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GATE Exam 2018 Mechanical Engineering (ME-2) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _________.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

6. Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

(A) 0

(B) 2

(D) 8

Answer: (C)

7. A wire would enclose an area of 1936 m², if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

8. A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

10. An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Mechanical Engineering (Set 2)

Q. 1 – Q. 25 carry one mark each.

1. The Fourier cosine series for an even function f(x) is given by

The value of the coefficient a² for the function f(x) = cos²(x) in [0, π] is

(A) –0.5

(B) 0.0

(D) 1.0

Answer: (C)

2. The divergence of the vector field

(A) 0

(B) e^x cosy + e^x sin y

(D) 2e^x sin y

Answer: (C)

3. Consider a function u which depends on position x and time t. The partial differential equation

is known as the

(A) Wave equation

(B) Heat equation

(D) Elasticity equation

Answer: (B)

4. If y is the solution of the differential equation the value of y(–1) is

(A) −2

(B) −1

(D) 1

Answer: (C)

5. The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is

Answer: (B)

6. A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is

(A) 5

(B) 20

(D) 2000

Answer: (D)

7. In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?

(A) Transmissibility will increase.

(B) Transmissibility will decrease.

(D) Time period of free oscillations will decrease.

Answer: (C)

8. Pre-tensioning of a bolted joint is used to

(A) strain harden the bolt head

(B) decrease stiffness of the bolted joint

(D) prevent yielding of the thread root

Answer: (C)

9. The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 μm. If the peak wavelength of emitted radiation changes to 2.90 μm, then the temperature (in K) of the black body is

(A) 500

(B) 1000

(D) 8000

Answer: (B)

10. For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (Δs) from state 1 to 2?

Answer: (A)

11. Select the correct statement for 50% reaction stage in a steam turbine.

(A) The rotor blade is symmetric.

(B) The stator blade is symmetric.

(D) The absolute exit flow angle is equal to inlet angle of rotor blade.

Answer: (D)

12. Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by

Answer: (A or D)

13. During solidification of a pure molten metal, the grains in the casting near the mould wall are

(A) coarse and randomly oriented

(B) fine and randomly oriented

(D) coarse and ordered

Answer: (B)

14. Match the following products with the suitable manufacturing process

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

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

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

Answer: (C)

15. Feed rate in slab milling operation is equal to

(A) rotation per minute (rpm)

(B) product of rpm and number of teeth in the cutter

(D) product of rpm, feed per tooth and number of teeth in contact

Answer: (C)

16. Metal removal in electric discharge machining takes place through

(A) ion displacement

(B) melting and vaporization

(D) plastic shear

Answer: (B)

17. The preferred option for holding an odd-shaped workpiece in a centre lathe is

(A) live and dead centres

(B) three jaw chuck

(D) four jaw chuck

Answer: (D)

18. A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is

(A) 64

(B) 212

(D) 1200

Answer: (C)

19. If then det(A^–1) is ________(correct to two decimal places).

Answer: (0.25 to 0.25)

20. A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ________ (correct to two decimal places).

Answer: (35.24 to 35.44)

21. Fatigue life of a material for a fully reversed loading condition is estimated from

σ_a = 1100 N^–0.15

where σ_a is the stress amplitude in MPa and N is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of 1 × 10⁵ cycles under the same loading condition is ________ (correct to two decimal places).

Answer: (190.00 to 200.00)

22. The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is δ_L. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to δ_L)is ________ (correct to two decimal places).

Answer: (41.30 to 41.50)

23. An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in kJ/cycle) is ______ (correct to two decimal places).

Answer: (62.00 to 63.00)

24. The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).

Answer: (0.36 to 0.40)

25. A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in m) by the ball is __________ (correct to two decimal places).

Answer: (Marks to All)

Q. 26 – Q. 55 carry two marks each.

26. Let z be a complex variable. For a counter-clockwise integration around a unit circle C , centred at origin,

the value of A is

(A) 2/5

(B) 1/2

(D) 4/5

Answer: (A)

27. L et X₁ and X₂ be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X₁, X₂) is

(A) exponentially distributed with mean 1/6

(B) exponentially distributed with mean 2

(D) normally distributed with mean 1/6

Answer: (A)

28. For a position vector the norm of the vector can be defined as Given a function

Answer: (C)

29. In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180° m/s². If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2) of point R is

(A) 8∠233°

(B) 10∠225°

(D) 8∠217°

Answer: (D)

30. A rigid rod of length 1 m is resting at an angle θ = 45° as shown in the figure. The end P is dragged with a velocity of 5 U  m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is

(A) 5

(B) 6

(D) 10

Answer: (A)

31. A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment 𝑇 = 150 Nm is applied at a distance of 100 mm from end P. The torsional reactions (𝑇_𝑃, 𝑇_𝑄 ) in Nm at the ends P and Q respectively are

(A) (50, 100)

(B) (75, 75)

(D) (120, 30)

Answer: (C)

32. In a cam-follower, the follower rises by h as the cam rotates by δ (radians) at constant angular velocity ω (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period. Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is

(A) 4hω/δ

(B) hω

(D) 2hω

Answer: (C)

33. A bimetallic cylindrical bar of cross sectional area 1 m² is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10^–6 in Steel bar and compressive axial strain of magnitude 10^–6 in Aluminum bar, the magnitude of the required force P (in kN) along the indicated direction is

(A) 70

(B) 140

(D) 280

Answer: (D)

34. Air flows at the rate of 1.5 m³/s through a horizontal pipe with a gradually reducing crosssection as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2 kg/m³ and assume inviscid
incompressible flow. The change in pressure (p₁ – p₂) (in kPa) between sections 1 and 2 is

(A) –1.28

(B) 2.56

(D) 1.28

Answer: (A)

35. The problem of maximizing z = x₁ – x₂ subject to constraints x₁ + x₂ ≤ 10, x₁ ≥ 0, x₂ ≥ 0 and x₂ ≤ 5 has

(A) no solution

(B) one solution

(D) more than two solutions

Answer: (B)

36. Given the ordinary differential equation

with the value of y(1) is _________ (correct to two decimal places).

Answer: (1.45 to 1.48)

37. A thin-walled cylindrical can with rigid end caps has a mean radius R= 100 mm and a wall thickness of t = 5. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ___________ (correct to two decimal places).

Answer: (4.80 to 5.20)

38. A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between –10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the
material is 600 MPa. The bar cross-section is square with side a. If the factor of safety is 2, the value of a (in mm), according to the modified Goodman’s criterion, is ________ (correct to two decimal places).

Answer: (31.60 to 31.65)

39. A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s²) of the centre of the disc is ________ (correct to two decimal places).

Answer: (6.60 to 6.70)

40. A frictionless circular piston of area 10^–2 m² and mass 100 kg sinks into a cylindrical container of the same area filled with water of density 1000 kg/m³ as shown in the figure. The container has a hole of area 10^–3 m² at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is _____ (correct to three decimal places).

Answer: (1.400 to 1.500)

41. A 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is 350 K. The value of Stefan- Boltzmann constant, σ is 5.67 × 10^–8 W/m² K⁴. Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in W/m²) is ________ (correct to two decimalplaces).

Answer: (385.00 to 395.00)

42. Air is held inside a non-insulated cylinder using a piston (mass M=25 kg and area A=100 cm²) and stoppers (of negligible area), as shown in the figure. The initial pressure P_i and temperature T_i of air inside the cylinder are 200 kPa and 400°C, respectively. The ambient pressure P_∞ and temperature T_∞ are 100 kPa and 27°C, respectively. The temperature of the air inside the cylinder (°C) at which the piston will begin to move is _________ (correct to two decimal places).

Answer: (145.00 to 150.00)

43. A standard vapor compression refrigeration cycle operating with a condensing temperature of 35°C and an evaporating temperature of –10°C develops 15 kW of cooling. The p-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is 0.75, the magnitude of compressor power (in kW) is _________ (correct to two decimal places).

Answer: (9.50 to 10.50)

44. A mbient air is at a pressure of 100 kPa, dry bulb temperature of 30°C and 60% relative humidity. The saturation pressure of water at 30°C is 4.24 kPa. The specific humidity of air (in g/kg of dry air) is ________ (correct to two decimal places).

Answer: (16.00 to 16.50)

45. A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m³/s at 450 rpm. Take the water density and the acceleration due to gravity as 10³ kg/m³ and 10 m/s², respectively. Assume no losses both in model and prototype turbines. The power (in MW) of a full sized turbine while working under a head of 30 m is _______ (correct to two decimal places).

Answer: (28.85 to 29.25)

46. The true stress (in MPa) versus true strain relationship for a metal is given by

σ = 1020ε^0.4

The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is 100 mm². The cross-sectional area at the time of necking (in mm²) is ________ (correct to two decimal places)

Answer: (65.00 to 70.00)

47. A steel wire is drawn from an initial diameter (d_i) of 10 mm to a final diameter (d_f) of 7.5 mm. The half cone angle (α) of the die is 5° and the coefficient of friction (μ) between the die and the wire is 0.1. The average of the initial and final yield stress [σ_Y)avg] is 350 MPa. The equation for drawing stress σ_f, (in MPa) is given as:

The drawing stress (in MPa) required to carry out this operation is _________ (correct to two decimal places).

Answer: (315.00 to 317.00)

48. Following data correspond to an orthogonal turning of a 100 mm diameter rod on a lathe. Rake angle: +15° ; Uncut chip thickness: 0.5 mm; nominal chip thickness after the cut: 1.25 mm. The shear angle (in degrees) for this process is _______ (correct to two decimal places).

Answer: (22.00 to 24.00)

49. T aylor’s tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in 20 mm thick mild steel plates. In test 1, a drill lasted 300 holes at 150 rpm while in test 2, another drill lasted 200 holes at 300 rpm. The maximum number of holes that can be made by another drill from the above batch at 200 rpm is ______ (correct to two decimal places).

Answer: (252.00 to 254.00)

50. F or sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov’s law for the estimation of the total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal places)

Answer: (42.00 to 52.00)

51. The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is _______.

Answer: (7 to 7 or 11 to 11)

52. A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The material removal rate (in mm³/min) is expressed as

4 × 10⁴ IT^–1.23

where I = 300 A and the melting point of the material, T = 1600°C . The time (in minutes) for machining this hole is ________ (correct to two decimal places)

Answer: (7.00 to 7.30)

53. A welding operation is being performed with voltage = 30 V and current = 100 A. The cross-sectional area of the weld bead is 20 mm². The work-piece and filler are of titanium for which the specific energy of melting is 14 J/mm³. Assuming a thermal efficiency of the welding process 70%, the welding speed (in mm/s) is __________ (correct to two decimal places).

Answer: (7.49 to 7.51)

54. S team in the condenser of a thermal power plant is to be condensed at a temperature of 30°C with cooling water which enters the tubes of the condenser at 14°C and exits at 22°C. The total surface area of the tubes is 50 m², and the overall heat transfer coefficient is 2000 W/m² K. The heat transfer (in MW) to the condenser is ______ (correct to two decimal places).

Answer: (1.14 to 1.16)

55. A vehicle powered by a spark ignition engine follows air standard Otto cycle (γ=1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is _______ (correct to two decimal places).

Answer: (7.40 to 7.80)

GATE Exam 2018 Mechanical Engineering (ME-1) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

4. A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m² of area. What is the area of the original rectangle in square meters?

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

8. From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Mechanical Engineering (Set 1)

Q. 1 – Q. 25 carry one mark each.

1. Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is

(A) 1/72

(B) 1/55

(D) 1/27

Answer: (B)

2. The rank of the matrix is

(A) 1

(B) 2

(D) 4

Answer: (B)

3. According to the Mean Value Theorem, for a continuous function f(x) in the interval [a, b], there exists a value ξ in this interval such that

(A) f(ξ) (b – a)

(B) f(b)(ξ – a)

(D) 0

Answer: (A)

4. F(z) is a function of the complex variable z = x + iy given by

F(z) = iz + k Re(z) + i Im(z)

For what value of k will F(z) satisfy the Cauchy-Riemann equations?

(A) 0

(B) 1

(D) y

Answer: (B)

5. A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

The tensions in the strings are

(A) T₁ = 100 N and T₂ = 0 N

(B) T₁ = 0 N and T₂ = 100 N

(D) T₁ = 25 N and T₂ = 75 N

Answer: (B)

6. If σ₁ and σ₃ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

Answer: (B)

7. The equation of motion for a spring-mass system excited by a harmonic force is

where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to

Answer: (D)

8. For an Oldham coupling used between two shafts, which among the following statements are correct?

I. Torsional load is transferred along shaft axis.

II. A velocity ratio of 1:2 between shafts is obtained without using gears.

III. Bending load is transferred transverse to shaft axis.

IV. Rotation is transferred along shaft axis.

(A) I and III

(B) I and IV

(D) II and IV

Answer: (B)

9. For a two-dimensional incompressible flow field given by where A > 0, which one of the following statements is FALSE?

(A) It satisfies continuity equation.

(B) It is unidirectional when x → 0 and y → ∞

(D) It is irrotational.

Answer: (C)

10. Which one of the following statements is correct for a superheated vapour?

(A) Its pressure is less than the saturation pressure at a given temperature.

(B) Its temperature is less than the saturation temperature at a given pressure.

(D) Its enthalpy is less than the enthalpy of the saturated vapour at a given pressure.

Answer: (A)

11. In a linearly hardening plastic material, the true stress beyond initial yielding

(A) increases linearly with the true strain

(B) decreases linearly with the true strain

(D) remains constant

Answer: (A)

12. The type of weld represented by the shaded region in the figure is

(A) groove

(B) spot

(D) plug

Answer: (C)

13. Using the Taylor’s tool life equation with exponent n = 0.5 if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

(A) 4

(B) 2

(D) 0.5

Answer: (A)

14. A grinding ratio of 200 implies that the

(A) grinding wheel wears 200 times the volume of the material removed

(B) grinding wheel wears 0.005 times the volume of the material removed

(D) ratio of volume of abrasive particle to that of grinding wheel is 200

Answer: (B)

15. Interpolator in a CNC machine

(A) controls spindle speed

(B) coordinates axes movements

(D) commands canned cycle

Answer: (B)

16. The time series forecasting method that gives equal weightage to each of the m most recent observations is

(A) Moving average method

(B) Exponential smoothing with linear trend

(D) Kalman Filter

Answer: (A)

17. The number of atoms per unit cell and the number of slip systems, respectively, for a facecentered cubic (FCC) crystal are

(A) 3, 3

(B) 3, 12

(D) 4, 48

Answer: (C)

18. A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is

(A) 33.3

(B) 3.33

(D) 0.0033

Answer: (C)

19. A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial load (in kN) is ____ (correct to two decimal places).

Answer: (1.00 to 1.20)

20. A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is __________.

Answer: (1 to 1)

21. If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is _____ (correct to two decimal places).

Answer: (8.00 to 8.50)

22. A flat plate of width L = 1 m is pushed down with a velocity U = 0.01 m/s towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, u_avg of the fluid (in m/s) draining out at the instant shown in the figure is _____________(correct to three decimal places).

Answer: (0.045 to 0.055)

23. An ideal gas undergoes a process from state 1 (T₁ = 300 K p₁ = 100 kPa) to state 2 (T2 = 600 K, p₂ = 500 kPa). The specific heats of the ideal gas are : C_p = 1 kJ/kg-K and C_v = 0.7 kJ/kg-K. The change in specific entropy of the ideal gas from state 1 to state 2 (in kJ/kg-K) is ___________(correct to two decimal places).

Answer: (0.20 to 0.22)

24. For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is _______ (correct to two decimal places).

Answer: (0.45 to 0.52)

25. T he height (in mm) for a 125 mm sine bar to measure a taper of 27 ̊ 32′ on a flat work piece is _______ (correct to three decimal places).

Answer: (57.000 to 58.000)

Q. 26 – Q. 55 carry two marks each.

26. Let X₁, X₂ be two independent normal random variables with means μ1, μ2 and standard deviations μ₁, μ₂, respectively. Consider Y = X₁ – X₂; μ1 = μ2 =1, σ₁ = 1, σ₂ = 2. Then,

(A) Y is normally distributed with mean 0 and variance 1

(B) Y is normally distributed with mean 0 and variance 5

(D) Y has mean 0 and variance 1, but is NOT normally distributed

Answer: (B)

27. The value of the integral

over the closed surface S bounding a volume V, where is the position vector and is the normal to the surface S, is

(A) V

(B) 2V

(D) 4V

Answer: (C)

28. A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s² and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

(A) 1

(B) 2

(D) ∞

Answer: (C)

29. The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress σ_y (in kPa) is

(A) 9.45

(B) 18.88

(D) 75.50

Answer: (C)

30. An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100 teeth on the outer surface. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm in the clockwise direction, then the rpm of D in the clockwise direction is

(A) 240

(B) –240

(D) –375

Answer: (C)

31. A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30° as shown in the figure.

The glue used at the interface fails if

Criterion 1: the maximum normal stress exceeds 2.5 MPa.

Criterion 2: the maximum shear stress exceeds 1.5 MPa.

Assume that the interface fails before the logs fail. When a uniform tensile stress of 4 MPa is applied, the interface

(A) fails only because of criterion 1

(B) fails only because of criterion 2

(D) does not fail

Answer: (C)

32. A self-aligning ball bearing has a basic dynamic load rating (C₁₀, for 10⁶ revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in 10⁶ revolutions) is

(A) below 0.5

(B) 0.5 to 0.8

(D) above 1.0

Answer: (A)

33. A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m) where the jet strikes the floor is

(A) 0.5

(B) 1.0

(D) 4.0

Answer: (B)

34. In a Lagrangian system, the position of a fluid particle in a flow is described as x = x₀e^–kt and y = y₀e^kt where t is the time while 𝑥_𝑜, 𝑦_𝑜, and k are constants. The flow is

(A) unsteady and one-dimensional

(B) steady and two-dimensional

(D) unsteady and two-dimensional

Answer: (B)

35. The maximum reduction in cross-sectional area per pass ( R ) of a cold wire drawing process is

R = 1 – e^{–(n + 1)}

where n represents the strain hardening coefficient. For the case of a perfectly plastic material, R is

(A) 0.865

(B) 0.826

(D) 0.632

Answer: (D)

36. The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure is _______ (correct to two decimal places).

Answer: (52.00 to 54.00)

37. An explicit forward Euler method is used to numerically integrate the differential equation

using a time step of 0.1. With the initial condition y(0) = 1 , the value of (1) y computed by this method is ___________ (correct to two decimal places).

Answer: (2.55 to 2.65)

38. F(s) is the Laplace transform of the function

f(t) = 2t²e^–t

F(1) is ________ (correct to two decimal places).

Answer: (0.48 to 0.52)

39. A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).

Answer: (29.8 to 30.1)

40. A machine of mass 𝑚 = 200 kg is supported on two mounts, each of stiffness 𝑘 = 10 kN/m. The machine is subjected to an external force (in N) 𝐹(𝑡) = 50 cos 5𝑡. Assuming only vertical translatory motion, the magnitude of the dynamic force (in N)
transmitted from each mount to the ground is ______ (correct to two decimal places).

Answer: (33.00 to 33.50)

41. A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45° and a force of 40 N is acting towards the left on the slider. The length of the crank is 30 mm and the connecting rod is 70 mm. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is
_________ (correct to two decimal places).

Answer: (1.00 to 1.20)

42. A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles.

The total flow rate Q through the sprinkler is 1 litre/sec and the cross-sectional area of each exit nozzle is 1 cm². Assuming equal flow rate through both arms and a frictionless hinge, the steady state angular speed of rotation (in rad/s) of the sprinkler is ______ (correct to two decimal places).

Answer: (9.50 to 10.50)

43. A solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall as shown in the figure below. A thin oil film of thickness h = 0.15 mm provides lubrication between the block and the wall. The surface area of the face of the block in contact with the oil film is 0.04 m^2. The velocity distribution within the oil film gap is linear as shown in the figure. Take dynamic viscosity of oil as 7×10^-3 Pa-s and acceleration due to gravity as 10 m/s². Neglect weight of the oil. The terminal velocity V (in m/s) of the block is _________ (correct to one decimal place).

Answer: (10.6 to 10.8)

44. A tank of volume 0.05 m³ contains a mixture of saturated water and saturated steam at 200°C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg K) of the mixture is ___________ (correct to two decimal places).

Answer: (2.45 to 2.55)

45. Steam flows through a nozzle at a mass flow rate of with a heat loss of 5 kW. The enthalpies at inlet and exit are 2500kJ/kg and 2350 kJ/kg, respectively. Assuming negligible velocity at inlet (C₁ ≈ 0), the velocity (C₂ ) of steam (in m/s) at the nozzle exit is __________ (correct to two decimal places).

Answer: (445.00 to 450.00)

46. An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air: c_p = 1.005 kJ/kg K, c_v = 0.718 kJ/kg K, R = 0.287 kJ/kg K. The maximum temperature (in K) of the cycle is _________ (correct to one decimal place).

Answer: (1402.0 to 1406.0)

47. A plane slab of thickness L and thermal conductivity k is heated with a fluid on one side (P), and the other side (Q) is maintained at a constant temperature, T_Q of 25°C, as shown in the figure. The fluid is at 45°C and the surface heat transfer coefficient, h, is 10 W/m²k . The steady state temperature, T_P, (in °C) of the side which is exposed to the fluid is _______
(correct to two decimal places).

Answer: (33.50 to 34.30)

48. The true stress (σ) – true strain (ε) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of 0.5. Then from point A, there is unloading up to point B, i.e., to stress of 100 MPa. Given that the Young’s modulus E = 200 GPa, the natural strain at point B (ε_B)is _________ (correct to three decimal places).

Answer: (0.498 to 0.498)

49. An orthogonal cutting operation is being carried out in which uncut thickness is 0.010 mm, cutting speed is 130 m/min, rake angle is 15° and width of cut is 6 mm. It is observed that the chip thickness is 0.015 mm, the cutting force is 60 N and the thrust force is 25 N. The ratio of friction energy to total energy is __________ (correct to two decimal places).

Answer: (0.39 to 0.49)

50. A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is _________________ (correct to two decimal places).

Answer: (0.69 to 0.70)

51. The minimum value of 3𝑥 + 5𝑦

such that:

is _______.

Answer: (0 to 0)

52. Pocessing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest processing time rule is ___________ (correct to two decimal places).

Answer: (6.31 to 6.35)

53. The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force 𝐹 = 100 𝑁 is applied at the free end of the lever as shown. Given that the coefficient of friction between the shoe and the drum is 0.3, the braking torque (in Nm ) applied on the
drum is _______ (correct to two decimal places).

Answer: (8.00 to 9.00)

54. Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. Assuming g = 10 m/s², the normal force (in N) at Q is _______ (correct to two decimal places).

Answer: (419.00 to 421.00)

55. An electrochemical machining (ECM) is to be used to cut a through hole into a 12 mm thick aluminum plate. The hole has a rectangular cross-section, 10 mm × 30 mm. The ECM operation will be accomplished in 2 minutes, with efficiency of 90%. Assuming specific removal rate for aluminum as 3.44 × 10^-2 mm³/(A s), the current (in A) required is __________ (correct to two decimal places).

Answer: (968.80 to 969.20)

GATE Exam 2018 Mathematics (MA) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _________.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

(A) 0

(B) 2

(D) 8

Answer: (C)

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Mathematics

Q.1–Q.25 carry one mark each

1. The principal value of (–1)^(–2i/π) is

(A) e²

(B) e²ⁱ

(D) e^–2

Answer: (A)

2. Let f : ℂ → ℂbe an entire function with f(0) = 1, f(1) = 2 and f′ (0) = 0. If there exists M > 0 such that |f″ (z)| ≤ M for all z ∈ ℂ, then f(2) =

(A) 2

(B) 5

(D) 5 + 2i

Answer: (B)

3. In the Laurent series expansion of valid for |z – 1| > 1, the coefficient of is

(A) –2

(B) –1

(D) 1

Answer: (C)

4. Let X and Y be metric spaces, and let f : X → Y be a continuous map. For any subset S of X, which one of the following statements is true?

(A) If S is open, then f(S) is open

(B) If S is connected, then f(S) is connected

(D) If S is bounded, then f(S) is bounded

Answer: (B)

5. The general solution of the differential equation is given by (with an arbitrary positive constant k)

Answer: (C)

6. Let p_n(x) be the polynomial solution of the differential equation

with p_n(1) = 1 for n = 1, 2, 3, …….. If

then α_n is

(A) 2n

(B) 2n + 1

(D) 2n + 3

Answer: (D)

7. In the permutation group S_6,the number of elements of order 8 is

(A) 0

(B) 1

(D) 4

Answer: (A)

8. Let R be a commutative ring with 1 (unity) which is not a field. Let I ⊂ R be a proper ideal such that every element of R not in I is invertible in R: Then the number of maximal deals of R is

(A) 1

(B) 2

(D) infinite

Answer: (A)

9. Let f : ℝ → ℝ be a twice continuously differentiable function. The order of convergence of the secant method for finding root of the equation f(x) = 0 is

Answer: (A)

10. The Cauchy problem uu_x + yu_y = x with u(x, 1) = 2x, when solved using its characteristic equations with an independent variable t, is found to admit of a solution in the form

Then f(s, t) =

Answer: (A)

11. An urn contains four balls, each ball having equal probability of being white or black. Three black balls are added to the urn. The probability that five balls in the urn are black is

(A) 2=7

(B) 3=8

(D) 5=7

Answer: (B)

12. For a linear programming problem, which one of the following statements is FALSE?

(A) If a constraint is an equality, then the corresponding dual variable is unrestricted in sign

(B) Both primal and its dual can be infeasible

(D) Even if both primal and dual are feasible, the optimal values of the primal and the dual can differ

Answer: (D)

13. Let , where a, b, c, f are real numbers and f ≠ 0: The geometric multiplicity of the largest eigenvalue of A equals _______.

14. Consider the subspaces

of ℝ³ . Then the dimension of W₁ +W₂ equals ______.

Answer: (1 to 1)

15. Let V be the real vector space of all polynomials of degree less than or equal to 2 with real coefficients. Let T : V → V be the linear transformation given by

T(p) = 2p + p′

where p′ is the derivative of p. Then the number of nonzero entries in the Jordan canonical form of a matrix of T equals __________.

Answer: (5 to 5)

16. Let I = [2, 3), J be the set of all rational numbers in the interval [4, 6], K be the Cantor (ternary) set, and let L = {7 + x : x ∈ K}. Then the Lebesgue measure of the set I ∪ J ∪ L equals _____.

Answer: (1 to 1)

17. Let u(x, y, z) = x² – 2y + 4y² for (x, y, z) ∈ ℝ³. Then the directional derivative of u in the direction at the point (5, 1, 0) is _______.

Answer: (6 to 6)

18. If the Laplace transform of y(t) is given by then y(0) + y′(0) = ________.

Answer: (1 to 1)

19. The number of regular singular points of the differential equation

in the interval is equal to ________.

Answer: (2 to 2)

20. Let F be a field with 7⁶ elements and let K be a subfield of F with 49 elements. Then the dimension of F as a vector space over K is _________.

Answer: (3 to 3)

21. Let C([0, 1]) be the real vector space of all continuous real valued functions on [0, 1], and let T be the linear operator on C([0, 1]) given by

Then the dimension of the range space of T equals____________.

Answer: (2 to 2)

22. Let a ∈ (–1, 1) be such that the quadrature rule

is exact for all polynomials of degree less than or equal to 3: Then 3a² = ______.

Answer: (1 to 1)

23. Let X and Y have joint probability density function given by

If f_Y denotes the marginal probability density function of Y , then f_Y (1=2) =_______.

Answer: (1 to 1)

24. Let the cumulative distribution function of the random variable X be given by

Then ℙ (X = 1/2) = _______.

Answer: (0.25 to 0.25)

25. Let {X_j} be a sequence of independent Bernoulli random variables with ℙ (X_j = 1) = 1/4 and let Then Y_n converges, in probability to ________.

Answer: (0.25 to 0.25)

Q.26-Q.55 carry two marks each

26. Let Γ be the circle given by z = 4e^iθ, where θ varies from 0 to 2π Then

(A) 2πi(e² – 1)

(B) πi(1 – e²)

(D) 2πi(1 – e²)

Answer: (C)

27. The image of the half plane Re(z) + Im(z) > 0 under the map is given by

(A) Re(w) > 0

(B) Im (w) > 0

(D) |w| < 1

Answer: (D)

28. Let D ⊂ ℝ² denote the closed disc with center at the origin and radius 2. Then

(A) π(1 – e^–4)

(B)

(D)

Answer: (A)

29. Consider the polynomial p(X) = X⁴ + 4 in the ring ℚ[X} of polynomials in the variable X with coefficients in the field ℚ of rational numbers. Then

(A) the set of zeros of p(X) in C forms a group under multiplication

(B) p(X) is reducible in the ring ℚ[X]

(D) the splitting field of p(X) has degree 4 over ℚ

Answer: (B)

30. Which one of the following statements is true?

(A) Every group of order 12 has a non-trivial proper normal subgroup

(B) Some group of order 12 does not have a non-trivial proper normal subgroup

(D) Every group of order 12 has an element of order 12

Answer: (A)

31. For an odd prime p, consider the ring Then the element 2 in is

(A) a unit

(B) a square

(D) irreducible

Answer: (D)

32. Consider the following two statements:

P : The matrix has infinitely many LU factorizations, where L is lower triangular with each diagonal entry 1 and U is upper triangular

Q : The matrix has no LU factorization, where L is lower triangular with each diagonal entry 1 and U is upper triangular.

Then which one of the following options is correct?

(A) P is TRUE and Q is FALSE

(B) Both P and Q are TRUE

(D) Both P and Q are FALSE

Answer: (B)

33. If the characteristic curves of the partial differential equation μ(x, y) =c₁ and v(x, y) = c₂, where c₁ and c₂ are constants, then

Answer: (A)

34. Let f : X → Y be a continuous map from a Hausdorff topological space X to a metric space Y . Consider the following two statements:

P: f is a closed map and the inverse image f^–1 (y) = {x ∈ X : f(x) = y} is compact for each y ∈ Y.

Q: For every compact subset K ⊂ Y, the inverse image f^–1 (K) is a compact subset of X:

Which one of the following is true?

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

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

(D) neither P implies Q nor Q implies P

Answer: (C)

35. Let X denote ℝ² endowed with the usual topology. Let Y denote R endowed with the co-finite topology. If Z is the product topological space Y × Y, then

(A) the topology of X is the same as the topology of Z

(B) the topology of X is strictly coarser (weaker) than that of Z

(D) the topology of X cannot be compared with that of Z

Answer: (C)

36. Consider ℝⁿ with the usual topology for n = 1, 2, 3. Each of the following options gives topological spaces X and Y with respective induced topologies. In which option is X homeomorphic to Y ?

Answer: (A)

37. Let {X_i} be a sequence of independent Poisson() variables and let Then the limiting distribution of is the normal distribution with zero mean and variance given by

(A) 1

(B) √λ

(D) λ²

Answer: (C)

38. Let X₁, X₂, . . . , X_n be independent and identically distributed random variables with probability density function given by

Also let Then the maximum likelihood estimator of θ is

Answer: (C)

39. Consider the Linear Programming Problem (LPP):

where α is a constant. If (3, 0) is the only optimal solution, then

(A) α < –2

(B) –2 < α < 1

(D) α < 2

Answer: (D)

40. Let M₂(ℝ) be the vector space of all 2 ×2 real matrices over the field R: Define the linear transformation S : M₂(ℝ) → M₂(ℝ) by S(X) = 2X + X^T , where X^T denotes the transpose of the matrix X: Then the trace of S equals ____.

Answer: (10 to 10)

41. Consider ℝ³ with the usual inner product. If d is the distance from (1, 1, 1) to the subspace
span(1, 1, 0), (0, 1, 1)g of ℝ³then |3d² = _________.

Answer: (1 to 1)

42. Consider the matrix A = I₉ – 2u^Tu with where I9 is the 9 × 9 identity matrix and uT is the transpose of u. If λ and μ are two distinct eigenvalues of A, then |λ – μ| = _____.

Answer: (2 to 2)

43. Let f(z) = z³e^z2 for z ∈ ℂ and let Γ be the circle z = e^iθ, where θ varies from 0 to 4π. Then

Answer: (6 to 6)

44. Let S be the surface of the solid

V = {(x, y, z) : 0 ≤ x ≤ 1, 0 ≤ 2, 0 ≤ z ≤ 3}.

Let denote the unit outward normal to S and let

Then the surface integral equals ________.

Answer: (18 to 18)

45. Let A be a 3 × 3 matrix with real entries. If three solutions of the linear system of differential equations are given by

then the sum of the diagonal entries of A is equal to ______.

Answer: (2 to 2)

46. If is a solution of the differential equation xy″ + αy′ + βx³y = 0

For some real numbers α and β, then αβ = _______.

Answer: (4 to 4)

47. Let L²([0, 1]) be the Hilbert space of all real valued square integrable functions on [0, 1] with the usual inner product. Let Φ be the linear functional on L²([0, 1]) defined by

where μ denotes the Lebesgue measure on [0, 1] Then || Φ|| = ______.

Answer: (3 to 3)

48. Let U be an orthonormal set in a Hilbert space H and let x ∈ H be such that ||x|| = 2. Consider the set

Then the maximum possible number of elements in E is _______.

Answer: (64 to 64)

49. If p(x) = 2 –(x + 1) + x(x + 1) – βx(x + 1) (x – α) interpolates the points (x, y) in the table

then α + β = ______.

Answer: (3 to 3)

50. If then (a₀ + a₁)π = ______.

Answer: (2 to 2)

51. For n = 1, 2, . . ., let _____.

Answer: (1 to 1)

52. Let X₁, X2, X3, X4 be independent exponential random variables with mean 1, 1/2, 1/3, 1/4, respectively. Then Y = min(X1, X2, X3, X4) has exponential distribution with mean equal to _______.

