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Gate 2017 Mining Engineering Question Paper 12th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mining Engineering 12th Feb 2017

Subject Name: Mining Engineering

Duration : 180

Total Marks: 100

1. Which one of the following plots represents the relationship xy = c, where c is a positive constant

(A) I

(B) II

(D) IV

Ans: (C)

2. F(y) and f(y) are the probability distribution function and density function respectively of continuous variable Y in the interval (0, ∞). Which one of the following is TRUE?

(A)

(B)

(C)

(D)

Ans: (B)

3. The position vector of a moving particle is given by The acceleration of the particle in the direction of the motion is

(A)

(B)

(C)

(D)

Ans: (D)

4. The value of

(A)

(B)

(D) 0

Ans: (A)

5. Components of a 2-D stress tensor in Cartesian coordinate are σ_xx = 5.0 MPa, σ_yy = −10.0 MPa, and τ_xy = 2.0 MPa. The traction vector in MPa acting on a plane having outward normal is

(A)

(B)

(C)

(D)

Ans: (B)

6. If only two members form a truss joint and no external load or support reaction is applied to the joint, the members

(A) have infinite force

(B) have equal but opposite force

(D) have unequal forces

Ans: (C)

7. A multi-pint borehole extensometer is used to monitor

(A) convergence between the roof and the floor

(B) strain between fixed points along a borehole

(D) changing distances between fixed points along a borehole

Ans: (D)

8. The failure load of a point load test specimen having diameter 45 mm is 6000 N. The uncorrected point load index in MPa is ______

Ans: (2.9 to 3.0)

9. The beam shown in the figure is hinged at one end and rested on a roller at the other end. The free body diagram of the system is

(A)

(B)

(C)

(D)

Ans: (C)

10. Mineral A and B are produced from a deposit. Mineral A and B will be called coproducts if

(A) economics of mining depends upon the extraction of either mineral A or B

(B) economics of mining depends upon the extraction of both the minerals A and B

(D) minerals A and B are produced in equal quantity

Ans: (B)

11. Semi-variogam modeling is used for reserve estimation of mineral deposit by

(A) polygonal method

(B) distance weighting method

(D) nearest neighbor method

Ans: (C)

12. Which one of the following does NOT belong to the direct operating cost of mine?

(A) Administrative cost

(B) Royalty

(D) Explosive cost

Ans: (A)

13. Lane’s algorithm is applied to determine

(A) mill cut-off grade

(B) mine production rate

(D) ultimate pit

Ans: (A)

14. In an underground coal mine a driller, wearing personal protective equipment, was going to workplace along the travelling roadway. A piece of rock fell down from the roof and hit the person on head causing serious injury. The cause of accident is

(A) unsafe act of the driller

(B) job stress

(D) unsafe condition

Ans: (D)

15. In a PERT network, the “time estimates” of an activity are the following: Optimistic time – 2 days, Most likely time – 4 days, and Pessimistic time – 12 days. The expected time and standard deviation of the activity in days are respectively

(A) 6.0 and 2.78

(B) 5.0 and 1.66

(D) 5.0 and 2.78

Ans: (B)

16. The magnetic bearing of a line is 65°30ʹ. If the declination is 4°30ʹW, the true bearing of the line in degrees is _____

Ans: (60 to 62)

17. A vertical photograph of a 40 m high hill is taken from 4.4 km height. If the focal length of the camera is 15 cm, the scale of the photograph is _____

(A) 1 in 29067

(B) 1 in 7267

(D) 1 in 9688

Ans: (A)

18. The operating conditions of a rotary rock drill are: applied thrust: 6.75 kN, revolution : 180 rpm, and penetration rate : 0.15 m/min. The work done per revolution in N-m is _____

Ans: (5.15 to 6.0)

19. The Absolute amount of energy and density of a booster and ANFO are given below.

The Relative bulk strength of booster is _______

Ans: (113 to 116 OR 1.13 to 1.16)

20. A deeply seated ore body dips at 70° having an average width of 60 m, The ore body, hanging wall, and footwall are competent. The suitable stoping method for this ore body is

(A) Post pillar cut and fill

(B) Shrinkage stoping

(D) Transverse sublevel open stoping

Ans: (D)

21. The results of the crossing point temperature experiments for coal A and B are shown in the figure.

The correct interpretation of the plot is that

(A) coal A is more prone to spontaneous heating than coal B

(B) coal B is more prone to spontaneous heating than coal A

(D) coal B is more prone to coal dust explosion than coal A

Ans: (B)

22. The “yellow boy” formed due to acid mine drainage mainly consists of

(A) Ferrous hydroxide

(B) Ferrous sulfate

(D) Ferric sulfate

Ans: (C)

23. A double ended ranging drum shearer is employed in a longwall mine of face length 150 m. The mining height is 3.5 m and depth of the web cut is 0.76 m. The cycle time for unidirectional cutting is 40 min. Considering bulk density of the coal to be 1.4 t/m³, hourly production from the face in tonne is ______

Ans: (835 to 840)

24. The strength of a stranded wire rope is proportional to

(A) the diameter of the rope

(B) square of the diameter of the rope

(D) inverse of the diameter of the rope

Ans: (B)

25. A 20 m thick and 30 m wide confined aquifer has two monitoring wells spaced 500 m apart along the direction of groundwater flow. The difference in water level between the wells is 2 m. The hydraulic conductivity is 50 m/day. The rate of flow in m³/day is

(A) 4

(B) 12

(D) 120

Ans: (D)

26. The y intercept of the tangent of curve y = x³ – x² + x – 1 at x = 1 is ____

Ans: (−2.0)

27. A rectangle has two of its corners on the x axis and the other two on the parabola y = 12 – x². The largest area of the rectangle is ______

Ans: (32)

28. The area of cross-section (x) of four rock samples and the respective applied loads (y) at failure under uniaxial loading are given below :

If the best fit line y = 4.88 x represents the above data, the coefficient of determination (R²) of the best fit line is _____

Ans: (0.96 to 0.98)

29. The following reading refer to a reciprocal leveling at staff stations A and B respectively:

The reduced level (RL) of staff station B in m is ______

Ans: (123 to 124.5)

30. The areas within the contour lines of a proposed site for an overburden dump are as follows:

The total volume of overburden in cubic meter that could be dumped within the 120 m and 195 m contour levels is _______

Ans: (174765 to 174765)

31. Total ore mined from a sub-level open stope of a copper deposit is measured to be 100000 tonne. The ore recovery and ore dilution during stoping are 90% and 20% respectively. The in situ Cu grade of the ore in the stope is 0.65%. The selling price of copper is Rs. 400/kg of metal. Ignoring any other metal losses in the downstream process of the ore, the revenue generated by selling the ore in Crores of rupees is ______

Ans: (20 to 23)

32. The block grade model of an ore deposit is shown in the figure below. The relationship between block value per tone (B_v) in rupees and the block grade in percentage (x) is given below:

B_v = −38500 + 700 × x, for x ≥ 55%

= −300 otherwise

The each square block contains 1000 tonne of material and the overall pit slope angle is 45°, the total value of pit determined by the floating cone algorithm in Lakhs of rupees is _____

Ans: (25 to 27)

33. A mine is being developed by bord and pillar method with a gallery size of 4.8 m ×4 m. The mine operates in 3 shifts per day and 6 faces are blasted per shift. The average pull per round of blast is 1.2 m and the bulk density of coal is 1.4 t/m³. If the OMS is 2.5, then the average manpower deployed in the development section per shift is ______

Ans: (46 to 47)

34. Consider the following linear programming problem:

Maximize Z = 6X + 10Y

Subject to X ≤ 4

Y ≤ 6

3X + 2Y ≤ 18

X ≥ 0, Y≥0

The maximum value of the objective function is ______

Ans: (71 to 73)

35. A mining company having three mines A, B and C supplies coal to three power plants P, Q and R located close to the mines. The daily production capacities of the three mines in tonnes are 700, 1200 and 1100 respectively. The daily requirements at the power plants in tones are 1000, 1000, and 1000 respectively. The transportation costs in rupees per tonne is given in the matrix below:

The total cost of coal transportation in rupees from the three mines to three power plants using the least-cost method is ______

Ans: (65000 to 67000)

36. The series-parallel configuration of a system, consisting of 6 independent components A, B, C, D, E and F with their individual reliability, is

Shown in the figure :

The reliability of the system is _____

Ans: (0.96 to 0.97)

37. 500 coal miners were randomly selected from an underground coal mine. It was found that 50 workers experienced an injury in the year 2014. The distribution of injury based on younger age group (age ≤ 40 years) and older age group (age > 40 years) generated the following cross classification table.

The odd of injury for the younger age group compared to the older age group is _______

Ans: (1.6 to 1.7)

38. A bord and pillar panel is being planned at a depth of 300 m. The dimension of square pillar is 35 m centre-to-centre. The average unit weight of the overburden rock is 25 kN/m³. If the strength of the pillar is 14.0 MPa,the gallery width in m for a safety factor of 1.3 is _____

Ans: (5.5 to 6.0)

39. A sandstone sample having 15% moisture content and volume of 75 cm³ weighs 180 g. If the grain density is 2.6 g/cm³, porosity of the sample in % is _______

Ans: (19.5 to 20)

40. Let σ₁ and σ₃ are major and minor principal stresses respectively. The equation σ₁ = f(σ₃) denotes the failure envelop of a rock as shown in the figure. Match the zones (P, Q, R and S) with the legend code.

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

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

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

Ans: (B)

41. A blasted muck of mass m is being lifted from a shaft of diameter d by an arrangement of two pulleys as shown in the figure. Ignoring friction in the pulleys, as the height h decreases, tension in the ropes

(A) increases

(B) decreases

(D) increases until h > d, then decreases

Ans: (A)

42. The longitudinal section of stope is given in the figure. Match the different labeled stope features (P, Q, R, S and T) with their corresponding nomenclatures.

(A) P-2, Q-3, R-1, S-5, T-4

(B) P-5, Q-1, R-2, S-3, T-4

(D) P-1, Q-5, R-3, S-4, T-2

Ans: (C)

43. To break a volume of 30000 cubic meter of overburden per month in an open cast mine, the number of blast hole drills required for the following data is _____

Spacing and burden of blast holes : 6.0 m × 4.0 m

Hours scheduled per shift : 5

Number of shifts per day : 2

Weeks per month : 4

Drilling days per week : 5

Drilling rate : 30.67 m/h

Ans: (1 to 3)

44. Two inclined coal seams with their accesses are shown in the figure. Match the labeled access (P, Q, R, S) with their corresponding names.

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

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

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

Ans: (D)

45. Ground reaction curve (GRC) of a tunnel roof under hydrostatic stress field is given b y p_g = 10 – 0.75u, where p_g is the required support pressure in MPa and u is radial displacement in mm. A uniform support is installed at the boundary of the tunnel providing support reaction (SR) as p_s = 1.5 – 3.0, for u ≥ 2 mm. Considering GRC = SR, the support pressure in MPa is _____

Ans: (5.5 to 6.0)

46. If the rank of the following matrix is less than 3, the values of x are

(A) 1, −1/2

(B) 1, 1/2

(D) 2, −3/4

Ans: (A)

47. The discharge rate of a water pump is 0.25 m³/s. The diameter of the discharge and suction nozzles are 300 and 350 respectively. The measured pressure at the discharge end located 0.25 m above the centerline of the impeller is 150 kN/m² and the pressure at the suction gage located at the centre line of the impeller 20 kN/m². Specific weight of water is 9810 N/m³ The total dynamic head for the above installation in m is ______

Ans: (13.5 to 14.0)

48. In a mine, 200 and 250 persons are deployed in t he Panels A and B (shown in figure) respectively in the largest shift. The panel produce 400 and 500 tonne/day respectively. The resistances of panels A and B are 0.3 ns²m⁻⁸ and 0.4 Ns²m⁻⁸ respectively and the combined resistance of shaft and trunk airways is 0.5 Ns²m⁻⁸. The operating static pressure of the fan in Pa to provide the minimum air quantities in the panels as per CMR 1957 is ____

Ans: (1185 to 1189)

49. In an auxiliary ventilation system, a fan is installed inside a 100 m long and 600 mm diameter duct to ventilate a blind heading face. The frictional coefficient of the duct is 0.0066 Ns²m⁻⁴ and the static pressure characteristic of the fan is represented by :

P_s = 5Q² – 250Q + 1000

where, P_s is in Pa and Q is in m³/s. The quantity of air delivered by the fan in m³/s is _______

Ans: (2.5 to 2.8)

50. A stream flowing at 15 m³/s has a tributary feeding into it with a flow rate of 7 m³/s. The concentrations of chloride at the upstream of the junction and that of the tributary are 30 mg/L, and 50 mg/L respectively. Treating chloride as conservative substance and assuming complete mixing of two stream, the concentration of chloride in mg/L at the downstream is ______

Ans: (36 to 37)

51. A sample of mine water has 100 mg/L of Ca²⁺ and 10 mg/L of Mg²⁺. The equivalent weights of Ca²⁺ and Mg²⁺ are 20 mg/meq and 12.2 mg/meq respectively. The hardness of mine water in unit of mg/L as CaCO₃ is _______

Ans: (290 to 292)

52. A 1.1 m wide belt conveyor carries materials of bulk density 1.35 t/m³ at a speed of 1.75 m/s. The average cross-sectional area of material is equal to w²/11, where w is the width of the belt in m. The carrying capacity of the conveyor in t/h is ______

Ans: (935 to 936)

53. In a book of 600 pages, there are 60 typographical errors. Assuming Poisson distribution for the number of errors per page, the probability of no errors ini randomly chosen 4 pages is ______

Ans: (0.66 to 0.68)

54. Match the special methods of shaft sinking with rock mass conditions and scope of application.

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

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

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

Ans: (D)

55. A wheel of radius 0.5 m rotates under a moment of 2000 N-m as shown in the figure. A block brake is used to stop the wheel. If the coefficient of static friction between the wheel and the block brake is 0.3, the smallest force of P in N required to stop the wheel is _______

Ans: (5975 to 5990)

56. The bacteria in milk are destroyed when it ____ heated to 80 degree Celsius.

(A) would be

(B) will be

(D) was

Ans: (C)

57. _______ with someone else’s email account is now a very serious offence.

(A) Involving

(B) Assisting

(D) Incubating

Ans: (C)

58. Consider the following sentences:

All benches are beds. No bed is a bulb. Some bulbs are lamps.

Which of the following can be inferred?

i. Some beds are lamps.

ii. Some lamps are beds.

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (D)

59. If the radius of a right circular cone is increased by 50%, its volume increases by

(A) 75%

(B) 100%

(D) 237.5%

Ans: (C)

60. The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9, 16, 18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is

(A) 5

(B) 6

(D) 8

Ans: (D)

61. The old concert hall was demolished because of fears that the foundation would be affected by the construction of the new metro line in the area. Modern technology for underground metro construction tried to mitigate the impact of pressurized air pockets created by the excavation of large amounts of soil. But even with these safeguards, it was feared that the soil below the concert hall would not be stable.

From this, one can infer that

(A) the foundations of old buildings create pressurized air pockets underground, which are difficult to handle during metro construction.

(B) metro construction has to be done carefully considering its impact on the foundations of existing buildings.

(D) pressurized air can be used to excavate large amounts of soil from underground areas.

Ans: (B)

62. Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. .Preferences of lower ranked applicants are ignored during allocation.

Given that data below, which room will Ajit stay in?

(A) P

(B) Q

(D) S

Ans: (B)

63. The last digit (2171)⁷ + (2172)⁹ + (2173)¹¹ + (2174)¹³ is

(A) 2

(B) 4

(D) 8

Ans: (B)

64. Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects, Job Q on 3 objects, Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

(A) 2 hours

(B) 2.5 hours

(D) 3.5 hours

Ans: (A)

65. The bar graph below shows the output of five carpenters over one month, each of whom made different items of furniture: chairs, tables, and beds.

Consider the following statements.

i. The number of beds made by carpenter C2 is exactly the same as the number of tables made by carpenter C3.

ii. The total number of chairs made by all carpenters is less than the total number of tables.

Which one of the following is true?

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (C)

Gate 2017 Mechanical Engineering Question Paper 4th Feb 2017 Session 2 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mechanical Engineering 4th Feb 2017 Session 2

Subject Name: Mechanical Engineering

Duration : 180

Total Marks: 100

1. A mass m of a perfect gas at pressure p₁ and volume V₁ undergoes an isothermal process. The final pressure is p₂ and volume is V₂. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is

(A)

(B)

(C)

(D)

Ans: (B)

2. Which one of the following statements is TRUE for the ultrasonic machining (USM) process?

(A) In USM, the tool vibrates at subsonic frequency.

(B) USM does not employ magnetostrictive transducer.

(D) USM often uses a slurry comprising abrasive-particles and water.

Ans: (D)

3. The standard deviation of linear dimensions P and Q are 3μm, respectively. When assembled, the standard deviation (in μm) of the resulting linear dimension (P+Q) is ________

Ans: (5)

4. The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes.

(A) 2P

(B) 4P

(D) 16P

Ans: (D)

5. The state of stress at a point is σ_x = σ_y = σ_z = τ_xz = τ_zx = τ_yz = τ_zy = 0 and τ_xy = τ_yx = 50MPa. The maximum normal stress (in MPa) at that point is _________

Ans: (49.9 to 50.1)

6. The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___________

Ans: (5)

7. Which one of the following statement is TRUE?

(A) Both Pelton and Francis turbines are impulse turbines.

(B) Francis turbine is a reaction turbine but Kaplan turbine is an impulse turbine.

(D) Kaplan turbine is an axial – flow reaction turbine.

Ans: (D)

8. Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ____________

Ans: (0.75)

9. A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear)

(A)

(B)

(C)

(D)

Ans: (A)

10. It is desired to make a product having T-shaped cross-section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?

(A) Welding

(B) Casting

(D) Machining

Ans: (C)

11. The heat loss from a fin is 6W. The effectiveness and efficiency of the fin are 3 and 0.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is __________.

Ans: (7.9 to 8.1)

12. For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?

(A) 6 per hour

(B) 10 per hour

(D) 24 per hour

Ans: (D)

13. For the stability of a floating body the

(A) centre of buoyancy must coincide with the centre of gravity

(B) centre of buoyancy must be above the centre of gravity

(D) metacentre must be above the centre of gravity

Ans: (D)

14. The divergence of the vector −yi + xj __________

Ans: (0)

15. For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x) = 5x²+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x =10 mm is ________.

Ans: (110)

16. A sample of 15 data is a follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is

(A) 4

(B) 13

(D) 20

Ans: (C)

17. If a mass of moist air contained in a closed metallic vessel is heated, then its

(A) relative humidity decreases

(B) relative humidity increases

(D) specific humidity decreases

Ans: (A)

18. In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100mm and 160mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counterclockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is _____________

Ans: (0.99 to 1.01)

19. A machine component made of a ductile material is subjected to a variable loading with σ_min = −50 MPa and σ_max = 50 MPa. If the corrected endurance limit and the yield strength for the material are σ_e = 100 MPa and σ_y = 300 MPa, the factor of safety is ______

Ans: (1.99 to 2.01)

20. The crystal structure of aluminium is

(A) body-centred cubic

(B) face-centred cubic

(D) body-centred tetragonal

Ans: (B)

21. A steel bar is held by two fixed supports as shown in the figure and is subjected to an increases of temperature ∆T =100℃. and 200GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is

Ans: (218 to 222)

22. The Laplace transform of te^t is

(A)

(B)

(C)

(D)

Ans: (B)

23. Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by τ_w. The axial positions x1 and x2 on the plate are measured from the leading edge in the direction of flow. If x₂ > x₁, then

(A)

(B)

(C)

(D)

Ans: (C)

24. A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency ω of this single degree of freedom system is

(A)

(B)

(C)

(D)

Ans: (A)

25. Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe₃C) is _________.

Ans: (6.3 to 7.0)

26. In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the maximum shear angle to the minimum shear angle during machining is ___________

Ans: (1.45 to 1.53)

27. A cylindrical pin of diameter is electroplated. Plating thickness is 2.0^±0.005 mm. Neglecting the gauge tolerance, the diameter (in mm, up to 3 decimal points accuracy) of the GO ring gauge to inspect the plated pin is _________.

Ans: (29.030 to 29.030)

28. A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.

Ans: (6)

29. In a counter-flow heat exchanger, water is heated at the rate of 1.5kg/s from 40°C to 80°C by an oil entering at 120°C and leaving at 60°C. The specific heats of water and oil are 4.2kJ/kg.K and 2kJ/kg.K respectively. The overall heat transfer coefficient is 400 W/m².K. The required heat transfer surface area (in m²) is

(A) 0.104

(B) 0.022

(D) 21.84

Ans: (D)

30. The rod PQ of length L = √2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s². The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML²/12). At this instant, the magnitude of angular acceleration (in radian/s2) of the rod is ____________

Ans: (7.25 to 7.75)

31. A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt C is.

(A) 13

(B) 15

(D) 30

Ans: (C)

32. The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m³ and 300K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5bar. If the gas constant of air is R = 287 J/kg. K and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel is

(A) 1.67

(B) 3.33

(D) 6.66

Ans: (C)

33. For the laminar flow of water over a sphere, the drag coefficient C_F is defined as C_F = F/(ρU²D²), where F is the drag force, ρ is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m³. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________

Ans: (19.9 to 20.1)

34. A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

(A) −0.5

(B) −0.69

(D) −1.0

Ans: (B)

35. A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is _________.

Ans: (120)

36. In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg and 1800 kJ/kg, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg and 124 kJ/kg, respectively. The specific steam consumption (in kg/k W.h) of the cycle is ______

Ans: (3.5 to 3.7)

37. A calorically perfect gas (specific heat at constant pressure 1000 J/kg.K) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K and 400 K. respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is.

(A) 6.14

(B) 7.00

(D) 8.00

Ans: (B)

38. Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For m₁ = 10kg, m₂ = 5kg and m₃ = 2.5 kg and for a shaft angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is _________.

Ans: (0)

39. A strip of 120 mm width and 8mm thickness is rolled between two 300 mm-diameter rolls to get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30 m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive the two rolls is _________.

Ans: (9.4 to 9.8)

40. A product made in two factories p and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:

Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (X-Y), in Rupees, is

(A) 0

(B) 15

(D) 105

Ans: (A)

41. One kg of an ideal gas (gas constant R = 287 J/kg.K) undergoes an irreversible process from state-1 (1 bar, 300 K) to state -2 (2 bar, 300 K). The change in specific entropy (s₂ – s₁) of the gas (in J/kg. K) in the process is ___________

Ans: (−201 to −197)

42. A 60 mm-diameter water jet strikes a plate containing a hole of 40mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is 1000 kg/m³. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________

Ans: (627 to 629)

43. The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m³ flowing through a pipe. The acceleration due to gravity is 9.81 m/s². If the manometric fluid is water (density 1000 kg/m³) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is ____________

Ans: (19 to 21)

44. A metal ball of diameter 60mm is initially at 220 °C. The ball is suddenly cooled by an air jet of 20°C. The heat transfer coefficient is 200 W/m².K and 9000kg/m³, respectively. The ball temperature (in °C) after 90 seconds will be approximately.

(A) 141

(B) 163

(D) 210

Ans: (A)

45. A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction μ varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is _________

Ans: (0.49 to 0.51)

46. The surface integral over the surface S of the sphere x² + y² + z² = 9, where F=(x+y) i+ (x+z) j+(y+z) k and n is the unit outward surface normal, yields ______.

Ans: (225 to 227)

47. Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of the total acceleration (in m/s²) of point P of the block with respect to fixed point O is ________

Ans: (243 to 244)

48. During the turning of a 20mm-diameter steel bar at a spindle speed of 400 rpm, a tool life of 20 minute is obtained. When the same bar is turned at 200 rpm, the tool life becomes 60 minute. Assume that Taylor‟s tool life equation is valid. When the bar is turned at 300 rpm, the tool life (in minute) is approximately.

(A) 25

(B) 32

(D) 50

Ans: (B)

49. Consider the matrix whose eigenvectors corresponding to eigenvalues λ₁ and λ₂ are respectively. The value of is ______

Ans: (0)

50. The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s², the natural frequency (in radian/s) of the compound pendulum is _________.

Ans: (15 to 16)

51. Consider the differential equation 3y”(x) + 27y(x) = 0 with initial conditions y(0) = 0 and y'(0) = 200. The value of y at x = 1 is ______

Ans: (93 to 95)

52. If f(z) = (x² + ay²) + ibxy is a complex analytic function of z = x + iy, where , then

(A) a = −1, b = −1

(B) a = −1, b = 2

(D) a = 2, b = 2

Ans: (B)

53. A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:

The minimum project completion time (in days) is ______

Ans: (30)

54. Maximize Z = 5x₁ + 3x₂

Subject to

x₁ + 2x₁₂ ≤ 10,

x₁ – x₂ ≤ 8,

x₁, x₁₂ ≥ 0.

In the starting Simplex tableau, x₁ and x₂ are non-basic variables and the value of Z is zero. The value of Z in the next Simplex tableau is _________.

Ans: (40)

55. The principal stresses at a point in a critical section of a machine component are σ₁ = 60MPa, σ₂ = 5MPa and σ₃ = −40 Mpa. For the material of the component, the tensile yield strength is σ_y = 200 MPa. According to the maximum shear stress theory, the factor of safety is

(A) 1.67

(B) 2.00

(D) 4.00

Ans: (B)

56. If you choose plan P, you will have to _______ plan Q, as these two are mutually _________.

(A) forgo, exclusive

(B) forget, inclusive

(D) adopt, intrusive

Ans: (A)

57. P looks at Q while Q looks at R. P is married, R is not. The number of people in which a married person is looking at an unmarried person is

(A) 0

(B) 1

(D) Cannot be determined

Ans: (B)

58. If a and b are integers and a – b is even, which of the following must always be even?

(A) ab

(B) a² + b² + 1

(D) ab – b

Ans: (D)

59. A couple has 2 children. The probability that both children are boys if the older one is a boy is

(A) 1/4

(B) 1/3

(D) 1

Ans: (C)

60. The ways in which this game can be played __________ potentially infinite.

(A) is

(B) is being

(D) are being

Ans: (C)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following closest in meaning to “cleaving”?

