) 180.0 dB

(B) 80.4 dB

(D) 150.0 dB

Answer: (B)

MSQ

43. During night, in troposphere, which of the following is/are NOT correct

(A) NO₂ + hυ → NO + O

(B) Most of the NOx (i.e., NO + NO₂) converts to NO

(D) Most of the NOx (i.e., NO + NO₂) converts to NO₂

Answer: (A, B)

44. A typical plasmid-free bacterial cell having a single chromosome consists of ~55% protein, ~3% DNA and ~21% RNA, where “%” represents percentage of dry weight. Assuming there are 2500 different types of protein molecules (with at least one copy number) being expressed in a living bacterial cell at any given time, which of the following statement(s) is/are NOT correct with respect to the number of intracellular DNA, RNA and protein molecules?

(A) DNA = RNA = Protein ≥ 2500

(B) DNA = RNA = 1; Protein ≥ 2500

(D) DNA = 1; RNA > Protein ≥ 2500

Answer: (A, B, C)

45. Average values of the re-aeration rate constant for river X and river Y are 0.92 per day and 1.12 per day, respectively. Average de-oxygenation rate constants for the same rivers are 0.23 per day and 0.35 per day respectively. Then, which of the following statement(s) is/are correct?

(A) Self-purification capacity of river Y is more than that of river X.

(B) Self-purification capacity of river X is more than that of river Y.

(D) Pollutants in river X are more biodegradable than that in river Y.

Answer: (B, C)

46. Which of the following statement(s) is/are NOT correct while comparing continuously stirred tank reactor (CSTR) and plug flow reactor (PFR)?

(A) CSTR and PFR are normally operated under steady state condition.

(B) There is complete homogeneity in the CSTR while there are concentration variations within the PFR.

(D) Reaction kinetics do not play any role in choosing between a CSTR and PFR

Answer: (C, D)

47. According to the National Ambient Air Quality Standards (Central Pollution Control Board, Govt. of India, notification 2009) which of the following statement(s) is/are correct?

(A) SO₂ and NO₂ have annual average standards; while O₃ and CO have eight hour average standards.

(B) SO₂ and CO have annual average standards; while O₃ and NO₂ have eight hour average standards.

(D) SO₂ and NO₂ have 24 hour average standards; while O₃ and CO have hourly average standards.

Answer: (A, D)

48. Consider the figure shown below for three different cases:

Which of the following statement(s) is/are correct for surface level emissions, given the environmental temperature?

(A) Case P represents unstable atmosphere and results in higher dispersion of emissions.

(B) Case Q represents subsidence inversion and results in higher dispersion of emissions than Case P.

(D) Case R represents subsidence inversion and results in lower dispersion of emissions than Case P.

Answer: (A, D)

49. As per the Solid Waste Management Rules of 2016 (Govt. of India), which of the following statement(s) is/are correct?

(A) Biodegradable wastes should be processed biologically preferably in decentralized facilities at the sources of generation.

(B) Biodegradable wastes should be processed biologically preferably in centralized facilities away from the sources of generation.

(D) Non-biodegradable components with a heat content more than 1500 kcal/kg should be used for power generation or Refuse Derived Fuel (RDF) manufacture.

Answer: (A, D)

50. Carbon cycle, nitrogen cycle and phosphorus cycle play important role in the ecosystems. Which of the following statement(s) is/are NOT correct about the phosphorus cycle?

(A) Shortage of phosphorus can be a limiting factor in many ecosystems, however, its excess can stimulate eutrophication.

(B) Organic phosphates exist in various rock and soil minerals.

(D) Human interventions like application of phosphorus fertilizers cause much phosphorus to get into the ocean

Answer: (B, C)

51. Which of the following statement(s) is/are correct regarding National Green Tribunal (NGT) of India?

(A) NGT Act 2010 draws inspiration from the India’s constitutional provision of Article 21 – Protection of life and personal liberty, which assures the citizens of India the right to a healthy environment.

(B) A retired Judge of the Supreme Court, can be the Chairperson of the NGT.

(C) NGT Act 2017 is based on the India’s constitutional provision of Article 361 -Protection of Biodiversity and Environmental Protection, which bestows the citizens of India with a duty to protect all abiotic and biotic components of the environment.

(D) The NGT is mandated to make and endeavor for disposal of applications or appeals finally within 45 days of filing of the same.

Answer: (A, B)

52. The area of the region (rounded off to one decimal place) enclosed between the curves y = x and y = 3√x and between the lines x = 0 and x = 1 is ________units.

Answer: (1.5 to 1.5)

53. An individual has four different email accounts. 60% of emails come into his corporate account, 30% come into his gmail account and remaining 10% are equally divided into his yahoo and zoho accounts. Only 1% of the emails in his corporate accounts are spam, whereas corresponding percentages for gmail, yahoo and zoho accounts are 2%, 3% and 3%, respectively. Assuming that the same spam filter is used in all the four email accounts, the probability (in percentage, rounded off to one decimal place) of having a randomly selected email as spam is _____

Answer: (1.5 to 1.5)

54. A solution has 0.001 mole/L zinc ions having pH of 6. Solubility product of zinc hydroxide is given as 8×10⁻¹⁸ (mole/L)³. Ignoring activity corrections, the ratio (rounded off to two decimal places) of reaction coefficient to solubility product would be

Answer: (0.01 to 0.02)

55. The Henry’s law constant of CO₂ is 3.4×10⁻² M per atm in neutral water at 25° The dissolved CO₂ (i.e., CO₂.H₂O) at equilibrium undergoes the following reactions.

CO₂.H₂O ⇌ H⁺ + HCO₃⁻ (Equilibrium constant = 4.3 × 10⁻⁷ M)

HCO₃⁻ ⇌ H⁺ + CO₃²⁻ (Equilibrium constant = 4.7 × 10⁻¹¹ M)

If ambient CO₂ concentration is 300 ppm, the total dissolved CO₂ (in µM, rounded off to one decimal place) is _____.

Answer: (54.0 to 54.2)

56. An isolated storm of 3 hours occurred over a catchment area in the following manner

Total rainfall excess (in cm, rounded off to one decimal place) over the catchment for the above storm is ______.

Answer: (3.0 to 3..0)

57. Two reservoirs having a difference of 20 m in their water surface elevations are connected through a confined aquifer (thickness = 5 m, length = 2 km, hydraulic conductivity K = 3 × 10⁻³ m/s, and porosity η = 0.3) as shown in the following figure (drawn not to scale).

If the Reservoir 1 is contaminated by a pollutant then the time (in days, rounded off to one decimal place) taken by the pollutant to reach to the Reservoir 2 under advection will be ____.

Answer: (230.0 to 233.0)

58. A venturimeter along with a differential manometer was installed to measure flow in a water pipeline as shown in the following figure (not drawn to scale).

Taking specific weight of water as 9810 N/m³ , the pressure difference (in Pa, rounded off to one decimal place) between point Q and P is ____.

Answer: (7160.0 to 7163.0)

59. Two reservoirs having a difference of 10 m in their water surface elevations are connected by a pipeline (diameter = 10 cm, length = 50 m, and friction factor f = 0.02). If the last 25 m length of the pipeline is replaced by a same material pipe of diameter 20 cm then neglecting minor losses the discharge (in %, rounded off to one decimal place) will increase by ____.

Answer: (39.0 to 40.0)

60. The depth of flow (in m, rounded off to two decimal places) in a hydraulically efficient rectangular channel (n = 1/80) to carry a discharge of 64 m³/s at bed slope 0.01 is _____.

Answer: (1.95 to 2.05)

61. Clean water is passed through a bed of uniform spherical sand at a filtration velocity of 0.002 m/sec. The sand grains are 0.4 mm in diameter and have a specific gravity of 2.65. Bed depth is 0.67m and porosity (η) is 0.35. Given, water density = 998.2 kg/m³; water dynamic viscosity = 1.002 × 10⁻³s. Friction factor (f) is given as: f = 1.75 + {150× (1-η)/(Re)} where Re is Reynolds number. The headloss (in m, rounded off to three decimal places) calculated using the Carmen-Kozney equation is _______.

Answer: (1.150 to 1.350)

62. A sewage treatment plant with a capacity of 10 million litres per day (MLD) is treating the sewage through an aerobic biological process. The inlet and outlet BOD are measured as 100 and 30 mg/l, respectively. If the mixed microbial culture has an observed biomass yield of 0.5 g Volatile Suspended Solids (VSS)/g BOD, the sludge production rate (in kg per day, rounded off to one decimal place) when the plant is operating at 80% capacity will be ______.

Answer: (280.0 to 280.0)

63. A centrifuge is processing 1000 litres per hour of water containing 2 g per litre of suspended solids. The thickened slurry coming out of the centrifuge has solids concentration of 20 g per 100 ml. If the centrifuge has 99% efficiency based on solids separation, the flow rate (in litres per hour, rounded off to one decimal place) of the supernatant stream will be ______.

Answer: (989.0 to 991.0)

64. A ground level source emits 1000 g per day of SO₂. In vicinity of the source, ambient temperature is measured at 10 m and 110 m as 25°C and 24.5°C, respectively. The mean wind speed is found to be 2 m per second. The dispersion coefficients at 1000 m downwind distance from the source are given in table below:

Estimated ground level concentration (in µg/m³, rounded off to two decimal places) of SO₂ at a downwind distance of 1000 m (at the plume centerline) from the source is ______.

Answer: (1.68 to 1.72)

65. Figure below gives the heat inflow into the furnace of a waste-to-energy plant along with the heat outflows from the furnace.

Assume: (i) total heat loss equal to 3% of heat released while burning waste, (ii)

sensible heat of the waste is negligible, (iii) complete burning of the waste is ensured. If the waste feed rate into this plant is 70 kg/h, the heat content of the waste (in kcal/kg, rounded off to one decimal place) is _____.

Answer: (1467.00 to 1469.00)

GATE Exam 2022 Electrical Engineering (EE) Question Paper With Answer Key

July 15, 2022 by suresh84

GATE-2022

EE: Electrical Engineering

General Aptitude

1. As you grow older, an injury to your _________ may take longer to _________.

(A) heel / heel

(B) heal / heel

(D) heel / heal

Answer: (D)

2. In a 500 m race, P and Q have speeds in the ratio of 3 ∶ Q starts the race when P has already covered 140 m.

What is the distance between P and Q (in m) when P wins the race?

(A) 20

(B) 40

(D) 140

Answer: (A)

3. Three bells P, Q, and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.

If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?

(A) 5:00 PM

(B) 5:30 PM

(D) 6:30 PM

Answer: (A)

4. Given below are two statements and four conclusions drawn based on the statements.

Statement 1: Some bottles are cups.

Statement 2: All cups are knives.

Conclusion I: Some bottles are knives.

Conclusion II: Some knives are cups.

Conclusion III: All cups are bottles.

Conclusion IV: All knives are cups.

Which one of the following options can be logically inferred?

(A) Only conclusion I and conclusion II are correct

(B) Only conclusion II and conclusion III are correct

(D) Only conclusion III and conclusion IV are correct

Answer: (A)

What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

(A) 0

(B) 1/3

(D) 1

Answer: (A)

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Humans engage in altruism due to guilt but not empathy

(B) Humans engage in altruism due to empathy but not guilt

(D) Humans engage in altruism due to empathy but not familiarity

Answer: (C)

7. There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely.

The two dice are thrown once independently at random.

What is the probability that the outcomes on the dice were composed only ofany combination of the following possible outcomes: Q, U and V?

(A) 1/4

(B) 3/4

(D) 5/36

Answer: (A)

What is the price of the item at the online store S (in Rs.) if there are no other charges than what is described above?

(A) 2500

(B) 2250

(D) 1500

Answer: (B)

9. The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.

Consider the following statements:

• The line segment joining R and S is longer than the line segment joining P and Q.

• The line segment joining R and S is perpendicular to the line segment joining P and Q.

• The line segment joining R and U is parallel to the line segment joining T and Q.

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

(A) The line segment joining R and T is parallel to the line segment joining Q and S

(B) The line segment joining T and Q is parallel to the line joining P and U

(D) The line segment joining Q and S is perpendicular to the line segment joining Rand P

Answer: (A)

10.

Which one of the following is a part of a possible trajectory of the ant during the movement?

Answer: (C)

Electrical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. The transfer function of a real system, H(s), is given as:

where A, B, C and D are positive constants. This system cannot operate as

(A) low pass filter.

(B) high pass filter.

(D) an integrator

Answer: (B OR D)

12. For an ideal MOSFET biased in saturation, the magnitude of the small signal current gain for a common drain amplifier is

(A) 0

(B) 1

(D) infinite

Answer: (D)

13. The most commonly used relay, for the protection of an alternator against loss of excitation, is

(A) offset Mho relay.

(B) over current relay.

(D) Buchholz relay.

Answer: (A)

14. The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘r’, as shown in the figure below, is

(A) 4r

(B) 1.414r

(D) 1.723r

Answer: (D)

15. The valid positive, negative and zero sequence impedances (in p.u.), respectively, for a 220 kV, fully transposed three-phase transmission line, from the given choices are

(A) 1.1, 0.15 and 0.08

(B) 0.15, 0.15 and 0.35

(D) 0.1, 0.3 and 0.1

Answer: (B)

16. The steady state output (V_out), of the circuit shown below, will

(A) saturate to +V_DD

(B) saturate to −V_EE

(D) become equal to –0.1 V

Answer: (B)

17. The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is −180°. This system has

(A) one LHP pole and one RHP zero at the same frequency.

(B) one LHP pole and one LHP zero at the same frequency.

(D) two RHP poles and one LHP zero.

Answer: (A)

18. A balanced Wheatstone bridge ABCD has the following arm resistances:

R_AB = 1 kΩ ± 2.1%; R_BC = 100 Ω ± 0.5%; R_CD is an unknown resistance;

R_DA = 300 Ω ± 0.4%. The value of R_CD and its accuracy is

(A) 30 Ω± 3 Ω

(B) 30 Ω± 0.9 Ω

(D) 3000 Ω± 3 Ω

Answer: (B)

19. The open loop transfer function of a unity gain negative feedback system is given by The range of k for which the system is stable, is

(A) k> 3

(B) k< 3

(D) k< 5

Answer: (C)

20. Consider a 3 × 3 matrix A whose (i, j)-th element, a_{i, j} = (i – j)³. Then the matrix A will be

(A) symmetric.

(B) skew-symmetric.

(D) null.

Answer: (B)

21. In the circuit shown below, a three-phase star-connected unbalanced load is connected to a balanced three-phase supply of 100√3 V with phase sequence ABC. The star connected load has Z_A = 10 Ω and Z_B = 20∠60°Ω. The value of Z_C in Ω, for which the voltage difference across the nodes n and n’ is zero, is

(A) 20∠− 30°

(B) 20∠30°

(D) 20∠60°

Answer: (C)

22. A charger supplies 100 W at 20 V for charging the battery of a laptop. The power devices, used in the converter inside the charger, operate at a switching frequency of 200 kHz. Which power device is best suited for this purpose?

(A) IGBT

(B) Thyristor

(D) BJT

Answer: (C)

23. A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is for the region r < b where r is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for r < b) is

Answer: (C)

24. The type of single-phase induction motor, expected to have the maximum power factor during steady state running condition, is

(A) split phase (resistance start).

(B) shaded pole.

(D) capacitor start, capacitor run.

Answer: (D)

25. For the circuit shown below with ideal diodes, the output will be

(A) V_out = V_in for V_in> 0

(B) V_out = V_in for V_in< 0

(D) V_out = −V_in for V_in< 0

Answer: (A)

26.A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter. (in integer)

Answer: (10 to 10)

27. An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ________. (round off to nearest integer)

Answer: (48 to 48)

28. The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The Q-factor of the network is __________. (round off to nearest integer)

Answer: (250 to 250)

29. The maximum clock frequency in MHz of a 4-stage ripple counter, utilizing flip-flops, with each flip-flop having a propagation delay of 20 ns, is ___________. (round off to one decimal place)

Answer: (12.3 to 12.7)

30. If only 5% of the supplied power to a cable reaches the output terminal, the power loss in the cable, in decibels, is _________. (round off to nearest integer)

Answer: (13 to 13)

31. In the circuit shown below, the switch S is closed at t = 0. The magnitude of the steady state voltage, in volts, across the 6 Ω resistor is _________. (round off to two decimal places).

Answer: (4.95 to 5.05)

32. A single-phase full-bridge diode rectifier feeds a resistive load of 50 Ω from a 200 V, 50 Hz single phase AC supply. If the diodes are ideal, then the active power, in watts, drawn by the load is _____________. (round off to nearest integer).

Answer: (795 to 805)

33. The voltage at the input of an AC-DC rectifier is given by v(t) = 230√2 sin ωt where ω = 2π × 50 rad/s. The input current drawn by the rectifier is given by

The input power factor, (rounded off to two decimal places), is, ________lag.

Answer: (0.43 to 0.47)

34. Two balanced three-phase loads, as shown in the figure, are connected to a 100√3 V, three-phase, 50 Hz main supply. Given Z₁ = (18 + j24) Ω and Z₂ = (6 + j8)Ω. The ammeter reading, in amperes, is _______. (round off to nearest integer)

Answer: (20 to 20)

35. The frequencies of the stator and rotor currents flowing in a three-phase 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is _______. (round off to nearest integer)

Answer: (580 to 590)

Q.36 – Q.65 Carry TWO marks Each

36. The output impedance of a non-ideal operational amplifier is denoted by Z_out. The variation in the magnitude of Z_out with increasing frequency, f, in the circuit shown below, is best represented by

Answer: (C)

37. An LTI system is shown in the figure where

The steady state output of the system, to the input r(t), is given as

y(t) = a + b sin(10t + θ). The values of ‘a’ and ‘b’ will be

(A) a = 1, b = 10

(B) a = 10, b = 1

(D) a = 100, b = 1

Answer: (A)

38. The open loop transfer function of a unity gain negative feedback system is given as

The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below.The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s),corresponding to the Nyquist contour, is denoted as N. Then N equals to

(A) 0

(B) 1

(D) 3

Answer: (B)

39. The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as ζ and ω_n, respectively. The values of ζ and ω_n are

(A) ζ = 0.5 and ω_n = 10 rad/s

(B) ζ = 0.1 and ω_n = 10 rad/s

(D) ζ = 0.707 and ω_n = 100 rad/s

Answer: (A)

40. e^A denotes the exponential of a square matrix A. Suppose 𝜆 is an eigenvalue and v is the corresponding eigen-vector of matrix A.

Consider the following two statements:

Statement 1 :e^λ is an eigenvalue of e^A.

Statement 2: v is an eigen-vector of e^A.

Which one of the following options is correct?

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

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

(D) Both the statements are false.

Answer: (C)

41. Let Then f(x) decreases in the interval

(A) x ∈ (1, 2)

(B) x ∈ (2, 3)

(D) x ∈ (0.5, 1)

Answer: (A)

42. Consider a matrix

The matrix A satisfies the equation 6A⁻¹ = A² + cA + dI, where c and d are scalars and I is the identity matrix.

Then (c + d) is equal to

(A) 5

(B) 17

(D) 11

Answer: (A)

43. The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by

Plant 1 : C₁ = 350 + 6P₁ + 0.004P₁²

Plant 2: C₂ = 450 + aP₂ + 0.003P₂²

where P₁ and P₂ are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power (𝜆) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are

(A) 200, 350

(B) 250, 300

(D) 350, 200

Answer: (B)

44. The current gain (I_out/I_in) in the circuit with an ideal current amplifier given below is

(A) C_f/C_c

(B) –C_f/C_c

(D) –C_c/C_f

Answer: (C)

45. If the magnetic field intensity (H) in a conducting region is given by the expression, The magnitude of the current density, in A/m², at x = 1 m, y = 2 m, and z = 1 m, is

(A) 8

(B) 12

(D) 20

Answer: (B)

46. Let a causal LTI system be governed by the following differential equation where x(t) and y(t) are the input and output respectively. Its impulse response is

Answer: (D)

47. Let an input x(t) = 2 sin(10πt) + 5cos(15πt) + 7sin(42πt) + 4cos(45πt) is passed through an LTI system having an impulse response, The output of the system is

(A) 2sin (10πt) + 5cos (15πt)

(B) 5cos (15πt) + 7 sin (42πt)

(D) 2sin (10πt) + 4cos (45πt)

Answer: (C)

48. Consider the system as shown below

where y(t) = x(e^t). The system is

(A) linear and causal.

(B) linear and non-causal.

(D) non-linear and non-causal.

Answer: (B)

49. The discrete time Fourier series representation of a signal x[n] with period N is written as A discrete time periodic signal with period N = 3, has the non-zero Fourier series coefficients: a₋₃ = 2 and a₄ = 1. The signal is

Answer: (B)

50. Let, f(x, y, z) = 4x² + 7xy + 3xz² . . The direction in which the function f(x, y, z) increases most rapidly at point P = )1, 0, 2) is

Answer: (B)

51. Let R be a region in the first quadrant of the xy plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region R?

Answer: (C)

52. Let The value of where V is the volume enclosed by the unit cube defined by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and 0 ≤ z ≤1, is

(A) 3

(B) 8

(D) 5

Answer: (C)

53. As shown in the figure below, two concentric conducting spherical shells, centered at r = 0 and having radii r = c and r = d are maintained at potentials such that the potential V(r) at r = c is V₁ and V(r) at r = d is V₂. Assume that V(r) depends only on r, where r is the radial distance. The expression for V(r) in the region between r = c and r = d is

Answer: (B)

54. Let the probability density function of a random variable x be given as f(x) = ae⁻^2|x|

The value of ‘a’ is _____.

Answer: (0.99 to 1.01)

55. In the circuit shown below, the magnitude of the voltage V₁ in volts, across the 8 kΩ resistor is ______. (round off to nearest integer)

Answer: (98 to 102)

56. Two generating units rated for 250 MW and 400 MW have governor speed regulations of 6% and 6.4%, respectively, from no load to full load. Both the generating units are operating in parallel to share a load of 500 MW. Assuming free governor action, the load shared in MW, by the 250 MW generating unit is_________. (round off to nearest integer)

Answer: (188 to 192 OR 198 to 202)

57. A 20 MVA, 11.2 kV, 4-pole, 50 Hz alternator has an inertia constant of 15 MJ/MVA. If the input and output powers of the alternator are 15 MW and 10 MW, respectively, the angular acceleration in mechanical degree/s² (round off to nearest integer)

Answer: (74 to 76)

58. Consider an ideal full-bridge single-phase DC-AC inverter with a DC bus voltage magnitude of 1000 V. The inverter output voltage v(t) shown below, is obtained when diagonal switches of the inverter are switched with 50 % duty cycle. The inverter feeds a load with a sinusoidal current given by, where ω = 2π/T. The active power, in watts, delivered to the load is _________.(round off to nearest integer)

Answer: (3170 to 3190)

59. For the ideal AC-DC rectifier circuit shown in the figure below, the load current magnitude is I_dc = 15 A and is ripple free. The thyristors are fired with a delay angle of 45°. The amplitude of the fundamental component of the source current, in amperes, is ________. (round off to two decimal places)

Answer: (17.3 to 18)

60. A 3-phase grid-connected voltage source converter with DC link voltage of 1000 V is switched using sinusoidal Pulse Width Modulation (PWM) technique. If the grid phase current is 10 A and the 3-phase complex power supplied by the converter is given by (−4000 − j3000) VA, then the modulation index used in sinusoidal PWM is ________. (round off to two decimal places)

Answer: (0.46 to 0.48)

61. The steady state current flowing through the inductor of a DC-DC buck boost converter is given in the figure below. If the peak-to-peak ripple in the output voltage of the converter is 1 V, then the value of the output capacitor, in µF, is ________. (round off to nearest integer)

Answer: (165 to 171)

62. A 280 V, separately excited DC motor with armature resistance of 1 Ω and constant field excitation drives a load. The load torque is proportional to the speed. The motor draws a current of 30 A when running at a speed of 1000 rpm. Neglect frictional losses in the motor. The speed, in rpm, at which the motor will run, if an additional resistance of value 10 Ω is connected in series with the armature, is ________. (round off to nearest integer)

Answer: (480 to 485)

63. A 4-pole induction motor with inertia of 0.1 kg-m² drives a constant load torque of 2 Nm. The speed of the motor is increased linearly from 1000 rpm to 1500 rpm in 4 seconds as shown in the figure below. Neglect losses in the motor. The energy, in joules, consumed by the motor during the speed change is ________. (round off to nearest integer)

Answer: (675 to 700 OR 1725 to 1740)

64. A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has asynchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is 10 kW while the power factor is 0.8 leading. The loss in the motor is 2 kW. The magnitude of the per phase excitation emf of the motor, in volts, is _______. (round off to nearest integer).

Answer: (240 to 248)

65. A 3-phase, 415 V, 4-pole, 50 Hz induction motor draws 5 times the rated current at rated voltage at starting. It is required to bring down the starting current from the supply to 2 times of the rated current using a 3-phase auto transformer. If the magnetizing impedance of the induction motor and no load current of the auto transformer is neglected, then the transformation ratio of the auto transformer is given by ____________. (round off to two decimal places).

Answer: (0.61 to 0.65)

GATE Exam 2022 Electronics and Communication Engineering (EC) Question Paper With Answer Key

July 12, 2022 by suresh84

GATE-2022

EC: Electronics and Communications Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. X speaks _________ Japanese _________ Chinese.

(A) neither / or

(B) either / nor

(D) also / but

Answer: (C)

2. A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.

If R gets Rs 1000 more than S, what is the share of Q (in Rs)?

(A) 500

(B) 1000

(D) 2000

Answer: (D)

3. A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.

Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.

What is the shortest distance between PQ and SR (in cm)?

(A) 1.80

(B) 2.40

(D) 5.76

Answer: (B)

4. The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?

(A) 15

(B) 20

(D) 26

Answer: (B)

If the security guard does not move around the posted location and has a 360o view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.

(A) P and Q

(B) Q

(D) R and S

Answer: (C)

Which one of the following is the correct logical inference based on the information in the above passage?

(A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous

(B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects

(D) Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence

Answer: (D)

7. Consider the following inequalities.

(i) 2x − 1 > 7

(ii) 2x − 9 < 1

Which one of the following expressions below satisfies the above two inequalities?

(A) x ≤ −4

(B) −4 <x ≤ 4

(D) x ≥ 5

Answer: (C)

8. Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.

What is the area enclosed by the quadrilateral?

(A) 4

(B) 4√2

(D) 8√2

Answer: (C)

Statement of P: R has copied in the exam.

Statement of Q: S has copied in the exam.

Statement of R: P did not copy in the exam.

Statement of S: Only one of us is telling the truth.

Statement of T: R is telling the truth.

The investigating team had authentic information that S never lies.

Based on the information given above, the person who has copied in the exam is

(A) R

(B) P

(D) T

Answer: (B)

10. Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.

Let X, Y and Z represent the following operations:

X: rotation of the square by 180 degree with respect to the

S-Q axis.

Y: rotation of the square by 180 degree with respect to the P-R axis.

Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.

Consider the following three distinct sequences of operation (which are applied

in the left to right order).

(1) XYZZ

(2) XY

(3) ZZZZ

Which one of the following statements is correct as per the information provided above?

(A) The sequence of operations (1) and (2) are equivalent

(B) The sequence of operations (1) and (3) are equivalent

(D) The sequence of operations (1), (2) and (3) are equivalent

Answer: (B)

Electronics and Communications Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Consider the two-dimensional vector field denote the unit vectors along the x-axis and the y-axis, respectively. A contour C in the x-y plane, as shown in the figure, is composed of two horizontal lines connected at the two ends by two semicircular arcs of unit radius. The contour is traversed in the counter-clockwise sense. The value of the closed path integral is ______.

(A) 0

(B) 1

(D) −1

Answer: (A)

12. Consider a system of linear equations Ax = b, where

This system of equations admits _____.

(A) a unique solution for x

(B) infinitely many solutions for x

(D) exactly two solutions for x

Answer: (C)

13. The current I in the circuit shown is ________.

(A) 1.25 × 10⁻³A

(B) 0.75 × 10⁻³A

(D) 1.16 × 10⁻³A

Answer: (B)

14. Consider the circuit shown in the figure. The current I flowing through the 10 Ω resistor is _________.

(A) 1 A

(B) 0 A

(D) -0.1 A

Answer: (B)

15. The Fourier transform X(jω) of the signal is ______.

Answer: (A)

16. Consider a long rectangular bar of direct band gap p-type semiconductor. The equilibrium hole density is 10¹⁷ cm⁻³ and the intrinsic carrier concentration is 10¹⁰ cm⁻³. Electron and hole diffusion lengths are 2 μm and 1 μm, respectively.

The left side of the bar (x = 0) is uniformly illuminated with a laser having photon energy greater than the band gap of the semiconductor. Excess electron-hole pairs are generated ONLY at x = 0 because of the laser. The steady state electron density at x = 0 is 10¹⁴ cm⁻³ due to laser illumination. Under these conditions and ignoring electric field, the closest approximation (among the given options) of the steady state electron density at x = 2 μm, is

(A) 0.37 × 10¹⁴ cm⁻³

(B) 0.63 × 10¹³ cm⁻³

(D) 10³ cm⁻³

Answer: (A)

17. In a non-degenerate bulk semiconductor with electron density n = 10¹⁶ cm⁻³, the value of E_C – E_Fn = 200 meV, where E_C and E_Fn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 10¹⁰ cm⁻³. For n = 0.5 × 10¹⁶ cm⁻³, , the closest approximation of the value of (E_C – E_Fn), among the given options, is ______.