Answer: (0.1 to 0.1)

53. Let X be the number of heads in 4 tosses of a fair coin by Person 1 and let Y be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of ℙ(X = Y ) correct up to three decimal places is

Answer: (0.272 to 0.274)

54. Let X₁ ad X₂ be independent geometric random variables with the same probability mas function given by ℙ(X = k) = p(1 – p)^k–1, k = 1, 2, …. . Then the value of ℙ(X₁ = 2|X₁ + X₂ = 4) correct up to three decimal places is_______.

Answer: (0.332 to 0.334)

55. A certain commodity is produced by the manufacturing plants P₁ and P₂ whose capacities are 6 and 5 units, respectively. The commodity is shipped to markets M₁, M₂, M₃ and M₄ whose requirements are 1, 2, 3 and 5 units, respectively. The transportation cost per unit from plant P_i to market M_j is as follows

Then the optimal cost of transportation is ________.

Answer: (57 to 57)

GATE Exam 2018 Instrumentation Engineering (IN) Question Paper With Answer Key

June 7, 2023November 22, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

6. An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

8. To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

10. In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another unrelated study, it was found that the revenue from cracker sales in India which remained fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006. The solid line in the graph below refers to annual sale of crackers and the dashed line refers to the annual crow births in India. Choose the most appropriate inference from the above data.

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Instrumentation Engineering

Q. 1 – Q. 25 carry one mark each.

1. Let 𝑁 be a 3 by 3 matrix with real number entries. The matrix 𝑁 is such that 𝑁² = 0. The eigen values of N are

(A) 0, 0, 0

(B) 0,0,1

(D) 1,1,1

Answer: (A)

2. Let be two complex variable functions. Here is the complex conjugate of z. Choose the correct answer.

(A) Both 𝑓₁(𝑧) and 𝑓₂(𝑧) are analytic

(B) Only 𝑓₁(𝑧) is analytic

(D) Both 𝑓₁(𝑧) and 𝑓₂(𝑧) are not analytic

Answer: (B)

3. 𝑋 and 𝑌 are two independent random variables with variances 1 and 2, respectively. Let 𝑍 = 𝑋 − 𝑌. The variance of 𝑍 is

(A) 0

(B) 1

(D) 3

Answer: (D)

4. Consider two functions 𝑓(𝑥) = (𝑥 − 2)² and 𝑔(𝑥) = 2𝑥 − 1, where 𝑥 is real. The smallest value of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥) 𝑖𝑠 _______.

Answer: (1 to 1)

5. Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is

(A) 5/16

(B) 3/16

(D) 9/16

Answer: (B)

6. A series R-C circuit is excited by a 1∠0 V sinusoidal ac voltage source. The locus diagram of the phasor current 𝐼= (x + jy) A, when C is varied, while keeping R fixed, is

Answer: (A)

7. The Thevenin equivalent circuit representation across terminals p-q of the circuit shown in the figure is a

(A) 1 V source in series with 150 kΩ

(B) 1 V source in parallel with 100 kΩ

(D) 2 V source in parallel with 200 kΩ

Answer: (C)

8. A coil having an impedance of (10 + j100) Ω is connected in parallel to a variable capacitor as shown in figure. Keeping the excitation frequency unchanged, the value of the capacitor is changed so that parallel resonance occurs. The impedance across terminals p-q at resonance (in Ω) is ______.

Answer: (1009 to 1011)

9. Two periodic signals 𝑥(𝑡) and 𝑦(𝑡) have the same fundamental period of 3 seconds. Consider the signal 𝑧(𝑡) = 𝑥(−𝑡) + 𝑦(2𝑡 + 1). The fundamental period of 𝑧(𝑡) in seconds is

(A) 1

(B) 1.5

(D) 3

Answer: (D)

10. Consider signal Let 𝛿(𝑡) denote the unit impulse (Dirac-delta) function. The value of the integral

(A) 2

(B) 1

(D) 3

Answer: (A)

11. An ideal square wave with period of 20 ms shown in the figure, is passed through an ideal low pass filter with cut-off frequency 120 Hz. Which of the following is an accurate description of the output?

(A) Output is zero.

(B) Output consists of both 50 Hz and 100 Hz frequency components.

(D) Output is a square wave of fundamental frequency 50 Hz.

Answer: (C)

12. An input 𝑝(𝑡) = sin(𝑡) is applied to the system The corresponding steady state output is 𝑦(𝑡) = sin(𝑡 + 𝜑), where the phase 𝜑 (in degrees), when restricted to 0° ≤ 𝜑 ≤ 360°, is ______ .

Answer: (90 to 90 or -270 to -270)

13. The approximate phase response of is

Answer: (A)

14. Consider the transfer function The phase margin of 𝐺(𝑠) in degrees is ____.

Answer: (180 to 180 or -180 to -180)

15. I n the given circuit, assume that the opamp is ideal and the transistor has a β of 20. The current Io (in μA) flowing through the load Z_L is ____.

Answer: (0 to 0)

16. The diodes given in the circuit are ideal. At t = 60 ms, V_pq (in Volts) is ____.

Answer: (10 to 10)

17. For the 3-bit binary counter shown in the figure, the output increments at every positive transition in the clock (CLK). Assume ideal diodes and the starting state of the counter as 000. If output high is 1 V and output low is 0 V, the current I (in mA) flowing through the 50 Ω resistor during the 5th clock cycle is (up to one decimal place) ______.

18. The representation of the decimal number (27.625)10 in base-2 number system is

(A) 11011.110

(B) 11101.101

(D) 10111.110

Answer: (C)

19. The number of comparators required for implementing an 8-bit flash analog-to-digital converter is

(A) 8

(B) 128

(D) 256

Answer: (C)

20. A voltage of 6 cos(100πt) V is fed as y-input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively

(A) 1 V/div and 1 ms/div

(B) 1 V/div and 2 ms/div

(D) 2 V/div and 2 ms/div

Answer: (D)

21. A 300 V, 5A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100th division. The power consumed by the load (in Watts) is _____ .

Answer: (200 to 200)

22. As shown in the figure, temperature θ is measured using a K type thermocouple. It has a sensitivity of 40 μV/°C. The gain (G) of the ideal instrumentation amplifier is 25. If the output V_o is 96 mV, then the value of θ (in °C) is ____.

Answer: (95 to 97)

23. A piezoelectric pressure sensor has a bandpass characteristic with cut-off frequencies of 0.1 Hz and 1 MHz, and a sensitivity of 100 mV/kPa. The sensor is subjected to a static constant pressure of 100 kPa. Its steady-state output will be

(A) 0 V

(B) 0.1 V

(D) 10 V

Answer: (A)

24. An amplitude modulated signal is shown in the figure. The modulation index is (up to one decimal place) ______.

Answer: (0.3 to 0.3)

25. An optical pulse containing 6 × 10⁶ photons is incident on a photodiode and 4.5 × 10⁶ electron-hole pairs are created. The maximum possible quantum efficiency (in %) of the photodiode is _______ .

Answer: (75 to 75)

Q. 26 – Q. 55 carry two marks each.

26. Given the value of the line integral along the straight line c from (0,0,0) to (1,1,1) is

(A) 3/16

(B) 0

(D) –1

Answer: (D)

27. Two bags 𝐴 and 𝐵 have equal number of balls. Bag 𝐴 has 20% red balls and 80% green balls. Bag 𝐵 has 30% red balls, 60% green balls and 10% yellow balls. Contents of Bags 𝐴 and 𝐵 are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

(A) 20%

(B) 25%

(D) 40%

Answer: (B)

28. Consider the following system of linear equations:

3𝑥 + 2𝑘𝑦 = −2
𝑘𝑥 + 6𝑦 = 2

Here 𝑥 and 𝑦 are the unknowns and 𝑘 is a real constant. The value of 𝑘 for which there are infinite number of solutions is

(A) 3

(B) 1

(D) −6

Answer: (C)

29. Consider the following equations

where p and q are constants. 𝑉(𝑥, 𝑦) that satisfies the above equations is

Answer: (D)

30. In the given circuit, superposition is applied. When V₂ is set to 0 V, the current I₂ is -6 A. When V₁ is set to 0 V, the current I₁ is +6 A. Current I₃ (in A) when both sources are applied will be (up to two decimal places) _____.

Answer: (0.95 to 1.05)

31. In the figure, an RLC load is supplied by a 230 V, 50 Hz single phase source. The magnitude of the reactive power (in VAr) supplied by the source is ________.

Answer: (66 to 68)

32. In the given circuit, the mesh currents I₁, I₂ and I₃ are

(A) I₁ = 1 A, I₂ = 2 A and I₃ = 3 A

(B) I₁ = 2 A, I₂ = 3 A and I₃ = 4 A

(D) I₁ = 4 A, I₂ = 5 A and I₃ = 6 A

Answer: (A)

33. The Fourier transform of a signal 𝑥(𝑡), denoted by x(𝑗ω), is shown in the figure.

Let 𝑦(𝑡) = 𝑥(𝑡) + 𝑒^𝑗𝑡 𝑥(𝑡). The value of Fourier transform of 𝑦(𝑡) evaluated at the angular frequency ω= 0.5 rad/s is

(A) 0.5

(B) 1

(D) 2.5

Answer: (C)

34. Let 𝑦[𝑛] = 𝑥[𝑛] ∗ ℎ[𝑛], where ∗ denotes convolution and 𝑥[𝑛] and ℎ[𝑛] are two discrete time sequences. Given that the 𝑧-transform of 𝑦[𝑛] is 𝑌(𝑧) = 2 + 3𝑧⁻¹ + 𝑧⁻², the 𝑧-transform of 𝑝[𝑛] = 𝑥[𝑛] ∗ ℎ[𝑛 − 2] is

(A) 2 + 3𝑧 + 𝑧⁻²

(B) 3𝑧 + 𝑧⁻²

(D) 2𝑧⁻²+ 3𝑧⁻³ + 𝑧⁻⁴

Answer: (D)

35. For the sequence 𝑥[𝑛] = {1,−1,1,−1}, with 𝑛 = 0,1,2,3, the DFT is computed as for 𝑘 = 0,1,2,3. The value of 𝑘 for which 𝑋(𝑘) is not zero is

(A) 0

(B) 1

(D) 3

Answer: (C)

36. Consider the standard negative feedback configuration with and H(S) = 1/2. The number of clockwise encirclements of (−1,0) in the Nyquist plot of the Loop transfer-function 𝐺(𝑠)𝐻(𝑠) is _____

Answer: (0 to 0)

37. Consider the linear system with initial condition The solution 𝑥(𝑡) for this system is

(B).

Answer: (D)

38. Consider a standard negative feedback configuration with and For the closed loop system to have poles on the imaginary axis, the value of 𝛼 should be equal to (up to one decimal place)_____.

Answer: (8.9 to 9.1)

39. Unit step response of a linear time invariant (LTI) system is given by 𝑦(𝑡) = (1 − 𝑒^−2𝑡)𝑢(𝑡). Assuming zero initial condition, the transfer function of the system is

Answer: (D)

40. In the given relaxation oscillator, the opamps and the zener diodes are ideal. The frequency (in kHz) of the square wave output v_o is _____.

Answer: (Marks to All)

41. An opamp that is powered from a ±5V supply is used to build a non-inverting amplifier having a gain of 15. The slew rate of the opamp is 0.5 × 10⁶ V/s. For a sinusoidal input with amplitude of 0.3 V, the maximum frequency (in kHz) up to which it can be operated without any distortion is (up to one decimal place) ___.

Answer: (17.5 to 17.9)

42. The circuit given uses ideal opamps. The current I (in μA) drawn from the source vs is (up to two decimal places) ____.

Answer: (0.98 to 1.00)

43. The product of sum expression of a Boolean function 𝐹(𝐴, 𝐵, 𝐶) of three variables is given by

The canonical sum of product expression of 𝐹(𝐴, 𝐵, 𝐶) is given by

Answer: (B)

44. A 2-bit synchronous counter using two J-K flip flops is shown. The expressions for the inputs to the J-K flip flops are also shown in the figure. The output sequence of the counter starting from Q₁Q₂ = 00 is

(A) 00 → 11 → 10 → 01 → 00 ⋅ ⋅ ⋅
(B) 00 → 01 → 10 → 11 → 00 ⋅ ⋅ ⋅
(C) 00 → 01 → 11 → 10 → 00 ⋅ ⋅ ⋅
(D) 00 → 10 → 11 → 01 → 00 ⋅ ⋅ ⋅

Answer: (C)

45. A portion of an assembly language program written for an 8-bit microprocessor is given below along with explanations. The code is intended to introduce a software time delay. The processor is driven by a 5 MHz clock. The time delay (in μs) introduced by the program is _______.

MVI B, 64H ; Move immediate the given byte into register B. Takes 7 clock periods.

LOOP : DCR B ; Decrement register B. Affects Flags. Takes 4 clock periods.

JNZ LOOP ; Jump to address with Label LOOP if zero flag is not set. Takes 10 clock periods when jump is performed and 7 clock periods when jump is not performed.

Answer: (279 to 282)

46. The Boolean function 𝐹( 𝑋, 𝑌) realized by the given circuit is

Answer: (A)

47. The voltage and current drawn by a resistive load are measured with a 300 V voltmeter of accuracy ±1% of full scale and a 5 A ammeter of accuracy ±0.5% of full scale. The readings obtained are 200 V and 2.5 A. The limiting error (in %) in computing the load resistance is (up to two decimal places) ____.

Answer: (2.49 to 2.53)

48. A high Q coil having distributed (self) capacitance is tested with a Q-meter. First resonance at ω₁ = 10⁶ rad/s is obtained with a capacitance of 990 pF. The second resonance at ω₂ = 2 × 10⁶ rad/s is obtained with a 240 pF capacitance. The value of the inductance (in mH) of the coil is (up to one decimal place) ______.

Answer: (0.9 to 1.1)

49. The inductance of a coil is measured using the bridge shown in the figure. Balance (D = 0) is obtained with C₁ = 1 nF, R₁ = 2.2 MΩ, R₂ = 22.2 kΩ, R₄ = 10 kΩ. The value of the inductance Lx (in mH) is ______.

Answer: (221 to 223)

50. The average velocity v of flow of clear water in a 100 cm (inner) diameter tube is measured using the ultrasonic flow meter as shown in the figure. The angle θ is 45°. The measured transit times are t₁ = 0.9950 ms and t₂ = 1.0000 ms. The velocity v (in m/s) in the pipe is (up to one decimal place) ___.

Answer: (3.5 to 5.7)

51. A 1000 Ω strain gage (R_g) has a gage factor of 2.5. It is connected in the bridge as shown in figure. The strain gage is subjected with a positive strain of 400 μm/m. The output V_o (in mV) of the bridge is (up to two decimal places) _____.

Answer: (0.48 to 0.51)

52. Assuming ideal opamp, the RMS voltage (in mV) in the output V_o only due to the 230 V, 50 Hz interference is (up to one decimal place) _____.

Answer: (10.6 to 11.0)

53. The sampling rate for Compact Discs (CDs) is 44,000 samples/s. If the samples are quantized to 256 levels and binary coded, the corresponding bit rate (in bits per second) is _____.

Answer: (35200 to 35200)

54. A Michelson Interferometer using a laser source of wavelength 𝜆₀ = 500 nm, with both the mirrors (𝑀₁& 𝑀₂) fixed and positioned equidistant from the splitter/combiner is shown in the figure. When a dielectric plate of refractive index 𝑛 = 1.5, of thickness 𝒕 , is placed in front of the mirror 𝑀₂, a dark fringe is observed on the detector. When the dielectric plate is removed without changing the position of the mirrors 𝑀₁& 𝑀₂, a bright fringe is observed on the detector. The minimum thickness 𝒕 (in nm) of the dielectric is ________.

Answer: (249 to 251)

55. A multi-mode optical fiber with a large core diameter has a core refractive index 𝑛₁ = 1.5 and cladding refractive index 𝑛₂ = 1.4142. The maximum value of 𝜃_𝐴 (in degrees) for which the incident light from air will be guided in the optical fiber is ±______.

Answer: (29 to 31)

GATE Exam 2018 Geology and Geophysics (GG) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

PART A: COMPULSORY SECTION FOR ALL CANDIDATES

Q. 1 – Q. 25 carry one mark each.

1. Which one of the following periods has the longest time duration?

(A) Ordovician

(B) Cretaceous

(D) Silurian

Answer: (B)

2. A siliciclastic sedimentary rock consisting predominantly of the same type of gravel-sized clasts is called

(A) Polymict conglomerate.

(B) Arkose.

(D) Petromict conglomerate.

Answer: (C)

3. Brown coal that has high moisture content and commonly retains many of the original wood fragments is called

(A) Anthracite.

(B) Bituminous coal.

(D) Peat.

Answer: (C)

4. The speed of revolution of the Earth around the Sun is

(A) maximum at Perihelion.

(B) minimum at Perihelion.

(D) equal at Aphelion and Perihelion.

Answer: (A)

5. The geometrical factor for the following electrode configuration is

(A) 𝜋𝑎

(B) 2𝜋𝑎

(D) 4𝜋𝑎

Answer: (D)

6. Which one of the following geophysical methods uses the physical property ‘Dielectric Constant’?

(A) Gravity

(B) Ground Penetrating Radar

(D) Self-Potential

Answer: (B)

7. Pascal second is a unit of

(A) seepage force.

(B) dynamic viscosity.

(D) permeability.

Answer: (B)

8. Which one of the following statements is CORRECT?

(A) Strength of a rock decreases with increase in confining pressure.

(B) Strength of a rock increases with increase in temperature.

(D) Strength of a rock increases with increase in pore water pressure.

Answer: (C)

9. The geomorphic feature ‘horns’ are formed by

(A) wind erosion.

(B) river erosion.

(D) glacial erosion.

Answer: (D)

10. A melanocratic porphyritic rock containing phenocrysts of biotite, with feldspar restricted to the groundmass, is called

(A) trachyte.

(B) dacite.

(D) lamprophyre.

Answer: (D)

11. The supercontinent that existed in the late Mesoproterozoic to early Neoproterozoic time was

(A) Kenorland.

(B) Columbia.

(D) Pangaea.

Answer: (C)

12. The figure below shows the triple junction between three plates A, B and C. The boundary between the plates A and B is a ridge with a half-spreading rate of 4 cm/year. The A-C and B-C boundaries are collinear and orthogonal to the A-B ridge. The A-C boundary is a dextral transform fault with a relative velocity of 6 cm/year. The boundary between plates B and C is a

(A) dextral transform fault with a relative velocity of 10 cm/year.

(B) dextral transform fault with a relative velocity of 2 cm/year.

(D) sinistral transform fault with a relative velocity of 6 cm/year.

Answer: (C)

13. A rock follows Mohr-Coulomb failure criterion. Which one of the Mohr-Coulomb failure envelopes shown below allows failure of the rock under stress state Y, but not under stress state X?

(A) PP’

(B) QQ’

(D) SS’

Answer: (A)

14. The maximum and the minimum principal stresses are denoted by σ1 and σ3, respectively. The differential stress can have an absolute value greater than σ1 when

(A) σ₁ and σ₃ are both compressive.

(B) σ₁ is compressive and σ₃ is tensile.

(D) σ₁ and σ₃ are both tensile.

Answer: (B)

15. The geoid can be best defined as

(A) an oblate spheroid that best approximates the shape of the earth.

(B) a surface over which the value of gravity is constant.

(D) an equipotential surface of gravity of the earth.

Answer: (D)

16. For a layered isotropic medium with a flat horizontal free surface, match the wave types listed in Group-I with their corresponding polarizations listed in Group II.

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

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

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

Answer: (B)

17. A ‘gentle’ fold with an interlimb angle equal to 160° appears tight (apparent interlimb angle equal to 20) in horizontal section. According to the plunge of the fold axis, it can also be classified as

(A) horizontal fold.

(B) gently plunging fold.

(D) vertical fold.

Answer: (B)

18. The unit of shear modulus (rigidity modulus) is

(A) kg m^-1s^-2

(B) m² s^-2

(D) m^-1

Answer: (A)

19. With increasing activity of silica, the CORRECT order of appearance of minerals in a weathering environment with constant ratio of activities of K⁺ and H⁺ is

(A) gibbsite → kaolinite → pyrophyllite

(B) gibbsite → pyrophyllite → kaolinite

(D) pyrophyllite → gibbsite → kaolinite

Answer: (A)

20. Match the items listed in Group-I with those listed in Group-II.

Group-I Group-II
P. Mica 1. Beldih
Q. Uranium 2. Koderma
R. Phosphate 3. Agucha
S. Zinc 4. Gogi

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

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

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

Answer: (B)

21. Which one of the following corrections is always added during reduction of the observed gravity data?

(A) Latitude

(B) Free-air

(D) Terrain

Answer: (D)

22. The magnitudes of the total geomagnetic field at the equator and pole are denoted by B_E and B_P, respectively. Which one of the following is TRUE?

(A) B_P ≈ 4 B_E

(B) B_P ≈ 2 B_E

(D) B_P ≈ 1/2 B_E

Answer: (B)

23. Assume a flat earth with crustal thickness of 35 km and average crustal and upper mantle P-wave velocities of 6.4 km.s^–1 and 8.1 km.s^–1, respectively. The minimum distance from the epicenter of a near surface earthquake at which Pn-waves are observed is _______ km.

Answer: (85 to 95)

24. Given that the velocity of P-waves in a sandstone matrix is 5600 m/s and that in oil is 1200 m/s, the velocity of P-wave propagation in oil saturated sandstone with 30% porosity is ___________ m/s. (Use Wyllie time average equation.)

Answer: (2660 to 2670)

25. If the total porosity of a soil is 20%, its void ratio (%) is _________.

Answer: (25 to 25)

PART B (SECTION 1): FOR GEOLOGY CANDIDATES ONLY

Q. 26 – Q. 55 carry two marks each.

26. Which one of the following Himalayan lithounits predates India-Eurasia collision?

(A) Kasauli sandstone

(B) Rangit Pebble Slate

(D) Lower Karewa sandstone

Answer: (B)

27. Which one of the following ore minerals shows internal reflection?

(A) Orpiment

(B) Magnetite

(D) Molybdenite

Answer: (A)

28. Which one is CORRECT for the following equilibrium reaction between quartz and magnetite:

(A) 1000 ln α = Δ_qtz-mg where α = K^1/n (K is the equilibrium constant at the specified temperature and n is a constant quantity)

(B) 1000 ln α = Δ_qtz-mgwhere α = Kⁿ (K is the equilibrium constant at the specified temperature and n is the number of exchangeable atomic sites)

(C) (ln α/1000) = Δ_qtz-mgwhere α = K^1/n (K is the equilibrium constant at the specified temperature and n is a constant quantity)

(D) 1000 ln α = Δ_qtz-mg where α = K^1/n (K is the equilibrium constant at the specified temperature and n is the number of exchangeable atomic sites)

Answer: (D)

29. Match the modes of life (listed in Group I) with the corresponding bivalve genera (listed in Group II).

Group I Group II
P. Burrowing 1. Mytilus
Q. Recumbent unattached 2. Pecten
R. Byssally attached 3. Mya
S. Swimming 4. Gryphaea

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

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

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

Answer: (B)

30. Based on the hypothetical litholog given below that shows a continuous succession of sedimentary rocks, which one of the following statements is CORRECT?

(A) The rocks range from Cambrian to Cretaceous and show change in depositional environment from marine to continental.

(B) The rocks range from Cambrian to Triassic and show change in depositional environment from marine to continental.

(D) The rocks are Palaeozoic in age and show change in depositional environment from marine to continental.

Answer: (A)

31. Which one of the following cladograms shows the CORRECT interrelationships among the major groups of vertebrates?

(A) Cladogram I

(B) Cladogram II

(D) Cladogram IV

Answer: (A)

32. Which one of the following stratigraphic successions is in the CORRECT chronological order (from older to younger)?

(A) Rajmahal, Dubrajpur, Barakar

(B) Fenestella Shale, Muth Quartzite, Syringothyris Limestone

(D) Singhbhum Granite, Kolhan Group, Older Metamorphic Gneiss

Answer: (C)

33. Match the items listed in Group I with their appropriate description listed in Group II.

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

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

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

Answer: (B)

34. Which one of the following is an image rectification technique?

(A) Histogram equalization

(B) Density slicing

(D) Rubbersheeting

Answer: (D)

35. Match the items listed in Group I with those in Group II.

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

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

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

Answer: (D)

36. Match the items listed in Group I with those listed in Group II.

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

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

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

Answer: (A)

37. In the hypothetical isobaric ternary liquidus projection diagram given below, solid phases A, B, C, D and E exist in equilibrium with liquid. The reaction taking place at the isobaric invariant point W is

(A) Liquid (at W) = B + D + E

(B) Liquid (at W) = A + B + D

(D) Liquid (at W) + B + D = E

Answer: (D)

38. Match the optical properties listed in Group I with the corresponding mineral in Group II.

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

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

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

Answer: (A)

39. The reaction

muscovite + quartz = K-feldspar + sillimanite + water

(A) takes place within the greenschist facies.

(B) takes place within the amphibolite facies.

(D) takes place within the granulite facies.

Answer: (B)

40. Match the items listed in Group I with those in Group II.

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

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

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

Answer: (C)

41. The figure below is a schematic section showing the initial stages of development of a thrust fault (FF’) having a typical ramp and flat geometry, with the thrust sheet being transported from east to west. With respect to the synform and antiform created in Stage 2, which one of the options below is CORRECT for the next increment of movement on the fault plane?

(A) The synform and the antiform will both move westward.

(B) The synform will remain in position, while the antiform will grow in amplitude.

(D) The geometry will remain unchanged.

Answer: (B)

42. Which one of the following is the CORRECT chronological sequence for Iron formations?

(A) Algoma type > Superior type > Rapitan type > Minette type

(B) Superior type > Algoma type > Rapitan type > Minette type

(D) Algoma type > Minette type > Superior type > Rapitan type

Answer: (A)

43. Assertion (a): High-temperature, low-pressure metamorphism occurs on the over-riding plate near convergent plate margins.

Reason (r): Partial melting in the mantle wedge generates magmas that rise to form the arc.

(A) (a) is true but (r) is false.

(B) (a) is false but (r) is true.

(D) Both (a) and (r) are true and (r) is not the correct reason for (a).

Answer: (C)

44. Two coeval primary aqueous biphase fluid inclusions, X (liquid-rich) and Y (vapour-rich), occur in the same grain of the host mineral. Which one of the following situations most likely indicates boiling of the fluid?

(A) X homogenizes to liquid and Y homogenizes to vapour at different temperatures.

(B) Both homogenize to liquid at the same temperature.

(D) X homogenizes to liquid and Y homogenizes to vapour at the same temperature.

Answer: (D)

45. Du ring bench blasting in a quarry, 50 kg of an explosive with a yield of 5 MegaJoule/kg isrequired to break 100 m³ of marble. In this case, the energy expended in breaking a unit volume of marble in MegaNewton/m² would be _________________.

Answer: (2.5 to 2.5)

46. The stretching lineation on the axial plane (S₂) of a reclined fold on the S1 foliation makes an angle of 30° with the S₁/S₂ intersection lineation. The rake of the stretching lineation on the axial plane in degrees is ______________.

Answer: (60 to 60)

47. A basaltic magma has an initial nickel concentration of 300 ppm. Olivine crystallizes from this magma by equilibrium crystallization (Case I) or fractional crystallization (Case II). Then, the absolute value of the difference between the nickel concentrations of the liquids remaining after 25% crystallization in these two cases is _______________. (Use K_D,Ni olivine/melt = 10).

Answer: (69 to 71)

48. The difference in the number of faces in forms {hkl} and {111} in the holosymmetric class of the isometric system is _______________.

Answer: (40 to 40)

49. An inclined cylindrical confined aquifer has coefficient of permeability of 40 m/day. The horizontal distance between two vertical wells penetrating the aquifer is 800 m. The water surface elevations in the wells are 50 m and 45 m above a common horizontal datum. The absolute value of Darcy flux through the aquifer is ______________ m/day.

Answer: (0.25 to 0.25)

50. The mass and volume of a natural soil sample are 2.1 kg and 1×10^-3 m³, respectively. When fully dried, the mass of the soil sample becomes 2 kg without any change in volume. Assuming the specific gravity of soil particles to be 2.5, and water density of 1000 kg/m³, the degree of saturation of the natural soil sample is _______________%.

Answer: (50 to 50)

51. For a granitic rock mass, joint set number (Jn) = 9, joint water reduction factor (Jw) = 1, joint alteration number (Ja) = 1, stress reduction factor (SRF) = 1, rock quality designation (%) = 84 and joint roughness number (Jr) = 3. The Q-value as per Barton’s Q-system of rock mass classification (year 1974) is _______________.

Answer: (28 to 28)

52. A sun synchronous satellite is at an altitude of 300 km and the spectrometer makes an angular coverage angle of 12. The Swath (GFOV) of the satellite is ______________ km.

Answer: (62 to 64)

53. The stability field boundary between two minerals A and B is linear with a positive slope in P-T space. The molar entropy of A and B are 85.5 and 92.5 Joules K^-1, respectively and their respective molar volumes are 35.5 and 38.2 cc. The slope of the phase boundary in P-T space is _____________ bar K^-1.

Answer: (24 to 26)

54. Five moles of gas A (volume V₁) and 3 moles of gas B (volume V₂) were kept in separate containers. These two gases are completely transferred to a new container of volume V. Assuming isothermal condition, and that the work done is only mechanical, the entropy change of the system is ____________ Joules K^-1. (R = 8.3 J K^-1 mole^-1)

Answer: (42 to 45)

55. The value of Eh corresponding to the upper limit of natural surface aqueous environment at pH of 8.0 is _____________ V.

Answer: (0.7 to 0.8)

PART B (SECTION 2): FOR GEOPHYSICS CANDIDATES ONLY

Q. 56 – Q. 85 carry two marks each.

56. The maximum number of linearly independent rows of an m × n matrix G where m > n is

(A) m.

(B) n.

(D) 0.

Answer: (B)

57. The impulse response of the Kirchhoff pre-stack time migration operator for non-zero offsets in a homogeneous and isotropic medium is _______.

(A) a circle.

(B) a parabola.

(D) an ellipse.

Answer: (D)

58. A solution to the eikonal equation |∇τ| = 1/υ₀ for a homogeneous and isotropic medium in cartesian coordinates is

Answer: (A)

59. The formula for the ‘forward’ Fourier transform is and that for the ‘inverse’ Fourier transform is Then, the forward Fourier transform of the function f(ω) = e^–2ω is

(A) 2𝛿(𝑡).

(B) 𝛿(2𝑡).

(D) 𝛿(𝑡 − 2).

Answer: (C or D)

60. Which one of the following rock types has the highest bulk magnetic susceptibility value?

(A) Gabbro

(B) Marble

(D) Limestone

Answer: (A)

61. Figure 1 is a schematic diagram of four seismic events in t-x (time-offset) domain and Figure 2 is the result of transformation from t-x domain to f-kx (frequency-horizontal wavenumber) domain. Match the events in t-x domain in Figure 1 with their counterparts in f-kx domain in Figure 2.

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

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

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

Answer: (C)

62. There is a change in the values of the bulk modulus and density across the Gutenberg discontinuity (from mantle to outer core). Which one of the following statements is CORRECT?

(A) Both bulk modulus and density increase.

(B) Both bulk modulus and density decrease.

(D) Bulk modulus increases and density decreases.

Answer: (A)

63. Multi-electrode resistivity survey is carried out by placing 10 equispaced electrodes (denoted by arrows in the figure below) on the surface of the earth. The points of observations in the distance-apparent depth plane are marked as solid dots in the figure shown below. Considering the mid-point of the 4-electrode array as the point of observation in the lateral direction, identify the CORRECT electrode configuration used for the survey.

(A) Multi-electrode Wenner array.

(B) Multi-electrode Axial Dipole-dipole array.

(D) Multi-electrode Axial Pole-dipole array.

Answer: (B)

64. Match the Electromagnetic methods in Group I with the corresponding quantity measured by them given in Group II.

(A) P-3, Q-2, R-4, S-5

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

(D) P-1, Q-2, R-5, S-3

Answer: (C)

65. Dip angle electromagnetic response measured along a profile over multiple conductors is shown in the figure below. Which of the crossover points P, Q and R represent the CORRECT locations of conductors beneath them?

(A) P, Q and R

(B) Q and R

(D) P and Q

Answer: (C)

66. The effect of small scale near surface inhomogeneities can be removed from magnetic data by

(A) upward continuation.

(B) downward continuation.

(D) reduction to pole.

Answer: (A)

67. The frequencies of the primary magnetic field generated by worldwide thunderstorm activity vary in the range

(A) 10^-6 Hz -10^-3 Hz

(B) 10^-3 Hz ^-1 Hz

(D) 10³ Hz -10⁶ Hz

Answer: (C)

68. Assertion (a): The Static Self-Potential for a thick, clean freshwater bearing sandstone formation is positive.

Reason(r): Resistivity of the formation water is less than the resistivity of salt water mudfiltrate.

(A) Both (a) and (r) are true and (r) is the correct reason for (a).

(B) Both (a) and (r) are true and (r) is not the correct reason for (a)

(D) (a) is true but (r) is false.

Answer: (D)

69. Which one of the following well log responses characterizes an overpressured zone in the subsurface?

(A) High velocity and high resistivity.

(B) Low velocity and low density.

(D) Low velocity and high density.

Answer: (B)

70. The angle of inclination of the remanent magnetization measured on a basalt flow at a location P (28°N 85°E) is 40°. The palaeomagnetic latitude of the basalt flow is _______°N.