(A) Deteriorating

(B) Arguing

(D) Splitting

Ans: (D)

62. There 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how may ways can 4 such pairs be formed?

(A) 74

(B) 76

(D) 80

Ans: (C)

63. In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10°C) and a month in summer (average temperature 30°C).

Consider the following statements based on the data shown above:

(i) Over the given months, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer.

(ii) There are at last four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.

Which one of the following options is correct?

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (B)

64. All people in a certain island are either „Knights‟ or „Knaves‟ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

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

(A) Both P and Q are knights

(B) P is a knight; Q is a knave

(D) The identities of P, Q cannot be determined

Ans: (D)

65. X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5days to plough the same field. How many days will it take X bullocks alone to plough the field?

(A) 30

(B) 35

(D) 45

Ans: (A)

Gate 2017 Mechanical Engineering Question Paper 4th Feb 2017 Session 1 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mechanical Engineering 4th Feb 2017 Session 1

Subject Name: Mechanical Engineering

Duration : 180

Total Marks: 100

1. A motor driving a solid circular steel shaft transmits 40kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is ________MPa.

Ans: (60.79)

2. Consider the following partial differential equation for u(x,y) with the constat c > 1 :

Solution of this equation is

(A) u(x, y) = f(x + cy)

(B) u(x, y) = f(x – cy)

(D) u(x, y) = f(cx – y)

Ans: (B)

3. The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered by the particle from t = 0 to t= 5 s is __________m.

Ans: (11)

4. The damping ratio for a viscously damped spring mass system, governed by the relationship is given by

(A)

(B)

(C)

(D)

Ans: (B)

5. The differential equation for y(x) with the two boundary conditions has

(A) no solution

(B) exactly two solutions

(D) infinitely many solutions

Ans: (A)

6. Metric thread of 0.8 mm pitch is to be cut on a lathe. Pitch of the lead screw is 1.5 mm. If the spindle rotates at 1500 rpm, the speed of rotation of the lead screw (rpm) will be _________

Ans: (800)

7. The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.

Ans: (2909.9)

8. A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t², θ(t) = t, where t is time. The kinetic energy of the particle at time t = 2 is

(A) 4

(B) 12

(D) 24

Ans: (C)

9. The Poisson’s ratio for a perfectly incompressible linear elastic material is

(A) 1

(B) 0.5

(D) infinity

Ans: (B)

10. A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300K. The Coefficient of Performance (COP) of the heat pump is ___________.

Ans: (1.66)

11. Which one of the following is NOT a rotating machine?

(A) Centrifugal pump

(B) Gear pump

(D) Vane pump

Ans: (C)

12. Consider the schematic of a riveted lap joint subjected to tensile load F, as shown below. Let d be the diameter of the rivets, and S_f be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.

(A)

(B)

(C)

(D)

Ans: (A)

13. Water (density =1000 kg/m³) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s. If the pressure drop across the pipe is 100 kPa, the minimum power required to pump the water across the pipe, in watts, is _______

Ans: (100)

14. For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?

(A) It increases until the flow is fully developed.

(B) It is constant and is equal to the average velocity in the fully developed region.

(D) It is constant but always lower than the average velocity in the fully developed region.

Ans: (B)

15. Cylindrical pins of diameter 15^±⁰²⁰ mm are being produced on a machine. Statistical quality control tests show a mean of 14.995 mm and standard deviation of 0.004mm. The process capability index C_p is

(A) 0.833

(B) 1.667

(D) 3.750

Ans: (B)

16. The product of Eigen values of the matrix P is

(A) −6

(B) 2

(D) −2

Ans: (B)

17. Match the processes with their characteristics.

(A) P – 2, Q – 3, R – 1, S – 4

(B) P – 3, Q – 2, R – 1, S – 4

(D) P – 2, Q – 4, R – 3, S – 1

Ans: (A)

18. The Value of

(A) 0

(B) 3

(D) −1

Ans: (D)

19. In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will

(A) Increase by 25%

(B) Increase by 50%

(D) Reduce by 50%

Ans: (D)

20. A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ______.

Ans: (3.5)

21. Consider the two dimensional velocity field given by where a₁, b₁ , a₂ and b₂ are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?

(A) a₁ + b₁ = 0

(B) a₁ + b₂ = 0

(D) a₂ + b₁ = 0

Ans: (B)

22. Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.

(A) d/2

(B) πd/2

(D) πd

Ans: (A)

23. Saturated steam at 100°C condenses on the outside of a tube. Cold fluid enters the tube at 20° C and exists at 50°C. The value of the Log Mean Temperature Difference (LMTD) is ________°C.

Ans: (63.82)

24. In a metal forming operation when the material has just started yielding, the principal stresses are σ₁ = +180MPa, σ₂ = −100MPa, σ₃ = 0. Following Von Mises’ criterion, the yield stress is ________ MPa.

Ans: (245.76)

25. In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to

(A) Yield stress

(B) Proportional limit

(D) Fracture stress.

Ans: (C)

26. A parametric curve defined by in the range 0 ≤ u ≤ 1 is rotated about the X – axis by 360 degrees. Area of the surface generated is

(A) π/2

(B) π

(D) 4π

Ans: (C)

27. Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is 20μm, The central line average surface roughness Ra (in μm) is

(A) 5

(B) 6.67

(D) 20

Ans: (A)

28. A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L / 3from one of its ends. The bar is further supported using springs, each of stiffness k, located at the two ends. A particle of mass m = M/4 is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about O, the natural frequency of the systems is.

(A)

(B)

(C)

(D)

Ans: (B)

29. A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm², length = 1m, Young’s moduls = 100 GPa) from a height H of 10mm as shown (Figure is not to scale). If g = 10m/s², the maximum compression of the elastic bar is _______ mm.

Ans: (1.51)

30. One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at constant volume, c_v = 1000J/kg.K) n = at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100kJ of work is done on the system by a stirrer. The increase in entropy of the system is _________ J/K.

Ans: (287)

31. For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3m and 4m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________ radian/s.

Ans: (0.264)

32. In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100rpm. Let the number of teeth on the sun, planet and outer gears to be 50, 25, and 100, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is _________.

Ans: (3)

33. Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30°C and the relative humidity is 55%. Given that the saturation pressure of water at 30°C is 4246 Pa, the mass of water vapor per kg of dry air is _____________ grams.

Ans: (14.87)

34. Following data refers to the jobs (P, Q, R, S) which have arrived at a machine for scheduling. The shortest possible average flow time is ___________ days.

Ans: (15)

35. Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ____________.

Ans: (15)

36. Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below:

——————————–

N60 G01 X 30 Y 55 Z – 5 F 50

N70 G02 X 50 Y 35 R 20

N80 G01 Z 5

——————————–

The coordinates of the centre of the circular arc are :

(A) (30, 55)

(B) (50, 55)

(D) (30, 35)

Ans: (D)

37. Two black surfaces, AB and BC, of lengths 5m and 6m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor F₁₂ = 0.5 T₁ = 800 K, T₂ = 600 K, T_surrounding = 300 K and Stefan Boltzmann constant, σ = 5.67 × 10⁻⁸ W/(m²K⁴), the transfer rate from Surface 2 to the surrounding environment is ______kW.

Ans: (13.8)

38. Consider the matrix

Which one of the following statements about P is INCORRECT?

(A) Determinant of P is equal to 1.

(B) P is orthogonal.

(D) All Eigen values of P are real numbers

Ans: (D)

39. The Pressure ratio across a gas turbine (for air, specific heat at constant pressure, c_p =1040J / kg.K and ratio of specific heats, γ =1.4) is 10. If the inlet temperature to the turbine is 1200K and the isentropic efficiency is 0.9, the gas temperature at turbine exit is ______ K.

Ans: (679.38)

40. An initially stress-free massless elastic beam of length L and circular cross-section with diameter d (d << L) is held fixed between two walls as shown. The beam material has Young’s modulus E and coefficient of thermal expansion α .

If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to

(A) d

(B) d²

(D) d⁴

Ans: (B)

41. For the vector the value of is ______

Ans: (0)

42. A 10 mm deep cylindrical cup with diameter of 15mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto 2 decimal points accuracy) of the blank is _________ mm.

Ans: (28.72)

43. A machine element has an ultimate strength (σ_u) of 600 N/mm², and endurance limit (σ_en) of 250 N/mm². The fatigue curve for the element on log-log plot is shown below. If the element is to be designed for a finite of 10000 cycles, the maximum amplitude of a completely reversed operating stress is _________ N/mm².

Ans: (386.19)

44. A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s² and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.

Ans: (2.042)

45. Air contains 79% N₂ and 21% O₂ on a molar basis. Methane (CH₄) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N₂ in the products is __________

Ans: (73.83)

46. P(0,3), Q(0.5, 4), and R (1,5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson’s rule within limits x = 0 and x =1 for the curve. The difference between the two results will be.

(A) 0

(B) 0.25

(D) 1

Ans: (A)

47. Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×10⁷ W/m³. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.

Ans: (10)

48. Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is.

(A)

(B)

(C)

(D)

Ans: (A)

49. A block of length 200mm is machined by a slab milling cutter 34mm in diameter. The depth of cut and table feed are set at 2mm and 18mm/minute, respectively. Considering the approach and the over travel of the cutter to be same, the minimum estimated machining time per pass is _____________ minutes.

Ans: (12)

50. A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100e⁻^x GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.

Ans: (1.71)

51. Consider steady flow of an incompressible fluid through two long and straight pipes of diameters d₁ and d₂ arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, f = K(Re)⁻ⁿ where K and n are known positive constants and Re is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe 1 to that in pipe 2, is given by

(A)

(B)

(C)

(D)

Ans: (D)

52. The velocity profile inside the boundary layer for flow over a flat plate is given as where U_∞ is the free stream velocity and δ is the local boundary layer thickness. If δ * is the local displacement thickness, the value of is

(A)

(B)

(C)

(D)

Ans: (B)

53. For a steady flow, the velocity field is The magnitude of the acceleration of a particle at (1, −1) is

(A) 2

(B) 1

(D) 0

Ans: (C)

54. Two cutting tools with tool life equations given below are being compared :

Tool 1L VT^0.1 = 150

Tool 2: VT^0.3 = 300

Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ____ m/minute.

Ans: (106.21)

55. A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains, ε_xx = 0.001, ε_yy = 0.002, γ_xy = 0.003. The deformed length of the elongated diagonal, up to three decimal places, is _____ units.

Ans: (5.013)

56. A right – angled cone (with base radius 5cm and height 12cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.

By what angle (in radians) about P does the cone travel?

(A)

(B)

(C)

(D)

Ans: (D)

57. In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

(A) Rs. 20,000

(B) Rs. 30,000

(D) Rs. 40,000

Ans: (B)

58. As the two speakers became increasingly agitated, the debate became __________.

(A) lukewarm

(B) poetic

(D) heated

Ans: (D)

59. P,Q, and R talk about S’s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one Car. Only one of P, Q and R is right the number cars owned by S is.

(A) 0

(B) 1

(D) Cannot be determined

Ans: (A)

60. He was one of my best __________ and I felt his loss _________.

(A) friend, keenly

(B) friends, keen

(D) friends, keenly

Ans: (D)

61. Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, “There is no way you are good enough to play for your country.’’ James replied, “Maybe not, but at least I am the best player in my own family.”

Which one of the following can be inferred from this conversation?

(A) Mark was known to play better than James

(B) Steve was known to play better than Mark

(D) James played better than Steve

Ans: (B)

62. “Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that ‘A stronger instance than this of European prejudice with relation to this country has never come under my observations’ had no effect on his superiors.”

According to this paragraph, which of the statements below is most accurate?

(A) Stuart’s commander – in chief was moved by this demonstration of his prejudice.

(B) The Europeans were accommodating of the sepoys’ desire to weak their caste – marks.

(D) The commander– in – Chief was exempt from the European preiudice that dictated how the sepoys were to dress.

Ans: (C)

63. The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8(in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 litre of milk is plotted as a function of time, at two different temperatures, 25°C and 37°C.

Consider the following statements based on the data shown above:

(i) The growth in bacterial population stops earlier at 37°C as compared to 25°C

(ii) The time taken for curd formation at 25°C is twice the time taken at 37°C

Which one of the following options is correct?

(A) Only i

(B) only ii

(D) Neither i nor ii

Ans: (A)

64. Let S₁ be the plane figure consisting of the points (x,y) given by the inequalities |x – 1| ≤ 2 and |y + 2| ≤ Let S₂ be the plane figure given by the inequalities x – y ≥ −2, y ≥ 1, and x ≤ 3 Let S be the union of S₁ and S₂. The area of S is

(A) 26

(B) 28

(D) 34

Ans: (C)

65. What is the sum of the missing digits in the subtraction problem below?

(A) 8

(B) 10

(D) Cannot be determined

Ans: (D)

Gate 2017 Mathematics Question Paper 5th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mathematics 5th Feb 2017

Subject Name: Mathematics

Duration : 180

Total Marks: 100

1. Consider the vector space V = {a₀ + a₁x + a₂x² : a_i ∈ ℝ for i = 0, 1, 2} of polynomials of degree at most 2. Let f : V → ℝ be a linear functional such that f(1 + x) = 0, f(1 – x²) = 0 and f(x² – x) = 2. Then f(1 + x + x²) equals _____.

Ans: (1)

2. Let A be a 7 × 7 matrix such that 2A² A⁴ = I, where I is the identity matrix. If A has two distinct eigenvalues and each eigenvalue has geometric multiplicity 3, then the total number of nonzero entries in the Jordan canonical form of A equals ____.

Ans: (8)

3. Let f(z) = (x² + y²) + i2xy and g(z) = 2xy + i(y² – x²) for z = x + iy ∈ ℂ. Then, in the complex plane ℂ,

(A) f is analytic and g is not analytic

(B) f is not analytic and g is analytic

(D) both f and g are analytic

Ans: (B)

4. If is the Laurent series of the function for z ∈ ℂ\{2}, then a₋₂ equals _____.

Ans: (48)

5. Let f_n : [0, 1] → ℝ be given by Then the sequence (f_n)

(A) converges uniformly on [0,1]

(B) does NOT converge uniformly on [0, 1] but has a subsequence that converges uniformly on [0, 1]

(D) converges pointwise on [0, 1] but does NOT have a subsequence that converges uniformly on [0, 1]

Ans: (D)

6. Let C : x² + y² = 9 be the circle in ℝ² oriented positively. Then equals ____.

Ans: (36)

7. Consider the following statements :

(P) : There exists an unbounded subset of ℝ whose Lebesgue measure is equal to 5.

(Q) If f : ℝ → ℝ is continuous and g : ℝ → ℝ is such that f = g almost everywhere on ℝ, then g must be continuous almost everywhere on ℝ.

Which of the above statements hold TRUE?

(A) Both P and Q

(B) Only P

(D) Neither P nor Q

Ans: (B)

8. If x³y² is an integrating factor of (6y² + a xy) dx + (6xy + bx²) dy = 0, where a, b ∈ ℝ, then

(A) 3a – 5b = 0

(B) 2a – b = 0

(D) 2a + b = 0

Ans: (A)

9. If x(t) and y(t) are the solutions of the system with the initial conditions x(0) = 1 and y(0) = 1, then x(π/2) + y(π/2) equals _____.

Ans: (0)

10. If y = 3e^2x + e^−2x – αx is the solution of the initial value problem where α, β ∈ ℝ, ,then

(A) α = 3 and β = 4

(B) α = 1 and β = 2

(D) α = 1 and β = −2

Ans: (C)

11. Let G be a non-abelian group of order 125. Then the total number of elements in Z(G) = {x ∈ G : g x = x g for all g ∈ G} equals ______.

Ans: (5)

12. Let F₁ and F₂ be subfields of a finite field F consisting of 2⁹ and 2⁶ elements, respectively. Then the total number of elements in F₁ ⋂ F₂ equals ____.

Ans: (8)

13. Consider the normed linear space ℝ² equipped with the norm given by ||(x, y)|| = |x| + |y| and the subspace X = {(x, y) ∈ ℝ² : x = y}. Let f be the linear functional on X given by f(x, y) = 3x. If g(x, y) = αx + βy, α, β ∈ ℝ, is a Hahn-Banach extension of f on ℝ² then α – β equals _____.

Ans: (0)

14. In n ∈ ℤ, define where i² = −1. Then equals

(A) cosh(π)

(B) sinh(π)

(D) sinh(2π)

Ans: (D)

15. If the fourth order divided difference of f(x) = αx⁴ + 5x³ + 3x + 2, α ∈ ℝ, at the points 0.1, 0.2, 0.3, 0.4, 0.5 is 5, then α equals ___.

Ans: (5)

16. If the quadrature rule where c₁, c₂ ∈ ℝ, is exact for all polynomials of degree ≤ 1, then c₁ + 3c₂ equals _____.

Ans: (1)

17. If u(x, y) = 1 + x + y + f(xy), where f : ℝ² → ℝ is a differentiable function, then u satisfies

(A)

(B)

(C)

(D)

Ans: (C)

18. The partial differential equation is

(A) hyperbolic along the line x + y = 0

(B) elliptic along the line x – y = 0

(D) parabolic along the line x + y = 0

Ans: (D)

19. Let X and Y be topological spaces and let f : X → Y be a continuous surjective function. Which one of the following statements is TRUE?

(A) If X is separable, then Y is separable

(B) If X is first countable, then Y is first countable

(D) If X is regular then Y is regular

Ans: (A)

20. Consider the topology T = {U ⊆ ℤ: ℤ\U is finite or 0 ∉ U} on ℤ. Then, the topological space (ℤ, T) is

(A) compact but NOT connected

(B) connected but NOT compact

(D) neither compact nor connected

Ans: (A)

21. Let F(x) be the distribution function of a random variable X. Consider functions :

G₁(x) = (f(x))³, x ∈ ℝ,

G₂(x) = 1 – (1 – F(x))⁵, x ∈ ℝ.

Which of the above functions are distribution functions?

(A) Neither G₁ nor G₂

(B) Only G₁

(D) Both G₁ and G₂

Ans: (D)

22. Let X₁, X₂, …., X_n (n ≥ 2) be independent and identically distributed random variables with finite variance σ² and let Then the covariance between is

(A) 0

(B) −σ²

(C)

(D)

Ans: (A)

23. Let X₁, X₂, …., X_n(n ≥ 2) be a random sample from a N(μ, σ²) population, where σ² = 144. The smallest n such that the length of the shortest 95% confidence interval for μ will not exceed 10 is _____.

Ans: (23)

24. Consider the linear programming problem (LPP) :

Maximize 4x₁ + 6x₂

Subject to x₁ + x₂ ≤ 8,

2x₁ + 3x₂ ≥ 18,

x₁ ≥ 6, x₂ is unrestricted in sign.

Then the LPP has

(A) no optimal solution

(B) only one basic feasible solution and that is optimal

(D) infinitely many optimal solutions

Ans: (B)

25. For a linear programming problem (LPP) and its dual, which one of the following is NOT TRUE?

(A) The dual of the dual is primal

(B) If the primal LPP has an unbounded objective function, then the dual LPP is infeasible

(D) If the primal LPP has a finite optimal solution, then the dual LPP also has a finite optimal solution

Ans: (C)

26. If U and V are null spaces of , respectively, then the dimension of the subspace U + V equals ______.

Ans: (3)

27. Given two n × n matrices A and B with entries in ℂ, consider the following statements:

(P): If A and B have the same minimal polynomial, then A is similar to B.

(Q) : If A has n distinct eigenvalues, then there exists u ∈ ℂⁿ such that u, Au, ,…, Aⁿ⁻¹u are linearly independent.

Which of the above statements hold TRUE?

(A) Both P and Q

(B) Only P

(D) Neither P nor Q

Ans: (C)

28. Let A = (a_ij) be a 10 × 10 matrix such that a_ij = 1 for i ≠ j and a_ij = α + 1, where α > 0. Let λ and μ be the largest and the smallest eigenvalues of A, respectively. If λ + μ = 24, then α equals ______.

Ans: (7)

29. Let C be the simple, positively oriented circle of radius 2 centered at the origin in the complex plane. Then equals ______.

Ans: (3)

30. Let Re(z) and Im(z), respectively, denote the real part and the imaginary part of a complex number z. Let T : ℂ ⋃ {∞} → ℂ ⋃ {∞} be the bilinear transformation such that T(6) = 0, T(3 – 3i) = i and T(0) = ∞. Then, the image of D = {z ∈ ℂ : |z – 3| < 3} under the mapping w = T(z) is

(A) {w ∈ ℂ : Im(w) < 0}

(B) {w ∈ ℂ : Re(w) < 0}

(D) {w ∈ ℂ : Re(w) > 0}

Ans: (D)

31. Let (x_n) and (y_n) be two sequences in a complete metric space (X, d) such that and and for all n ∈ ℕ. Then

(A) both (x_n) and (y_n) converge

(B) (x_n) converges but (y_n) need NOT converge

(D) neither (x_n) nor (y_n) converges

Ans: (B)

32. Let f : [0, 1] → ℝ be given by f(x) = 0 if x is rational, and if x is irrational then f(x) = 9ⁿ, where n is the number of zeroes immediately after the decimal point in the decimal representation of x. Then the Lebesgue integral equals _____.

Ans: (9)

33. Let f : ℝ² → ℝ be defined by Then, at (0, 0),

(A) f is continuous and the directional derivative of f does NOT exist in some direction

(B) f is NOT continuous and the directional derivatives of f exist in all directions

(D) f is differentiable

Ans: (C)

34. Let D be the region in ℝ² bounded by the parabola y² = 2x and the line y = x. Then equals _______.

Ans: (2)

35. Let y₁(x) = x³ and y₂(x) = x²|x| for x ∈ ℝ.

Consider the following statements.

(P) : y₁(x) and y₂(x) are linearly independent solutions of

on ℝ.

(Q) : The Wronskian for all x ∈ ℝ.

Which of the above statement hold TRUE?

(A) Both P and Q

(B) Only P

(D) Neither P nor Q

Ans: (A)

36. Let α and β with α > β be the roots of the indicial equation of at x = −1. Then α − 4β equals _____.

Ans: (2)

37. Let S₉ be the group of all permutations of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Then the total number of elements of S₉ that commute with in S₉ equals _______.

Ans: (24)

38. Let ℚ[x] be the ring of polynomials over ℚ. Then the total number of maximal ideals in the quotient ring ℚ[x]/(x⁴ – 1) equals ____.

Ans: (3)

39. Let {e_n : n ∈ ℕ} be an orthonormal basis of a Hilbert space H. Let T : H → H be given by For each n ∈ ℕ, define T_n : H → H by Then

(A) ||T_n – T|| → 0 as n → ∞

(B) ||T_n – T|| ↛ 0 as n → ∞ but for each x ∈ H, ||T_nx – Tx|| → 0 as n → ∞

(D) there exist x, y ∈ H such that as n → ∞

Ans: (A)

40. Consider the subspace of the Hilbert space ℓ² of all square summable real sequences. For n ∈ ℕ, define T_n : V → ℝ by

Consider the following statements:

(P): {T_n : n ∈ ℕ} is pointwise bounded on V.

(Q): {T_n : n ∈ ℕ}is uniformly bounded on {x ∈ V : ||x||₂ = 1}.

Which of the above statements hold TRUE?

(A) Both P and Q

(B) Only P

(D) Neither P nor Q

Ans: (B)

41. Let p(x) be the polynomial of degree at most 2 that interpolates the data (−1, 2), (0, 1) and (1, 2). If q(x) is a polynomial of degree at most 3 such that p(x) + q(x) interpolates the data (−1, 2), (0, 1), (1, 2) and (2, 11), then q(3) equals ______.

Ans: (24)

42. Let J be the Jacobi iteration matrix of the linear system

Consider the following statements :

(P): One of the eigenvalues of J lies in the interval [2, 3]

(Q): The Jacobi iteration converges for the above system.

Which of the above statements hold TRUE?

(A) Both P and Q

(B) Only P

(D) Neither P nor Q

Ans: (B)

43. Let u(x, y) be the solution of satisfying the condition u(x, y) = 1 on the circle x² + y² = 1. Then u(2, 2) equals _____.

Ans: (64)

44. Let u(r, θ) be the bounded solution of the following boundary value problem in polar coordinates:

u(2, θ) = cos² θ, 0 ≤ θ ≤ 2π.

Then u(1, π/2) + u(1, π/4) equals

(A) 1

(B) 9/8

(D) 3/8

Ans: (C)

45. Let T_u and T_d denote the usual topology and the discrete topology on ℝ, respectively.

Consider the following three topologies:

T₁ = Usual topology on ℝ² = ℝ × ℝ,

T₂ = Topology generated by the basis {U × V : U ∈ T_d, V ∈ T_u} on ℝ × ℝ,

T₃ = Dictionary order topology on ℝ × ℝ.

Then

(A)

(B)

(C)

(D)

Ans: (D)

46. Let X be a random variable with probability mass function for n = 1, 2, ….. . Then E(X – 3 |X > 3) equals _____.

Ans: (4)

47. Let X and Y be independent and identically distributed random variables withi probability mass function p(n) = 2⁻ⁿ, n = 1, 2….. .