(A) 226 meV

(B) 174 meV

(D) 182 meV

Answer: (C)

18. Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width (𝑊) to gate length (L) ratios (W/L) of the transistors are as shown. Both the transistors have the same gate oxide capacitance per unit area. For the pMOSFET, the threshold voltage is −1 V and the mobility of holes is 40 cm²/V.s. For the nMOSFET, the threshold voltage is 1 V and the mobility of electrons is 300 cm²/V.s. The steady state output voltage V_O is ______.

(A) equal to 0 V

(B) more than 2 V

(D) equal to 2 V

Answer: (C)

19. Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A₀, A₁, A₂, and A₃ are _____.

(A) A₀ = 0, A₁ = 0, A₂ = 1, A₃ = 1

(B) A₀ = 1, A₁ = 0, A₂ = 1, A₃ = 0

(D) A₀ = 1, A₁ = 1, A₂ = 0, A₃ = 0

Answer: (C)

20. The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and −1 V, respectively. The MOSFET substrates are connected to their respective sources. Ignore leakage currents and assume that the capacitors are initially discharged. For the applied voltages as shown, the steady state voltages are _____.

(A) V₁ = 5V, V₂ = 5V

(B) V₁ = 5V, V₂ = 4V

(D) V₁ = 4V, V₂ = −5V

Answer: (C)

21. Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K = 2. The complete Nyquist plot of the transfer function G(s) is shown in the figure. Note that the Nyquist contour has been chosen to have the clockwise sense. Assume G(s) has no poles on the closed right-half of the complex plane. The number of poles of the closed-loop transfer function in the closed right-half of the complex plane is ______.

(A) 0

(B) 1

(D) 3

Answer: (C)

22. The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note that K is varied from 0 to ∞.

Select the transfer function G(s) that results in the root-locus plot of the closed-loop system as shown in the figure.

Answer: (A)

23. The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure.

Statement I: The system is necessarily a pure delay system for inputs which are band limited to–α≤ f ≤α.

Statement II: For any wide-sense stationary input process with power spectral density S_X(f), the output power spectral density S_Y(f) obeys S_Y(f) = S_X(f) for –α≤ f ≤α.

Which one of the following combinations is true?

(A) Statement I is correct, Statement II is correct

(B) Statement I is correct, Statement II is incorrect

(D) Statement I is incorrect, Statement II is incorrect

Answer: (C)

24. In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is 2sin(t + π/2). The displacement current (in Amperes) through the capacitor is ____.

(A) 2sin(t)

(B) 2sin(t + π)

(D) 0

Answer: (C)

25. Consider the following partial differential equation (PDE)

where a and b are distinct positive real numbers. Select the combination(s) of values of the real parametersξ and η such that f(x, y) = e⁽^ξ^x+)is a solution of the given PDE.

Answer: (A, B)

26. An ideal OPAMP circuit with a sinusoidal input is shown in the figure. The 3 dB frequency is the frequency at which the magnitude of the voltage gain decreases by 3 dB from the maximum value. Which of the options is/are correct?

(A) The circuit is a low pass filter.

(B) The circuit is a high pass filter.

(D) The 3 dB frequency is 1000/3 rad/s.

Answer: (B, C)

27. Select the Boolean function(s) equivalent to x + yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.

(A) x + z + xy

(B) (x + y) (x + z)

(D) x + xz + xy

Answer: (B, C)

28. Select the correct statement(s) regarding CMOS implementation of NOT gates.

(A) Noise Margin High (NM_H) is always equal to the Noise Margin Low (NM_L),irrespective of the sizing of transistors.

(B) Dynamic power consumption during switching is zero.

(D) Mobility of electrons never influences the switching speed of the NOT gate.

Answer: (C)

29. Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?

(A) H(X) ≤ log₂ K bits

(B) H(X) ≤H(2X)

(D) H(X) ≤H(2^X)

Answer: (A, B, D)

30. Consider the following wave equation,

Which of the given options is/are solution(s) to the given wave equation?

(A) f(x, t) = e⁻^(x^–^100t)2 + e^(x^–^100t)2

(B) f(x, t) = e⁻^x(x^–^100t) + 0.5e⁻^x(x⁺^1000t)

(D) f(x, t) = e^j100^π(−^100x⁺^t) + e^j100^π^{(100x + t)}

Answer: (A, C)

31. The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler has taken 5 wickets each. The median number of wickets taken by the bowler in a match is ________ (rounded off to one decimal place).

Answer: (4.0 to 4.0)

32. A simple closed path 𝐶 in the complex plane is shown in the figure. If

where𝑖 = √−1, then the value of 𝐴 is ______ (rounded off to two decimal places).

Answer: (0.50 to 0.50)

33. Let x₁(t) = e⁻^tu(t) and x₂(t) = u(t) – u(t – 2), where u(∙) denotes the unit step function.

If y(t) denotes the convolution of x₁(t) and x₂(t), then (rounded off to one decimal place).

Answer: (0.0 to 0.0)

34. An ideal MOS capacitor (p-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with V_G = 2V. The corresponding inversion charge density (Q_IN) is 2.2 μC/cm². Assume oxide capacitance per unit area as C_OX = 1.7 μF/cm². For V_G= 4V, the value of Q_IN is _____ μC/cm²(rounded off to one decimal place).

Answer: (5.5 to 5.7)

35. A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _______ mega-bits per second (rounded off to one decimal place).

Answer: (2.99 to 3.01)

Q.36 – Q.65 Carry TWO marks Each

36. The function f(x) = 8 log_e x – x² + 3 attains its minimum over the interval [1, e] at x = ____.

(Here log_ex is the natural logarithm of x.)

(A) 2

(B) 1

(D) 1+e/2

Answer: (B)

37. Let α, β be two non-zero real numbers and v₁, v₂ be two non-zero real vectors of size 3 × 1. Suppose that v₁ and v₂ satisfy v₁^Tv₂ = 0, v₁^Tv₁ = 1, and v₂^Tv₂ = 1.Let A be the 3 × 3 matrix given by:

A = αv₁v₁^T + βv₂v₂^T

The eigenvalues of A are ____.

(A) 0, α, β

(B) 0, α + β, α−β

(C)

(D)

Answer: (A)

38. For the circuit shown, the locus of the impedance Z(jω) is plotted as 𝜔 increases from zero to infinity. The values of R₁ and R₂ are:

(A) R₁ = 2 kΩ, R₂ = 3 kΩ

(B) R₁ = 5kΩ, R₂ = 2kΩ

(D) R₁ = 2 kΩ, R₂ = 5kΩ

Answer: (A)

39. Consider the circuit shown in the figure with input V(t) in volts. The sinusoidal steady state current I(t) flowing through the circuit is shown graphically (where t is in seconds). The circuit element Z can be_____.

(A) a capacitor of 1 F

(B) an inductor of 1 H

(D) an inductor of √3 H

Answer: (B)

40. Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 μm and width 100 μ The product of electron mobility (μ_n) and oxide capacitance per unit area (C_OX) is μ_nC_OX = 1 mA/V². . The threshold voltage of the transistor is 1 V. For a gate-to-source voltage V_GS = [2 – sin2t)] V and drain-to source voltage V_DS = 1 V (substrate connected to the source), the maximum value of the drain-to-source current is ________.

(A) 40 mA

(B) 20mA

(D) 5mA

Answer: (C)

41. For the following circuit with an ideal OPAMP, the difference between the maximum and the minimum values of the capacitor voltage (V_c) is _______.

(A) 15 V

(B) 27 V

(D) 14 V

Answer: (C)

42. A circuit with an ideal OPAMP is shown. The Bode plot for the magnitude (in dB)of the gain transfer function (A_V(jω) = V_out(jω)/V_injω)) of the circuit is also provided (here, ω is the angular frequency in rad/s). The values of R and C are ___________.

(A) R = 3 kΩ, C = 1 μF

(B) R = 1 kΩ, C = 3μF

(D) R = 3kΩ, C = 2μF

Answer: (A)

43. For the circuit shown, the clock frequency is f₀ and the duty cycle is 25%. For the signal at the Q output of the Flip-Flop, _______.

(A) frequency is f₀/4 and duty cycle is 50%

(B) frequency is f₀/4 and duty cycle is 25%

(D) frequency is f₀ and duty cycle is 25%

Answer: (A)

44. Consider an even polynomial p(s) given by

p(s) = s⁴ + 5s² + 4 + K,

where K is an unknown real parameter. The complete range of K for which p(s) hasall its roots on the imaginary axis is ________.

(A) −4 ≤ K ≤ 9/4

(B) −3≤ K ≤ 9/2

(D) −5≤ K ≤ 0

Answer: (A)

45. Consider the following series:

For which of the following combinations of c, d values does this series converge?

(A) c = 1, d = −1

(B) c = 2, d = 1

(D) c = 1, d = −2

Answer: (B, D)

46. The outputs of four systems (S₁, S₂, S₃, and S₄) corresponding to the input signals in(t), for all time 𝑡, are shown in the figure.

Based on the given information, which of the four systems is/are definitely NOTLTI (linear and time-invariant)?

(A) S₁

(B) S₂

(D) S₄

Answer: (C, D)

47. Select the CORRECT statement(s) regarding semiconductor devices.

(A) Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium.

(B) Collector region is generally more heavily doped than Base region in a BJT.

(D) Mobility of electrons always increases with temperature in Silicon beyond 300 K.

Answer: (A, C)

48. A state transition diagram with states A, B, and C, and transition probabilities p₁, p₂ …, p₇ is shown in the figure (e.g., p₁denotes the probability of transition from state A to B). For this state diagram, select the statement(s) which is/are universally true.

(A) p₂ + p₃ = p₅ + p₆

(B) p₁ + p₃ = p₄ + p₆

(D) p₂ + p₅ + p₇ = 1

Answer: (A, C)

49. Consider a Boolean gate (D) where the output Y is related to the inputs A and B as where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, ________ (select the correct option(s)).

(A) NAND logic can be implemented

(B) OR logic cannot be implemented

(D) AND logic cannot be implemented

Answer: (A, C)

50. Two linear time-invariant systems with transfer functions

have unit step responses y₁(t) and y₂(t), respectively. Which of the following statements is/are true?

(A) y₁(t) and y₂(t) have the same percentage peak overshoot.

(B) y₁(t) and y₂(t)have the same steady-state value.

(D) y₁(t) and y₂(t)have the same 2% settling time.

Answer: (A)

51. Consider an FM broadcast that employs the pre-emphasis filter with frequency response

where ω₀ = 10⁴ rad/sec.

For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of (R, C) values is/are ________.

(A) R = 1 kΩ, C = 0.1 μF

(B)R = 2kΩ, C = 1 μF

(C)R = 1 kΩ, C = 2μF

(D)R = 2kΩ, C = 0.5μF

Answer: (A)

52. A wave guide consists of two infinite parallel plates (perfect conductors) at a separation of 10⁻⁴ cm, with air as the dielectric. Assume the speed of light in air to be 3 × 10⁸ m/s. The frequency/frequencies of TM waves which can propagate in this wave guide is/are _______.

(A) 6 × 10¹⁵ Hz

(B) 0.5 × 10¹² Hz

(D) 1 × 10¹³ Hz

Answer: (MTA)

53. The value of the integral where D is the shaded triangular region shown in the diagram, is _____ (rounded off to the nearest integer).

Answer: (512 to 512)

54. A linear 2-port network is shown in Fig. (a). An ideal DC voltage source of 10 V is connected across Port 1. A variable resistance R is connected across Port 2. As R is varied, the measured voltage and current at Port 2 is shown in Fig. (b) as a V₂ versus – I₂ Note that for V₂ = 5 V, I₂ = 0 mA, and for V₂ = 4 V, I₂= −4 mA.

When the variable resistance R at Port 2 is replaced by the load shown in Fig. (c),the current I₂ is _______ mA (rounded off to one decimal place).

Answer: (3.9 to 4.1)

55. For a vector the 8-point discrete Fourier transform (DFT) is denoted by

Here, j = √−1. If [1, 0, 0, 0, 2, 0, 0, 0] and then the value of y[0] is _________ (rounded off to one decimal place).

Answer: (7.9 to 8.1)

56. A p-type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at x = ±2l_n, where l_n = 10⁻⁴ cm is the diffusion length of electrons. Assume electronic charge, q = −6 × 10⁻¹⁹ C. The profiles of photo-generation rate of carriers and the recombination rate of excess minority carriers (R) are shown. Under these conditions, the magnitude of the current density due to the photo-generated electrons at x = +2l_n is _________ mA/cm² (rounded off to two decimal places).

Answer: (0.57 to 0.61)

57. A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal voltage gain is ________ (rounded off to two decimal places).

Answer: (0.70 to 0.80)

58. Consider the circuit shown with an ideal OPAMP. The output voltage V₀is__________V (rounded off to two decimal places).

Answer: (-0.55 to -0.45)

59. Consider the circuit shown with an ideal long channel nMOSFET (enhancement mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with V_GG and V_DD such that it acts as a linear amplifier. v_i is the small-signal ac input voltage. v_A and v_B represent the small-signal voltages at the nodes A and B, respectively. The value of v_A/v_Bis ________ (rounded off to one decimal place).

Answer: (-2.1 to -1.9)

60. The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r(t), y(t), and d(t), respectively. Let the error signal be defined as e(t) = r(t) − y(t). Assuming the reference input r(t) = 0 for all 𝑡, the steady-state error e(∞), due to a unit step disturbance d(t), is _________ (rounded off to two decimal places).

Answer: (-0.11 to -0.09)

61. The transition diagram of a discrete memory less channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.

The parameter α lies in the interval [0.25, 1]. The value of α for which the capacity of this channel is maximized, is ________ (rounded off to two decimal places).

Answer: (1.00 to 1.00)

62. Consider communication over a memory less binary symmetric channel using a(7, 4) Hamming code. Each transmitted bit is received correctly with probability (1 − ϵ), and flipped with probability ϵ. For each code word transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error.

For ϵ = 0.1, the probability that a transmitted code word is decoded correctly is_______ (rounded off to two decimal places).

Answer: (0.84 to 0.86)

63. Consider a channel over which either symbol x_A or symbol x_B is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for Y given x_A and x_B are:

where u(⋅) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).

Answer: (0.22 to 0.25)

64. Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x), as shown in the figure.

Consider a 1 bit quantizer that maps positive samples to value α and others to valueβ. If α* and β* are the respective choices forα and βthat minimize the mean square quantization error, then (α* −β*) = _________ (rounded off to two decimal places).

Answer: (1.15 to 1.18)

65. In an electrostatic field, the electric displacement density vector, is given by

where are the unit vectors along x-axis, y-axis, and z-axis, respectively.Consider a cubical region R centered at the origin with each side of length 1 m, and vertices at (±0.5 m, ±0.5 m, ±0.5 m). The electric charge enclosed within R is_________ C (rounded off to two decimal places).

Answer: (0.48 to 0.52)

GATE Exam 2022 Chemistry (CY) Question Paper With Answer Key

July 12, 2022 by suresh84

GATE-2022

CY: Chemistry

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Inhaling the smoke from a burning _________ could _________ you quickly.

(A) tire / tier

(B) tire / tyre

(D) tyre / tier

Answer: (C)

2. A sphere of radius r cm is packed in a box of cubical shape.

What should be the minimum volume (in cm³) of the box that can enclose the sphere?

(A) r³/8

(B) r³

(D) 8r³

Answer: (D)

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

(A) 26.8

(B) 60.0

(D) 127.5

Answer: (C)

4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

• P sits next to S and T.

• Q sits diametrically opposite to P.

• The shortest distance between S and R is equal to the shortest distance between T and U.

Based on the above statements, Q is a neighbor of

(A) U and S

(B) R and T

(D) P and S

Answer: (C)

5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

(A) 4

(B) 3

(D) 1

Answer: (C)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information given in the above passage?

(A) GSR is an alternative to regular rice, but it grows only in an extreme weather

(B) GSR may be used in future in response to adverse effects of climate change

(D) Regular rice will continue to provide good yields even in extreme weather

Answer: (B)

(A) 1/16

(B) 5/64

(D) 7/64

Answer: (D)

8. Consider the following inequalities.

(i) 3p − q< 4

(ii) 3q − p< 12

Which one of the following expressions below satisfies the above two inequalities?

(A) p + q < 8

(B) p + q = 8

(D) p + q ≥ 16

Answer: (A)

9. Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.

Conclusion II: All engineers are actors.

Conclusion III: No actor is a writer.

Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Only conclusion II and conclusion III are correct

(D) Either conclusion III or conclusion IV is correct

Answer: (C)

10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

Answer: (C)

Chemistry

Q.11 – Q.35 Carry ONE mark Each

11. The major product M formed in the following reaction is

Answer: (B)

12. The starting material Y in the following reaction is

Answer: (B)

13. The major product in the given reaction is Q. The mass spectrum of Q shows {[M] = molecular ion peak}

(A) [M], [M+2] and [M+4] with relative intensity of 1:2:1

(B) [M] and [M+2] with relative intensity of 1:1

(D) [M] and [M+2] with relative intensity of 2:1

Answer: (A)

14. A tripeptide on treatment with PhNCS (pH = 8.0) followed by heating with dilute HCl afforded a cyclic compound M and a dipeptide. The dipeptide on treatment with PhNCS (pH = 8.0) followed by heating with dilute HCl afforded a cyclic compound N and an acyclic compound O. The CORRECT sequence (from N- to C-terminus) of the tripeptide is

(A) glycine-phenylalanine-valine

(B) valine-phenylalanine-glycine

(D) glycine-phenylalanine-alanine

Answer: (A)

15. The major product M in the following reaction is

Answer: (A)

16. The major product T formed in the following reaction is

Answer: (A)

17. In differential thermal analysis (DTA)

(A) the temperature differences between the sample and reference are measured as a function of temperature

(B) the differences in heat flow into the reference and sample are measured as a function of temperature

(D) the glass transition is observed as a sharp peak

Answer: (A)

18. The v_O−O resonance Raman stretching frequency (cm⁻¹) of the coordinated dioxygen in oxy-hemoglobin and oxy-hemocyanin appears, respectively, nearly at

(A) 1136 and 744

(B) 1550 and 744

(D) 744 and 1550

Answer: (A)

19. The number of metal-metal bond(s), with σ, π, and δ character, present in [Mo₂(CH₃CO₂)₄] complex is(are), respectively,

(A) 1, 2, 1

(B) 1, 2, 0

(D) 1, 1, 1

Answer: (A)

20. 1s_A and 1s_B are the normalized eigenfunctions of two hydrogen atoms H_A and H_B, respectively. If 𝑆 = ⟨1s_A|1s_B⟩, the option that is ALWAYS CORRECT is

(A) S = 1

(B) S = 0

(D) 0 ≤ S ≤ 1

Answer: (D)

21. The pure vibrational spectrum of a hypothetical diatomic molecule shows three peaks with the following intensity at three different temperatures.

The CORRECT statement is

(A) Peak I appears at the lowest energy

(B) Peak II appears at the lowest energy

(D) Peak I appears at the highest energy

Answer: (C)

22. The point group of SF₆ is

(A) D_6h

(B) O_h

(D) C_6v

Answer: (B)

23. A point originally at (1, 3, 5) was subjected to a symmetry operation that shifted the point to (−1, −3, 5). Subsequently, the point at (−1, −3, 5) was subjected to another symmetry operation that shifted this point to(−1, −3, −5). The symmetry operators are, respectively,

Answer: (B)

24. Adsorption of a gas with pressure P on a solid obeys the Langmuir adsorption isotherm. For a fixed fractional coverage, the correct relation between K and P at a fixed temperature is

[K = k_a/k_b, k_a and k_bare the rate constants for adsorption and desorption, respectively. Assume non-dissociative adsorption.]

(A) K ∝ P⁻^1/2

(B) K ∝ P

(D) K ∝ P^1/2

Answer: (C)

25. The temperature dependence of the rate constant for a second-order chemical reaction obeys the Arrhenius equation. The SI unit of the ‘pre-exponential factor’ is

(A) s⁻¹

(B) m³mol⁻¹s⁻¹

(D) (m³ mol⁻¹)² s⁻¹

Answer: (B)

26. The CORRECT reagent(s) for the given reaction is(are)

(A) H₂O₂, NaOH

(B)

(D) SO₃·pyridine, Me₂SO

Answer: (A, B)

27. The CORRECT statement(s) about the ¹H NMR spectra of compounds P and Q is (are)

(A) P shows a sharp singlet at δ = 3.70 ppm (for H_a and H_b)

(B) Q shows a sharp singlet at δ = 3.70 ppm (for H_a and H_b)

(D) Q shows a AB-quartet centered at δ = 3.63 ppm (for H_a and H_b)

Answer: (A, D)

28. The CORRECT statement(s) about thallium halides is(are)

(A) TlF is highly soluble in water whereas other Tl-halides are sparingly soluble

(B) TlF adopts a distorted NaCl structure

(D) Both TlBr and TlCl have CsCl structure

Answer: (A, B, D)

29. The CORRECT statement(s) about the spectral line broadening in atomic spectra is(are)

(A) The collision between atoms causes broadening of the spectral line

(B) Shorter the lifetime of the excited state, the broader is the line width

(D) In flame and plasma, the natural line broadening exceeds the collisional line broadening

Answer: (A, B, C)

30. Match the CORRECT option(s) from column A with column B according to the metal centre present in the active site of metalloenzyme.

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

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

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

Answer: (A)

31. The CORRECT statement(s) about the following phase diagram for a hypothetical pure substance X is(are)

(A) The molar volume of solid X is less than the molar volume of liquid X

(B) X does not have a normal boiling point

(D) On increasing the pressure of the gas isothermally, it is impossible to reach solid phase before reaching liquid phase

Answer: (B, C)

32. The parameter(s) fixed for each system in a canonical ensemble is(are)

(A) temperature

(B) pressure

(D) composition

Answer: (A, C, D)

33. The number of peaks exhibited by T in its broadband proton decoupled ¹³C NMR spectrum recorded at 25°C in CDCl₃ is

Answer: (8 to 8)

34. The diffraction angle (in degree, rounded off to one decimal place) of (321) sets of plane of a metal with atomic radius 0.125 nm, and adopting BCC structure is ______

(Given: the order of reflection is 1 and the wavelength of X-ray is 0.0771 nm)

Answer: (59.0 to 61.0)

35. For the angular momentum operator and the spherical harmonics Y_lm (θ, ϕ),

The value of n is _____

Answer: (5 to 5)

Q.36 – Q.65 Carry TWO marks Each

36. The major product P obtained in the following reaction sequence is

Answer: (A)

37. The major product Q in the given reaction is

Answer: (A)

38. The major product P in the following reaction is

Answer: (A)

39. The major product P in the reaction sequence is

Answer: (A)

40. The major products P and Q in the following reaction sequence are

Answer: (B)

41. The major products M and N in the given reaction sequence are

Answer: (B)

42. Three different crystallographic planes of a unit cell of a metal are given below(solid circles represent atom). The crystal system of the unit cell is

(A) triclinic

(B) monoclinic

(D) orthorhombic

Answer: (D)

43. The number of equivalents of H₂S gas released from the active site of rubredoxin,2-iron ferredoxin, and 4-iron ferredoxin when treated with mineral acid, respectively, are

(A) 4, 6, 8

(B) 0, 2, 4

(D) 0, 2, 3

Answer: (B)

44. The number of v_{S = O} stretching vibration band(s) observed in the IR spectrum of the high-spin [Mn(dmso)₆]³⁺ complex (dmso: dimethylsulfoxide) is

(A) only one

(B) two with intensity ratio 1:2

(D) six with intensity ratio 1:1:1:1:1:1

Answer: (B)

45.

*indicates a radioactive isotope

The rate constants in the given self-exchange electron transfer reactions at acertain temperature follow

(A) k₁₁> k₂₂> k₃₃

(B) k₂₂> k₁₁> k₃₃

(D) k₂₂> k₃₃> k₁₁

Answer: (B)

46. The CORRECT distribution of the products in the following reaction is

Answer: (C)

47. The addition of K₄[Fe(CN)₆] to a neutral aqueous solution of the cationic species of a metal produces a brown precipitate that is insoluble in dilute acid. The cationic species is

(A) Fe³⁺

(B) UO₂²⁺

(D) Cu²⁺

Answer: (D)

48. The electronic spectrum of a Ni(II) octahedral complex shows four d-d bands, labelled as P, Q, R, and S. Match the bands corresponding to the transitions.

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

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

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

Answer: (B)

49. In the following table, the left column represents the rigid-rotor type and the right column shows a set of molecules.

The CORRECT match is

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

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

(D) P-5, Q-4, R-3, S-2

Answer: (B)

50. The CORRECT statement regarding the following three normal modes of vibration of SO₃ is

(A) (I) and (II) are infrared active while (III) is infrared inactive

(B) (I) is infrared inactive while (II) and (III) are infrared active

(D) None of the modes are infrared active since SO₃ has zero dipole moment

Answer: (B)

51. The reaction(s) that yield(s) 3-phenylcyclopentanone as the major product is(are)

Answer: (A, B)

52. The reaction(s) that yield(s) M as the major product is(are)

Answer: (A, B, D)

53. The CORRECT statement(s) regarding B₁₀H₁₄ is (are)

(A) Brønsted acidity of B₁₀H₁₄ is higher than that of B₅H₉

(B) Structurally B₁₀H₁₄ is a closo-borane

(D) Both B₁₀H₁₄ and B₁₀H₁₂(SEt₂)₂ have the same number of valence electrons

Answer: (A, C, D OR A, C)

54. The CORRECT statement(s) about the Group-I metals is(are)

(A) Reactivity of Group-I metals with water decreases down the group

(B) Among the Group-I metals, Li spontaneously reacts with N₂ to give a red-brown layer-structured material

(D) All the Group-I metal halide are high-melting colorless crystalline solids

Answer: (B, C, D)

55. The compound(s) that satisfies/satisfy the 18-electron rule is(are)

(Atomic number of Os = 76, Rh = 45, Mo = 42, and Fe = 26)

Answer: (A, D)

56. For three operators

Answer: (B, D)

57. The difference between the number of Gauche-butane interactions present in P and Q is

Answer: (1 to 1)

58. The calculated magnetic moment (in BM, rounded off to two decimal places) of aCe³⁺ complex is

Answer: (2.52 to 2.56)

59. The state of the electron in a He⁺ion is described by the following normalized wave function,

Here, R_nl and Y_lmrepresent the radial and angular components of the eigenfunctions of He⁺ion, respectively, and x is an unknown constant. If the energy of the ion is measured in the above state, the probability (rounded off to two decimal places) of obtaining the energy of−2/9 atomic unit is

Answer: (0.18 to 0.20)

60. A certain wavefunction for the hydrogen-like atom is given by

The number of node(s) in this wave function is

Answer: (2 to 2)

61. EMF of the following cell

Cu│CuSO₄(aq,1.0mol/kg)│Hg₂SO₄(s)│Hg(l)│Pt

at 25 °C and 1 bar is 0.36 V. The value of the mean activity coefficient (rounded off to three decimal places) of CuSO₄ at 25 °C and 1 bar is

[Given: Standard electrode potential values at 25 °C for

Cu²⁺ + 2e⁻→ Cu and

Hg₂SO₄ + 2e⁻ → 2Hg + SO₄²⁻

are 0.34 V and 0.62 V, respectively.

Consider: RT/F at 25 °C = 0.0256 V]

Answer: (0.042 to 0.046)

62. The radius of gyration (in nm, rounded off to one decimal place), for three dimensional random coil linear polyethylene of molecular weight 8,40,000 is

[Given: C−C bond length = 0.154 nm]

Answer: (15.2 to 15.6)

63. The activation energy of the elementary gas-phase reaction O₃ + NO → NO₂ + O₂is 10.5 kJ mol⁻¹. The value of the standard enthalpy of activation (rounded off to two decimal places in kJ mol⁻¹) at 25 °C is

[Given: R is 8.314 J mol⁻¹ K⁻¹]

Answer: (5.50 to 5.60)

64. In a collection of molecules, each molecule has two non-degenerate energy levels that are separated by 5000 cm⁻¹. On measuring the population at a particular temperature, it was found that the ground state population is 10 times that of the upper state. The temperature (in K, rounded off to the nearest integer) of measurement is

[Given: Value of the Boltzmann constant = 0.695 cm⁻¹ K⁻¹]

Answer: (3100 to 3150)

65. The change in entropy of the surroundings (in J K⁻¹, rounded off to two decimal places) to convert 1 mol of super cooled water at 263 K to ice at 263 K at 1 bar is

[Consider : ∆_fusH° at 273 K = 6.0 kJ mol⁻¹, and the molar heat capacity of water is higher than that of ice by 37.0 J K⁻¹ mol⁻¹ in the temperature range of 263 K to273 K]

Answer: (21.20 to 21.60)

GATE Exam 2022 Computer Science and Information Technology (CS) Question Paper With Answer Key

July 12, 2022 by suresh84

GATE-2022

CS: Computer Science and Information Technology

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The _________ is too high for it to be considered _________.