Answer: (22.5 to 23.0)

71. Using the Gutenberg-Richter recurrence relationship, the mean annual rate of exceedance of earthquake occurrence in a seismic belt is 0.3 per year for an earthquake of magnitude 6.0. The return period for an earthquake of magnitude 6.0 in this belt is ______ years.

Answer: (3.0 to 3.5)

72. In the figure below, Z denotes the depth to the center of a buried sphere from the surface and X_1/2 denotes the half-width of the profile at half the maximum value of gravity. Then, the ratio Z/X_1/2 is ________.

Answer: (1.2 to 1.4)

73. Two survey vessels with shipborne gravimeters are cruising towards each other at a speed of 6 knots each along an east-west course. The difference in gravity readings of the two gravimeters is 63.5 mGal at the point at which the survey vessels cross each other. The latitude along which the survey vessels are cruising is ______°N.

Answer: (44.5 to 46.0)

74. A gravity reading is taken in a stationary helicopter hovering 1 km above mean-sea level at a particular location. The difference in the value of g measured in the helicopter and at mean sea level vertically beneath the helicopter is ____________ mGals.

Answer: (300 to 320 or -320 to -300)

75. The P-wave velocity and the Poisson’s ratio for a homogeneous and isotropic sedimentary rock are 2500 m/s and 0.3, respectively. The S-wave velocity for the rock is ________m/s.

Answer: (1330 to 1340)

76. A plane electromagnetic (EM) wave travelling vertically downwards with a frequency of 1000 Hz in a homogeneous medium has a skin depth of 100 m. The ratio of the amplitude of the EM wave at a depth of 75 m with respect to the amplitude at the Earth’s surface is ___________.

Answer: (0.46 to 0.49)

77. A student interpreted a four layer Schlumberger resistivity sounding data and obtained the resistivities (ρ) and thicknesses (h) as follows: ρ₁=100 Ωm, ρ₂=20 Ωm, ρ₃=1500 Ωm and ρ₄=50 Ωm; h1=50 m, h₂=10 m and h₃=20 m. The same data is interpreted by another student who obtains ρ₃=2000 Ωm. Then, according to the principle of equivalence, the value of h₃ interpreted by the second student is ________m. (All other model parameters estimated by both the students are the same.)

Answer: (15 to 15)

78. The apparent resistivities obtained at 0.1 Hz and 10 Hz in the frequency domain I.P. measurement are 100 Ωm and 80 Ωm, respectively. The Percentage Frequency Effect is _________.

Answer: (25 to 25)

79. A 15 Volt power supply is applied across a cylindrical container (diameter = 0.20 m and length = 0.50 m). Currents of 750 mA and 500 mA are measured when the container is filled with (i) brine only, and (ii) rock sample fully saturated with brine, respectively. The formation factor of the rock sample is __________.

Answer: (1.50 to 1.50)

80. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is _______.

Answer: (6.9 to 7.1)

81. Consider a laterally homogeneous and isotropic earth model with a flat horizontal surface and three horizontal layers underlain by a half-space. A seismic reflection survey was simulated on this model with the sources and receivers placed on the surface. The table below lists the root mean square (rms) velocities, Vr_ms, and zero-offset two-way traveltimes t0 for the three reflection events from the bottom of each of the three layers observed in a pre-stack CDP (CMP) gather. The interval velocity of the second layer is _______ m/s.

Answer: (1770 to 1790)

82. A spherically symmetric vector field The flux of the vector field through a sphere of unit radius is _________.

(Use 𝜋 = 3.14)

Answer: (-3.142 to -3.140)

83. A horizontally travelling surface wave with a wavelength of 20 m is attenuated by a linear and uniform receiver array consisting of 4 receivers if the minimum receiver spacing is ________ m.

Answer: (5.0 to 5.0)

84. An end-on marine survey is carried out with equal and uniform shot and receiver spacing. If the total number of shots fired is 50 and a total of 10000 traces are recorded, the maximum fold for the survey is _______.

Answer: (50 to 50 or 100 to 100)

85. The highest singular value of the matrix

Answer: (2.8 to 3.0)

GATE Exam 2018 Ecology and Evolution (EY) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-1

Q. 1 – Q. 5 carry one mark each.

1. “ Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”

The words that best fill the blanks in the above sentence are

(A) principle, principal

(B) principal, principle

(D) principal, principal

Answer: (A)

2. “ Her _______ should not be confused with miserliness; she is ever willing to assist those in need.”

The word that best fills the blank in the above sentence is

(A) cleanliness

(B) punctuality

(D) greatness

Answer: (C)

3. Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

(A) 1

(B) 7

(D) 700

Answer: (B)

(A) 1125

(B) 2250

(D) 4500

Answer: (B)

5. A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

(A) 63

(B) 72

(D) 90

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. F or integers 𝑎, 𝑏 and 𝑐, what would be the minimum and maximum values respectively of 𝑎 + 𝑏 + 𝑐 if log |𝑎| + log |𝑏| + log |𝑐| = 0?

(A) -3 and 3

(B) -1 and 1

(D) 1 and 3

Answer: (A)

7. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?

(A) 𝑎 and 𝑏 are both odd

(B) 𝑎 and 𝑏 are both even

(D) 𝑎 is odd and 𝑏 is even

Answer: (D)

(A) 210 and 140

(B) 162.5 and 187.5

(D) 175 and 200

Answer: (D)

9. Which of the following functions describe the graph shown in the below figure?

(A) 𝑦 = ||𝑥| + 1| − 2

(B) 𝑦 = ||𝑥| − 1| − 1

(D) 𝑦 = ||𝑥 − 1| − 1|

Answer: (B)

10. Consider the following three statements:

(i) Some roses are red.

(ii) All red flowers fade quickly.

(iii) Some roses fade quickly.

Which of the following statements can be logically inferred from the above statements?

(A) If (i) is true and (ii) is false, then (iii) is false.

(B) If (i) is true and (ii) is false, then (iii) is true.

(D) If (i) and (ii) are false, then (iii) is false.

Answer: (C)

Ecology and Evolution

Q. 1 – Q. 25 carry one mark each.

1. During the Pleistocene, which of the following groups experienced the largest mass extinction?

(A) Large dinosaurs

(B) Large mammals

(D) Trilobites

Answer: (B)

2. In group living species, the term “dilution effect” refers to

(A) reduction in aggression among individuals with increasing group size

(B) reduction in the mobility of individuals with increasing group size

(D) reduction in the risk of predation of individuals with increasing group size

Answer: (D)

3. Which of the following diversity indices best captures species turnover across habitats?

(A) α

(B)β

(D) δ

Answer: (B)

4. A duck egg is removed from its mother’s nest and incubated by a barnyard hen. The duckling hatches out in the presence of the barnyard hen and stays in her nest. After a couple of days, the duckling is presented with a choice between its biological
mother and the hen that incubated it. The duckling approaches and follows the hen. This set of observations demonstrates the phenomenon of

(A) habituation

(B) imprinting

(D) sensitization

Answer: (B)

5. If both of your ears were located next to each other in the middle of your face, you would have difficulty in resolving the

(A) direction of a sound

(B) duration of a sound

(D) pitch of a sound

Answer: (A)

6. Forager bees communicate the distance of a food source using a waggle dance uponreturn to the hive. It is observed that the number of waggles of a dance increases linearly with the distance to the food source. This tells us that the

(A) number of waggles and distance to food source is negatively correlated

(B) number of waggles and distance to food source is positively correlated

(D) number of waggles and the distance to the food source are uncorrelated

Answer: (B)

7. Male frogs display to females by producing loud acoustic signals. The use of these signals by bats to locate frogs and prey upon them is an example of

(A) aposematism

(B) deception

(D) mimicry

Answer: (C)

8. A non-venomous, non-toxic species of snake is brightly coloured and closely resembles a venomous snake species in the same habitat. This is most likely a case of

(A) aggressive mimicry

(B) Batesian mimicry

(D) Müllerian mimicry

Answer: (B)

9. The value of the resting membrane potential of a typical neuron is closest to the equilibrium potential of which of the following ions?

(A) Ca⁺⁺

(B) K⁺

(D) Na⁺

Answer: (B)

10. A plant species found in India produces flowers that are white, fragrant, and tubular.

Which of the following is the most likely pollinating agent?

(A) Hummingbirds

(B) Lorises

(D) Wind

Answer: (C)

11. Which of the following can be used to test differences between mean tree heights in a tropical versus a temperate forest?

(A) Binomial test

(B) Linear regression

(D) Student’s t-test

Answer: (D)

12. For a species, assuming a relatively short time scale and no evolution, increased interspecific competition will result in a

(A) larger fundamental niche

(B) larger realized niche

(D) smaller realized niche

Answer: (D)

13. In which of the following mating systems is sperm competition likely to evolve?

(A) Monoandry

(B) Monogamy

(D) Polygyny

Answer: (C)

14. Copies of genes that arrive in a particular genome by horizontal gene transfer are known as

(A) analogs

(B) homologs

(D) xenologs

Answer: (D)

15. In which of the following plants is the dominant stage of the life cycle haploid?

(A) Cycads

(B) Ferns

(D) Mosses

Answer: (D)

16. Which of the following is NOT typically a characteristic of early successional pioneer plants relative to late successional plants in a tropical rain forest?

(A) Higher shade tolerance

(B) Smaller seed size

(D) Wind dispersed seeds

Answer: (A)

17. Natural populations often deviate from Hardy-Weinberg equilibrium. One possible reason for this is

(A) no migration

(B) no selection

(D) small population sizes

Answer: (D)

18. Which of the following is NOT an example of phenotypic plasticity?

(A) Density-dependent swarming behavior in locusts

(B) Increase in DDT resistance in mosquitos

(D) Temperature-dependent sex determination in turtles

Answer: (B)

19. Which of the following is NOT a characteristic of r-selected species?

(A) Early sexual maturity

(B) High juvenile mortality

(D) Large number of offspring

Answer: (C)

20. A scientist finds a new species of insect and sends a sample to a museum for confirmation. The curator of the museum designates it as a holotype for the newly identified species and asks the scientist to also provide samples of the opposite sex.

This sample of the opposite sex is called the

(A) allotype

(B) isotype

(D) neotype

Answer: (A)

21. Which of the following is NOT essential for a behavioural trait to evolve by natural selection?

(A) The behavioural trait differs among individuals

(B) The behavioural trait is determined at least in part by genes

(D) The behavioural trait is determined entirely by genes

Answer: (D)

22. El Niño Southern Oscillation (ENSO) events have occurred approximately every 3-7 years over the last century. The cause of these ENSO events is related to

(A) large-scale air-sea interactions in the Pacific Ocean

(B) strong monsoon winds in the Indian Ocean

(D) unsustainable overfishing in North Atlantic Ocean

Answer: (A)

23. If the mean of a sample is 5, and the variance is 25, the PERCENT coefficient of variation is ___.

Answer: (99 to 101)

24. Consider a diploid population at Hardy-Weinberg equilibrium. For a locus with two alleles, the frequency of the A1A1 genotype is 0.01. The frequency of heterozygotes A₁A₂ is ____ (answer up to 2 decimal places).

Answer: (0.179 to 0.181)

25. In a food chain, the efficiency of transfer of energy from one trophic level to the next is 10%. The PERCENTAGE of energy that is expected to transfer from the second to the fourth level is ____.

Answer: (0.99 to 1.01)

Q. 26 – Q. 55 carry two marks each.

26. Which of the following is an adaptation for osmoregulation in freshwater teleost fish?

(A) Excreting large quantities of dilute urine

(B) Excreting large quantities of uric acid

(D) Excreting large quantities of uracil

Answer: (A)

27. The latitudinal diversity gradient is defined as the decrease in the number of species from the equator to the poles. This can result from

(A) greater energy input at the poles

(B) greater land mass at the poles

(D) greater speciation rates at the poles

Answer: (C)

28. Identify the graph in which natural selection on beak size is LEAST likely to be occurring? For each of the graphs, the slope of the regression line and the associated p-value is given.

Answer: (C)

29. Some species of spiders add additional silk ‘decorations’ to their webs. It is hypothesized that these decorations serve either to lure flies (prey) or to decrease bird (predator) attacks on the spiders. The appropriate way to test these hypotheses would be to compare numbers of

(A) predators and prey approaching decorated webs

(B) predators and prey approaching undecorated webs

(D) predators and prey approaching both decorated and undecorated webs

Answer: (D)

30. The figure below shows mean annual temperatures (°C) and mean annual precipitation (cm per year) from multiple sites in four regions in India.

From this climatic information, we can infer that P, Q, R, and S are LIKELY to be located in:

(A) P: Andaman, Q: Meghalaya, R: Ladakh, S: Rajasthan

(B) P: Ladakh, Q: Rajasthan, R: Andaman, S: Meghalaya

(D) P: Rajasthan, Q: Andaman, R: Meghalaya, S: Ladakh

Answer: (B)

31. For a pair of interacting species, increased specialization and decreased niche breadth in both species would result in

(A) decreased intraspecific competition and increased interspecific competition

(B) decreased intraspecific competition and decreased interspecific competition

(D) increased intraspecific competition and decreased interspecific competition

Answer: (D)

32. Males of a bird species provide parental care by feeding nestlings before they fledge. Which of the following is a PROXIMATE explanation for this behaviour?

(A) Feeding nestlings increases their survivorship after fledging

(B) High prolactin levels cause males to feed their nestlings

(D) Males that provide parental care have higher fitness

Answer: (B)

33. The courtship display of a spider species consists of both visual and vibrational signals. Females respond to the display by approaching males. In an experiment, females were presented with 3 treatments: i) only videos of displaying males, ii) only vibrational signals of the display, and iii) both videos of displaying males and vibrational signals. The results are given below:

Results from this experiment show that

(A) vibrational signals are necessary to evoke a response

(B) vibrational signals are sufficient to evoke a response

(D) visual signals are necessary to evoke a response

Answer: (D)

34. Moth ears typically consist of a membranous eardrum backed by an air cavity. Ears in different phylogenetic groups of moths have evolved on different body parts. Moth ears are thus best described as

(A) convergent organs

(B) homologous organs

(D) vestigeal organs

Answer: (A)

35. Increased anthropogenic disturbance has resulted in an overall decrease in densities of trees and an increase in fragmentation of forests. Which of the following types of trees will have the greatest reduction in reproductive success?

(A) Dioecious species

(B) Monoecious species

(D) Self-incompatible hermaphrodites

Answer: (A)

36. A study examined the effect of neighbours on plants when grown at low or high altitudes. The researcher measured Relative Neighbour Effect (RNE), defined as: RNE = Biomass with neighbours – Biomass without neighbours.

The results shown above demonstrate

(A) competition at both altitudes

(B) competition at high altitudes, and facilitation at low altitudes

(D) facilitation at both altitudes

Answer: (C)

37. Match the combination of flora and fauna from the list, to the state where they are found.

(A) P: Assam; Q: Jammu & Kashmir; R: West Bengal; S: Sikkim

(B) P: Jammu & Kashmir; Q: Assam; R: West Bengal; S: Sikkim

(D) P: Sikkim; Q: West Bengal; R: Assam; S: Jammu & Kashmir

Answer: (C)

38. A parent population (P) is split into three daughter populations (Q, R, and S) which grow in three different habitats. After 1000 generations, the equilibrium frequency distribution of a trait in each of the daughter populations is shown in the figure below. For reference, the vertical line represents the mean of the parent population.

From this information, one can infer that the subpopulations experienced the following selection regimes

(A) Q: Directional; R: Stabilizing; S: No selection

(B) Q: Directional; R: Stabilizing; S: Stabilizing

(D) Q: Stabilizing; R: Directional; S: No selection

Answer: (A)

39. The character matrix below lists four taxa (P-S) and their nine characters (i-ix). A character state is designated as ‘0’ if it is ancestral and ‘1’ if it is derived. Which of the following phylogenetic trees is obtained by cladistic analysis of these data?

Answer: (A)

40. The reactions below (R1 and R2) represent different carbon fixation pathways in photosynthesis.

RuBP represents Ribulose bisphosphate.

Rubisco represents RuBP carboxylase-oxygenase.

PGA represents Phosphoglyceric acid.

PEP represents Phosphoenolpyruvate.

Which of the following is CORRECT?

(A) R1 and R2 both occur in C-3 and CAM photosynthesis

(B) R1 occurs in C-4 photosynthesis; R2 occurs in C-3 photosynthesis

(D) R1 occurs in C-4 and CAM photosynthesis; R2 occurs in C-3 photosynthesis

Answer: (C)

41. A fish species is sexually dimorphic: males possess ultraviolet (UV) spots on their bodies which are lacking in females. Females prefer males with larger and more intense UV spots as mates. Which of the following statements is a plausible reason
for the spots being coloured ultraviolet?

(A) Females assess males from long distances

(B) Females are not sensitive to UV light

(D) Ultraviolet spots are more conspicuous to predators

Answer: (A or D)

42. A climate scientist notices a trend in atmospheric CO₂ concentrations (in ppm) at a research station. Although overall CO₂ is rising over decades, there are intra-annual fluctuations, as shown in the figure below.

These fluctuations can be attributed to

(A) burning of fossil fuels by automobiles and industry

(B) oscillations due to El Niño and La Niña events

(D) seasonal trends in photosynthesis and respiration

Answer: (D)

43. Four islands differ in size (small = 10 km², large = 100 km²) and distance from the mainland (near = 50 km, far = 500 km).

Island P is small and near the mainland;

Island Q is small and far from the mainland;

Island R is large and near the mainland;

Island S is large and far from the mainland

Let NP, NQ, NR and NS denote the number of species on islands P, Q, R and S, respectively. Which of the following is consistent with the theory of island biogeography?

(A) N_Q > N_S > N_P > N_R

(B) N_R > N_Q > N_P > N_S

(D) N_R > N_P > N_S > N_Q

Answer: (D)

44. The rate of population growth (dN/dt) over time (t) is shown below.

For the above population, which of the following plots of population (Popn.) size (N) vs. time (t) is CORRECT?

(A)

(B)

(C)

(D)

Answer: (A)

45. The pedigree below details a late onset genetic disease among humans. Males are represented as squares and females as circles. Individuals with the disease are depicted as black, and those without it are depicted as white. Which of the following
best describes the pattern of inheritance of the disease-causing gene?

(A) Mitochondrial

(B) X-linked dominant

(D) Y-linked

Answer: (C)

46. Match the following scientists with the concepts or theories they are associated with.

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

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

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

Answer: (C)

47. Which of the following is an example of complete intrinsic post-zygotic reproductive isolation between two species P and Q?

(A) P and Q can mate and have fertile offspring

(B) P and Q can mate but their offspring are inviable

(D) P and Q have different courtship behaviour

Answer: (B)

48. Match the animals to their locomotor adaptation.

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

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

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

Answer: (B)

49. Paralogs are genes that are the products of gene duplication events within a species. Orthologs are genes in different species that share a common ancestral gene. The figure below describes the evolutionary history of a hypothetical gene X in organism Y. This gene undergoes a duplication event. Later, Y splits into two species Y₁ and Y₂, and this gives rise to four copies of the gene – P, Q, R and S. Which option best describes the relationships between the four copies of the gene X?

(A) P & Q are orthologs, Q & R are paralogs

(B) R & S are orthologs, S & Q are paralogs

(D) P & R are orthologs, R & S are paralogs

Answer: (D)

50. The frequency distribution of beak sizes of a bird species is symmetric but not normally distributed. If the mean value of beak size is 6 mm, standard deviation is 25 mm and kurtosis is 10, then the median is ____ mm.

Answer: (5.9 to 6.1)

51. An altruist provides help worth 10 units of fitness to a recipient, at a personal cost of 1 unit of fitness. As per kin-selection theory, the minimum value of genetic relatedness between the actors and the recipients that is necessary to maintain altruism in the population is _____ (answer up to 1 decimal place).

Answer: (0.09 to 0.11)

52. A population grows from a size of 100 individuals at t = 0, to 1000 individuals at t = 100, following density-independent growth. The ratio of per-capita growth rates at the initial (at t = 0) to the final (t = 100) time is ____.

Answer: (0.99 to 1.01)

53. The probability that a bush has a cricket is 0.1. The probability of a spider being present on a bush is 0.2. When both a spider and a cricket are present on a bush, the probability of encountering each other is 0.2. The probability of a spider consuming a cricket it encounters is 0.5. Assuming that predation only occurs on bushes, the probability that a cricket is preyed on by a spider is ____ (answer up to 3 decimal places).

Answer: (0.0019 to 0.0021)

54. A plant produces seeds that can be dispersed by birds or mammals. The probability that a seed is dispersed by a bird is 0.25, and by a mammal is 0.5. The bird can disperse a seed to three patches A, B, or C with a probability 0.5, 0.4 or 0.1, respectively. On the other hand, the mammal disperses a seed to the same patches A, B, or C, with a probability 0.15, 0.8 and 0.05, respectively. The probability that a given seed is dispersed to patch B is ___ (answer up to 1 decimal place).

Answer: (0.49 t 0.51)

55. The species area relationship of trees in Mudumalai Tiger Reserve is given by S = 0.1 × A^0.3, where S is the number of species in a given area A. When log S is plotted against log A, the slope of the resulting relationship is _____ (answer up to 1
decimal place).

Answer: (0.299 to 0.301)

GATE Exam 2018 Electrical Engineering (EE) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-6

Q. 1 – Q. 5 carry one mark each.

1. “ Since you have gone off the ________, the _________ sand is likely to damage the car.”

The words that best fill the blanks in the above sentence are

(A) course, coarse

(B) course, course

(D) coarse, coarse

Answer: (A)

2. “ A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas.”

The word that best fills the blank in the above sentence is

(A) detailed

(B) simple

(D) convoluted

Answer: (D)

3. The three roots of the equation 𝑓(𝑥) = 0 are 𝑥 = {−2, 0, 3}. What are the three values of 𝑥 for which 𝑓(𝑥 − 3) = 0?

(A) −5, −3, 0

(B) −2, 0, 3

(D) 1, 3, 6

Answer: (D)

4. For what values of 𝑘 given below is an integer?

(A) 4, 8, 18

(B) 4, 10, 16

(D) 8, 26, 28

Answer: (C)

5. Functions 𝐹(𝑎, 𝑏) and 𝐺(𝑎, 𝑏) are defined as follows:

𝐹(𝑎, 𝑏) = (𝑎 − 𝑏)2 and 𝐺(𝑎, 𝑏) = |𝑎 − 𝑏|, where |𝑥| represents the absolute value of 𝑥.

What would be the value of 𝐺(𝐹(1, 3), 𝐺(1, 3))?

(A) 2

(B) 4

(D) 36

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

6. An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How many distinct passwords are possible?

(A) 6,760

(B) 13,520

(D) 1,05,456

Answer: (C)

7. In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?

(A) RSTN

(B) TLPH

(D) XSVR

Answer: (C)

8. A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?

(A) 0

(D) 5/12

Answer: (Marks to All)

9. A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles of each colour used in the current design. The cost of each marble increased by 25%. Therefore, the designer decided to reduce equal numbers of marbles of each colour to keep the total cost unchanged. What is the percentage of blue marbles in the new design?

(A) 35.75

(B) 40.25

(D) 46.25

Answer: (C)

10. P , Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available.

(i) The boat held two persons on each of the three forward trips across the lake and one person on each of the two return trips.

(ii) P is unable to row when someone else is in the boat.

(iii) Q is unable to row with anyone else except R.

(iv) Each person rowed for at least one trip.

(v) Only one person can row during a trip.

Who rowed twice?

(A) P

(B) Q

(D) S

Answer: (C)

Electrical Engineering

Q. 1 – Q. 25 carry one mark each.

1. A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

(A) 4.8

(B) 6.8

(D) 10.8

Answer: (A)

2. I n a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is

(A) 0

(B) 45

(D) 90

Answer: (B)

3. A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is true for instantaneous load voltage and current?

(A) v_o ≥ 0 & i_o < 0

(B) v_o < 0 & i_o <0

(D) v_o > 0 & i_o ≥ 0

Answer: (C)

4. Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated appropriately is (are)

(A) Triac only

(B) Triac and MOSFET

(D) Thyristor and Triac

Answer: (B)

5. Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

(A) 0.532

(B) 0.632

(D) 0.866

Answer: (D)

6. Consider a lossy transmission line with V₁ and V₂ as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively. The steady-state stability limit for the transmission line will be

Answer: (B)

7. The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

(A) 11

(B) 12

(D) 14

Answer: (B)

8. In the figure, the voltages are 𝑣₁(𝑡) = 100cos⁡(𝜔𝑡), 𝑣₂(𝑡) = 100cos⁡(𝜔𝑡 + 𝜋/18) and 𝑣₃(𝑡) = 100cos⁡(𝜔𝑡 + 𝜋/36). The circuit is in sinusoidal steady state, and 𝑅 << 𝜔𝐿. 𝑃₁, 𝑃₂ and 𝑃₃ are the average power outputs. Which one of the following statements is true?

(A)⁡𝑃₁ = 𝑃₂ = 𝑃3 = 0

(B)⁡𝑃₁ < 0, 𝑃₂ > 0, 𝑃3 > 0

(C)⁡𝑃₁ < 0, 𝑃₂ > 0, 𝑃3 < 0

(D)⁡𝑃₁ > 0, 𝑃₂ < 0, 𝑃3 > 0

Answer: (C)

9. Match the transfer functions of the second-order systems with the nature of the systems given below.

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

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

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

Answer: (C)

10. A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x – y plane to be a conducting ground plane. Take ∈₀ = 8.85 × 10^–12 The z component of the E field at (0, 0, 0.1) is closest to

(A) 899.18 V/m

(B) –899.18 V/m

(D) –999.09 V/m

Answer: (D)

11. Let f be a real-valued function of a real variable defined as f(x) = x² for x ≥ 0 and f(x) = –x² for x < 0.Which one of the following statements is true?

(A) f(x) is discontinuous at x = 0.

(B) f(x)is continuous but not differentiable at x = 0.

(D) f(x) is differentiable but its first derivative is not differentiable at x = 0.

Answer: (D)

12. The value of the directional derivative of the function Φ(x, y, z) = xy² + yz² + zx² at the point (2, -1, 1) in the direction of the vector 𝐩 = 𝐢 + 2𝐣 + 2𝐤 is

(A) 1

(B) 0.95

(D) 0.9

Answer: (A)

13. The value of the integral in counter clockwise direction around a circle 𝐶 of radius 1 with center at the point 𝑧 = −2 is

(A) πi/2

(B) 2πi

(D) –2πi

Answer: (A)

14. In the logic circuit shown in the figure, Y is given by

(A) Y = ABCD

(B) Y = (A + B)(C + D)

(D) Y = AB + CD

Answer: (D)

15. The op-amp shown in the figure is ideal. The input impedance v_in/i_in is given by

Answer: (B)

16. A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

(A) k x(t) , where k is an eigenvalue

(B) k e^jωtx(t) , where k is an eigenvalue and e^jωt is a complex exponential signal

(D) k H(ω) , where k is an eigenvalue and H(ω) is a frequency response of the system

Answer: (A)

17. Consider a non-singular 2×2 square matrix A . If trace(A) = 4 and trace(A²) = 5, the determinant of the matrix A is _________(up to 1 decimal place).

Answer: (5.5 to 5.5)

18. Let f be a real-valued function of a real variable defined as f(x) = x – [x], where [x] denotes the largest integer less than or equal to x. The value of is _______ (up to 2 decimal places).

Answer: (0.49 to 0.51)

19. In the two-port network shown, the h₁₁ parameter in ohms is _____________ (up to 2 decimal places).

Answer: (0.45 to 0.55)

20. The series impedance matrix of a short three-phase transmission line in phase coordinates If the positive sequence impedance is (1 + 𝑗⁡10)⁡Ω, and the zero sequence is (4 + ⁡𝑗⁡31)⁡Ω, then the imaginary part of 𝑍𝑚 (in Ω) is ______(up to 2 decimal places).

Answer: (7.0 to 7.0)

21. The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are 𝑗0.1 pu,⁡ 𝑗0.05 pu and 𝑗0.01 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. If the grounding impedance of the generator is 𝑗0.01 pu, then the magnitude of fault current for a b-phase to ground fault (in kA) is __________ (up to 2 decimal places).

Answer: (73.0 to 74.0)

22. A 1000 × 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are _____ (up to 2 decimal places).

Answer: (3500.0 to 3500.0)

23. The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If I0 = 20 A, the rms value of fundamental component of the current is ___________A (up to 2 decimal places).

Answer: (16.90 to 17.70)

24. A separately excited dc motor has an armature resistance 𝑅_𝑎 = 0.05⁡Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed of the motor (in radian/s) for an armature voltage of 150 V is _____ (up to 2 decimal places).

Answer: (600.0 to 600.0)

25. Consider a unity feedback system with forward transfer function given by

The steady-state error in the output of the system for a unit-step input is _________(up to 2 decimal places).

Answer: (0.65 to 0.69)

Q. 26 – Q. 55 carry two marks each.

26. A transformer with toroidal core of permeability μ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius r << R, and neglecting any leakage flux, the best estimate for the mean radius R is

Answer: (D)

27. A 0-1 Ampere moving iron ammeter has an internal resistance of 50 mΩ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in mΩ of the shunt coil respectively are

(A) 2, 5.55

(B) 2, 1

(D) 11.1, 2

Answer: (A)

28. The positive, negative and zero sequence impedances of a three phase generator are 𝑍₁, 𝑍₂ and 𝑍₀ respectively. For a line-to-line fault with fault impedance 𝑍_𝑓 ,⁡the fault current is ⁡𝐼_𝑓1 = 𝑘𝐼_𝑓 , where 𝐼_𝑓 is the fault current with zero fault impedance. The relation between 𝑍_𝑓 and 𝑘 is

Answer: (A)

29. Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G₁and G₂ are Q_G1 and Q_G2 respectively. The per unit values of Q_G1, Q_G2, and line reactive power loss (Q_loss) respectively are

(A) 5. 00, 12.68, 2.68

(B) 6.34, 10.00, 1.34

(D) 5.00, 11.34, 1.34

Answer: (C)

30. The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, 𝑃 = 1.4 sin 𝛿 + 0.15 sin 2𝛿, where 𝛿 is the load angle. Newton- Raphson method is used to calculate the value of 𝛿 for 𝑃 = ⁡0.8 pu. If the initial guess is 30°, then its value (in degree) at the end of the first iteration is

(A) 15°

(B) 28.48°

(D) 31.20°

Answer: (C)

31. A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the figure. Assume i(0) = 0, v(0) = 0. Which one of the following circular loci represents the plot of i(t) versus v(t) ?

(A)

(B)

(C)

(D)

Answer: (B)

32. The equivalent impedance Z_eq for the infinite ladder circuit shown in the figure is

(A) j12 Ω

(B) –j12 Ω

(D) 13 Ω

Answer: (A)

33. Consider a system governed by the following equations

The initial conditions are such that and Which one of the following is true?

(A) x_1f < x_2f < ∞

(B) x_2f < x_1f < ∞

(D) x_1f = x_2f = ∞

Answer: (C)

34. The number of roots of the polynomial, 𝑠⁷ +⁡𝑠⁶ + 7𝑠⁵ + 14𝑠⁴ + 31𝑠³ + 73𝑠² + 25𝑠 + 200,⁡in the open left half of the complex plane is

(A) 3

(B) 4

(D) 6

Answer: (A)

35. If 𝐶⁡is a circle |𝑧| = 4 and

(A) 1

(B) 0

(D) -2

Answer: (B)

36. Which one of the following statements is true about the digital circuit shown in the figure

(A) It can be used for dividing the input frequency by 3.

(B) It can be used for dividing the input frequency by 5.

(D) It cannot be reliably used as a frequency divider due to disjoint internal cycles.

Answer: (B)

37. Digital input signals 𝐴, 𝐵, 𝐶 with 𝐴 as the MSB and 𝐶 as the LSB are used to realize the Boolean function 𝐹 = 𝑚₀ + 𝑚₂ + 𝑚₃ + 𝑚₅ + 𝑚₇, where⁡𝑚𝑖 ⁡denotes⁡the⁡𝑖𝑡ℎ⁡minterm. In addition, 𝐹 has a don’t care for 𝑚1. The simplified expression for 𝐹 is given by

Answer: (B)

38. Consider the two continuous-time signals defined below:

These signals are sampled with a sampling period of T = 0.25 seconds to obtain discretetime signals x₁[n] and x₂[n], respectively. Which one of the following statements is true?

(A) The energy of x₁[n]is greater than the energy of x₂[n].

(B) The energy of x₂[n] is greater than the energy of x₁[n].

(D) Neither x₁[n] nor x₂[n] is a finite-energy signal.

Answer: (A)

39. The signal energy of the continuous-time signal x(t) =[(t -1) u(t -1)]-[(t -2)u(t -2)]-[(t -3)u(t -3)]+[(t -4)u(t -4)] is

(A) 11/3

(B) 7/3

(D) 5/3

Answer: (D)

40. The Fourier transform of a continuous-time signal x(t) is given by and ω denotes frequency. Then the value of |lnx(t)| at t = 1 is ___________ (up to 1 decimal place). ( ln denotes the logarithm to base e )

Answer: (9.5 to 10.5)

41. In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain 𝛽 = 100. The base-emitter voltage drop is a constant, 𝑉_𝐵𝐸 = 0.7⁡𝑉. The value of the Thevenin equivalent resistance 𝑅_𝑇ℎ (in Ω) as shown in the figure is ______ (up to 2 decimal places).

Answer: (89.0 to 91.5)

42. As shown in the figure, 𝐶 is the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of the integral ∫_C (y² + 2yx)dx + (2xy + x²)dy

Answer: (0.0 to 0.0)

43. Let f(x) = 3x³ – 7x² + 5x + 6. The maximum value of f (x) over the interval [0, 2] is _______ (up to 1 decimal place).

Answer: (11.5 to 12.5)

44. Let and B = A³ – A²– 4A + 5I, where I is the 3 × 3 identity matrix. The determinant of B is ________ (up to 1 decimal place).