Then P(X ≥ 2Y) equals (rounded to 2 decimal places) ____.

Ans: (0.27 to 0.30)

48. Let X₁, X₂, …. be a sequence of independent and identically distributed Poisson random variables with mean 4. Then equals ____.

Ans: (0.67 to 0.70)

49. Let X and Y be independent and identically distributed exponential random variables with probability density function

The P(max(X, Y) < 2) equals (rounded to 2 decimal places)______.

Ans: (0.73 to 0.77)

50. Let E and F be any two events with P(E) = 0.4, P(F) = 0.3 and P(F\E) = 3 P(F\E^C). Then P(E\F) equals (rounded to 2 decimal places)______.

Ans: (0.65 to 0.68)

51. Let X₁, X₂…, X_m (m ≥ 2) be a random sample from a binomial distribution with parameters n = 1 and p, p ∈ (0, 1), and let

Then a uniformly minimum variance unbiased estimator for p(1 – p) is

(A)

(B)

(C)

(D)

Ans: (A)

52. Let X₁, X₂, …., X₉ be a random sample from a N(0, σ²) population. For teting H₀ : σ² = 2 against H₁ : σ² = 1, the most powerful test rejects H₀ if where c is to be chosen such that the level of significance is 0.1. Then the power of this test equals ______.

Ans: (0.49 to 0.51)

53. Let X₁, X₂,…, X_n (n ≥ 2) be a random sample from a N(θ, θ) population, where θ > 0, and let Then the maximum likelihood estimator of θ is

(A)

(B)

(C)

(D)

Ans: (D)

54. Consider the following transportation problem. The entries inside the cells denote per unit cost of transportation from the origins to the destinations.

The optimal cost of transportation equals ______.

Ans: (590)

55. Consider the linear programming problem (LPP) :

Maximize kx₁ + 5x₂

subject to x₁ + x₂ ≤ 1,

2x₁ + 3x₂ ≤ 1,

x₁, x₂ ≥ 0.

If x^* = (x₁^*, x₂^*) is an optimal solution of the above LPP with k = 2, then the largest value of k (rounded to 2 decimal places) for which x^* remains optimal equals ______.

Ans: (3.32 to 3.34)

56. The ninth and the tenth of this month are Monday and Tuesday _______.

(A) figuratively

(B) retrospectively

(D) rightfully

Ans: (C)

57. It is _______ to read this year’s textbook ______ the last year’s

(A) easier, than

(B) most easy, than

(D) easiest, from

Ans: (A)

58. A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

(A) Only P’s drink

(B) Only P’s drink and S’s age

(D) Only P’s drink, Q’s drink and S’s age

Ans: (B)

59. Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?

(A) 8 km, East

(B) 12 km, North

(D) 10 km, North

Ans: (A)

60. 500 students are taking one or more courses out of Chemistry, Physics and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A) 37

(B) 43

(D) 53

Ans: (D)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following statements best reflects the author’s opinion?

(A) An intimate association does not allow for the necessary perspective.

(B) Matters are recorded with an impartial perspective.

(D) Actors are typically associated with the impartial recording of matters.

Ans: (A)

62. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A) X is the mother-in-law of R

(B) P and R are not married to each other

(D) Q cannot be married to R

Ans: (D)

63. 1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A) 3000

(B) 3300

(D) 3900

Ans: (C)

64. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A) 781

(B) 791

(D) 891

Ans: (C)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of geographical region. Contour lines are shown at 25 m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A) P to Q

(B) P to R

(D) P to T

Ans: (B)

Gate 2017 Instrumentation Engineering Question Paper 12th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Instrumentation Engineering 12th Feb 2017

Subject Name: Instrumentation Engineering

Duration : 180

Total Marks: 100

1. A system is described by the following differential equation:

Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is

(A)

(B)

(C)

(D)

Ans: (B)

2. If v is a non-zero vector of dimension 3×1, then the matrix A=vv^T has a rank = _______

Ans: (1)

3. A periodic signal x(t) is shown in the figure. The fundamental frequency of the signal x (t) in Hz is________

Ans: (1)

4. The silicon diode, shown in the figure, has a barrier potential of 0.7 V. There will be no forward current flow through the diode, if V_dc, in volt, is greater than

(A) 0.7

(B) 1.3

(D) 2.6

Ans: (D)

5. For a first order low pass filter with unity d.c. gain and -3 dB corner frequency of 2000π rad/s, the transfer function H( jω ) is

(A)

(B)

(C)

(D)

Ans: (C)

6. A and B are the logical inputs and X is the logical output shown in the figure. The output X is related to A and B by

(A)

(B)

(C)

(D)

Ans: (C)

7. The most suitable pressure gauge to measure pressure in the range of 10⁻⁴ to 10⁻³ torr is

(A) Bellows

(B) Barometer

(D) Pirani gauge

Ans: (D)

8. The standard for long distance analog signal transmission in process control industry is

(A) 4-20 mV

(B) 0-20 mA

(D) 0-5V

Ans: (C)

9. If a continuous-time signal x(t) = cos(2πt) is sampled at 4 Hz, the value of the discrete-time sequence x(n) at n = 5 is

(A) −0.707

(B) −1

(D) 1

Ans: (C)

10. The term hysteresis is associated with

(A) ON-OFF control

(B) P-I control

(D) Ratio control

Ans: (A)

11. A current waveform, i(t), shown in the figure, is passed through a Permanent Magnet Moving coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is

(A) −0.25 A

(B) −0.12A

(D) 0.5 A

Ans: (A)

12. The connection of two 2-port networks is shown in the figure. The ABCD parameters of N1 and N2 networks are given as

The ABCD parameters of the combined 2-port network are

(A)

(B)

(C)

(D)

Ans: (A)

13. The figure shows a shape ABC and its mirror image A₁B₁C₁ across the horizontal axis (X – axis). The coordinate transformation matrix that maps ABC to A₁B₁C₁ is

(A)

(B)

(C)

(D)

Ans: (D)

14. The differential amplifier, shown in the figure, has a differential gain of A_d = 100 and common mode gain of A_c = 0.1. If V₁ = 5.01 V and V₂ = 5.00 V, then V₀, in volt (up to one decimal place) is ______.

Ans: (1.4 to 1.6)

15. A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at Node-1 is – 1 V, then the voltage at Node-2 is _________V.

Ans: (2)

16. The eigen values of the matrix are

(A) −1, 5, 6

(B) 1, −5 ± j6

(D) 1, 5, 5

Ans: (C)

17. The figure shows a phase locked loop. The output frequency is locked at f₀ = 5kHz. The value of f_i in kHz is __________.

Ans: (1)

18. Identify the instrument that does not exist:

(A) Dynamometer-type ammeter

(B) Dynamometer-type wattmeter

(D) Moving-iron wattmeter

Ans: (D)

19. The output V_o shown in the figure, in volt, is close to

(A) −20

(B) −15

(D) 0

Ans: (B)

20. An 8-bit microcontroller with 16 address lines has 3 fixed interrupts i.e., Int1, Int2 and Int3 with corresponding interrupt vector addresses as 0008H. 0010H and 0018H. To execute a 32-byte long Interrupt Service Subroutine for Int1 starting at the address ISSI, The location 0008H onwards should ideally contain

(A) a CALL to ISSI

(B) an unconditional JUMP to ISSI

(D) only ISSI

Ans: (A or B)

21. A series R-L-C circuit is excited with a 50V, 50 Hz sinusoidal source. The voltage across the resistance and the capacitance are shown in the figure. The voltage across the inductor (V_L) is __________V

Ans: (50)

22. The condition for oscillation in a feedback oscillator circuit is that at the frequency of oscillation, initially the loop gain is greater than unity while the total phase shift around the loop in degree is

(A) 0

(B) 90

(D) 270

Ans: (A)

23. Let z = x + jy where

(A) cos z

(B)

(D)

Ans: (B)

24. The region of Convergence (ROC) of the Z-transform of a causal unit step discrete-time sequence is

(A) |z| < 1

(B) |z| ≤ 1

(D) |z| ≥ 1

Ans: (C)

25. The pressure drop across an orifice plate for a particular flow rate is 5 kg/m². If the flow rate is doubled (within the operating range of the orifice), the corresponding pressure drop in kg/m³ is

(A) 2.5

(B) 5.0

(D) 25.0

Ans: (C)

26. The two-input voltage multiplier, shown in the figure, has a scaling factor of 1 and produces voltage output. If V₁ = +15V and V₂ = +3V, the value of V₀ in volt is _______.

Ans: (−5 to 5)

27. For the circuit, shown in the figure, the total real power delivered by the source to the loads is _________kW

Ans: (1.75 to 1.96)

28. The magnetic flux density of an electromagnetic flow meter is 100 mWb/m². The electrodes are wall-mounted inside the pipe having a diameter of 0.25m. A voltage of 1V is generated when a conducting fluid is passed through the flow meter. The volumetric flow rate of the fluid in m³/s is ____________.

Ans: (1.9 to 2)

29. In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by where V_GS is in V. If V_s = +5V, then the value of R_S in kΩ is ______.

Ans: (9.9 to 10.1)

30. The hot junction of a bare thermocouple, initially at room temperature (30℃), is suddenly dipped in molten metal at t = 0s. The cold junction is kept at room temperature. The thermocouple can be modeled as a first-order instrument with a time constant of 1.0s and a static sensitivity of 10μV/℃. If the voltage, measured across the thermocouple indicates 10.0 mV at t = 1.0s, then the temperature of the molten metal in ℃ is __________.

Ans: (1605 to 1618)

31. A series R-L-C circuit is excited with an a.c. voltage source. The quality factor (Q) of the circuit is given as Q = 30. The amplitude of current in ampere at upper half-power frequency will be __________.

Ans: (6 to 7)

32. An angle modulated signal with carrier frequency ω_c = 2π × 10⁶ rad/s is given by φ_m(t) = cos(ω_ct + 5sin(1000πt)) + 10sin(2000πt). The maximum deviation of the frequency in the angle modulated signal from that of the carrier is _________ kHz.

Ans: (12 to 13)

33. Three DFT coefficients, out of five DFT coefficients of a five-point real sequence are given as : X(0) = 4, X(1) = 1 – j1 and X(3) = 2 + j2. Then zero-th value of the sequence x(n), x(0), is

(A) 1

(B) 2

(D) 4

Ans: (B)

34. A closed-loop system is shown in the figure. The system parameter α is not known. The condition for asymptotic stability of the closed loop system is

(A) α < −0.5

(B) −0.5 < α < 0.5

(D) α > 0.5

Ans: (D)

35. The power delivered to a single phase inductive load is measured with a dynamometer type wattmeter using a potential transformer (PT) of turns ratio 200:1 and the current transformer (CT) of turns ratio 1:5. Assume both the transformers to be ideal. The power factor of the load is 0.8. If the wattmeter reading is 200W, then the apparent power of the load in kVA is _________.

Ans: (250)

36. The overall closed loop transfer function represented in the figure, will be

(A)

(B)

(C)

(D)

Ans: (A)

37. When the voltage across a battery is measured using a d.c. potentiometer, the reading shows 1.08V. But when the same voltage is measured using a Permanent Magnet Moving Coil (PMMC) voltmeter, the voltmeter reading shows 0.99V. If the resistance of the voltmeter is 1100Ω, the internal resistance of the battery, in Ω, is _________.

Ans: (100)

38. The probability that a communication system will have high fidelity is 0.81. The probability that the system will have both high fidelity and high selectivity is 0.18. The probability that a given system with high fidelity will have high selectivity is

(A) 0.181

(B) 0.191

(D) 0.826

Ans: (C)

39. The current response of a series R-L circuit to a unit step voltage is given in the table. The value of L is ___________H.

Ans: (1)

40. A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If V_o =+ 2.0V, then the value of x is __________.

Ans: (0.19 to 0.21)

41. The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between ±7V. The width of the hysteresis band is _________V.

Ans: (0.6 to 0.7)

42. The loop transfer function of a closed-loop system is given by The breakaway point of the root-loci will be ____________.

Ans: (−1.2 to 1.0)

43. The unbalanced voltage of the Wheatstone bridge, shown in the figure, is measured using digital voltmeter having infinite input impedance and a resolution of 0.1mV. If R = 1000Ω, then the minimum value of ∆R in Ω to create detectable unbalanced voltage is _________.

Ans: (0.17 to 0.23)

44. In the circuit diagram, shown in the figure, S1 was closed and S2 was open for a very long time. At t = 0, S₁ is opened and S₂ is closed. The voltage across the capacitor, in volt, at t = 5 μs is _______

Ans: (1.43 to 1.63)

45. The block diagram of a closed-loop control system is shown in the figure. The values of k and k_p are such that the system has a damping ratio of 0.8 and an undamped natural frequency ω_n of 4 rad/s respectively. The value of k_p will be ___________.

Ans: (0.32 to 0.4)

46. Assuming the op-amp shown in the figure to be ideal, the frequency at which the magnitude of V_o will be 95% of the magnitude of V_in is ____________kHz.

Ans: (2.9 to 3)

47. The following table lists an nth order polynomial f(x) = a_nxⁿ + a_{n – 1}x^{n – 1}+…+a₁x + a₀ and the forward differences evaluated at equally spaced values of x. The order of the polynomial is

(A) 1

(B) 2

(D) 4

Ans: (D)

48. Consider two discrete-time signals:

x₁(n) = {1, 1} and x₂(n) = {1, 2}, for n = 0.1.

The Z-transform of the convoluted sequence x(n) = x₁(n) * x₂(n) is

(A) 1 + 2z⁻¹ + 3z⁻²

(B) z² + 3z + 2

(D) z⁻² + 3z⁻³ + 2z⁻⁴

Ans: (C)

49. In the a.c. bridge, shown in the figure, R = 10³Ω and C = 10⁻⁷ F. If the bridge is balanced at a frequency ω₀, the value of ω₀ in rad/s is ________.

Ans: (10000)

50. The junction semiconductor temperature sensor shown in the figure is used to measure the temperature of hot air. The output voltage V_o is 2.1V. The current output of the sensor is given by I = TμA where T is the temperature in K. Assuming the opamp to be ideal, the temperature of the hot air in ℃ is approximately ___________.

Ans: (76 to 78)

51. In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by A_m(t) = 100 cos (ω_ct) + 50 cos(ω_mt) cos (ω_ct), where ω_c is the carrier frequency and ω_m is the modulation frequency. The power carried by the sidebands in % of total power is ________%

Ans: (11 to 11.2)

52. The angle between two vectors and in radian is _____.

Ans: (0.65 to 0.8)

53. Quantum efficiency of a photodiode (ratio between the number of liberated electrons and the number of incident photons) is 0.75 at 830 nm. Given Plank’s constant h = 6.624 × 10⁻³⁴ J, the charge of an electron e = 1.6 × 10⁻¹⁹ C and the velocity of light in the photodiode C_m = 2 × 10⁸ m/s. For an incident optical power of 100 μW at 830 n, the photocurrent in μA is _______.

Ans: (74.5 to 75.5)

54. The two inputs A and B are connected to an R-S latch via two AND gates as shown in the figure. If A = 1 and B = 0, the output is

(A) 00

(B) 10

(D) 11

Ans: (B)

55. The Laplace transform of a causal signal y(t) is The value of the signal y(t) at t = 0.1 s is _______ unit.

Ans: (−2.4 to −2.0)

56. The event would have been successful if you ______ able to come.

(A) are

(B) had been

(D) would have been

Ans: (B)

57. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

(A) 2, Red

(B) 2, 3, Red

(D) 2, red, blue

Ans: (C)

58. What is the value of x when

(A) 1

(B) −1

(D) Cannot be determined

Ans: (B)

59. There was no doubt that their work was thorough.

Which of the words below is closest in meaning to the underlined word above?

(A) Pretty

(B) Complete

(D) Haphazard

Ans: (B)

60. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

(A) 1/9

(B) 2/9

(D) 4/9

Ans: (B)

61. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

(A) The centre operates on a first-come-first-served basis but with variable service times, depending on specific customer needs.

(B) Customers were served in an arbitrary order since they took varying amounts of time for service completion in the centre.

(C) Since some people came out within a few minutes of entering the centre. The system is likely to operate on a last-come-first-served basis.

(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Ans: (A)

62. The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (D)

63. A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri, Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok.

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

i. Pelling is at a higher elevation than Kalimpong

ii. Kalimpong is at a lower elevation than Darjeeling

iii. Kalimpong is at a higher elevation than siliguri

iv. Siliguri is at a lower elevation than Gangtok

(A) Only ii

(B) Only ii and iii

(D) Only iii and iv

Ans: (C)

64. P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats.

Which of the following must necessarily be true?

(A) P is immediately to the right of R

(B) T is immediately to the left of P

(D) U is immediately to the right of R or P is immediately to the left of T

Ans: (C)

65. Budhan covers a distance of f19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

(A) 1

(B) 4

(D) 6

Ans: (D)

Gate 2017 Geology and Geophysics Question Paper 4th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Geology and Geophysics 4th Feb 2017

Subject Name: Geology and Geophysics

Duration : 180

Total Marks: 100

1. Which one of the following is a continental hotspot?

(A) Reunion

(B) Macdonald

(D) Afar

Ans: (D)

2. The diagram given below shows a Mohr circle for two-dimensional stress with points numbered as shown. The mean stress and the maximum shear stress are given by which one of the following number pairs?

(A) 1, 2

(B) 1, 3

(D) 2, 3

Ans: (B)

3. Which type of fault is developed in the setting shown in the figure below? Velocity vectors on either side of the fault are given in the figure.

(A) Normal

(B) Dextral strike-slip

(D) Thrust

Ans: (A)

4. The age of most of the bituminous coal seams of India is

(A) Silurian.

(B) Miocene.

(D) Permian.

Ans: (D)

5. The time equivalent of the time-stratigraphic team ‘Series’ is

(A) Epoch.

(B) Period.

(D) Stage.

Ans: (A)

6. Match the following stratigraphic units of India (Group-I) with their age (Group-II)

Group-I Group-II

(P) Barakar Formation (1) Miocene

(Q) Warakali (Varkala) Formation (2) Cretaceous

(R) Bagh Beds (3) Proterozoic

(S) Bhander Limestone (4) Eocene

(5) Permian

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

(B) P-1, Q-4, R-2, S-5

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

Ans: (A)

7. Universal Transverse Mercator (UTM) is a type of

(A) conical projection

(B) gnomonic projection

(D) cylindrical projection

Ans: (D)

8. The groundwater flow equation where h refers to the hydraulic head and x, y, z are coordinates, is valid when the flow condition is

(A) steady state in isotropic media.

(B) unsteady state in isotropic media.

(D) unsteady state in anisotropic media.

Ans: (A)

9. Los Angeles abrasion test was conducted for a granite aggregate with an initial weight of 4800 grams. After the test, the aggregate weighed 3504 grams. The Los Angeles abrasion value is _______%

Ans: (27)

10. Brightness temperature is a function of surface temperature and

(A) transmittance.

(B) reflectance.

(D) emissivity.

Ans: (D)

11. Which one of the following minerals has poor cleavage in all directions?

(A) Fluorite

(B) Orthoclase

(D) Muscovite

Ans: (C)

12. The figure below shows the intercepts of the plane HKL with the crystallographic axes a, b, c. The Miller index of the plane HKL is

(A) (243)

(B) (342)

(D) (634)

Ans: (B)

13. Match the rocks listed in Group-I with the corresponding general rock classification listed in Group-II.

Group-I Group-II

P. Granite 1. Extrusive igneous rock

Q. Basalt 2. Biochemical sedimentary rock

R. Gneiss 3. Intrusive igneous rock

S. Sandstone 4. Metamorphic rock

5. Clastic sedimentary rock

(A) P-1; Q-3; R-5; S-2

(B) P-4; Q-5; R-1; S-2

(D) P-3; Q-4; R-1; S-5

Ans: (C)

14. Which one of the following oceanic ridges is known to be aseismic?

(A) Carlsberg

(B) Mid Atlantic

(D) Southwest Indian

Ans: (C)

15. Isogonic lines are contours of equal magnetic

(A) inclination.

(B) declination.

(D) horizontal field intensity.

Ans: (B)

16. Match the geophysical terms in Group-I with their corresponding units of measurements in Group-II

Group-I Group-II

P. Transit time 1. mGal

Q. Conductivity 2. Nano Tesla

R. Gravity anomaly 3. Siemens

S. Magnetic field intensity 4. millivolt

5. microsecond per feet

(A) P-5; Q-4; R-2; S-1

(B) P-5; Q-4; R-3; S-2

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

Ans: (C)

17. The Maxwell’s equation based on Ampere’s law is

(A)

(B)

(C)

(D)

Ans: (B)

18. The normal gravity formula (for e.g. GRS80) is a function of

(A) geocentric latitude.

(B) geodetic latitude.

(D) altitude.

Ans: (B)

19. A seismic reflection survey was carried out over a subsurface consisting of a stack of horizontal isotropic layers. In the common midpoint (CMP) domain, the moveout (traveltime v/s offset) curve for any primary reflection event is best approximated by

(A) an ellipse.

(B) a parabola.

(D) a hyperbola.

Ans: (D)

20. Assertion(a) : Magnetic stripes are observed around mid-oceanic ridge regions.

Reason (R): The earth’s magnetic field undergoes reversals of polarity.

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

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

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

Ans: (C)

21. A seismic gap refers to a

(A) time gap between two great earthquakes.

(B) distance gap between the epicenters of two great earthquakes.

(D) wide gap in the earth created by a great earthquake.

Ans: (C)

22. The travel time difference between the arrival times of a shear wave (S) and primary wave (P) observed on a seismogram recorded at an epicentral distance of 100 km from a near surface earthquake is ______s.

(Assume the average P and S wave velocities to be 6.0 km/s and 3.5 km/s, respectively).

Ans: (11.8 to 12.0)

23. The percentage increase in P-wave velocity (km/s) across the Mohorovicic discontinuity from the lower crust to the upper mantle beneath a carton is approximately________(%)

Ans: (12 to 22)

24. Which one amongst the following logging tools has the largest depth of investigation?

(A) Density

(B) Laterolog 3

(D) Neutron

Ans: (B)

25. The most abundant radioactive isotope in the continental crust is

(A) ⁴⁰K

(B) ²³²Th

(D) ²³⁸U

Ans: (A)

Geology (Part B) (Section-1)

26. Stylolitic foliation developed during diagenetic processes is typically

(A) parallel to bedding.

(B) perpendicular to bedding.

(D) vertical.

Ans: (A)

27. A coal seam with an attitude 090°, 50°S outcrops at an elevation of 1400 m in an area that has flat topography. A vertical exploratory drill hole will intersect the seam

(A) north of the outcrop at elevations greater than 1400 m.

(B) north of outcrop at elevations less than 1400 m.

(D) south of the outcrop at elevations greater than 1400 m.

Ans: (C)

28. Earthquakes result in the formation of which one of the following features?

(A) Porphyroblast

(B) Porphyroclast

(D) Pressure shadow

Ans: (C)

29. In a bilaterally symmetrical brachiopod fossil, the angle between the hinge line and the median line changes to 45° after deformation. The shear strain observed in the deformed fossil is _______.

Ans: (1)

30. The empirical probability distribution of gold (Au) grades shows a unimodal distribution with mode = 2 g/t, median = 3 g/t, and mean = 5 g/t. This probability distribution is

(A) positively skewed.

(B) negatively skewed.

(D) platykurtic.

Ans: (A)

31. A limb of a non-plunging fold with an attitude 070°, 40°S is rotated about is fold axis 30° clockwise (looking towards ENE). The plunge amount of the pole to the fold limb after rotation is ______ degrees.

Ans: (20)

32. The Bulk Silicate Earth (BSE) is best approximated by the average

(A) enriched upper mantle composition.

(B) mantle and continental crust composition.

(D) primitive upper mantle composition

Ans: (B)

33. Which one of the following is the stable mineral assemblage in metamorphism of a rock with politic bulk composition under granulite facies?

(A) staurolite + muscovite + sillimanite + K-feldspar

(B) phengite + garnet + chloritoid + biotite

(D) gamet + cordierite + K-fledspar + sillimanite

Ans: (D)

34. The given P-T diagram shows four distinct metamorphic paths designated as 1, 2, 3 and 4. Which one of these P-T paths represents crustal thickening in a collisional tectonic setting?

(A) 1

(B) 2

(D) 4

Ans: (B)

35. The pressure on a rock overlain by a 7 km thick basaltic crust (ρ = 3100 kg m⁻³) is _____ kilobar.

(Use g = 9.8 ms⁻²; 10⁵ Pa = 1 bar)

Ans: (2.0 to 2.2)

36. The given T-X diagram shows the phase relations in olivine solid solution at 1 bar pressure. If ‘P’ is the initial position of melt, the proportion of melt at 1500℃ is ______%.

Ans: (32 to 34)

37. Fluorite crystal (CaF₂) adopts face-centered cubic structure with lattice parameter a = 5.463Å. If the ionic radius of anion (F⁻) is 1.71 Å, the ionic radius of cation (Ca²⁺) is _______Å.

Ans: (2.1 to 2.2)

38. The diagram below shows the interference figure of a mineral. The mineral is

(A) uniaxial positive.

(B) biaxial negative.

(D) biaxial positive.

Ans: (C)

39. The standard thermodynamic data for enstatite (Mg₂Si₂O₆) and forsterite (Mg₂SiO₄) is given in the table below. The Gibb’s free energy of the reaction Mg₂SiO₄ + SiO₂ = Mg₂Si₂O₆ at 600 K and 1 bar is _____ J.