(A) fair / fare

(B) faer / fair

(D) fare / fair

Answer: (D)

2. A function y(x) is defined in the interval [0, 1] on the x-axis as

Which one of the following is the area under the curve for the interval [0, 1] on

the x-axis?

(A) 5/6

(B) 6/5

(D) 6/13

Answer: (C)

3. Let r be a root of the equation x² + 2x + 6 = 0.

Then the value of the expression (r + 2)(r + 3)(r + 4)(r + 5) is

(A) 51

(B) −51

(D) −126

Answer: (D)

4. Given below are four statements.

Statement 1: All students are inquisitive.

Statement 2: Some students are inquisitive.

Statement 3: No student is inquisitive.

Statement 4: Some students are not inquisitive.

From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

(A) Statement 1 and Statement 3

(B) Statement 1 and Statement 2

(D) Statement 3 and Statement 4

Answer: (A)

5. A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.

From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome.The player should use all the five plates exactly once. The plates can be rotated in their plane.

Answer: (B)

6. Some people believe that “what gets measured, improves”. Some others believe that “what gets measured, gets gamed”. One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes. However, the same metrics are counterproductive in organizations with poor work culture.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Metrics are useful in organizations with poor work culture

(B) Metrics are useful in organizations with good work culture

(D) Metrics are never useful in organizations with good work culture

Answer: (B)

7. In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.

Which one of the following is the correct logical inference based on the information provided in the above passage?

(A) Equal number of boys and girls qualified

(B) Equal number of boys and girls appeared for the test

(D) The number of boys who qualified the test is less than the number of girls whoqualified

Answer: (D)

8. A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.

First ball is drawn. What is the probability of getting an orange ball in the next draw?

(A) 1/2

(B) 8/25

(D) 23/50

Answer: (D)

9. The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:

• The line joining P and R is parallel to the line joining Q and S.

• P is placed on the side opposite to the corner T.

• S and U cannot be placed on the same side.

Which one of the following statements is correct based on the above information?

(A) P cannot be placed at a corner

(B) S cannot be placed at a corner

(D) R cannot be placed at a corner

Answer: (B)

10. A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.

What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

(A) 2

(B) 4

(D) 3

Answer: (D)

Computer Science and Information Technology

Q.11 – Q.35 Carry ONE mark Each

11. Which one of the following statements is TRUE for all positive functions f (n) ?

(A) f(n²) = θ (f(n)²),when f(n) is a polynomial

(B) f(n² ) = o(f (n)²)

(D) f(n²) = Ω(f (n)²)

Answer: (A)

12. Which one of the following regular expressions correctly represents the language of the finite automaton given below?

(A) ab*bab* + ba*aba*

(B) (ab*b)*ab* + (ba*a)*ba*

(D) (ba*a + ab*b)*(ab* + ba*)

Answer: (D)

13. Which one of the following statements is TRUE?

(A) The LALR(1) parser for a grammar G cannot have reduce-reduce conflict if the LR(1) parser for G does not have reduce-reduce conflict.

(B) Symbol table is accessed only during the lexical analysis phase.

(D) LR(1) parsing is sufficient for deterministic context-free languages.

Answer: (D)

14. In a relational data model, which one of the following statements is TRUE?

(A) A relation with only two attributes is always in BCNF.

(B) If all attributes of a relation are prime attributes, then the relation is in BCNF.

(D) BCNF decompositions preserve functional dependencies.

Answer: (A)

15. Consider the problem of reversing a singly linked list. To take an example, given the linked list below,

the reversed linked list should look like

Which one of the following statements is TRUE about the time complexity of algorithms that solve the above problem in O(1) space?

(A) The best algorithm for the problem takes θ(n) time in the worst case.

(B) The best algorithm for the problem takes θ (n log n) time in the worst case.

(D) It is not possible to reverse a singly linked list in O(1) space.

Answer: (A)

16. Suppose we are given n keys, m hash table slots, and two simple uniform hash functions 1 h and 2 h . Further suppose our hashing scheme uses 1 h for the odd keys and 2 h for the even keys. What is the expected number of keys in a slot?

(A) m/n

(B) n/m

(D) n/2m

Answer: (B)

17. Which one of the following facilitates transfer of bulk data from hard disk to main memory with the highest throughput?

(A) DMA based I/O transfer

(B) Interrupt driven I/O transfer

(D) Programmed I/O transfer

Answer: (A)

18. Let R1 and R2 be two 4-bit registers that store numbers in 2’s complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

(A) R1 = 1011 and R2 = 1110

(B) R1 = 1100 and R2 = 1010

(D) R1 = 1001 and R2 = 1111

Answer: (B)

19. Consider the following threads, T₁, T₂, and T₃ executing on a single processor, synchronized using three binary semaphore variables, S₁, S₂, and S₃, operated upon using standard wait() and signal(). The threads can be context switched in any order and at any time.

Which initialization of the semaphores would print the sequence BCABCABCA….?

(A) S₁ = 1; S₂ = 1; S₃ = 1

(B) S₁ = 1; S₂ = 1; S₃ = 0

(D) S₁ = 0; S₂ = 1; S₃ = 1

Answer: (C)

20. Consider the following two statements with respect to the matrices A_m_×_n, B_n_×_m, C_n_×_n and D_n_×_n.

Statement 1: tr(AB) = tr(BA)

Statement 2: tr(CD) = tr(DC)

where tr() represents the trace of a matrix. Which one of the following holds?

(A) Statement 1 is correct and Statement 2 is wrong.

(B) Statement 1 is wrong and Statement 2 is correct.

(D) Both Statement 1 and Statement 2 are wrong.

Answer: (C)

21. What is printed by the following ANSI C program?

(A) 1, 10, 11

(B) 1, 10, 14

(D) 10, 10, 14

Answer: (D)

22. Consider an enterprise network with two Ethernet segments, a web server and a firewall, connected via three routers as shown below.

What is the number of subnets inside the enterprise network?

(A) 3

(B) 12

(D) 8

Answer: (C)

Q.23 – Q.27 Multiple Select Questions (MSQ), carry ONE mark each.

23. Which of the following statements is/are TRUE?

(A) Every subset of a recursively enumerable language is recursive.

(B) If a language L and its complement are both recursively enumerable, then L must be recursive.

(D) If L₁ and L₂ are regular, then L₁ ⋂ L₂ must be deterministic context-free.

Answer: (B, C, D)

24. Let WB and WT be two set associative cache organizations that use LRU algorithm for cache block replacement. WB is a write back cache and WT is a write through cache. Which of the following statements is/are FALSE?

(A) Each cache block in WB and WT has a dirty bit.

(B) Every write hit in WB leads to a data transfer from cache to main memory.

(D) A read miss in WB will never lead to eviction of a dirty block from WB.

Answer: (A, B, D)

25. Consider the following three relations in a relational database.

Employee(eId, Name), Brand(bId, bName), Own(eId, bId)

Which of the following relational algebra expressions return the set of eIds

who own all the brands?

(A) Π_eld(Π_{eld, bld}(Own)/ Π_bld(Brand))

(B) Π_eld(Own) – Π_eld((Π_eld(Own) × Π_bld(Brand)) – Π_{eld, bld}(Own))

(D) Π_eld((Π_eld(Own) × Π_bld(Own))/ Π_bld(Brand))

Answer: (A, B)

26. Which of the following statements is/are TRUE with respect to deadlocks?

(A) Circular wait is a necessary condition for the formation of deadlock.

(B) In a system where each resource has more than one instance, a cycle in its wait-for graph indicates the presence of a deadlock.

(C) If the current allocation of resources to processes leads the system to unsafe state, then deadlock will necessarily occur.

(D) In the resource-allocation graph of a system, if every edge is an assignment edge, then the system is not in deadlock state.

Answer: (A, D)

27. Which of the following statements is/are TRUE for a group G ?

(A) If for all x, y ∈ G, (xy)² = x² y², then G is commutative.

(B) If for all x ∈ G, x²= 1, then G is commutative. Here, 1 is the identity element of G.

(D) If G is commutative, then a subgroup of G need not be commutative.

Answer: (A, B, C)

Q.28 – Q.35 Numerical Answer Type (NAT), carry ONE mark each.

28. Suppose a binary search tree with 1000 distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assuming that the array indices start with 0, the 3rd largest element of the tree is stored at index________.

Answer: (509 to 509)

29. Consider the augmented grammar with {+, *, (, ), id} as the set of terminals.

S’ → S

S → S + R | R

R → R* P | P

P → (S) | id

If I₀ is the set of two LR(0) items {[S’ → S ], [S → S, + R]}, then goto(closure(I₀), +) contains exactly __________ items.

Answer: (5 to 5)

30. Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then the maximum number of edges it can have is _________.

Answer: (36 to 36)

31. Consider a relation R(A, B,C,D, E) with the following three functional dependencies.

AB → C; BC → D; C → E;

The number of superkeys in the relation R is _______.

Answer: (8 to 8)

32. The number of arrangements of six identical balls in three identical bins is______.

Answer: (7 to 7)

33. A cache memory that has a hit rate of 0.8 has an access latency 10 ns and miss penalty 100 ns. An optimization is done on the cache to reduce the miss rate. However, the optimization results in an increase of cache access latency to 15 ns, whereas the miss penalty is not affected. The minimum hit rate (rounded off to two decimal places) needed after the optimization such that it should not increase the average memory access time is _______.

Answer: (0.85 to 0.85)

34. The value of the following limit is _______.

Answer: (-0.5 to -0.5)

35. Consider the resolution of the domain name www.gate.org. in by a DNS resolver. Assume that no resource records are cached anywhere across the DNS servers and that iterative query mechanism is used in the resolution. The number of DNS query-response pairs involved in completely resolving the domain name is__________.

Answer: (4 to 4)

Q.36 – Q.45 Multiple Choice Questions (MCQ), carry TWO marks each.

36. Which one of the following is the closed form for the generating function of the sequence {a_n}_n_≥₀ defined below?

Answer: (A)

37. Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trace of

(A) A³

(B) A³ divided by 2

(D) A³ divided by 6

Answer: (D)

38. Which one of the following statements is FALSE?

(A) The TLB performs an associative search in parallel on all its valid entries using page number of incoming virtual address.

(B) If the virtual address of a word given by CPU has a TLB hit, but the subsequent search for the word results in a cache miss, then the word will always be present in the main memory.

(D) In a system that uses hashed page tables, if two distinct virtual addresses V1 and V2 map to the same value while hashing, then the memory access time of these addresses will not be the same.

Answer: (C)

39. Let R_i(z) and W_i(z) denote read and write operations on a data element z by a transaction T_i, respectively. Consider the schedule S with four transactions.

S:R₄(x)R₂(x)R₃(x)R₁(y)W₁(y)W₂(x)W₃(y)R₄(y)

Which one of the following serial schedules is conflict equivalent to S?

(A) T₁ → T₃ → T₄ T₂

(B) T₁ → T₄ → T₃ T₂

(D) T₃ → T₁ → T₄ T₂

Answer: (A)

40. Consider a digital display system (DDS) shown in the figure that displays the contents of register X. A 16-bit code word is used to load a word in X, either from S or from R. S is a 1024-word memory segment and R is a 32-word register file. Based on the value of mode bit M, T selects an input word to load in X. P and Q interface with the corresponding bits in the code word to choose the addressed word. Which one of the following represents the functionality of P, Q, and T?

(A) P is 10:1 multiplexer; Q is 5:1 multiplexer; T is 2:1 multiplexer

(B) P is 10:2¹⁰ decoder; Q is 5:2⁵ decoder; T is 2:1 encoder

(D) P is 1:10 de-multiplexer; Q is 1:5 de-multiplexer; T is 2:1 multiplexer

Answer: (C)

41. Consider three floating point numbers A , B and C stored in registers RA, RB and RC, respectively as per IEEE-754 single precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

Which one of the following is FALSE?

(A) A + C = 0

(B) C = A + B

(D) (B – C) > 0

Answer: (B)

42. Consider four processes P, Q, R, and S scheduled on a CPU as per round robin algorithm with a time quantum of 4 units. The processes arrive in the order P, Q, R, S, all at time t = 0. There is exactly one context switch from S to Q, exactly one context switch from R to Q, and exactly two context switches from Q to R. There is no context switch from S to P. Switching to a ready process after the termination of another process is also considered a context switch. Which one of the following is NOT possible as CPU burst time (in time units) of these processes?

(A) P = 4, Q = 10, R = 6, S = 2

(B) P = 2, Q = 9, R = 5, S = 1

(D) P = 3, Q = 7, R = 7, S = 3

Answer: (D)

43. What is printed by the following ANSI C program?

Answer: (A)

44. What is printed by the following ANSI C program?

ASCII encoding for relevant characters is given below

Answer: (A)

45. Consider solving the following system of simultaneous equations using LU decomposition.

x₁ + x₂ – 2x₃ = 4

x₁ + 3x₂ – x₃ = 7

2x₁ + x₂ – 5x₃ = 7

where L and U are denoted as

Which one of the following is the correct combination of values for L₃₂, U₃₃, and x₁ ?

Answer: (D)

Q.46 – Q.555 Multiple Select Questions (MSQ), carry TWO marks each.

46. Which of the following is/are undecidable?

(A) Given two Turing machines M₁ and M₂, decide if L(M₁) = L(M₂).

(B) Given a Turing machine M, decide if L(M) is regular.

(D) Given a Turing machine M, decide if M takes more than 1073 steps on every

Answer: (A, B, C)

47. Consider the following languages:

L₁ = {aⁿwaⁿ | w ∈ {a, b}^*}

L₂ = {wxw^R | w, x ∈ {a, b}^*, |w|, |x| > 0}

Note that w^R is the reversal of the string w. Which of the following is/are TRUE?

(A) L₁ and L₂ are regular.

(B) L₁ and L₂ are context-free.

(D) L₁ and L₂ are context-free but not regular.

Answer: (A, B, C)

48. Consider the following languages:

L₁ ={ww| w ∈{a,b}^*}

L₂ ={aⁿbⁿc^m |m,n ≥ 0}

L₃ ={a^mbⁿcⁿ |m,n ≥ 0}

Which of the following statements is/are FALSE?

(A) L₁ is not context-free but L₂ and L₃ are deterministic context-free.

(B) Neither L₁ nor L₂ is context-free.

(D) Neither L₁ nor its complement is context-free.

Answer: (B, C, D)

49. Consider a simple undirected weighted graph G, all of whose edge weights are distinct. Which of the following statements about the minimum spanning trees of G is/are TRUE?

(A) The edge with the second smallest weight is always part of any minimum spanning tree of G .

(B) One or both of the edges with the third smallest and the fourth smallest weights are part of any minimum spanning tree of G .

(C) Suppose S ⊆ V be such that S ≠ϕ and S ≠ V. Consider the edge with the minimum weight such that one of its vertices is in S and the other in V \ S . Such an edge will always be part of any minimum spanning tree of G.

(D) G can have multiple minimum spanning trees.

Answer: (A, B, C)

50. The following simple undirected graph is referred to as the Peterson graph.

Which of the following statements is/are TRUE?

(A) The chromatic number of the graph is 3.

(B) The graph has a Hamiltonian path.

(D) The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)

Answer: (A, B, C)

51. Consider the following recurrence:

Then, which of the following statements is/are TRUE?

(A) f(2ⁿ – 1) = 2ⁿ – 1

(B) f(2ⁿ) = 1

(D) f(2ⁿ + 1) = 2ⁿ + 1

Answer: (A, B, C)

52. Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

(A) The diagonal entries of A² are the degrees of the vertices of the graph.

(B) If the graph is connected, then none of the entries of Aⁿ⁻¹ + I_n can be zero.

(D) If there is at least a 1 in each of A ’s rows and columns, then the graph must be

connected.

Answer: (A)

53. Which of the following is/are the eigenvector(s) for the matrix given below?

Answer: (A, C, D)

54. Consider a system with 2 KB direct mapped data cache with a block size of 64 bytes. The system has a physical address space of 64 KB and a word length of 16 bits. During the execution of a program, four data words P, Q, R, and S are accessed in that order 10 times (i.e., PQRSPQRS…). Hence, there are 40 accesses to data cache altogether. Assume that the data cache is initially empty and no other data words are accessed by the program. The addresses of the first bytes of P, Q, R, and S are 0xA248, 0xC28A, 0xCA8A, and 0xA262, respectively. For the execution of the above program, which of the following statements is/are TRUE with respect to the data cache?

(A) Every access to S is a hit.

(B) Once P is brought to the cache it is never evicted.

(D) Every access to R evicts Q from the cache.

Answer: (A, B, D)

55. Consider routing table of an organization’s router shown below:

Which of the following prefixes in CIDR notation can be collectively used to correctly aggregate all of the subnets in the routing table?

(A) 12.20.164.0/20

(B) 12.20.164.0/22

(D) 12.20.168.0/22

Answer: (B, D)

Q.56 – Q.65 Numerical Answer Type (NAT), carry TWO marks each.

56. Consider the relational database with the following four schemas and their respective instances.

The number of rows returned by the above SQL query is _______.

Answer: (2 to 2)

57. Consider a network with three routers P, Q, R shown in the figure below. All the links have cost of unity.

The routers exchange distance vector routing information and have converged on the routing tables, after which the link Q−R fails. Assume that P and Q send out routing updates at random times, each at the same average rate. The probability of a routing loop formation (rounded off to one decimal place) between P and Q, leading to count-to-infinity problem, is ______.

Answer: (0.5 to 0.5)

58. Let G(V , E) be a directed graph, where V = {1, 2, 3, 4, 5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A.

A[i][j] = 1 indicates a directed edge from node i to node j. A directed spanning tree of G, rooted at r ∈ V , is defined as a subgraph T of G such that the undirected version of T is a tree, and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is ______.

Answer: (24 to 24)

59. Consider a 100 Mbps link between an earth station (sender) and a satellite (receiver) at an altitude of 2100 km. The signal propagates at a speed of 3 × 10⁸ m/s. The time taken (in milliseconds, rounded off to two decimal places) for the receiver to completely receive a packet of 1000 bytes transmitted by the sender is_________.

Answer: (7.07 to 7.09)

60. Consider the data transfer using TCP over a 1 Gbps link. Assuming that the maximum segment lifetime (MSL) is set to 60 seconds, the minimum number of bits required for the sequence number field of the TCP header, to prevent the sequence number space from wrapping around during the MSL is ______.

Answer: (33 to 33)

61. A processor X₁ operating at 2 GHz has a standard 5-stage RISC instruction pipeline having a base CPI (cycles per instruction) of one without any pipeline hazards. For a given program P that has 30% branch instructions, control hazards incur 2 cycles stall for every branch. A new version of the processor X₂ operating at same clock frequency has an additional branch predictor unit (BPU) that completely eliminates stalls for correctly predicted branches. There is neither any savings nor any additional stalls for wrong predictions. There are no structural hazards and data hazards for X₁ and X₂. If the BPU has a prediction accuracy of 80%, the speed up (rounded off to two decimal places) obtained by X₂ over X₁ in executing P is_ ______.

Answer: (1.42 to 1.45)

62. Consider the queues Q₁ containing four elements and Q₂ containing none (shown as the Initial State in the figure). The only operations allowed on these two queues are Enqueue (Q, element) and Dequeue (Q), The minimum number of Enqueue operations on Q₁ required to place the elements of Q₁ in Q₂ in reverse order (shown as the Final State in the figure) without using any additional storage is _______.

Answer: (0 to 0)

63. Consider two files systems A and B , that use contiguous allocation and linked allocation, respectively. A file of size 100 blocks is already stored in A and also in B. Now, consider inserting a new block in the middle of the file (between 50th and 51st block), whose data is already available in the memory. Assume that there are enough free blocks at the end of the file and that the file control blocks are already in memory. Let the number of disk accesses required to insert a block in the middle of the file in A and B are n_A and n_B respectively, then the value of n_A + n_B is _____.

Answer: (153 to 153)

64. Consider a demand paging system with four page frames (initially empty) and LRU page replacement policy. For the following page reference string

7, 2, 7, 3, 2, 5, 3, 4, 6, 7, 7,1, 5, 6,1

the page fault rate, defined as the ratio of number of page faults to the number of memory accesses (rounded off to one decimal place) is_ ______.

Answer: (0.6 to 0.6)

65. Consider the following grammar along with translation rules.

Here # and % are operators and id is a token that represents an integer and id_•val represents the corresponding integer value. The set of non-terminals is {S,T, R, P} and a subscripted non-terminal indicates an instance of the non-terminal.

Using this translation scheme, the computed value of S_•val for root of the parse tree for the expression 20 #10%5 #8%2%2 is _______.

Answer: (80 to 80)

GATE Exam 2022 Chemical Engineering (CH) Question Paper With Answer Key

July 12, 2022 by suresh84

GATE-2022

CH: Chemical Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Inhaling the smoke from a burning _________ could _________ you quickly.

(A) tire / tier

(B) tire / tyre

(D) tyre / tier

Answer: (C)

2. A sphere of radius r cm is packed in a box of cubical shape.

What should be the minimum volume (in cm³) of the box that can enclose the sphere?

(A) r³/8

(B) r³

(D) 8r³

Answer: (D)

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

(A) 26.8

(B) 60.0

(D) 127.5

Answer: (C)

4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

• P sits next to S and T.

• Q sits diametrically opposite to P.

• The shortest distance between S and R is equal to the shortest distance between T and U.

Based on the above statements, Q is a neighbor of

(A) U and S

(B) R and T

(D) P and S

Answer: (C)

5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

(A) 4

(B) 3

(D) 1

Answer: (C)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information given in the above passage?

(A) GSR is an alternative to regular rice, but it grows only in an extreme weather

(B) GSR may be used in future in response to adverse effects of climate change

(D) Regular rice will continue to provide good yields even in extreme weather

Answer: (B)

(A) 1/16

(B) 5/64

(D) 7/64

Answer: (D)

8. Consider the following inequalities.

(i) 3p − q< 4

(ii) 3q − p< 12

Which one of the following expressions below satisfies the above two in equalities?

(A) p + q < 8

(B) p + q = 8

(D) p + q ≥ 16

Answer: (A)

9. Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.

Conclusion II: All engineers are actors.

Conclusion III: No actor is a writer.

Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Only conclusion II and conclusion III are correct

(D) Either conclusion III or conclusion IV is correct

Answer: (C)

10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

Answer: (C)

Chemical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. The value of (1 + i)¹², where i = √−1, is

(A) −64i

(B) 64i

(D) −64

Answer: (D)

12. Given matrix the ordered pair (x, y) for which det(A) = 0 is

(A) (1,1)

(B) (1,2)

(D) (2,1)

Answer: (B)

13. Let f(x) = e⁻^|x|, where x is real. The value of at x = −1 is

(A) −e

(B) e

(D) −1/e

Answer: (C)

14. The value of the real variable x ≥ 0, which maximizes the function f(x) = x^e e⁻^x is

(A) e

(B) 0

(D) 1

Answer: (A)

15. For a single component system at vapor-liquid equilibrium, the extensive variables A, V, S and N denote the Helmholtz free energy, volume, entropy, and number of moles, respectively, in a given phase. If superscripts (v) and (l) denote the vapor and liquid phase, respectively, the relation that is NOT CORRECT is

Answer: (D)

16. Consider turbulent flow in a pipe under isothermal conditions. Let r denote the radial coordinate and z denote the axial flow direction. On moving away from the wall towards the center of the pipe, the rz-component of the Reynolds stress

(A) Increases and then decreases

(B) Decreases and then increases

(D) Only increases

Answer: (A)

17. Consider two stationary spherical pure water droplets of diameters d₁ and 2d₁. CO₂ diffuses into the droplets from the surroundings. If the rate of diffusion of CO₂ into the smaller droplet is W₁mol s⁻¹, the rate of diffusion of CO₂ into the larger droplet is

(A) 2W₁

(B) 4W₁

(D) 0.5W₁

Answer: (A)

18. In soap manufacturing, the triglycerides present in oils and fats are hydrolyzed to mainly produce

(A) Fatty acids and glycerol

(B) Glycerol only

(D) Glycerol and paraffins

Answer: (A)

19. The chemical formula of Glauber’s salt, used in the Kraft process, is

(A) Na₂CO₃.10H₂O

(B) Na₂S₂O₄.2H₂O

(D) Na₂SO₄.10H₂O

Answer: (D)

20. Catalytic reforming is commonly used in the petroleum industry to improve fuel quality. The undesirable reaction in the catalytic reforming of naphtha is

(A) Hydrocracking of paraffins

(B) Dehydrogenation of naphthenes

(D) Cyclization of paraffins

Answer: (A)

21. A control system on the jacket side of a reactor is shown in the figure. Pressurized water flows through the jacket to cool the reactor. The heated water flashes in the boiler. The exothermic reaction heat thus generates steam. Fresh boiler feed water (BFW) is added to make-up for the loss of water as steam. Assume that all control valves are air-to-open. The controller action, ‘direct’ or ‘reverse’, is defined with respect to the controller. Select the option that correctly specifies the action of the controllers.

(A) PC: Reverse, LC: Direct, TC: Reverse

(B) PC: Direct, LC: Reverse, TC: Direct

(D) PC: Reverse, LC: Direct, TC: Direct

Answer: (C)

22. Liquid flowing through a heat exchanger (HX) is heated. A bypass stream is provided to control the temperature of the heated exit stream. From the given plumbing options, the one that provides the most effective temperature control for large disturbances while avoiding vaporization in the heat exchanger is

Answer: (C)

23. The appropriate feed forward compensator, G_ff, in the shown block diagram is

Answer: (A)

24. Choose the option that correctly pairs the given measurement devices with the quantities they measure.

(A) I-E II-C III-D IV-B V-A

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

(D) I-D II-C III-A IV-E V-C

Answer: (B)

25. A simple distillation column is designed to separate an ideal binary mixture to specified distillate and bottoms purities at a given column pressure. If RR_min is the minimum reflux ratio for this separation, select the statement that is NOT CORRECT with regard to the variation in the total annualized cost (TAC) of the column with reflux ratio (RR).

(A) TAC has a minimum with respect to RR

(B) The sharpest rise in TAC occurs as RR approaches RR_min from above

(D) TAC increases with RR for RR >>RR_min

Answer: (C)

26. The reaction A → B is carried out isothermally on a porous catalyst. The intrinsic reaction rate is kC_A², where k is the rate constant and C_A is the concentration of A. If the reaction is strongly pore-diffusion controlled, the observed order of the reaction is

(A) 1

(B) 2

(D) √2

Answer: (C)

27. In an enzymatic reaction, an inhibitor (I) competes with the substrate (S) to bind with the enzyme (E), thereby reducing the rate of product (P) formation. The competitive inhibition follows the reaction mechanism shown below. Let [S] and [I] be the concentration of S and I, respectively, and r_s be the rate of consumption of S. Assuming pseudo-steady state, the correct plot of is

Answer: (A)

28. The area of a circular field is 25 m². The radius, r, is to be determined using the Newton-Raphson iterative method. For an initial guess of r = 2.500 m, the revised estimate of r after one iteration is ___________ m (rounded off to three decimal

places).

Answer: (2.830 to 2.850)

29. 5 moles of liquid benzene, 8 moles of liquid toluene and 7 moles of liquid xylene are mixed at 25 °C and 1 bar. Assuming the formation of an ideal solution and using the universal gas constant R = 8.314 J mol⁻¹ K⁻¹, the total entropy change is _______ J K⁻¹ (rounded off to one decimal place).

Answer: (178.7 to 180.7)

30. A perfectly insulated double pipe heat exchanger is operating at steady state. Saturated steam enters the inner pipe at 100 °C and leaves as saturated water at 100 °C. Cooling water enters the outer pipe at 75 °C and exits at 95 °C. The overall heat transfer coefficient is 1 kW m⁻² K⁻¹ and the heat transfer area is 1 m². The average specific heat capacity of water at constant pressure is 4.2 kJ kg⁻¹ K⁻¹. The required cooling water flow rate is ________ kg s⁻¹ (rounded off to two decimal places).

Answer: (0.14 to 0.15)

31. Consider steady-state diffusion in a binary A-B liquid at constant temperature and pressure. The mole-fraction of A at two different locations is 0.8 and 0.1. Let N_A1be the diffusive flux of A calculated assuming B to be non-diffusing, and N_A2 be the diffusive flux of A calculated assuming equimolar counter-diffusion. The quantity is ______ (rounded off to one decimal place).

Answer: (53.0 to 54.0)

32. Consider interphase mass transfer of a species S between two immiscible liquids A and B. The interfacial mass transfer coefficient of S in liquid A is twice of that in liquid B. The equilibrium distribution of S between the liquids is given by y_S^A = 0.5y_S^B, where y_S^A and y_S^B are the mole-fractions of S in A and B, respectively. The bulk phase mole-fraction of S in A and B is 0.10 and 0.02, respectively. If the steady-state flux of S is estimated to be 10 kmol h⁻¹ m⁻², the mass transfer coefficient of S in A is ________ kmol h⁻¹ m⁻² (rounded off to one decimal place).