Answer: (0.9 to 1.1)

45. The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates covering it entirely, the capacitance becomes 86 pF. Neglecting the fringing effects, the relative permittivity of the dielectric is _____________ (up to 2 decimal places).

Answer: (2.50 to 2.55)

46. The unit step response y(t) of a unity feedback system with open loop transfer function is shown in the figure. The value of K is _______ (up to 2 decimal places).

Answer: (8.0 to 8.0)

47. A three-phase load is connected to a three-phase balanced supply as shown in the figure. If V_an = 100∠0° V, V_bn = 100∠–120° V and V_cn = 100∠–240° V(angles are considered positive in the anti-clockwise direction), the value of R for zero current in the neutral wire is ___________Ω (up to 2 decimal places).

Answer: (5.70 to 5.85)

48. The voltage across the circuit in the figure, and the current through it, are given by the following expressions:

𝑣(𝑡) = 5 − 10 cos(𝜔𝑡 + 60°)⁡V
𝑖(𝑡) = 5 + 𝑋 cos(𝜔𝑡) A

where 𝜔 = 100⁡𝜋⁡radian/s. If the average power delivered to the circuit is zero, then the value of 𝑋 (in Ampere) is _____ (up to 2 decimal places).

Answer: (10.0 to 10.0)

49. A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by where V_m = 80π volts and 𝛼 is the firing angle. If the power delivered to the lossless battery is 1600 W, 𝛼 in degree is________ (up to 2 decimal places).

Answer: (90.0 to 90.0)

50. T he figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value. The load resistance is 1Ω. The capacitor voltage has negligible ripple. Both converters operate in the continuous conduction mode. The switching frequency is 1 kHz, and the switch control signals are as shown. The circuit operates in the steady state. Assuming that the converters share the load equally, the average value of 𝑖_𝑆1, the current of switch S1 (in Ampere), is _____ (up to 2 decimal places).

Answer: (11.50 to 13.50)

51. A 3-phase 900 kVA, 3 kV/√3 kV (Δ/Y), 50 Hz transformer has primary (high voltage side) resistance per phase of 0.3 Ω and secondary (low voltage side) resistance per phase of 0.02 Ω. Iron loss of the transformer is 10 kW. The full load % efficiency of the transformer operated at unity power factor is _______ (up to 2 decimal places).

Answer: (97.20 to 97.55)

52. A 200 V DC series motor, when operating from rated voltage while driving a certain load, draws 10 A current and runs at 1000 r.p.m. The total series resistance is 1 Ω. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by 44%. The speed of the motor in r.p.m. (rounded to the nearest integer) is ________ .

Answer: (823 to 827)

53. A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value of the inductor, L is 5 mH and the ideal switch, S is operated with a switching frequency of 5 kHz with a duty ratio of 0.4. Once the circuit has attained steady state and assuming the diode D to be ideal, the power transferred from B1 to B2 (in Watt) is ___________ (up to 2 decimal places).

Answer: (12.0 to 12.0)

54. The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are R₁ = R₂= X₁₁ = X₁₂ = 12Ω, X_M = 240Ω and s is the slip. At no-load, the motor speed can be approximated to be the synchronous speed. The no-load lagging power factor of the motor is___________ (up to 3 decimal places).

Answer: (0.104 to .0112)

55. The voltage 𝑣(𝑡) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency 𝜔 = 100 radian/s. When the inductor current 𝑖(𝑡) is in phase with the voltage 𝑣(𝑡), the magnitude of the impedance Z (in Ω) seen between the terminals a and b is ________ (up to 2 decimal places).

Answer: (50.0 to 50.0)

GATE Exam 2018 Electronics and Communication Engineering (EC) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-5

Q. 1 – Q. 5 carry one mark each.

1. “ By giving him the last ______ of the cake, you will ensure lasting _____ in our house today.”

The words that best fill the blanks in the above sentence are

(A) peas, piece

(B) piece, peace

(D) peace, peas

Answer: (B)

2. “ Even though there is a vast scope for its ________, tourism has remained a/an _________ area.”

The words that best fill the blanks in the above sentence are

(A) improvement, neglected

(B) rejection, approved

(D) interest, disinterested

Answer: (A)

3. If the number 715∎423 is divisible by 3 (∎ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ∎ is _________.

(A) 0

(B) 2

(D) 6

Answer: (B)

4. What is the value of

(A) 2

(B) 7/4

(D) 4/3

Answer: (D)

5. A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

(A) 1.5

(B) 3

(D) 6

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?

(A) 5,00,000

(B) 6,21,000

(D) 7,50,000

Answer: (B)

7. Two alloys A and B contain gold and copper in the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is ______.

(A) 5:10

(B) 7:13

(D) 9:13

Answer: (B)

8. The Cricket Board has long recognized John’s potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression into big scores. Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain. After many years, it appears that the team has finally found a complete captain. Which of the following statements can be logically inferred from the above paragraph?

(i) Even as a junior cricketer, John was considered a good captain.

(ii) Finding a complete captain is a challenge.

(iii) Fans and the Cricket Board have differing views on what they want in a captain.

(iv) Over the past three seasons John has accumulated big scores.

(A) (i), (ii) and (iii) only

(B) (iii) and (iv) only

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

Answer: (C)

9. A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident.

(i) 85% of cabs in the city are green and the remaining cabs are blue.

(ii) A witness identified the cab involved in the accident as blue.

(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.

Which of the following options is closest to the probability that the accident was caused by a blue cab?

(A) 12%

(B) 15%

(D) 80%

Answer: (C)

10. A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming crowded and polluted like any other major beach resorts.

Which one of the following statements can be logically inferred from the information given in the above paragraph?

(A) The culture and tradition of the local people will be influenced by the tourists.

(B) The region will become crowded and polluted due to tourism.

(D) Helicopter connectivity would lead to an increase in tourists coming to the region.

Answer: (D)

Electronics and Communication Engineering

Q. 1 – Q. 25 carry one mark each.

1. Two identical nMOS transistors M₁ and M₂ are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals. V_bias and V_D are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as while the output resistance is where 𝑖𝐷 is the current flowing into the drain of M₂ . Let 𝑔_𝑚1, 𝑔_𝑚2 be the transconductances and 𝑟_𝑜1, 𝑟_𝑜2 be the output resistances of transistors M₁ and M₂, respectively.

Which of the following statements about estimates for 𝑔_𝑚 and 𝑟_𝑜 is correct?

Answer: (C)

2. In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e. 𝑣𝐼𝑁 (𝑡) = 𝑢(𝑡) volts. Also, at 𝑡 = 0, the voltage across each of the capacitors is zero.

The time 𝑡, in milliseconds, at which the output voltage 𝑣_𝑂𝑈𝑇 crosses −10 V is

(A) 2.5

(B) 5

(D) 10

Answer: (C)

3. A good transimpedance amplifier has

(A) low input impedance and high output impedance.

(B) high input impedance and high output impedance.

(D) low input impedance and low output impedance.

Answer: (D)

4. Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

Answer: (C)

5. The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

(A) Both the criteria provide information relative to the stable gain range of the system.

(B) The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.

(C) The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion.

(D) The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

Answer: (D)

6. Consider 𝑝(𝑠) = 𝑠³ + 𝑎²𝑠² + 𝑎¹𝑠 + 𝑎0 with all real coefficients. It is known that its derivative 𝑝′(𝑠) has no real roots. The number of real roots of 𝑝(𝑠) is

(A) 0

(B) 1

(D) 3

Answer: (B)

7. In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

(A) The hole and electron diffusion current components are in the same direction.

(B) The hole and electron drift current components are in the same direction.

(D) On an average, electrons drift and diffuse in the same direction.

Answer: (D)

8. The logic function f(X, Y) realized by the given circuit is

(A) NOR

(B) AND

(D) XOR

Answer: (D)

9. A function 𝐹(𝐴, 𝐵, 𝐶) defined by three Boolean variables A, B and C when expressed as sum of products is given by

where, are the complements of the respective variables. The product of sums (POS) form of the function F is

Answer: (C)

10. The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:

(A) P: Open Circuit, Q: Short Circuit, R: Matched Load

(B) P: Open Circuit, Q: Matched Load, R: Short Circuit

(D) P: Short Circuit, Q: Open Circuit, R: Matched Load

Answer: (C)

11. Let M be a real 44 matrix. Consider the following statements:

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?

(A) S1 implies S2

(B) S1 implies S3

(D) S3 implies S2

Answer: (C)

12. Let where a and b are constants. If at x = 1 and y = 2, then the relation between a and b is

(A) a = b/4

(B) a = b/2

(D) a = 4b

Answer: (D)

13. A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30° . Which one of the following statements about the system is TRUE?

(A) It has two more poles at 0.5∠30° and 4∠0°.

(B) It is stable only when the impulse response is two-sided.

(D) It has constant phase response over the entire z-plane.

Answer: (B)

14. Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎_𝑘, that is

The same function 𝑥(𝑡) can also be considered as a periodic function with period 𝑇′ = 40. Let 𝑏_𝑘 be the Fourier series coefficients when period is taken as 𝑇′. If then is equal to

(A) 256

(B) 64

(D) 4

Answer: (C)

15. Consider the following amplitude modulated signal:

𝑠(𝑡) = cos(2000 𝜋𝑡) + 4 cos(2400 𝜋𝑡) + cos(2800 𝜋𝑡).

The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is __________.

Answer: (0.12 to 0.13)

16. Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in this code is at least 2. The maximum number of codewords such a code can contain is _________.

Answer: (16 to 16)

17. A binary source generates symbols 𝑋 ∈ {−1,1} which are transmitted over a noisy channel. The probability of transmitting 𝑋 = 1 is 0.5. Input to the threshold detector is 𝑅 = 𝑋 + 𝑁. The probability density function 𝑓𝑁(𝑛) of the noise 𝑁 is shown below.

If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.

Answer: (0.12 to 0.14)

18. A p-n step junction diode with a contact potential of 0.65V has a depletion width of 1μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is _______.

Answer: (0.40 to 0.43)

19. A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is _______.

Answer: (5 to 5)

20. There are two photolithography systems: one with light source of wavelength λ1 = 156 nm (System 1) and another with light source of wavelength λ₂ = 325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are Lmin1 and Lmin2 respectively, the ratio L_min1/L_min2 (correct to two decimal places) is__________.

Answer: (0.47 to 0.51)

21. A lossy transmission line has resistance per unit length R = 0.05 Ω . The line is distortionless and has characteristic impedance of 50Ω . The attenuation constant (in Np/m, correct to three decimal places) of the line is _______.

Answer: (0.001 to 0.001)

22. Consider matrix The number of distinct real values of k for which the equation Ax = 0 has infinitely many solutions is _______.

Answer: (2 to 2)

23. Let X₁ , X₂ , X₃ and X₄ be independent normal random variables with zero mean and unit variance. The probability that 4 X is the smallest among the four is _______.

Answer: (0.25 to 0.25)

24. Taylor series expansion of around 𝑥 = 0 has the form

𝑓(𝑥) = 𝑎₀ + 𝑎₁𝑥 + 𝑎²𝑥² + ⋯

The coefficient 𝑎₂ (correct to two decimal places) is equal to _______.

Answer: (-0.01 to 0.01)

25. The ABCD matrix for a two-port network is defined by:

The parameter B for the given two-port network (in ohms, correct to two decimal places) is _______.

Answer: (4.3 to 5.3)

Q. 26 – Q. 55 carry two marks each.

26. The circuit shown in the figure is used to provide regulated voltage (5 V) across the 1kΩ resistor. Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a minimum required Zener current, min I_Zmin = 2 MA to its maximum allowable current. The input voltage I V may vary by 5% from its nominal value of 6 V. The resistance of the diode in the breakdown region is negligible.

The value of R and the minimum required power dissipation rating of the diode, respectively, are

(A) 186 Ω and 10 mW

(B) 100 Ω and 40 mW

(D) 186 Ω and 40 mW

Answer: (B)

27. Let c(t) = A_c cos(2πf_ct) and m(t) = cos(2πf_mt). It is given that f_c >> 5f_m. The signal c(t) + m(t) is applied to the input of a non-linear device, whose output v₀(t) is related to the input vi(t) as v₀(t) = av_i(t) + bv_i²(t), where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency f_c and bandwidth 3f_m , to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then a/b is

(A) 0.25

(B) 0.5

(D) 2

Answer: (D)

28. Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density S_N(f) = 0.5 W/Hz as input to a filter with impulse response 0.5e^–t2/2 (where 𝑡 is in seconds) resulting in output 𝑌(𝑡). The power in 𝑌(𝑡) in watts is

(A) 0.11

(B) 0.22

(D) 0.44

Answer: (B)

29. The state equation and the output equation of a control system are given below:

The transfer function representation of the system is

Answer: (A)

30 Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The builtin voltages of red, green and blue diodes are V_R, V_G and V_B, respectively. Assume donor and acceptor doping to be the same (NA and N_D, respectively) in the p and n sides of all the three diodes.
Which one of the following relationships about the built-in voltages is TRUE?

(A) V_R > V_G > V_B

(B) V_R < V_G < V_B

(D) V_R > V_G < V_B

Answer: (B)

31. A four-variable Boolean function is realized using 41 multiplexers as shown in the figure.

The minimized expression for F(U,V,W, X) is

Answer: (C)

32. A 2 × 2 ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals that select the word lines and B0 and B1 are signals that are output of the sense amps based on the stored data corresponding to the bit lines during the read operation.

During the read operation, the selected word line goes high and the other word line is in a high impedance state. As per the implementation shown in the circuit diagram above, what are the bits corresponding to D_ij (where i = 0 or 1 and j = 0 or 1) stored in the ROM?

(A)

(B)

(C)

(D)

Answer: (A)

33. The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is

(A) 0.12

(B) 0.23

(D) 2.3

Answer: (B)

34. A curve passes through the point (x = 1, y = 0) and satisfies the differential equation The equation that describes the curve is

Answer: (A)

35. For the circuit given in the figure, the voltage V_C (in volts) across the capacitor is

Answer: (C)

36. For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is _______.

Answer: (0.284 to 0.348)

37. A dc current of 26μA flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, the diode has a junction capacitance of 0.5 nF . Its neutral region resistances can be neglected. Assume that the room temperature thermal equivalent voltage is 26 mV.

For ω = 2 × 10⁶ rad/s , the amplitude of the small-signal component of diode current (in μA, correct to one decimal place) is _______.

Answer: (6.2 to 6.6)

38. An op-amp based circuit is implemented as shown below.

In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node A, connected to the negative input of the op-amp as indicated in the figure is _________.

Answer: (0.4 to 0.6)

39. T he input 4sinc(2𝑡) is fed to a Hilbert transformer to obtain 𝑦(𝑡), as shown in the figure below:

Here The value (accurate to two decimal places) of is _______.

Answer: (8 to 8)

40 A random variable 𝑋 takes values −0.5 and 0.5 with probabilities 1/4 and 3/4, respectively. The noisy observation of 𝑋 is 𝑌 = 𝑋 + 𝑍, where 𝑍 has uniform probability density over the interval (−1, 1). 𝑋 and 𝑍 are independent. If the MAP rule based detector outputs as

then the value of 𝛼 (accurate to two decimal places) is _______.

Answer: (-0.5 to -0.5)

41. For a unity feedback control system with the forward path transfer function

The peak resonant magnitude M_r of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.

Answer: (14 to 17)

42. The figure below shows the Bode magnitude and phase plots of a stable transfer function

Consider the negative unity feedback configuration with gain 𝑘 in the feedforward path. The closed loop is stable for 𝑘 < 𝑘₀ . The maximum value of 𝑘₀ is ______.

Answer: (0.1 to 0.1)

43. In the circuit shown below, the (𝑊/𝐿) value for M2 is twice that for M₁. The two nMOS transistors are otherwise identical. The threshold voltage 𝑉𝑇 for both transistors is 1.0V. Note that 𝑉_𝐺𝑆 for M₂ must be > 1.0 V.

Answer: (0.41 to 0.435)

44. A solar cell of area 1.0 cm² , operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open circuit voltage of 0.65 V. Assuming room temperature operation and thermal equivalent voltage of 26mV, the open circuit voltage (in volts, correct to two decimal places) at 0.2 sun intensity is _______.

Answer: (0.59 to 0.63)

45. A junction is made between p^– Si with doping density N_A1 = 10¹⁵ cm^–3 and p Si with doping density N_A2 = 10¹⁷ cm^–3.

Given: Boltzmann constant k = 1.38 x 10^–23 J.K^–1, electronic charge q = 1.6 x 10^–19 C. Assume 100% acceptor ionization.

At room temperature (T = 300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be _________________.

Answer: (0.11 to 0.13)

46. In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data 𝐷_𝑖𝑛 using clock 𝐶𝐾. The XOR gate outputs 3.3 volts for logic HIGH and 0 volts for logic LOW levels. The data bit and clock periods are equal and the value of Δ𝑇/𝑇_𝐶𝐾 = 0.15, where the parameters Δ𝑇 and 𝑇_𝐶𝐾 are shown in the figure. Assume that the Flip-Flop and the XOR gate are ideal.

If the probability of input data bit (𝐷_𝑖𝑛) transition in each clock period is 0.3, the average value (in volts, accurate to two decimal places) of the voltage at node 𝑋, is _______.

Answer: (0.82 to 0.86)

47. The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for
LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes are intentionally shorted to implement “wired logic”. Such shorted nodes will be HIGH only if the outputs of all the gates whose outputs are shorted are HIGH.

The number of distinct values of 𝑋₃𝑋₂𝑋₁𝑋₀ (out of the 16 possible values) that give 𝑌 = 1 is _______.

Answer: (8 to 8)

48. T he cutoff frequency of TE₀₁ mode of an air filled rectangular waveguide having inner dimensions a cm × b cm ( ab ) is twice that of the dominant TE₁₀ mode. When the waveguide is operated at a frequency which is 25% higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be 4 cm. The value of b (in cm, correct to two decimal places) is _______.

Answer: (0.7 to 0.8)

49. A uniform plane wave traveling in free space and having the electric field

is incident on a dielectric medium (relative permittivity > 1, relative permeability = 1) as shown in the figure and there is no reflected wave.

The relative permittivity (correct to two decimal places) of the dielectric medium is ___________.

Answer: (1.9 to 2.1)

50. The position of a particle 𝑦(𝑡) is described by the differential equation:

The initial conditions are The position (accurate to two decimal places) of the particle at 𝑡 = 𝜋 is _______.

Answer: (-0.23 to -0.19)

51. The contour C given below is on the complex plane z = x + iy , where

The value of the integral is _______.

Answer: (2 to 2)

52. Let r = x² + y – z and z³ – xy + yz + y³ = 1.Assume that 𝑥 and 𝑦 are independent variables. At (𝑥, 𝑦, 𝑧) = (2, −1,1), the value (correct to two decimal places) of is ________.

Answer: (4.4 to 4.6)

53. Consider the network shown below with 𝑅1 = 1Ω, 𝑅2 = 2Ω and 𝑅3 = 3Ω. The network is connected to a constant voltage source of 11V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is _______.

Answer: (7.9 to 8.1)

54. A band limited low-pass signal 𝑥(𝑡) of bandwidth 5 kHz is sampled at a sampling rate 𝑓𝑠. The signal 𝑥(𝑡) is reconstructed using the reconstruction filter 𝐻(𝑓) whose magnitude response is shown below:

The minimum sampling rate 𝑓_𝑠 (in kHz) for perfect reconstruction of 𝑥(𝑡) is _______.

Answer: (13 to 13)

55. Let 𝑋[𝑘] = 𝑘 + 1, 0 ≤ 𝑘 ≤ 7 be 8-point DFT of a sequence 𝑥[𝑛],

where

The value (correct to two decimal places) of

Answer: (2.90 to 3.10)

GATE Exam 2018 Chemistry (CY) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

CHEMISTRY

Q. 1 – Q. 25 carry one mark each.

1. The major product formed in the following reaction is

Answer: (C)

2. The major product formed in the following reaction is

Answer: (D)

3. The major product of the following intramolecular cycloaddition reaction is

Answer: (D)

4. The major product of the following reaction is

Answer: (B)

5. The major product formed in the following reaction sequence is

Answer: (B)

6. The major product formed in the following reaction sequence is

Answer: (A)

7. The spherical harmonic function, with appropriate values of l and m, is an eigenfunction of operator. The corresponding eigenvalue is

(A)

(B)

(C)

(D)

Answer: (A)

8. Consider the operators, are the
position and linear momentum operators, respectively. The commutator, is equal to

(A) ih

(B) –ih

(D) –h

Answer: (C)

9. The temperature derivative of electrochemical cell potential E at constant pressure, is given by

Answer: (B)

10. For an ionic micelle-forming surfactant near its critical micelle concentration (CMC), the dependence of molar conductivity and surface tension on surfactant concentration is best represented by

Answer: (B)

11. According to Eyring transition state theory for a bimolecular reaction, the activated complex has

(A) no vibrational degrees of freedom.

(B) vibrational degrees of freedom but they never participate in product formation.

(D) one low frequency vibration that leads to product formation.

Answer: (D)

12. Based on Wade’s rule, the structure-type of [B₅H₈]^– is

(A) closo

(B) nido

(D) hypho

Answer: (B)

13. The coordination geometries around the copper ion of plastocyanin (a blue-copper protein) in oxidized and reduced form, respectively, are

(A) tetrahedral and square-planar

(B) square-planar and tetrahedral

(D) ideal tetrahedral for both

Answer: (C)

14. The water exchange rates for the complex ions follow the order

Answer: (D)

15. The lowest energy d → d transition of the complexes follow the order

Answer: (A)

16. T he symmetry label of valence p orbitals of a metal ion in an octahedral ligand field is

(A) t1_g

(B) t1_u

(D) t2_g

Answer: (B)

17. The bond angle (Ti—C—C) in the crystal structure of

is severely distorted due to

(A) hydrogen-bonding interaction

(B) agostic interaction

(D) higher formal charge on metal

Answer: (B)

18. The molar heat capacity of a substance is represented in the temperature range 298 K to 400 K by the empirical relation C_{p, m} = 14 + bT J K^–1 mol^–1, where b is a constant. The molar enthalpy change when the substance is heated from 300 K to 350 K is 2 kJ mol^–1. The value of b is___________ J K^–2 mol^–1. (Up to two decimal places)

Answer: (0.07 to 0.09)

19. For low partial pressure of ozone (O₃), the adsorption of ozone on graphite surface is fully dissociative in nature, and follows Langmuir isotherm. Under these conditions, if the dependence of the surface coverage of graphite (θ) on partial pressure of ozone (P_O3) is given by the value of x is___________. (Up to two decimal places)

Answer: (0.32 to 0.34)

20. For the radioactive isotope ¹³¹I, the time required for 50% disintegration is 8 days. The time required for the 99.9% disintegration of 5.5 g of ¹³¹I is ________ days. (Up to one decimal place)

Answer: (79.1 to 80.6)

21. Two moles of an ideal gas X and two moles of an ideal gas Y, initially at the same temperature and pressure, are mixed under isothermal-isobaric condition. The entropy change on mixing is __________J K^–1. (Up to one decimal place. Use R = 8.31 J K^–1 mol^–1)

Answer: (22.0 to 24.0)

22. The energy of a hydrogen molecule in its ground state equilibrium configuration is –31.7 eV. Its dissociation energy is _________ eV. (Up to one decimal place)

Answer: (4.4 to 4.6)

23. The total number of valence electrons in W(η³-Cp)(η⁵-Cp)(CO)₂ is ______. (Atomic number of W = 74)

Answer: (18.0 to 18.0)

24. In the 1H NMR spectrum of an organic compound recorded on a 300 MHz instrument, a proton resonates as a quartet at δ4.20 ppm. The individual signals of the quartet appear at δ4.17, 4.19, 4.21 and 4.23 ppm. The coupling constant J in Hz is ______.

Answer: (6.0 to 6.0)

25. In the electron ionization (EI) mass spectra, methyl hexanoate, methyl heptanoate and methyl octanoate give the same base peak. The m/z value of the base peak is ______.

Answer: (73.8 to 74.2)

Q. 26 – Q. 55 carry two marks each.

26. In the following reaction,

(A) X is the major product and Y is the minor product

(B) X is the only product

(D) X is the minor product and Y is the major product

Answer: (A)

27. The enantiomeric pair, among the following, is

(A)

(B)

(C)

(D)

Answer: (D)

28. The major product formed in the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (A)

29. The major product in the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (A)

30. The major product formed in the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (D)

31. The major product of the following reaction sequence is

(A)

(B)

(C)

(D)

Answer: (D)

32. The major product formed in the following retro-aldol reaction is

(A)

(B)

(C)

(D)

Answer: (B)

33. The elimination product of the following reaction is

(A) I₂

(B) CH₃I

(D) I₃^–

Answer: (C)

34. A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is Using only the first order correction, the total ground state energy of the anharmonic oscillator is

(Note: For a one-dimensional harmonic oscillator

Answer: (A)

35. The O₂ coordinated to metal ion centres in oxy-myoglobin and oxy-hemocyanin exists, respectively, as

(A) superoxide and peroxide

(B) superoxide and superoxide

(D) superoxide and oxygen

Answer: (A)

36. Spectroscopic ground state term symbols of cobalt ions in [Co(H₂O)₆]²⁺ and [CoCl₄]^2–, respectively, are

(A) ²T_1g and ^4A2

(B) ⁴T1_g and ^4A2

(D) ²T₁ and ⁴A₁

Answer: (B)

37. Generally, the coordination number and the nature of the electronic absorption band (f → f transition) of lanthanide(III) ion in their complexes are, respectively,

(A) greater than 6 and sharp

(B) 6 and broad

(D) greater than 6 and broad

Answer: (A)

38. Second-order rate constant for the reaction between [Co(NH₃)₅X]ⁿ⁺ (n = 3 for X = NH₃ and H₂O; n = 2 for X = Cl^–) and [Cr(H₂O)₆]²⁺ at room temperature varies with the X as

(A) NH₃ > H₂O > Cl^–

(B) Cl^– > H₂O > NH₃

(D) H₂O > NH₃ > Cl^–

Answer: (B)

39. For the following reaction sequence,

X and Y, respectively, are

(A) {HB(NH)}₃ and {H(OH)B(NH₂)}₃

(B) {HB(NH)}₃ and {HB(NH₂OH)}₃

(D) (NH₄){(H)₂(BH₂)₃} and {HB(NH₂OH)}₃

Answer: (A)

40. For an inverse spinel, AB2O4, the A and B, respectively, can be

(A) Ni(II) and Ga(III)

(B) Zn(II) and Fe(III)

(D) Mn(II) and Mn(III)

Answer: (A)

41. The reaction of PCl₃ with PhLi in 1:3 molar ratio yields X as one of the products, which on further treatment with CH₃I gives Y. The reaction of Y with n-BuLi gives product Z. The products X, Y and Z, respectively, are

(A) [PPh₄]Cl, [Ph₂P=CH₂] and Ph₂P(n-Bu)

(B) PPh₃, [Ph₃PI](CH₃) and Ph₂P(n-Bu)₃

(D) [PPh₄]Cl, [Ph₃P=CH₂] and [Ph₃P(n-Bu)]Li

Answer: (C)

42. The reaction of equimolar quantities of Fe(CO)5 and OH– gives a complex species X which on further reaction with MnO2 gives species Y. X and Y, respectively, are

(A) [Fe(CO)₅(OH)]^– and Fe²(CO)⁹

(B) [Fe(CO)₄]^2– and Mn₂(CO)₁₀

(D) [HFe(CO)₄]– and Fe₃(CO)₁₂

Answer: (D)

43. The rate constant of a first order reaction, X → Y is 1.6 × 10^–3 s^–1 at 300 K. Given that the activation energy of the reaction is 28 kJ mol^–1 and assuming Arrhenius behavior for the temperature dependence, the total time required to obtain 90% of Y at 350 K is_____________ s. (Up to one decimal place. Use R = 8.31 J K^–1 mol^–1 )

Answer: (280 to 300)

44. The molar conductivity of a 0.01 M weak acid (HX) at 298 K, measured in a conductivity cell with cell constant of 0.4 cm^–1, is 64.4 S cm² mol^–1. The limiting molar conductivities at infinite dilution of H+ and X– at 298 K are 350 and 410 S cm² mol^–1, respectively. Ignoring activity coefficients, the pKa of HX at 298 K is___________. (Up to two decimal places)

Answer: (4.01 to 4.21)

45. The Latimer diagram of oxygen is given below. The value of x is ________ V. (Up to two decimal places)

Answer: (1.22 to 1.24)

46. At temperature T, the canonical partition function of a harmonic oscillator with fundamental frequency (ν) is given by

For , the probability of finding the harmonic oscillator in its ground vibrational state is ________. (Up to two decimal places)

Answer: (0.93 to 0.97)

47. The enthalpy of vaporization of a liquid at its boiling point (T_b = 200 K ) is 15.3 kJ mol^–1. If the molar volumes of the liquid and the vapour at 200 K are 110 and 12000 cm³ mol^–1respectively, then the slope of the liquid-vapour boundary is _________ kPa K^–1. (Up to two decimal places. Note: 1 Pa = 1 J m^–3)

Answer: (6.20 to 6.60)

48. In a molecule XY, let Ψ_X and Ψ_Y denote normalized atomic orbitals of atoms X and Y, respectively. A normalized molecular orbital of XY is given by Ψ₊= 0.56(Ψ_X + Ψ_Y ) . The value of the overlap integral of X and Y is _________________. (Up to two decimal places)

Answer: (0.55 to 0.65)

49. The absorption maxima of two dyes X and Y are 520 and 460 nm, respectively. The absorbance data of these dyes measured in a 1 cm path length cell are given in the table below.

The concentration of Y in the mixture is __________ mM. (Up to two decimal places)

Answer: (7.4 to 8.2)

50. The π electrons in benzene can be modelled as particles in a ring that follow Pauli’s exclusion principle. Given that the radius of benzene is 1.4 Å, the longest wavelength of light that is absorbed during an electronic transition in benzene is __________ nm. (Up to one decimal place. Use me = 9.1 × 10^–31 kg, h = 6.6 × 10^–34 J s, c = 3.0 × 10⁸ ms^–1)

Answer: (210.0 to 216.0)

51. The spacing between the two adjacent lines of the microwave spectrum of H³⁵Cl is 6.35 × 10¹¹ Hz . Given that the bond length of D³⁵Cl is 5% greater than that of H³⁵Cl, the corresponding spacing for D³⁵Cl is _______ × 10¹¹ Hz (Up to two decimal places)

Answer: (2.80 to 3.10)

52. For a diatomic vibrating rotor, in vibrational level υ = 3 and rotational level J, the sum of the rotational and vibrational energies is 11493.6 cm^–1. Its equilibrium oscillation frequency is 2998.3 cm^–1, anharmonicity constant is 0.0124 and rotational constant under rigid rotor approximation is 9.716 cm^–1. The value of J is ___________. (Up to nearest integer)

Answer: (12 to 12)

53. Number of carbonyl groups present in the final product of the following reaction sequence is ___________.

Answer: (4.0 to 4.0)

54. A tetrapeptide, made up of natural amino acids, has alanine as the N-terminal residue which is coupled to a chiral amino acid. Upon complete hydrolysis, the tetrapeptide gives glycine, alanine, phenylalanine and leucine. The number of possible sequences of the tetrapeptide is ____.

Answer: (4.0 to 4.0)

55. The strongest band observed in the IR spectrum of the final product of the following reaction appears, approximately, at ______ × 100 cm^–1. (Up to one decimal place)

Answer: (16.99 to 17.31)

GATE Exam 2018 Computer Science and Information Technology (CS) Question Paper With Answer Key

June 7, 2023November 21, 2018 by suresh84

Computer Science and Information Technology

General Aptitude (GA) Set-3

Q. 1 – Q. 5 carry one mark each.

1. “ From where are they bringing their books? ________ bringing _______ books from _____.”

The words that best fill the blanks in the above sentence are

(A) Their, they’re, there

(B) They’re, their, there

(D) They’re, there, there

Answer: (B)

2. “ A _________ investigation can sometimes yield new facts, but typically organized ones are more successful.”

The word that best fills the blank in the above sentence is

(A) meandering

(B) timely

(D) systematic

Answer: (A)

3. The area of a square is 𝑑. What is the area of the circle which has the diagonal of the square as its diameter?

(A) 𝜋𝑑

(B) 𝜋𝑑²

Answer: (D)

4. W hat would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of 7 in each case?

(A) 3047

(B) 6047

(D) 63847

Answer: (C)

5. What is the missing number in the following sequence?

2, 12, 60, 240, 720, 1440, _____, 0

(A) 2880

(B) 1440

(D) 0

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen in the town and Rs 1000 to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only 8/9th of the eligible men and 2/3rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

(A) 1,50,000

(B) 2,00,000

(D) 1,51,000

Answer: (B)

7. If 𝑝𝑞𝑟 ≠ 0 and what is the value of the product 𝑥𝑦𝑧?

(A) −1

(B) 1/pqr

(D) 𝑝𝑞𝑟

Answer: (C)

8. In a party, 60% of the invited guests are male and 40% are female. If 80% of the invited guests attended the party and if all the invited female guests attended, what would be the ratio of males to females among the attendees in the party?

(A) 2:3

(B) 1:1

(D) 2:1

Answer: (B)

9. In the figure below, ∠𝐷𝐸𝐶 + ∠𝐵𝐹𝐶 is equal to ____________

(A) ∠𝐵𝐶𝐷 − ∠𝐵𝐴𝐷

(B) ∠𝐵𝐴𝐷 + ∠𝐵𝐶𝐹

(D) ∠𝐶𝐵𝐴 + ∠𝐴𝐷𝐶

Answer: (A)

10. A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?

(A) Three green faces and four red faces.