(Assuming C_p = 0 for all minerals in the reaction)

Ans: (−5300 to −4700)

40. The modal abundance in an ultramafic rock and the partition coefficients of lutetium (Lu) in clinopyroxene, orthopyroxene, olivine and plagioclase are tabulated below. The bulk distribution coefficient of lutetium (D_Lu) in the ultramafic rock is _____

Ans: (0.39 to 0.41)

41. Match the following classical ore deposits (Group-I) with their associated ore minerals (Group-II)

Group-I Group-II

P. Sudbury type deposit 1. Molybdenite

Q. Mississippi valley type deposit 2. Uraninite and chalcopyrite

R. Climax type deposit 3. Pentlandite

S. IOCG type deposit 4. Psilomelane

5. Sphalerite and Galena

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

(B) P-3; Q-5; R-1; S-2

(D) P-3; Q-5; R-2; S-4

Ans: (B)

42. Which one of the following microfossils is commonly used in biostratigraphic correlation of Palaeozoic marine strata?

(A) Angiosperm pollen

(B) Diatoms

(D) Chitinozoans

Ans: (D)

43. Given below are pairs of “living fossils”. Which one of the following is a brachiopod-molusc pair?

(A) Lingula, Nautihus

(B) Ginkgo, Metasequia

(D) Coelacanths, Sikhotealinia

Ans: (A)

44. Match the sedimentary rocks and their features listed in Group I with depositional environments listed in Group II.

Group I

(P) Sandstone with herring-bone cross bedding

(Q) Chalk with coccolith

(R) Well sorted arenite with large cross bedding (5-10 m thick)

(S) Poorly sorted sediments with faceted and striated pebbles

Group II

(1) Eolian

(2) Glacial

(3) Sabhka

(4) Tidal

(5) Pelagic

(A) P-2; Q-1; R-4; S-5

(B) P-4; Q-5; R-1; S-2

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

Ans: (B)

45. Arrange the following stratigraphic formations sequentially from older to younger.

(P) Jodhpur Sandstone

(Q) Cambay Shale

(R) Kajrahat Limestone

(S) Tipam Sandstone

(A) P, R, Q, S

(B) R, Q, P, S

(D) R, P, Q, S

Ans: (D)

46. 2 g air dried coal contains 0.2 g moisture, 0.3 g ash and 0.5 g volatile matter. The volatile matter content in the coal in dry mineral matter free (d.m.f.) basis is _______%.

(mineral matter content = 1.1 × ash content)

Ans: (33.5 to 34.5)

47. The approximate temperature for ‘oil window’ ranges from

(A) 30℃ to 50℃

(B) 60℃ to 160℃

(D) 260℃ to 350℃

Ans: (B)

48. Which one of the following biopolymers is the major source of liquid hydrocarbons?

(A) Lignin

(B) Proteins

(D) Carbohydrates

Ans: (C)

49. The hydraulic conductivity (K) of an isotropic aquifer is 10 m/day. If the hydraulic head within the aquifer drops 4 m over a distance of 750 m, the groundwater flow velocity within the aquifer is ______ m/day.

(Up to third decimal place)

Ans: (0.05 to 0.055)

50. Drainage network of a watershed ordered as per the Strahler method is given below. Maximum observed bifurcation ratio for the given network is _____.

Ans: (2.55 to 2.65)

51. In a vertical aerial photo, the top and bottom of a tower built on a flat terrain is displaced by 2 mm. In the photograph, the distance between top of the tower and nadir point is 100 mm. The flying height of the aircraft was 3000 m above the ground. The estimated height of the tower is _____m.

Ans: (60)

52. Brazilian test was conducted on a rock sample having radius of 27 mm and thickness of 22 mm. The failure load was 5 kN. The tensile strength of the rock is ______ N/mm².

Ans: (2.50 to 3.00)

53. The average assay (a) and area of influence (A) of a placer gold deposit of uniform thickness sampled at four locations W, X, Y and Z are given below. The weighted average assay of the ore body is ______ g/t.

Ans: (21.00 to 22.00)

54. The minimum and maximum values of the digital number (DN) of a remote sensing image are 8 and 32 respectively. The digital data was linearly stretched between 0 and 255 by using min-max linear stretching method. The post stretched integer DN value of a pixel with an original DNA value of 27 will be _______.

Ans: (201 to 204)

55. The length and width of concave and convex sides of a landslide is shown in the figure below. The Dilation Index of the landslide is ______.

Ans: (2)

Geophysics (Part B) (Section-2)

56. Which one of the following seismic phases is observable in the P-wave shadow zone?

(A) P

(B) PmP

(D) PKiKP

Ans: (D)

57. Consider a geological body buried at the equator at a certain depth. If the same body were to be buried at the North pole at the same depth, how would the gravity and magnetic field responses measured overt the body differ? Assume the same magnetic susceptibility and density contrasts. (Consider only geomagnetic induction).

(A) Both gravity and magnetic field responses do not change.

(B) Both gravity and magnetic field responses change significantly.

(D) Gravity field response does not change but magnetic field response changes significantly.

Ans: (D)

58. Given the Bouguer density of 2.8 g/cc, the Bouguer correction for a gravity station at an elevation of 30 m above the datum is ____ mGals.

(Use π = 3.14).

Ans: (3.3 to 3.7)

59. Given the following data for a resistivity sounding experiment over a two-layered half-space, the resistivity transform for the top layer is ______Ωm

(Data : resistivity of top layer ρ₁ = 10 Ωm, resistivity of half space ρ₂ = 100 Ωm, thickness of top layer h₁ = 10 m and current electrode spacing AB/2 = 5 m).

Ans: (9.7 to 10.8)

60. The ratio of eccentricity to the polar flattening of an ellipsoidal Earth with equatorial radius ‘e’ and polar radius ‘p’ can be expressed as

(A)

(B)

(C)

(D)

Ans: (C)

61. The vertical field intensity anomaly ∆z due to a vertically polarized vertical dyke is given by

where M is the magnitude of intensity of magnetization. All relevant parameters are provided in the figure below. The dyke has 1% magnetite (magnetic susceptibility of magnetite = 0.5 SI unit) distributed homogeneously. Then, the magnitude of peak vertical field intensity over the dyke is _______nT.

Ans: (76 to 84)

62. In magneto-telluric (MT) experiment over a homogeneous and isotropic half-space, the apparent resistivity is 50 Ωm for an electric field intensity of 12 mV/km and time period of 10 s. Then the magnetic field strength is _____ nT.

Ans: (2.3 to 2.5)

63. The apparent resistivity for Wenner and Schlumberger configurations in an electrical sounding experiment is the same for a certain electrode spacing ‘a’ (Wenner configuration). Given the current electrode spacing of 18 m and the potential electrode spacing of 2 m for a Schlumberger configuration, the value of ‘a’ is ______m.

Ans: (19 to 21)

64. In a time-domain (T-D) induced polarization experiment with a steady voltage of 10 mV during the current flow interval, the voltage decay after the current cut-off is given by v(t) = 4.0e⁻^3t mV. The chargegability after current cut-off between t₁ = 1 s and t₂ = 4 s is _____ms.

Ans: (0.56 to 0.62)

65. Which one of the following statements is TRUE for a near surface earthquake occurring in a homogeneous, isotropic Earth?

(A) Rayleigh waves are generated.

(B) Love waves are generated.

(D) P waves undergo refraction.

Ans: (A)

66. A dynamic range of 60 dB in power corresponds to an increase in amplitude by a factor of ______.

Ans: (100)

67. The slope of the Wadati plot obtained using the P and S arrival times of local earthquake is 1.0. The corresponding Vp/Vs ratio of the subsurface medium is ______.

Ans: (2)

68. The beach ball figure given below depicts the focal mechanism of an earthquake. The shaded and unshaded portions indicate compressional and dilatational quadrants, respectively. FP1 is the fault plane solution. The focal mechanism and FP1 represent

(A) a thrust fault with strike 45° and dip 30° with the tension axis in the compression quadrant.

(B) a normal fault with strike 45° and dip 30° with the tension axis in the compression quadrant.

(D) a normal fault with strike 225° and dip 60° with the pressure axis in the compression quadrant.

Ans: (A)

69. The characteristic log responses of a thick coal seam are

(A) low transit time, low resistivity and high gamma ray count.

(B) low transit time, high resistivity and low gamma ray count.

(D) high transit time, low resistivity and high gamma ray count.

Ans: (C)

70. The SP response of a thick, clean sandstone bed is −54 mV. Given the mud filtrate resistivity to be 0.45 Ωm at a formation temperature (T_f) of 130℉ and the coefficient, K = 77.29, the formation water resistivity is _____Ω

Ans: (0.08 to 0.10)

71. Which one of the following log responses is TRUE for a porous and permeable sandstone bed, when the resistivity of the mud filtrate used is equal to the resistivity of the formation water?

(A) A large negative SP is observed.

(B) A large positive SP is observed.

(D) LLm and LLd logs overlap with each other.

Ans: (D)

72. The number of half-lives (T_1/2) required for a certain amount of radioactive isotope in a rock to reduce to 3% of its original amount is ________.

Ans: (5.05 to 5.07)

73. VLF fields can be measured over continental distances (r) because

(A) the magnetic field decreases at the rate 1/r and the output power at the transmitting station is 1 to 10 kW

(B) the magnetic field decreases at the rate 1/r³ and the output power at the transmitting station is 1 to 10 kW.

(D) the magnetic field decreases at the rate 1/r² and the output power at the transmitting station is 100 to 1000 kW.

Ans: (C)

74. Convolution of two box car functions of different widths yields a

(A) step function.

(B) trapezoidal function.

(D) sinc function.

Ans: (B)

75. Assuming the Z-transform to be defined with Z as the unit delay operator, the pole of the infinite sequence is at Z= ______.

Ans: (2)

76. Normal moveout (NMO) correction was applied to seismic data in the common midpoint (CMP) domain. The frequency distortion due to “NMO stretch” is highest for

(A) larger offsets of deeper reflections.

(B) smaller offsets of shallower reflections.

(D) smaller offsets of deeper reflections.

Ans: (C)

77. Consider a hypothetical zero-offset seismic reflection survey acquired over a reflector whose dip is 30°. The velocity of the medium above the reflector is 2 km/s and the trace spacing is 25 m. The maximum unaliased frequency in the data is _____ Hz.

(Hint : The difference in traveltime between adjacent traces should be less than or equal to half a cycle.)

Ans: (40)

78. In statistical wavelet deconvolution, the reflectivity series is assumed to be a random sequence. Then, the autocorrelation of the wavelet is

(A) a scaled version of the autocorrelation of the seismic trace.

(B) a random sequence.

(D) dirac-delta function.

Ans: (A)

79. A vector field u is expressed by its Helmoholtz decomposition as u = ∇ϕ + ∇ × ψ, with and ψ = zy²I + xzj + x² The magnitude of the divergence of the vector field u at (1, 1, 1) is _______.

Ans: (1)

80. In the figure shown below, a ray corresponding to a P-wave is incident on the interface between layer 1 and layer 2 at an angle of 30°. The P-wave velocity is 1 km/s, 1.2 km/s and 1.5 km/s in layer 1, layer 2 and the half space, respectively. The emergence angle of the ray into the half space is _____ degrees.

Ans: (48 to 49)

81. How do the P-wave velocity (V_P), S-wave velocity (V_S), and Poisson’s ratio (σ) change from a water saturated sandstone to a gas saturated sandstone?

(A) V_P increases, V_S decreases and σ increases.

(B) V_P decreases, V_S remains the same and σ decreases.

(D) V_P, V_S and σ all remain constant.

Ans: (B)

82. Consider a vertical Seismic Profiling (VSP) data acquisition experiment as shown in the figure below. The subsurface consists of a horizontal layer of 2 km thickness underlain by a semi-infinite half-space. The P-wave velocities (V_P) in the first layer and the half-space are 2.0 km/s and 2.5 km/s, respectively. The vertical well has a string of receivers (denoted by inverted triangles) spaced 10 m apart, with the shallowest receiver at a depth of 0.5 km and the deepest receiver at a depth of 1.5 km. The source (denoted by star) is placed 0.5 km from the well head. The traveltime of the primary reflections event at the deepest receiver is ______s.

Ans: (1.20 to 1.35)

83. Which one of the following sets of vectors {v₁, v₂, v₃} is linearly dependent?

(A) v₁ = (0, −1, 3) v₂ = (2, 0, 1), v₃ = (−2, −1, 3)

(B) v₁ =(2, −2, 0), v₂ = (0, 1, −1), v₃ = (0, 4, 2)

(D) v₁ = (1, 4, 7), v₂ = (2, 5, 8), v₃ = (3, 6, 9)

Ans: (D)

84. The condition number for the matrix is ___.

Ans: (1.5)

85. Match the items listed in Group I with their respective analytical expressions in Group II.

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

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

(D) P-4, Q-3, R-1, S-5

Ans: (B)

General Aptitude

86. The ways in which this game can be played ______ potentially infinite.

(A) is

(B) is being

(D) are being

Ans: (C)

87. If you choose plan P, you will have to _____ plan Q, as these two are mutually______.

(A) forgo, exclusive

(B) forget, inclusive

(D) adopt, intrusive

Ans: (A)

88. If a and b are integers and a – b is even, which of the following must always be even?

(A) ab

(B) a² + b² + 1

(D) ab – b

Ans: (D)

89. A couple has 2 children. The probability that both children are boys if the older one is a boy is

(A) 1/4

(B) 1/3

(D) 1

Ans: (C)

90. P looks at Q while Q looks at R. P is married, R is not. The number of pairs of people in which a married person is looking at an unmarried person is

(A) 0

(B) 1

(D) Cannot be determined

Ans: (B)

91. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lives too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following is closest in meaning to ‘cleaving’?

(A) deteriorating

(B) arguing

(D) splitting

Ans: (D)

92. X bullocks and Y tractors take 8 days to plough a field. If we halve the number bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take X bullocks alone to plough the field?

(A) 30

(B) 35

(D) 45

Ans: (A)

93. There are 4 women P, Q, R, S and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?

(A) 74

(B) 76

(D) 80

Ans: (C)

94. All people in a certain island are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identify. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

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

(A) Both P and Q are knights

(B) P is a knight; Q is a knave

(D) The identities of P, Q cannot be determined

Ans: (D)

95. In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10℃) and a month is summer (average temperature 30℃)

Consider the following statements based on the data shown above :

i. Over the given months, the difference between the maximum and the minimum pollutants concentrations is the same in both winter and summer.

ii. There are at least four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.

Which one of the following options is correct?

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (B)

Gate 2017 Ecology and Evolution Question Paper 5th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Ecology and Evolution 5th Feb 2017

Subject Name: Ecology and Evolution

Duration : 180

Total Marks: 100

1. The larvae of the monarch butterfly feed exclusively on milkweed plants. These larvae are relatively less susceptible to predation because they are:

(A) Chemically protected

(B) Highly aggressive

(D) Visually cryptic

Ans: (A)

2. Which one of the following evolutionary processes best describes Red Queen dynamics?

(A) Co-evolution

(B) Convergent evolution

(D) Parallel evolution

Ans: (A)

3. Social behaviours can evolve to increase or decrease the fitness of the recipient of the behavior. A behavior is considered to be spiteful, when the fitness impact on the actor is _____, while the fitness impact on the recipient is _____.

(A) negative; negative

(B) negative; positive

(D) positive; positive

Ans: (A)

4. Which of the following set of animals belongs to the group Afrotheria?

(A) Elephant, dugong, elephant shrew, kangaroo rat

(B) Elephant, hyrax, elephant shrew, dugong

(D) Elephant shrew, dugong, aardvark, pika

Ans: (B)

5. What genetic markers are required to determine paternity in birds?

(A) Microsatellites

(B) Mitochondrial DNA

(D) Z chromosome markers

Ans: (A)

6. Species 1 and 2 are sympatric, but species 2 has a wider physiological tolerance than species 1. The two species simultaneously invade a new environment that has an average temperature of 22 degrees C. What are the expected outcomes for species 1 and 2?

(A) Both species will survive in the long term

(B) Neither species will survive in the long term

(D) Species 2 will outcompete species 1

Ans: (D)

7. Plants have evolved many morphological adaptations to extreme environmental conditions. Which of the following is NOT an adaptation to desert life?

(A) Dense coat of hairs or spines

(B) High density of stomata

(D) Succulent or thick leaves

Ans: (B)

8. When large mammals walk in the forest and trample small plants, those plants die. This interspecies relationship is a form of :

(A) Amensalism

(B) Commensalism

(D) Parasitism

Ans: (A)

9. The population of a widely distributed species gets divided into two subpopulations due to the appearance of a mountain barrier. Eventually these subpopulations evolve into two separate species. This is a case of :

(A) Allopatric speciation

(B) Parapatric speciation

(D) Sympatric speciation

Ans: (A)

10. In a population, the frequency of genotypes at a locus are A₁A₁ = 0.16, A₁A₂ = 0.48, A₂A₂ = 0.36. The probability of fixation of the A₁ allele by genetic drift is _______.

Ans: (0.39 to 0.40)

11. The percent sequence divergence in the mitochondrial cytochrome b gene between two species was found to be 5%. Much of this divergence in the coding region would be contributed by changes at the :

(A) First position of the codon

(B) Second position of the codon

(D) Intron

Ans: (C)

12. In haplo-diploid insects, males are haploid and females are diploid. A female, who is heterozygous for a recessive red-eye colour mutation, mates with a wild-type black-eyed male. What would be the percentage of eye colour phenotypes among their daughters?

(A) 100% red-eye

(B) 100% black-eye

(D) 66.7% black-eye

Ans: (B)

13. What is relationship between effective population size (N_e) and total population size (N) of any naturally occurring eukaryotic population?

(A) N_e is greater than N

(B) N_e is less than N

(D) N_e is unrelated to N

Ans: (B)

14. The figure below represents the phylogenetic relationship of taxa P-S. Assuming that the branch lengths are proportional to divergence time, which among the following species pairs would be expected to show the most post-zygotic isolation?

(A) P & S

(B) Q & R

(D) S & R

Ans: (B)

15. Members of which of the following animal phyla are exclusively marine?

(A) Cnidaria

(B) Echinodermata

(D) Porifera

Ans: (B)

16. Some amphibians, such as axolotl larvae, rarely metamorphose into an adult form in spite of being sexually mature. This phenomenon of retention of larval characters in the adult form is known as :

(A) Neoteny

(B) Ontogeny

(D) Polyphenism

Ans: (A)

17. Plants are classified into the following major categories : division, class, , order and family. These four categories generally have specific suffixes. Which among the following describes the correct order of specific suffixes for the categories of division, class, order and family respectively?

(A) −ales, −opsida, −phyta, −aceae

(B) −opsida, −phyta, −aceae, −ales

(D) −phyta, −opsida, −ales, −aceae

Ans: (D)

18. The Indian cricket team captain has lost the coin toss for nine consecutive games. Assuming that an unbiased coin is being used throughout the tournament, the chance that the Indian captain will win the toss on the 10^th game is ______.

Ans: (0.499 to 0.501)

19. Consider the function y = e^x. The slope of this function at x = 10 is

(A) 0

(B) 10

(D) 10 e¹⁰

Ans: (C)

20. Which of the following best demonstrates the phenomenon of a sign stimulus as defined in classical ethology? A male stickleback fish performing an aggressive display when presented with :

(A) A diamond-shaped model with the lower half painted red

(B) A life-like model of a male stickleback fish with a red belly

(D) A video-recording of another male stickleback fish with a red belly

Ans: (A)

21. Eating puffer fish can sometimes be fatal for human beings. This is because puffer fish carry a potent toxin known as :

(A) Botulinum toxin

(B) Bungarotoxin

(D) Tetrodotoxin

Ans: (D)

22. The ‘Selfish Herd’ hypothesis for group behavior predicts :

(A) Competition among individuals for central positions in groups

(B) Competition among individuals for peripheral positions in groups

(D) Co-operative defence against predators

Ans: (A)

23. Birds that inhabit forests typically produce calls in the form of low-pitched whistles. The most likely reason is that low-pitched whistles :

(A) Area easy to localize

(B) Experience high levels of scattering

(D) Travel faster than high-pitched whistles

Ans: (C)

24. At mid-latitudes, which of the following biomes is associated with hot dry summers and cool rainy winters?

(A) Boreal Forests

(B) Chapparal Forests

(D) Temperate Grasslands

Ans: (B)

25. Rafflesia arnoldii produces one of the largest flowers on earth and is typically pollinated by :

(A) Bats

(B) Bees

(D) Flies

Ans: (D)

26. Lantana camara is an invasive weed introduced into India from South America. If you characterize the genetic variation of this species in both its native and introduced populations, the South American population is expected to have :

(A) higher number of alleles per locus than the Indian population

(B) higher homozygosity than the Indian population

(D) lower genetic diversity than the Indian population

Ans: (A)

27. Which of the following combination of properties of neuronal circuits mediating escape behavior in animals would make them most effective at evading predators?

(A) large-diameter axons and chemical synapses

(B) Large-diameter axons and electrical synapses

(D) Small-diameter axons and electrical synapses

Ans: (B)

28. An experimentalist rejects a null hypothesis because she finds a p-value to be 0.01. This implies that :

(A) There is a 1% chance that the alternative hypothesis explains the data

(B) There is a 1% chance that the null hypothesis explains the data

(D) There is a 99% chance that the null hypothesis explains the data

Ans: (B)

29. A student counts every individual blackbuck in two grasslands. He finds 2100 and 2300 blackbuck in the two areas. Which statistical test is required to establish that these two population sizes are different?

(A) Chi-square test

(B) F-test

(D) Student’s t-test

Ans: (C)

30. The plot below shows the fitness of two traits as a function of relative frequency of trait-1 in the population. The solid line represents the fitness of trait-1 and the dotted line represents the fitness of trait-2. Which of the following is most likely to be TRUE?

(A) Either Trait-1 or Trait-2 will take over the population

(B) Only Triat-1 will take over the population

(D) Trait-1 and Trait-2 will oscillate over time

Ans: (A)

31. The following figure shows the phylogeny of insect species 1-5. Each of these 5 insect species harbours a specific bacterial endosymbiont. S R, Q, T and P are the endosymbiont bacteria associated with insect species 1, 2, 3, 4 and 5, respectively.

Which one of the following symbiont phylogenetic trees suggests host shift by these endosymbionts?

(A)

(B)

(C)

(D)

Ans: (C)

32. P to T are islands of different sizes at different distances from the mainland, where the distance x < y < z. The area of island P > Q > R = S = T. Assuming that there is migration only from the mainland to islands and not between islands, which of the following is NOT true about species richness on these islands?

(A) P > Q > R

(B) R > S > T

(D) S < Q < P

Ans: (C)

33. The frequency of an allele at a locus on the non-recombining region of the Y chromosome in humans is 0.3. If the population size is N and the sex ratio is 1 : 1, what is the number of copies of the alleles in the population ?

(A) 0.3 N/4

(B) 0.3 N/2

(D) 0.6 N

Ans: (B)

34. The species compositions of three areas, P, Q and R are shown below :

P : Cobra, Gecko, Crow, Viper

Q : Viper, Tiger, Salamander, Fish

R : Salamander, Viper, Frog, Chameleon

Based on the relationship between species, one can determine the phylogenetic diversity of each region. Which of the following captures the order of phylogenetic diversity of these regions?

(A) Q > P = R

(B) Q = R > P

(D) R > Q > P

Ans: (C)

35. Recent paleogenomic studies indicate that some groups of living humans have Neanderthal genes in their genomes. What is the best explanation for this phenomenon?

(A) Modern humans descended directly from Neanderthals

(B) Neanderthals are still living among us

(D) Some ancestors of living humans hybridized with the Neanderthals

Ans: (D)

36. A population grows as per the equation dn/dt = rn (1 – n/1000) where n is the population density, r is the intrinsic growth rate and 1000 is the carrying capacity. The growth rate of the population is maximum at a population density o f _________

Ans: (499.9 to 500.1)

37. An ecology exam paper has a large number of multiple choice questions with five options each, of which only one is correct. An unprepared student picks one of the five given options randomly, and attempts all questions. A correct answer yields one mark whereas a wrong answer yields negative x mark(s). To ensure that an unprepared student most likely gets zero marks, the value of x must be _______(write only the magnitude, not the sign).

Ans: (0.249 to 0.251)

38. Increasing atmospheric CO₂ concentration is likely to benefit C3 plants more than C4 plants because :

(A) C4 photosynthesis is inhibited by increasing CO₂

(B) Carboxylation increase relative to oxygenation in C3 plants

(D) Transpiration increases with increasing Co₂ in C4 plants

Ans: (B)

39. In meta communities composed of species A and B, the rates of colonization of habitat patches by A and C are C_A and C_B. The rates of extinction for species A and B in the absence of competition, are E_A and E_B. Species A is the superior competitor within any given patch. Which one of the following conditions is necessary to allow the continued persistence of species B?

(A) E_A > E_B

(B) C_B/E_B > C_A/E_A

(D) C_B > C_A

Ans: (B)

40. Batesian and Mullerian mimicry are effective anti-predatory defences because predators show :

(A) Habituation

(B) Imprinting

(D) Learning by positive reinforcement

Ans: (C)

41. A species possesses ten types of olfactory receptors (encoded by ten unique gene sequences) but i s able to perceptually distinguish a hundred different odorants. This is possible because each olfactory receptor type :

(A) binds to a subset of the 100 odorant molecules with unequal affinities

(B) binds to all 100 types of odorant molecules with equal affinity

(D) is specific and binds only one species of odorant molecule

Ans: (A)

42. Among vertebrates, male-only parental care is more commonly found among fishes and amphibians than birds and mammals. The most likely reason for this is because fishes and amphibians are characterized by :

(A) External fertilization

(B) Moist skin

(D) Sexual dimorphism

Ans: (A)

43. Guppies are fish that typically have blue, red and yellow spots on their bodies. In an experiment, one group of guppies was subjected to treatment X, where they were maintained and allowed to breed for several generations in ponds containing their natural predator species. A second group of fish was subjected to treatment Y, where they were maintained and allowed to breed for the same number of generations in ponds from which all predators were removed. After several generations, it was found that guppies subjected to treatment X had lost their blue spots, whereas those subjected to treatment Y showed an increase in the number of blue spots. Based on these observations, which one of t he following statements can be rejected?