Answer: (221.0 to 223.0)

33. A wet solid containing 20% (w/w) moisture (based on mass of bone-dry solid) is dried in a tray-dryer. The critical moisture content of the solid is 10% (w/w). The drying rate (kg m⁻² s⁻¹) is constant for the first 4 hours, and then decreases linearly to half the initial value in the next 1 hour. At the end of 5 hours of drying, the percentage moisture content of the solid is _______% (w/w) (rounded off to one decimal place).

Answer: (8.0 to 8.4)

34. A process described by the transfer function is forced by a unit step input at time t = 0. The output value immediately after the step input (at t = 0⁺) is ________ (rounded off to the nearest integer).

Answer: (2 to 2)

35. A compressor with a life of 10 years costs Rs 10 lakhs. Its yearly operating cost is Rs 0.5 lakh. If the annual compound interest rate is 8%, the amount needed at present to fund perpetual operation of the compressor is Rs ______ lakhs (rounded to first decimal place).

Answer: (24.7 to 25.1)

Q.36 – Q.65 Carry TWO marks Each

36. The partial differential equation

where, t ≥ 0 and x∈ [0,1], is subjected to the following initial and boundary conditions:

The value of t at which is

(A) 1

(B) e

(D) 1/e

Answer: (A)

37. N moles of an ideal gas undergo a two-step process as shown in the figure. Let P, V and T denote the pressure, volume and temperature of the gas, respectively. The gas, initially at state-1 (P₁, V₁, T₁), undergoes an isochoric (constant volume) process to reach state-A, and then undergoes an isobaric (constant pressure) expansion to reach state-2 (P₂, V₂, T₂). For an ideal gas, C_P – C_V = NR, where C_Pand C_V are the heat capacities at constant pressure and constant volume, respectively, and assumed to be temperature independent. The heat gained by the gas in the two-step process is given by

(A) P₂(V₂ – V₁) + C_V (T₂ – T₁)

(B) P₂(V₂ – V₁) + C_P (T₂ – T₁)

(D) P₂V₂ – P₁V₁

Answer: (A)

38. A horizontal cylindrical water jet of diameter D₁ = 2 cm strikes a vertical solid plate with a hole of diameter D₂ = 1 cm, as shown in the figure. A part of the jet passes through the hole and the rest is deflected along the plate. The density of water is 1000 kg m⁻³. If the speed of the jet is 20 m s⁻¹, the magnitude of the horizontal force, in N, required to hold the plate stationary is

(A) 30 π

(B) 10 π

(D) 5 π

Answer: (A)

39. Consider a horizontal rod of radius a R (a< 1) in a stationary pipe of radius R. The rod is pulled coaxially at a constant velocity V as shown in the figure. The annular region is filled with a Newtonian incompressible fluid of viscosity μ. The steady state fully developed axial velocity profile in the fluid is given by where r is the radial coordinate. Ignoring end effects, the magnitude of the pulling force per unit rod length is

Answer: (B)

40. Consider a bare long copper wire of 1 mm diameter. Its surface temperature is T_sand the ambient temperature is T_a (T_s>T_a). The wire is to be coated with a 2 mm thick insulation. The convective heat transfer coefficient is 20 W m⁻² K⁻¹. Assume that T_s and T_a remain unchanged. To reduce heat loss from the wire, the maximum allowed thermal conductivity of the insulating material, in W m⁻¹ K⁻¹, rounded off to two decimal places, is

(A) 0.02

(B) 0.04

(D) 0.01

Answer: (A)

41. Two large parallel planar walls are maintained at 1000 K and 500 K. Parallel radiation shields are to be installed between the two walls. Assume that the emissivities of the walls and the shields are equal. If the melting temperature of the shields is 900 K, the maximum number of shield(s) that can be installed between the walls is (are)

(A) 1

(B) 0

(D) 3

Answer: (A)

42. Saturated steam condenses on a vertical plate maintained at a constant wall temperature. If x is the vertical distance from the top edge of the plate, then the local heat transfer coefficient h(x) ∝Γ(x)⁻^1/3, where Γ(x) is the local mass flow rate of the condensate per unit plate width. The ratio of the average heat transfer coefficient over the entire plate to the heat transfer coefficient at the bottom of the plate is

(A) 4

(B) 4/3

(D) 3

Answer: (B)

43. Match the product in Group-1 with the manufacturing process in Group-2. The correct combination is

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

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

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

Answer: (C)

44. The directional derivative of f(x, y, z) = 4x² + 2y² + z² at the point (1,1,1) in the direction of the vector is _______ (rounded off to two decimal places).

Answer: (4.20 to 4.30)

45. Consider a sphere of radius 4, centered at the origin, with outward unit normal on its surface S. The value of the surface integral is _______ (rounded off to one decimal place).

Answer: (191.9 to 192.1)

46. The equation with the initial condition y(x = 0) = 1 is to be solved using a predictor-corrector approach. Use a predictor based on the implicit Euler’s method and a corrector based on the trapezoidal rule of integration, each with a full-step size of 0.5. Considering only positive values of y, the value of y at x = 0.5 is ______ (rounded off to three decimal places).

Answer: (0.860 to 0.880)

47. A substance at 4 °C has a thermal expansion coefficient an isothermal compressibility, and a molar volume v = 8 × 10⁻⁶ m³ mol⁻¹. If s is the molar entropy, then at 4 °C, the quantity evaluated for the substance is __________ J mol⁻¹ K⁻¹ (rounded off to the nearest integer).

Answer: (0 to 0)

48. The molar excess Gibbs free energy (g^E) of a liquid mixture of A and B is given by

where x_A and x_B are the mole fraction of A and B, respectively, the universal gas constant, R = 8.314 J K⁻¹ mol⁻¹, T is the temperature in K, and C₁, C₂ are temperature-dependent parameters. At 300 K, C₁ = 0.45 and C₂ = −0.018. If γ_Aand γ_B are the activity coefficients of A and B, respectively, the value of at 300 K and 1 bar is ______ (rounded off to the nearest integer).

Answer: (0 to 0)

49. For a pure substance, the following data at saturated conditions are given:

Assume that the vapor phase behaves ideally, the molar volume of the liquid is negligible, and the latent heat of vaporization is constant over the given temperature range. The universal gas constant, R = 8.314 J K⁻¹ mol⁻¹. From the above data, the estimated latent heat of vaporization at 360 K is _______ kJ/mol (rounded off to one decimal place).

Answer: (36.3 to 38.3)

50. Consider the process flow sheet in the figure. An irreversible liquid-phase reaction A → B (reaction rate –r_A = 164 x_Akmol m⁻³ h⁻¹) occurs in a 1 m³ continuous stirred tank reactor (CSTR), where x_A is the mole fraction of A. A small amount of inert,I, is added to the reactor. The reactor effluent is separated in a perfect splitter to recover pure B product down the bottoms and a B-free distillate. A fraction of the distillate is purged and the rest is recycled back to the reactor. At a particular steady state, the product rate is 100 kmol h⁻¹, the recycle rate is 200 kmol h⁻¹ and the purge rate is 10 kmol h⁻¹. Given the above information, the inert feed rate into the process is ____________ kmol h⁻¹ (rounded off to two decimal places).

Answer: (0.95 to 1.05)

51. Two reservoirs located at the same altitude are connected by a straight horizontal pipe of length 120 m and inner diameter 0.5 m, as shown in the figure. A pump transfers the liquid of density 800 kg m⁻³ at a flow rate of 1 m³ s⁻¹ from Reservoir-1 to Reservoir-2. The liquid levels in Reservoir-1 and Reservoir-2 are 2 m and 10 m, respectively. Assume that the reservoirs’ cross-section areas are large enough to neglect the liquid velocity at the top of the reservoirs. All minor losses can be ignored. The acceleration due to gravity is 9.8 ms⁻². If the friction factor for the pipe-flow is 0.01, the required power of the pump is _______ kW (rounded off to one decimal place).

Answer: (87.0 to 88.0 OR 161.7 to 163.2)

52. A venturi meter (venturi coefficient, C_v = 0.98) is connected to a pipe of inner diameter 50 mm. Water (density 1000 kg m⁻³) is flowing through the pipe. The pressure-drop measured across the venturi meter is 50 kPa. If the venturi throat diameter is 20 mm, the estimated flow rate of water is ______ ×10⁻³ m³ s⁻¹(rounded off to two decimal places).

Answer: (3.10 to 3.17)

53. In a constant-rate cake filtration operation, the collected filtrate volumes are 120 m³and 240 m³at 1 min and 2 min, respectively. Assume the cake resistance to be constant and the filter medium resistance to be negligible. If the pressure-drop across the cake is 10 kPa at 1 min, its value at 2 min is _________ kPa (rounded off to the nearest integer).

Answer: (20 to 20)

54. A cylindrical fin of diameter 24 mm is attached horizontally to a vertical planar wall. The heat transfer rate from the fin to the surrounding air is 60% of the heat transfer rate if the entire fin were at the wall temperature. If the fin effectiveness is 10, its length is ________ mm (rounded off to the nearest integer).

Answer: (94 to 94)

55. A single-effect evaporator with a heat transfer area of 70 m² concentrates a salt solution using steam. The salt solution feed rate and temperature are 10000 kg h⁻¹and 40 °C, respectively. The saturated steam feed rate and temperature are 7500 kg h⁻¹ and 150 °C, respectively. The boiling temperature of the solution in the evaporator is 80 °C. The average specific heat of the solution is 0.8 kcal kg⁻¹ K⁻¹.The latent heat of vaporization is 500 kcal kg⁻¹. If the steam-economy is 0.8, the overall heat transfer coefficient is ________ kcal h⁻¹ m⁻² K⁻¹ (rounded off to the nearest integer).

Answer: (675 to 680)

56. An equimolar binary mixture is to be separated in a simple tray-distillation column. The feed rate is 50 kmol min⁻¹. The mole fractions of the more volatile component in the top and bottom products are 0.90 and 0.01, respectively. The feed as well as the reflux stream are saturated liquids. On application of the McCabe-Thiele method, the operating line for the stripping section is obtained as

y = 1.5x – 0.005

where y and x are the mole fractions of the more volatile component in the vapour and liquid phases, respectively. The reflux ratio is _______ (rounded off to two decimal places).

Answer: (0.61 to 0.65)

57. The dry-bulb temperature of air in a room is 30 °C. The Antoine equation for water is given as

where T is the temperature in K and P^sat is the saturation vapor pressure in bar. The latent heat of vaporization of water is 2000 kJ kg⁻¹, the humid heat is 1.0 kJ kg⁻¹ K⁻¹, and the molecular weights of air and water are 28 kg kmol-1 and 18 kg kmol⁻¹, respectively. If the absolute humidity of air is Y’ kg moisture per kg dry air, then for a wet-bulb depression of 9°C, 1000 × Y’ = ________ (rounded off to one decimal place).

Answer: (10.0 to 12.0)

58. In the block diagram shown in the figure, the transfer function with K > 0 and τ > 0. The maximum value of K below which the system remains stable is __________ (rounded off to two decimal places).

Answer: (0.70 to 0.72)

59. Consider the tank level control system shown in the figure, where the cross-section area of the tank is A. Assume perfect flow controllers (FC). The level controller(LC) is proportional-integral (PI). For an integral time, τ_I, the level controller gain,K_C, is tuned for critical damping. The value of is ________ (rounded off to the nearest integer).

Answer: (-4 to -4 OR 4 to 4)

60. Consider a single-input-single-output (SISO) system with the transfer function

where the time constants are in minutes. The system is forced by a unit step input at time t = 0. The time at which the output response reaches the maximum is ________ minutes (rounded off to two decimal places).

Answer: (0.54 to 0.56)

61. Information for a proposed greenfield project is provided in the table. The discounted cash flow for the fourth year is Rs _______ crores (rounded off to one decimal place).

Answer: (52.0 to 54.0)

62. Consider the process in the figure. The liquid phase elementary reactions

occur in the continuous stirred tank reactor (CSTR), where x_j is the mole fraction of the 𝑗th component (j = A, B, P, S) in the CSTR. It is given that k₂ = k₃. All process feed, process exit and recycle streams are pure. At steady state, the net generation rate of the undesired product, S, in the CSTR is zero. As q = x_A/x_Bis varied at constant reactor temperature, the reactor volume is adjusted to maintain a constant single-pass conversion of B. For a fixed product rate and 90%conversion of B in the reactor, the value of q that minimizes the sum of the molar flow rates of the A and S recycle streams is ________ (round off to one decimal place).

Answer: (3 to 3)

63. An elementary irreversible liquid-phase reaction, 2A → B, is carried out under isothermal conditions in a 1 m³ideal plug flow reactor (PFR) as shown in the figure. The volumetric flow rate of fresh A, v₁ = 10 m³ h⁻¹, and its concentration C_A1 = 2 kmol m⁻³. For a recycle ratio R =0 , the conversion of A at location 2 with respect to the fresh feed (location 1) is 50%. For R → ∞, the corresponding conversion of A is _________% (rounded off to one decimal place).

Answer: (38.0 to 38.5)

64. An elementary irreversible gas-phase reaction, A → B + C, is carried out at fixed temperature and pressure in two separate ideal reactors: (i) a 10 m³plug flow reactor (PFR), (ii) a 10 m³ continuous-stirred tank reactor (CSTR). If pure A is fed at 5 m³ h⁻¹ to the PFR operating at 400 K, the conversion is 80%. If a mixture of 50 mol% of A and 50 mol% of an inert is fed at 5 m³ h⁻¹ to the CSTR operating at 425 K, the conversion is 80%. The universal gas constant R = 8.314 J mol⁻¹ K⁻¹. Assuming the Arrhenius rate law, the estimated activation energy is__________kJ mol⁻¹ (rounded off to one decimal place).

Answer: (47.0 to 49.0)

65. An elementary irreversible liquid-phase reaction, where the rate constant k = 2 L mol⁻¹ min⁻¹, takes place in an isothermal non-ideal reactor. The E-curve in a tracer experiment is shown in the figure. Pure P (2 mol L⁻¹) is fed to the reactor. Using the segregated model, the percentage conversion of P at the exit of the reactor is __________% (rounded off to the nearest integer).

Answer: (50 to 50)

GATE Exam 2022 Civil Engineering (CE-2) Question Paper With Answer Key

July 11, 2022 by suresh84

GATE-2022

CE2: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The movie was funny and I _________.

(A) could help laughing

(B) couldn’t help laughed

(D) could helped laughed

Answer: (C)

What is the value of

(A) 0.75

(B) 1.25

(D) 3.25

Answer: (B)

3. Both the numerator and the denominator of 3/5 are increased by a positive integer, x, and those of 15/17 are decreased by the same integer. This operation results in the same value for both the fractions.

What is the value of x?

(A) 1

(B) 2

(D) 4

Answer: (C)

4. A survey of 450 students about their subjects of interest resulted in the following outcome.

• 150 students are interested in Mathematics.

• 200 students are interested in Physics.

• 175 students are interested in Chemistry.

• 50 students are interested in Mathematics and Physics.

• 60 students are interested in Physics and Chemistry.

• 40 students are interested in Mathematics and Chemistry.

• 30 students are interested in Mathematics, Physics and Chemistry.

• Remaining students are interested in Humanities.

Based on the above information, the number of students interested in Humanities is

(A) 10

(B) 30

(D) 45

Answer: (D)

For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?

Answer: (A)

Q.6 – Q. 10 Carry TWO marks each.

6. In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sales in the shops in these malls is generally low.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Fewer people are visiting the malls but spending more

(B) More people are visiting the malls but not spending enough

(D) Fewer people are visiting the malls and not spending enough

Answer: (B)

7. In a partnership business the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.

What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?

(A) 22 : 23 : 24

(B) 22 : 33 : 50

(D) 63 : 86 : 110

Answer: (D)

8. Consider the following equations of straight lines:

Line L1: 2x – 3y = 5

Line L2: 3x + 2y = 8

Line L3: 4x – 6y = 5

Line L4: 6x – 9y = 6

Which one among the following is the correct statement?

(A) L1 is parallel to L2 and L1 is perpendicular to L3

(B) L2 is parallel to L4 and L2 is perpendicular to L1

(D) L4 is perpendicular to L2 and L4 is parallel to L3

Answer: (D)

9. Given below are two statements and four conclusions drawn based on the statements.

Statement 1: Some soaps are clean.

Statement 2: All clean objects are wet.

Conclusion I: Some clean objects are soaps.

Conclusion II: No clean object is a soap.

Conclusion III: Some wet objects are soaps.

Conclusion IV: All wet objects are soaps.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Either conclusion I or conclusion II is correct

(D) Only conclusion I and conclusion III are correct

Answer: (D)

10. An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.

The ant first turns 72° anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.

(1) moves forward for 10 cm.

(2) turns 144° clockwise.

The pattern made by the trace left behind by the ant is

Answer: (C)

Civil Engineering (C-2)

Q.11 – 35 Carry ONE mark each.

11. The function f(x, y) satisfies the Laplace equation

∇²f(x, y) = 0

on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3.

The numerical value of f(0, 0) is:

(A) 0

(B) 2

(D) 1

Answer: (C)

12.

Answer: (MTA)

13. For a linear elastic and isotropic material, the correct relationship among Young’s modulus of elasticity (E), Poisson’s ratio (v ), and shear modulus (G) is

Answer: (A)

14. Read the following statements relating to flexure of reinforced concrete beams:

(I) In over-reinforced sections, the failure strain in concrete reaches earlier than the yield strain in steel.

(II) In under-reinforced sections, steel reaches yielding at a load lower than the

load at which the concrete reaches failure strain.

(III) Over-reinforced beams are recommended in practice as compared to the under-reinforced beams.

(IV) In balanced sections, the concrete reaches failure strain earlier than the yield strain in tensile steel.

Each of the above statements is either True or False.

Which one of the following combinations is correct?

(A) I (True), II (True), III (False), IV (False)

(B) I (True), II (True), III (False), IV (True)

(D) I (False), II (True), III (True), IV (False)

Answer: (A)

15. Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties):

Which one of the following combinations is correct?

(A) (i) – (P), (ii) – (Q) and (T), (iii) – (R) and (S)

(B) (i) – (Q) and (T), (ii) – (P) and (S), (iii) – (R)

(D) (i) – (T), (ii) – (S), (iii) – (P) and (Q)

Answer: (A)

16. Consider a beam PQ fixed at P, hinged at Q, and subjected to a load F as shown in figure (not drawn to scale). The static and kinematic degrees of indeterminacy, respectively, are

(A) 2 and 1

(B) 2 and 0

(D) 2 and 2

Answer: (A)

17. Read the following statements:

(P) While designing a shallow footing in sandy soil, monsoon season is considered for critical design in terms of bearing capacity.

(Q) For slope stability of an earthen dam, sudden drawdown is never a critical condition.

(R) In a sandy sea beach, quicksand condition can arise only if the critical hydraulic gradient exceeds the existing hydraulic gradient.

(S) The active earth thrust on a rigid retaining wall supporting homogeneous cohesionless backfill will reduce with the lowering of water table in the backfill.

Which one of the following combinations is correct?

(A) (P)-True, (Q)-False, (R)-False, (S)-False

(B) (P)-False, (Q)-True, (R)-True, (S)-True

(D) (P)-False, (Q)-True, (R)-False, (S)-False

Answer: (A)

18. Stresses acting on an infinitesimal soil element are shown in the figure (with σ_z> σ_x). The major and minor principal stresses are σ₁ and σ₃, respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane?

Answer: (A)

19. Match Column X with Column Y:

Which one of the following combinations is correct?

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

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

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

Answer: (A)

20. In a certain month, the reference crop evapotranspiration at a location is 6 mm/day. If the crop coefficient and soil coefficient are 1.2 and 0.8, respectively, the actual evapotranspiration in mm/day is

(A) 5.76

(B) 7.20

(D) 8.00

Answer: (A)

21. The dimension of dynamic viscosity is:

(A) ML⁻¹T⁻¹

(B) ML⁻¹T⁻²

(D) ML⁰T⁻¹

Answer: (A)

22. A process equipment emits 5 kg/h of volatile organic compounds (VOCs). If a hood placed over the process equipment captures 95% of the VOCs, then the fugitive emission in kg/h is

(A) 0.25

(B) 4.75

(D) 0.48

Answer: (A)

23. Match the following attributes of a city with the appropriate scale of measurements.

Which one of the following combinations is correct?

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

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

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

Answer: (A)

24. If the magnetic bearing of the Sun at a place at noon is S 2° E, the magnetic declination (in degrees) at that place is

(A) 2° E

(B) 2° W

(D) 4° W

Answer: (A)

25. P and Q are two square matrices of the same order. Which of the following statement(s) is/are correct?

(A) If P and Q are invertible, then [PQ]⁻¹ = Q⁻¹P⁻¹.

(B) If P and Q are invertible, then [QP]⁻¹ = P⁻¹Q⁻¹.

(D) If P and Q are not invertible, then [PQ]⁻¹ = Q⁻¹P⁻¹.

Answer: (A, B)

26. In a solid waste handling facility, the moisture contents (MC) of food waste, paper waste, and glass waste were found to be MCf, MCp, and MCg, respectively. Similarly, the energy contents (EC) of plastic waste, food waste, and glass waste were found to be ECpp, ECf, and ECg, respectively. Which of the following statement(s) is/are correct?

(A) MCf > MCp > MCg

(B) ECpp > ECf > ECg

(D) ECpp < ECf < ECg

Answer: (A, B)

27. To design an optimum municipal solid waste collection route, which of the following is/are NOT desired:

(A) Collection vehicle should not travel twice down the same street in a day.

(B) Waste collection on congested roads should not occur during rush hours in morning or evening.

(D) The last collection point on a route should be as close as possible to the waste disposal facility.

Answer: (C)

28. For a traffic stream, v is the space mean speed, k is the density, q is the flow, v_f is the free flow speed, and k_j is the jam density. Assume that the speed decreases linearly with density.

Which of the following relation(s) is/are correct?

Answer: (B, D)

29. The error in measuring the radius of a 5 cm circular rod was 0.2%. If the cross-sectional area of the rod was calculated using this measurement, then the resulting absolute percentage error in the computed area is______. (round off to two decimal places)

Answer: (0.39 to 0.41)

30. The components of pure shear strain in a sheared material are given in the matrix form:

Here, Trace (ε) = 0. Given P = Trace (ε⁸) and Q = Trace (ε¹¹). The numerical value of (P + Q) is ______. (in integer)

Answer: (32 to 32)

31. The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0 % to minimize the friction on the sample as the sampler tube enters into the soil.

The inside diameter (in mm) of the cutting edge is _________. (round off to two decimal places)

Answer: (49.49 to 49.52)

32. A concentrically loaded isolated square footing of size 2 m × 2 m carries a concentrated vertical load of 1000 kN. Considering Boussinesq’s theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to 10 % of the vertical load intensity will be ___________. (round off to two decimal places)

Answer: (4.35 to 4.39)

33. In a triaxial unconsolidated undrained (UU) test on a saturated clay sample, the cell pressure was 100 kPa. If the deviatoric stress at failure was 150 kPa, then the undrained shear strength of the soil is ______ kPa. (in integer)

Answer: (75 to 75)

34. A flood control structure having an expected life of n years is designed by considering a flood of return period T years. When T = n, and n → ∞, the structure’s hydrologic risk of failure in percentage is _______. (round off to one decimal place)

Answer: (63.0 to 63.5)

35. The base length of the runway at the mean sea level (MSL) is 1500 m. If the runway is located at an altitude of 300 m above the MSL, the actual length (in m) of the runway to be provided is _________. (round off to the nearest integer)

Answer: (1602 to 1606)

Q. 36 – 65 Carry TWO marks each.

36. Consider the polynomial f(x) = x³ – 6x² + 11x – 6 on the domain S given by 1 ≤ x ≤ 3. The first and second derivatives are f'(x) and f”(x).

Consider the following statements:

I. The given polynomial is zero at the boundary points x = 1 and x = 3.

II. There exists one local maxima of f(x) within the domain S.

III. The second derivative f′′(x) > 0 throughout the domain S.

IV. There exists one local minima of f(x) within the domain S.

The correct option is:

(A) Only statements I, II and III are correct.

(B) Only statements I, II and IV are correct.

(D) Only statements II and IV are correct.

Answer: (B)

37. An undamped spring-mass system with mass m and spring stiffness k is shown in the figure. The natural frequency and natural period of this system are ω rad/s and T s, respectively. If the stiffness of the spring is doubled and the mass is halved, then the natural frequency and the natural period of the modified system, respectively, are

(A) 2ω rad/s and T/2 s

(B) ω/2 rad/s and 2T s

(D) ω rad/s and T s

Answer: (A)

38. For the square steel beam cross-section shown in the figure, the shape factor about z − z axis is S and the plastic moment capacity is M_P. Consider yield stress f_y = 250 MPa and a = 100 mm.

The values of S and M_P (rounded-off to one decimal place) are

(A) S = 2.0, M_P = 58.9 kN-m

(B) S = 2.0, M_P = 100.2 kN-m

(D) S = 1.5, M_P = 100.2 kN-m

Answer: (A)

39. A post-tensioned concrete member of span 15 m and cross-section of 450 mm × 450 mm is prestressed with three steel tendons, each of cross-sectional area 200 mm². The tendons are tensioned one after another to a stress of 1500 MPa. All the tendons are straight and located at 125 mm from the bottom of the member. Assume the prestress to be the same in all tendons and the modular ratio to be 6. The average loss of prestress, due to elastic deformation of concrete, considering all three tendons is

(A) 14.16 MPa

(B) 7.08 MPa

(D) 42.48 MPa

Answer: (A)

40. Match the following in Column X with Column Y:

Which one of the following combinations is correct?

(A) (P)-(I), (Q)-(II), (R)-(V), (S)-(V)

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

(D) (P)-(I), (Q)-(II), (R)-(V), (S)-(VI)

Answer: (A)

41. A soil sample is underlying a water column of height h₁, as shown in the figure. The vertical effective stresses at points A, B, and C are σʹ_A, σʹ_B, and σʹ_C, respectively. Let γ_sat and γʹ be the saturated and submerged unit weights of the soil sample, respectively, and γ_w be the unit weight of water. Which one of the following expressions correctly represents the sum (σʹ_A + σʹ_B + σʹ_C)?

(A) (2h₂ + h₃)γʹ

(B) (h₁ + h₂ + h₃)γʹ

(D) (h₁ + h₂ + h₃)γ_sat

Answer: (A)

42. A 100 mg of HNO₃ (strong acid) is added to water, bringing the final volume to 1.0 liter. Consider the atomic weights of H, N, and O, as 1 g/mol, 14 g/mol, and 16 g/mol, respectively. The final pH of this water is

(Ignore the dissociation of water.)

(A) 2.8

(B) 6.5

(D) 8.5

Answer: (A)

43. In a city, the chemical formula of biodegradable fraction of municipal solid waste (MSW) is C₁₀₀H₂₅₀O₈₀ The waste has to be treated by forced-aeration composting process for which air requirement has to be estimated.

Assume oxygen in air (by weight) = 23 %, and density of air = 1.3 kg/m³. Atomic mass: C = 12, H = 1, O = 16, N = 14.

C and H are oxidized completely whereas N is converted only into NH₃ during oxidation.

For oxidative degradation of 1 tonne of the waste, the required theoretical volume of air (in m³/tonne) will be (round off to the nearest integer)

(A) 4749

(B) 8025

(D) 1092

Answer: (A)

44. A single-lane highway has a traffic density of 40 vehicles/km. If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) between the vehicles is

(A) 3.00

(B) 2.25

(D) 6.25 × 10⁻⁴

Answer: (A)

45. Let y be a non-zero vector of size 2022 × 1. Which of the following statement(s) is/are TRUE?

(A) yy^T is a symmetric matrix.

(B) y^Ty is an eigenvalue of yy^T.

(D) yy^T is invertible.

Answer: (A, B)

46. Which of the following statement(s) is/are correct?

(A) If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the deflection at any point is equal to the load applied at that point.

(B) If a linearly elastic structure is subjected to a set of loads, the partial derivative of the total strain energy with respect to the load at any point is equal to the deflection at that point.

(C) If a structure is acted upon by two force system P_a and P_b, in equilibrium separately, the external virtual work done by a system of forces P_b during the deformations caused by another system of forces P_a is equal to the external virtual work done by the P_a system during the deformation caused by the P_b system.

(D) The shear force in a conjugate beam loaded by the M/EI diagram of the real beam is equal to the corresponding deflection of the real beam.

Answer: (A, B, C)

47. Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section is y₂ and that at its upstream section is y₁. The correct statement(s) for the choked and unchoked conditions in the channel is/are

(A) In choked condition, y₁ decreases if the flow is supercritical and increases if the flow is subcritical.

(B) In choked condition, y₂ is equal to the critical depth if the flow is supercritical or subcritical.

(D) In choked condition, y₁ increases if the flow is supercritical and decreases if the flow is subcritical.