(B) Four green faces and three red faces.

(D) Six green faces and one red face.

Answer: (C)

COMPUTER SCIENCE AND INFORMATION TECHNOLOGY

Q. 1 – Q. 25 carry one mark each.

1. Which one of the following is a closed form expression for the generating function of the
sequence {a_n}, where an = 2n + 3 for all n = 0, 1, 2,… ?

Answer: (D)

2. Consider the following C program.

The output of this program is:

(A) 0, c

(B) 0, a+2

(D) ‘0’, ‘c’

Answer: (A)

3. A queue is implemented using a non-circular singly linked list. The queue has a head pointer and a tail pointer, as shown in the figure. Let n denote the number of nodes in the queue. Let enqueue be implemented by inserting a new node at the head, and dequeue be implemented by deletion of a node from the tail.

Which one of the following is the time complexity of the most time-efficient implementation of enqueue and dequeue, respectively, for this data structure?

(A) θ(1), θ(1)

(B) θ(1), θ(n)

(D) θ(n), θ(n)

Answer: (B)

4. Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

Answer: (D)

5. Consider the following processor design characteristics.

I. Register-to-register arithmetic operations only

II. Fixed-length instruction format

III. Hardwired control unit

Which of the characteristics above are used in the design of a RISC processor?

(A) I and II only

(B) II and III only

(D) I, II and III

Answer: (D)

6. Let N be an NFA with n states. Let k be the number of states of a minimal DFA which is equivalent to N. Which one of the following is necessarily true?

(A) 𝑘 ≥ 2𝑛

(B) 𝑘 ≥ 𝑛

(D) 𝑘 ≤ 2𝑛

Answer: (D)

7. The set of all recursively enumerable languages is

(A) closed under complementation.

(B) closed under intersection.

(D) an uncountable set.

Answer: (B)

8. Which one of the following statements is FALSE?

(A) Context-free grammar can be used to specify both lexical and syntax rules.

(B) Type checking is done before parsing.

(D) Arguments to a function can be passed using the program stack.

Answer: (B)

9. The following are some events that occur after a device controller issues an interrupt while process L is under execution.

(P) The processor pushes the process status of L onto the control stack.

(Q) The processor finishes the execution of the current instruction.

(R) The processor executes the interrupt service routine.

(S) The processor pops the process status of L from the control stack.

(T) The processor loads the new PC value based on the interrupt.

Which one of the following is the correct order in which the events above occur?

(A) QPTRS

(B) PTRSQ

(D) QTPRS

Answer: (A)

10. Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is M units if the corresponding memory page is available in memory, and D units if the memory access causes a page fault. It has been experimentally measured that the average time taken for a memory access in the process is X units.

Which one of the following is the correct expression for the page fault rate experienced by the process?

(A) (D – M) / (X – M)

(B) (X – M) / (D – M)

(D) (X – M) / (D – X)

Answer: (B)

11. In an Entity-Relationship (ER) model, suppose R is a many-to-one relationship from entity set E1 to entity set E2. Assume that E1 and E2 participate totally in R and that the cardinality of E1 is greater than the cardinality of E2.

Which one of the following is true about 𝑅?

(A) Every entity in E1 is associated with exactly one entity in E2.

(B) Some entity in E1 is associated with more than one entity in E2.

(D) Every entity in E2 is associated with at most one entity in E1.

Answer: (A)

12. Consider the following two tables and four queries in SQL.

Which one of the queries above is certain to have an output that is a superset of the outputs of the other three queries?

(A) Query 1

(B) Query 2

(D) Query 4

Answer: (D)

13. Match the following:

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

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

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

Answer: (C)

14. Consider the following statements regarding the slow start phase of the TCP congestion control algorithm. Note that cwnd stands for the TCP congestion window and MSS denotes the Maximum Segment Size.

(i) The cwnd increases by 2 MSS on every successful acknowledgment.

(ii) The cwnd approximately doubles on every successful acknowledgement.

(iii) The cwnd increases by 1 MSS every round trip time.

(iv) The cwnd approximately doubles every round trip time.

Which one of the following is correct?

(A) Only (ii) and (iii) are true

(B) Only (i) and (iii) are true

(D) Only (i) and (iv) are true

Answer: (C)

15. Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each dice are equi-probable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial is _____.

Answer: (0.021 to 0.024)

16. The value of correct to three decimal places
(assuming that 𝜋 = 3.14 ) is _____.

Answer: (0.27 to 0.30)

17. Consider a matrix Note that v^T denotes the transpose of v. The largest eigenvalue of A is _____.

Answer: (3 to 3)

18. The chromatic number of the following graph is _______.

Answer: (3 to 3)

19. Let G be a finite group on 84 elements. The size of a largest possible proper subgroup of G is ________.

Answer: (42 to 42)

20. The postorder traversal of a binary tree is 8,9,6,7,4,5,2,3,1. The inorder traversal of the same tree is 8,6,9,4,7,2,5,1,3. The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is ______.

Answer: (4 to 4)

21. Consider the following C program:

The output of this program is _____.

Answer: (4 to 4)

22. Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.

The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of “in” is _____.

Answer: (2 to 2)

23. A 32-bit wide main memory unit with a capacity of 1 GB is built using 256M × 4-bit DRAM chips. The number of rows of memory cells in the DRAM chip is 2¹⁴. The time taken to perform one refresh operation is 50 nanoseconds. The refresh period is 2 milliseconds. The percentage (rounded to the closest integer) of the time available for performing the memory read/write operations in the main memory unit is __________.

Answer: (59.0 to 60.0)

24. Consider a system with 3 processes that share 4 instances of the same resource type. Each process can request a maximum of 𝐾 instances. Resource instances can be requested and released only one at a time. The largest value of 𝐾 that will always avoid deadlock is ____.

Answer: (2 to 2)

25. Consider a long-lived TCP session with an end-to-end bandwidth of 1 Gbps (= 10⁹ bits-persecond). The session starts with a sequence number of 1234. The minimum time (in seconds, rounded to the closest integer) before this sequence number can be used again is _______.

Answer: (34 to 35)

Q. 26 – Q. 55 carry two marks each.

26. Consider a matrix P whose only eigenvectors are the multiples of

Consider the following statements.

(I) P does not have an inverse

(II) P has a repeated eigenvalue

(III) P cannot be diagonalized

Which one of the following options is correct?

(A) Only I and III are necessarily true

(B) Only II is necessarily true

(D) Only II and III are necessarily true

Answer: (D)

27. Let N be the set of natural numbers. Consider the following sets.

P: Set of Rational numbers (positive and negative)

Q: Set of functions from {0, 1} to N

R: Set of functions from N to {0, 1}

S: Set of finite subsets of N.

Which of the sets above are countable?

(A) Q and S only

(B) P and S only

(D) P, Q and S only

Answer: (D)

28. Consider the first-order logic sentence

where 𝜓(𝑠, 𝑡, 𝑢, 𝑣, 𝑤, 𝑥, 𝑦) is a quantifier-free first-order logic formula using only predicate symbols, and possibly equality, but no function symbols. Suppose 𝜑 has a model with a universe containing 7 elements.

Which one of the following statements is necessarily true?

(A) There exists at least one model of 𝜑 with universe of size less than or equal to 3.

(B) There exists no model of 𝜑 with universe of size less than or equal to 3.

(D) Every model of 𝜑 has a universe of size equal to 7.

Answer: (A)

29. Consider the following C program:

The output of the program above is

(A) Hi Bye Bye Hi

(B) Hi Bye Hi Bye

(D) Bye Hi Bye Hi

Answer: (A)

30. Let G be a simple undirected graph. Let T_D be a depth first search tree of G. Let T_B be a breadth first search tree of G. Consider the following statements.

(I) No edge of G is a cross edge with respect to T_D. (A cross edge in G is between two nodes neither of which is an ancestor of the other in T_D.)

(II) For every edge (u,v) of G, if u is at depth i and v is at depth j in T_B, then |𝑖 − 𝑗| = 1. Which of the statements above must necessarily be true?

(A) I only

(B) II only

(D) Neither I nor II

Answer: (A)

31. Assume that multiplying a matrix G₁ of dimension 𝑝 × 𝑞 with another matrix G2 of dimension 𝑞 × 𝑟 requires 𝑝𝑞𝑟 scalar multiplications. Computing the product of n matrices G₁G₂G₃…G_ncan be done by parenthesizing in different ways. Define G_i G_i+1 as an explicitly computed pair for a given paranthesization if they are directly multiplied. For example, in the matrix multiplication chain G₁G₂G₃G₄G₅G₆ using parenthesization (G₁(G₂G₃))(G₄(G₅G₆)), G₂G₃ and G₅G₆ are the only explicitly computed pairs.

Consider a matrix multiplication chain F₁F₂F₃F₄F₅, where matrices F₁, F₂, F₃, F₄ and F₅ are of dimensions 2×25, 25×3, 3×16, 16×1 and 1×1000, respectively. In the parenthesization of F₁F₂F₃F₄F₅ that minimizes the total number of scalar multiplications, the explicitly computed pairs is/are

(A) F₁F₂ and F₃F₄ only

(B) F₂F₃ only

(D) F₁F₂ and F₄F₅ only

Answer: (C)

32. Consider the following C code. Assume that unsigned long int type length is 64 bits.

The value returned when we call fun with the input 2⁴⁰ is

(A) 4

(B) 5

(D) 40

Answer: (B)

33. Consider the unsigned 8-bit fixed point binary number representation below,

b₇ b₆ b₅ b₄ b₃ . b2 b₁ b₀

where the position of the binary point is between b₃ and b₂. Assume b₇ is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:

(i) 31.500 (ii) 0.875 (iii) 12.100 (iv) 3.001

Which one of the following statements is true?

(A) None of (i), (ii), (iii), (iv) can be exactly represented

(B) Only (ii) cannot be exactly represented

(D) Only (i) and (ii) cannot be exactly represented

Answer: (C)

34. The size of the physical address space of a processor is 2^𝑃 bytes. The word length is 2^𝑊 bytes. The capacity of cache memory is 2^𝑁 bytes. The size of each cache block is 2^𝑀 words. For a 𝐾-way set-associative cache memory, the length (in number of bits) of the tag field is

(A) 𝑃 − 𝑁 − log₂ 𝐾

(B) 𝑃 − 𝑁 + log₂ 𝐾

(D) 𝑃 − 𝑁 − 𝑀 − 𝑊 + log₂ 𝐾

Answer: (B)

35. Consider the following languages:

Which of the languages above are context-free?

(A) I and IV only

(B) I and II only

(D) II and IV only

Answer: (B)

36. Consider the following problems. 𝐿(𝐺) denotes the language generated by a grammar 𝐺. 𝐿(𝑀) denotes the language accepted by a machine 𝑀.

(I) For an unrestricted grammar 𝐺 and a string 𝑤, whether 𝑤 ∈ 𝐿(𝐺)

(II) Given a Turing machine M, whether L(M) is regular

(III) Given two grammars 𝐺₁ and 𝐺₂, whether 𝐿(𝐺₁) = 𝐿(𝐺₂)

(IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language.

Which one of the following statements is correct?

(A) Only I and II are undecidable

(B) Only III is undecidable

(D) Only I, II and III are undecidable

Answer: (D)

37. A lexical analyzer uses the following patterns to recognize three tokens T₁, T₂, and T₃ over the alphabet {a,b,c}.

Note that ‘x?’ means 0 or 1 occurrence of the symbol x. Note also that the analyzer outputs the token that matches the longest possible prefix.

If the string 𝑏𝑏𝑎𝑎𝑐𝑎𝑏𝑐 is processed by the analyzer, which one of the following is the sequence of tokens it outputs?

(A) 𝑇₁𝑇₂𝑇₃

(B) 𝑇₁𝑇₁𝑇₃

(D) 𝑇₃𝑇₃

Answer: (D)

38. Consider the following parse tree for the expression a#b$c$d#e#f, involving two binary operators $ and #.

Which one of the following is correct for the given parse tree?

(A) $ has higher precedence and is left associative; # is right associative

(B) # has higher precedence and is left associative; $ is right associative

(D) # has higher precedence and is right associative; $ is left associative

Answer: (A)

39. I0n a system, there are three types of resources: E, F and G. Four processes P₀, P₁, P₂ and P₃ execute concurrently. At the outset, the processes have declared their maximum resource requirements using a matrix named Max as given below. For example, Max[P₂,F] is the maximum number of instances of F that P₂ would require. The number of instances of the resources allocated to the various processes at any given state is given by a matrix named Allocation.

Consider a state of the system with the Allocation matrix as shown below, and in which 3 instances of E and 3 instances of F are the only resources available.

From the perspective of deadlock avoidance, which one of the following is true?

(A) The system is in safe state.

(B) The system is not in safe state, but would be safe if one more instance of E were available

(D) The system is not in safe state, but would be safe if one more instance of G were available

Answer: (A)

40. C onsider the following solution to the producer-consumer synchronization problem. The shared buffer size is 𝑁. Three semaphores empty, full and mutex are defined with respective initial values of 0, 𝑁 and 1. Semaphore empty denotes the number of available slots in the buffer, for the consumer to read from. Semaphore full denotes the number of available slots
in the buffer, for the producer to write to. The placeholder variables, denoted by P, Q, R, and S, in the code below can be assigned either empty or full. The valid semaphore operations are: wait() and signal().

Which one of the following assignments to P, Q, R and S will yield the correct solution?

(A) P: full, Q: full, R: empty, S: empty

(B) P: empty, Q: empty, R: full, S: full

(D) P: empty, Q: full, R: full, S: empty

Answer: (C)

41. C onsider the relations r(A, B) and s(B, C), where s.B is a primary key and r.B is a foreign key referencing s.B. Consider the query

Let LOJ denote the natural left outer-join operation. Assume that r and s contain no null values.

Which one of the following queries is NOT equivalent to Q?

(A) 𝜎_𝐵<5(𝑟 ⋈ 𝑠)

(B) 𝜎_𝐵<5(𝑟 𝐿𝑂𝐽 𝑠)

(D) 𝜎_𝐵<5(𝑟) 𝐿𝑂𝐽 𝑠

Answer: (C)

42. Consider the following four relational schemas. For each schema, all non-trivial functional dependencies are listed. The underlined attributes are the respective primary keys.

Which one of the relational schemas above is in 3NF but not in BCNF?

(A) Schema I

(B) Schema II

(D) Schema IV

Answer: (B)

43. Let G be a graph with 100! vertices, with each vertex labelled by a distinct permutation of the numbers 1,2, … , 100. There is an edge between vertices 𝑢 and 𝑣 if and only if the label of 𝑢 can be obtained by swapping two adjacent numbers in the label of 𝑣. Let 𝑦 denote the degree of a vertex in G, and 𝑧 denote the number of connected components in G. Then, 𝑦 + 10𝑧 = _____.

Answer: (109 to 109)

44. Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (𝐻), medium (𝑀) and low (𝐿). Let 𝑃(𝐻_𝐺 ) denote the probability that Guwahati has high temperature. Similarly, 𝑃(𝑀_𝐺 ) and 𝑃(𝐿_𝐺 ) denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use 𝑃(𝐻_𝐷 ), 𝑃(𝑀_𝐷) and 𝑃(𝐿_𝐷) for Delhi.

The following table gives the conditional probabilities for Delhi’s temperature given Guwahati’s temperature.

Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature (𝐻_𝐺 ) then the probability of Delhi also having a high temperature (𝐻_𝐷) is 0.40; i.e., 𝑃(𝐻_𝐷|𝐻_𝐺 ) = 0.40. Similarly, the next two entries are 𝑃(𝑀_𝐷|𝐻_𝐺 ) = 0.48 and 𝑃(𝐿_𝐷|𝐻_𝐺 ) = 0.12. Similarly for the other rows.

If it is known that 𝑃(𝐻_𝐺 ) = 0.2, 𝑃(𝑀_𝐺 ) = 0.5, and 𝑃(𝐿_𝐺 ) = 0.3, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _______.

Answer: (0.60 to 0.62)

45. Consider the following program written in pseudo-code. Assume that x and y are integers.

The number of times that the print statement is executed by the call Count(1024,1024) is _____.

Answer: (10230 to 10230)

46. The number of possible min-heaps containing each value from {1, 2, 3, 4, 5, 6, 7}exactly once is _____.

Answer: (80 to 80)

47. Consider the following undirected graph G:

Choose a value for x that will maximize the number of minimum weight spanning trees (MWSTs) of G. The number of MWSTs of G for this value of x is ______.

Answer: (4 to 4)

48. Consider the weights and values of items listed below. Note that there is only one unit of each item.

The task is to pick a subset of these items such that their total weight is no more than 11 Kgs and their total value is maximized. Moreover, no item may be split. The total value of items picked by an optimal algorithm is denoted by 𝑉opt. A greedy algorithm sorts the items by their value-to-weight ratios in descending order and packs them greedily, starting from the first item in the ordered list. The total value of items picked by the greedy algorithm is denoted by 𝑉_greedy. The value of 𝑉_opt − 𝑉_greedy is ____________.

Answer: (16 to 16)

49. Consider the minterm list form of a Boolean function 𝐹 given below.

Here, 𝑚 denotes a minterm and 𝑑 denotes a don’t care term. The number of essential prime implicants of the function 𝐹 is ______.

50. The instruction pipeline of a RISC processor has the following stages: Instruction Fetch (IF), Instruction Decode (ID), Operand Fetch (OF), Perform Operation (PO) and Writeback (WB). The IF, ID, OF and WB stages take 1 clock cycle each for every instruction. Consider a sequence of 100 instructions. In the PO stage, 40 instructions take 3 clock cycles each, 35 instructions take 2 clock cycles each, and the remaining 25 instructions take 1 clock cycle each. Assume that there are no data hazards and no control hazards.

The number of clock cycles required for completion of execution of the sequence of instructions is ______.

Answer: (219 to 219)

51. A processor has 16 integer registers (R0, R1, .. , R15) and 64 floating point registers (F0, F1,… , F63). It uses a 2-byte instruction format. There are four categories of instructions: Type-1, Type-2, Type-3, and Type-4. Type-1 category consists of four instructions, each with 3 integer register operands (3Rs). Type-2 category consists of eight instructions, each with 2 floating point register operands (2Fs). Type-3 category consists of fourteen instructions, each with one integer register operand and one floating point register operand (1R+1F). Type-4 category consists of N instructions, each with a floating point register
operand (1F).

The maximum value of N is __________.

Answer: (32 to 32)

52. Given a language 𝐿, define 𝐿𝑖 as follows:

The order of a language L is defined as the smallest k such that 𝐿^𝑘 = 𝐿^𝑘+1.

Consider the language L₁ (over alphabet 0) accepted by the following automaton.

The order of L₁ is _____.

Answer: (2 to 2)

53. Consider a storage disk with 4 platters (numbered as 0, 1, 2 and 3), 200 cylinders (numbered as 0, 1, … , 199), and 256 sectors per track (numbered as 0, 1, … , 255). The following 6 disk requests of the form [sector number, cylinder number, platter number] are received by the disk controller at the same time:

[120, 72, 2] , [180, 134, 1] , [60, 20, 0] , [212, 86, 3] , [56, 116, 2] , [118, 16, 1]

Currently the head is positioned at sector number 100 of cylinder 80, and is moving towards higher cylinder numbers. The average power dissipation in moving the head over 100 cylinders is 20 milliwatts and for reversing the direction of the head movement once is 15 milliwatts. Power dissipation associated with rotational latency and switching of head between different platters is negligible.

The total power consumption in milliwatts to satisfy all of the above disk requests using the Shortest Seek Time First disk scheduling algorithm is _______.

Answer: (85 to 85)

54. Consider an IP packet with a length of 4,500 bytes that includes a 20-byte IPv4 header and a 40-byte TCP header. The packet is forwarded to an IPv4 router that supports a Maximum Transmission Unit (MTU) of 600 bytes. Assume that the length of the IP header in all the outgoing fragments of this packet is 20 bytes. Assume that the fragmentation offset value stored in the first fragment is 0.

The fragmentation offset value stored in the third fragment is _______.

Answer: (144 to 144)

55. Consider a simple communication system where multiple nodes are connected by a shared broadcast medium (like Ethernet or wireless). The nodes in the system use the following carrier-sense based medium access protocol. A node that receives a packet to transmit will carrier-sense the medium for 5 units of time. If the node does not detect any other transmission in this duration, it starts transmitting its packet in the next time unit. If the node detects another transmission, it waits until this other transmission finishes, and then begins to carrier-sense for 5 time units again. Once they start to transmit, nodes do not perform any collision detection and continue transmission even if a collision occurs. All transmissions last for 20 units of time. Assume that the transmission signal travels at the speed of 10 meters per unit time in the medium.

Assume that the system has two nodes P and Q, located at a distance d meters from each other. P starts transmitting a packet at time t=0 after successfully completing its carrier-sense phase. Node Q has a packet to transmit at time t=0 and begins to carrier-sense the medium.

The maximum distance d (in meters, rounded to the closest integer) that allows Q to successfully avoid a collision between its proposed transmission and P’s ongoing transmission is _____.

Answer: (50 to 50)

GATE Exam 2018 Chemical Engineering (CH) Question Paper With Answer Key

June 7, 2023November 20, 2018 by suresh84

CHEMICAL ENGINEERING

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

CHEMICAL ENGINEERING

Q. 1 – Q. 25 carry one mark each.

1. Consider the following two equations:

The above set of equations is represented by

Answer: (C)

2. The fourth order Runge-Kutta (RK4) method to solve an ordinary differential equation is given as

For a special case when the function f depends solely on x, the above RK4 method reduces to

(A) Euler’s explicit method

(B) Trapezoidal rule

(D) Simpson’s 1/3 rule

Answer: (D)

3. A watch uses two electronic circuits (ECs). Each EC has a failure probability of 0.1 in one year of operation. Both ECs are required for functioning of the watch. The probability of the watch functioning for one year without failure is

(A) 0.99

(B) 0.90

(D) 0.80

Answer: (C)

4. The figure which represents (x in radians) is

Answer: (B)

5. The terminal velocity of a spherical particle in gravitational settling under Stokes’ regime varies

(A) linearly with the particle diameter

(B) linearly with the viscosity of the liquid

(D) inversely with the density of particle

Answer: (C)

6. Critical speed of a ball mill depends on

(A) the radius of the mill (shell) and the radius of the particles

(B) the radius of the mill (shell) and the density of the particles

(D) the radius of the balls and the radius of the mill (shell)

Answer: (D)

7. Economy of evaporators used for concentrating sugarcane juice is

Answer: (C)

8. Segmental baffles in a 2-4 shell and tube heat exchanger

(A) change the flow pattern of the tube side fluid and increase the overall heat transfer coefficient

(B) increase the heat transfer coefficient in the shell side and support the tubes

(D) increase the number of passes in the shell side and increase the heat transfer coefficient in the tube side

Answer: (B)

9. In connection with petroleum refining, identify the incorrect statement among the following options.

(A) Desalting of crude oil is done before processing it in atmospheric distillation unit

(B) A stream of hydrogen is produced in catalytic reforming of naphtha

(D) Cetane number indicates the quality of petrol / motor spirit

Answer: (D)

10. Polyvinyl chloride is produced by

(A) co-polymerization

(B) addition-type kinetics

(D) reacting hydrochloric acid with polyethylene

Answer: (B)

11. The molecular formula of the predominant chemical compound in commercial sugar is

(A) C₁₂H₂₂O₁₁

(B) C₁₂H₂₄O₁₂

(D) C₆H₁₂O₆

Answer: (A)

12. Two packed towers are designed for the same mass velocity of the gas. The first has liquid and gas flow rates of 30 kg/s and 1.2 kg/s, respectively, while the corresponding flow rates in the second tower are 67.5 kg/s and 1.8 kg/s. The ratio of the design diameter of the wider tower to that of the narrower tower is

(A) 2

(B) 1.8

(D) 1.225

Answer: (D)

13. The Annual Fixed Charges (AFC) and Annual Utilities Costs (AUC) of a distillation column being designed are expressed in terms of the reflux ratio (R) as

The reflux ratio (R_opt) for optimizing the total cost of the distillation column may be found by solving

Answer: (B)

14. Consider the following properties:

(P) temperature

(Q) specific gravity

(R) chemical potential

(S) volume

The option which lists ALL the intensive properties is

(A) P

(B) P and Q

(D) P, Q, R and S

Answer: (C)

15. Liquid phase isomerization of o-xylene to p-xylene using a zeolite catalyst was carried out in a CSTR. Three sets of kinetic data at different temperatures and stirring speeds were obtained as shown below.

The operating condition at which the reaction rate is not controlled by external mass transfer resistance is

(A) T = 500 K; rpm = 3000

(B) T = 600 K; rpm = 1000

(D) T = 700 K; rpm = 2000

Answer: (A)

16. Choose the correct statement

In viscose rayon manufacturing process,

(A) carbon disulphide used as reactant for xanthate formation is regenerated in a later step

(B) caustic soda used as reactant for steeping of cellulose is regenerated in a later step

(D) the spun viscose rayon is hardened in an alkali bath

Answer: (A)

17. The reactant (M) is converted into product (N) in the presence of catalyst in a fixed bed reactor. All the flow rates (F, G, H, P and R) in mol/s, and mole fraction of reactant (M) in these streams (x_F, x_G, x_H, x_P and x_R) are shown in the diagram.

The overall fractional conversion is

Answer: (D)

18. A first-order process having a transfer function, is controlled by a proportional controller with gain of 3.2. The process time constant is in minutes. Addition of the integral control action with an integral time constant of 5 minutes leads to increase in

(A) offset

(B) speed of response

(D) proportional band

Answer: (C)

19. According to the surface renewal theory, the unit of fractional rate of surface renewal is

(A) m² s^-2

(B) m² s^-1

(D) s^-1

Answer: (D)

20. For absorption of H₂S from a mixture with hydrocarbon vapour into an aqueous alkanolamine solution, the liquid phase mass transfer resistance is

(A) significantly higher than that of the gas phase

(B) negligible compared to that of the gas phase

(D) dependent on the gas phase mass transfer resistance

Answer: (B)

21. For a chemical reaction, the ratio of rate constant at 500 K to that at 400 K is 2.5. Given R = 8.314 J mol^-1 K^-1, the value of activation energy (in kJ/mol) is

(A) 10.5

(B) 12.0

(D) 18.4

Answer: (C)

22. Pitot tube is used to measure

(A) liquid level in a tank

(B) flow velocity at a point

(D) vorticity

Answer: (B)

23. A venturi meter is installed to measure the flow rate of water in a 178 mm diameter (ID) pipe. The throat diameter is 102 mm. The differential pressure measured using a manometer is 154.3 kN/m². The data given are:
discharge coefficient = 0.98; water density = 1000 kg/m³. The volumetric flow rate of water (in m³/s) is _________.

Answer: (0.145 to 0.155)

24. The ammonia (NH₃) oxidation process occurs over a catalyst as

4NH₃ + 5O₂ → 6H₂O + 4NO

Air is supplied such that oxygen (O₂) is 20% in excess of that required for complete conversion of NH₃. The mole fraction of O₂ in inlet gas mixture (NH₃ + air) is ______ (rounded off to third decimal place)

Answer: (0.170 to 0.200)

25. The initial water level in a tank is 4 m. When the valve located at the bottom is opened, the rate of change of water level (L) with respect to time (t) is, where k = 0.6 m s–^3/2 The level of water (in m) in the tank at time 0.5 s after opening the valve is ____________ (rounded off to second decimal place).

Answer: (3.7 to 3.9)

Q. 26 – Q. 55 carry two marks each.

26. Match the equipment in Column A with the corresponding process in Column B

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

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

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

Answer: (B)

27. In the year 2005, the cost of a shell and tube heat exchanger with 68 m² heat transfer area was Rs. 12.6 Lakh. Chemical Engineering Index for cost in 2005 was 509.4 and now the index is 575.4. Based on index of 0.6 for capacity scaling, the present cost (in Lakhs of rupees) of a similar heat exchanger having 100 m² heat transfer area is estimated to be

(A) 17.94

(B) 19.94

(D) 22.94

Answer: (A)

28. A furnace installed at a cost of Rs. 24 Lakh is expected to serve its useful life of 5 years. Salvage value of the furnace is Rs. 8 Lakh. The interest rate compounded annually is 8%. The estimated capitalized cost (in Lakhs of rupees) is

(A) 30

(B) 34.09

(D) 58.09

Answer: (D)

29. G denotes the Gibbs free energy of a binary mixture, nT denotes the total number of moles present in the system, μ_i is the chemical potential of the ith component (μ_i ≠ 0 and μ₁ > μ₂) and x_i is the mole fraction of the ith component. The correct variation of G/n_T (in J/mol) at constant temperature and pressure is given by

Answer: (C)

30. A person is drowning in sea at location R and the lifeguard is standing at location P. The beach boundary is straight and horizontal, as shown in the figure.

The lifeguard runs at a speed of V_L and swims at a speed of V_S. In order to reach to the drowning person in optimum time, the lifeguard should choose point Q such that

Answer: (D)

31. The decay ratio for a system having complex conjugate poles as is

(A) 7 × 10^–1

(B) 8 × 10^–2

(D) 10 × 10^–4

Answer: (C)

32. Match the items in Column A with the items in Column B

Here, Φ denotes the phase shift, K1 and K2 the process gains, τ the time constant, and AR the amplitude ratio.

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

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

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

Answer: (D)

33. In a laboratory batch setup, reaction of P over a catalyst was studied at various temperatures. The reactions occurring are

P → 2Q ; P → R

At the end of one hour of operation, the batch contains x_P, x_Q and x_R mole fractions of P, Q and R components, respectively. The mole fractions of product components (x_Q and x_R) were found to vary linearly with temperature as given in the figure.

If the yield of Q based on reactant P consumed (Y_Q) at 25°C was found to be 0.40, then the value of Y_Q at 60°C is ____________ (rounded off to second decimal place).

Answer: (0.40 to 0.40)

34. An insulated storage tank contains 1000 kg liquid of specific heat 10 kJ kg^-1 K^-1. The liquid is heated by saturated steam, condensing in a helical coil at a temperature of 180°C. The heat transfer area of the coil is 0.1 m². If the overall heat transfer coefficient is constant at 1000 W m^-2 K^-1, then the time (in hours) required to raise the temperature of the liquid in the tank from 20°C to 80°C is ____________ (rounded off to second decimal place).

Answer: (12.75 to 13.25)

35. The wall of a pipe of radius 1 m is at a uniform temperature of 200°C, and is covered by insulation of thickness 0.1 m. The ambient air outside the insulated pipe is at 20°C and has heat transfer coefficient of 10 W m^-2 K^-1. The thermal conductivity of the insulation material is 0.05 W m^-1 K-1. If the heat transfer occurs at steady state, the temperature (in°C) of the outer surface of insulation is __________ (rounded off to second decimal place).

Answer: (27.8 to 28.6)

36. Vapour bubbles are formed in the nucleate boiling regime at a frequency of 10 bubbles per second per nucleation site. There are 100 nucleation sites per m² of heating area. The latent heat of vapourization and the density of vapour under the operating condition are 1000 kJ/kg and 1 kg/m³ respectively. The diameter of each bubble is 10^-3 m. Assume that the entire heat supplied is used for vapour generation. The heat flux (in Watt per m² of heating area) is ______________ (rounded off to third decimal place).

Answer: (0.51 to 0.54)

37. Under isothermal condition, a vertical tube of length L = 100 m contains a gas of molecular weight equal to 60. The pressure and temperature at the top of the tube are 100 kPa and 25°C respectively. Consider the universal gas constant and acceleration due to gravity as 8.314 J mol^-1 K^-1 and 9.81 m s^-2 respectively. If the gas is ideal, the pressure (in kPa) at the bottom of the tube will be ____________ (rounded off to third decimal place).

Answer: (102.37 to 102.44)

38. At a shear rate of 10 s^-1, the apparent viscosity of a non-Newtonian liquid was found to be 1 Pa s. At a shear rate of 100 s^-1, the apparent viscosity of the same liquid was found to be 0.5 Pa s. If the liquid follows power law behavior, the apparent viscosity (in Pa s) at a shear stress of 10 N m^-2 is _____________ (rounded off to two decimal place).

Answer: (0.98 to 1.02)

39. A CSTR and a PFR of equal volume are connected in series as shown below to carry out a first-order, isothermal, liquid phase reaction

The rate constant is 0.2 s^-1. The space-time is 5 s for both the reactors. The overall fractional conversion of A is ____________ (rounded off to third decimal place).

Answer: (0.80 to 0.84)

40. T he elementary second-order liquid phase reaction A + B → C + D is carried out in an isothermal plug flow reactor of 2 m³ volume. The inlet volumetric flow rate is 10 m³/h. The initial concentrations of both A and B are 2 kmol/m³. The rate constant is given as 2.5 m³ kmol^-1 h^-1. The percentage conversion of A is ____________.

Answer: (50 to 50)

41. It is decided to extract A from a feed containing 20 mol% A and 80 mol% B in two ideal cross-current stages as shown below, using equal amount of pure solvent C in each stage.

Components B and C are immiscible. 60% of A in the feed is extracted in Stage 1. The equilibrium relation is given by Y* = 1.5 X where,

X = moles of A per mole of B in raffinate

Y* = moles of A per mole of C in extract in equilibrium with raffinate

The mol % of A in raffinate from Stage 2 is __________ (rounded off to second decimal place).

Answer: (3.75 to 3.95)

42. A binary distillation column is designed by McCabe-Thiele method to get a distillate mole fraction of 0.9. The enriching section operating line has an intercept with y-axis at 0.3 mole fraction. The ratio of liquid to vapour molar flow rate in the enriching section is _____________ (rounded off to third decimal place).