(A) Blue spots on guppies are subject to natural selection

(B) Blue spots on guppies may be subject to sexual selection

(D) Blue spots are likely to make guppies less conspicuous to predators

Ans: (D)

44. Which of the following is NOT a plausible explanation for the evolution of seed dispersal mechanisms in plants?

(A) Long-distance dispersal benefits the dispersal agent

(B) Seed dispersal agents carry seeds to areas favourable for germination

(D) The area close to the parent plant is not optimal because of competition with kin

Ans: (A)

45. Which of the following evolutionary changes was NOT associated with the colonization of land by plants?

(A) Acquisition of dynein-mediated transport

(B) Acquisition of Jasmonic acid signaling

(D) Acquisition of seed desiccation tolerance

Ans: (A)

46. For a given low population size, which of these plant species are more likely to experience Allee effects?

(A) Asexual plants

(B) Bisexual plants

(D) Monoecious plants

Ans: (C)

47. Which of the following combinations of leaf traits is most likely to be observed in terrestrial plant communities that occur in low-nutrient environment with herbivory?

(A) High levels of protein and high levels of chemical defences

(B) High levels of protein and low levels of chemical defences

(D) Low levels of protein and low levels of chemical defences

Ans: (C)

48. Which of the following sets of parameters form the basis of Holdridge’s lifezone classification?

(A) Altitude, Mean Annual Biotemperature, Annual Precipitation

(B) Annual Precipitation, Mean Annual Biotemperature, Length of dry season

(D) Potential Evapotranspiration Ratio, Mean Annual Biotemperature, Annual Precipitation

Ans: (D)

49. The Annual Net Primary Productivity (ANPP) of ecosystems varies with the type of biome. Which of the following represents the correct order of ANPP values?

(A) Temperate Broadleaf Forest > Tropical Moist Forest > Boreal Forest > Savanna

(B) Tropical Moist Forest > Savanna > Temperate Broadleaf Forest > Boreal Forest

(D) Tropical Moist Forest > Temperate Broadleaf Forest > Savanna > Boreal Forest

Ans: (D)

50. Which of these communities (R1, R2, R3, and R4) each with 80 species and represented by their Species Rank-Abundance curves, is likely to have the highest value of Shannon’s index of species diversity?

(A) R1

(B) R2

(D) R4

Ans: (A)

51. In any experimental design, we prefer a large sample size because :

(A) It reduces errors in the estimation of the mean effect

(B) It reduces the possibility of outliers

(D) It reduces variability between different data points

Ans: (A)

52. In haplo-diploid insects, males are haploid and females are diploid. For a haplo-diploid species, assume that each individual mates only once. The minimum coefficient of relatedness between two female cousins, whose maternal grandmother is the same, is ________(enter answer to 4 decimal places).

Ans: (0.185 to 0.190)

53. Match the scientists with the concept or theories they are most famously associated with :

(A) P – i; Q – iii; R – iv; S – ii

(B) P – iv; Q – iii; R – ii; S – i

(D) P – iv; Q – i; R – ii; S – iii

Ans: (C)

54. Which of the following graphs best represents the function given by the following equation :

(A)

(B)

(C)

(D)

Ans: (A)

55. On the semi-arid plateaus of the Western Ghats, raptors, lizards and grasshoppers dominate the community of animals. Raptors prey primarily on lizards, which prey primarily on grasshoppers. If raptor density declines significantly, which of the following is expected?

(A) Both grasshopper and plant densities will increase

(B) Only grasshopper density will increase

(D) Plant density will decrease

Ans: (C)

56. She has a sharp tongue and it can occasionally turn ______

(A) hurtful

(B) left

(D) vital

Ans: (A)

57. I ____ make arrangements had I ____ informed earlier.

(A) could have, been

(B) would have, being

(D) had been, been

Ans: (A)

58. In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%.while other consumption increases by 70%

Which of the following statements is correct?

(A) The ratio of household to other consumption is 8/17

(B) The ratio of household to other consumption is 1/17

(D) There are errors in the official’s statement.

Ans: (D)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

(A) 120

(B) 144

(D) 212

Ans: (B)

60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?

i. At least one bench is a table

ii. At least one shelf is a bench

iii. At least one chair is a table

iv. All benches are chairs.

(A) Only i

(B) Only ii

(D) Only iv

Ans: (B)

61. ‘If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this multilation will have in the respective section, and ultimately on Asia, you will not find events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word ‘antagonistic’ is closest in meaning to

(A) impartial

(B) argumentative

(D) hostile

Ans: (D)

62. T.U.V.W.W.X.Y. and Z are seated around a circular table. T’s neighbours are Y and V. Z is seated third to the left of T and second to the right of S. U;s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

(A) X

(B) W

(D) T

Ans: (A)

63. Trucks (10 m long) and cars (5 long) go on a single lane bridge. There must be gap of at least 20 m after each truck and a gap of atleast 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately. What is the maximum number of vehicles that can use the bridge in one hour?

(A) 1440

(B) 1200

(D) 600

Ans: (A)

64. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

(A) 56

(B) 52

(D) 44

Ans: (A)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

(A) Up-Down-Up-Down

(B) Down-Up-Down-Up

(D) Up-Down-Up

Ans: (C)

Gate 2017 Electrical Engineering Question Paper 11th Feb 2017 Session 2 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electrical Engineering 11th Feb 2017 Session 2

Subject Name: Electrical Engineering

Duration : 180

Total Marks: 100

1. In the circuit shown, the diodes are ideal, the inductance is small, and I_o ≠ Which one of the following statements is true?

(A) D₁ conducts for greater than 180° and D₂ conducts for greater than 180°

(B) D₂ conducts for more than 180° and D₂ conducts for 180°

(D) D₁ conducts for more than 180° and D₂ conducts for 180°

Ans: (A)

2. For a 3-input logic circuit shown below, the output Z can be expressed as

(A)

(B)

(C)

(D)

Ans: (C)

3. An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is

(A) 1/2

(B) 4/9

(D) 6/9

Ans: (A)

4. When a unit ramp input is applied to the unity feedback system having closed loop transfer function the steady state error will be

(A)

(B)

(C)

(D)

Ans: (D)

5. A three-phase voltage source inverter with ideal devices operating in o 180 conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is V_dc. The peak of the fundamental component of the phase voltage is

(A)

(B)

(C)

(D)

Ans: (B)

6. The figures show diagrammatic representations of vector fields respectively. Which one of the following choices is true?

(A)

(B)

(C)

(D)

Ans: (C)

7. Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.

Ans: (0.9)

8. Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.

(A) uniformly over the entire volume of the sphere

(B) uniformly over the outer surface of the sphere

(D) along a straight line passing through the centre of the sphere

Ans: (B)

9. The transfer function C(s) of a compensator is given below.

The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is

(A) 0.1 < ω < 1

(B) 1 < ω < 10

(D) ω > 100

Ans: (A)

10. The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts.

For the given circuit, Y_bus and Z_bus are bus admittance matrix and bus impedance matrix, respectively, each of size 2× 2. Which one of the following statements is true?

(A) Both Y_bus and Z_bus are symmetric

(B) Y_bus is symmetric and Z_bus is unsymmetric

(D) Both Y_bus and Z_bus are unsymmetric

Ans: (D)

11. A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in Hz of the voltage ripple on the DC side is

(A) 25

(B) 50

(D) 300

Ans: (C)

12. Let x and y be integers satisfying the following equations

2x² + y² = 34

x + 2y = 11

The value of (x + y) is ________.

Ans: (7)

13. Consider a function f(x, y, z) given by

f(x, y, z) = (x² + y² – 2z²) (y² + z²)

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is ________

Ans: (40)

14. For the given 2-port network, the value of transfer impedance Z₂₁ in ohms is_______

Ans: (3)

15. The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ______. (Give the answer up to one decimal place.)

Ans: (100)

16. The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are ideal. The firing angles of the thyristors T₁ and T₂ are 90° and 270°, respectively.

The RMS value of the current through diode D₃ in amperes is ________

Ans: (0)

17. In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100× If there are 20 PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.

Ans: (61)

18. A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

(A) 1500

(B) 1470

(D) 154

Ans: (C)

19. Two resistors with nominal resistance values R₁ and R₂ have additive uncertainties ∆R₁ and ∆R₂, respectively. When these resistances are connected in parallel, the standard deviation of the error in the equivalent resistance R is

(A)

(B)

(C)

(D)

Ans: (A)

20. The nominal- π circuit of a transmission line is shown in the figure.

Impedance and reactance X = 3300Ω. The magnitude of the characteristic impedance of the transmission line, in Ω, is _______________. (Give the answer up to one decimal place.)

Ans: (406.2)

21. The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

Which one of the following is TRUE about the frequency selectivity of these systems?

(A) All three are high-pass filters.

(B) All three are band-pass filters.

(D) P is a low-pass filter, Q is a band-pass filter and R is a high-pass filter.

Ans: (B)

22. The mean square value of the given periodic waveform f (t) is_________

Ans: (6)

23. A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHZ. The frequency of the vertical input is

(A) 1.5 kHz

(B) 2 kHz

(D) 4.5 kHz

Ans: (D)

24. Let y² – 2y + 1 = x and √x + y = 5. The value of x + √y equals ______. (Give the answer up to three decimal places)

Ans: (5.732)

25. If a synchronous motor is running at a leading power factor, its excitation induced voltage (E_f) is

(A) equal to terminal voltage V_t

(B) higher than the terminal voltage V_t

(D) dependent upon supply voltage V_t

Ans: (B)

26. Which of the following systems has maximum peak overshoot due to a unit step input?

(A)

(B)

(C)

(D)

Ans: (C)

27. Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length D_ab = D_bc = D_ca = 1m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01m. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω/ km (rounded off to three decimal places) is ________

Ans: (0.289)

28. Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel to share a load of 600 MW. Assuming free governor action, the load shared by the larger unit is _______ MW.

Ans: (400)

29. For the network given in figure below, the Thevenin‟s voltage V_ab is

(A) −1.5 V

(B) −0.5 V

(D) 1.5 V

Ans: (A)

30. The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is

(A) 1000 samples/s

(B) 1500 sample/s

(D) 3000samples/s

Ans: (B)

31. A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance R_a = 0.02Ω. When the motor operates at rated speed and with rated terminal voltage, the electromagnetic torque developed by the motor is 70 Nm. Neglecting the rotational losses of the machine, the current drawn by the motor from the 220 V supply is

(A) 34.2 A

(B) 30 A

(D) 4.84 A

Ans: (B)

32. A cascade system having the impulse responses is shown in the figure below, where symbol ↑ denotes the time origin.

The input sequence x (n) for which the cascade system produces an output sequence is

(A)

(B)

(C)

(D)

Ans: (D)

33. For the circuit shown in the figure below, it is given that The transistor has β = 29 and V_BE = 0.7 V when the B-E junction is forward biased.

For this circuit, the value of is

(A) 43

(B) 92

(D) 129

Ans: (D)

34. A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running steadily at synchronous speed and delivering 60 MW power at a power angle of 10 electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for 10 cycles, the value of the power angle after 5 cycles is ________ electrical degrees.

Ans: (12.7)

35. For the circuit shown below, assume that the OPAMP is ideal.

Which one of the following is TRUE?

(A) V_o = v_s

(B) v_o = 1.5v_s

(D) v_o = 5v_s

Ans: (C)

36. The root locus of the feedback control system having the characteristic equation s² + 6Ks + 2s + 5 = 0 where K > 0, enters into the real axis at

(A) s = −1

(B) s = −√5

(D) s = √5

Ans: (B)

37. For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions

The minimum number of clock cycles after which the output Z would again become zero is ________

Ans: (6)

38. In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is

(A) 1 nF

(B) 1 μF

(D) 10 mF

Ans: (D)

39. In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is ________. (Give the answer up to one decimal place.)

Ans: (40)

40. In the circuit shown in the figure, the diode used is ideal. The input power factor is _______. (Give the answer up to two decimal places.)

Ans: (0.707)

41. Consider the system described by the following state space representation

If u(t) is a unit step input and the value of output y(t) at t = 1 sec (rounded off to three decimal places) is ________

Ans: (1.2838)

42. A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R₁ = 0.3Ω, R₂ = 0.3Ω, X₁ = 0.41Ω, X₂ = 0.41Ω Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3-phase AC source is __________.

Ans: (71.04)

43. A 25 kVA, 400 V, ∆ – connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is 360 V. Neglecting the armature resistance and magnetic saturation, its voltage regulation (in % with respect to terminal voltage), when the generator delivers the rated load at 0.8 pf leading, at rated terminal voltage is _________.

Ans: (−14.6)

44. If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA. Y− ∆ transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is_____.

Ans: (37.879)

45. For the balanced Y-Y connected 3-Phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of 0.6 leading.

The approximate value of the impedance Z is

(A) 33∠−53.1°Ω

(B) 60∠53.1°Ω

(D) 180∠−53.1°Ω

Ans: (C)

46. A thin soap bubble of radius R = 1 cm, and thickness a = 3.3μm(a <<R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius r. The volume of the soap in the thin bubble is 4πR²a and that of the drop is The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is __________. (Give the answer up to two decimal places.)

Ans: (10.03)

47. The value of the contour integral in the complex-plane

Along the contour |Z| = 3, taken counter-clockwise is

(A) −18πi

(B) 0

(D) 48πi

Ans: (C)

48. Let

Consider the composition of f and g, i.e., (f ∘ g) (x) = f(g(x)). The number of discontinuities in (f ∘ g) present in the interval (−∞, 0) is:

(A) 0

(B) 1

(D) 4

Ans: (A)

49. A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω, and the shunt field resistance is 240Ω. The no load speed, in rpm, is ________.

Ans: (1241.82)

50. A 10 ½ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with a gating time of one second and (ii) Period mode of operation (in the x 10 ns scale). The frequency of the unknown input (reading obtained) in Hz is _______.

Ans: (10000)

51. A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y} , where var {.} denotes the variance, equals

(A)

(B)

(C)

(D)

Ans: (C)

52. The figure below shows a half-bridge voltage source inverter supplying an RL-load with The desired fundamental frequency of the load voltage is 50 Hz. The switch control signals of the converter are generated using sinusoidal pulse width modulation with modulation index. M = 0.6. At 50 Hz, the RL-load draws an active power of 1.44 kW. The value of DC source voltage V_DC in volts is

(A) 300√2

(B) 500

(D) 1000√2

Ans: (C)

53. The range of K for which all the roots of the equation s³ + 3s² + 2s + K = 0 are in the left half of the complex s-plane is

(A) 0 < K < 6

(B) 0 < K < 16

(D) 6 < K < 16

Ans: (A)

54. The eigen values of the matrix given below are

(A) (0, −1, −3)

(B) (0, −2, −3)

(D) (0, 1, 3)

Ans: (A)

55. A 3-phase 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25Ω and 3.925Ω If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.

Ans: (0.737)

56. There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W, Z is to the East of X and the West of V, W is to the West of Y. Which is the building in the middle?

(A) V

(B) W

(D) Y

Ans: (A)

57. Saturn is _________ to be seen on a clear night with the naked eye.

(A) enough bright

(B) bright enough

(D) bright as enough

Ans: (B)

58. Choose the option with words that are not synonyms.

(A) aversion, dislike

(B) luminous, radiant

(D) yielding, resistant

Ans: (D)

59. There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

(A) 1/5

(B) 7/30

(D) 4/15

Ans: (D)

60. A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

(A) 12

(B) 15

(D) 19

Ans: (B)

61. An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

(A) P

(B) Q

(D) S

Ans: (C)

62. There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

(A) The box labelled “Apples”

(B) The box labelled “Apples and Oranges”

(D) Cannot be determined

Ans: (B)

63. “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”

The author’s belief that ideology is not as important as literature is revealed by the word:

(A) ‘culture’

(B) ‘seemingly’

(D) ‘political’

Ans: (B)

64. X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number 3 X will have

(A) 90 digits

(B) 91 digits

(D) 93 digits

Ans: (A)

65. The number of roots of e^x + 0.5x² – 2 = 0 in the range [−5, 5] is

(A) 0

(B) 1

(D) 3

Ans: (C)

Gate 2017 Electrical Engineering Question Paper 11th Feb 2017 Session 1 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electrical Engineering 11th Feb 2017 Session 1

Subject Name: Electrical Engineering

Duration : 180

Total Marks: 100

1. Consider

Here, represents the largest integer less than or equal to t and denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

Ans: (0)

2. A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are V_an = 220 sin (100 πt) V and i_a = 10 sin(100 πt)A, respectively. Similarly for phase-b the instantaneous voltage and current are V_bn = 220 cos(100 πt) V and i_b = 10 cos(100 πt) A, respectively.

The total instantaneous power flowing form the source to the load is

(A) 2200 W

(B) 2200 sin² (100 πt) W

(D) 2200 sin(100 πt) cos (100 πt) W

Ans: (A)

3. A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor (UPF). The synchronous reactance of the motor is 30 Ω per phase. The load angle is 30°. The power delivered to the motor in kW is _______.

Ans: (835 to 842)

4. For a complex number z, is

(A) −2i

(B) −i

(D) 2i

Ans: (D)

5. Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are released but are constrained to move along the same straight line. Which of these will collide first?

(A) The particles will never collide

(B) All will collide together

(D) Electron and Neutron

Ans: (D)

6. Let z(t) = x(t) * y(t), where “ * ” denotes convolution. Let C be a positive real-valued constant. Choose the correct expression for z (ct).

(A) c.x(ct) * y(ct)

(B) x(ct) * y(ct)

(D) c.x(ct) * y(t)

Ans: (A)

7. A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are Y₁₁ = −j12pu, Y₂₂ = −j15pu and Y₃₃ = −j7pu

The per unit values of the line reactances p, q and r shown in the figure are

(A) p = −0.2, q = −0.1, r = −0.5

(B) p = 0.2, q = 0.1, r = 0.5

(D) p = 5, q =10, r = 2

Ans: (B)

8. The equivalent resistance between the terminals A and B is ______ Ω.

Ans: (2.9 to 3.1)

9. The Boolean expression simplifies to

(A)

(B)

(C)

(D)

Ans: (A)

10. The following measurements are obtained on a single phase load:

V = 220V ±1%, I = 5.0A ±1% and W = 555W±2%. If the power factor is calculated using these measurements, the worst case error in the calculated power factor in percent is ______.

Ans: (4)

11. The transfer function of a system is given by, . Let the output of the system be v_o(t) = V_m sin(ωt + φ) for the input v_i(t) = V_m sin(ωt). Then the minimum and maximum values of φ (in radians) are respectively

(A)

(B)

(C)

(D)

Ans: (D)

12. The matrix has three distinct eigenvalues and one of its eigenvectors is

Which one of the following can be another eigenvector of A?

(A)

(B)

(C)

(D)

Ans: (C)

13. For the power semiconductor devices IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?

(A) All of the four are majority carrier devices.

(B) All the four are minority carrier devices

(D) MOSFET is majority carrier device, whereas IGBT, Diode, Thyristor are minority carrier devices.

Ans: (D)

14. Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30° is _______.

Ans: (1.01 to 1.06)

15. A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

(A) bend closer to the cylinder axis

(B) bend farther away from the axis

(D) cease to exist inside the cylinder

Ans: (A)

16. Let where R is the region shown in the figure and c = 6 × 10⁻⁴. The value of I equals ______.

Ans: (0.99 to 1.01)

17. Consider the system with following input-output relation y[n] = (1 + (−1)ⁿ)x[n] where, x[n] is the input and y[n] is the output. The system is

(A) invertible and time invariant

(B) invertible and time varying

(D) non-invertible and time varying

Ans: (D)

18. The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of

(A) 150 ns has to be inserted into the y-channel

(B) 150 ns has to be inserted into the x-channel

(D) 100 ns has to be inserted into both x and y channels

Ans: (A)

19. A 3-phase voltage source inverter is supplied from a 600V DC source as shown in the figure below. For a star connected resistive load of 20 Ω per phase, the load power for 120o device conduction, in kW is __________.

Ans: (8.5 to 9.5)

20. A closed loop system has the characteristic equation given by s³ + Ks² + (K + 2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?

(A) 0 < K < 0.5

(B) 0.5 < K < 1

(D) K > 1

Ans: (D)

21. A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is

(A) 1350

(B) 1650

(D) 2250

Ans: (C)

22. For the circuit shown in the figure below, assume that diodes D₁, D₂ and D₃ are ideal.

The DC components of voltages v₁ and v₂, respectively are

(A) 0 V and 1 V

(B) −0.5 V and 0.5 V

(D) 1 V and 1 V

Ans: (B)

23. A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator bus G1 is considered as slack bus, and the load buses L3 and L4 are voltage controlled buses. The generator at bus G2 cannot supply the required reactive power demand, and hence it is operating at its maximum reactive power limit. The number of non-linear equations required for solving the load flow problem using Newton-Raphson method in polar form is _______

Ans: (14)

24. The power supplied by the 25 V source in the figure shown below is ________W.

Ans: (248 to 252)

25. In the converter circuit shown below, the switches are controlled such that the load voltage v_o(t) is a 400 Hz square wave.

The RMS value of the fundamental component of v_o(t) in volts is _______.

Ans: (196 to 200)

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

(A)

(B)

(C)

(D)

Ans: (D)

27. A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4Ω and 0.1 Ω The load torque varies as the square of the speed. The flux in the motor may be taken as being proportional to the armature current. To reduce the speed of the motor by 50% the resistance in ohms that should be added in series with the armature is _________.

Ans: (9.5 to 12)

28. The transfer function of the system Y(s)/U(s) whose state-space equations are given below is:

(A)

(B)

(C)

(D)

Ans: (D)

29. The load shown in the figure is supplied by a 400 V (line to line) 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in position N, the three watt-meters W₁, W₂ and W₃ read 577.35 W each. If the switch is moved to position Y, the readings of the watt-meters in watts will be:

(A) W₁ = 1732 and W₂ = W₃ = 0

(B) W₁ = 0, W₂ = 1732 and W₃ = 0

(D) W₁ = W₂ = 0 and W₃ = 1732

Ans: (D)

30. Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1.

A₁ , B₁,C₁, D₁, A₂, B₂, C₂ and D₂ are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source V_T and impedance Z_T connected in series, then

(A)

(B)

(C)

(D)

Ans: (D)

31. The circuit shown in the figure uses matched transistors with a thermal voltage V_T = 25mV. The base currents of the transistors are negligible. The value of the resistance R in kΩ that is required to provide 1μA bias current for the differential amplifier block shown is ______.

Ans: (170 to 174)

32. The figure below shows an uncontrolled diode bridge rectifier supplied form a 220 V, 50 Hz 1-phase ac source. The load draws a constant current I_o= 14A. The conduction angle of the diode D₁ in degrees is___________.

Ans: (220 to 230)

33. Consider the differential equation with y(1) = 2π. There exists a unique solution for this differential equation when t belongs to the interval

(A) (−2, 2)

(B) (−10, 10)

(D) (0, 10)

Ans: (A)

34. A separately excited DC generator supplies 150 A to a 145 V DC grid. The generator is running at 800 RPM. The armature resistance of the generator is 0.1 Ω . If the speed of the generator is increased to 1000 RPM, the current in amperes supplied by the generator to the DC grid is _______.

Ans: (548 to 552)

35. In the circuit shown below, the maximum power transferred to the resistor R is _______ W.

Ans: (3 to 3.1)

36. Let a causal LTI system be characterized by the following differential equation, with initial rest condition

Where x(t) and y(t) are the input and output respectively. The impulse response of the system is (u(t) is the unit step function)

(A) 2e⁻^2tu(t) – 7e⁻^5tu(t)

(B) −2e⁻^2tu(t) + 7e⁻^5tu(t)

(D) −7e⁻^2tu(t) + 2e⁻^5tu(t)

Ans: (B)

37. The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be

(A)

(B)

(C)

(D)

Ans: (A)

38. The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for t ≥ 0, is

(A) 2.5e⁻^4t

(B) 5e⁻^4t

(D) 5e⁻^0.25t

Ans: (A)

39. The bus admittance matrix for a power system network is

There is a transmission line, connected between buses 1 and 3, which is represented by the circuit shown in figure.

If this transmission line is removed from service, What is the modified bus admittance matrix?

(A)

(B)

(C)

(D)

Ans: (C)

40. In the system whose signal flow graph is shown in the figure, U₁(s) and U₂ (s) are inputs. The transfer function is

(A)

(B)

(C)

(D)

Ans: (A)

41. For a system having transfer function a unit input is applied at time t = 0. The value of the response of the system at t = 1.5 sec is _____.

Ans: (0.550 to 0.556)

42. The magnitude of magnetic flux density (B) in micro Teslas (μT) at the center of a loop of wire wound as a regular hexagon of side length 1m carrying a current (I=1A), and placed in vacuum as shown in the figure is __________.

Ans: (0.65 to 0.75)

43. The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sin δ, where δ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to 1 pu. If one of the transmission line circuits is removed, the maximum value of δ as the rotor swings, is 1.221 radian. If the expression for electrical power with one transmission line circuit removed is P_max sinδ, the value of P_max, in pu is ______.