Answer: (A, B, C)

48. The concentration s(x,t) of pollutants in a one-dimensional reservoir at position x and time t satisfies the diffusion equation on the domain 0 ≤ x ≤ L, where D is the diffusion coefficient of the pollutants. The initial condition s(x, 0) is defined by the step-function shown in the figure.

The boundary conditions of the problem are given by at the boundary points x = 0 and x = L at all times. Consider D = 0.1 m²/s, s₀ = 5 μmol/m, and L = 10 m.

The steady-state concentration at the center x = L/2 of the reservoir (in μmol/m) is _____. (in integer)

Answer: (2 to 2)

49. A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is ______. (round off to three decimal places)

Answer: (0.018 to 0.020)

50. Consider two linearly elastic rods HI and IJ, each of length b, as shown in the figure. The rods are co-linear, and confined between two fixed supports at H and J. Both the rods are initially stress free. The coefficient of linear thermal expansion is 𝛼 for both the rods. The temperature of the rod IJ is raised by ∆T, whereas the temperature of rod HI remains unchanged. An external horizontal force P is now applied at node I. It is given that α = 10⁻⁶°C⁻¹, ∆T = 50°C, b = 2m, AE = 10⁶ The axial rigidities of the rods HI and IJ are 2AE and AE, respectively.

To make the axial force in rod HI equal to zero, the value of the external force P (in N) is _______. (round off to the nearest integer)

Answer: (47 to 53)

51. The linearly elastic planar structure shown in the figure is acted upon by two vertical concentrated forces. The horizontal beams UV and WX are connected with the help of the vertical linear spring with spring constant k = 20 kN/m. The fixed supports are provided at U and X. It is given that flexural rigidity EI = 10⁵ kN-m², P = 100 kN, and a = 5 m. Force Q is applied at the center of beam WX such that the force in the spring VW becomes zero.

The magnitude of force Q (in kN) is ________. (round off to the nearest integer)

Answer: (620 to 660)

52. A uniform rod KJ of weight w shown in the figure rests against a frictionless vertical wall at the point K and a rough horizontal surface at point J. It is given that w = 10 kN, a = 4 m and b = 3 m.

The minimum coefficient of static friction that is required at the point J to hold the rod in equilibrium is ________. (round off to three decimal places)

Answer: (0.350 to 0.400)

53. The activities of a project are given in the following table along with their durations and dependency.

The total float of the activity E (in days) is _______. (in integer)

Answer: (1 to 1)

54. A group of total 16 piles are arranged in a square grid format. The center-tocenter spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pile are 1 m and 20 m, respectively. The design capacity of each pile is 1000 kN in the vertical downward direction. The pile group efficiency (η_g) is given by

where m and n are number of rows and columns in the plan grid of pile arrangement, and

The design value of the pile group capacity (in kN) in the vertical downward direction is _______. (round off to the nearest integer)

Answer: (11000 to 11200)

55. A saturated compressible clay layer of thickness h is sandwiched between two sand layers, as shown in the figure. Initially, the total vertical stress and pore water pressure at point P, which is located at the mid-depth of the clay layer, were 150 kPa and 25 kPa, respectively. Construction of a building caused an additional total vertical stress of 100 kPa at P. When the vertical effective stress at P is 175 kPa, the percentage of consolidation in the clay layer at P is ______. (in integer)

Answer: (50 to 50)

56. A hydraulic jump takes place in a 6 m wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m³/s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is ___________. (round off to two decimal places)

(Consider the acceleration due to gravity as 10 m/s².)

Answer: (0.20 to 0.41)

57. A pump with an efficiency of 80% is used to draw groundwater from a well for irrigating a flat field of area 108 hectares. The base period and delta for paddy crop on this field are 120 days and 144 cm, respectively. Water application efficiency in the field is 80%. The lowest level of water in the well is 10 m below the ground. The minimum required horse power (h.p.) of the pump is _______. (round off to two decimal places)

(Consider 1 h.p. = 746 W; unit weight of water = 9810 N/m³ )

Answer: (30.00 to 32.00)

58. Two discrete spherical particles (P and Q) of equal mass density are independently released in water. Particle P and particle Q have diameters of 0.5 mm and 1.0 mm, respectively. Assume Stokes’ law is valid.

The drag force on particle Q will be________ times the drag force on particle P. (round off to the nearest integer)

Answer: (8 to 8)

59. At a municipal waste handling facility, 30 metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be 10%. The ideal moisture content for composting this mixture is 50%. The amount of water to be added to this mixture to bring its moisture content to the ideal condition is _______metric ton. (in integer)

Answer: (24 to 24)

60. A sewage treatment plant receives sewage at a flow rate of 5000 m³/day. The total suspended solids (TSS) concentration in the sewage at the inlet of primary clarifier is 200 mg/L. After the primary treatment, the TSS concentration in sewage is reduced by 60 %. The sludge from the primary clarifier contains 2 % solids concentration. Subsequently, the sludge is subjected to gravity thickening process to achieve a solids concentration of 6 %. Assume that the density of sludge, before and after thickening, is 1000 kg/m³.

The daily volume of the thickened sludge (in m³/day) will be_______. (round off to the nearest integer).

Answer: (10 to 10)

61. A sample of air analyzed at 25 °C and 1 atm pressure is reported to contain 0.04 ppm of SO₂. Atomic mass of S = 32, O = 16.

The equivalent SO₂ concentration (in µg/m³) will be__________. (round off to the nearest integer)

Answer: (102 to 108)

62. A parabolic vertical crest curve connects two road segments with grades +1.0% and −0%. If a 200 m stopping sight distance is needed for a driver at a height of 1.2 m to avoid an obstacle of height 0.15 m, then the minimum curve length should be ______ m. (round off to the nearest integer)

Answer: (270 to 275)

63. Assuming that traffic on a highway obeys the Greenshields model, the speed of a shockwave between two traffic streams (P) and (Q) as shown in the schematic is _______ kmph. (in integer)

Answer: (15 to 15)

64. It is given that an aggregate mix has 260 grams of coarse aggregates and 240 grams of fine aggregates. The specific gravities of the coarse and fine aggregates are 2.6 and 2.4, respectively. The bulk specific gravity of the mix is 2.3.

The percentage air voids in the mix is ____________. (round off to the nearest integer)

Answer: (8 to 8)

65. The lane configuration with lane volumes in vehicles per hour of a four-arm signalized intersection is shown in the figure. There are only two phases: the first phase is for the East-West and the West-East through movements, and the second phase is for the North-South and the South-North through movements. There are no turning movements. Assume that the saturation flow is 1800 vehicles per hour per lane for each lane and the total lost time for the first and the second phases together is 9 seconds.

The optimum cycle length (in seconds), as per the Webster’s method, is _________. (round off to the nearest integer)

Answer: (37 to 37)

GATE Exam 2022 Civil Engineering (CE-1) Question Paper With Answer Key

July 11, 2022 by suresh84

GATE-2022

CE1: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. You should _________ when to say _________.

(A) no / no

(B) no / know

(D) know / no

Answer: (D)

2. Two straight lines pass through the origin (x₀, y₀) = (0,0). One of them passes through the point (x₁, y₁) = (1,3) and the other passes through the point (x₂, y₂) = (1, 2).

What is the area enclosed between the straight lines in the interval [0, 1] on the 𝑥-axis?

(A) 0.5

(B) 1.0

(D) 2.0

Answer: (A)

3. If

p ∶ q = 1 ∶ 2

q ∶ r = 4 ∶ 3

r ∶ s = 4 ∶ 5

and u is 50% more than s, what is the ratio p ∶ u?

(A) 2 : 15

(B) 16 :15

(D) 16 : 45

Answer: (D)

4. Given the statements:

• P is the sister of Q.

• Q is the husband of R.

• R is the mother of S.

• T is the husband of P.

Based on the above information, T is ______ of S.

(A) the grandfather

(B) an uncle

(D) a brother

Answer: (B)

5. In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

(A) Area of SPQT = Area of RUVZ = Area of PXWR

(B) Area of SPQT = Area of PXWR = Area of RUVZ

(D) Area of PXWR = Area of RUVZ = Area of SPQT

Answer: (B)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Healthy eating is important for those with good health conditions, but not for others

(B) Eating healthy can be started at any age, earlier the better

(D) Healthy eating is more important for adults than kids

Answer: (B)

If at the end of that investment year, Q receives 4/9 of the total profit, what is the value of x (in Rs.) ?

(A) 2500

(B) 3000

(D) 8437

Answer: (B)

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.

From the data presented above, which one of the following is CORRECT?

(A) mean > mode > median

(B) mode > median > mean

(D) median > mode > mean

Answer: (B)

9. In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.

For example, a person at a given position Y can move only to the positions marked X on the right.

Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is

(A) 4

(B) 5

(D) 7

Answer: (B)

10.

Which one of the following represents a possible unfolding of the cube?

Answer: (MTA)

(CE Set-1) Civil Engineering

Q.11 – 35 Carry ONE mark each.

11. Consider the following expression:

z = siny(y + it) + cos(y – it)

where z, y, and t are variables, and i=√−1 is a complex number. The partial differential equation derived from the above expression is

Answer: (A)

12. For the equation

the correct description is

(A) an ordinary differential equation of order 3 and degree 2.

(B) an ordinary differential equation of order 3 and degree 3.

(D) an ordinary differential equation of order 3 and degree 3/2.

Answer: (A)

13. The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is

(A) 7.5 MPa

(B) 15.0 MPa

(D) 22.5 MPa

Answer: (A OR B)

14. In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of

(A) Young’s modulus of elasticity of reinforcement material to Young’s modulus of elasticity of concrete.

(B) Young’s modulus of elasticity of concrete to Young’s modulus of elasticity of reinforcement material

(D) Young’s modulus of elasticity of reinforcement material to the shear modulus of concrete

Answer: (A)

15. Which of the following equations is correct for the Pozzolanic reaction?

(A) Ca(OH)2 + Reactive Superplasticiser + H2O → C-S-H

(B) Ca(OH)₂ + Reactive Silicon dioxide + H2O → C-S-H

(D) Ca(OH)₂ + Reactive Sulphur + H₂O → C-S-H

Answer: (B)

16. Consider the cross-section of a beam made up of thin uniform elements having thickness t (t << a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure.

The coordinates of the shear center of this cross-section are:

(A) x = 0, y = 3a

(B) x = 2a, y = 2a

(D) x = −2a, y = a

Answer: (A)

17. Four different soils are classified as CH, ML, SP, and SW, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement in the decreasing order of hydraulic conductivity?

(A) SW, SP, ML, CH

(B) CH, ML, SP, SW

(D) ML, SP, CH, SW

Answer: (A)

18. Let σ’_v and σ’_h denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankine’s passive earth pressure condition?

(A) σ’_v < σ’_h

(B) σ’_v > σ’_h

(D) σ’_v + σ’_h = 0

Answer: (A)

19. With respect to fluid flow, match the following in Column X with Column Y:

Which one of the following combinations is correct?

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

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

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

Answer: (A)

20. Let Ψ represent soil suction head and K represent hydraulic conductivity of the soil. If the soil moisture content θ increases, which one of the following statements is TRUE?

(A) Ψ decreases and K increases.

(B) Ψ increases and K decreases.

(D) Both Ψ and K increase.

Answer: (A)

21. A rectangular channel with Gradually Varied Flow (GVF) has a changing bed slope. If the change is from a steeper slope to a steep slope, the resulting GVF profile is

(A) S₃

(B) S₁

(D) either S₁ or S₂, depending on the magnitude of the slopes

Answer: (A)

22. The total hardness in raw water is 500 milligram per liter as CaCO₃. The total hardness of this raw water, expressed in milligram equivalent per liter, is

(Consider the atomic weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol, respectively.)

(A) 10

(B) 100

(D) 5

Answer: (A)

23. An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean sea level, then the scale of the photograph is

(A) 1 : 20000

(B) 1 : 20

(D) 1 :

Answer: (A)

24. A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m

The corrected horizontal length (in m) of the line PQ will be

(A) 342.52

(B) 349.30

(D) 350.70

Answer: (A)

25. The matrix M is defined as

and has eigenvalues 𝟓 and − 𝟐. The matrix Q is formed as Q = M³ – 4M² – 2M

Which of the following is/are the eigenvalue(s) of matrix Q ?

(A) 15

(B) 25

(D) −30

Answer: (A, C)

26. For wastewater coming from a wood pulping industry, Chemical Oxygen Demand (COD) and 5-day Biochemical Oxygen Demand (BOD₅) were determined. For this wastewater, which of the following statement(s) is/are correct?

(A) COD > BOD₅

(B) COD ≠ BOD₅

(D) COD = BOD₅

Answer: (A, B)

27. Which of the following process(es) can be used for conversion of salt water into fresh water?

(A) Microfiltration

(B) Electrodialysis

(D) Reverse osmosis

Answer: (B, D)

28. A horizontal curve is to be designed in a region with limited space. Which of the following measure(s) can be used to decrease the radius of curvature?

(A) Decrease the design speed.

(B) Increase the superelevation.

(D) Restrict vehicles with higher weight from using the facility.

Answer: (A, B)

29. Consider the following recursive iteration scheme for different values of variable 𝑃 with the initial guess x₁ = 1

For P = 2 x₅ is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x₅ is obtained to be 1.732, rounded-off to three decimal places.

If P = 10, the numerical value of x₅ is ______. (round off to three decimal places)

Answer: (3.100 to 3.200)

30. The Fourier cosine series of a function is given by:

For f(x) = cos⁴x, the numerical value of (f₄ + f₅) is ______. (round off to three decimal places)

Answer: (0.120 to 0.130)

31. An uncompacted heap of soil has a volume of 10000 m³ and void ratio of 1. If the soil is compacted to a volume of 7500 m³, then the corresponding void ratio of the compacted soil is ________.(round off to one decimal place)

Answer: (0.5 to 0.5)

32. A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is ________. (in integer)

Answer: (4 to 4)

33. At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance q_c was 1000 kPa at a certain depth. The friction ratio (f_r) was estimated as 1 % at the same depth.

The value of sleeve (side) friction (in kPa) at that depth was _________. (in integer)

Answer: (10 to 10)

34. During a particular stage of the growth of a crop, the consumptive use of water is 2.8 mm/day. The amount of water available in the soil is 50 % of the maximum depth of available water in the root zone. Consider the maximum root zone depth of the crop as 80 mm and the irrigation efficiency as 70 %.

The interval between irrigation (in days) will be _______. (round off to the nearest integer)

Answer: (MTA)

35. The bearing of a survey line is N31°17ʹW. Its azimuth observed from north is ______ deg. (round off to two decimal places)

Answer: (328.60 to 328.80)

Q.36 – 65 Carry TWO marks each.

36. The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45° clockwise rotation of the coordinate system about the positive x-axis are

(A) (1, 0, √2)

(B) (1, 0, −√2)

(D) (−1, 0, −√2)

Answer: (A)

37. A semi-circular bar of radius R m, in a vertical plane, is fixed at the end G, as shown in the figure. A horizontal load of magnitude P kN is applied at the end H. The magnitude of the axial force, shear force, and bending moment at point Q for θ = 45°, respectively, are

Answer: (A)

38. A weld is used for joining an angle section ISA 100 mm × 100 mm × 10 mm to a gusset plate of thickness 15 mm to transmit a tensile load. The permissible stress in the angle is 150 MPa and the permissible shear stress on the section through the throat of the fillet weld is 108 MPa. The location of the centroid of the angle is represented by C_yy in the figure, where C_yy = 28.4 mm. The area of cross-section of the angle is 1903 mm². Assuming the effective throat thickness of the weld to be 0.7 times the given weld size, the lengths L₁ and L₂ (rounded off to the nearest integer) of the weld required to transmit a load equal to the full strength of the tension member are, respectively

(A) 541 mm and 214 mm

(B) 214 mm and 541 mm

(D) 151 mm and 380 mm

Answer: (A)

39. The project activities are given in the following table along with the duration and dependency

Which one of the following combinations is correct?

(A) Total duration of the project = 22 days, Critical path is Q → S

(B) Total duration of the project = 20 days, Critical path is Q → T

(D) Total duration of the project = 20 days, Critical path is P → R

Answer: (A)

40. The correct match between the physical states of the soils given in Group I and the governing conditions given in Group II is

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

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

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

Answer: (A)

41. As per Rankine’s theory of earth pressure, the inclination of failure planes is with respect to the direction of the minor principal stress..

The above statement is correct for which one of the following options?

(A) Only the active state and not the passive state

(B) Only the passive state and not the active state

(D) Neither active nor passive state

Answer: (C)

42. Henry’s law constant for transferring O₂ from air into water, at room temperature, is 1.3 Given that the partial pressure of O₂ in the atmosphere is 0.21 atm, the concentration of dissolved oxygen (mg/liter) in water in equilibrium with the atmosphere at room temperature is

(Consider the molecular weight of O₂ as 32 g/mol)

(A) 8.7

(B) 0.8

(D) 0.2

Answer: (A)

43. In a water sample, the concentrations of Ca²⁺, Mg²⁺ and HCO⁻₃ are 100 mg/L, 36 mg/L and 122 mg/L, respectively. The atomic masses of various elements are: Ca = 40, Mg = 24, H = 1, C = 12, O = 16.

The total hardness and the temporary hardness in the water sample (in mg/L as CaCO₃) will be

(A) 400 and 100, respectively.

(B) 400 and 300, respectively.

(D) 800 and 200, respectively.

Answer: (A)

44. Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by k_P. k_Q, k_R, and k_S, respectively. The correct order of these densities is

(A) k_P > k_Q > k_R > k_S

(B) k_S > k_R > k_Q > k_P

(D) k_Q > k_R > k_P > k_S

Answer: (A)

45. Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statement(s) is/are TRUE about the function f(x) = max{3 − x, x − 1} ?

(A) It is continuous on its domain

(B) It has a local minimum at x = 2.

(D) It is differentiable on its domain.

Answer: (A, B)

46. A horizontal force of P kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the following statement(s) is/are correct?

(A) The motion of the body will occur by overturning.

(B) Sliding of the body never occurs.

(D) The motion of the body will occur by sliding only.

Answer: (A, C OR A, B, C)

47. In the context of cross-drainage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/are

(A) In an aqueduct, natural drain water goes under the irrigation canal, whereas in a super-passage, natural drain water goes over the irrigation canal.

(B) In a level crossing, natural drain water goes through the irrigation canal

(C) In an aqueduct, natural drain water goes over the irrigation canal, whereas in a super-passage, natural drain water goes under the irrigation canal.

(D) In a canal syphon, natural drain water goes through the irrigation canal.

Answer: (A, B)

48. Consider the differential equation

For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is _________. (round off to one decimal place)

Answer: (6.3 to 6.5)

49. A set of observations of independent variable (x) and the corresponding dependent variable (y) is given below

Based on the data, the coefficient a of the linear regression model y = a + bx is estimated as 6.1.

The coefficient b is ______________ . (round off to one decimal place)

Answer: (1.9 to 1.9)

50. The plane truss shown in the figure is subjected to an external force P. It is given that P = 70 kN, a = 2 m, and b = 3 m.

The magnitude (absolute value) of force (in kN) in member EF is _______. (round off to the nearest integer)

Answer: (28 to 32)

51. Consider the linearly elastic plane frame shown in the figure. Members HF, FK and FG are welded together at joint F. Joints K, G and H are fixed supports. A counter-clockwise moment M is applied at joint F. Consider flexural rigidity EI = 10⁵ kN-m² for each member and neglect axial deformations.

If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment M (in kN-m) to maintain static equilibrium is ___________. (round off to the nearest integer)

Answer: (57 to 63)

52. Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is _________ kNm. (in integer)

Answer: (180 to 180)

53. A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of Fe 415 grade steel. The design shear strength for this beam is 0.66 N/mm². The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of Fe 415 grade steel is __________mm. (round off to the nearest integer)

Answer: (100 to 102)

54. A square concrete pile of 10 m length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is _______ mm. (in integer)

(Bearing capacity factor N_c = 9; adhesion factor α = 0.7)

Answer: (400 to 400)

55. A raft foundation of 30 m × 25 m is proposed to be constructed at a depth of 8 m in a sand layer. A 25 m thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50 % consolidation settlement in 10 minutes.

The time (in days) required for 25 % consolidation settlement of the raft foundation will be ________. (round off to the nearest integer)

Answer: (1730 to 1740)

56. A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of stream flow hydrograph resulting from this event are given in the table.

Considering a constant baseflow of 10 m³/s, the peak flow ordinate (in m³ /s) of one-hour unit hydrograph for the watershed is ________. (in integer)

Answer: (12 to 12)

57. Two reservoirs are connected by two parallel pipes of equal length and of diameters 20 cm and 10 cm, as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is 5 m, the ratio of discharge in the larger diameter pipe to the discharge in the smaller diameter pipe is _________. (round off to two decimal places)

(Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)

Answer: (5.60 to 5.70)

58. Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m³/s. Take g = 9.8 m/s².

The bed width (in m) at contraction, which just causes the critical flow, is _______ without changing the upstream water level. (round off to two decimal places)

Answer: (2.05 to 2.35)

59. A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of N, H, and O as 14 g/mol, 1 g/mol, and 16 g/mol, respectively. In this wastewater, the concentration of ammonia is 34 mg NH₃/liter and that of nitrate is 6.2 mg NO₃⁻/liter. The total nitrogen concentration in this wastewater is _______ milligram nitrogen per liter. (round off to one decimal place)

Answer: (29.0 to 30.0)

60. A 2 % sewage sample (in distilled water) was incubated for 3 days at 27 °C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxygen demand (BOD) rate constant at 27 °C was found to be 0.23 day⁻¹ (at base e).

The ultimate BOD (in mg/L) of the sewage will be__________. (round off to the nearest integer)

Answer: (1000 to 1005)

61. A water treatment plant has a sedimentation basin of depth 3 m, width 5 m, and length 40 m. The water inflow rate is 500 m³/h. The removal fraction of particles having a settling velocity of 1.0 m/h is_______. (round off to one decimal place)

(Consider the particle density as 2650 kg/m³ and liquid density as 991 kg/m³)

Answer: (0.38 to 0.42)

62. A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase due to start-up and clearance is 2 s, the effective green time of each phase is ______s. (in integer)

Answer: (48 to 48)

63. At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is ______. (round off to two decimal places)

Answer: (0.78 to 0.82)

64. The vehicle count obtained in every 10 minute interval of a traffic volume survey done in peak one hour is given below.

The peak hour factor (PHF) for 10 minute sub-interval is _______.

(round off to one decimal place)

Answer: (0.8 to 0.8)

65. For the dual-wheel carrying assembly shown in the figure, P is the load on each wheel, a is the radius of the contact area of the wheel, s is the spacing between the wheels, and d is the clear distance between the wheels. Assuming that the ground is an elastic, homogeneous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth z = d/2 to the ESWL at depth z = 2s is ________. (round off to one decimal place)

(Consider the influence angle to be 45° for the linear dispersion of stress with depth)

Answer: (0.5 to 0.5)

GATE Exam 2022 Biotechnology (BT) Question Paper With Answer Key

July 11, 2022 by suresh84

GATE-2022

BT: Biotechnology

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. You should _________ when to say _________.

(A) no / no

(B) no / know

(D) know / no

Answer: (D)

2. Two straight lines pass through the origin (x₀, y₀) = (0,0). One of them passes through the point (x₁, y₁) = (1,3) and the other passes through the point (x₂, y₂) = (1, 2).

What is the area enclosed between the straight lines in the interval [0, 1] on the 𝑥-axis?

(A) 0.5

(B) 1.0

(D) 2.0

Answer: (A)

3. If

p ∶ q = 1 ∶ 2

q ∶ r = 4 ∶ 3

r ∶ s = 4 ∶ 5

and u is 50% more than s, what is the ratio p ∶ u?

(A) 2 : 15

(B) 16 :15

(D) 16 : 45

Answer: (D)

4. Given the statements:

• P is the sister of Q.

• Q is the husband of R.

• R is the mother of S.

• T is the husband of P.

Based on the above information, T is ______ of S.

(A) the grandfather

(B) an uncle

(D) a brother

Answer: (B)

5. In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

(A) Area of SPQT = Area of RUVZ = Area of PXWR

(B) Area of SPQT = Area of PXWR = Area of RUVZ

(D) Area of PXWR = Area of RUVZ = Area of SPQT

Answer: (B)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Healthy eating is important for those with good health conditions, but not for others

(B) Eating healthy can be started at any age, earlier the better

(D) Healthy eating is more important for adults than kids

Answer: (B)

If at the end of that investment year, Q receives 4/9 of the total profit, what is the value of x (in Rs.) ?

(A) 2500

(B) 3000

(D) 8437

Answer: (B)

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.

From the data presented above, which one of the following is CORRECT?

(A) mean > mode > median

(B) mode > median > mean

(D) median > mode > mean

Answer: (B)

9. In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.

For example, a person at a given position Y can move only to the positions marked X on the right.

Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is

(A) 4

(B) 5

(D) 7

Answer: (B)

10.

Which one of the following represents a possible unfolding of the cube?

Answer: (MTA)

Biotechnology

Q.11 – Q.35 Carry ONE mark each.

11. What is the order of the differential equation given below?

(A) 1

(B) 2

(D) 4

Answer: (B)

12. If the eigenvalues of a 2×2 matrix P are 4 and 2, then the eigenvalues of the matrix P⁻¹ are

(A) 0, 0

(B) 0.0625, 0.25

(D) 2, 4

Answer: (C)

13. For a double-pipe heat exchanger, the inside and outside heat transfer coefficients are 100 and 200 W m⁻² K⁻¹, respectively. The thickness and thermal conductivity of the thin-walled inner pipe are 1 cm and 10 W m⁻¹ K⁻¹, respectively. The value of the overall heat transfer coefficient is _______ W m-2 K⁻¹.

(A) 0.016

(B) 42.5

(D) 310

Answer: (C)

14. Match the media component (Column I) with its role (Column II).

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

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

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

Answer: (D)

15. The binding free energy of a ligand to its receptor protein is −11.5 kJ mol⁻¹ at 300 K. What is the value of the equilibrium binding constant?

User R = 8.314 J mol⁻¹K⁻¹.

(A) 0.01

(B) 1.0

(D) 100.5

Answer: (D)

16. The overall stoichiometry for an aerobic cell growth is

3C₆H₁₂O₆ + 2.5NH₃ + O₂ → 1.5C_aH_bO_cN_d + 3CO₂ + 5H₂O

What is the elemental composition formula of the biomass?

(A) C₉H_18.2O₅N_1.667

(B) C₉H_22.33O₆N_1.667

(D) C₁₀H_22.33O₆N_1.667

Answer: (D)

17. In binomial nomenclature, the name of a bacterial strain is written with the first letter of ______ word(s) being capitalized.

(A) first

(B) second

(D) first and second

Answer: (A)

18. The type of nucleic acid present in λ-phage is

(A) Double stranded DNA

(B) Single stranded circular DNA

(D) Single stranded RNA

Answer: (A)

19. Which of the following statements about reversible enzyme inhibitors are CORRECT?

(P) Uncompetitive inhibitors bind only to the enzyme-substrate complex

(Q) Non-competitive inhibitors bind only at a different site from the substrate

(R) Competitive inhibitors bind to the same site as the substrate

(A) P and Q only

(B) P and R only

(D) P, Q and R

Answer: (D)

20. Match the component of eukaryotic cells (Column I) with its respective function (Column II).

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

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

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

Answer: (A)

21. In animal cells, the endogenously produced miRNAs silence gene expression by

(A) base pairing with the 3′-untranslated region of specific mRNAs

(B) blocking mRNA synthesis

(D) base pairing with the 3′ region of specific rRNAs

Answer: (A)

22. Terpenoids are made of ________ units

(A) amino acid

(B) carbohydrate

(D) triacylglycerol

Answer: (C)

23. Match the microbial product (Column I) with its respective application (Column II).

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

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

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

Answer: (D)

24. Which of the following is NOT used for generating an optimal alignment of two nucleotide sequences?

(A) Gap penalties

(B) Match scores

(D) Nucleotide composition

Answer: (D)

25. The recognition sequences of four Type-II restriction enzymes (RE) are given below. The symbol (↓) indicates the cleavage site. Identify the RE that generates sticky ends.

(A) RE1 – 5̍ G↓GATCC 3̍

(B) RE2 – 5̍ CTG↓CAG 3̍

(D) RE4 – 5̍ AG↓CT 3̍

Answer: (A)

26. Among individuals in a human population, minor variations exist in nucleotide sequences of chromosomes. These variations can lead to gain or loss of sites for specific restriction enzymes. Which of the following technique is used to identify such variations?

(A) Polymerase dependent fragment insertion

(B) Real-time polymerase chain reaction

(D) Reverse transcriptase polymerase chain reaction

Answer: (C)

27. Assuming independent assortment and no recombination, the number of different combinations of maternal and paternal chromosomes in gametes of an organism with a diploid number of 12 is _________.

Answer: (64 to 64)

28. A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is 0.5 The initial concentrations of biomass and substrate are 2 g L⁻¹ and 200 g L⁻¹, respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is ______ g L⁻¹.