Answer: (0.65 to 0.68)

43. A fiberboard sheet (1.5 m × 2.0 m × 15 mm) is being dried by suspending it horizontally in a current of hot, dry air. The edges are insulated so that drying takes place only from the top and bottom surfaces. The wet sheet weighing 16 kg with initial moisture content of 60% loses moisture at a constant rate of 1.25 × 10^-5 kg m^-2 s^-1 until the moisture content falls to 30%. All moisture contents are on dry basis. The time required for drying during constant rate period (in hour) is _____________ (rounded off to third decimal place).

Answer: (11.0 to 11.3)

44. Consider the following transfer function:

where, the natural period of oscillation is in min. The amplitude ratio at a frequency of 0.5 rad/min is_____________ (rounded off to second decimal place).

Answer: (0.41 to 0.42)

45 For a closed-loop system, consider the following transfer functions:

process Gp(s), controller Gc(s), measuring device Gm(s), and final control element Gf(s)

The offset in the closed loop response due to a unit step change introduced in the set point of the output variable is ________.

Answer: (0.2 to 0.2)

46. If then the value of is ________

Answer: (0 to 0)

47. For the matrix if det stands for the determinant and A^T is the transpose of A then the value of det( A^TA) is ____________

Answer: (1 t0 1)

48. An azeotropic mixture of ethanol and water is to be separated in a distillation column using benzene as an entrainer. At the column operating conditions, two liquid phases are formed on a tray. The degree(s) of freedom of the system for the choice of intensive properties at equilibrium is(are) ___________

Answer: (1 to 1(or) 2 to 2)

49. The volume of liquid filled in a spherical storage tank of radius R is computed from height of liquid, h, in the outside tube (neglecting the volume of liquid in the outside tube) as

The estimate of liquid height (in m) to store V = 30 m³ of water in R = 3 m tank, after performing ONE iteration of Secant method, using 1 m and 3 m as two initial guesses of liquid height is ______________ (rounded off to second decimal place).

Answer: (1.80 to 2.00)

50. In a closed piston-cylinder system, methane was observed to obey the following equation of state

P (V – nb) = nRT

where b = 0.029 m³/mol. The temperature and volume are 500°C and 5 m³ respectively for 100 moles of methane. At this state of the system, the isobaric rate of change of temperature with volume (in°C/m³) is __________ (rounded off to second decimal place).

Answer: (367 to 369)

51. A set of standard stainless steel pipes, each of internal diameter 26.65 mm and 6000 mm length, is used to make a plug flow reactor by joining them in series to carry out degradation of polyethylene. Seven such pipes are required to obtain a conversion of 66% at 450 K. The minimum number of standard 8000 mm long pipes of the same internal diameter to be procured for obtaining at least 66% conversion under the same reaction conditions is ___________.

Answer: (6 to 6)

52. Hydrogenation of benzene is to be carried out using Ni (density = 8910 kg/m³) as catalyst, cast in the form of non-porous hollow cylinders, as shown below. The reaction occurs on all the surfaces of the hollow cylinder. During an experiment, one such cylinder is suspended in the reactant stream. If the observed rate of reaction is 0.39 mol (m² of catalyst surface)^-1 min^-1, then the rate of reaction in mol (kg of catalyst)^-1 min^-1 is _____________ (rounded off to three decimal places).

Answer: (0.034 to 0.043)

53. T he humidity of air at a dry-bulb temperature of 65°C is 0.025 kg water/kg dry air. The latent heat of vaporization of water at 0°C is 2500 kJ/kg. The psychrometric ratio of air is 0.95 kJ (kg dry air)^-1 K^-1. Considering 0°C as reference temperature, the enthalpy of air (in kJ/kg) at its adiabatic saturation temperature of 35°C is ___________ (rounded off to two decimal places).

Answer: (124 to 125)

54. In a roll crusher, rolls of diameter 1 m each are set in such a manner that minimum clearance between the crushing surfaces is 15 mm. If the angle of nip is 31o, the maximum diameter of the particle (in mm) which can be crushed is ____________ (rounded off to third decimal place).

Answer: (52 to 54)

55. A hot liquid is to be cooled in a 1-1 shell and tube heat exchanger from 80°C to 50°C. Cooling water enters the tube side at 30°C, and exits at 45°C. The properties of the liquids are constant. Also, the overall heat transfer coefficient is same for counter-current and cocurrent modes. The percentage saving in heat transfer area for counter-current option with respect to the area of co-current option is __________ (rounded off to third decimal place).

Answer: (26.5 to 27.5)

GATE Exam 2018 Civil Engineering (CE-2) Question Paper With Answer Key

June 7, 2023November 19, 2018 by suresh84

Civil Engineering (CE-2)

General Aptitude (GA) Set-8

1. “ His face ___________ with joy when the solution of the puzzle was _______ to him.”

The words that best fill the blanks in the above sentence are

(A) shone, shown

(B) shone, shone

(D) shown, shown

Answer: (A)

2. “ Although it does contain some pioneering ideas, one would hardly characterize the work as _________.”

The word that best fills the blank in the above sentence is

(A) innovative

(B) simple

(D) boring

Answer: (A)

3. where 𝑎, 𝑏, 𝑛 and 𝑚 are
natural numbers. What is the value of

(A) 2𝑎²𝑏²

(B) 𝑎⁴𝑏⁴

(D) 𝑎² + 𝑏²

Answer: (B)

4. A three-member committee has to be formed from a group of 9 people. How many such distinct committees can be formed?

(A) 27

(B) 72

(D) 84

Answer: (D)

5. For non-negative integers, 𝑎, 𝑏, 𝑐, what would be the value of 𝑎 + 𝑏 + 𝑐 if log 𝑎 + log 𝑏 + log 𝑐 = 0?

(A) 3

(B) 1

(D) −1

Answer: (A)

Q. 6 – Q. 10 carry two marks each.

6. In manufacturing industries, loss is usually taken to be proportional to the square of the deviation from a target. If the loss is Rs. 4900 for a deviation of 7 units, what would be the loss in Rupees for a deviation of 4 units from the target?

(A) 400

(B) 1200

(D) 2800

Answer: (C)

7. A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15th July of the same year?

(A) 12:45 PM

(B) 12:58 PM

(D) 2:00 PM

Answer: (B)

8. The annual average rainfall in a tropical city is 1000 mm. On a particular rainy day (24-hour period), the cumulative rainfall experienced by the city is shown in the graph. Over the 24-hour period, 50% of the rainfall falling on a rooftop, which had an obstructionfree area of 50 m², was harvested into a tank. What is the total volume of water collected in the tank in liters?

(A) 25,000

(B) 18,750

(D) 3,125

Answer: (C)

9. Given that 𝑥 ≠ 𝑦 ≠ 𝑧, what is the value of the product 𝑃𝑄𝑅?

(A) 0

(B) 1

(D) 10^𝑥𝑦𝑧

Answer: (B)

10. Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A+B+C), (C+D+E), (E+F+G) and (G+H+K) is equal to 13. Which integer does E represent?

(A) 1

(B) 4

(D) 7

Answer: (B)

Civil Engineering (Set 2)

Q. 1 – Q. 25 carry one mark each.

1. The solution of the equation passing through the point (1,1) is

(A) x

(B) x²

(D) x^-2

Answer: (C)

2. The graph of a function f(x) is shown in the figure.

For f(x) to be a valid probability density function, the value of h is

(A) 1/3

(B) 2/3

(D) 3

Answer: (A)

3. A probability distribution with right skew is shown in the figure.

The correct statement for the probability distribution is

(A) Mean is equal to mode

(B) Mean is greater than median but less than mode

(D) Mode is greater than median

Answer: (C)

4. All the members of the planar truss (see figure), have the same properties in terms of area of cross-section (A) and modulus of elasticity (E).

For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the truss is:

(A) There are 3 members in tension, and 2 members in compression

(B) There are 2 members in tension, 2 members in compression, and 1 zero-force member

(D) There are 2 members in tension, and 3 zero-force members

Answer: (D)

5. The setting time of cement is determined using

(A) Le Chatelier apparatus

(B) Briquette testing apparatus

(D) Casagrande’s apparatus

Answer: (C)

6. A structural member subjected to compression, has both translation and rotation restrained at one end, while only translation is restrained at the other end. As per IS 456 : 2000, the effective length factor recommended for design is

(A) 0.50

(B) 0.65

(D) 0.80

Answer: (D)

7. A vertical load of 10 kN acts on a hinge located at a distance of L/4 from the roller support Q of a beam of length L (see figure).

The vertical reaction at support Q is

(A) 0.0 kN

(B) 2.5 kN

(D) 10.0 kN

Answer: (A)

8. A flownet below a dam consists of 24 equipotential drops and 7 flow channels. The difference between the upstream and downstream water levels is 6 m. The length of the flow line adjacent to the toe of the dam at exit is 1 m. The specific gravity and void ratio of the soil below the dam are 2.70 and 0.70, respectively. The factor of safety against piping is

(A) 1.67

(B) 2.5

(D) 4

Answer: (D)

9. The contact pressure and settlement distribution for a footing are shown in the figure.

The figure corresponds to a

(A) rigid footing on granular soil

(B) flexible footing on granular soil

(D) rigid footing on cohesive soil

Answer: (A)

10. Which one of the following statements is NOT correct?

(A) When the water content of soil lies between its liquid limit and plastic limit, the soil is said to be in plastic state.

(B) Boussinesq’s theory is used for the analysis of stratified soil.

(D) For saturated dense fine sand, after applying overburden correction, if the Standard Penetration Test value exceeds 15, dilatancy correction is to be applied.

Answer: (B)

11. The clay mineral, whose structural units are held together by potassium bond is

(A) Halloysite

(B) Illite

(D) Smectite

Answer: (B)

12. D upuit’s assumptions are valid for

(A) artesian aquifer

(B) confined aquifer

(D) unconfined aquifer

Answer: (D)

13. For a given discharge in an open channel, there are two depths which have the same specific energy. These two depths are known as

(A) alternate depths

(B) critical depths

(D) sequent depths

Answer: (A)

14. As per IS 10500:2012, for drinking water in the absence of alternate source of water, the permissible limits for chloride and sulphate, in mg/L, respectively are

(A) 250 and 200

(B) 1000 and 400

(D) 500 and 1000

Answer: (B)

15. In the figures, Group I represents the atmospheric temperature profiles (P, Q, R and S) and Group II represents dispersion of pollutants from a smoke stack (1, 2, 3 and 4). In the figures of Group I, the dashed line represents the dry adiabatic lapse rate, whereas the horizontal axis represents temperature and the vertical axis represents the altitude.

The correct match is

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

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

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

Answer: (A)

16. Peak Hour Factor (PHF) is used to represent the proportion of peak sub-hourly traffic flow within the peak hour. If 15-minute sub-hours are considered, the theoretically possible range of PHF will be

(A) 0 to 1.0

(B) 0.25 to 0.75

(D) 0.5 to 1.0

Answer: (C)

17. As per IRC:37-2012, in order to control subgrade rutting in flexible pavements, the parameter to be considered is

(A) horizontal tensile strain at the bottom of bituminous layer

(B) vertical compressive strain on top of subgrade

(D) vertical deflection at the surface of the pavement

Answer: (B)

Q.18 The initial concavity in the load-penetration curve of a CBR test is NOT due to

(A) uneven top surface

(B) high impact at start of loading

(D) soft top layer of soaked soil

Answer: (B)

19. Probability (up to one decimal place) of consecutively picking 3 red balls without replacement from a box containing 5 red balls and 1 white ball is ______

Answer: (0.5 to 0.5)

20. The quadratic equation 2x² – 3x + 3 = 0 is to be solved numerically starting with an initial guess as x₀ = 2. The new estimate of x after the first iteration using Newton-Raphson method is ______

Answer: (1 to 1)

21. As per IS 456 : 2000, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section (considering effective depth in the calculation of area) using Fe500 grade steel is ______

Answer: (0.17 to 0.17)

22. A reinforced-concrete slab with effective depth of 80 mm is simply supported at two opposite ends on 230 mm thick masonry walls. The centre-to-centre distance between the walls is 3.3 m. As per IS 456 : 2000, the effective span of the slab (in m, up to two decimal places) is ______

Answer: (3.15 to 3.15)

23. A fillet weld is simultaneously subjected to factored normal and shear stresses of 120 MPa and 50 MPa, respectively. As per IS 800 : 2007, the equivalent stress (in MPa, up to two decimal places) is ______

Answer: (147.50 to 148.50)

24. The intensity of irrigation for the Kharif season is 50% for an irrigation project with culturable command area of 50,000 hectares. The duty for the Kharif season is 1000 hectare/cumec. Assuming transmission loss of 10%, the required discharge (in cumec, up to two decimal places) at the head of the canal is ______

Answer: (27.00 to 28.00)

25. A culvert is designed for a flood frequency of 100 years and a useful life of 20 years. The risk involved in the design of the culvert (in percentage, up to two decimal places) is ______

Answer: (17.50 to 18.50)

Q. 26 – Q. 55 carry two marks each.

26. The matrix has

(A) real eigenvalues and eigenvectors

(B) real eigenvalues but complex eigenvectors

(D) complex eigenvalues and eigenvectors

Answer: (D)

27. The Laplace transform F (s) of the exponential function, f(t) = e^at when t ≥ 0, where a is a constant and (s – a) > 0, is

Answer: (B)

28. The rank of the following matrix is

(A) 1

(B) 2

(D) 4

Answer: (B)

29. Two rigid bodies of mass 5 kg and 4 kg are at rest on a frictionless surface until acted upon by a force of 36 N as shown in the figure. The contact force generated between the two bodies is

(A) 4.0 N

(B) 7.2 N

(D) 16.0 N

Answer: (D)

30. Four bolts P, Q, R and S of equal diameter are used for a bracket subjected to a load of 130 kN as shown in the figure.

The force in bolt P is

(A) 32.50 kN

(B) 69.32 kN

(D) 119.32 kN

Answer: (B)

31. A singly-reinforced rectangular concrete beam of width 300 mm and effective depth 400 mm is to be designed using M25 grade concrete and Fe500 grade reinforcing steel. For the beam to be under-reinforced, the maximum number of 16 mm diameter reinforcing bars that can be provided is

(A) 3

(B) 4

(D) 6

Answer: (C)

32. A 3 m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of 30° and unit weight of 20 kN/m3. If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall is

(A) 0

(B) 30

(D) 270

Answer: (C)

33. Three soil specimens (Soil 1, Soil 2 and Soil 3), each 150 mm long and 100 mm diameter, are placed in series in a constant head flow set-up as shown in the figure. Suitable screens are provided at the boundaries of the specimens to keep them intact. The values of coefficient of permeability of Soil 1, Soil 2 and Soil 3 are 0.01, 0.003 and 0.03 cm/s, respectively.

The value of h in the set-up is

(A) 0 mm

(B) 40 mm

(D) 560 mm

Answer: (B)

34. In a 5 m wide rectangular channel, the velocity u distribution in the vertical direction y is given by u = 1.25y^1/6. The distance y is measured from the channel bed. If the flow depth is 2 m, the discharge per unit width of the channel is

(A) 2.40 m³/s/m

(B) 2.80 m³/s/m

(D) 12.02 m³/s/m

Answer: (A)

35. A car follows a slow moving truck (travelling at a speed of 10 m/s) on a two-lane two-way highway. The car reduces its speed to 10 m/s and follows the truck maintaining a distance of 16 m from the truck. On finding a clear gap in the opposing traffic stream, the car accelerates at an average rate of 4 m/s², overtakes the truck and returns to its original lane.
When it returns to its original lane, the distance between the car and the truck is 16 m. The total distance covered by the car during this period (from the time it leaves its lane and subsequently returns to its lane after overtaking) is

(A) 64 m

(B) 72 m

(D) 144 m

Answer: (B)

36. A level instrument at a height of 1.320 m has been placed at a station having a Reduced Level (RL) of 112.565 m. The instrument reads –2.835 m on a levelling staff held at the bottom of a bridge deck. The RL (in m) of the bottom of the bridge deck is

(A) 116.720

(B) 116.080

(D) 111.050

Answer: (A)

37. The value (up to two decimal places) of a line integral along C which is a straight line joining (0,0) to (1,1) is ______

Answer: (0.60 to 0.70)

38. An 8 m long simply-supported elastic beam of rectangular cross-section (100 mm × 200 mm) is subjected to a uniformly distributed load of 10 kN/m over its entire span. The maximum principal stress (in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at 2 m from the support is ______

Answer: (0.0 to 0.0)

39. A prismatic beam P-Q-R of flexural rigidity EI = 1 × 10⁴ kNm² is subjected to a moment of 180 kNm at Q as shown in the figure.

The rotation at Q (in rad, up to two decimal places) is ______

Answer: (0.01 to 0.01 (or) ‐0.01 to ‐0.01)

40. A prismatic propped cantilever beam of span L and plastic moment capacity M_p is subjected to a concentrated load at its mid-span. If the collapse load of the beam is the value of α is ______

Answer: (6.0 to 6.0)

41. A 6 m long simply-supported beam is prestressed as shown in the figure.

The beam carries a uniformly distributed load of 6 kN/m over its entire span. If the effective flexural rigidity EI = 2 × 10⁴ kN/m² and the effective prestressing force is 200 kN, the net increase in length of the prestressing cable (in mm, up to two decimal places) is ______

Answer: (0.10 to 0.12)

42. A cable PQ of length 25 m is supported at two ends at the same level as shown in the figure. The horizontal distance between the supports is 20 m. A point load of 150 kN is applied at point R which divides it into two equal parts.

Neglecting the self-weight of the cable, the tension (in kN, in integer value) in the cable due to the applied load will be ______

Answer: (125 to 125)

43. The compression curve (void ratio, e vs. effective stress, σ′_v) for a certain clayey soil is a straight line in a semi-logarithmic plot and it passes through the points (e = 1.2; σ′_v= 50 kPa) and (e = 0.6; σ′_v= 800 kPa). The compression index (up to two decimal places) of the soil is ______

Answer: (0.45 to 0.55)

44. The total horizontal and vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa, respectively. The static pore-water pressure is 30 kPa. At failure, the excess pore-water pressure is measured to be 94.50 kPa, and the shear stresses on the vertical and horizontal planes passing through the point X are zero. Effective cohesion is 0 kPa and effective angle of internal friction is 36°. The shear strength (in kPa, up to two decimal places) at point X is ______

Answer: (51.50 to 53.50)

45. A group of nine piles in a 3 × 3 square pattern is embedded in a soil strata comprising dense sand underlying recently filled clay layer, as shown in the figure. The perimeter of an individual pile is 126 cm. The size of pile group is 240 cm × 240 cm. The recently filled clay has undrained shear strength of 15 kPa and unit weight of 16 kN/m³.

The negative frictional load (in kN, up to two decimal places) acting on the pile group is ______

Answer: (472.00 to 472.50)

46. A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids (S₁, S₂) are given in the figure.

The gauge pressure value (in kN/m², up to two decimal places) of 𝑝₁ is ______

Answer: (-.90 to -8.0)

47. The total rainfall in a catchment of area 1000 km², during a 6 h storm, is 19 cm. The surface runoff due to this storm computed from triangular direct runoff hydrograph is 1×10⁸ m³. The Φ_index for this storm (in cm/h, up to one decimal place) is ______

Answer: (1.50 to 1.50)

48. A rough pipe of 0.5 m diameter, 300 m length and roughness height of 0.25 mm, carries water (kinematic viscosity = 0.9 × 10^–6 m²/s) with velocity of 3 m/s. Friction factor (f) for laminar flow is given by f = 64/R_e, and for turbulent flow it is given by Re = Reynolds number, r = radius of pipe, k = roughness height and g = 9.81 m/s². The head loss (in m, up to three decimal places) in the pipe due to friction is ______

Answer: (4.50 to 4.70)

49. A flocculation tank contains 1800 m³ of water, which is mixed using paddles at an average velocity gradient G of 100/s. The water temperature and the corresponding dynamic viscosity are 30°C and 0.798 × 10^-3 Ns/m², respectively. The theoretical power required to achieve the stated value of G (in kW, up to two decimal places) is ______

Answer: (14.00 to 15.00)

50. A coal containing 2% sulfur is burned completely to ash in a brick kiln at a rate of 30 kg/min. The sulfur content in the ash was found to be 6% of the initial amount of sulfur present in the coal fed to the brick kiln. The molecular weights of S, H and O are 32, 1 and 16 g/mole, respectively. The annual rate of sulfur dioxide (SO₂) emission from the kiln (in tonnes/year, up to two decimal places) is ______

Answer: (590.00 to 595.00)

51. At a small water treatment plant which has 4 filters, the rates of filtration and backwashing are 200 m³/d/m² and 1000 m³/d/m², respectively. Backwashing is done for 15 min per day. The maturation, which occurs initially as the filter is put back into service after cleaning, takes 30 min. It is proposed to recover the water being wasted during backwashing and maturation. The percentage increase in the filtered water produced (up to two decimal places) would be ______

Answer: (7.75 to 7.95)

52. A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids is shown in the figure.

S₀, S = readily biodegradable soluble BOD, mg/L
Q, Q_r, Q_w = flow rates, m³/d
X₀, X, X_e, X_u = microorganism concentrations (mixed-liquor volatile suspended solids or MLVSS), mg/L

The mean cell residence time (in days, up to one decimal place) is ______

Answer: (7.5 to 7.5)

53. The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are 80 kmph and 100 vehicles/km respectively. The traffic flow (in vehicles/h, up to one decimal place) corresponding to a speed of 40 kmph is ______

Answer: (2000.0 to 2000.0)

54. A 7.5 m wide two-lane road on a plain terrain is to be laid along a horizontal curve of radius 510 m. For a design speed of 100 kmph, super-elevation is provided as per IRC: 73- 1980. Consider acceleration due to gravity as 9.81 m/s². The level difference between the inner and outer edges of the road (in m, up to three decimal places) is ______

Answer: (0.520 to 0.530)

55. An aerial photograph of a terrain having an average elevation of 1400 m is taken at a scale of 1:7500. The focal length of the camera is 15 cm. The altitude of the flight above mean sea level (in m, up to one decimal place) is ______

Answer: (2520.0 to 2530.0)

GATE Exam 2018 Civil Engineering (CE-1) Question Paper With Answer Key

June 7, 2023November 19, 2018 by suresh84

Civil Engineering CE-1

General Aptitude (GA) Set-7

Q. 1 – Q. 5 carry one mark each.

1. “ The driver applied the _______ as soon as she approached the hotel where she wanted to take a ________.”

The words that best fill the blanks in the above sentence are

(A) brake, break

(B) break, break

(D) break, brake

Answer: (A)

2. “ It is no surprise that every society has had codes of behaviour; however, the nature of these codes is often _________.”

The word that best fills the blank in the above sentence is

(A) unpredictable

(B) simple

(D) strict

Answer: (A)

3. Hema’s age is 5 years more than twice Hari’s age. Suresh’s age is 13 years less than 10 times Hari’s age. If Suresh is 3 times as old as Hema, how old is Hema?

(A) 14

(B) 17

(D) 19

Answer: (D)

4. Tower A is 90 m tall and tower B is 140 m tall. They are 100 m apart. A horizontal skywalk connects the floors at 70 m in both the towers. If a taut rope connects the top of tower A to the bottom of tower B, at what distance (in meters) from tower A will the rope intersect the skywalk?

(A) 22.22

(B) 50

(D) 77.78

Answer: (Marks to All)

5. The temperature 𝑇 in a room varies as a function of the outside temperature 𝑇₀ and the number of persons in the room 𝑝, according to the relation 𝑇 = Κ (Θ𝑝 + 𝑇₀), where Θ and Κ are constants. What would be the value of Θ given the following data?

(A) 0.8

(B) 1.0

(D) 10.0

Answer: (B)

Q. 6 – Q. 10 carry two marks each.

6. A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?

(A) 48

(B) 52

(D) 108

Answer: (C)

7. The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in Rs.) of two wires of lengths 4 m and 6m?

(A) 768

(B) 832

(D) 1600

Answer: (B)

8. Which of the following function(s) is an accurate description of the graph for the range(s) indicated?

(i) 𝑦 = 2𝑥 + 4 for −3 ≤ 𝑥 ≤ −1

(ii) 𝑦 = |𝑥 − 1| for −1 ≤ 𝑥 ≤ 2

(iii) 𝑦 = ||𝑥| − 1| for −1 ≤ 𝑥 ≤ 2

(iv) 𝑦 = 1 for 2 ≤ 𝑥 ≤ 3

(A) (i), (ii) and (iii) only.

(B) (i), (ii) and (iv) only.

(D) (ii) and (iv) only.

Answer: (B)

9. Consider a sequence of numbers 𝑎₁, 𝑎₂, 𝑎₃, ⋯ , 𝑎_𝑛 where for each integer 𝑛 > 0. What is the sum of the first 50 terms?

(A)

(B)

(C)

(D)

Answer: (C)

10. Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are positioned in the figure such that (A × B × C), (B × G × E) and (D × E × F) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F or G?

(A) 4

(B) 5

(D) 9

Answer: (B)

Civil Engineering (Set 1)

Q. 1 – Q. 25 carry one mark each.

1. Which one of the following matrices is singular?

Answer: (C)

2. For the given orthogonal matrix Q,

The inverse is

Answer: (C)

3. At the point 𝑥 = 0, the function 𝑓(𝑥) = 𝑥³ has

(A) local maximum

(B) local minimum

(D) neither local maximum nor local minimum

Answer: (D)

4. A column of height h with a rectangular cross-section of size a×2a has a buckling load of P. If the cross-section is changed to 0.5a × 3a and its height changed to 1.5h, the buckling load of the redesigned column will be

(A) P/12

(B) P/4

(D) 3P/4

Answer: (A)

5. A steel column of ISHB 350 @72.4 kg/m is subjected to a factored axial compressive load of 2000 kN. The load is transferred to a concrete pedestal of grade M20 through a square base plate. Consider bearing strength of concrete as 0.45f_ck, where f_ck is the characteristic strength of concrete. Using limit state method and neglecting the self weight of base plate and steel column, the length of a side of the base plate to be provided is

(A) 39 cm

(B) 42 cm

(D) 48 cm

Answer: (D)

6. The Le Chatelier apparatus is used to determine

(A) compressive strength of cement

(B) fineness of cement

(D) soundness of cement

Answer: (D)

7. The deformation in concrete due to sustained loading is

(A) creep

(B) hydration

(D) shrinkage

Answer: (A)

8. A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. The shear stress component 𝜏_𝑥𝑦 at Point ‘M’ in the cross-section of the beam at a distance of 1 m from the fixed end is

(A) 0.0 MPa

(B) 0.51 MPa

(D) 2.0 MPa

Answer: (A)

9. Two rectangular under-reinforced concrete beam sections X and Y are similar in all aspects except that the longitudinal compression reinforcement in section Y is 10% more. Which one of the following is the correct statement?

(A) Section X has less flexural strength and is less ductile than section Y

(B) Section X has less flexural strength but is more ductile than section Y

(D) Sections X and Y have equal flexural strength and ductility

Answer: (C)

10. The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation where the water level is at a depth much greater than the width of footing, is approximately

(A) 0

(B) 25

(D) 100

Answer: (C)

11. The width of a square footing and the diameter of a circular footing are equal. If both the footings are placed on the surface of sandy soil, the ratio of the ultimate bearing capacity of circular footing to that of square footing will be

(A) 4/3

(B) 1

(D) 2/3

Answer: (C)

12. Bernoulli’s equation is applicable for

(A) viscous and compressible fluid flow

(B) inviscid and compressible fluid flow

(D) viscous and incompressible fluid flow

Answer: (C)

13. There are 20,000 vehicles operating in a city with an average annual travel of 12,000 km per vehicle. The NOx emission rate is 2.0 g/km per vehicle. The total annual release of NOx will be

(A) 4,80,000 kg

(B) 4,800 kg

(D) 48 kg

Answer: (A)

14. A bitumen sample has been graded as VG30 as per IS : 73-2013. The ‘30’ in the grade means that

(A) penetration of bitumen at 25°C is between 20 and 40

(B) viscosity of bitumen at 60°C is between 2400 and 3600 Poise

(D) elastic recovery of bitumen at 15°C is more than 30%

Answer: (B)

15. The speed-density relationship for a road section is shown in the figure.

The shape of the flow-density relationship is

(A) piecewise linear

(B) parabolic

(D) initially parabolic then linear

Answer: (C)

16. A well-designed signalized intersection is one in which the

(A) crossing conflicts are increased

(B) total delay is minimized

(D) cycle time is equal to the sum of red and yellow times in all phases

Answer: (B)

17. A flow field is given by 𝑢 = 𝑦², 𝑣 = −𝑥𝑦, 𝑤 = 0. Value of the z-component of the angular velocity (in radians per unit time, up to two decimal places) at the point (0, −1, 1) is ______

Answer: (1.50 to 1.50)

18. The frequency distribution of the compressive strength of 20 concrete cube specimens is given in the table.

If 𝜇 is the mean strength of the specimens and 𝜎 is the standard deviation, the number of specimens (out of 20) with compressive strength less than 𝜇 − 3𝜎 is ______

Answer: (0 to 0)

19. In a fillet weld, the direct shear stress and bending tensile stress are 50 MPa and 150 MPa, respectively. As per IS 800: 2007, the equivalent stress (in MPa, up to two decimal places) will be ______

Answer: (173.10 to 173.30)

20. In a shrinkage limit test, the volume and mass of a dry soil pat are found to be 50 cm³ and 88 g, respectively. The specific gravity of the soil solids is 2.71 and the density of water is 1 g/cc. The shrinkage limit (in %, up to two decimal places) is ______

Answer: (19.50 to 20.50)

21. A core cutter of 130 mm height has inner and outer diameters of 100 mm and 106 mm, respectively. The area ratio of the core cutter (in %, up to two decimal places) is ______

Answer: (12.30 to 12.40)

22. A 1:50 model of a spillway is to be tested in the laboratory. The discharge in the prototype spillway is 1000 m³/s. The corresponding discharge (in m³/s, up to two decimal places) to be maintained in the model, neglecting variation in acceleration due to gravity, is ______

Answer: (0.05 to 0.06)

23. A 10 m wide rectangular channel carries a discharge of 20 m³/s under critical condition. Using g = 9.81 m/s², the specific energy (in m, up to two decimal places) is ______

Answer: (1.10 to 1.20)

24. For routing of flood in a given channel using the Muskingum method, two of the routing coefficients are estimated as C₀ = –0.25 and C1 = 0.55. The value of the third coefficient C₂ would be ______

Answer: (0.70 to 0.70)

25. A city generates 40×106 kg of municipal solid waste (MSW) per year, out of which only 10% is recovered/recycled and the rest goes to landfill. The landfill has a single lift of 3 m height and is compacted to a density of 550 kg/m³. If 80% of the landfill is assumed to be MSW, the landfill area (in m², up to one decimal place) required would be ______

Answer: (27271 to 27274)

Q. 26 – Q. 55 carry two marks each.

26. The value of the integral

(A) π²/8

(B) π²/4

(D) π²

Answer: (B)

27. A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0×1011 N/m². The maximum bending stress at the fixed end of the cantilever is

(A) 20.0 MPa

(B) 37.5 MPa

(D) 75.0 MPa

Answer: (B)

28. A cylinder of radius 250 mm and weight, W = 10 kN is rolled up an obstacle of height 50 mm by applying a horizontal force P at its centre as shown in the figure.

All interfaces are assumed frictionless. The minimum value of P is

(A) 4.5 kN

(B) 5.0 kN

(D) 7.5 kN

Answer: (D)

29. A plate in equilibrium is subjected to uniform stresses along its edges with magnitude 𝜎_𝑥𝑥 = 30 MPa and 𝜎_𝑦𝑦 = 50 MPa as shown in the figure.