Ans: (1.21 to 1.23)

44. A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Z_m = (12.50 + j15.75)Ω (main winding), Z_a = (24.50 + j12.75)Ω (auxiliary windings). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.

Ans: (95 to 100)

45. A function f(x) is defined as where x ∈ ℝ.

Which one of the following statement is TRUE?

(A) f(x) is NOT differentiable at x=1 for any values of a and b.

(B) f(x) is differentiable at x = 1 for the unique values of a and b

(D) f(x) is differentiable at x = 1 for all values of a and b.

Ans: (A)

46. Consider a causal and stable LTI system with rational transfer function H(z). Whose corresponding impulse response begins at n = 0. Furthermore, The poles of H(z) are for k = 1, 2, 3, 4. The zeros of H(z) are all at z = 0. Let g[n] = jⁿh[n]. The value of g[8] equals

Ans: (0.06 to 0.65)

47. Only one of the real roots of f(x) = x⁶ – x – 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is ________.

Ans: (10)

48. Two parallel connected, three-phase, 50Hz, 11kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid. Current supplied by both the machines are equal. Synchronous reactances of machine A and machine B are 1Ω and 3Ω Assuming the magnetic circuit to be linear, the ratio of excitation current of machine A to that of machine B is ________.

Ans: (2.05 to 2.13)

49. The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero).

Ans: (0.1)

50. Let the signal be passed through an LTI system with frequency response H(ω) , as given in the figure below

The Fourier series representation of the output is given as

(A) 4000 + 4000cos(2000πt) + 4000cos(4000πt)

(B) 2000 + 2000 cos(2000πt) + 2000 cos(4000πt)

(D) 2000 cos(2000πt)

Ans: (C)

51. The logical gate implemented using the circuit shown below where. V₁ and V₂ are inputs (with 0 V as digital 0 and 5 V as digital 1) and V_OUT is the output is

(A) NOT

(B) NOR

(D) XOR

Ans: (B)

52. A load is supplied by a 230 V, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that 1 kW ≤ P ≤ 2kW and 1kVAR ≤ Q ≤ A capacitor connected across the load for power factor correction generates 1 kVAR reactive power. The worst case power factor after power factor correction is

(A) 0.447 lag

(B) 0.707 lag

(D) 1

Ans: (B)

53. The input voltage V_DC of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The range of duty ratio D of the converter for which the magnitude of the steady state output voltage remains constant at 48 V is

(A)

(B)

(C)

(D)

Ans: (A)

54. A three-phase, three winding ∆/∆/Y (1.1 kV/6.6kv/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV winding and 300 kVA load at 0.6 power factor lag from the 400 V winding. The RMS line current in ampere drawn by the 1.1 kV winding from the mains is _______.

Ans: (623 to 627)

55. Consider the line integral where z = x + iy. The line C is shown in the figure below.

The value of I is.

(A)

(B)

(C)

(D)

Ans: (B)

56. Research in the workplace reveals that people work for many

(A) money beside

(B) beside money

(D) besides money

Ans: (D)

57. The probability that a k-digit number does NOT contain the digits 0.5, or 9 is

(A) 0.3^k

(B) 0.6^k

(D) 0.9^k

Ans: (C)

58. Find the smallest number y such that y × 162 is a perfect cube.

(A) 24

(B) 27

(D) 36

Ans: (D)

59. After Rajendra Chola returned from his voyage to Indoneisa, he _______ to visit the temple in Thanjavur.

(A) was wishing

(B) is wishing

(D) had wished

Ans: (C)

60. Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?

(A) Rahul and Murali

(B) Srinivas and Anil

(D) Srinivas and Rahul

Ans: (C)

61. Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

(A) 2

(B) 3

(D) Cannot be determined

Ans: (A)

62. The expression is equal to

(A) the maximum of x and y

(B) the minimum of x and y

(D) none of the above

Ans: (B)

63. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m. Which of the villages P,Q,R,S,T get submerged?

(A) P, Q

(B) P, Q, T

(D) Q, R, S

Ans: (C)

64. Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white, Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

(A) 21

(B) 18

(D) 14

Ans: (D)

65. “The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history.”

Which of the following statements best reflects the author’s opinion?

(A) Nationalists are highly imaginative.

(B) History is viewed through the filter of nationalism.

(D) Nationalism has to be both adequately and properly imagined.

Ans: (B)

Gate 2017 Electronics and Communication Engineering Question Paper 5th Feb 2017 Session 2 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electronics and Communication Engineering 5th Feb 2017 Session 2

Subject Name: Electronics and Communication Engineering

Duration : 180

Total Marks: 100

1. Consider the circuit shown in the figure.

The Boolean expression F implemented by the circuit is

(A)

(B)

(C)

(D)

Ans: (B)

2. An LTI system with unit sample response h[n] = 5δ[n] – 7δ[n – 1] + 7δ[n – 3] – 5δ[n – 4] is a

(A) Low – pass filter

(B) high – pass filter

(D) band – stop filter

Ans: (C)

3. In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V. The ratio is _______.

Ans: (0.19 to 0.21)

4. In a DRAM,

(A) periodic refreshing is not required

(B) information is stored in a capacitor

(D) both read and write operations can be performed simultaneously

Ans: (B)

5. Consider an n-channel MOSFET having width W, length L, electron mobility in the channel μ_n and oxide capacitance per unit are C_0%. If gate-to-source voltage V_GS = 0.7V, drain-to-source voltage V_DS = 0.1V, (μ_nC_0%) = 100μA/V², threshold voltage V_TH = 0.3 V and (W/L) = 50 then the transconductance g_m(in mA/V) is _______.

Ans: (0.45 to 0.55)

6. Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.

For some charge placed on this structure, the potential and surface electric field on S1 are V_a and E_a, and that on S2 are V_b and E_b, respectively, which of the following is CORRECT?

(A) V_a = V_b and E_a < E_b

(B) V_a > V_b and E_a > E_b

(D) V_a > V_b and E_a = E_b

Ans: (C)

7. For the circuit shown in the figure, P and Q are the inputs and Y is the output.

The logic implemented by the circuit is

(A) XNOR

(B) XOR

(D) OR

Ans: (B)

8. An n-channel enhancement mode MOSFET is biased at V_GS > V_TH and V_DS > (V_GS – V_TH), where V_GS is the gate-to-source voltage, V_DS is the drain-to-source voltage and V_TH is the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a

(A) voltage source with zero output impedance

(B) voltage source with non-zero output impedance

(D) current source with infinite output impedance

Ans: (C)

9. A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10Ω, 5Ω, 2Ω are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ____________.

Ans: (2.12 to 2.16)

10. An npn bipolar junction transistor (BJT) is operating in the active region. If the reverse bias across the base – collector junction is increased, then

(A) the effective base width increases and common – emitter current gain increases

(B) the effective base width increases and common – emitter current gain decreases

(D) the effective base width decreases and common – emitter current gain decreases

Ans: (C)

11. Consider the state space realization with the initial condition where u(t) denotes the unit step function. The value of is ________.

Ans: (4.99 to 5.01)

12. The rank of the matrix is _______.

13. A two – wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is ______________

Ans: (48.0 to 51.0)

14. The input x(t) and the output y (t) of a continuous-time system are related as The system is

(A) Linear and time-variant

(B) Linear and time-invariant

(D) Non-linear and time-invariant

Ans: (B)

15. Which of the following statements is incorrect?

(A) Lead compensator is used to reduce the settling time.

(B) Lag compensator is used to reduce the steady state error.

(D) Lag compensator always stabilizes an unstable system.

Ans: (D)

16. The residues of a function are

(A)

(B)

(C)

(D)

Ans: (B)

17. A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is _______

Ans: (7)

18. The general solution of the differential equation in terms of arbitrary constants K₁ and K₂ is

(A)

(B)

(C)

(D)

Ans: (A)

19. Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P?

(A)

(B)

(C)

(D)

Ans: (C)

20. The output V₀ of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is ____________.

Ans: (3.15 to 3.21)

21. Consider the random process X(t) = U + Vt, where U is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is ____________

Ans: (2)

22. For the system shown in the figure, Y (s) / X (s) = __________.

Ans: (0.95 to 1.05)

23. The smaller angle (in degrees) between the planes x + y + z =1 and 2x – y + 2z = 0 is ________.

Ans: (54.0 to 55.0)

24. Consider the circuit shown in the figure. Assume base-to- emitter voltage V_BE=0.8 V and common base current gain (α) of the transistor is unity.

The value of the collector- to – emitter voltage V_CE (in volt) is _______.

Ans: (5.5 to 6.5)

25. In the figure, D1 is a real silicon pn junction diode with a drop of 0.7V under forward bias condition and D2 is a zener diode with breakdown voltage of -6.8 V. The input Vin(t) is a periodic square wave of period T, whose one period is shown in the figure.

Assuming 10τ << T.where τ is the time constant of the circuit, the maximum and minimum values of the output waveform are respectively,

(A) 7.5 V and –20.5V

(B) 6.1 V and –21.9V

(D) 6.1 V and –22.6 V

Ans: (A)

26. If the vector is irrotational, then the values of the constants k₁, k₂ and k₃ respectively, are

(A) 0.3, –2.5, 0.5

(B) 0.0, 3.0, 2.0

(D) 4.0, 3.0, 2.0

Ans: (B)

27. The un-modulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduced to 40%, then the maximum un-modulated carrier power (in kW) that can be used without overloading the transmitter is ___________

Ans: (5.19 to 5.23)

28. Consider an LTI system with magnitude response

And phase response Arg {H(f)} = −2f.

If the input to the system is

Then the average power of the output signal y(t) is

Ans: (7.95 to 8.05)

29. A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV. E_C – F_F = 0.9 eV, where E_C and E_F are the conduction band minimum and the Fermi energy levels of Si, respectively. Oxide ∈_r = 3.9, ∈₀ = 8.85 × 10⁻¹⁴ F/cm. oxide thickness t_ox = 0.1 μm and electronic charge q = 1.6 × 10⁻¹⁹ If the measured flat band voltage of the capacitor is −1V, then the magnitude of the fixed charge at the oxide-semiconductor interface, in nC/cm², is ______.

Ans: (6.85 to 6.95)

30. An electron (q₁) is moving in free space with velocity 10⁵ m/s towards a stationary electron (q₂) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is _______×10⁻⁸

[Given, mass of electron m = 9.11 × 10⁻³¹ kg, charge of electron e = −1.6 × 10⁻¹⁹ C, and permittivity ε₀ = (1/36π) × 10⁻⁹ F/m]

Ans: (4.55 to 5.55)

31. The values of the integrals are

(A) same and equal to 0.5

(B) same and equal to –0.5

(D) – 0.5 and 0.5, respectively

Ans: (C)

32. Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is _________.

Ans: (2.4 to 2.6)

33. Figure I shows a 4-bits ripple carry adder realized using full adders and Figure II shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure II are 20 ns, 15 ns and 10 ns respectively. Assume all the inputs to the 4-bit adder are initially reset to 0.

At t=0, the inputs to the 4-bit adder are changed to

X₃X₂X₁X₀ = 1100, Y₃Y₂Y₁Y₀ = 0100 and Z₀ = 1.

The output of the ripple carry adder will be stable at t (in ns) = ___________

Ans: (70)

34. The permittivity of water at optical frequencies is 1.75 ε₀ . It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5m, as shown in the figure. The critical angle is θ_c.

The value of d (in meter) is _____________

Ans: (4.2 to 4.4)

35. A unity feedback control system is characterized by the open-loop transfer function

The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below.

If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right –half of the s-plane is

(A) 0

(B) 1

(D) 3

Ans: (C)

36. The signal x(t) = sin(14000πt), where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :

What is the number of sinusoids in the output and their frequencies in kHz?

(A) Number = 1, frequency = 7

(B) Number = 3, frequencies= 2,7,11

(D) Number = 2, frequencies = 2, 11

Ans: (B)

37. A unity feedback control system is characterized by the open-loop transfer function

The value of k for which the system oscillates at 2 rad/s is ________.

Ans: (0.74 to 0.76)

38. Consider the circuit shown in the figure.

The Thevenin equivalent resistance (in Ω ) across P – Q is _________.

Ans: (−1.01 to −0.99)

39. The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = [sin(t)/πt]u(t), where u(t) is a unit step function, the system output y(t) as t → ∞ is ______.

Ans: (0.45 to 0.55)

40. An integral I over a counter clock wise circle C is given by . If C is defined as |z| = 3, then the value of I is

(A) −πi sin(1)

(B) −2πi sin(1)

(D) −4πi sin(1)

Ans: (D)

41. Consider a binary memory less channel characterized by the transition probability diagram shown in the figure.

The channel is

(A) Lossless

(B) Noiseless

(D) Deterministic

Ans: (C)

42. An abrupt pn junction (located at x = 0) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the x-direction is E(x). Which of the following figures represents the electric field profile near the pn junction?

(A)

(B)

(C)

(D)

Ans: (A)

43. A second – order LTI system is described by the following state equations,

Where x₁ (t) and x₂(t) are the two state variables and r(t) denotes the input. The output c(t) = x₁(t). The system is

(A) Undamped (oscillatory)

(B) Under damped

(D) Over damped

Ans: (D)

44. Consider the parallel combination of two LTI systems shown in the figure.

The impulse responses of the systems are

h₁(t) = 2δ(t + 2) – 3δ(t + 1)

h₂(t) = δ(t – 2)

If the input x(t) is a unit step signal, then the energy of y(t) is ____________.

Ans: (7.0)

45. Assuming that transistors M₁ and M₂ are identical and have a threshold voltage of 1V, the state of transistors M₁ and M₂ are respectively.

(A) Saturation, Saturation

(B) Linear, Linear

(D) Saturation, Linear

Ans: (C)

46. A programmable logic array (PLA) is shown in the figure.

The Boolean function F implemented is

(A)

(B)

(C)

(D)

Ans: (C)

47. A modulating signal given By x(t) = 5 sin(4π10³t – 10π cos 2π10³t)V is fed to a phase modulator with phase deviation constant k_p = 0.5 rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________

Ans: (69.9 to 70.1)

48. The minimum value of the function in the interval −100 ≤ x ≤ 100 occurs at x = _____.

Ans: (−100.01 to −99.99)

49. The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0. The current i(t) (in ampere) at t = 0.5 seconds is ________

Ans: (8.0 to 8.3)

50. In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors Q₁, Q₂….., Q₃₂ are identical in all respects and have infinitely large values of common – emitter current the relation I_C = I_S exp ((V_BE/V_T), where I_s is the saturation current. Assume that the voltage V_P shown in the figure is 0.7 V and the thermal voltage V_T = 26m V.

The output voltage V_out(in volts) is __________.

Ans: (1.1 to 1.2)

51. The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input „In‟ and an output „Out‟. The initial state of the FSM is S₀.

If the input sequence is 10101101001101, starting with the left-most bit, then the number times „Out‟ will be 1 is __________.

Ans: (4)

52. Standard air – filled rectangular waveguides of dimensions a = 2.29 cm and b= 1.02 cm are designed for radar applications. It is desired that these waveguides operate only in the dominatnt TE₁₀ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is

(A) 8.19 GHz ≤ f ≤ 13.1 GHz

(B) 8.19 GHz ≤ f ≤ 12.45 GHz

(D) 1.64 GHz ≤ f ≤ 10.24 GHz

Ans: (B)

53. For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J_L) is 2.5 mA/cm² and the open-circuit voltage (V_oc) is 0.451 V. Consider thermal voltage (V_T) to be 25 mV. If the intensity of the incident light is increased by 20 times, assuming that the temperature remains unchanged V_∝ (in volts) will be _______.

Ans: (0.51 to 0.54)

54. In the circuit shown, transistors Q₁ and Q₂ are biased at a collector current of 2.6mA. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of 26 mV, the magnitude of voltage gain V₀/Vs in the mid-band frequency range is _____________ (up to second decimal place).

Ans: (49.0 to 51.0)

55. Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double that of T1. Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage of T2 is double that of T1, where V_GS and V_TH are the gate – to – source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T₁ are I_D1 and g_m1 respectively, the corresponding values of these two parameters for T2 are

(A) 8I_D1 and 2g_m1

(B) 8I_D1 and 4g_m1

(D) 4I_D1 and 2g_m1

Ans: (B)

56. The ninth and the tenth of this month are Monday and Tuesday ___________.

(A) figuratively

(B) retrospectively

(D) rightfully

Ans: (C)

57. 500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186). Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A) 37

(B) 43

(D) 53

Ans: (D)

58. It is _________ to read this year’s textbook __________ the last year’s.

(A) easier, than

(B) most easy, than

(D) easiest, from

Ans: (A)

59. Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?

(A) 8km, East

(B) 12 km, North

(D) 10km, North

Ans: (A)

60. A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking beer. What must be checked to ensure that the rule is being followed?

(A) Only P’s drink

(B) Only P’s drink and S’s age

(D) Only P’s drink, Q’s drink and S’s age

Ans: (B)

61. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A) X is the mother-in-law of R

(B) P and R are not married to each other

(D) Q cannot be married to R

Ans: (D)

62. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A) 781

(B) 791

(D) 891

Ans: (C)

63. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A) P to Q

(B) P to R

(D) P to T

Ans: (B)

64. 1200 men and 500 women can build a bridge in 2weeks. 900men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A) 3000

(B) 3300

(D) 3900

Ans: (C)

65. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following statements best reflects the author’s opinion?

(A) An intimate association does not allow for the necessary perspective.

(B) Matters are recorded with an impartial perspective.

(D) Actors are typically associated with the impartial recording of matters.

Ans: (A)

Gate 2017 Electronics and Communication Engineering Question Paper 5th Feb 2017 Session 1 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Electronics and Communication Engineering 5th Feb 2017 Session 1

Subject Name: Electronics and Communication Engineering

Duration : 180

Total Marks: 100

1. The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 μs, then the number of T-states needed for executing the instruction is

(A) 1

(B) 6

(D) 8

Ans: (C)

2. Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as

Which one of the following statements is true about the system?

(A) It is causal and stable

(B) It is causal but not stable

(D) It is neither causal nor stable

Ans: (A)

3. Consider the following statement about the linear dependence of the real valued functions y₁ = 1, y₂ = x and y₃ = x², over the field of real numbers.

I. y₁, y₂ and y₃ are linearly independent on −1 ≤ x ≤ 0

II. y₁, y₂ and y₃ are linearly dependent on 0 ≤ x ≤ 1

III. y₁, y₂ and y₃ are linearly independent on 0 ≤ x ≤ 1

IV. y₁, y₂ and y₃ are linearly dependent on −1 ≤ x ≤ 0

Which one among the following is correct?

(A) Both I and II are true

(B) Both I and III are true

(D) Both III and IV are true

Ans: (B)

4. Consider the 5 × 5 matrix

It is given that A has only one real eigen value. Then the real eigen value of A is

(A) −2.5

(B) 0

(D) 25

Ans: (C)

5. The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is V(ℓ) = e−^{−γℓ +jωt} volts, Where ℓ is the distance along the length of the cable in meters. γ = (0.1 + j40)m⁻¹ is the complex propagation constant, and ω = 2π × 10⁹ rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.

Ans: (0.85 to 0.88)

6. A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement is true?

(A) Silicon atoms act as p-type dopants in Arsenic sites and n-type dopants in Gallium sites

(B) Silicon atoms act as n-type dopants in Arsenic sites and p-type dopants in Gallium sites

(D) Silicon atoms act as n-type dopants in Arsenic as well as Gallium sites

Ans: (A)

7. The rank of the matrix is

(A) 0

(B) 1

(D) 3

Ans: (C)

8. For a narrow base PNP BJT, the excess minority carrier concentration (∆n_E for emitter, ∆p_B for base. ∆n_C for collector) normalized to equilibrium minority carrier concentration (n_E0 for emitter, p_B0 for base, n_C0 for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?

(A) Forward active

(B) Saturation

(D) Cutoff

Ans: (C)

9. The Miller effect in the context of a Common Emitter amplifier explains

(A) an increase in the low-frequency cutoff frequency

(B) an increase in the high-frequency cutoff frequency

(D) a decrease in the high-frequency cutoff frequency

Ans: (D)

10. Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output latch in percentage is ___________.

Ans: (2.9 to 30.1)

11. Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?

(A)

(B)

(C)

(D)

Ans: (A)

12. In the latch circuit shown, the NAND gates have non-zero, but unequal propagation delays. The present input condition is: P = Q = “0”. If the input condition is changed simultaneously to P = Q = “1”, the outputs X and Y are

(A) X = “1”, Y = “1”

(B) either X = “1”, Y = “0” or X = “0”, Y = “1”

(D) X = “0”, Y = “0”

Ans: (B)

13. Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) __________.

Ans: (0.027 to 0.028)

14. A periodic signal x(t) has a trigonometric Fourier series expansion

If x(t) = −x – (t) = −x(t – π/ω₀), we can conclude that

(A) a_n are zero for all and b_n are zero for n even

(B) a_n are zero for all n and b_n are zero for n odd

(D) a_n are zero for n odd and b_n are zero for n even

Ans: (A)

15. The open loop transfer function

Where p is an integer, is connected in unity feedback configuration as shown in figure.

Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.

Ans: (0.99 to 1.01)

16. An n⁺ − n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of N_D1 = 1 × 10¹⁸ cm⁻³ and N_D2 = 1 × 10¹⁵ cm⁻³ corresponding to the n⁺ and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic carrier concentration to be n_i = 1 × 10¹⁰ cm⁻³. What is the magnitude of the built-in potential of this device?

(A) 0.748V

(B) 0.460V

(D) 0.173V

Ans: (D)

17. For the operational amplifier circuit shown, the output saturation voltages are ±15V. The upper and lower threshold voltages for the circuit are, respectively.

(A) +5V and −5V

(B) +7V and −3V

(D) +3V and −3V

Ans: (B)

18. In the circuit shown, the positive angular frequency ω (in radians per second) at which magnitude of the phase difference between the voltages V₁ and V₂ equals is________.

Ans: (0.9 to 1.1)

19. In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is inter symbol interference zero?

(A)

(B)

(C)

(D)

Ans: (B)

20. Consider a stable system with transfer function

Where b₁,….,b_p and a₁,….a_q are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to −60 dB decade as ω→∞. A possible pair of values for p and q is

(A) p = 0 and q = 3

(B) p =1and q = 7

(D) p = 3 and q = 5

Ans: (A)

21. A good transconductance amplifier should have

(A) high input resistance and low output resistance

(B) low input resistance and high output resistance

(D) low input and output resistance

Ans: (C)

22. Let (X₁ ,X₂) be independent random variables. X₁ has been 0 and variance 1, while X₂ has mean 1 and variance 4. The mutual information I(X₁ : X₂) between X₁ and X₂ in bits is _______.

Ans: (0)

23. Consider the following statements for continuous-time linear time invariant (LTI) systems.

I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.

II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

(A) Both I and II are true

(B) Both I and II are not true

(D) Only II is true

Ans: (D)

24. Which one of the following statements about differential pulse code modulation (DPCM) is true?

(A) The sum of message signal sample with its prediction is quantized

(B) The message signal sample is directly quantized, and its prediction is not used

(D) The difference of message signal sample with its predictions is quantized

Ans: (D)

25. Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

(A) increases by a factor of 2

(B) decrease by a factor 2

(D) decreases by a factor of √2

Ans: (C)

26. Starting with x = 1, the solution of the equation x³ + x = 1, after two iterations of Newton-Rapson’s method (up to two decimal places) is ________.

Ans: (0.65 to 0.72)

27. In binary frequency shift keying (FSK), the given signal waveform are

u₀(t) = 5 cos(20000πt); 0≤t ≤ T, and

u₁(t) = 5 cos(22000πt); 0≤t≤T

Where T is the bit-duration interval and t is in seconds. Both u₀(t) and u₁(t) are zero outside the interval 0 ≤ t ≤ T. With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u₀(t) and u₁(t) uncorrelated is

(A) 0.25 ms

(B) 0.5 ms

(D) 1.0 ms

Ans: (B)

28. For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector current are equal. Given that V_T = 25 mV, V_BE = 0.7V, and the BJT output resistance r₀ is practically infinite. Under these conditions, the midband voltage gain magnitude. A_c = |V_o/V_i|V/V, is ____________.

Ans: (127.0 to 129.0)

29. The figure shows an RLC circuit exited by the sinusoidal voltage 100cos (3t) volts, where t is in seconds. The ratio is _________.

Ans: (2.55 to 2.65)

30. Which one of the following is the general solution of the first order differential equation where x, y are real?

(A) y = 1 + x + tan⁻¹ (x + c), where c is a constant

(B) y = 1 + x + tan(x + c), where c is a constant

(D) y = 1 – x + tan(x + c), where c is a constant

Ans: (D)

31. A linear time invariant (LTI) system with the transfer function is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed loop system is stable for

(A) K > 1.5

(B) 1 < K < 1.5

(D) no positive value of K

Ans: (A)

32. Let where x, y, z are real, and let C be th straight line segment from point A : (0, 2, 1) to point B : (4, 1, −1). The value of I is _______.

Ans: (−11.1 to −10.9)

33. As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentration of N_D1 = 10¹⁴ cm⁻³ and N_D2 = 10¹⁶ cm⁻³ in the n-regions of the diodes, and uniform acceptor doping concentration of N_Al = 10¹⁴ cm⁻³ and N_A2 = 10¹⁶ cm⁻³ in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is >> built-in potentials of the diodes, the ratio C₂/C₁ of their reverse bias capacitances for the same applied reverse bias, is __________.

Ans: (10.0 to 10.0)

34. An optical fiber is kept along the The refractive indices for the electric fields along directions in the fiber are n_x = 1.5000 and n_y = 1.5001, respectively (n_x ≠ n_y due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5μm. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeter, is ___________.