Answer: (102 to 102)

29. The degree of reduction of lactic acid (C₃H₆O₃) is _________.

Answer: (4 to 4)

30. Consider a nonlinear algebraic equation, xlnx + x − 1 = 0. Using the Newton-Raphson method, with the initial guess of x₀ = 3, the value of 𝑥 after one iteration (rounded off to one decimal place) is _______.

Answer: (1.2 to 1.4)

31. The probability density function of a random variable X is p(x) = 2e⁻^2x_.The probability P(1 ≤ X ≤ 2) (rounded off to two decimal places) is _______.

Answer: (0.11 to 0.13)

32. The maximum value of the function f (x) = 3x² − 2x³ for x > 0 is _____.

Answer: (1 to 1)

33. The specific growth rate of a yeast having a doubling time of 0.693 h (rounded off to nearest integer) is_______h⁻¹.

Answer: (1 to 1)

34. A fermentation broth of density 1000 kg m⁻³ and viscosity 10⁻³ kg m⁻¹ s⁻¹ is mixed in a 100 L fermenter using a 0.1 m diameter impeller, rotating at a speed of 2 s⁻¹.The impeller Reynolds number is _______.

Answer: (20000 to 20000)

35. For a pure species, the slope of the melting line at −2°C is −0665 × 10⁶ Pa K⁻¹.

The difference between the molar volumes of the liquid and solid phase at −2°C −4.5 × 10⁻⁶ m³mol⁻¹.

The value of the latent heat of fusion (rounded off to nearest integer) is ________ J mol⁻¹.

Answer: (6067 to 6223)

Q.36 – Q.65 Carry TWO marks each.

36. Which of the following conditions will contribute to the stability of a gene pool in a natural population?

(P) Large population

(Q) No net mutation

(R) Non-random mating

(S) No selection

(A) P only

(B) P and Q only

(D) P,Q and S only

Answer: (D)

37. Match the media component used in mammalian cell culture (Column I) with its respective role (Column II).

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

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

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

Answer: (A)

38. Match the cell type (Column I) with its function (Column II)

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

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

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

Answer: (B)

39. A 2×2 matrix P has an eigenvalue λ₁ = 2 with eigvenvector and another eigenvalue λ₂ = 5, with eigenvector The matrix P is

Answer: (B)

40. Match the stationary phase (Column I) with its corresponding chromatography technique (Column II).

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

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

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

Answer: (B)

41. Which of the following statements are CORRECT for a controller?

(P) In a proportional controller, a control action is proportional to the error

(Q) In an integral controller, a control action is proportional to the derivative of the error

(R) There is no “offset” in the response of the closed-loop first-order process with a proportional controller

(S) There is no “offset” in the response of the closed-loop first-order process with a proportional-integral controller

(A) P and Q only

(B) P and R only

(D) Q and S only

Answer: (C)

42. Which of the following are CORRECT about protein structure?

(P) Secondary structure is formed by a repeating pattern of interactions among the polypeptide backbone atoms

(Q) Tertiary structure is the three-dimensional arrangement of the polypeptide backbone atoms only

(R) Quaternary structure refers to an assembly of multiple polypeptide subunits

(A) P and Q only

(B) P and R only

(D) P, Q and R

Answer: (B)

43. The enzymes involved in ubiquitinylation of cell-cycle proteins are

(A) E₁ and E₂ only

(B) E₁ and E₃ only

(D) E₁, E₂ and E₃

Answer: (D)

44. The maximum parsimony method is used to construct a phylogenetic tree for a set of sequences. Which one of the following statements about the method is CORRECT?

(A) It predicts the tree that minimizes the steps required to generate the observed variations

(B) It predicts the tree that maximizes the steps required to generate the observed variations

(D) It employs probability calculations to identify the tree

Answer: (A)

45. Which of the following spectroscopic technique(s) can be used to identify all the functional groups of an antibiotic contaminant in food?

(P) Infrared

(Q) Circular dichroism

(R) Nuclear magnetic resonance

(S) UV-Visible

(A) P only

(B) P and R only

(D) P, Q, R and S

Answer: (B)

46. Adenine can undergo a spontaneous change to hypoxanthine in a cell, leading to a DNA base pair mismatch. The CORRECT combination of enzymes that are involved in repairing this damage is

(A) Nuclease, DNA polymerase, DNA ligase

(B) Nuclease, DNA ligase, helicase

(D) Primase, helicase, DNA polymerase

Answer: (A)

47. Consider the ordinary differential equation If y(1) = 1, the value(s) of y(1.5) , using the Euler’s implicit method [y_n+1 = y_n + hf(x_n+1, y_n+1)] with a step size of h =0.5 is (are)

(A) −1 − 5√0.3

(B) −1 + 5√0.3

(D) 1 – 5√0.3

Answer: (A, B)

48. Which of the following statements are CORRECT for an enzyme entrapped in a spherical particle?

(A) Effectiveness factor is ratio of the reaction rate with diffusion-limitation to the reaction rate without diffusion-limitation

(B) Internal diffusion is rate-limiting at low values of Thiele modulus

(D) Internal diffusion-limitation can be reduced by decreasing the size of the particle

Answer: (A, C, D)

49. Which of the following is(are) COMMON feature(s) for both aerobic and anaerobic bacterial cultures?

(A) Glycolysis

(B) NAD⁺ is the oxidising agent

(D) Two net ATP molecules formed per glucose molecule

Answer: (A, B)

50. Which of the following plot(s) is(are) CORRECT for an enzyme that obeys Michaelis-Menten kinetics, assuming [S] << K_m ?

[S] is the concentration of the substrate, K_m is the Michaelis constant, and v₀ is the initial reaction velocity.

Answer: (A, D)

51. Which of the following statement(s) is(are) CORRECT regarding the lac operon in E. coli when grown in the presence of glucose and lactose?

(A) At low glucose level, the operon is activated

(B) At high glucose level, the operon is activated to enable the utilization of lactose

(D) Binding of lactose to the lac repressor induces the operon

Answer: (A, C)

52. Emerging viruses such as SARS-CoV2 cause epidemics. Which of the following process(es) contribute to the rise of such viruses?

(A) Mutation of existing virus

(B) Jumping of existing virus from current to new hosts

(D) Replication of virus outside a host

Answer: (A, B, C)

53. Introduction of foreign genes into plant cells can be carried out using

(A) Agrobacterium

(B) CaCl₂ mediated plasmid uptake

(D) Gene gun

Answer: (A, C, D)

54. Which of the following statement(s) regarding trafficking in eukaryotic cells is(are) CORRECT?

(A) Dynamin binds GTP and is involved in vesicle budding

(B) Dynamin is involved in cytoskeletal remodelling

(D) Dynein binds GTP and is involved in movement of organelles along microtubules

Answer: (A, C)

55. Consider a random variable X with mean μ_x = 0.1 and variance σ_X² = 0.2 A. A new random variable Y = 2X + 1 is defined. The variance of the random variable Y (rounded off to one decimal place) is ________.

Answer: (0.8 to 0.8)

56. For x₁ > 0 and x₂ > 0, the value of is ________.

Answer: (1 to 1)

57. Figure below depicts simplified metabolic and transport reactions taking place in the production of B from A in a cell. The subscript ‘i’ refers to intracellular metabolites. r_j is the jth reaction flux in Under pseudo-steady-state condition, the following reaction fluxes are available.

r₁ = 4, r₃ = 1 and r₆ = 1.

The transport flux of B, r₄, is ________

Answer: (2 to 2)

58. The amount of biomass in a reactor at the end of the batch process is 50 g. Fedbatch operation is initiated by feeding the substrate solution at a constant rate of 1 L h-1. The concentration of substrate in the feed is 50 g L⁻¹. The maximum biomass yield Assuming the system is at quasi-steady state, the maximum amount of biomass after 5 h of feeding is _______ g.

Answer: (150 to 150)

59. An enzyme catalyzes the conversion of substrate A into product B. The rate equation for this reaction is . Substrate A at an initial concentration of 10 mol L-1 enters an ideal mixed flow reactor (MFR) at a flow rate of 10 L min⁻¹. The volume of the MFR required for 50% conversion of substrate to product is ________ L.

Answer: (100 to 100)

60. Liquid-phase mass transfer coefficient (k_L) is measured in a stirred tank vessel using steady-state method by sparging air. Oxygen uptake by the microorganism is measured. The bulk concentration of O₂ is 10⁻⁴ mol L⁻¹. Solubility of O2 in water at 25°C is 10⁻³ mol L⁻¹.

If the oxygen consumption rate is 9×10⁻⁴ mol L⁻¹ s⁻¹, and interfacial area is 100 m²/m³, the value of kL is __________cm s⁻¹.

Answer: (1 to 1)

61. Consider a piston-cylinder assembly shown in the figure below. The walls of the cylinder are insulated. The cylinder contains 1 mole of an ideal gas at 300 K and the piston is held initially at the position z₁ using a stopper. After the stopper is removed, the piston suddenly rises against atmospheric pressure (1.013×10⁵ Pa) to the new position z₂ where it is held by another stopper.

The heat capacity (C_v) of the gas is 12.5 J mol⁻¹ K⁻¹. The cross-sectional area of the cylinder is 10⁻³ m². Assume the piston is weightless and frictionless.

If z₂ – z₁ = 1 m, the final temperature of the gas (rounded off to nearest integer) is _______K.

Answer: (291 to 293)

62. Consider the growth of S. cerevisiae under aerobic condition in a bioreactor and the specific growth rate of yeast is 0.5 h⁻¹. The overall reaction of the process is 2C₆H₁₂O₆ +0.2NH₃+10.35O₂ → CH₈O_0.5N_0.2+0.2C₂H₆O+10.6CO₂+10.8H₂O

The heat of combustion values for different compounds are tabulated below with the reference to CO₂, H₂O, O₂, and N₂ at standard conditions.

The specific rate of heat production (rounded off to nearest integer) is ________ kJ mol⁻¹ h⁻¹.

Answer: (2420 to 2430)

63. A pilot sterilization was carried out in a vessel containing 100 m³ medium with an initial spore concentration of 10⁸ spores/ml. The accepted level of contamination after sterilization is 1 spore in the entire vessel. The specific death rate constant for the spore is 2 min⁻¹ at 121° Assuming no death takes place during the heating and cooling cycles, the holding time at 121°C (rounded off to nearest integer) is _______min.

Answer: (17 to 19)

64. A circular plasmid has three different but unique restriction sites for enzymes ‘a’, ‘b’ and ‘c.’ When enzymes ‘a’ and ‘b’ are used together, two fragments of equal size are generated. Enzyme ‘c’ creates fragments of equal size only from one of the fragments generated by those cleaved by ‘a’ and ‘b’. The plasmid is treated with a mixture of ‘a’, ‘b’ and ‘c’ and analysed by agarose gel electrophoresis. The number of bands observed in the gel is _______.

Answer: (2 to 2)

65. A bacterial strain is grown in nutrient medium at 37°C under aerobic conditions. The medium is inoculated with 10² cells from a seed culture. If the number of cells in the culture is 10⁵ after 10 hours of growth, the doubling time of the strain (rounded off to nearest integer) is _______h.

Answer: (1 to 1)

GATE Exam 2022 Biomedical Engineering (BM) Question Paper With Answer Key

July 11, 2022 by suresh84

GATE-2020

BM: Biomedical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The _________ is too high for it to be considered _________.

(A) fair / fare

(B) faer / fair

(D) fare / fair

Answer: (D)

2. A function y(x) is defined in the interval [0, 1] on the x-axis as

Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

(A) 5/6

(B) 6/5

(D) 6/13

Answer: (C)

3. Let r be a root of the equation x² + 2x + 6 = 0.

Then the value of the expression (r + 2)(r + 3)(r + 4)(r + 5) is

(A) 51

(B) −51

(D) −126

Answer: (D)

4. Given below are four statements.

Statement 1: All students are inquisitive.

Statement 2: Some students are inquisitive.

Statement 3: No student is inquisitive.

Statement 4: Some students are not inquisitive.

From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

(A) Statement 1 and Statement 3

(B) Statement 1 and Statement 2

(D) Statement 3 and Statement 4

Answer: (A)

5. A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.

Answer: (B)

Which one of the following is the CORRECT logical inference based on the information in the above passage?

(A) Metrics are useful in organizations with poor work culture

(B) Metrics are useful in organizations with good work culture

(D) Metrics are never useful in organizations with good work culture

Answer: (B)

Which one of the following is the correct logical inference based on the information provided in the above passage?

(A) Equal number of boys and girls qualified

(B) Equal number of boys and girls appeared for the test

(D) The number of boys who qualified the test is less than the number of girls who qualified

Answer: (D)

First ball is drawn. What is the probability of getting an orange ball in the next draw?

(A) 1/2

(B) 8/25

(D) 23/50

Answer: (D)

9. The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:

• The line joining P and R is parallel to the line joining Q and S.

• P is placed on the side opposite to the corner T.

• S and U cannot be placed on the same side.

Which one of the following statements is correct based on the above information?

(A) P cannot be placed at a corner

(B) S cannot be placed at a corner

(D) R cannot be placed at a corner

Answer: (B)

What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.

(A) 2

(B) 4

(D) 3

Answer: (D)

Biomedical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. If the given matrices satisfy A² = kA – 2I, the value of coefficient k is ______.

(A) 1

(B) 2

(D) 4

Answer: (A)

12. Evaluation of the integral results in

(A) sin⁻¹(x – 1) + c

(B) cos⁻¹(x – 1) + c

(C)

(D)

Answer: (A)

13. If identify the INVALID operation on

Answer: (B)

14. x(t) is a real continuous-time signal whose magnitude frequency response (|X(jω)|) is shown below. After sampling x(t) at 100 rad.s⁻¹, the spectral point P is down-converted to ________ rad.s⁻¹ in the spectrum of the sampled signal.

(A) 12.5

(B) 25

(D) 37.5

Answer: (D)

15. Discrete signals x[n] and y[n] are shown below. The cross-correlation r_xy [0] is ______.

(A) 2√2

(B) 1/2√2

(D) 1/√2

Answer: (B)

16. In the circuit diagram shown below, the logic gates operate with a supply voltage of 1 V. NAND and XNOR have 200 ps and 400 ps input-to-output delay, respectively.

At time t = T, A(t) = 0, B(t) = 1 and Z(t) = 0. When the inputs are changed to A(t) = 1, B(t) = 0 at t = 2T, a 1 V pulse is observed at 𝑍. The pulse width ofthe 1 V pulse is _________ ps.

(A) 100

(B) 200

(D) 600

Answer: (B)

17. Input bits X and Y are added by using the combinational logic as shown below. S represents the sum of the two bits. For a correct implementation of the sum, the signals D₀, D₁, D₂, D₃ are ________, respectively.

(A) 1, 0, 0, 1

(B) 0, 1, 0, 1

(D) 0, 1, 1, 0

Answer: (A)

18. The time delay between the peaks of the voltage signals v₁(t) = 2cos(6t + 60°) and v₂(t) = −3 sin (6t) is ______ s.

(A) 300π/360

(B) 10π/360

(D) 200π/360

Answer: (C)

19. For the balanced Owen-bridge circuit shown in the figure, the values of L_x and R_x are:

Answer: (B)

20. Myopia occurs when the focal point falls ________ the retina. This can be corrected using a _______ lens.

(A) in front of, convex

(B) behind, convex

(D) behind, concave

Answer: (C)

21. Choose the correct sequence for the direction of blood flow in a healthy human being starting and ending with the left ventricle.

(A) Left ventricle → Aorta → Systemic arteries → Systemic veins → Vena cavae →Pulmonary vein → Pulmonary artery → Right ventricle → Left ventricle

(B) Left ventricle → Aorta → Systemic arteries → Systemic veins → Vena cavae →Right ventricle → Pulmonary artery → Pulmonary vein → Left ventricle

(C) Left ventricle → Systemic arteries → Aorta → Systemic veins → Right ventricle →Pulmonary artery → Pulmonary vein → Left ventricle

(D) Left ventricle → Aorta → Systemic arteries → Vena cavae → Systemic veins →Right ventricle → Pulmonary artery → Pulmonary vein → Left ventricle

Answer: (B)

22. In a healthy adult, which one of the following regions of the brain contains primarily white matter?

(A) Cerebral cortex

(B) Basal ganglia

(D) Corpus callosum

Answer: (D)

23. Skeletal muscles are recruited to lift loads. If the force generated in the muscle due to contraction is not sufficient to lift the load, it is known as _____ contraction.

(A) Isometric

(B) Isotonic

(D) Isoinertial

Answer: (A)

24. Backscattered electron detector of a scanning electron microscope is used to

(A) study surface topography of the sample

(B) quantify surface roughness

(D) contrast areas with different chemical compositions

Answer: (D)

25. In the process of obtaining a Magnetic Resonance Image (MRI), the terms T1 and T2 time constants of the material are very crucial to decide on getting suitable

weighted images. Choose the correct explanation relating to these two constants

from the following options.

(A) T1 is the spin-lattice or longitudinal relaxation time, and T2 is the spin-spin or transverse relaxation time

(B) T1 and T2 indicate the durations that Free Induction Decay (FID) signal to be recorded in x and y axes directions, respectively

(C) T1 and T2 refer to the durations of flipping pulses used to tilt the resultant magnetic vector into x-y plane and inverse z-direction, respectively

(D) T1 is the spin-spin or transverse relaxation time, and T2 is the spin-lattice or longitudinal relaxation time

Answer: (A)

26. Given x is real, identify all the even-functions among the following:

(A) x|x|

(B) cos(x)/x

(D) e⁻^|x|

Answer: (C, D)

27. An ideal coronary stent should

(A) be thrombo resistant

(B) promote accumulation of smooth muscle cells

(D) support deposition of extracellular matrix

Answer: (A, C)

28. Which of the following statements related to the safety of biomedical instruments are TRUE?

(A) When a person is exposed to an electrical hazard, let-go current is defined as the maximum current at which the subject can withdraw voluntarily

(B) Microshock is a physiological response resulting from an electrical current passing through heart

(C) The patient in an intensive care unit is being exposed to the danger of microshock because of using internal conductive electrodes in the vicinity of the heart

(D) The 50 Hz safe current limit for a microshock is greater than 50 mA

Answer: (A, B, C)

29. Which of the following statements related to the operating principle of pulse oximetry are CORRECT?

(A) Pulse oximeter can non-invasively determine arterial oxygen saturation (SpO₂) by analyzing the light transmitted through the skin during the systolic phase of the blood flow through the tissue

(B) In a pulse oximeter, isosbestic wavelength is the wavelength at which Hb and HbO₂ have same optical absorbance

(C) Pulse oximeter can accurately determine the SpO₂ of blood by computing the ratio of absorbances at 660 nm and 905 nm wavelengths

(D) Pulse oximeter can accurately determine the SpO₂ of blood by computing the ratio of absorbances at 850 nm and 950 nm wavelengths

Answer: (A, B, C)

30. Which of the following statements related to biomedical measurements are TRUE?

(A) Electrical activity of neurons in the peripheral nervous system can be measured by ENG

(B) Electrical activity of the retina in response to light stimulus can be measured using EOG

(D) P wave in ECG manifests ventricular repolarization

Answer: (A, C)

31. Which of the following mechanical prosthetic valves were invented as a replacement for diseased heart valves?

(A) Globe valve

(B) Ball and cage valve

(D) Swing check valve

Answer: (B, C)

32. Due to the current COVID pandemic conditions, assume that positive or negative status of any individual are equally likely. There are 3 members in a family. If one of the members has tested COVID positive, the conditional probability that at least 2 members are COVID positive is _____ (rounded off to three decimal places).

Answer: (0.570 to 0.572)

33. A series RLC circuit with R = 10 Ω, L = 50 mH and C = 100 μF connected to 200 V, 50 Hz supply consumes power P. The value of L is changed such that this circuit consumes same power P but operates with lagging power factor. The new value of L is _____ mH (rounded off to two decimal places).

Answer: (152.01 to 152.99)

34. The thickness of piezoelectric crystal (PZT5A) used in ultrasound applications will determine the resonant frequency of the transducer. To work at a resonance frequency of 5 MHz, the thickness of a PZT5A transducer must be _______ mm (rounded off to three decimal places).

Given: The velocity of sound in PZT5A is 4350 m.s⁻¹.

Answer: (0.434 to 0.436)

35. Power consumed by the 3 Ω resistor is 12 W in the given circuit. The value of the resistor R in the circuit is ________ Ω.

Answer: (6 to 6)

Q.36 – Q.65 Carry TWO marks Each

36. In the complex 𝑧-domain, the value of the integral is

Answer: (A)

37. Solution of the differential equation is

Answer: (A)

38. An input x(t) is applied to a system with a frequency transfer function given by H(jω) as shown below. The magnitude and phase response of the transfer function are shown below. If y(t_d ) = 0 for x(t) = u(y), the time t_d (> 0) is ______ μs.

(A) 100 ln(2)

(B) 10 ln(2)

(D) ln(2)

Answer: (A)

39. The block diagram of a two-tap high-pass FIR filter is shown below. The filter transfer function is given by H(z) = Y(z)/X(z).

If ratio of the maximum to minimum value of H(z) is 2 and |H(z)|_max = 1, the coefficients β₀ and β₁ are ______ and ______, respectively.

(A) 0.75, −0.25

(B) 0.67, 0.33

(D) −0.64, 0.36

Answer: (A)

40. The block diagrams of an ideal system and a real system with their impulse responses are shown below. An auxiliary path is added to the delayed impulse response in the real system.

For a unit impulse input (x(t) = δ(t)) to both systems, gain β is chosen such that y(4T) is same for both systems. The value of β is _______.

(A) e⁻³^αT (1 − e^−2αT)

(B) −e^−αT (1 − e^−3αT)

(D) e⁻²^αT (1 − e^−2αT)

Answer: (C)

41. A filter is designed using opamps, resistors, and capacitors as shown below. Opamps are ideal with infinite gain and infinite bandwidth. If V₀ (𝑠)/V_i (s) is an all-pass transfer function, the value of resistor R2 is ______________ kΩ.

(A) 1

(B) 10

(D) 2

Answer: (B)

42. If

where F(s) is the Laplace transform of the function f(t), then the value of g(t) at𝑡 = 0 is _______.

(A) −11

(B) −5

(D) ∞

Answer: (A)

43. Consider the Einthoven’s triangle of frontal ECG for the 3 electrodes RA, LA and LL shown in the figure. The augmented lead vectors bisect the bipolar lead vectors. At the peak of R wave, the cardiac vector M points vertically downwards with |M| = 5 mV.

The voltages on leads I and II are ______ mV and ______ mV, respectively.

(A) 0, 4.33

(B) 2.17, 0

(D) 4.33, 0

Answer: (A)

44. Which one of the following statements is TRUE?

(A) A myelinated axon has a greater ATP requirement than an unmyelinated axon of the same diameter and length

(B) An unmyelinated axon has a greater ATP requirement than a myelinated axon of the same diameter and length

(D) An unmyelinated axon always has a greater ATP requirement than a myelinated axon irrespective of their diameter and length

Answer: (B)

45. The deltoid muscle connects the humerus to the shoulder blade and facilitates out stretching of the arm as shown in the figure. The humerus is connected to the shoulder blade with a ball and socket joint.

Assume the equivalent weight (W) of the arm to be 30 N and acts vertically down at a horizontal distance of 30 cm.

Assume that the deltoid muscle is connected to the humerus at a distance of 15 cmand makes an average angle of 20º with the horizontal. The magnitude of tension in the deltoid muscle is ________ N.

(A) 31.9

(B) 63.8

(D) 175.4

Answer: (D)

46. For blood flow through arteries, which one of the following relations approximates the pulse wave propagation speed (C) as a function of the inner diameter (D) of the artery, wall thickness (t), modulus of elasticity (E), and fluid density (ρ).

Answer: (A)

47. A person has a total blood volume of 5 L. Out of this total assume that 4 L is contained in the systemic circulation and 1 L in pulmonary circulation. The cardiac output of the person is 5 L.min⁻¹. Time taken for a drop of blood to go from right ventricle to left ventricle is _________ s.

(A) 60

(B) 20

(D) 12

Answer: (D)

48. Based on the stress-strain curves of three different materials (X, Y, and Z) shown in the figure, which one of the following choices is CORRECT?

(A) X – Titanium, Y – Hydroxyapatite, Z – Polyethylene

(B) X – Hydroxyapatite, Y – Titanium, Z – Polyethylene

(D) X – Polyethylene, Y – Titanium, Z – Hydroxyapatite

Answer: (B)

49. Consider two radionuclides P and Q. Suppose the half-life of P (t^P_1/2) is four times that of Q(t^Q_1/2). At time t = 0, there are N₀ atoms of both radionuclides. When will the radioactivity of the two radionuclides be equal?

(A) t = t^P_1/2

(B) t = 0.66t^P_1/2

(D) t = 1.5t^P_1/2

Answer: (B)

50. In a biological study, the experimental values measured from 6 subjects are given in the table below. Using this data, the linear regression coefficient for estimating the weight of the heart based on the systolic pressure is _______ (rounded off to two decimal places).

Answer: (3.27 to 3.31)

51. Using divergence theorem, evaluate the integral where S is the surface of the cone x² + y²≤ z², 0 ≤ z ≤ 3. If is vector function with outer unit normal vector the value of the integral is _______ (rounded off to the nearest integer).

Answer: (111 to 114)

52. The magnitude of the current gain in the circuit below is ______ (rounded off to two decimal places).

Answer: (75.49 to 76.01)

53. The linear temperature coefficient of the material of a wire is x × 10⁻⁴°C⁻¹. The resistance of this wire increased from 50 Ω at 25°C to 60 Ω at 75° The value of x is _________ (rounded off to two decimal places).

Answer: (44.35 to 44.55)

54. A series RLC circuit is connected to 220 V, 50 Hz supply. For a fixed value of R and C, the inductor L is varied to deliver the maximum current. This value is 0.4 A and the corresponding potential drop across the capacitor is 330 V. The value of the inductor L is _______ H (rounded off to two decimal places).

Answer: (2.59 to 2.70)

55. In the circuit diagram shown below, the MOSFET is biased in saturation region. The MOSFET has a threshold voltage V_th = 0.5 V, width W = 100 μm, length L = 0.1 μm, and μ_nC_ox = 100 μA.V⁻².

Assuming v_i = 1 mV as a small-signal input to MOSFET, the magnitude of the output voltage V_o is _____ mV (accurate to two decimal places). Ignore channel-length modulation for the MOSFET.

Answer: (6.25 to 6.25)

56. In the circuit diagram shown below, BJTs are biased with V_EB = 0.7 V. Neglect the base current for operating point calculations. Assume infinite input and output impedance for the BJTs.

The output voltage V_o with small input voltage v_i = 10 mV is _____ mV (rounded off to one decimal place). The thermal voltage V_T = 25 mV at room temperature.

Answer: (6.2 to 6.8)

57. An ideal opamp with an infinite gain and infinite bandwidth is connected in feedback as shown below. The output voltage V_o for the given input voltages in the circuit is _______ V (accurate to one decimal place).

Answer: (4.6 to 4.6)

58. Independent voltage measurements (μ ± σ) of three sensors where μ and σ are the mean and standard deviation of the measurements, respectively are as follows:

v₁ = 4.52 ± 0.02 V, v₂ = 4.21 ± 0.20 V, v₃ = 3.96 ± 0.15 V.

The measurement uncertainty in v₁ + v₂ + v₃ is _____ V (rounded off to two decimal places).

Answer: (0.25 to 0.26)

59. A moving coil voltmeter has an internal resistance of 50 Ω. The scale of the meter is divided into 100 equal divisions. When a potential of 1 V is applied to terminals of voltmeter, a deflection of 100 divisions is obtained. However, it is desired that when a potential of 500 V is applied to the terminals, a deflection of 100 divisions should be obtained.

The value of resistance that needs to be connected in series to achieve this is________ Ω.

Answer: (24950 to 24950)

60. A Hall effect flow meter is used to measure the volumetric flow through a blood vessel. The flow meter induces a magnetic field across the vessel and uses a voltmeter to measure the voltage across the vessel which is normal to both magnetic field and blood flow. A caliper is used to measure the vessel diameter.The system calculated the flow rate to be 100 cm³.s⁻¹ using the known magnetic field, and measured values of voltage and vessel diameter.

After the measurement, a calibration is performed, and it is discovered that the voltmeter was measuring 40% larger than the actual value and the caliper was measuring the diameter 10% smaller than the actual value.

Assuming a uniform flow profile along the vessel and ignoring viscosity, the actual blood flow is ________ cm³.s⁻¹ (rounded off to two decimal places).

Answer: (78.71 to 79.91)

61. A catheter based arterial blood pressure measurement device uses a flexible diaphragm mounted with four identical strain gauges in a Wheatstone bridge configuration as shown in the figure. Assume that the strain gauges have a nominal resistance value of RG = 10 kΩ, Gauge Factor G = 40 and Young’s Modulus E = 10 MPa. Blood pressure variations results in small finite change in strainϵ (ϵ > 0).

If V_o is the output voltage of the Wheatstone bridge and σ is the stress in MPa, the sensitivity V₀/σ is _____ V.Mpa⁻¹.