The Young’s modulus of the material is 2×10¹¹ N/m² and the Poisson’s ratio is 0.3. If 𝜎_𝑧𝑧 is negligibly small and assumed to be zero, then the strain 𝜀_𝑧𝑧 is

(A) -120×10^-6

(B) – 60×10^-6

(D) 120 ×10^-6

Answer: (A)

30. The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments M and 2M.

The slope at P will be

(A) 0

(B) ML/(9EI)

(D) ML/(3EI)

Answer: (C)

31. A 0.5 m × 0.5 m square concrete pile is to be driven in a homogeneous clayey soil having undrained shear strength, cu = 50 kPa and unit weight, γ = 18.0 kN/m³. The design capacity of the pile is 500 kN. The adhesion factor α is given as 0.75. The length of the pile required for the above design load with a factor of safety of 2.0 is

(A) 5.2 m

(B) 5.8 m

(D) 12.5 m

Answer: (C)

32. A closed tank contains 0.5 m thick layer of mercury (specific gravity = 13.6) at the bottom. A 2.0 m thick layer of water lies above the mercury layer. A 3.0 m thick layer of oil (specific gravity = 0.6) lies above the water layer. The space above the oil layer contains air under pressure. The gauge pressure at the bottom of the tank is 196.2 kN/m². The density of water is 1000 kg/m³ and the acceleration due to gravity is 9.81 m/s². The value of pressure in the air space is

(A) 92.214 kN/m²

(B) 95.644 kN/m²

(D) 99.321 kN/m²

Answer: (A)

33. A rapid sand filter comprising a number of filter beds is required to produce 99 MLD of potable water. Consider water loss during backwashing as 5%, rate of filtration as 6.0 m/h and length to width ratio of filter bed as 1.35. The width of each filter bed is to be kept equal to 5.2 m. One additional filter bed is to be provided to take care of break-down,repair and maintenance. The total number of filter beds required will be

(A) 19

(B) 20

(D) 22

Answer: (C or D)

34. A priority intersection has a single-lane one-way traffic road crossing an undivided twolane two-way traffic road. The traffic stream speed on the single-lane road is 20 kmph and the speed on the two-lane road is 50 kmph. The perception-reaction time is 2.5 s, coefficient of longitudinal friction is 0.38 and acceleration due to gravity is 9.81 m/s². A clear sight triangle has to be ensured at this intersection. The minimum lengths of the sides of the sight triangle along the two-lane road and the single-lane road, respectively will be

(A) 50 m and 20 m

(B) 61 m and 18 m

(D) 122 m and 36 m

Answer: (C)

35. The following details refer to a closed traverse:

The length and direction (whole circle bearing) of closure, respectively are

(A) 1 m and 90°

(B) 2 m and 90°

(D) 2 m and 270°

Answer: (A or C)

36. A square area (on the surface of the earth) with side 100 m and uniform height, appears as 1 cm² on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, is

(A) 800 m

(B) 1500 m

(D) 3150 m

Answer: (C)

37. T he solution at 𝑥 = 1, 𝑡 = 1 of the partial differential equation subject to initial conditions of 𝑢(0) = 3𝑥 and is ______

(A) 1

(B) 2

(D) 6

Answer: (D)

38. The solution (up to three decimal places) at 𝑥 = 1 of the differential equation subject to boundary conditions is ______

Answer: (0.36 to 0.37)

39. Variation of water depth (𝑦) in a gradually varied open channel flow is given by the first order differential equation

Given initial condition: 𝑦(𝑥 = 0) = 0.8 𝑚. The depth (in m, up to three decimal places) of flow at a downstream section at x = 1 m from one calculation step of Single Step Euler Method is ______

Answer: (0.78 to 0.80)

40. An RCC short column (with lateral ties) of rectangular cross section of 250 mm × 300 mm is reinforced with four numbers of 16 mm diameter longitudinal bars. The grades of steel and concrete are Fe415 and M20, respectively. Neglect eccentricity effect. Considering limit state of collapse in compression (IS 456 : 2000), the axial load carrying capacity of the column (in kN, up to one decimal place), is ______

Answer: (815 to 830 (or) 905 to 920)

41. An RCC beam of rectangular cross section has factored shear of 200 kN at its critical section. Its width b is 250 mm and effective depth d is 350 mm. Assume design shear strength 𝜏𝑐 of concrete as 0.62 N/mm² and maximum allowable shear stress 𝜏_{𝑐,𝑚𝑎𝑥} in concrete as 2.8 N/mm². If two legged 10 mm diameter vertical stirrups of Fe250 grade steel are used, then the required spacing (in cm, up to one decimal place) as per limit state method will be ______

Answer: (7.0 to 9.0)

42. The dimensions of a symmetrical welded I-section are shown in the figure.

The plastic section modulus about the weaker axis (in cm³, up to one decimal place) is ______

Answer: (88.0 to 92.0)

43. Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in the figure.

Given that E = 2×10¹¹ N/m², A = 10 mm², L = 1 m and P = 1 kN. The horizontal displacement of Joint C (in mm, up to one decimal place) is ______

Answer: (2.60 to 2.80)

44. At a construction site, a contractor plans to make an excavation as shown in the figure.

The water level in the adjacent river is at an elevation of +20.0 m. Unit weight of water is 10 kN/m³. The factor of safety (up to two decimal places) against sand boiling for the proposed excavation is ______

Answer: (1.00 to 1.03)

45. A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of 200 kPa. The deviator stress at failure was found to be 400 kPa. An identical specimen of the same clay sample is isotropically consolidated to a confining pressure of 200 kPa and subjected to standard undrained triaxial compression test. If the deviator stress at failure is 150 kPa, the pore pressure developed (in kPa, up to one decimal place) is ______

Answer: (124 to 126)

46. The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be ______

Answer: (416.0 to 420.0)

47. A rigid smooth retaining wall of height 7 m with vertical backface retains saturated clay as backfill. The saturated unit weight and undrained cohesion of the backfill are 17.2 kN/m³and 20 kPa, respectively. The difference in the active lateral forces on the wall (in kN per meter length of wall, up to two decimal places), before and after the occurrence of tension
cracks is ______

Answer: (45 to 49 or -49 to -45)

48. Rainfall depth over a watershed is monitored through six number of well distributed rain gauges. Gauged data are given below

The Thiessen mean value (in mm, up to one decimal place) of the rainfall is ______

Answer: (478.5 to 479.5)

49. The infiltration rate 𝑓 in a basin under ponding condition is given by 𝑓 = 30 + 10𝑒^−2𝑡, where, 𝑓 is in mm/h and t is time in hour. Total depth of infiltration (in mm, up to one decimal place) during the last 20 minutes of a storm of 30 minutes duration is ______

Answer: (11.0 to 12.0)

50. I n a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are 0.05 m³/s and 0.25 m/s, respectively. If the full scale structure (30 times bigger) is subjected to a discharge of 270 m³/s, then the time scale (model to full scale) value (up to two decimal places) is ______

Answer: (0.15 to 0.25)

51. A water sample analysis data is given below

The carbonate hardness (expressed as mg/L of CaCO₃, up to one decimal place) for the water sample is ______

Answer: (272.0 to 274.0)

52. T he ultimate BOD (𝐿₀) of a wastewater sample is estimated as 87% of COD. The COD of this wastewater is 300 mg/L. Considering first order BOD reaction rate constant k (use natural log) = 0.23 per day and temperature coefficient θ = 1.047, the BOD value (in mg/L, up to one decimal place) after three days of incubation at 27°C for this wastewater will be
______

Answer: (154.0 to 161.0)

53. A waste activated sludge (WAS) is to be blended with green waste (GW). The carbon (C) and nitrogen (N) contents, per kg of WAS and GW, on dry basis are given in the table.

The ratio of WAS to GW required (up to two decimal places) to achieve a blended C:N ratio of 20:1 on dry basis is ______

Answer: (1.60 to 1.70)

54. Given the following data: design life n = 15 years, lane distribution factor D = 0.75, annual rate of growth of commercial vehicles r = 6%, vehicle damage factor F = 4 and initial traffic in the year of completion of construction = 3000 Commercial Vehicles Per Day (CVPD). As per IRC:37-2012, the design traffic in terms of cumulative number of standard axles (in million standard axles, up to two decimal places) is ______

Answer: (75.00 to 78.00)

55. A n aircraft approaches the threshold of a runway strip at a speed of 200 km/h. The pilot decelerates the aircraft at a rate of 1.697 m/s² and takes 18 s to exit the runway strip. If the deceleration after exiting the runway is 1 m/s², then the distance (in m, up to one decimal place) of the gate position from the location of exit on the runway is ______

Answer: (311.0 to 319.0)

GATE Exam 2018 Biotechnology (BT) Question Paper With Answer Key

June 7, 2023November 19, 2018 by suresh84

Biotechnology

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Biotechnology

Q. 1 – Q. 25 carry one mark each.

1. Consider an unfair coin. The probability of getting heads is 0.6. If you toss this coin twice, what is the probability that the first or the second toss is heads?

(A) 0.56

(B) 0.64

(D) 0.96

Answer: (C)

2. If serum is removed from the growth medium of human embryonic kidney cell line (HEK), then the cells will

(A) proliferate faster

(B) proliferate normally

(D) undergo immediate apoptosis

Answer: (C)

3. The repeat sequence of telomere in humans is

(A) 5′-TATAAT-3′

(B) 5′-TTAGGG-3′

(D) 5′-AAAAAA-3′

Answer: (B)

4. If a segment of a sense strand of DNA is 5-ATGGACCAGA-3, then the resulting RNA sequence after transcription is

(A) 5′-AGACCAGGTA-3′

(B) 5′-UCUGGUCCAU-3′

(D) 5′-AUGGACCAGA-3′

Answer: (D)

5. Which one of the following is an example of a neurotoxin?

(A) Cholera toxin

(B) Streptolysin-O

(D) Diphtheria toxin

Answer: (C)

6. Which of the following components constitute a molecular mechanics force field?

P. Bond stretching

Q. Bond angle bending

R. Torsional bond rotation

S. Non-bonded interactions

(A) P and Q only

(B) P, Q and R only

(D) P, Q, R and S

Answer: (D)

7. Which one of the following BLAST search programs is used to identify homologs of a genomic DNA query in a protein sequence database?

(A) blastp

(B) blastn

(D) tblastn

Answer: (C)

8. A mixture contains three similarly sized peptides P, Q and R. The peptide P is positively charged, Q is weakly negative and R is strongly negative. If this mixture is passed through an ion-exchange chromatography column containing an anionic resin, their order of elution will be

(A) P, Q, R

(B) R, Q, P

(D) P, Q and R elute together

Answer: (B)

9. Which one of the following is INCORRECT about protein structures?

(A) A protein fold is stabilized by favorable non-covalent interactions

(B) All parts of a fold can be classified as helices, strands or turns

(D) The peptide bond is nearly planar

Answer: (B)

10. Which one of the following metabolic processes in mammalian cells does NOT occur in the mitochondria?

(A) Citric acid cycle

(B) Oxidative phosphorylation

(D) Glycolysis

Answer: (D)

11. Which one of the following is NOT a principal component of innate immunity?

(A) Mucosal epithelia

(B) Dendritic cells

(D) Memory B-cells

Answer: (D)

12. Which of the following technique(s) can be used to study conformational changes in myoglobin?

P. Mass spectrometry

Q. Fluorescence spectroscopy

R. Circular dichroism spectroscopy

S. Light microscopy

(A) P only

(B) P and S only

(D) S only

Answer: (C)

13. Which one of the following bioreactor configurations is the basis for a trickling biological filter?

(A) Stirred tank

(B) Packed bed

(D) Fluidized bed

Answer: (B)

14. Cell type A secretes molecule X into the culture medium. Cell type B in the same culture responds to the molecule X by expressing protein Y. Which one of the following modes of signaling represents the interaction between A and B?

(A) Autocrine

(B) Juxtacrine

(D) Intracrine

Answer: (C)

15. Which one of the following statements is true for actin?

(A) Actin filament is structurally polarized and the two ends are not identical

(B) De novo actin polymerization is a single-step process

(D) Actin forms spindle fibers during mitosis

Answer: (A)

16. Standard error is

(A) the probability of a type I error in a statistical test

(B) the error in estimating a sample standard deviation

(D) the standard deviation of distribution of sample means

Answer: (D)

17. Which one of the following techniques is used to monitor RNA transcripts, both temporally and spatially?

(A) Northern blotting

(B) In situ hybridization

(D) Western blotting

Answer: (B)

18. Identify the character based method(s) used for the construction of a phylogenetic tree.

P. Maximum parsimony

Q. Neighbor joining

R. Maximum likelihood

S. Bootstrapping

(A) Q only

(B) P and R only

(D) S only

Answer: (B)

19. Which one of the following is the solution for 𝑐𝑜𝑠²𝑥 + 2𝑐𝑜𝑠𝑥 + 1 = 0, for values of 𝑥 in the range of 0°<𝑥<360°?

(A) 45°

(B) 90°

(D) 270°

Answer: (C)

20. Which one of the following plant secondary metabolites is a natural insecticide?

(A) Digitoxin

(B) Pyrethrin

(D) Avenacin A-1

Answer: (B)

21. The determinant of the matrix is _________

Answer: (-10 to -10)

22. T he variable 𝑧 has a standard normal distribution. If 𝑃(0 ≤ 𝑧 ≤ 1) = 0.34, then 𝑃(𝑧² > 1) is equal to (up to two decimal places) _________

Answer: (0.32 to 0.32)

23. T he absorbance of a solution of tryptophan measured at 280 nm in a cuvette of 2.0 cm path length is 0.56 at pH 7. The molar extinction coefficient (ε) for tryptophan at 280 nm is 5600 M-1cm-1 at pH 7. The concentration of tryptophan (in μM) in the solution is _________

Answer: (50 to 50)

24. A single stem cell undergoes 10 asymmetric cell divisions. The number of stem cells at the end is _________

Answer: (1 to 1)

25. G enomic DNA isolated from a bacterium was digested with a restriction enzyme that recognizes a 6-base pair (bp) sequence. Assuming random distribution of bases, the average length (in bp) of the fragments generated is _________

Answer: (4096 to 4096)

Q. 26 – Q. 55 carry two marks each.

26. In leguminous plants, both the rhizobium genes and the plant genes influence nodulation and nitrogen fixation. Which one of the following functions is NOT encoded by the host plant genes?

(A) Production of inducers that modify rhizobial cell wall

(B) Production of flavonoid inducers

(D) Root hair curling

Answer: (D)

27. Which of the following cytokines are endogenous pyrogens?

P. Tumor necrosis factor-α

Q. Interleukin-1

R. Transforming growth factor-β

S. Interleukin-10

(A) P and Q only

(B) P and R only

(D) Q and S only

Answer: (A)

28. Match the classes of RNA molecules in Group I with their functions in Group II.

(A) P-3, Q-5, R-2, S-4

(B) P-1, Q-3, R-2, S-5

(D) P-4, Q-1, R-2, S-5

Answer: (D)

29. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]

Assertion: Ab initio gene finding algorithms that predict protein coding genes in eukaryotic genomes are not completely accurate.

Reason: Eukaryotic splice sites are difficult to predict.

(A) Both [a] and [r] are false

(B) [a] is true but [r] is false

(D) Both [a] and [r] are true but [r] is not the correct reason for [a]

Answer: (C)

30. Which one of the following amino acids is catalyzed by activated macrophages to produce reactive nitrogen species?

(A) Arginine

(B) Asparagine

(D) Histidine

Answer: (A)

31. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]

Assertion: The association constant in water for the G-C base pair is three times lower than that for the A-T base pair.

Reason: There are three hydrogen bonds in the G-C base pair and two in the A-T base pair.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) [a] is false but [r] is true

(D) Both [a] and [r] are true and [r] is not the correct reason for [a]

Answer: (B)

32. Which one of the combinations of the following statements is true about antibody structure?

P. Limited proteolysis of rabbit IgG with the enzyme pepsin generates two antigen-binding regions (Fab) and an Fc fragment

Q. Limited proteolysis of rabbit IgG with the enzyme papain generates a single bivalent antigen-binding region F(ab′)2 and peptide fragments

R. The Fc fragment of IgG can self-associate and crystallize into a lattice S. The F(ab′)2 fragment of IgG is composed of both light and heavy chains

(A) P and Q only

(B) P and R only

(D) Q and S only

Answer: (C)

33. Which one of the following statements is true with regard to processing and presentation of protein antigens?

(A) In the class II MHC pathway, protein antigens in the cytosol are processed by proteasomes

(B) In the class I MHC pathway, extracellular protein antigens are endocytosed into vesicles and processed

(C) In the class I MHC pathway, transporter associated antigen processing (TAP) protein is required for translocating rocessed peptides generated in the cytosol

(D) Invariant chain in endoplasmic reticulum is involved in transport of peptides and loading of class I MHC

Answer: (C)

34. Which of the following are true about bacterial superoxide dismutase?

P. Present in obligate aerobes

Q. Present in facultative anaerobes

R. Present in aerotolerant anaerobes

S. Absent in obligate aerobes

(A) P and Q only

(B) P, Q and R only

(D) Q and S only

Answer: (B)

35. Which of the following are true with regard to anaerobic respiration in bacteria?

P. The final electron acceptor is an inorganic substance other than molecular oxygen

Q. The number of ATP molecules produced per glucose molecule is more than that produced in aerobic respiration

R. The number of ATP molecules produced per glucose molecule is less than that produced in aerobic respiration

S. Only substrate level phosphorylation is used to generate ATP

(A) P and S only

(B) Q and S only

(D) P, Q and S only

Answer: (C)

36. Shear stress versus shear rate behavior of four different types of fluids (I, II, III and IV) are shown in the figure below.

Which one of the following options is correct?

(A) I-Newtonian, II-Bingham plastic, III-Dilatant, IV-Pseudoplastic

(B) I-Pseudoplastic, II-Dilatant, III-Newtonian, IV-Bingham plastic

(D) I-Newtonian, II-Bingham plastic, III-Pseudoplastic, IV-Dilatant

Answer: (D)

37. An analysis of DNA-protein interactions was carried out using all DNA-protein complexes in the protein data bank (PDB). The frequency distribution of four amino acid residues, represented as P, Q, R and S, occurring in non-covalent interactions between the protein and DNA backbone is shown below.

Which one of the following is correct?

(A) P-Lys, Q-Arg, R-Gln, S-Glu

(B) P-Gln, Q-Glu, R-Lys, S-Arg

(D) P-His, Q-Glu, R-Gln, S-Lys

Answer: (A)

38. A pedigree of an inheritable disease is shown below.

What type of inheritance does the disease follow?

(A) Autosomal dominant

(B) X-linked dominant

(D) Autosomal recessive

Answer: (C)

39. Match the industrial products mentioned in Group I with their producer organisms in Group II

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

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

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

Answer: (D)

40. 5′ capping of mRNA transcripts in eukaryotes involves the following events:

P. Addition of GMP on the 5′ end

Q. Removal of γ-phosphate of the triphosphate on first base at the 5′ end

R. 5′-5′ linkage between GMP and the first base at 5′ end

S. Addition of methyl group to N7 position of guanine

Which one of the following is the correct sequence of events?

(A) P, Q, R, S

(B) P, R, Q, S

(D) Q, P, S, R

Answer: (C)

41. Calculate the following integral (up to two decimal places)

Answer: (5.30 to 5.34)

42. The probability distribution for a discrete random variable 𝑋 is given below.

The expectation value of 𝑋 is (up to one decimal place) _________

Answer: (2.1 to 2.1)

43. If 1+𝑟 + 𝑟²+ 𝑟3+⋯∞ = 1.5,

then, 1 + 2𝑟 + 3𝑟² + 4𝑟³+⋯∞= (up to two decimal places) _________

Answer: (2.25 to 2.25)

44. Moist heat sterilization of spores at 121°C follows first order kinetics as per the expression:

where, N is the number of viable spores, t is the time, kd is the rate constant and is the rate of change of viable spores.

If k_d value is 1.0 min^-1, the time (in minutes) required to reduce the number of viable spores from an initial value of 10¹⁰ to a final value of 1 is (up to two decimal places) _________

Answer: (23.02 to 23.04)

45. An aqueous solution containing 6.8 mg/L of an antibiotic is extracted with amyl acetate. If the partition coefficient of the antibiotic is 170 and the ratio of water to solvent is 85, then the extraction factor is _________

Answer: (2 to 2)

46. A microbial strain is cultured in a 100 L stirred fermenter for secondary metabolite production. If the specific rate of oxygen uptake is 0.4 h^-1 and the oxygen solubility in the broth is 8 mg/L, then the volumetric mass transfer coefficient (KLa) (in s^-1) of oxygen required to achieve a maximum cell concentration of 12 g/L is (up to two decimal places) _________

Answer: (0.16 to 0.17)

47. In a chemostat, the feed flow rate and culture volume are 100 ml/h and 1.0 L, respectively. With glucose as substrate, the values of μ_max and K_s are 0.2 h^-1 and 1 g/L, respectively. For a glucose concentration of 10 g/L in the feed, the effluent substrate concentration (in g/L) is _________

Answer: (1 to 1)

48. Mammalian cells in active growth phase were seeded at a density of 1×10⁵ cells/ml. After 72 hours, 1×10⁶ cells/ml were obtained. The population doubling time of the cells in hours is (up to two decimal places) _________

Answer: (21.00 to 22.00)

49. Y east converts glucose to ethanol and carbon dioxide by glycolysis as per the following reaction:

C₆H₁₂O₆ → 2C₂H₅OH + 2CO₂

Assuming complete conversion, the amount of ethanol produced (in g) from 200 g of glucose is (up to two decimal places) _________

Answer: (102.00 to 103.00)

50. At the end of a batch culture, glucose solution is added at a flow rate of 200 ml/h. If the culture volume after 2 h of glucose addition is 1000 ml, the initial culture volume (in ml) is _________

Answer: (600 to 600)

51. Consider the following alignment of two DNA sequences:

Assuming an affine gap scoring scheme of an identity matrix for substitution, a gap initiation penalty of 1 and a gap extension penalty of 0.1, the score of the alignment is (up to one decimal place) _________

Answer: (1.8 to 1.9)

52. First order deactivation rate constants for soluble and immobilized amyloglucosidase enzyme are 0.03 min^-1 and 0.005 min^-1, respectively. The ratio of half-life of the immobilized enzyme to that of the soluble enzyme is (rounded off to the nearest integer) _________

Answer: (6 to 6)

53. Consider a simple uni-substrate enzyme that follows Michaelis-Menten kinetics. When the enzyme catalyzed reaction was carried out in the presence of 10 nM concentration of an inhibitor, there was no change in the maximal velocity. However, the slope of the Lineweaver-Burk plot increased 3-fold. The dissociation constant for the enzyme-inhibitor complex (in nM) is _________

Answer: (5 to 5)

54. The product of complete digestion of the plasmid shown below with EcoRI and HaeIII was purified and used as a template in a reaction containing Klenow fragment of DNA polymerase, dNTPs and [α-³²P]-dATP in a suitable reaction buffer. The product thus obtained was purified and subjected to gel electrophoresis followed by autoradiography.

The number of bands that will appear on the X-ray film is _________

Answer: (2 to 2)

55. A rod shaped bacterium has a length of 2 μm, diameter of 1 μm and density the same as that of water. If proteins constitute 15% of the cell mass and the average protein has a mass of 50 kDa, the number of proteins in the cell is _________
(1 Da = 1.6 × 10^-24g)

Answer: (2900000 to 3200000)

GATE Exam 2018 Architecture and Planning (AR) Question Paper With Answer Key

June 7, 2023November 19, 2018 by suresh84

Architecture and Planning

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Architecture and Planning

1. In a Colour Wheel, Red and Blue colours are

(A) Tertiary

(B) Complementary

(D) Primary

Answer: (D)

2. In a bird’s eye perspective view of a cuboid, the maximum number of vanishing points is

(A) 1

(B) 2

(D) 6

Answer: (C)

3. The compressive strength of M-25 concrete is

(A) 25 kg/sqm

(B) 25 N/sqmm

(D) 2.5 N/sqmm

Answer: (B)

4.In Critical Path Method (CPM) for time scheduling, ‘forward pass calculation’ is carried out for determining

(A) Late start and early finish time

(B) Early start and early finish time

(D) Early start and late finish time

Answer: (B)

5. Collapse of the World Trade Center (WTC), New York, in 2001, was due to

(A) Wind load failure

(B) Foundation failure

(D) Thermal performance failure of structural steel

Answer: (D)

6. During the construction of tall buildings, the equipment used for hoisting building materials to the upper floors is a

(A) Goods lift

(B) Capsule lift

(D) Tower crane

Answer: (D)

7. A Rock-cut style of architecture is represented by

(A) Shyama Rama Temple, Bishnupur

(B) Kailasa Temple, Ellora

(D) Sanchi Stupa, Sanchi

Answer: (B)

8. ‘Area based development’ and ‘Pan city development’ are part of

(A) Smart City Mission

(B) Digital India Mission

(D) Atal Innovation Mission

Answer: (A)

9. In mass transportation, LRTS stands for

(A) Light Rail Transit System

(B) Linear Rail Transit System

(D) Linear Rail Transportation System

Answer: (A)

10. The structural grid type shown in the figure below is a

(A) Tartan Grid

(B) Square Grid

(D) Irregular Grid

Answer: (A)

11. Assuming other variables remaining constant, the Tropical Summer Index

(A) Increases with increase in air velocity

(B) Decreases with increase in wet-bulb temperature

(D) Increases with increase in vapour pressure

Answer: (D)

12. Government of India’s urban development program ‘HRIDAY’ stands for

(A) Heritage Rejuvenation Implementation Development Aayog Yojana

(B) Heritage Review Implementation Development Augmentation Yojana

(D) Heritage City Improvement and Development Aawas Yojana

Answer: (C)

13. As per the Urban and Regional Development Plan Formulation and Implementation (URDPFI) guidelines, the plan period considered in a ‘Perspective plan’ is

(A) 1-10 years

(B) 11-15 years

(D) 35-45 years

Answer: (C)

14. The Hall of Nations, New Delhi, was designed by

(A) Charles Correa

(B) Raj Rewal

(D) A. P. Kanvinde

Answer: (B)

15. As per the National Building Code of India 2016, the minimum turning radius (in metres) required for fire tender movement is

(A) 8.0

(B) 8.5

(D) 9.5

Answer: (C)

16. Sidi Bashir Mosque with ‘Shaking Minarets’ is located in

(A) Ajmer

(B) Allahabad

(D) Amritsar

Answer: (C)

17. ‘Sight Distance’ is considered in the design of

(A) Road intersection

(B) Fenestration

(D) Auditorium

Answer: (A)

18. In India, the term ‘Town Planning Scheme’ refers to

(A) Land renewal

(B) Land rejuvenation

(D) Land readjustment

Answer: (D)

19. Bamboo is a type of

(A) Shrub

(B) Timber

(D) Perennial grass

Answer: (D)

20. According to the UN, one of the components for measuring ‘inclusive growth’ is

(A) Economic well-being

(B) Physical infrastructure

(D) Life expectancy

Answer: (A or B Or C)

21. The unit of measurement of Damp Proof Course (DPC) in building construction is

(A) kg

(B) cum

(D) rm

Answer: (C)

22. Which of the following is NOT a Building Information Modeling software tool

(A) Adobe Illustrator

(B) Bentley Microstation

(D) Graphisoft ARCHICAD

Answer: (A)

23. The concentric circles in a solar chart represent

(A) Azimuth angle

(B) Altitude angle

(D) Vertical shadow angle

Answer: (B)

24. A room of 3m × 3m × 3m has a reverberation time of 0.8 sec. Using Sabine’s method, the total absorption in the room is _____________ sabin (up to one decimal place).

Answer: (5.3 to 5.7)

25. A 25 storeyed building has 5 lifts. The resulting waiting time is 35 sec and ‘Return Travel Time’ is 175 sec. The number of lifts required for reducing waiting time to 25 sec, without increasing the lift speed, is _______________

Answer: (7.0 to 7.0)

Q. 26 – Q. 55 carry two marks each.

26. Match the planning documents in Group-I with their respective government schemes in Group-II

(A) P-4, Q-1, R-5, S-2

(B) P-3, Q-5, R-4, S-2

(D) P-3, Q-5, R-4, S-1

Answer: (D)

27. Associate the fire safety requirements for high rise buildings in Group-I with corresponding standards of the National Building Code of India 2016 in Group-II

(A) P-4, Q-1, R-5, S-2

(B) P-3, Q-5, R-4, S-1

(D) P-4, Q-5, R-1, S-3

Answer: (C)

28. Match the photometric quantities in Group-I with their respective units in Group-II

(A) P-3, Q-2, R-5, S-4

(B) P-5, Q-4, R-2, S-1

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

Answer: (D)

29. Associate the symbols in Group I with their meanings in Group II

(A) P-5, Q-3, R-1, S-2

(B) P-1, Q-5, R-3, S-4

(D) P-5, Q-3, R-4, S-2

Answer: (D)

30. Match the elements in Group-I with the building components in Group-II

(A) P-5, Q-3, R-4, S-1

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

(D) P-5, Q-3, R-4, S-2

Answer: (D)

31. Match the iconic architectural examples in Group-I with their predominant structural systems in Group-II

(A) P-1, Q-3, R-5, S-4

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

(D) P-5, Q-4, R-3, S-2

Answer: (C)

32. Match the building materials in Group-I with their distinctive properties in Group-II

(A) P-5, Q-3, R-2, S-1

(B) P-5, Q-4, R-1, S-2

(D) P-4, Q-3, R-1, S-5

Answer: (B)

33. Match the built forms in Group-I with their descriptions in Group-II

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

(B) P-4, Q-3, R-1, S-5

(D) P-3, Q-1, R-5, S-2

Answer: (C)

34. Match the building configuration characteristics in Group-I with their seismic consequences in Group-II

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

(B) P-2, Q-3, R-1, S-5

(D) P-3, Q-5, R-2, S-1

Answer: (B)

35. Match the landscaping terms in Group-I with their descriptions in Group-II

(A) P-5, Q-3, R-1, S-4

(B) P-3, Q-5, R-1, S-4

(D) P-5, Q-2, R-4, S-1

Answer: (A)

36. Match the planning principles in Group-I with their descriptions in Group-II

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

(B) P-2, Q-1, R-5, S-3

(D) P-2, Q-3, R-5, S-4

Answer: (A)

37. Match the cities in Group-I with their planners in Group-II

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

(B) P-4, Q-1, R-5, S-2

(D) P-2, Q-3, R-4, S-5

Answer: (C)

38. Match the Temples in Group-I with their Dynastic period in Group-II

(A) P-4, Q-5, R-1, S-2

(B) P-5, Q-1, R-2, S-3

(D) P-4, Q-1, R-2, S-5

Answer: (A)

39. Match the Buildings in Group-I with their Architects in Group-II

(A) P-3, Q-4, R-2, S-5

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

(D) P-2, Q-5, R-4, S-3

Answer: (A)

40. Match the following urban conservation themes in Group-I with their respective descriptions in Group-II

(A) P-2, Q-5, R-4, S-3

(B) P-2, Q-1, R-4, S-5

(D) P-3, Q-1, R-3, S-5

Answer: (B)

41. A Single Phase Neutral (SPN) electrical circuit has a power consumption of 330W. Considering a voltage of 110V and power factor of 0.8, the electrical current drawn is ___________ Amp (up to one decimal place).

Answer: (3.7 to 3.8)

42. A building with 100 sqm roof area is connected to a 72 cum rainwater collection tank. If the rainfall is 60 mm per hour and the loss during water storage is 20%, then the time taken to fill the tank completely is_______ hours.

Answer: (15.0 to 15.0)

43. The planning norms for provision of schools in a given town is shown in the table below

Total land area required for providing all types of schools for a population of 200,000 is ___________ hectares.

Answer: (104 to 104)

44. In a mixed use development on a 2.0 hectare site with 2.0 FAR, the ratio of residential to commercial floor area is 3:2. The minimum parking (in ECS) needed per 100 sqm of residential and commercial floor area is 1.0 and 1.25 respectively. Considering full FAR utilization, the total parking requirement is ____________ ECS.

Answer: (440 to 440)

45. A plotted housing scheme on a site of 12 hectare has 60% saleable area. The average unit cost of land development is INR 300 million per hectare. If the profit margin is 20%, then the selling price of land per hectare is __________ million INR.

Answer: (600 to 600)

46. An isolated enclosure shown in the Figure has inlet P and outlet Q of 2 sqm each, on the opposite walls. The outdoor wind speed is 5 m/sec. If the coefficient of effectiveness is 0.6, the rate of natural ventilation in the enclosure due to wind action is _________ cum/hr.

Answer: (21600 to 21600)

47. A 5m × 5m × 3m room has four 230 mm thick external brick walls. Total wall fenestration is 10 sqm. The temperature difference between indoor and outdoor is 2 degC. The air to air transmittance values for 230 mm thick brick wall and 200 mm thick aerated concrete block wall are 2.4 and 1.7 W/sqm degC respectively. If the brick walls are replaced with the aerated concrete block walls, then the change in conductive heat flow through the walls is _________W.

Answer: (69.5 to 70.5)

48. For an activity, ‘optimistic time duration’ is 4 days, ‘pessimistic time duration’ is 11 days and ‘most-likely time duration’ is 8 days. The PERT value of time duration is______ days (up to one decimal place).

Answer: (7.8 to 7.9)

49. In the Figure, the negative bending moment at point A of the cantilever is ________ kNm.

Answer: (224 to 226)

50. The water consumption of a high rise apartment building with 60 dwelling units having an average household size of 5 persons is 135 lpcd. Assuming 80% of the total use is met with recycled water supply, the daily domestic demand for the building is _________ litres.

Answer: (8100 to 8100)

51. In India, for 1.0 cum of M-20 grade concrete, the number of cement bags required is ________ (up to two decimal places).

Answer: (5 to 9)

52. The sound power level of an outdoor non-directional point source is 90 dB. Considering an atmospheric impedance of 400 rayls, the sound pressure level at 10 m distance from the source is _______ dB.

Answer: (58 to 60)

53. The live load and dead load in a three storeyed residential building, transferred through a single column, is 12 tons and 18 tons respectively. If the soil bearing capacity is 10 ton/sqm and the factor of safety is 1.5, the area of column footing is _____________ sqm (up to one decimal place).

Answer: (4.0 to 5.0)

54. The indoor illumination requirement for a building is 350 Lux. If the daylight factor is 2.7 and the design sky illuminance is 9000 Lux, then the required supplementary artificial lighting is ____________ Lux.

Answer: (107 to 107)

55. Two design options of a business building on a 10.0 hectare site are being compared for built up area. Floor to floor height of Option A is 3.6 m and that of Option B is 4.5 m. If the maximum allowable building height is 45 m with same ground coverage for both options, the additional built up area achievable in Option A over Option B is______percent.

Answer: (20 to 20)

GATE Exam 2018 Agricultural Engineering (AG) Question Paper With Answer Key

June 7, 2023November 19, 2018 by suresh84

Agricultural Engineering

General Aptitude (GA) Set-4

Q. 1 – Q. 5 carry one mark each.

1. “ When she fell down the _______, she received many _______ but little help.”

The words that best fill the blanks in the above sentence are

(A) stairs, stares

(B) stairs, stairs

(D) stares, stares

Answer: (A)

2. “ In spite of being warned repeatedly, he failed to correct his _________ behaviour.”