Ans: (0.36 to 0.38)

35. Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that

x[0] = 1, x[1] = 2, x[2] = 1, h[0] = 1.

Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _______.

Ans: (31)

36. Which one of the following options correctly describes the locations of the roots of the equations s⁴ + s² + 1 = 0 on the complex plane?

(A) Four left half plane (LHP) roots

(B) One right half plane (RHP) root, one LHP root and two roots on the imaginary axis

(D) All four roots are on the imaginary axis

Ans: (C)

37. The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n = 1 × 10¹⁶ cm⁻³ and electronic charge q = 1.6 × 10⁻¹⁹ C. If a bias of 5V is applied across a 1 μm region of this semiconductor, the resulting current density in this region, in kA/cm², is ________.

Ans: (1.5 to 1.7)

38. For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage V_tn = 1V and its transconductance parameter Neglect channel length modulation and body bias effects. Under these conditions, the drain current I_D in mA is _________.

Ans: (1.9 to 2.1)

39. Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response

As shown in Figure (b). The output of the lowpass filter is Y(t).

Let E be the expectation operator and consider the following statements.

I. E(X(t)) = E(Y(t))

II. E(X²(t)) = E(Y²(t))

III. E(Y²(t)) = 2

Select the correct option:

(A) only I is true

(B) only II and III are true

(D) only I and III are true

Ans: (A)

40. As shown a uniformly doped Silicon (Si) bar of length L = 0.1 μm with a donor concentration N_D = 10¹⁶ cm⁻³ is illuminated at x = 0 such that electron and hole pairs are generated at the rate of where G_L0 = 10¹⁷ cm⁻³ s⁻¹. Hole lifetime is 10⁻⁴ s, electronic charge q = 1.6 × 10⁻¹⁹ C, hole diffusion coefficient D_p = 100 cm²/s and low level injection condition prevails. Assuming linearly decaying steady state excess hole concentration that goes to 0 at x = L, the magnitude of the diffusion current density at x = L/2, in A/cm², is _______.

Ans: (15.9 to 16.1)

41. The Nyquist plot of the transfer function does not encircle the point (1 + j0) for K = 10 but does encircle the point (−1 + j0) for K = 100. Then the closed loop system (having unity gain feedback) is

(A) stable for K = 10 and stable for K = 100

(B) stable for K = 10 and unstable for K = 100

(D) unstable for K = 10 and unstable for K = 100

Ans: (B)

42. In the figure shown, the npn transistor acts as a switch

For the input V_in(t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage saturation V_CE(sat) = 0.2 V and base-to-emitter voltage V_BE = 0.7V. The minimum value of the common-base current gain (α) of the transistor for the switching should be _______.

Ans: (0.89 to 0.91)

43. A three dimensional region R of finite volume is described by x² + y² ≤ z³; 0 ≤ z ≤ 1, Where x, y, z are real. The volume of R(up to two decimal places) is _________.

Ans: (0.70 to 0.85)

44. The expression for an electric field in free space is

where x, y, z represent the spatial coordinates, t represents time, and ω, k are constants. This electric field

(A) does not represent a plane wave

(B) represents a circular polarized plane wave propagating normal to the z-axis

(D) represents a linearly polarized plane wave

Ans: (C)

45. A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are Q_AQ_B = 00, 01, 10 and 11.

Assume that X_IN = 1is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state Q_AQ_B = 00 and clocked, after a few clock cycles, it starts cycling through

(A) all of the four possible states if X_IN = 1

(B) three of the four possible states if X_IN = 1

(D) only two of the four possible states is X_IN = 0

Ans: (D)

46. Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a_k} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t)

I. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3a_k} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6π rad/s

For the three statements above, which one of the following is correct?

(A) only II and III are true

(B) only I and III are true

(D) only I is true

Ans: (B)

47. A 4-bit shift register circuit configured for right-shift operation, i.e, D_in → A, A → B, B → C, C → D, is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is _______.

Ans: (10.0 to 10.0)

48. Let for real x. From among the following choose the Taylor series approximation of f(x) around x = 0, which included all powers of x less than or equal to 3.

(A) 1 + x + x² + x³

(B)

(C)

(D)

Ans: (C)

49. The following FIVE instructions were executed on an 8085 microprocessor.

MVI A, 33H

MVI B, 78H

ADD B

CMA

ANI 32H

The Accumulator value immediately after the execution of the fifth instruction is

(A) 00H

(B) 10H

(D) 32H

Ans: (B)

50. In the circuit shown, the voltage V_IN(t) is described by:

Where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is ___________.

Ans: (0.30 to 0.40)

51. A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ ϕ ≤ π. Here the angle θ(0 ≤ θ < π) is measured from the z-axis, and the angle ϕ(0 ≤ ϕ ≤ 2π) is measured from the x-axis in the x-y plane.

(A) θ = 90°, ϕ = 45°

(B) θ = 45°, ϕ = 90°

(D) θ = 45°, ϕ = 135°

Ans: (A)

52. The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, A_o = 10⁵V/V and an open-loop cut-off frequency f_c = 8Hz. The voltage gain of the amplifier at 15 kHz, in V/V is _______.

Ans: (43.3 to 45.3)

53. Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by and h[n] = 0 for n < 0 and n > 2.

Let H(ω) be the discrete-time Fourier system transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H(ω₀) = 0 and 0 < ω₀ < π, the value of ω₀ (in radians) is equal to ________.

Ans: (2.05 to 2.15)

54. Which one of the following gives the simplified sum of products expression for the Boolean function F = m₀ + m₂ + m₃ + m₅, where m₀, m₂, m₃ and m₅ are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

(A)

(B)

(C)

(D)

Ans: (B)

55. A continuous time signal x(t) = 4 cos (200 πt) + 8 cos (400 πt), where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

Let y(t) be the output of this filter. The maximum value of |y(t)| is _______.

Ans: (7.90 to 8.10)

56. She has a sharp tongue and it can occasionally turn _______.

(A) hurtful

(B) left

(D) vital

Ans: (A)

57. Some table are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences?

(i) At least one bench is a table

(ii) At least one shelf is a bench

(iii) At least one chair is a table

(iv) All benches are chairs

(A) only (i)

(B) only (ii)

(D) only (iv)

Ans: (B)

58. 40% of deaths on city roads may be attributed to drunken driving. The number of degree needed to represent this as a slice of a pie chart is

(A) 120

(B) 144

(D) 212

Ans: (B)

59. In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statement is correct?

(A) The ratio of household to other consumption is 8/17

(B) The ratio of household to other consumption is 1/17

(D) There are errors in the official’s statement

Ans: (D)

60. I ________ made arrangements had I _________informed earlier.

(A) could have, been

(B) would have, being

(D) had been, been

Ans: (A)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word „antagonistic‟ is closest in meaning to

(A) impartial

(B) argumentative

(D) hostile

Ans: (D)

62. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

(A) 56

(B) 52

(D) 44

Ans: (A)

63. A contour line joints locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

(A) Up-Down-Up-Down

(B) Down-Up-Down-Up

(D) Up-Down-Up

Ans: (C)

64. Trucks (10m long) and cars (5 m long) go on a single lane bridge. There must be a gap of atleast 20 m after each truck and a gap of atleast 15m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternatively, what is the maximum number of vehicles that can use the bridge in one hour?

(A) 1440

(B) 1200

(D) 600

Ans: (A)

65. S, T, U, V, W, X, Y and Z are seated around a circular table. T‟s neighbours are Y and V. Z is seated third to the left of T and second to the right of S.U‟s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

(A) X

(B) W

(D) T

Ans: (A)

Gate 2017 Chemistry Question Paper 5th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Chemistry 5th Feb 2017

Subject Name: Chemistry

Duration : 180

Total Marks: 100

1. Consider N particle at temperature T, pressure P, volume V and chemical potential μ having energy E. The parameters that are kept constant for a canonical ensemble are

(A) N, V, T

(B) N, V, E

(D) μ, V, T

Ans: (A)

2. For ortho-hydrogen, the nuclear wave function and the rotational quantum number, respectively, are

(A) antisymmetric and even

(B) symmetric and odd

(D) antisymmetric and odd

Ans: (B)

3. m₁ and m₂ are the slopes (dp/dT) of the solid-liquid equilibrium lines in the P-T phase diagrams of H₂O and CO₂, respectively. For P < 10 atm, the values of m₁ and m₂ are

(A) m₁ > 0 and m₂ > 0

(B) m₁ > 0 and m₂ < 0

(D) m₁ < 0 and m₂ > 0

Ans: (D)

4. The rate constant of reaction is 1.25 × 10⁻⁴ mol L⁻¹ s⁻¹. If the initial concentration of the reactant is 0.250 mol L⁻¹, the total time (in seconds) required for complete conversion is _______

Ans: (1999 to 2001)

5. Consider the ideal gas of volume V at temperature T and pressure P. If the entropy of the gas is S, the partial derivative (∂P/∂S)_V is equal to

(A) (∂T/∂P)_S

(B) (∂T/∂V)_P

(D) (∂T/∂S)_P

Ans: (C)

6. The wavelength associated with a particle in one-dimensional box of length L is (n refers to the quantum number)

(A) 2L/n

(B) L/n

(D) L/2n

Ans: (A)

7. The dependence of rate constant k on temperature T (in K) of a reaction is given by the expression

ln k = [(−5000 K)/T] + 10

The activation energy of the reaction (in kJ mol⁻¹ is ______ (up to two decimal places)

Ans: (41.50 to 41.60)

8. The lowest energy of a quantum mechanical one-dimensional simple harmonic oscillator is 300 cm⁻¹. The energy (in cm⁻¹) of the next higher level is ______

Ans: (899 to 901)

9. The electronic ground state term for the chromium ion in [Cr(CN)₆]⁴⁻ is

(A) ³F

(B) ³H

(D) ⁵D

Ans: (B)

10. The ions exhibit intense ligand to metal charge transfer transition. The wavelengths of this transition follow the order

(A)

(B)

(C)

(D)

Ans: (C)

11. The lanthanide ion that exhibits color in aqueous solution is

(A) La(III)

(B) Eu(III)

(D) Lu(III)

Ans: (B)

12. The hapticity of cycloheptatriene, (C₇H₈), in Mo(C₇H₈)(CO)₃ is___________

Ans: (6)

13. The V_o-o resonance Raman stretching frequency (in cm⁻¹) of the O₂ coordinated to iron centre in oxy-hemoglobin nearly

(A) 1100

(B) 850

(D) 1950

Ans: (A)

14. The energy band diagram fro magnesium is (The hatched an unhatced regions in the figure correspond to filled and unfilled regions of the band, respectively.)

(A)

(B)

(C)

(D)

Ans: (D)

15. P, F and I represent primitive, face-centered and body-centered lattices, respectively. The lattice types of NaCl and CsCl, respectively, are

(A) F and I

(B) F and P

(D) P and I

Ans: (B)

16. The characteristic feature of an electron spin resonance (ESR) spectrum of frozen aqueous solution of CuSO₄∙5H₂O at 77 K is

(A) g_∥ > g_⊥

(B) g_∥ < g_⊥

(D) g_x ≠ g_y ≠ g_z

Ans: (A)

17. The most suitable reagent for the following transformation is

(A) Li/Liq. NH₃

(B) PtO₂/H₂

(D) B₂H₆

Ans: (A)

18. The major products M and N formed in the following reactions are

(A)

(B)

(C)

(D)

Ans: (C)

19. The ¹³C NMR spectrum of acetone-d₆ has a signal at 30 ppm as a septel in the intensity ratio

(A) 1 : 6 : 15 : 20 : 15 : 6 : 1

(B) 1 : 3 : 6 : 7 : 6 : 3 : 1

(D) 1 : 3 : 7 : 10 : 7 : 3 : 1

Ans: (B)

20. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Ans: (D)

21. The major product obtained in the following reaction is

(A)

(B)

(C)

(D)

Ans: (B)

22. In the two reaction sequence given below, the starting bis-sulfone acts as

(A) a dienophile and synthetic equivalent of acetylene

(B) a dienophile and synthetic equivalent of ethylene

(D) a dipolarophile and synthetic equivalent of ethylene

Ans: (A)

23. The major product formed in the following photochemical reaction is

(A)

(B)

(C)

(D)

Ans: (B)

24. The product formed in the following reaction is

(A)

(B)

(C)

(D)

Ans: (D)

25. The number of possible stereoisomers for cyclononene is _______

Ans: (3)

26. The mobility of a univalent ion in aqueous solution is 6.00 × 10⁻⁸ m² s⁻¹ V⁻¹ at 300 K. Its diffusion coefficient at 300 K is X × 10⁻⁹ m² s⁻¹. The value of X is __________ up to two decimal places)

Ans: (1.50 to 1.60)

27. For the following consecutive first order reactions

the time (in seconds) required for Y to reach its maximum concentration (assuming only X is present at time t = 0) is ___________(up to two decimal places)

Ans: (1.50 to 1.60)

28. Under physiological conditions, the conversion of CO₂ to bicarbonate ion by carbonic anhydrase enzyme (MW = 30,000 g mol⁻¹) has a turnover number of 4.00 × 10⁵ s⁻¹. The minimum amount of enzyme (in μg) required to convert 0.44 g of CO₂ to bicarbonate ions in 100 seconds is ______ (up to two decimal places)

Ans: (7.40 to 7.60)

29. Assume 1,3,5-hexatriene to be a linear molecule and model the π electrons as particles in a one-dimensional box of length 0.70 nm. The wavelength (in nm) corresponding to the transition from the ground-state to the first excited-state is _________

Ans: (225 to 240)

30. The standard Gibbs free energy change of the reaction shown below is −7 kJ mol⁻¹.

Sn(s) + Pb²⁺ = Sn²⁺ + Pb(s)

Given that E°(Pb²⁺/Pb) is −0.126 V, the value of E°(Sn²⁺/Sn) in V is ______ (up to two decimal places)

Ans: (−0.15 to −0.13)

31. The dissociative chemiosorption of X₂(g) on a metal surface follows Langmuir adsorption isotherm. The ratio of the rate constants of the adsorption and desorption processes is 4.0 atm⁻¹. The fractional surface coverage of X(adsorbed)at 1.0 atm pressure is ________ (up to two decimal places)

Ans: (0.65 to 0.70)

32. The ionic activity coefficients of Ca²⁺ and F⁻ are 0.72 and 0.28, respectively. The mean activity coefficient of CaF₂ is _______(up to two decimal places)

Ans: (0.36 to 0.40)

33. The angle of orientation (in degrees) of the angular momentum vector with respect to z-axis for I = 2 and m_l = +2 state of H-atom is ______(up to two decimal places)

Ans: (33.30 to 36.90)

34. The Gibbs free energy of mixing is denoted as ∆G_mix. 1.0 mole of He, 3.0 moles of Ne and 2.0 moles of Ar are mixed at the same pressure and temperature. Assuming ideal gas behavior, the value of ∆G_mix/RT is ______ (up to two decimal places)

Ans: (−6.10 to −6.05)

35. Ψ = [cϕ₁ – (1/√3)ϕ₂] represents a normalized molecular orbital constructed from two different atomic orbitals ϕ₁ and ϕ₂ that form an orthonormal set. The value of |c| is _________(up to two decimal places)

Ans: (0.80 to 0.84)

36. In cyclophosphazenes, (NPX₂)₃ (X = F, Cl, Br and Me), the s strength of P−N π-bond varies with X in the order

(A) F > Cl > Br > Me

(B) Me > F > Cl > Br

(D) Me > Br > Cl > F

Ans: (A)

37. The structure type and shape of the polyhedral (skeletal) framework of the carbonate, Me₂C₂B₁₀H₁₀, respectively, are

(A) nido and dodecahedron

(B) closo and icosahedron

(D) closo and dodecahedron

Ans: (B)

38. If ∆_o is the octahedral splitting energy and P is the electron pairing energy, then the crystal-field stabilization energy (CFSE) of [Co(NH₃)₆]²⁺ is

(A) −0.8 ∆₀ + 2P

(B) −0.8 ∆₀ + 1P

(D) −1.8∆₀ + 3P

Ans: (C)

39. The rates of substitution for the following reaction vary with L in the order

(A)

(B)

(C)

(D)

Ans: (D)

40. The product formed in the reaction of MeMn(CO)₅ with ¹³CO is

(A) (Me¹³CO)Mn(CO)₅

(B) (MeCO)Mn(CO)₅

(D) (Me¹³CO)Mn(CO₄)(¹³CO)

Ans: (C)

41. For the following three alkenes, 1, 2, and 3, the rates of hydrogenation using Wilkinson’s catalyst at 25℃ vary in the order

(A) 1 > 3 > 2

(B) 1 > 2 > 3

(D) 2 > 3 > 1

Ans: (B)

42. ²¹⁰Bi undergoes β⁻ decay to 1/8 of its initial amount in 15 days. The time required for its decay 1/4 of its initial amount is _______ days (up to two decimal places).

Ans: (9.90 to 10.10)

43. The metal ion and the macrocyclic skeleton present in the green pigment of plants, respectively, are

(A) Mg(II) and chlorin

(B) Mg(II) and corrin

(D) Mg(II) and porphine

Ans: (A)

44. The spinel structure of MgAl₂O₄ has cubic close packed arrangement of oxide ions. The fractions of the octahedral and tetrahedral sites occupied cations, respectively, are

(A) 1/8 and 1/2

(B) 1/4 and 1/2

(D) 1/2 and 1/8

Ans: (D)

45. The diffusion limiting current (I_d) at a dropping mercury electrode for an aqueous Mg(II) solution of concentration ‘c’ (mol L⁻¹) is 300 μ If ‘c’ is increased by 0.1 mol L⁻¹, I_d increases to 900 μA. The value of ‘c’ (in mol L⁻¹) is _______ (up to two decimal places)

Ans: (0.04 to 0.05)

46. The major product formed in the following reaction is

(A)

(B)

(C)

(D)

Ans: (C)

47. The product formed in the following photochemical reaction is

(A)

(B)

(C)

(D)

Ans: (D)

48. Among the following decahydroquinoline toluenesulfonates (Ts), the one that yields 9-methylamino-E-non-5-enal as a major product upon aqueous solvolysis is

(A)

(B)

(C)

(D)

Ans: (C)

49. The product obtained in the following solvolysis reaction is

(A) a racemic mixture of trans 1,2-diacetoxycyclohexane

(B) enantimerically pure trans 1,2-diacetoxycyclohexane

(D) a mixture of cis and trans 1, 2-diacetoxycyclohexane

Ans: (A)

50. The spectroscopic data for an organic compound with molecular formula C₁₀H₁₂O₂ are given below. IR band around 1750 cm⁻¹, ¹H NMR δ3 (m, 5H) 5.85 (Q, 1H, J = 7.2 Hz), 2.05 (s, 3H), 1.5 (d, 3H, J = 7.2 Hz) ppm. The compound is

(A) methyl 2-phenylpropionate

(B) 1-(phenylethyl) acetate

(D) methyl 3-phenylpropionate

Ans: (B)

51. The structure of the intermediate [P] and major product Q formed in the following reaction sequence are

(A)

(B)

(C)

(D)

Ans: (B)

52. Hydration of fumaric acid gives malic acid as shown below. Assume that addition of water takes place specifically from A face or B face. The correct statement pertaining to stereochemistry of malic acid formed is

(A) addition specifically from A face gives S isomer of malic acid

(B) addition specifically from B face gives S isomer of malic acid

(D) addition specifically from B face gives a racemic mixture of malic acid

Ans: (A)

53. Hydroboration of 2-butyne with (C₆H₁₁)₂BH yields the intermediate U, which on treatment with I₂ and NaOMe at −78℃, gives product V. The structures of U and V are

(A)

(B)

(C)

(D)

Ans: (D)

54. The structures of the major products W and X in the following synthetic scheme are

(A)

(B)

(C)

(D)

Ans: (D)

55. The major products Y and Z in the following reaction sequence are

(A)

(B)

(C)

(D)

Ans: (A)

56. She has a sharp tongue and it occasionally turn _______

(A) hurtful

(B) left

(D) vital

Ans: (A)

57. I_____ made arrangements had I _______ informed earlier.

(A) could have, been

(B) would have, being

(D) had been, been

Ans: (A)

58. In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statements is correct?

(A) The ratio of household to other consumption is 8/17

(B) The ratio of household to other consumption is 1/17

(D) There are errors in the official’s statement.

Ans: (D)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represents this as a slice of a pie chart is

(A) 120

(B) 144

(D) 212

Ans: (B)

60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?

i. At least one bench is a table

ii. At least one shelf is a bench

iii. At least one chair is a table

iv. All benches are chairs

(A) Only i

(B) Only ii

(D) Only iv

Ans: (B)

61. ‘If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these page; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word ‘antagonistic’ is closest in meaning to

(A) impartial

(B) argumentative

(D) hostile

Ans: (D)

62. S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbours are Y and V, Z is seated third to the left of T and second to the right of S,. U’s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

(A) X

(B) W

(D) T

Ans: (A)

63. Trucks (10 m long) and cars (5 m long) go on a single lane bridge.. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

(A) 1440

(B) 1200

(D) 600

Ans: (A)

64. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

(A) 56

(B) 52

(D) 44

Ans: (A)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

(A) Up-Down-Up-Down

(B) Down-Up-Down-Up

(D) Up-Down-Up

Ans: (C)

Gate 2017 Computer Science and Information Technology Question Paper 11th Feb 2017 Session 2 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Computer Science and Information Technology 11th Feb 2017 Session 2

Subject Name: Computer Science and Information Technology

Duration : 180

Total Marks: 100

1. Consider the set X={a, b,c,d,e} under the partial ordering

R={(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)}.

The Hasse diagram of the partial order (X, R) is shown below.

The minimum number of ordered pairs that need to be added to R to make (X, R) a lattice is ________.

Ans: (0)

2. Which of the following statements about parser is/are CORRECT?

I. Canonical LR is more powerful than SLR.

II. SLR is more powerful than LALR

III. SLR is more powerful than Canonical LR.

(A) I only

(B) II only

(D) II and III only

Ans: (A)

3. Match the following:

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

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

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

Ans: (A)

4. Let L₁, L₂ be any two context free languages and R be any regular language. Then which of the following is/are CORRECT ?

(A) I, II and IV only

(B) I and III only

(D) I only

Ans: (B)

5. G is undirected graph with n vertices and 25 edges such that each vertex of G has degree at least 3. Then the maximum possible value of n is ___________.

Ans: (16)

6. Let p, q, r denote the statements “It is raining ,“ It is cold”, and “ It is pleasant,” respectively. Then the statement “It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold” is represented by

(A) (¬p ⋀ r) ⋀ (¬r→p ⋀ q))

(B) (¬p ⋀ r) ⋀ ((p ⋀ q)→¬r )

(D) (¬p ⋀ r ) ⋀ (r→(p ⋀ q))

Ans: (A)

7. The Breadth First Search (BFS) algorithm has been implemented using the queue data structure. Which one of the following is a possible order of visiting the nodes in the graph below?

(A) MNOPQR

(B) NQMPOR

(D) POQNMR

Ans: (D)

8. Let be two matrices.

Then the rank of P + Q is _________.

Ans: (2)

9. Consider socket API on a Linux machine that supports connected UDP sockets. A connected UDP socket is a UDP socket on which connect function has already been called. Which of the following statements is/are CORRECT ?

I. A connected UDP socket can be used to communicate with multiple peers simultaneously.

II. A process can successfully call connect function again for an already connected UDP socket.

(A) I only

(B) II only

(D) Neither I nor IIs

Ans: (B)

10. The minimum possible number of states of a deterministic automaton that accepts the regular language

L = {w₁aw₂|w₁, w₂ ∈ {a, b}*, |w₁| = 2,|w₂| ≥ 3} is ______.

Ans: (8)

11. Consider the following tables T1 and T2.

In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with on delete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in table T1 on-delete set NULL and on-update cascade. In order to delete record from table T1, the number of additional records that need to be deleted from table T1 is ______________.

Ans: (0)

12. Which of the following is/are shared by all the threads in a process ?

I. Program counter II. Stack

III. Address space IV. Registers

(A) I and II only

(B) III only

(D) III and IV only

Ans: (B)

13. A circular queue has been implemented using a single linked list where each node consists of a value and a single pointer pointing to the next node. We maintain exactly two external pointers FRONT and REAR pointing to the front node and the rear node of the queue, respectively. Which of the following statements is/are CORRECT for such a circular queue, so that insertion and deletion operation can be performed in O (1) time ?

I. Next pointer of front node points to the rear node.

II. Next pointer of rear node points to the front node.

(A) I only

(B) II only

(D) Neither I nor II

Ans: (B)

14. Given the following binary number in 32-bit (single precision) IEEE-754 format:

00111110011011010000000000000000

The decimal value closest to this floating- point number is

(A) 1.45 × 10¹

(B) 1.45 × 10⁻¹

(D) 2.27 × 10¹

Ans: (C)

15. An ER model of a database consists of entity types A and B. These are connected by a relationship R which does not have its own attribute. Under which one of the following conditions, can the relational table for R be merged with that of A?

(A) Relationship R is one-to-many and the participation of A in R is total

(B) Relationship R is one-to-many and the participation of A in R is partial

(D) Relationship R is many-to one and the participation of A in R is partial

Ans: (C)

16. Match the algorithms with their time complexities:

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

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

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

Ans: (C)

17. Match the following according to input (from the left column) to the complier phase (in the right column) that processes it.

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

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

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

Ans: (C)

18. Consider the following statements about the routing protocols, Routing Information Protocol (RIP) and Open Shortest Path First (OSPF) in an IPv4 network.

I. RIP uses distance vector routing

II. RIP packets are sent using UDP

III. OSPF packets are sent using TCP

IV. OSPF operation is based on link-state routing

Which of the statements above are CORRECT?