Answer: (8 to 8)

62. A patient has a breathing rate of 18 breaths per minute, with a tidal volume of 500mL, having an anatomical dead space of 150 mL. If the person has a heart rate of 120 beats per minute and a stroke volume of 50 mL, the alveolar ventilation to perfusion ratio is _____________ (accurate to two decimal places).

Answer: (1.05 to 1.05)

63. Assume that the ratio of total blood volume in liters to total body weight in kg is 0.07 and the blood consists of plasma and RBCs only. The plasma volume of a 70-kg man with 52% hematocrit is ______ L (rounded off to two decimal places).

Answer: (2.29 to 2.41)

64. The 1st generation (1G) CT scanner uses a point X-ray source and a detector. The

source detector assembly can move linearly at a speed of 0.5 m.s⁻¹ and that it takes 0.5 s for source-detector assembly to rotate one angular increment, regardless of the angle.

This scanner is expected to collect 360 projections over 180° of span. The field of

view used for data collection has a diameter of 0.5 m. The scan time required is______ s.

Answer: (538 to 542)

65. The inverse square law has a very practical use in radiography. While taking an acceptable chest radiograph of a subject at a distance of 0.75 m from the X-ray generator, X-ray source settings were kept at 50 kVp, 50 mA.s.

If the subject is moved to a distance of 1 m, and the kVp is kept the same, the new value of mA.s to obtain the same exposure will be _____ mA.s (rounded off to two decimal places).

Answer: (88.86 to 88.92)

GATE Exam 2022 Architecture and Planning (AR) Question Paper With Answer Key

June 27, 2022 by suresh84

GATE-2022

AR: Architecture and Planning

General Aptitude

1. After playing _________ hours of tennis, I am feeling _________ tired to walk back.

(A) too / too

(B) too / two

(D) two / too

Answer: (D)

2. The average of the monthly salaries of M, N and S is Rs. 4000. The average of the monthly salaries of N, S and P is Rs. 5000. The monthly salary of P is Rs. 6000.

What is the monthly salary of M as a percentage of the monthly salary of P?

(A) 50%

(B) 75%

(D) 125%

Answer: (A)

3. A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph.

What percentage of the total distance is travelled at a uniform speed of 10 kmph?

(A) 28.25

(B) 37.25

(D) 50.00

Answer: (C)

Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutchis easier than Japanese, and Spanish is easier than French.

Based on the above information, which girl is learning the most difficult pair oflanguages?

(A) P

(B) Q

(D) S

Answer: (B)

A block with a trapezoidal cross-section is placed over a block with rectangularcross section as shown above.

Which one of the following is the correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow in the above figure?

Answer: (A)

Which one of the following is the CORRECT logical inference based on theinformation in the above passage?

(A) Wallets with a key are more likely to be returned because people do not careabout money

(B) Wallets with a key are more likely to be returned because people relate tosuffering of others

(D) Money is always more important than keys

Answer: (B)

7. A rhombus is formed by joining the midpoints of the sides of a unit square.

What is the diameter of the largest circle that can be inscribed within the rhombus?

(A) 1/√2

(B) 1/2√2

(D) 2√2

Answer: (A)

8. An equilateral triangle, a square and a circle have equal areas.

What is the ratio of the perimeters of the equilateral triangle to square to circle?

Answer: (B)

9. Given below are three conclusions drawn based on the following three statements.

Statement 1: All teachers are professors.

Statement 2: No professor is a male.

Statement 3: Some males are engineers.

Conclusion I: No engineer is a professor.

Conclusion II: Some engineers are professors.

Conclusion III: No male is a teacher.

Which one of the following options can be logically inferred?

(A) Only conclusion III is correct

(B) Only conclusion I and conclusion II are correct

(D) Only conclusion I and conclusion III are correct

Answer: (A)

10. In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?

(A) 11

(B) 12

(D) 2

Answer: (MTA)

PART A: Common FOR ALL CANDIDATES

Q.11 – Q .28 Carry ONE mark Each

11. The concentric circles in a sun-path diagram represent ___________.

(A) Altitude angle

(B) Azimuth angle

(D) Hour of the day

Answer: (A)

12. The operational guidelines on Credit Linked Subsidy Scheme for Economically Weaker Sections (EWS), January 2017, by the erstwhile Ministry of Housing & Urban Poverty Alleviation, Government of India, defines EWS households as those having an annual income up to ___________ (in Indian Rupees).

(A) 2,00,000

(B) 2,50,000

(D) 3,50,000

Answer: (C)

13. Which of the following is a Vector Graphics Software?

(A) Inkscape

(B) Odeon

(D) DesignBuilder

Answer: (A)

14. The main cable of a suspension bridge supports the deck with hangars. These hangars are equidistant along the length of the bridge and represent a uniformly distributed load. Assuming the cable to be weightless as compared to the applied loading, the best approximation of the shape that the cable takes for this loading is a ___________.

(A) Catenary curve

(B) Circular arc

(D) Hyperbolic curve

Answer: (C)

15. Arrange the following road types in descending order of accessibility.

(P) Arterial Road

(Q) Expressway

(R) Collector Road

(S) Local Street

(A) Q-P-R-S

(B) S-R-P-Q

(D) P-Q-S-R

Answer: (B)

16. The following two-dimensional visual composition represents _______.

(A) Interlocking

(B) Intersecting

(D) Interpenetrating

Answer: (C)

17. The Golden Ratio refers to ___________.

(A) 1:√2

(B) 2:(1 + √5)

(D) 16:9

Answer: (B)

18. Hogarth’s Line of Beauty is a ___________.

(A) Horizontal straight line

(B) Zigzag line

(D) Serpentine line

Answer: (D)

19. Which of the following sites were added to Ramsar List in the year 2020?

(A) Ashtamudi Wetland

(B) Asan Conservation Reserve

(D) Lonar Lake

Answer: (B, D)

20. Which of the following help(s) in keeping direct solar radiation out of the building?

(A) Mashrabiya

(B) Badgir

(D) Chajja

Answer: (A, D)

21. As per the Handbook of Professional Documents 2015, Council of Architecture, India, architects are liable ________.

(A) If the building is used for any other purpose than the one for which it was designed

(B) If any unauthorised changes or illegal modifications are made by theowner(s)/occupant(s)

(D) If the architect fails to attain the standard of care as prescribed by law

Answer: (C, D)

22. As per the United Nations Transforming our world: The 2030 agenda for sustainable development, 2015, which of the following Sustainable Development Goals (SDGs) directly address water related issues?

(A) SDG-1

(B) SDG-4

(D) SDG-14

Answer: (C, D)

23. For a masonry section, the line of action of force shifts to incorporate the effects of lateral forces and induced moments. Consider a masonry section of width 600 mm. Assuming a zero tensile stress capacity and a linear stress-strain response for the entire domain of loading, the minimum value of eccentricity at which the section will crack (in mm, rounded off to one decimal place) is ___________.

Answer: (97.0 to 103.0)

24. The maximum and minimum indoor dry bulb temperature of a room are 38°C and 34°C, respectively. If the corresponding outdoor maximum and minimum dry bulb

temperature are 42°C and 30°C, respectively, then the thermal damping of the room (in percentage, rounded off to two decimal places) is ________.

Answer: (66.00 to 67.00)

25. A building site measures 96 sq.cm on a scale of 1:12500. The actual area it represents (in hectare, in integer) is ________.

Answer: (150 to 150)

26. An off-street car parking lot contains a total of 75 bays. If the parking lot was used by 687 cars over a period of 12 hours, the average parking turn-over of the parking lot (in vehicles per hour per bay, rounded off to two decimal places) is ________.

Answer: (0.76 to 0.77)

27. The hydraulic radius of the following rectangular open drainage section (in mm, rounded off to two decimal places) is ________.

Answer: (135.00 to 138.00)

28. A town with 0.45 million population sends its entire organic waste to a composting site on a daily basis through a truck of 15 ton carrying capacity. Assume total waste generated per capita per day is 0.21 kg and 40% of the total waste is organic waste. The minimum number of weekly round trips required by the truck (in integer) will be ________.

Answer: (21 to 21)

Q.29 – Q .49 Carry TWO marks Each

29. The correct sequence of the following Construction Project Development stages, as per the National Building Code of India 2016 is ___________.

(P) Resource Planning

(Q) Project Inception

(R) Commissioning and Handing over

(S) Tendering

(T) Site Survey and Soil Investigation

(U)Selection of Construction Methodology

(A) P-Q-R-T-U-S

(B) T-Q-R-U-S-P

(D) Q-T-P-S-U-R

Answer: (C)

30. Match the aspects in Group I with the corresponding items in Group II.

(A) P-4, Q-5, R-2, S-3

(B) P-5, Q-1, R-4, S-2

(D) P-2, Q-5, R-4, S-3

Answer: (D)

31. Match the States in Group I with the corresponding Vernacular Building Typologies in Group II.

(A) P-4, Q-5, R-3, S-2

(B) P-5, Q-1, R-2, S-4

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

Answer: (D)

32. Match the examples in Group I with their corresponding typologies in Group II.

(A) P-2, Q-1, R-4, S-5

(B) P-4, Q-2, R-5, S-3

(D) P-3, Q-5, R-1, S-4

Answer: (C)

33. Match the Place(s)/Event(s) in Group I with the corresponding Heritage Significance/Characteristics in Group II.

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

(B) P-3, Q-4, R-5, S-1

(D) P-3, Q-2, R-5, S-4

Answer: (B)

34. Match the Urban Design Concepts in Group I with their corresponding Proponents in Group II.

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

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

(D) P-5, Q-4, R-2, S-3

Answer: (B)

35. In the following sketch, P, Q, R, and S refer to elements of an urban space. Identify P, Q, R, S.

(A) P-Path, Q-Vista, R- Edge, S-Landmark

(B) P-Vista, Q-Edge, R- Landmark, S-Path

(D) P-Landmark, Q-Edge, R- Path, S-Vista

Answer: (D)

36. As per the URDPFI Guidelines 2015, match the type of Health Care Facilities in Group I to the corresponding population served per unit in Group II.

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

(B) P-3, Q-1, R-5, S-4

(D) P-5, Q-1, R-2, S-3

Answer: (B)

37. Match the plan forms in Group I with their corresponding project names in Group II.

(A) P-3, Q-5, R-4, S-2

(B) P-4, Q-2, R-1, S-5

(D) P-3, Q-5, R-1, S-2

Answer: (D)

38. Match the Biosphere reserves in India in Group I with their corresponding locations in Group II.

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

(B) P-2, Q-3, R-1, S-5

(D) P-4, Q-5, R-1, S-3

Answer: (B)

39. In traditional Persian context, qanat system refers to

(A) An underground water-way, tunnelled and channelled

(B) A system where water is raised by a series of scoops fixed to a moving belt stretched between two wheels

(D) A system where water is conducted from enclosure to enclosure by straight forward gravity fall

Answer: (A, C, D)

40. Which of the following is/are classified as the Principles of Universal Design?

(A) Perceptible Information

(B) Tolerance for Error

(D) Simple and Intuitive Use

Answer: (A, B, D)

41. As per the URDPFI Guidelines 2015, which of the following Organoleptic and Physical parameters comply with the acceptable limit requirements of drinking water quality?

(A) Colour: Maximum 5 Hazen units

(B) Turbidity: Maximum 1 NTU

(D) Total Dissolved Solids: Maximum 500 mg/l

Answer: (A, B , D)

42. In an ideal air-conditioning cycle shown below, which of the following statement(s) is/are true in the segments P, Q, R, S?

(A) P: Vapour at low pressure

(B) Q: Vapour at low pressure

(D) S: Liquid-Vapour mixture at low pressure

Answer: (A, C, D)

43. Which of the following is/are the characteristic(s) of a Mughal Garden?

(A) Symmetrical and geometrical

(B) Fountain and channelled water

(D) Vista with terminal building

Answer: (A, B, D)

44. As per the Central Pollution Control Board’s National Air Quality Index (AQI) of India 2014, which of the following statement(s) is/are true?

(A) AQI is computed considering 8-hourly value of CO

(B) AQI is computed considering 2-hourly value of PM2.5

(D) AQI considers the CO₂ concentrations

Answer: (A, C)

45. The decadal population data of a city are given in the following Table. The domestic water consumption of the city is estimated to be 175 litres per capita per day in the year 2041. Considering 2011 population as the base year and using arithmetic growth method of population forecasting, the daily domestic water demand of the city in the year 2041 (in million litres per day, rounded off to two decimal places) will be ___________.

Answer: (53.00 to 56.00)

46. The activity duration, early start, early finish, late start, and late finish (in weeks) for activities P, Q, R, and S are shown in the following figure. The interfering float of activity R (in weeks, in integer) is _______.

Answer: (6 to 6)

47. A 230 mm thick brick wall of 10 m length and 3 m height is built using a Flemish bond. The size of the bricks used is 230 mm ×5 mm × 70 mm. Assuming a mortar thickness of 5 mm, the number of bricks required (in integer) is ___________.

Answer: (3400 to 3500)

48. The reflected ceiling plan and section of a reinforced cement concrete roof are shown in the following Figure. All the beams are 300 mm wide, 600 mm deep (including 150 mm slab) equidistantly placed center to center. Assuming 1% of concrete volume is occupied by reinforcement bars, the volume of concrete (in cubic meters, rounded off to two decimal places) is ______.

Answer: (24.50 to 25.30)

49. The following graph represents the income distribution among the population of a country. The Gini Coefficient of the country (rounded off to three decimal places) is ________.

Answer: (0.240 to 0.270)

PART B1: FOR Architecture CANDIDATES ONLY

Q.50 – Q.56 Carry ONE mark Each

50. Which of the following processes is used for surface treatment of metals?

(A) Soldering

(B) Thermoplating

(D) Riveting

Answer: (B)

51. Among the following monuments of ancient Greece, the only Octastyle Peripteral temple with eight towering Doric columns lining both east and west facades is _______.

(A) Temple of Athena

(B) Temple of Apollo

(D) Temple of Horus

Answer: (C)

52. An Ultrasonic Pulse Velocity (UPV) test was done on a hardened concrete element using a direct transmission method as per IS 516 (Part 5/Section 1): 2018. The distance between the transducer and receiver was 600 mm. The time taken for the induced wave to travel this distance is measured as 0.18 milliseconds. Based on the following Table, the concrete quality grading is ________.

(A) Excellent

(B) Good

(D) Poor

Answer: (C)

53. Which of the following is/are example(s) of Tomb Architecture of Ancient Egypt?

(A) Step Pyramid of Zoser, Sakkara

(B) Great Temple of Abu-Simbel

(D) Mastabas of Gizeh

Answer: (A, D)

54. If Aluminium : Anodisation :: Glazing : X, which of the following choices represent X?

(A) Hard coating

(B) External cement plastering

(D) Free-standing vertical greening

Answer: (A, C)

55. A black body radiant heating panel of 5 m² surface area at 35°C surface temperature is located 1 m away from a 1 m² surface at 20° The Stefan-Boltzmann constant is 5.6703×10⁻⁸ W m⁻² K⁻⁴. The rate of radiant heat emission by the radiant heating panel (in W, rounded off to two decimal places) is ________.

Answer: (2550.00 to 2560.00)

56. A hypothetical truss comprising of weightless members is shown in the following Figure. Assuming tension to be positive and compression to be negative, the value of force in member TU (in kN, rounded off to one decimal place) is ________.

Answer: (0.0 to 0.0)

Q.57 – Q .65 Carry TWO marks Each

57. Match the illustrations of Arch Types in Group I with their corresponding names in Group II.

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

(B) P-3, Q-1, R-2, S-5

(D) P-5, Q-4, R-3, S-1

Answer: (B)

58. Match the architectural projects in Group I with their corresponding architects in Group II.

(A) P-4, Q-5, R-2, S-3

(B) P-4, Q-1, R-5, S-2

(D) P-3, Q-5, R-1, S-2

Answer: (A)

59. Match the structural joining systems in Group I with the corresponding materials for which they are commonly used in Group II.

(A) P-4, Q-1, R-2, S-5

(B) P-3, Q-5, R-1, S-2

(D) P-4, Q-1, R-5, S-3

Answer: (D)

60. Match the Instruments in Group I with the corresponding climate parameters in Group II.

(A) P-3, Q-5, R-1, S-2

(B) P-3, Q-4, R-5, S-2

(D) P-1, Q-2, R-3, S-5

Answer: (A)

61. In traditional Indian temple architecture, which of the following statement(s) is/are true?

(A) Jagamohana refers to a dancing hall

(B) Gopuram refers to an entrance tower

(D) Vimana refers to the structure over the Garbhagriha

Answer: (B, C, D)

62. Which of the following factors impact Daylight Autonomy of a built space?

(A) Orientation of building

(B) Glare caused by daylight

(D) Fenestration size

Answer: (A, C, D)

63. For the beam shown in the following Figure, assuming a sagging moment (generating tensile stresses at the bottom fibre) as positive and a hogging moment (generating tensile stresses at the top fibre) as negative, the bending moment (in kN.m, rounded off to one decimal place) at section X-X is _________.

Answer: (-20.0 to -20.0)

64. The acoustical absorption of a wall panel in each octave band is tabulated below. The Noise Reduction Coefficient of the wall panel (rounded off to two decimal places) is ______.

Answer: (0.60 to 0.65)

65. A room is maintained at a wet bulb temperature of 25°C, globe temperature of 30°C, and air velocity of 0.5 m/s. The decrease in Tropical Summer Index when the air velocity is increased to 3 m/s (in °C, rounded off to two decimal places) is _________.

Answer: (-2.20 to -1.50 OR 1.50 to 2.20)

PART B2: FOR Planning CANDIDATES ONLY

Q.66 – Q.72 Carry ONE mark Each

66. Which of the following is the National Electronic Toll Collection System implemented by the National Payment Corporation of India?

(A) e-Pass

(B) E-ZPass

(D) FASTag

Answer: (D)

67. The shaded area in the following demand-supply graph is known as ______.

(A) Consumer Surplus

(B) Consumer Deficit

(D) Producer Deficit

Answer: (A)

68. Identify the following traffic interchange.

(A) Directional

(B) Trumpet

(D) Diamond

Answer: (C)

69. Which of the following is/are Value Capture Method(s)?

(A) Building construction fees

(B) Fees for changing agricultural to non-agricultural land use

(D) Premium on additional FSI/FAR

Answer: (B, D)

70. Which among the following is/are model(s) of Public-Private Partnership (PPP) used for infrastructure projects?

(A) BOLD

(B) BOLT

(D) BPOT

Answer: (B, C)

71. The measured spot speeds (in km/h) of 10 vehicles from a traffic stream are 45, 35, 25, 51, 45, 38, 61, 42, 47, and 49. The Time Mean Speed of the traffic stream (in km/h, rounded off to one decimal place) is ________.

Answer: (43.0 to 44.0)

72. In a township, the price of each house was 25,00,000 (in Indian Rupees) last month. The number of houses sold in a month (Q in thousands) is sensitive to the price of the house (P in Indian Rupees) and establishes a relationship as Q = 6685 – 0.00158 P. If the price of each house increases by 20% in the current month, then the decrease in sale of the houses (in percentage, rounded off to two decimal places) compared to last month will be ________.

Answer: (27.00 to 30.00)

Q.73 – Q.81 Carry TWO marks Each

73. Match the models in Group I with their corresponding applications in Group II.

(A) P-2, Q-1, R-5, S-4

(B) P-1, Q-5, R-2, S-3

(D) P-5, Q-3, R-4, S-2

Answer: (C)

74. Match the proponents in Group I with the corresponding theories in Group II.

(A) P-2, Q-4, R-3, S-5

(B) P-4, Q-2, R-5, S-1

(D) P-3, Q-5, R-2, S-4

Answer: (C)

75. Match the Artists/Scientists in Group I with their corresponding contributions in Group II.

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

(B) P-4, Q-1, R-5, S-2

(D) P-4, Q-3, R-5, S-1

Answer: (A)

76. In the conceptual diagram of the city given below, P, Q, R, and S refer to urban patterns. Among the choices given below, the correct association is

(A) P-Satellite town, Q-Urban fringe, R-TOD, S-Central Business District

(B) P-Central Business District, Q-Satellite town, R-TOD, S-Urban fringe

(D) P-Satellite town, Q-Central Business District, R-TOD, S-Urban fringe

Answer: (A)

77. Which among the following is/are the component(s) of the assimilative carrying capacity of urban environment?

(A) Air

(B) Water

(D) Soil

Answer: (A, B, D)

78. In the transportation network given below, P, Q, R, S, T, and U are the nodes and values mentioned on the links denote time in minutes. Which of the following options represent the minimum spanning tree?

(A) PQ, QR, QT, TS, SU

(B) PR, QR, RT, TU, SU

(D) PQ, QR, RS, ST, TU

Answer: (A, C)

79. A vehicle count survey (in Passenger Car Unit) is conducted on a mid-block section of a road at regular intervals of 15 minutes from 8:00 AM to 10:00 AM. Based on the data given in Table below, the Peak Hour Factor (rounded off to two decimal places) for the given survey duration is _______.

Answer: (0.83 to 0.87)

80. A land owner has shown interest in a Town Planning Scheme. Based on the details of the scheme given in the following Table, the estimated Net Benefit to the landowner after land development (in Indian Rupees, in integer) is _______.

Answer: (118000 to 122000)

81. The year-wise cash flows (in Indian Rupees) of a construction project are given inthe following Table. If the annual discount rate for the project is assumed to be 12%,the Net Present Value (in Indian Rupees, rounded off to two decimal places) for the project will be _______.

Answer: (3800.00 to 5020.00)

GATE Exam 2022 Agricultural Engineering (AG) Question Paper With Answer Key

June 26, 2022 by suresh84

GATE-2022

AG: Agricultural Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Inhaling the smoke from a burning _________ could _________ you quickly.

(A) tire / tier

(B) tire / tyre

(D) tyre / tier

Answer: (C)

2. A sphere of radius r cm is packed in a box of cubical shape.

What should be the minimum volume (in cm³) of the box that can enclose the sphere?

(A) r³/8

(B) r³

(D) 8r³

Answer: (D)

If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?

(A) 26.8

(B) 60.0

(D) 127.5

Answer: (C)

4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

• P sits next to S and T.

• Q sits diametrically opposite to P.

• The shortest distance between S and R is equal to the shortest distance between T and U.

Based on the above statements, Q is a neighbor of

(A) U and S

(B) R and T

(D) P and S

Answer: (C)

5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

(A) 4

(B) 3

(D) 1

Answer: (C)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on the information given in the above passage?

(A) GSR is an alternative to regular rice, but it grows only in an extreme weather

(B) GSR may be used in future in response to adverse effects of climate change

(D) Regular rice will continue to provide good yields even in extreme weather

Answer: (B)

(A) 1/16

(B) 5/64

(D) 7/64

Answer: (D)

8. Consider the following inequalities.

(i) 3p − q< 4

(ii) 3q − p< 12

Which one of the following expressions below satisfies the above two inequalities?

(A) p + q < 8

(B) p + q = 8

(D) p + q ≥ 16

Answer: (A)

9. Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.

Statement 2: No writer is an actor.

Statement 3: All actors are engineers.

Conclusion I: Some writers are engineers.

Conclusion II: All engineers are actors.

Conclusion III: No actor is a writer.

Conclusion IV: Some actors are writers.

Which one of the following options can be logically inferred?

(A) Only conclusion I is correct

(B) Only conclusion II and conclusion III are correct

(D) Either conclusion III or conclusion IV is correct

Answer: (C)

10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

Answer: (C)

Agricultural Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Determinant of a matrix remains unaltered if ______.

(A) its columns and rows are interchanged

(B) two parallel lines are identical

(D) each element of a line is multiplied by the same factor

Answer: (A)

12. The probability of having 53 Sundays in a randomly selected leap year is ______.

(A) 1/7

(B) 1/4

(D) 4/7

Answer: (C)

13. Function f(x) by Maclaurin’s series (as an infinite series) can be expressed as

Answer: (B)

14. The lowest temperature at which the fuel ceases to flow is known as ______.

(A) Pour point

(B) Cloud point

(D) Boiling point

Answer: (A)

15. Complement of the Solar Altitude angle is ______.

(A) Zenith angle

(B) Azimuth angle

(D) Profile angle

Answer: (A)

16. Annual cost of owning (fixed cost) a particular combine harvester is Rs. 3,00,000 whereas, operating it would cost additional Rs. 6,000 per hectare. If an entrepreneur wishes to offer the machine for custom hiring, the combination of annual use (ha) and custom rate (Rs. ha⁻¹), respectively, that would fetch him the break-even condition is ______.

(A) 200 and 7,500

(B) 210 and 6,300

(D) 250 and 6,100

Answer: (A)

17. In construction of gravel packed wells, the pack-aquifer ratio is generally defined as ______.

Answer: (A)

18. The shape of falling limb of a hydrograph is dependent on ______.

(A) basin and storm characteristics

(B) storm characteristics only

(D) direction of the rainfall only

Answer: (C)

19. Energy requirement (E) to produce a change (dX) in dimension X of a particular size can be expressed as where, c is constant and n according to Rittinger’s law is ______.

(A) 1/2

(B) √2

(D) 2

Answer: (D)

20. The ratio of inertial forces to viscous forces is knows as ___________.

(A) Froude number

(B) Reynolds number

(D) Biot number

Answer: (B)

21. The root of the equation sin x–4x + 1 = 0 after its first iteration, using Newton-Raphson method with an initial guess of x₀ = 0.2, is _________.[round off to three decimal places]

Answer: (0.250 to 0.350)

22. The slope of the function f(x) = 2x⁴ – 3x² + 5x at x = 2 is ________. [Answer in integer]

Answer: (57 to 57)

23. A single cylinder four-stroke diesel engine has an engine displacement volume of9 L, the engine rotates at 2400 rpm and its volumetric efficiency is 88%. The actual air inducted into the cylinder in m³ s⁻¹ is _________. [round off to three decimal places]

Answer: (0.157 to 0.159)

24. A two-wheel drive tractor is fitted with driving wheels having rolling radius of 860 mm. The effective gear ratio between the engine to the drive wheels is 98:1 and the power transmission efficiency at that gear ratio is 86%. If the engine torque is 520 N m, the ground thrust developed by the drive wheels in kN is __________.[round off to two decimal places]

Answer: (50.95 to 50.97)

25. A double acting hydraulic cylinder has bore and rod diameter of 76 mm and 25 mm,respectively. In extension as well as retraction strokes of the cylinder, the oil flow rate to the cylinder from the pump is 40 L min⁻¹. The velocity of the piston during retraction stroke in m s⁻¹ [round off to two decimal places]

(Take π = 3.14)

Answer: (0.14 to 0.18)

26. An open V-belt is wrapped around V-pulleys having effective diameters of 0.25 m and 0.65 m, and their centres are 1 m apart. Assuming ideal conditions, the wrap angle in degree for the smaller pulley is __________. [round off to two decimal places]

(Take π = 3.14)

Answer: (156.00 to 158.00)

27. Water from a confined aquifer having transmissivity of 1000 m² day⁻¹ is pumped through a fully penetrating well of 300 mm diameter at a rate of 1200 m³ day⁻¹. If the radius of influence is 400 m, the draw down in the well under steady-state flow condition in meter is ________. [round off to two decimal places]

(Take π = 3.14)

Answer: (1.48 to 1.53)

28. A stream of 200 L s⁻¹ is diverted from a canal to irrigate a wheat field in 8 hours. If the runoff from the field is 500 m³ and the conveyance efficiency is 75%, the application efficiency in per cent is ________. [round off to two decimal places]

Answer: (88.40 to 88.50)

29. The flow rate per unit width of a wide rectangular clean-earth channel is 20 m³ s⁻¹ m⁻¹. The calculated critical flow depth in meter will be __________.[round off to two decimal places]

(Take g = 9.81 m s⁻²)

Answer: (3.42 to 3.46)

30. The ratio of soil loss from the field plot length to that from the unit plot with a slope length of 22.13 m is 0.5. If the slope length from the watershed divide is 600 m and the slope gradient is 8%, the topographic factor in the Universal Soil Loss Equation is __________. [round off to two decimal places]

Answer: (4.35 to 4.45)

31. The area of a rectangular field was measured using a 30 m survey chain, which was later found to be 5 cm short. If the length and width of the field measured using this chain were 542 m and 554 m,respectively, the true area of the field in ha is________. [round off to two decimal places]

Answer: (29.90 to 29.95)

32. In a triple effect feed forward evaporator, pineapple juice is entering at the rate of 6.3 kg s⁻¹ and leaving the last effect as 50% concentrate. The system is using saturated steam of 2.48 kg s⁻¹ at 121.1 ºC. If vapour transferred from the first to the second effect, second to third effect and third to ambient are 5675, 6053 and 6416 kg h⁻¹, respectively, the steam economy of the evaporator is __________.[round off to two decimal places]

Answer: (2.00 to 2.04)

33. If an osmo-dehydrated fruit slice has 72% moisture content on wet basis, the moisture content of the same fruit slice on dry basis in per cent is ___________.[round off to one decimal place]

Answer: (256.5 to 257.5)

34. If the specific heat capacity (cp) of solids in potato is 837.36 J kg⁻¹ K⁻¹, then the specific heat capacity of potatoes in J kg⁻¹ K⁻¹ with 85% moisture content (wet-basis)is ________. [round off to two decimal places]

Answer: (3678.00 to 3698.00)

35. A milk sample contains 4×10⁵ spores of C. botulinum (D value of 1.2 min at 121.1 °C) and 7×10⁶ spores of L. monocytogenes (D value of 0.9 min at 121.1°C)per mL. If the milk is heated at a uniform temperature of 121.1°C to obtain aprobability of spoilage of 1 in 1000 cans, the minimum heating duration in minutes is ___________. [round off to two decimal places]

Answer: (10.20 to 10.40)

Q.36 – Q.65 Carry TWO marks Each

36. The function (x − 2)²(x + 2)² has

(A) minima at +2 and maxima at −2

(B) minima at −2 and maxima at +2

(D) maxima at −2 and +2

Answer: (C)

37. The matrix is singular for the following values of x

(A) x =0 and x = 3

(B) x =0 and x = −3

(D) x =0 and x = −6

Answer: (A)

38. A 5 × 20 cm seed drill has a ground drive wheel of rolling diameter 0.5 m. Whiletesting under laboratory condition, 320 gof seeds were collected in 20 revolutionsof the ground drive wheel. The same seeddrill when operated in a 2 ha field, amount

of seeds dropped was found to be 185 kg.The variation in the seed dropped betweenlaboratory and field conditions due to skidof ground drive wheel is ________

(Take π = 3.14)

(A) 6.38%

(B) 9.23%

(D) 12.26%

Answer: (B)

39. A 3.6 m combine harvester was tested over a crop strip of 20 m length and thefollowing data were obtained while testing:

Total material left over walker = 8.5 kg

Free seed over walker = 100 g

Unthreshed seed over walker = 50 g

Total material left over shoe = 5.5 kg

Free seed over shoe = 250 g

Unthreshed seed over shoe = 80 g

Total seed collected in the grain tank = 16.5 kg

The grain yield (tonne ha⁻¹) and cylinder loss (%), respectively, are

(A) 2.36 and 0.77

(B) 4.24 and 0.29

(D) 8.05 and 2.82

Answer: (A)

40. An ideal gas is compressed adiabatically (Adiabatic exponent γ =1.4) from 98 kPa

to 480 kPa and the specific volume of the gas at the beginning of the compression

stroke is 0.45 m3 kg⁻¹. The specific work done on the gas in kJ kg⁻¹ is _________.