The word that best fills the blank in the above sentence is

(A) rational

(B) reasonable

(D) good

Answer: (C)

3. For 0 ≤ 𝑥 ≤ 2𝜋, sin 𝑥 and cos 𝑥 are both decreasing functions in the interval ________.

(A)

(B)

(C)

(D)

Answer: (B)

4. The area of an equilateral triangle is √3. What is the perimeter of the triangle?

(A) 2

(B) 4

(D) 8

Answer: (C)

5. Arrange the following three-dimensional objects in the descending order of their volumes:

(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm

(ii) A cube of side 8 cm

(iii) A cylinder with base radius 7 cm and height 7 cm

(iv) A sphere of radius 7 cm

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

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

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

Answer: (D)

Q. 6 – Q. 10 carry two marks each.

(A) 72

(B) 73

(D) 75

Answer: (A)

7. A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

(A) 20

(B) 48

(D) 72

Answer: (C)

(A) 30,000

(B) 2,70,000

(D) 4,20,000

Answer: (D)

9. If 𝑥² + 𝑥 − 1 = 0 what is the value of

(A) 1

(B) 5

(D) 9

Answer: (C)

(A) There is a strong correlation between crow birth and cracker sales.

(B) Cracker usage increases crow birth rate.

(D) Increased birth rate of crows will cause an increase in the sale of crackers.

Answer: (A)

Agricultural Engineering

1. The general solution to the second order linear homogeneous differential equation y″ – 6y′ + 25y = 0 is

(A) e^3x(a cos 4x + b sin 4x)

(B) e^3ix(a cos 4x + b sin 4x)

(D) e^4ix(a cos 3x + b sin 3x)

Answer: (A)

2. Solution of f(x) = x⁴ +2 x³ – 4 x² + 3 x – 1 = 0 is

(A) 0.333

(B) 0.646

(D) 1.000

Answer: (C)

3. Integration of is

(A)

(B)

(C)

(D)

Answer: (D)

4. The type of the sequence is

(A) oscillatory

(B) bounded

(D) diverging

Answer: (C)

5. For accepting or rejecting a null hypothesis, which one of the following is NOT used as a significance test method in statistics?

(A) Z-test

(B) Student’s t-test

(D) Relative standard deviation

Answer: (D)

6. For a two-wheel drive tractor, use of differential lock in adverse field condition ensures

(A) equal distribution of torque to both the drive wheels.

(B) equal distribution of power to both the drive wheels.

(D) distribution of higher amount of torque to the wheel under better traction.

Answer: (D)

7. During field evaluation of a combine harvester, total grain collected at the grain tank was 135 kg. Amount of threshed grain found over walker and shoe were 0.65 kg and 2.4 kg, respectively. Unthreshed grain lost with straw and chaff were 4.54 kg and 0.28 kg, respectively. Threshing efficiency of the combine harvester in percent is

(A) 94.37

(B) 94.49

(D) 96.63

Answer: (D)

8. Match the following items of Column I with the corresponding items of Column II:

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

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

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

Answer: (B)

9. Constituents of the producer gas contributing to its heating value are

(A) CO and CO₂

(B) CH₄ and CO₂

(D) CO₂ and H₂

Answer: (C)

10. One of the key assumptions made by Dupuit-Forchheimer about the flow behavior in the porous medium towards subsurface drains is

(A) homogeneous medium

(B) isotropic medium

(D) uniform recharge

Answer: (C)

11. The depths from the soil surface to subsurface tile drains, impermeable soil layer and the highest water table are measured as 2.8 m, 5.0 m and 0.8 m, respectively. The effective hydraulic head for drainage in meter is

(A) 0.8

(B) 2.0

(D) 4.2

Answer: (B)

12. The discharge from a sprinkler nozzle depends on

(A) operating pressure and nozzle geometry.

(B) operating pressure and distribution pattern.

(D) operating pressure and application rate.

Answer: (A)

13. If the void ratio of a soil column is 0.43, the soil porosity is

(A) 0.30

(B) 0.40

(D) 0.75

Answer: (A)

14. Which one of the following is a WRONG statement?

(A) The head generated by a centrifugal pump at zero discharge is the ‘shutoff head’.

(B) To avoid cavitation in centrifugal pumps, the net positive suction head should be more than the theoretical atmospheric pressure.

(D) Most of the turbine pumps have operational characteristics closer to those of the centrifugal pumps than the propeller pumps.

Answer: (B)

15. If the departure and latitude of a line during Theodolite survey are 70.03 m and -100 m, respectively, the whole circle bearing of this line in degree is

(A) 55

(B) 125

(D) 145

Answer: (D)

16. Convective film heat transfer coefficient (h) of air (thermal conductivity=0.025 W m-1 K^-1) in W m-2 K^-1, trapped between two parallel glass panes in a window 1.5 mm apart, is

(A) 3.75

(B) 16.67

(D) 60.21

Answer: (B)

17. Log mean temperature difference (LMTD) correction factor (F) is applicable to

(A) Spiral tube heat exchanger

(B) Steam jacketed kettle

(D) Evaporator tubes

Answer: (C)

18. Which one of the following statements related to parboiling of paddy is NOT correct?

(A) Irreversible granule swelling occurs during heating.

(B) Parboiling process is used to salvage wet or damaged paddy.

(D) Milling yield of paddy increases due to starch gelatinization.

Answer: (C)

19. In refining of the rice bran oil for edible purpose, neutralization process is carried out mainly to remove

(A) wax and organic impurities

(B) gums and mucilage

(D) free fatty acids

Answer: (D)

20. Which one of the following chemicals is NOT used for fumigation in either horizontal or vertical storage structures to kill insects?

(A) Methyl bromide

(B) Phosphine

(D) Silver sulphate

Answer: (D)

21. Match the following agricultural/food by-products in Column I with their respective value added products in Column II.

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

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

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

Answer: (B)

22. An epicyclic gear train consists of a sun gear, four planet gears pinned on a planet carrier (which is mounted on the sun gear) and a fixed ring gear (in which the entire sun-planet gear assembly is inserted). If the ring gear has 56 teeth and each planet gear has 18 teeth, the number of teeth on the sun gear is _______.

Answer: (20.00 to 20.00)

23. A self-propelled power reaper with a 1.2 m wide cutter bar was operated at a forward speed of 4 km h^-1. Turning loss during operation was observed to be 25 minutes per hectare. Neglecting any other losses, the field efficiency of the reaper will be ________%.

Answer: (83.00 to 84.00)

24. T he porosity and compressibility of a 7.8 m thick confined aquifer are 0.25 and 1×10^-8 m² N^-1, respectively. The storage coefficient of the aquifer is 6.5×10^-4. To release 650 m³ of water from 1 km² of this aquifer, the average decline in hydraulic head will be ________m.

Answer: (1.00 to 1.00)

25. Molecular diffusivity (DAB) of water vapour in air is 2.6×10^-5 m² s^-1 over an effective distance of 3 mm. Density and coefficient of viscosity of air are 1.2 kg m^-3 and 2×10^-5 kg m^-1 s^-1, respectively. Sherwood Number (NSh) for water vapour in air is _________.

Answer: (1.00 to 1.00)

Q. 26 – Q. 55 carry two marks each.

26. Rank of a matrix is

(A) 1

(B) 2

(D) 4

Answer: (C)

27. A particle is subjected to forces P = 2 i – 5 j + 6 k and Q = – i + 2 j – k. The positional vectors are Work done by the resultant force (F = P + Q) to move the particle from A to B is

(A) 2

(B) -5

(D) -15

Answer: (D)

28. A two-wheel drive tractor weighing 18 kN has a wheel base 1.8 m. Its centre of gravity is located 600 mm ahead of the rear axle centre, under static condition, on a level ground. When this tractor is used to pull a disc plough hitched at a height of 390 mm from the ground, the draft observed is 6 kN. The change in reaction on rear wheels of the tractor due to pull in kN is

(A) 1.30

(B) 1.95

(D) 5.85

Answer: (A)

29. Match the following items in Column I with the corresponding items in Column II:

(A) P-4, Q-2, R-5, S-3, T-1

(B) P-4, Q-3, R-1, S-5, T-2

(D) P-3, Q-1, R-2, S-4, T-5

Answer: (C)

30. T he velocity (v) of a tractor, which starts from rest, is given at fixed intervals of time (t) as follows:

Using Simpson’s 1/3rd rule, the distance covered by the tractor in 20 minutes will be _________m.

Answer: (25.80 to 25.90)

31. In a box, there are 2 red, 3 black and 4 blue coloured balls. The probability of drawing 2 blue balls in sequence without replacing, and then drawing 1 black ball from this box is _________%.

Answer: (6.80 to 7.20)

32. An open belt drive system transmits 5 kW power using a flat belt of width and thickness as 80 mm and 5 mm, respectively. The driving shaft speed is 1500 rpm and the driven shaft speed is 500 rpm. The coefficient of friction between the belt and pulley is 0.20, and the wrap angle of the belt is 168°. If diameter of the smaller pulley is 200 mm, maximum stress induced in the belt will be _________ MPa.

Answer: (1.70 to 1.80)

33. A 2m³ biogas plant is to be operated using cow-dung as feedstock. The cow-dung is mixed with water in proportion of 1:1 (by weight) to form a slurry of density 1090 kg m^-3. The yield of biogas is 0.036 m³ kg^-1 of cow-dung. If the hydraulic retention time is 40 days, volume of the digester of the biogas plant will be ________ m³.

Answer: (3.90 to 4.20)

34. A power tiller with diesel engine produces 12 kW of brake power with a brake thermal efficiency of 30%. If the air-fuel ratio in the combustion process is 14:1 and heating value of the fuel is 45 MJ kg^-1, air consumption rate of the engine will be ________ kg h^-1.

Answer: (44.50 to 45.00)

35. Air enters into an engine cylinder at a pressure of 100 kPa and temperature of 300 K in the suction stroke of an ideal Otto cycle. The cylinder clearance volume is 600 cm³ and compression ratio is 8:1. The expansion stroke of the cycle is polytropic in nature. The pressure at the beginning of the expansion stroke is 10 MPa and the temperature at the end of the expansion stroke is 1800 K. The polytropic exponent of the expansion stroke is ________.

Answer: (1.30 to 1.39)

36. A tractor drawn five-tine sweep type cultivator is set at an angle (load angle) of 45° with the soil surface during its operation. The sweep of each tine experiences a normal force of 960 N on its surface. If the coefficient of soil-metal friction is 0.3, the total draft requirement of the cultivator is ________ kN.

Answer: (4.35 to 4.45)

37. A two-wheel drive tractor with rear wheel rolling radius of 600 mm develops a tractive force of 18.5 kN at a wheel slip of 12%. The engine speed is 2400 rpm and the transmission ratio from the engine to the rear wheels is 120:1. If the tractor experiences a motion resistance of 1.75 kN, the drawbar power developed by the tractor will be ________ kW.

Answer: (18.00 to 21.00)

38. A single plate dry clutch transmits 15 kW power at 1200 rpm. The clutch sustains a maximum axial load of 2.65 kN. The ratio of outer to inner diameter of the frictional surface is 1.25:1. Considering uniform wear with a coefficient of friction of 0.3 on both the frictional surfaces, the outer diameter of the clutch plate is ________ mm.

Answer: (166.00 to 168.00)

39. A precision seed planter can plant 10 seeds per revolution of the metering plate with a row to row distance of 450 mm at a speed of 6 km h^-1. A plant population of 36 plants per square meter is desired for the crop. The germination percentage of the seed is 90%. If the planter ground wheel has a rolling radius of 350 mm, the speed ratio of metering plate to the ground wheel required to obtain the desired plant population is ________.

Answer: (3.90 to 4.10)

40. The elevations of pressure gauge and porous cup of the tensiometer installed in unsaturated zone are 145.8 m and 144.2 m, respectively. Pressure measured at the gauge is -19.62×10³ N m^-2. The specific weight of water is 9810 N m^-3. The estimated pressure at the porous cup is ________ N m^-2.

Answer: (-3924 to -3924)

41. The drawdown at the well face of a 30 cm diameter fully penetrating well in a confined aquifer is 3 m. The radius of influence of this well is 3 km. For the same discharge and aquifer condition, the drawdown at 300 m away from the centre of the well is ______m.

Answer: (0.68 to 0.71)

42. A permanent matured orchard has a tree spacing of 4 m×5 m. Each tree has a shading area of 40% to be irrigated with the ‘pig tail’ pattern multi-exit drip emitters. The effective wetting geometry of each emitter is 2 m×2 m. The emitters have discharge constant and exponent of 0.3 and 0.6, respectively. The coefficient of variation of emitter discharge is 0.06. The average and minimum operating pressures are 120 kPa and 100 kPa, respectively. The emission uniformity of the emitters is ________%.

Answer: (83 to 86)

43. The 6-hour unit hydrograph of a watershed is represented by an isosceles triangle with the peak of 180 m³ s^-1 and time to peak of 18 hours. The phi-index (∅) of this watershed is 3.0 mm h^-1 and the constant baseflow is 20 m³ s^-1. The accumulated rainfall received in this watershed at 6 h and 12 h from the start of the storm are 38 mm and 106 mm, respectively. The resulting peak of the flood hydrograph due to this storm event is _______ m³ s^-1.

Answer: (1280 to 1280)

44. Three geometrically identical Lysimeters (A, B and C) installed in a paddy field have uniform initial ponding depths of 12 cm. After a week, the recorded water depths in A, Band C are 10.4 cm, 8.6 cm, and 7.0 cm, respectively. Rainfall received during this week is 15 mm, and the crop coefficient of paddy is 0.94. Lysimeter ‘A’ has a closed bottom with no plant. Lysimeter ‘B’ has an open bottom with no plant. Lysimeter ‘C’ has an open bottom with paddy plants. Neglecting the boundary effects and groundwater contribution in the Lysimeters, the weekly potential evapotranspiration will be _______ cm.

Answer: (5.00 to 5.00)

45. A rectangular chute spillway is designed for gully erosion control with a drop (H) of 5 m, peak flow of 1.81 m³ s^-1 and maximum inlet water level of 0.81 m. Frictional head loss over the apron is 20% of H. The design height of chute blocks is equal to the depth of flow in the water way. Acceleration due to gravity (g) is 9.81 m s^-2. If coefficient of discharge of the weir section is 1.66, height of the chute blocks is _______m.

Answer: (0.13 to 0.14)

46. Furrows of 120 m length with 0.5% slope are made at 90 cm spacing. The maximum nonerosive stream flow rate is applied in a furrow that takes 1.0 hour to reach the lower end. Then this flow rate is reduced to half of its size and, subsequently, continued for another 1.0 hour. The average depth of applied water is ________ cm.

Answer: (6.00 to 6.00)

47. A cylindrical tank of 1.5 m diameter and 4 m height is filled with a liquid by a pipe of 2.5 cm internal diameter. The density and dynamic viscosity of the liquid are 1050 kg m^-3and 1.6×10^-3 N s m^-2, respectively. If flow in the pipe is turbulent, the maximum time required to fill the tank is _______ hours.

Answer: (16.30 to 16.50)

48. In a falling film evaporator, the inside and outside diameters of the tube wall are 25 mm and 27 mm, respectively. The tube is made of SS304 (thermal conductivity=15 W m^-1 K^-1) and the inside convective film coefficient is 750 W m^-2 K^-1. Outside the tube wall, film coefficient of condensing steam is 7175 W m^-2 K^-1. Based on the inside area of the tube, the overall heat transfer coefficient is __________ W m^-2 K^-1.

Answer: (650 to 670)

49. Mass flow rate of outside air through a duct is 735 kg h^-1. Absolute humidity of air is 0.025 kg water vapour per kg dry air at 40°C. This air is mixed with equal quantity of moist exhaust air coming out of a counter current dryer at 55°C. The mixed air is heated up to 75°C to dry barley, fed at 174 kg h^-1 , at an initial moisture content of 31% (wet basis) to a final value of 7% (dry basis). The absolute humidity of the exhaust air from the dryer in ‘kg water vapour per kg dry air’ will be ________.

Answer: (0.086 to 0.089)

50. One ton of marine fishery products are to be brought down from 32°C temperature to -18°C in half an hour time using a plate freezer. The freezing point of 85% water (based on total mass of the product) present in the fish is -0.3°C. Specific heat capacities of fresh and frozen fish solids (15% of total mass) are 3.2 and 1.8 kJ kg^-1 K^-1, respectively. Specific heat capacity of fresh water is 4.2 kJ kg^-1 K^-1 and that of ice is 2.2 kJ kg^-1 K^-1. Latent heat of crystallization of water is 335 kJ kg^-1. For freezing the products, the compressor power consumption with a vapour compression refrigeration cycle (coefficient of performance, 3.66) is_________ kW.

Answer: (68.00 to 69.00)

51. Mycobacterium tuberculosis is having decimal reduction time of 13.5 s at 72°C. The count of the organism is to be reduced by eight logarithmic cycles in milk pasteurization with adequate holding at a temperature of 85°C. If Q₁₀ value for the organism is 7.5, the minimum holding time for the desired sterility of this particular organism at 85°C is_________ seconds.

Answer: (7.80 to 8.00)

52. A horizontal screw conveyor of length 3.2 m conveys solid grain having bulk density of 725 kg m^-3. The screw diameter, shaft diameter and pitch of the screw are 0.6 m, 0.24 m and 0.48 m, respectively. If the screw is operating with 80% of its volumetric capacity at a speed of 50 rpm, the actual discharge of the screw is_________ ton h^-1.

Answer: (196.00 to 200.00)

53. In a feed milling plant, it has been observed that 80% of the feed passes through IS sieve 340 (3.25 mm opening) and 80% of the ground feed passes through IS sieve 40 (0.42 mm opening). The power requirement to crush the material with a feed rate of 3 ton h^-1 is 6 kW. Power requirement to crush 2 ton h^-1 of the same feed using the above system so that 80% of the ground feed pass through IS sieve 15 (opening 0.157 mm) is _________kW.

Answer: (7.90 to 8.10)

54. Solid food particles having nominal size of 0.2 mm with shape factor of 0.8 and density of 1040 kg m-3 are to be fluidized using air at 28°C. The density and pressure of air at the above-mentioned condition are 1.175 kg m^-3 and 1.013×10⁵ Pa, respectively. The voidage at minimum fluidizing condition is 0.48. Use the value of ‘g’ as 9.81 m s^-2. If cross section of the empty bed is 0.5 m² and contains 520 kg of solids, the pressure drop at minimum fluidization condition is _______ kPa.

Answer: (9.80 to 10.40)

55. A single strength fruit juice is concentrated from 6% total solids (TS) to 24% by ultrafiltration. The feed stream has a flow rate of 12 kg min^-1. The ultrafiltration membrane tube has an inside diameter of 80 mm and the pressure difference applied across the membrane is 2 MPa. If the permeability constant is 4×10^-5 kg water m-² kPa^-1 s^-1, the length of the membrane tube is _________m.

Answer: (7.0 to 7.6)

GATE Exam 2018 Aerospace Engineering (AE) Question Paper With Answer Key

June 7, 2023November 19, 2018 by suresh84

Aerospace Engineering

General Aptitude (GA) Set-2

Q. 1 – Q. 5 carry one mark each.

1. “The dress _________ her so well that they all immediately _________ her on her appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented

(B) complimented, complemented

(D) complemented, complimented

Answer: (D)

2. “The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”
The word that best fills the blank in the above sentence is

(A) undiminished

(B) damaged

(D) uncertain

Answer: (A)

3. Find the missing group of letters in the following series:

BC, FGH, LMNO, _____

(A) UVWXY

(B) TUVWX

(D) RSTUV

Answer: (B)

4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(D) All the three shapes have the same area.

Answer: (A)

5. The value of the expression is _______.

(A) -1

(B) 0

(D) 3

Answer: (C)

Q. 6 – Q. 10 carry two marks each.

(A) 0

(B) 2

(D) 8

Answer: (C)

(A) 1096

(B) 1111

(D) 2486

Answer: (C)

(A) 50

(B) 89

(D) 175

Answer: (Marks to All)

9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54

(B) 65

(D) 76

Answer: (D)

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(D) One H will be followed by one T.

Answer: (B)

Aerospace Engineering

Q. 1 – Q. 25 carry one mark each.

1. Let be two distinct vectors that are not parallel. The vector is

(A) zero.

(B) orthogonal to alone.

(D) orthogonal to alone.

Answer: (D)

2. Consider the function All the roots of this function

(A) form a finite set of points.

(B) lie on an elliptical curve.

(D) lie on a hyperbolic curve.

Answer: (B)

3. Consider a vector field given by This vector field is

(A) divergence-free and curl-free.

(B) curl-free but not divergence-free.

(D) neither divergence-free nor curl-free.

Answer: (B)

4. A jet aircraft is initially flying steady and level at its maximum endurance condition. For the aircraft to fly steady and level, but faster at the same altitude, the pilot should

(A) increase thrust alone.

(B) increase thrust and increase angle of attack.

(D) reduce angle of attack alone.

Answer: (C)

5. The pilot of a conventional airplane that is flying steady and level at some altitude, deflects the port side aileron up and the starboard aileron down. The aircraft will then

(A) pitch, nose up.

(B) roll with the starboard wing up.

(D) roll with the port wing up.

Answer: (B)

6. A NACA 0012 airfoil has a trailing edge flap. The airfoil is operating at an angle of attack of 5 degrees with un-deflected flap. If the flap is now deflected by 5 degrees downwards, the C_L versus α curve

(A) shifts right and slope increases.

(B) shifts left and slope increases.

(D) shifts right and slope stays the same.

Answer: (C)

7. An airplane requires a longer ground roll to lift-off on hot summer days because

(A) the thrust is directly proportional to free-stream density.

(B) the thrust is directly proportional to weight of the aircraft.

(D) the runway friction is high on hot summer days.

Answer: (A)

8. The velocity profile in an incompressible, laminar boundary layer is shown in the figure below. U is the free-stream velocity, u(y) is the stream-wise velocity component. The area of the black shaded region in the figure below represents the

(A) boundary layer thickness.

(B) momentum thickness.

(D) shape factor.

Answer: (C)

9. The tangential velocity component ‘V’ of a spacecraft, which is in a circular orbit of radius ‘R’ around a spherical Earth (μ = GM → gravitational parameter of Earth) is given by the following expression.

(A)

(B)

(C)

(D)

Answer: (B)

10. Equation of the trajectory of a typical space object around any planet, in polar coordinates (r, θ) (i.e. a general conic section geometry), is given as follows. (h is angular momentum, μ is gravitational parameter, e is eccentricity, r is radial distance from the planet center, θ, is angle between vectors

(A)

(B)

(C)

(D)

Answer: (C)

11. In an elliptic orbit around any planet, the location at which a spacecraft has the maximum angular velocity is

(A) apoapsis.

(B) periapsis.

(D) a point at –90° from apoapsis.

Answer: (B)

12. The pitching moment of a positively cambered NACA airfoil about its leading edge at zero-lift angle of attack is

(A) negative.

(B) positive.

(D) zero.

Answer: (A)

13. In a low-speed wind tunnel, the angular location(s) from the front stagnation point on a circular cylinder where the static pressure equals the free-stream static pressure, is

(A) ± 38°

(B) ± 30°

(D) 0°

Answer: (B)

14. A thermocouple, mounted flush in an insulated flat surface in a supersonic laminar flow of air measures the

(A) static temperature.

(B) temperature greater than static but less than total temperature.

(D) temperature greater than total temperature.

Answer: (B)

15. A shock wave is moving into still air in a shock tube. Which one of the following happens to the air?

(A) static temperature increases, total temperature remains constant.

(B) static temperature increases, total temperature increases.

(D) static pressure increases, total temperature remains constant.

Answer: (B)

16. The highest limit load factor experienced by a civil transport aircraft is in the range

(A) 0.0 – 2.0

(B) 2.0 – 5.0

(D) 8.0 – 10.0

Answer: (B)

17. Determine the correctness or otherwise of the following statements, [a] and [r]:

[a] A closed-section box beam configuration is used in aircraft wings.

[r] Closed-section box beam configuration is capable of resisting torsional loads.

(A) Both [a] and [r] are true and [r] is the correct reason for [a].

(B) Both [a] and [r] are true but [r] is not the correct reason for [a].

(D) [a] is true but [r] is false.

Answer: (A)

18. The first law of thermodynamics is also known as conservation of

(A) mass.

(B) momentum.

(D) species.

Answer: (C)

19. In an ideal gas turbine cycle, the expansion in a turbine is represented by

(A) an isenthalpic process.

(B) an isentropic process.

(D) an isochoric process.

Answer: (B)

20. The determinant of the matrix is ______ (accurate to one decimal place).

Answer: (0.0 to 0.0)

21. The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K).

Answer: (1185.00 to 1186.50)

22. For a damped single degree of freedom system with damping ratio of 0.1, ratio of two successive peak amplitudes of free vibration is ___________ (accurate to two decimal places).

Answer: (1.75 to 1.95)

23. The natural frequency (in rad/s) of the spring-mass system shown in the figure below is _____ (accurate to one decimal place).

Answer: (2.0 to 2.0)

24. The stagnation pressures at the inlet and exit of a subsonic intake are 100 kPa and 98 kPa, respectively. The pressure recovery of this intake will be ______ (accurate to two decimal places).

Answer: (0.98 to 0.98)

25. A combustor is operating with a fuel-air ratio of 0.03. If the stoichiometric fuel-air ratio of the fuel used is 0.06, the equivalence ratio of the combustor will be _______ (accurate to two decimal places).

Answer: (0.50 to 0.50)

Q. 26 – Q. 55 carry two marks each.

26. The solution of the differential equation given that 𝑦=0 and at 𝑥=0 is

(A)

(B)

(C)

(D)

Answer: (B)

27. The relation between pressure (p) and velocity (V) for a steady, isentropic flow at two points along a streamline is, (c is a constant)

Answer: (C)

28. A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be –1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:

(A) –3.5

(B) –2.9

(D) –0.75

Answer: (C)

29. A solid circular shaft of diameter d is under pure torsion of magnitude T. The maximum tensile stress experienced at any point on the shaft is

(A)

(B)

(C)

(D)

Answer: (D)

30. A clamped-clamped beam, subjected to a point load P at the midspan, is shown in the figure below. The magnitude of the moment reaction at the two fixed ends of the beam is

(A) PL/2

(B) PL/4

(D) PL/16

Answer: (C)

31. Which of the following statement(s) is/are true about the state of a body in plane strain condition?

P: All the points in the body undergo displacements in one plane only, for example the x-y plane, leading to ε_zz = γ_xz = γ_yz = 0.

Q: All the components of stress perpendicular to the plane of deformation, for example the x-y plane, of the body are equal to zero, i.e. σ_zz = τ_xz = τ_yz = 0.

R: Except the normal component, all the other components of stress perpendicular to the plane of deformation of the body, for example the x-y plane, are equal to zero, i.e. σ_zz ≠ 0, τ_xz = τ_yz = 0.

(A) P only

(B) Q only

(D) P and R

Answer: (D)

32. An aircraft with a turbojet engine flies at a velocity of 100 m/s. If the jet exhaust velocity is 300 m/s, the propulsive efficiency of the engine, assuming a negligible fuel-air ratio, is

(A) 0.33

(B) 0.50

(D) 0.80

Answer: (B)

33. An aircraft with a turboprop engine produces a thrust of 500 N and flies at 100 m/s. If the propeller efficiency is 0.5, the shaft power produced by the engine is

(A) 50 kW

(B) 100 kW

(D) 500 kW

Answer: (B)

34. An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (𝛾) is 1.4, the isentropic efficiency of the compressor is

(A) 0.94

(B) 0.81

(D) 0.63

Answer: (B)

35. A rocket has an initial mass of 150 kg. After operating for a duration of 10 s, its final mass is 50 kg. If the acceleration due to gravity is 9.81 m/s² and the thrust produced by the rocket is 19.62 kN, the specific impulse of the rocket is

(A) 400 s

(B) 300 s

(D) 100 s

Answer: (C)

Q. 26 – Q. 55 carry two marks each.

36. Consider the vector field where The contour integral is tangent to the contour that encloses the origin, is __________ (accurate to two decimal places).

Answer: (6.25 to 6.35)

37. The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to equi-potential lines of the potential function is _______ (accurate to two decimal places).

Answer: (0.68 to 0.73)

38. Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m³, g = 9.81 m/s², R = 287 J/(kg-K)), the density (in kg/m³) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).

Answer: (0.85 to 0.88)

39. Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m³, g as 9.81 m/s² and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).

Answer: (9.80 to 9.81)

40. An aircraft with mass of 400,000 kg cruises at 240 m/s at an altitude of 10 km. Its lift to drag ratio at cruise is 15. Assuming g as 9.81 m/s², the power (in MW) needed for it to cruise is _______ (accurate to two decimal places).

Answer: (62.00 to 63.50)

41. A statically-stable aircraft has a 𝐶_𝐿𝛼= 5 (where the angle of attack, α, is measured in radians). The coefficient of moment of the aircraft about the center of gravity is given as 𝐶_{𝑀,𝑐.𝑔}=0.05−4𝛼. The mean aerodynamic chord of the aircraft wing is 1 m. The location (positive towards the nose) of the neutral point of the aircraft from the center of gravity is ______ (in m, accurate to two decimal places).

Answer: (-0.81 to -0.79)

42. An aircraft with a gross weight of 2000 kg, has a speed of 130 m/s at sea level, where the conditions are: 1 atmosphere (pressure), 288 K (temperature), and 1.23 kg/m³ (density). The speed (in m/s) required by the aircraft at an altitude of 9000 m, where the conditions are: 0.31 atmosphere, 230 K, and 0.47 kg/m³, to maintain a steady, level flight is ________ (accurate to two decimal places).

Answer: (209.00 t0 211.00)

43. A pitot probe on an aircraft in a steady, level flight records a pressure of 55,000 N/m². The static pressure and density are 45,280 N/m2 and 0.6 kg/m³, respectively. The wing area and the lift coefficient are 16 m² and 2, respectively. The wing loading (in N/m²) on this aircraft is _________ (accurate to one decimal place).

Answer: (18000 to 19440)

44. A spacecraft forms a circular orbit at an altitude of 150 km above the surface of a spherical Earth. Assuming the gravitational parameter, μ = 3.986 × 10¹⁴ m³/s² and radius of earth, RE = 6,400 km, the velocity required for the injection of the spacecraft, parallel to the local horizon, is _______________ (accurate to two decimal places).

Answer: (7.80 to 7.80 (or) 7800 to 7802)

45. Air at 50 kPa pressure and 400 K temperature flows in a duct at Mach 3.0. A part of the flow leaks through an opening on the duct wall into the ambient, where the pressure is 30 kPa. The maximum Mach number achieved in the discharge is _______ (accurate to two decimal places). (Ratio of specific heats of air is 𝛾=1.4).

Answer: (3.30 to 3.40)

46. Consider a 20° half-angle wedge in a supersonic flow at Mach 3.0 at standard sea-level conditions. If the shock-wave angle on the wedge is 36°, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).

Answer: (1.90 to 2.20)

47. The boundary layer thickness at the location of a sensor on a flat plate in an incompressible, laminar flow of air is required to be restricted to 1 mm for an effective measurement. If the flow velocity is 20 m/s with 1 bar pressure, 300 K temperature, and 1.789×10^˗5 kg/(m-s) viscosity, the maximum distance (in mm) of the sensor location from the leading edge is ________ (accurate to one decimal place).

Answer: (47.0 to 55.0)

48. Gross weight of an airplane is 7000 N, wing area is 16 m², and the maximum lift coefficient is 2.0. Assuming density at the altitude as 1.23 kg/m³, the stall speed (in m/s) of the aircraft is _________ (accurate to two decimal places).

Answer: (18.80 to 18.90)

49. A thin-walled tube with external radius of 100 mm and wall thickness of 2 mm, is fixed at one end. It is subjected to a compressive force of 1 N acting at a point on the circumference parallel to its length. The maximum normal stress (in kPa) experienced by the structure is _____________ (accurate to two decimal places).

Answer: (-2.50 to -2.20)

50. A 1 m long massless cantilever beam oscillates at 2Hz, while a 60 kg mass is attached at the tip of it. The flexural rigidity of the beam (in kN-m²) is _________________ (accurate to two decimal places)..

Answer: (3.10 to 3.20)

51. A cantilever beam having a rectangular cross-section of width 60 mm and depth 100 mm, is made of aluminum alloy. The material mechanical properties are: Young’s modulus, E = 73 GPa and ultimate stress, σ_u =480 MPa. Assuming a factor of safety of 4, the maximum bending moment (in kN-m) that can be applied on the beam is _____ (accurate to one decimal place).

Answer: (12.0 to 12.0)

52. The components of stress in a body under plane stress condition, in the absence of body forces, is given by:

𝜎_𝑥𝑥=𝐴𝑥²; 𝜎_𝑦𝑦= 12𝑥²−6𝑦² and 𝜎_𝑥𝑦=12𝑥𝑦.

The coefficient, A, such that the body is under equilibrium is _____ (accurate to one decimal place).

Answer: (-6.0 to -6.0)

53. An axial compressor rotor with 50 % degree of reaction, operates with an axial velocity of 200 m/s. The absolute flow angle at the inlet of the rotor is 22° with reference to the axial direction. If the axial velocity is assumed to remain constant through the rotor, the magnitude of the relative velocity (in m/s) at the rotor exit is __________ (accurate to one decimal place).

Answer: (215.0 to 216.5)

54. The relative velocity of air leaving a straight radial impeller of a centrifugal compressor is 100 m/s. If the impeller tip speed is 200 m/s, for a slip free operation, the absolute velocity (in m/s) at the impeller exit is _________ (accurate to one decimal place).

Answer: (222.0 to 225.0)

55. An aircraft wind tunnel model, having a pitch axis mass moment of inertia (I_yy) of 0.014 kg-m², is mounted in such a manner that it has pure pitching motion about its centre of gravity, where it is supported through a frictionless hinge. If the pitching moment (M) derivative with respect to angle of attack (α), denoted by ‘M_α’, is -0.504 N-m/rad and the pitching moment (M) derivative with respect to pitch rate (q), denoted by ‘M_q’, is -0.0336 N-m/(rad/s), the damping ratio of the resulting motion due to an initial disturbance in pitch angle is approximately _________ (accurate to three decimal places).

Answer: (0.195 to 0.205)