(A) 12.6

(B) 18.5

(D) 63.3

Answer: (D)

41. A sample of 90% saturated clay soil has void ratio and specific gravity of 0.8 and2.7, respectively. The bulk unit weight of soil in N m⁻³ is ____________.

(Take unit weight of water = 9.81×103 N m⁻³)

(A) 10594.80

(B) 18639.00

(D) 10.60

Answer: (B)

42. A parabolic shaped grass-waterway is to be designed to carry a flow of 2.85 m³ s⁻¹down the slope of 3%. The permissiblevelocity of water in the waterway is1.78 m s⁻¹. If the freeboard depth is excluded, the most appropriate top width in mand depth in m, respectively are

(Take Manning’s roughness coefficient = 0.04)

(A) 4 and 0.6

(B) 6 and 0.4

(D) 5.5 and 0.6

Answer: (B)

43. The pressure drop through a well-designed constriction is to be used for measuringthe velocity of flow through a circular pipe. If the pressure drop from a 0.1 mdiameter section to a 0.05 m diameter section of the pipe is 7.5 kPa, the velocity in m s⁻¹ in the 0.1 m diameter section of the pipe is ____________.

(Take density of liquid = 1000 kg m⁻³)

(A) 0.5

(B) 1.0

(D) 2.0

Answer: (B)

44. The water activity of potato is 0.942. As per Raoult’s law, the most efficient solutionfor osmotic dehydration of potato is ________.

(Molar mass of sucrose = 342 g mole⁻¹, and NaCl = 58.5 g mole⁻¹)

(A) 20% sucrose solution

(B) 20% NaCl solution

(D) 15% sucrose solution + 5% NaCl solution

Answer: (B)

45. The mass fraction retained on the ith sieve is x_i and is the average opening size of ith and (i-1)th sieves. The volume surface mean diameter of particles retained on n number of sieves is _________.

Answer: (A)

46. Match the following reactants in Column I with the most appropriate purpose usedin processing as mentioned in Column II.

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

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

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

Answer: (D)

47. Work done by a moving particle in the force field moving along the straight line from (0,0,0) to (1,2,3) is __________. [Answer in integer]

Answer: (28 to 28)

48. The power consumption readings (in watt) by an instrument at fixed intervals oftime (in seconds) are tabulated below:

Using Simpson’s 1/3rd rule, the energy expenditure of the instrument in joule is__________. [round off to two decimal places]

Answer: (29.20 to 29.50)

49. The root mean square acceleration for mechanical vibration of a tractor is 3.15 m s⁻² and its frequency is 80 Hz. The root mean square amplitude of the vibration in μm is ___________. [round off to two decimal places]

(Take π = 3.14)

Answer: (12.20 to 12.80)

50. The static weight on front and rear axles of a two-wheel drive tractor are 3 kN and 9 kN, respectively. The wheel-base of the tractor is 2.1 m and the tractor pulls a load of 7.5 kN. The perpendicular distance from the front wheel ground contact point to the line of pull is 680 mm. Neglecting the wheel contact off-set on the ground, the weight transfer onto the rear axle in kN is _________. [round off to two decimal places]

Answer: (2.30 to 2.60)

51. The crank radius and connecting rod length of an IC engine are 250 mm and 1000 mm, respectively. If the crank turns 100º from the head dead centre and the net force acting on the piston along its direction of motion is 35 kN, the turning moment of the crank shaft at that instant in kN m is ___________. [round off to two decimal places]

Answer: (8.00 to 8.50)

52. An engine develops 42 kW brake power when it runs with B20 fuel (80% biodiesel and 20% diesel by volume) with a brake thermal efficiency of 24%. The heating value of the fuel is 46.15 MJ kg⁻¹ and its density is 0.845 kg L⁻¹. The fuel consumption of the engine in L h⁻¹ will be ___________. [round off to two decimal places]

Answer: (14.00 to 18.00)

53. A tractor operated 12 × 60 cm boom sprayer had an overlap of 30 cm between the successive passes during field operation at an average speed of 4.2 km h⁻¹. A total time loss of 7.5 min ha⁻¹ was observed during turnings. Assuming no overlap of spray material between adjacent nozzles, the field efficiency of the sprayer in percent is __________. [round off to two decimal places]

Answer: (69.00 to 71.00)

54. A mild steel flange-mounted single shear pin (Ultimate shear strength = 42 MPa)of 10 mm diameter is used in a flange. The perpendicular distance between the axis of driving shaft and the shear pin axis is 100 mm. If the speed of the driving shaft is 300 rpm, the maximum power the shaft could transmit in kW before the failure of the pin is ___________. [round off to two decimal places]

[Take π = 3.14]

Answer: (10.20 to 10.50)

55. In a subsurface drainage network, 12 lateral drains each of 100 m long are laid at a spacing of 50 m. These lateral drains are connected to a collector drain. When the water table dropped 50 cm below the soil surface in 4 days, the average discharge at the outlet of the collector drain was found to be 12 L s⁻¹. The average drain able porosity of soil in per cent is ________. [round off to two decimal places]

Answer: (13.75 to 13.85)

56. A watershed with various land uses (as specified in the table below) receives a rainfall of 152.4 mm. If an initial abstraction (I_a) is 0.2 times the potential maximum retention (S), and the antecedent moisture content (AMC) of averaged condition is assumed, the depth of runoff volume in mm is ____________. [round off to two decimal places]

Answer: (111.80 to 112.00)

57. A trapezoidal weir has a side slope of 1 horizontal unit to 4 vertical units. The length of the weir is less than the width of the channel. If the head over the weir is 70 cm and the discharge is 0.85 m³ s⁻¹, the length of the weir in m is _______. [round off to two decimal places]

(Take coefficient of discharge = 0.62 and g = 9.81 m s⁻²)

Answer: (0.78 to 0.81)

58. The ordinates of an inflow hydrograph are provided in the table below. If the routing interval (Δt) is one hour, weighting factor in Muskingham equation (X) is 0.2, and the storage-time constant (time of travel of flood wave through the channel reach)(K) is 0.7 hour, using the Muskingham method of flood routing, the ordinate of the outflow (routed) hydrograph for 2nd hour in m³ s⁻¹ is _______. [round off to two decimal places]

Answer: (33.60 to 33.70)

59. A sprinkler irrigation system with an irrigation efficiency of 70% is used to irrigate 16 ha of maize crop. The crop evapotranspiration of 6 mm day⁻¹ is used for estimating the irrigation depth. If the irrigation system is operated 20 hours per day for 10 days, the system capacity in L s⁻¹ is _______. [round off to two decimal places]

Answer: (18.90 to 19.10)

60. A falling ball viscometer is used to determine the dynamic viscosity of sunflower oil. The viscometer has a tube length of 10 cm with the ball diameter of 0.68 mm.The densities of oil and the ball are 921 kg m⁻³ and 2420 kg m⁻³, respectively. If the ball takes 44.5 s to fall from top of the tube, the viscosity of the oil in Pa s is________. [round off to three decimal places].

(Take g = 9.81 ms⁻²)

Answer: (0.165 to 0.172)

61. A cylindrical metallic silo of 3 m internal diameter and 10 m depth is loaded with maize grain having bulk density of 720 kg m⁻³. The angle of internal friction between the maize grains is 24°, and that between the grain and wall is 22°. Using Airy’s theory, the calculated lateral pressure in kPa at the bottom of the silo is_________. [round off to two decimal place]

(Take g = 9.81 m s⁻²)

Answer: (23.80 to 24.50)

62. Parboiled paddy is to be dried in a tray dryer under steady state conditions from an initial free moisture content of 0.40 kg H₂O (kg dry solid)⁻¹ to final free moisture content of 0.02 kg H₂O (kg dry solid)-1. The dry solid mass is 99.8 kg and the top surface area for drying is 4.654 m². The drying is occurring in both constant and falling rate periods. If constant drying rate of 1.51 kg H₂O m⁻² h⁻¹ is followed up to a critical moisture content of 0.195 kg H₂O (kg dry solid)⁻¹, then the total drying time in hour will be __________. [round off to two decimal places]

Answer: (9.20 to 9.30)

63. Sweet sorghum with an initial average particle size of 4.0 mm was pulverized using a burr mill at two different gap settings between stones. The average feed rate of the material is 200 kg h⁻¹. The resultant flour was analyzed by IS sieves for particle size determination and was found to be 0.336 mm and 0.306 mm for the first and second gap settings, respectively. Using Kick’s law, if the power required to grind the sorghum at first setting is 7.2 kW, the power requirement in kW with the second setting is ___________. [round off to two decimal places]

Answer: (7.40 to 7.55)

64. A walk-in deep freezer wall is made of 120 mm thick brick layer on the out side followed by 75 mm thick concrete and 50 mm thick cork layers inside. The mean temperatures measured over inside and outside wall surfaces are −18°C and 24 °C,respectively. The thermal conductivity of brick, concrete and cork are 0.69, 0.76 and 0.043 W m⁻¹ K⁻¹, respectively. Considering one square meter wall surface area,the heat transfer rate in W is ____________. [round off to one decimal place]

Answer: (29.0 to 30.0)

65. In an effort to conserve energy, a grain dryer is being modified to reuse a part (10 m³ s⁻¹) of the exhaust airflow at 70 ºC and 30% relative humidity. This part of exhaust is mixed with 20 m³ s⁻¹ of ambient air at 30 ºC and 60 % relative humidity.The details of the two air-stream conditions are given below.

The absolute humidity of the mixed air will be __________. [round off to three decimal places]

Answer: (0.028 to 0.032)

GATE Exam 2022 Aerospace Engineering (AE) Question Paper With Answer Key

June 8, 2023June 26, 2022 by suresh84

GATE-2022

AE: Aerospace Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. Writing too many things on the ________ while teaching could make the students get _________.

(A) bored / board

(B) board / bored

(D) bored / bored

Answer: (B)

2. Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality on the real number line?

Answer: (C)

3. If f(x) = 2 ln (√e^x), what is the area bounded by f(x) for the interval [0, 2]on the x-axis?

(A) 1/2

(B) 1

(D) 4

Answer: (C)

4. A person was born on the fifth Monday of February in a particular year.

Which one of the following statements is correct based on the aboveinformation?

(A) The 2nd February of that year is a Tuesday

(B) There will be five Sundays in the month of February in that year

(D) All Mondays of February in that year have even dates

Answer: (A)

Which one of the groups given below can be assembled to get the shape that isshown above using each piece only once without overlapping with each other?(rotation and translation operations may be used).

Answer: (B OR C)

Q.6 – Q. 10 Carry TWO marks each.

Which one of the following is the CORRECT logical inference based on theinformation in the above passage?

(A) Having ultra-black skin is only advantageous to species S

(B) Species S with lower collagen in their skin are at an advantage because it helpsthem avoid predators

(D) Having ultra-black skin is only disadvantageous to species S but advantageousonly to their predators

Answer: (C)

7. For the past m days, the average daily production at a company was 100 units per day.

If today’s production of 180 units changes the average to 110 units per day,what is the value of m?

(A) 18

(B) 10

(D) 5

Answer: (C)

8. Consider the following functions for non-zero positive integers, p and q.

Which one of the following options is correct based on the above?

(A) f(2,2) = g(2,2)

(B) f(g(2,2), 2) < f(2, g(2,2)

(D) f(3,2) >g(3,2)

Answer: (A)

9. Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day startat 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.

If the person starts from R at 7 AM and is required to visit S and return to R,what is the minimum time required?

(A) 6 hours 30 minutes

(B) 3 hours 45 minutes

(D) 5 hours 15 minutes

Answer: (A)

What is the ratio of the areas of unshaded regions of case M to that of case N?

(A) 2 : 3

(B) 1 : 1

(D) 2 : 1

Answer: (B)

Aerospace Engineering

Q.11 – Q.35 Carry ONE mark Each

11. The equation of the straight line representing the tangent to the curve y = x² at the point (1,1) is

(A) y = 2x – 2

(B) x = 2y – 1

(D) x – 1 = 2(y – 1)

Answer: (C)

12. Let be the unit vectors in the x, y and z directions, respectively. If the vector is rotated about positive by 135°, one gets

Answer: (D)

13. Let x be a real number and i = √−Then the real part of cos(ix) is

(A) sinh x

(B) cosh x

(D) sin x

Answer: (B)

14. The point of maximum entropy on a Fanno-curve in a Temperature-Entropy (T-s) diagram represents the

(A) maximum flow Mach number

(B) minimum flow Mach number

(D) normal shock in the flow

Answer: (C)

15. Consider a two-dimensional potential flow over a cylinder. If the freestream speed is U_∞, the maximum speed on the cylinder surface is

(A) U_∞/2

(B) 3U_∞/2

(D) 4U_∞/3

Answer: (C)

16. Consider steady, two-dimensional, incompressible flow over a non-porous flat plate as shown in the figure. For the control volume PQRS, the speed, u_∞, at section PQ is uniform and the speed at section RS is given by where 𝑛 is a positive integer. The value of A₀ for which the flow through section PS will vanish is:

Answer: (B)

17. Consider the velocity distribution, u(y) shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is

(A) to the right

(B) to the left

(D) vertically downwards

Answer: (B)

18. The service ceiling of an airplane is the altitude

(A) at which maximum rate of climb is 100 m/min

(B) beyond which theoretically the airplane cannot sustain level flight

(D) at which maximum rate of climb is 100 ft/min

Answer: (D)

19. Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?

(A) It contributes to

(B) It makes

(D) It makes

Answer: (A)

20. A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised:

(A) only at the top fibres of the cross-section

(B) only at the bottom fibres of the cross-section

(D) only at the centroidal fibres of the cross-section

Answer: (B)

21. A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force F as shown. The force in QR is

(A) 0

(B) F(tensile)

(D) √2F (tensile)

Answer: (B)

22. The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

(A) Centroids of (i) and (ii) coincide while shear centers do not

(B) Shear centers of (i) and (ii) coincide while centroids do not

(D) Neither centroids nor shear centers of (i) and (ii) coincide

Answer: (A)

23. The region of highest static temperature in a rocket engine and the region of highest heat flux are ____________, respectively.

(A) nozzle throat and nozzle entry

(B) combustion chamber and nozzle throat

(D) nozzle throat and combustion chamber

Answer: (B)

24. If are three mutually perpendicular unit vectors, then can take

(A) 0

(B) 1

(D) ∞

Answer: (B, C)

25. Across an oblique shock wave in a calorifically perfect gas,

(A) the stagnation enthalpy changes

(B) the stagnation entropy changes

(D) the speed of sound changes

Answer: (B, D)

26. NACA 2412 airfoil has

(A) 4% maximum camber with respect to chord

(B) maximum camber at 40% chord

(D) maximum camber at 20% chord

Answer: (B, C)

27. For International Standard Atmosphere (ISA) up to 11 km, which of the following statement(s) is/are true?

(A) The hydrostatic/ aerostatic equation is used

(B) The temperature lapse rate is taken as−10⁻² K/m

(C) The sea level conditions are taken as: pressure, p_s = 1.01325 × 10⁵ Pa; temperature, T_s = 300 K; density, ρ_s = 1.225 kg/m³

(D) Air is treated as a perfect gas

Answer: (A, D)

28. Let σ and τ represent the normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under pure bending is/are:

Answer: (B, C)

29. An isotropic linear elastic material point under plane strain condition in the x-y plane always obeys:

(A) out-of-plane normal strain,ϵ_zz = 0

(B) out-of-plane normal stress,σ_zz = 0

(D) out-of-plane shear strain, γ_xz = 0

Answer: (A, C, D)

30. A high-pressure-ratio multistage axial compressor encounters an extreme loading mismatch during starting. Which of the following technique(s) can be used to alleviate this problem?

(A) Blade cooling

(B) Variable angle stator vanes

(D) Multi-spool shaft

Answer: (B, C, D)

31. The arc length of the parametric curve: x = cos θ, y = sin θ, z = θ from θ = 0 to θ = 2π is equal to ________ (round off to one decimal place).

Answer: (8.6 to 9.1)

32. An unpowered glider is flying at a glide angle of 10 degrees. Its lift-to-drag ratio is _______ (round off to two decimal places).

Answer: (5.5 to 5.80)

33. The two-dimensional plane-stress state at a point is:

σ_xx = 110 MPa; σ_yy = 30 MPa; τ_xy = 40 MPa.

The normal stress, σ_n, on a plane inclined 45° as shown in the figure is _____MPa(round off to the nearest integer).

Answer: (109 to 111)

34. In a static test, a turbofan engine with bypass ratio of 9 has core hot exhaust speed 1.5 times that of fan exhaust speed. The engine is operated at a fuel to air ratio of f = 0.03. Both the fan and the core streams have no pressure thrust. The ratio of fan thrust to thrust from the core engine is _______ (round off to one decimal place).

Answer: (5.7 to 6.0)

35. In a single stage turbine, the hot gases come out of stator/ nozzle at a speed of 500 m/s and at an angle of 70 degrees with the turbine axis as shown. The design speed of the rotor blade is 250 m/s at the mean blade radius. The rotor blade angle, β, at the leading edge is ________ degrees (round off to one decimal place).

Answer: (51.5 to 52.6)

Q.36 – Q.65 Carry TWO marks Each

36. The height of a right circular cone of maximum volume that can be enclosed within a hollow sphere of radius R is

Answer: (C)

37. Consider the differential equation

The boundary conditions are y = 0 and at x = 0.

Then the value of y at x = 1/2 is

(A) 0

(B) √e

(D)

Answer: (C)

38. Consider the partial differential equation where x, y are real.

If f(x, y) = a(x) b(y), where a(x) and b(y) are real functions, which one of the following statements can be true?

(A) a(x) is a periodic function and b(y) is a linear function

(B) both a(x) and b(y) are exponential functions

(D) both a(x) and b(y) are periodic functions

Answer: (C)

39. A cylindrical object of diameter 900 mm is designed to move axially in air at 60 m/s. Its drag is estimated on a geometrically half-scaled model in water, assuming flow similarity.

Coefficients of dynamic viscosity and densities for air and water are1.86 × 10⁻⁵ Pa-s, 1.2 kg/m³and 1.01 × 10⁻³ Pa-s, 1000 kg/m³ respectively.

Drag measured for the model is 2280 N. Drag experienced by the full-scale objectis ____ N (rounded off to the nearest integer).

(A) 322

(B) 644

(D) 2576

Answer: (B)

40. Consider a conventional subsonic fixed-wing airplane. 𝑒 is the Oswald efficiency factor and AR is the aspect ratio. Corresponding to the minimum which of the following relations is true?

Answer: (B)

41. A horizontal load F is applied at point R on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area, A₀, and made of the same material with Young’s modulus E.

The horizontal displacement of point R is:

Answer: (C)

42. Which of the following is NOT always true for a combustion process taking place in a closed system?

(A) Total number of atoms is conserved

(B) Total number of molecules is conserved

(D) Total mass is conserved

Answer: (B)

43. The real function 𝑦 = sin²(|x|) is

(A) continuous for all x

(B) differentiable for all x

(D) not differentiable at x = 0

Answer: (A, B)

44. A convergent nozzle fed from a constant pressure, constant temperature reservoir, is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit (marked as Q).

Flow through the nozzle can be assumed to be isentropic.

If the exit area of the nozzle is increased while all the reservoir parameters and ambient conditions remain the same, then at steady state

(A) the nozzle will remain choked

(B) the nozzle will be un-choked

(D) the Mach number at section P will decrease

Answer: (A, C)

45. For a conventional airplane in straight, level, constant velocity flight condition, which of the following condition(s) is/are possible on Euler angles (ϕ, θ, ψ), angle of attack (α) and the sideslip angle (β)?

(A) ϕ = 0°, θ = 2°, ψ = 0°, α = 2°, β = 0°

(B) ϕ = 5°, θ = 0°, ψ = 0°, α = 2°, β = 0°

(D) ϕ = 0°, θ = 5°, ψ = 0°, α = 2°, β = 5°

Answer: (A)

46. Consider a high Earth-orbiting satellite of angular momentum per unit mass and eccentricity e.

The mass of the Earth is M and G is the universal gravitational constant.

The distance between the satellite’s center of mass and the Earth’s center of mass is r, the true anomaly is θ, and the phase angle is zero.

Which of the following statements is/are true?

(A) The trajectory equation is

(B) The trajectory equation is

(D) The sum of potential energy and kinetic energy of the satellite is conserved

Answer: (B, C, D)

47. A rocket operates at an absolute chamber pressure of 20 bar to produce thrust, F₁. The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a convergent-divergent nozzle with exit to throat area ratio (A_e/A_t) of 3.5 and thrust coefficient, C_{F, 1} = 1.42.

The same rocket when operated at an absolute chamber pressure of 50 barproduces thrust F₂ and the thrust coefficient is C_F,₂.

Which of the following statement(s) is/are correct?

Answer: (B, D)

48. is a vector field where are the base vectors of a cartesian coordinate system.

Using the Gauss divergence theorem, the value of the outward flux of the vectorfield over the surface of a sphere of unit radius centered at the origin is________(rounded off to one decimal place).

Answer: (7.4 to 7.7)

49. The largest eigenvalue of the given matrix is _____.

Answer: (2 to 2)

50. A rotational velocity field in an air flow is given as with a = 10 s⁻¹, b = 20 s⁻¹.

The air density is 1.0 kg/m³ and the pressure at (x, y) = (0 m, 0 m) is 100 kPa.

Neglecting gravity, the pressure at (x, y) = (6 m, 8 m) is _____ kPa (rounded off to nearest integer).

Answer: (88 to 91)

51. Consider a circulation distribution over a finite wing given by the equation below.

The wingspan 𝑏 is 10 m, the maximum circulationΓ₀is 20 m²/s, density of air is1.2 kg/m³ and the free stream speed is 80 m/s.

The lift over the wing is ______N (rounded off to the nearest integer).

Answer: (9500 to 9800)

52. Consider a solid cylinder housed inside another cylinder as shown in the figure.Radius of the inner cylinder is 1 m and itsheight is 2 m. The gap between thecylinders is 5 mm and is filled with a fluid of viscosity 10⁻⁴ Pa-s.

The inner cylinder is rotating at a constant angular speed of 5 rad/s while the outercylinder is stationary. Friction at thebottom surfaces can be ignored. Velocityprofile in the vertical gap between thecylinders can be assumed to be linear.

The driving moment required for the rotating motion of the inner cylinder is____________ Nm (rounded off to two decimal places).

Answer: (1.24 to 1.28)

53. In a converging duct, area and velocity at section P are 1 m² and 15 m/s,respectively. The temperature of the fluid is 300 K.

Air flow through the nozzle can be assumed to be inviscid and isothermal.

Characteristic gas constant is 287 J/(kg-K) and ratio of specific heats is 1.4 for air.

To ensure that the air flow remains incompressible (Mach number, M ≤ 0.3) in the duct, the minimum area required at section Q is _____ m² (rounded off to two decimal places).

Answer: (0.14 to 0.15)

54. Consider a thin symmetric airfoil at 2 degree angle of attack in a uniform flow at 50 m/s. The pitching moment coefficient about its leading edge is _____ (rounded off to three decimal places).

Answer: (-0.057 to -0.053)

55. A convergent-divergent nozzle with adiabatic walls is designed for an exit Mach number of 2.3. It is discharging air to atmosphere under the conditions indicated in the figure.

Flow through the nozzle is inviscid, the characteristic gas constant for air is 287 J/kg-K), and γ = 1.4.

When the reservoir pressure is 25 bar (absolute), and temperature is 300 K, Prandtl-Meyer expansion waves appear at the nozzle exit as shown.

The minimum percentage change in the reservoir pressure required to eliminate the wave system at the nozzle exit under steady state is _______%.

Answer: (49 to 51 OR -51 to -49)

56. A conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at aconstant speed of 100 m/s at sea level.

Taking the acceleration due to gravity as 10 m/s², the bank angle of the airplane is ______ degrees.

Answer: (44 to 46)

57. Given: The tip deflection and tip slope for a tip loaded cantilever of length L are: respectively, where N is the tip force and EI is the flexural rigidity.

A cantilever PQ of rectangular cross-section is subjected to transverse load, F, at its mid-point. Two cases are considered as shown in the figure. In Case I, the end Q is free and in Case II, Q is simply supported.

The ratio of the magnitude of the maximum bending stress at P in Case I to that in Case II is ________ (rounded off to one decimal place).

Answer: (2.6 to 2.7)

58. A simply supported Aluminium column of length 1 m and rectangular cross-section w × t with t ≤ w, is subjected to axial compressive loading.

Young’s modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa.

The value of 𝑡 at which the failure load for yielding and buckling coincide is ______ mm.

Answer: (43 to 48)

59. A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the figure.

The allowable stress under uniaxial tension is 100 MPa.

Using maximum principal stress criterion, the minimum thickness, t, of the shaft so that it does not fail is _____ mm (rounded off to the nearest integer).

Answer: (1 to 1)

60. A 10 kN axial load is applied eccentrically on a rod of square cross-section (1 cm× 1 cm) as shown in the figure.

The strains measured by the two strain gages attached to the top and bottom surfaces at a distance of 0.5 m from the tip areϵ₁ = 0.0016 and ϵ₂ = 0.0004, respectively.

The eccentricity in loading,e, is ______ mm.

Answer: (0.95 to 1.05)

61. For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., 2𝑏 = 20 mm. Thickness is 0.6 mm. The second moment of area about a horizontal axis passing through the centroid is______ mm⁴.

Answer: (2700 to 2960)

62. A damper with damping coefficient, c, is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in figure. The system undergoes under-damped oscillations.

If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value

ofc is ____ Ns/m (rounded off to the nearest integer).

Answer: (19 to 21)

63. A uniform rigid prismatic bar of total mass m is suspended from a ceiling by two identical springs as shown in figure.

Letω₁ and ω₂be the natural frequencies of mode I and mode II respectively (ω₁<ω₂).

The value of ω₂/ω₁ is _________ (rounded off to one decimal place).

Answer: (1.7 to 1.8)

64. An ideal ramjet is to operate with exhaust gases optimally expanded to ambient pressure at an altitude where temperature is 220 K. The exhaust speed at the nozzle

exit is 1200 m/s at a temperature of 1100 K.

Given :γ = 1.4 at 220 K; R = 287 J/kg-K) for air

γ = 1.33 at 1100 K; R = 287 J/(kg-K) for exhaust gases.

The cruise speed of this ramjet is ________ m/s (rounded off to nearest integer).

Answer: (545 to 555)

65. A multistage axial compressor takes in air at 1 atm, 300 K and compresses it to a minimum of 5 atm.

The mean blade speed is 245 m/s and work coefficient, ∆C_θ/U is 0.55 for each stage. For air, use C_p = 1005 J/(kg-K), R = 287 J/(kg-K) and γ = 1.4.

If the compression is isentropic, the number of stages required is ___________(rounded off to the next higher integer).

Answer: (6 or greater than 6)