(A) I and IV only

(B) I, II and III only

(D) II, III and IV only

Ans: (C)

19. If and then the constants R and S are respectively

(A)

(B)

(C)

(D)

Ans: (C)

20. In a file allocation system, which of the following allocation schemes(s) can be used if no external fragmentation is allowed?

I. Contiguous II. Linked III. Indexed

(A) I and III only

(B) II only

(D) II and III only

Ans: (D)

21. Consider a quadratic equation x² – 13x + 36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = ___________.

Ans: (8)

22. Identify the language generated by the following grammar, where S is start variable.

S → XY

X → aX|a

Y → aYb|∈

(A) {a^mbⁿ| m ≥ n, n > 0}

(B) {a^mbⁿ|m ≥ n, n ≥ 0}

(D) {a^mbⁿ|m > n, n > 0}

Ans: (C)

23. The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is

(A) 571244

(B) 736251

(D) 136251

Ans: (D)

24. Consider the following function implemented in C:

void printxy (int x, int y) {

int *ptr ;

x = 0;

ptr = &x;

y = * ptr;

* ptr = l;

print f (“%d, %d,” x, y);

}

The output of invoking printxy (l, l) is

(A) 0, 0

(B) 0, 1

(D) 1, 1

Ans: (C)

25. The maximum number of IPv4 router addresses that can be listed in the record route (RR) option field of an IPv4 header is _________.

Ans: (9)

26. Consider a binary code that consists of only four valid code words as given below:

00000,01011,10101,11110

Let the minimum Hamming distance of the code be p and the maximum number of erroneous bits that can be corrected by the code be q. Then the values of p and q are

(A) p = 3 and q = 1

(B) p = 3 and q = 2

(D) p = 4 and q = 2

Ans: (A)

27. A system shares 9 tape drives. The current allocation and maximum requirement of tape drives for three processes are shown below:

Which of the following best describes current state of the system ?

(A) Safe, Deadlocked

(B) Safe, Not Deadlocked

(D) Not Safe, Not deadlocked

Ans: (B)

28. Two transactions T₁ and T₂ are given as

T₁ : r₁ (X) w₁ (X) r₁ (Y) w₁ (Y)

T₂ : r₂ (Y) w₂ (Y) r₂ (Z) w₂ (Z)

where r_i(V) denotes a read operation by transaction T_i on a variable V and w_i(V) denotes a write operations by transaction T_i on a variable V. The total number of conflict serializable schedules that can be formed by T1 and T2 is _____________.

Ans: (54)

29. If w, x, y, z are Boolean variables, then which one of the following is INCORRECT ?

(A) wx +w(x + y) + x(x + y)=x + wy

(B)

(C)

(D) (w + y)(wxy + wyz) = wxy + wyz

Ans: (C)

30. Consider the following C Program.

# include <stdio.h>

#include< string.h>

#int main ( ) {

char* c = “GATECSIT2017”;

char* p = c;

printf(“%d”, (int) strlen (c+2[p]-6[p]-1));

return 0;

}

The output of the program is _______________.

Ans: (2)

31. P and Q are considering to apply for a job. The probability that P applies for the job is The probability that P applies for the job given that Q applies for the job is and the probability that Q applies for the job given that P applies for the job Then the probability that P does not apply for the job given that Q does not apply for the job is

(A)

(B)

(C)

(D)

Ans: (A)

32. If the characteristics polynomial of 3× 3 matrix M over R ( the set of real numbers) is λ³ – 4λ² + aλ + 30, a ∈ R, and one eigenvalue of M is 2, then the largest among the absolute values of the eigenvalues of M is ________.

Ans: (5)

33. Consider the following expression grammar G:

E → E – T|T

T → T + F|F

F → (E) |id

Which of the following grammars is not left recursive, but is equivalent to G?

(A)

(B)

(C)

(D)

Ans: (C)

34. In a two-level cache system, the access times of L₁ and L₂ caches are 1 and 8 clock cycles, respectively. The miss penalty from L2 cache to main memory is 18 clock cycles . The miss rate of L₁ cache is twice that of L₂. The average memory access time (AMAT) of this cache system is 2 cycles. This miss rates of L₁ and L₂ respectively are :

(A) 0.111 and 0.056

(B) 0.056 and 0.111

(D) 0.1784 and 0.0892

Ans: (A)

35. Consider two hosts X and Y, connected by a single direct link of rate 10⁶ bits/sec. The distance between the two hosts is 10,000 km and the propagation speed along the link is 2 × 10⁸ m/sec. Host X sends a file of 50,000 bytes as one large message to host Y continuously. Let the transmission and propagation delays be p milliseconds and q milliseconds, respectively . Then the values of p and q are

(A) p = 50 and q = 100

(B) p = 50 and q = 400

(D) p = 400 and q = 50

Ans: (D)

36. Consider the recurrence function

Then T(n) in terms of θ notation is

(A) θ(log log n)

(B) θ(log n)

(D) θ(n)

Ans: (B)

37. If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X+2)²] equals ______.

Ans: (54)

38. Consider the following C function

int fun (int n) {

int i, j;

for (i = 1; i < = n; i++) {

for (j = 1 ; j < n ; j+=i) {

printf (“%d %d , i, j ) ;

}

Time complexity of fun in terms of θ notation is

(A) θ(n√n)

(B) θ(n²)

(D) θ (n² log n)

Ans: (C)

39. The pre-order transversal of a binary search tree is given by 12, 8, 6, 2, 7, 9, 10, 16, 15, 19, 17, 20. Then the post-order traversal of this tree is:

(A) 2,6,7,8,9,10,12,15,16,17,19,20

(B) 2,7,6,10,9,8,15,17,20,19,16,12

(D) 7,6,2,10,9,8,15,16,17,20,19,12

Ans: (B)

40. Consider the C program fragment below which is meant to divide x by y using repeated subtractions. The variables x, y, q and r are all unsigned int.

while (r >= y) {

r = r – y;

q = q +1;

}

Which of the following conditions on the variables x, y, q and r before the execution of the fragment will ensure that the loop terminates in a state satisfying the condition x = = (y*q + r)?

(A) (q = = r) && (r = =0)

(B) (x > 0) && (r = =x) && (y > 0)

(D) (q = = 0) && (y > 0)

Ans: (C)

41. A message is made up entirely of characters from the set X= {P,Q,R,S,T}. The table of probabilities for each of the characters is shown below:

If a message of 100 characters over X is encoded using Huffman coding, then the expected length of the encoded message in bits is_____

Ans: (225)

42. The next state table of a 2-bit saturating up-counter is given below.

The counter is built as a synchronous sequential circuit using T flip-flops. The expression for T₁ and T₀ are

(A)

(B)

(C)

(D)

Ans: (B)

43. Consider the set of processes with arrival time (in milliseconds). CPU burst time (in milliseconds), and priority (0 is the highest priority) shown below. None of the processes have I/O burst time.

The average waiting time (in milliseconds) of all the processes using preemptive priority scheduling algorithm is __________

Ans: (29)

44. For any discrete random variable X, with probability mass function P(X = j) = p_j, p_j ≥ 0, j ∈ {0,….. N} and define the polynomial function g_{x For a certain discrete random variable Y, there exists a scalar β ∈ [0, 1] such that g}_Y (z) = (1 – β+ βz)ⁿ. The expectation of Y is

(A) Nβ(1 – β)

(B) Nβ

(D) Not expressible in terms of N and β alone

Ans: (B)

45. The read access times and the hit ratios for different caches in a memory hierarchy are as given below.

The read access time of main memory is 90 nanoseconds. Assume that the caches use the referred word-first read policy and the write back policy. Assume that all the caches are direct mapped caches. Assume that the dirty bit is always 0 for all the blocks in the caches. In execution of a program, 60% of memory reads are for instruction fetch and 40% are for memory operand fetch. The average read access time in nanoseconds (up to 2 decimal places) is______.

Ans: (4.72)

46. If the ordinary generating function of a sequence then a₃ – a₀ is equal to ______.

Ans: (15)

47. Consider the following snippet of a C program. Assume that swap (&x, &y) exchanges the contents of x and y.

int main ( ) {

int array[]={3,5,1,4,6,2};

int done =0 ;

int i ;

while (done = = 0) {

done = 1;

for (i = 0; i <=4; i ++) {

if (array [i] < array [i +1]) {

swap (& array [i], &array [i+1]);

done = 0;

}

for (i = 5 ; i > =1; i –) {

if (array [i] > array [ i-1]) {

swap ( & array [i] , &array [i-1]);

done = 0;

}

printf ( “ %d “ , array [3] );

}

The output of the program is ____________.

Ans: (3)

48. Consider the following C program.

# include <stdio.h>

int main ( ) {

int m = 10;

int n, n1;

n = ++m;

n1 = m++;

n–;

–n1;

n – = nl;

printf (“%d”, n) ;

return 0;

}

The output of the program is ______________.

Ans: (0)

49. Consider the following database table named top _scorer.

Consider the following SQL query:

SELECT ta.player FROM top _scorer AS ta

WHERE ta.goals > ALL (SELECT tb. goals

FROM top _ scorer AS tb

WHERE tb.country = ‘Spain’)

AND ta.goals > ANY (SELECT tc. goals

FROM top_ scorer AS tc

WHERE tc.country = ‘Germany’)

The number of tuples returned by the above SQL query is ___________.

Ans: (7)

50. Given f (w, x, y, z) = ∑_m (0,1,2,3,7,8,10) + ∑_d (5,6,11,15), where d represents the don’t care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of f(w, x, y, z) ?

(A)

(B)

(C)

(D)

Ans: (A)

51. In a B⁺ tree, if the search –key value is 8 bytes long, the block size is 512 bytes and the block pointer size is 2 bytes, then maximum order of the B+ tree is _______________.

Ans: (52)

52. Let L(R) be the language represented by regular expression R. Let L(G) be the language generated by a context free grammar G. Let L (M) be the language accepted by a Turning machine M. Which of the following decision problems are undecidable ?

I. Given a regular expression R and a string w, is w ∈ L(R)?

II. Given a context-free grammar G, L(G) = ∅

III. Given a context-free grammar G, is L(G) = ∑^* for some alphabet ∑?

IV. Given a Turning machine M and a string w, is w ∈ L(M)?

(A) I and IV only

(B) II and III only

(D) III and IV only

Ans: (D)

53. Consider a machine with a byte addressable main memory of 2³²bytes divided into blocks of size 32 bytes. Assume that a direct mapped cache having 512 cache lines is used with this machine. The size of the tag field in bits is ______.

Ans: (18)

54. Let δ denote that transition function and denote the extended transition function of the ∈ − NFA whose transition table is given below:

Then (q₂, aba) is

(A) ∅

(B) {q₀, q₁, q₃}

(D) {q₀, q₂, q₃}

Ans: (C)

55. Consider the following languages.

L₁ = {a^p|p is a prime number}

L₂ = {aⁿb^mc^2m|n ≥ 0, m ≥ 0}

L₃ = {aⁿbⁿc²ⁿ|n ≥ 0}

L₄ = {aⁿbⁿ|n ≥ 1}

Which of the following are CORRECT ?

I. L₁ is context-free but not regular.

II. L₂ is not context-free.

III. L₃ is not context-free but recursive.

IV. L₄ is deterministic context-free.

(A) I ,II and IV only

(B) II and III only

(D) III and IV only

Ans: (D)

56. There are 3 red socks, 4 green socks and 3 blue socks, you choose 2 socks. The probability that they are of the same colour is ___________.

(A) 1/5

(B) 7/30

(D) 4/15

Ans: (D)

57. Choose the option with words that are not synonyms.

(A) aversion, dislike

(B) luminous, radiant

(D) yielding, resistant

Ans: (D)

58. There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the west of W. Z is to the East of X and the West of V. W is to the West of Y. Which is the building in the middle ?

(A) V

(B) W

(D) Y

Ans: (A)

59. A test has twenty questions worth 100 marks in total. There are two types of questions, multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?

(A) 12

(B) 15

(D) 19

Ans: (B)

60. Saturn is ____ to be seen on a clear night with the naked eye.

(A) enough bright

(B) bright enough

(D) bright as enough

Ans: (B)

61. “We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.”

The author’s belief that ideology is not as important as literature is revealed by the word:

(A) ‘culture’

(B) ‘seemingly’

(D) ‘political’

Ans: (B)

62. X is a 30 digit number starting with the digit 4 followed by the digit 7, then the number X³ will have

(A) 90 digits

(B) 91 digits

(D) 93 digits

Ans: (A)

63. There are three boxes, one contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?

(A) The box labelled ‘Apples’

(B) The box labelled ‘Apples and Oranges’

(D) Cannot be determined

Ans: (B)

64. An air pressure contour line joins locations in a region having the same atmospheric pressure . The following is an air contour plot of a geographical region . Contour lines are shown at 0.05 bar intervals in this plot.

If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

(A) P

(B) Q

(D) S

Ans: (C)

65. The number of roots of e^x + 0.5x² – 2 = 0 in the range [−5, 5] is

(A) 0

(B) 1

(D) 3

Ans: (A)

Gate 2017 Computer Science and Information Technology Question Paper 11th Feb 2017 Session 1 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Computer Science and Information Technology 11th Feb 2017 Session 1

Subject Name: Computer Science and Information Technology

Duration : 180

Total Marks: 100

1. Let X be a Gaussian random variable mean 0 and variance σ². Let Y=max(X, 0) where max (a,b) is the maximum of a and b. The median of Y is ____________.

Ans: (0)

2. Consider the Karnaugh map given below, where x represents “don’t care” and blank represents 0.

Assume for all inputs (a, b, c, d) the respective complements are also available. The above logic is implemented 2-input NOR gates only. The minimum number of gates required is ____________.

Ans: (1)

3. The statement (¬p) ⇒ (¬q) is logically equivalent to which of the statements below?

I. p ⇒ q

II. q ⇒ p

III. (¬q) ⋁ p

(¬p) ⋁ q

(A) I only

(B) I and IV only

(D) II and III only

Ans: (D)

4. Consider the following table:

Match the algorithms to the design paradigms they are based on.

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

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

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

Ans: (C)

5. A sender S sends a message m to receiver R, which is digitally signed by S with its private key. In this scenario, one or more of the following security violations can take place.

I. S can launch a birthday attack to replace m with a fraudulent message.

II. A third party attacker can launch a birthday attack to replace m with a fraudulent message.

III. R can launch a birthday attack to replace m with a fraudulent message.

Which of the following are possible security violations?

(A) I and II only

(B) I only

(D) II and III only

Ans: (B)

6. Consider the following grammar.

What is FOLLOW (Q) ?

(A) {R}

(B) {w}

(D) {w, $}

Ans: (C)

7. Consider the language L given by the regular expression (a + b)^*b(a + b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automation (DFA) accepting L is ___________.

Ans: (4)

8. Consider a two-level cache hierarchy with L1 and L2 caches. An application incurs 1.4 memory accesses per instruction on average. For this application, the miss rate of L1 cache 0.1, the L2 cache experiences, on average, 7 misses per 1000 instructions. The miss rate of L2 expressed correct to two decimal places is ___________.

Ans: (0.05)

9. Consider the following CPU processes with arrival times (in milliseconds) and length of CPU burst (in milliseconds) as given below:

If the pre-emptive shortest remaining time first scheduling algorithm is used to schedule the processes., then the average waiting time across all processes is ________ milliseconds.

Ans: (3)

10. Threads of a process share

(A) global variable but not heap.

(B) heap but not global variables.

(D) Both heap and global variables.

Ans: (D)

11. Let c₁ …… c_n be scalars, not all zero, such that where a_i are column vectors in Rⁿ. Consider the set of linear equations Ax = b

where A = [a_i……..a_n] and The set of equations has

(A) a unique solution at x = J_n where J_n denotes a n-dimensional vector of all 1

(B) no solution

(D) finitely many solutions.

Ans: (C)

12. Consider the C code fragment given below.

Assuming that m and n point to valid NULL- terminated linked lists, invocation of join will

(A) append list m to the end of list n for all inputs.

(B) either cause a null pointer dereference or append list m to the end of list n.

(D) append list n to the end of list m for all inputs.

Ans: (B)

13. The n-bit fixed-point representation of an unsigned real number real X uses f bits for the fraction part. Let i = n –f. The range of decimal values for X in this representation is

(A) 2⁻^f to 2ⁱ

(B) 2⁻^f to (2ⁱ – 2⁻^f)

(D) 0 to (2ⁱ – 2⁻^f)

Ans: (D)

14. Consider the following intermediate program in three address code

p = a− b

q = p *c

p = u * v

q = p + q

Which one of the following corresponds to a static single assignment form of the above code?

(A)

(B)

(C)

(D)

Ans: (B)

15. Consider the C struct defined below:

struct data {

int marks [100] ;

char grade;

int cnumber;

};

struct data student;

The base address of student is available in register R1. The field student.grade can be accessed efficiently using

(A) Post-increment addressing mode. (R1)+

(B) Pre-decrement addressing mode, -(R1)

(D) Index addressing mode, X(R1), where X is an offset represented in 2’s complement 16-bit representation.

Ans: (D)

16. Consider a TCP client and a TCP server running on two different machines. After completing data transfer, the TCP client calls close to terminate the connectional and a FIN segment is sent to the TCP server. Server-side TCP responds by sending an ACK which is received by the client-side TCP. As per the TCP connections state diagram (RFC 793), in which state does the client-side TCP connection wait for the FIN from the sever-side TCP?

(A) LAST-ACK

(B) TIME-WAIT

(D) FIN-WAIT-2

Ans: (D)

17. Consider the following context-free grammar over the alphabet ∑ = {a,b,c} with S as the start symbol.

S → abScT|abc T

T → bT|b

Which one of the following represents the language generated by the above grammar ?

(A) {(ab)ⁿ (cb)ⁿ | n ≥ 1}

(B)

(D) {(ab)ⁿ (cbⁿ)^m| m, n ≥ 1

Ans: (B)

18. Consider the first-order logic sentence F : ∀ z(∃yR (x, y)). Assuming non-empty logical domains, which of the sentences below are implied by F?

I. ∃y(∃xR(x, y)) II. ∃y(∀xR(x, y))

III. ∀y(∃xR (x, y)) IV. ¬∃x(∀y¬R(x, y))

(A) IV only

(B) I and IV only

(D) II and III only

Ans: (B)

19. When two 8-bit numbers A₇…..A₀ and B₇…..B₀ in 2’s complement representation (with A₀ and B₀ as the least significant bits ) are added using a ripple-carry adder, the sum bits obtained are S₇……S₀ and the carry bits are C₇….C₀. An overflow is said to have occurred if

(A) the carry bit C₇ is 1

(B) all the carry bits (C₇….C₀) are 1

(C)

(D)

Ans: (C)

20. Consider a database that has the relation schema EMP (EmpId, EmpName, and DeptName). An instance of the schema EMP and a SQL query on it are given below.

The output of executing the SQL query is _____.

Ans: (2.6)

21. The following functional dependencies hold true for the relational schema R{V,W,X,Y,Z}:

Which of the following is irreducible equivalent for this set of functional dependencies ?

(A)

(B)

(C)

(D)

Ans: (A)

22. Consider the following functions from positive integers to real numbers:

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

(A)

(B)

(C)

(D)

Ans: (B)

23. Let T be a tree with 10 vertices. The sum of the degrees of all the vertices in T is _________.

Ans: (18)

24. Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are :

Note: The height of a tree with a single node is 0.

(A) 4 and 15 respectively

(B) 3 and 14 respectively

(D) 3 and 15 respectively

Ans: (B)

25. Consider the following C code:

# include <stdio.h>

int * assignval (int *x, int val) {

*x = val;

return x;

}

void main ( ) {

int * x= malloc (sizeof (int));

if (NULL = = x) return;

x = assignval (x,0);

if(x) {

x=(int *) malloc (sizeof (int));

if (NULL = = x) return;

x = assignval (x, 10);

}

printf(“%d\n”, *x);

free (x);

}

The code suffers from which one of the following problems:

(A) compiler error as the return of malloc is not typecast appropriately.

(B) compiler error because the comparison should be made as x==NULL and not as shown.

(D) compiles successfully but execution may result in memory leak.

Ans: (D)

26. Consider a combination of T and D flip-flops connected as shown below. The output of the D flip-flop is connected to the input of the T flip-flop and the output of the T Flip-flop is connected to the input of the D Flip-flop.

Initially, both Q₀ and Q₁ are set to 1 (before the 1^st clock cycle). The outputs

(A) Q₁Q₀ after the 3^rd cycle are 11 and after the 4^th cycle are 00 respectively

(B) Q₁Q₀ after the 3^rd cycle are 11 and after the 4^th cycle are 01 respectively

(D) Q₁Q₀ after the 3^rd cycle are 01 and after the 4^th cycle are 01 respectively

Ans: (B)

27. The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.

Ans: (271)

28. Consider a RISC machine where each instruction is exactly 4 bytes long. Conditional and unconditional branch instructions use PC- relative addressing mode with Offset specified in bytes to the target location of the branch instruction. Further the Offset is always with respect to the address of the next instruction in the program sequence. Consider the following instruction sequence.

Instr. No. Instruction

i: add R2, R3, R4

i + 1; sub R5, R6, R7

i + 2; cmp R1, R9, R10

i + 3 beq R1, Offset

If the target of the branch instruction is i, then the decimal value of the Offset is __________.

Ans: (−16)

29. Consider the C functions foo and bar given below:

int foo (int val ) {

int x = 0;

while (val > 0) {

x = x + foo ( val –);

}

return val ;

}

int bar (int val ) {

int x = 0;

while (val > 0) {

x = x + bar (val – 1) ;

}

return val ;

}

Invocations of foo (3) and bar (3) will result in:

(A) Return of 6 and 6 respectively.

(B) Infinite loop and abnormal termination respectively.

(D) Both terminating abnormally

Ans: (B)

30. In a RSA cryptosystem a participant A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of A is 35. Then the private key of A is __________.

Ans: (11)

31. Let A be an array of 31 numbers consisting of sequence of 0’s followed by a sequence of 1’s. The problem is to find the smallest index i that A[i] is 1 by probing the minimum numbers of locations in A. The worst case number of probes performed by an optimal algorithm is _____________.

Ans: (5)

32. If G is grammar with productions

S → SaS|aSb|bSa|SS|∈

where S is the start variable, then which one of the following is not generated by G?

(A) abab

(B) aaab

(D) babba

Ans: (D)

33. The value of

(A) is 0

(B) is −1

(D) does not exist

Ans: (C)

34. Instructions execution in a processor is divided into 5 stages. Instruction Fetch (IF), Instruction Decode (ID) , Operand Fetch (OF), Execute (EX), and Write Back (WB), These stages take 5,4,20, 10 and 3 nanoseconds (ns) respectively. A pipelined implementation of the processor requires buffering between each pair of consecutive stages with a delay of 2ns. Two pipelined implementations of the processor are contemplated.

(i) a naïve pipeline implementation (NP) with 5 stages and

(ii) an efficient pipeline (EP) where the OF stage id divided into stages OF1 and OF2 with execution times of 12 ns and 8 ns respectively.

The speedup (correct to two decimals places) achieved by EP over NP in executing 20 independent instructions with no hazards is ________________.

Ans: (1.508)

35. Consider a database that has the relation schemas EMP(EmpId, EmpName, DepId). And DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus.

Which of the above queries are safe?

(A) (I) and (II) only

(B) (I) and (III) only

(D) (I), (II) and (III)

Ans: (D)

36. Recall that Belady’s anomaly is that the pages-fault rate may increase as the number of allocated frames increases. Now consider the following statements:

S1: Random page replacement algorithm (where a page chosen at random is replaced) suffers from Belady’s anomaly

S2: LRU page replacement algorithm suffers from Belady’s anomaly

Which of the following is CORRECT ?

(A) S1 is true, S2 is true

(B) S1 is true, S2 is false

(D) S1 is false, S2 is false

Ans: (B)

37. The output of executing the following C program is ________.

# include <stdio.h>

int total (int v) {

while (v) {

count + = v & 1;

v>> = 1;

}

return count;

}

void main ( ) {

static int x = 0;

int i = 5;

for (; i> 0; i–) {

x=x + total (i) ;

}

printf (“%d\n”, x) ;

}

Ans: (23)

38. Consider the following C program.

#include <stdio.h>

#include<string.h>

void printlength (char *s, char *t) {

unsigned int c = 0;

int len = ((strlen(s) – strlen (t)) > c) ? strlen(s): strlen(t);

printf (“%d\n”, len);

}

void main ( ) {

char *x = “abc”;

char *y =”defgh”;

printlength (x,y);

Recall that strlen is defined in string.h as returning a value of type size_t, which is an unsigned int. The output of the program is _____________.

Ans: (3)

39. Consider the following languages over the alphabet ∑ = {a, b, c}

Let L₁ = {aⁿbⁿc^m|m, n ≥ 0} and L₂ = {a^mbⁿcⁿ|m, n ≥ 0}

Which of the following are context-free languages ?

I. L₁ ⋃ L₂ II. L₁ ⋂ L₂

(A) I only

(B) II only

(D) Neither I nor II

Ans: (A)

40. Consider a 2-way set associative cache with 256 blocks and uses LRU replacement, Initially the cache is empty. Conflict misses are those misses which occur due the contention of multiple blocks for the same cache set. Compulsory misses occur due to first time access to the block. The following sequence of accesses to memory blocks.

(0,128,256,128,0,128,256,128,1,129,257,129,1,129,257,129)

is repeated 10 times. The number of conflict misses experienced by the cache is ___________.

Ans: (76)

41. Let u and v be two vectors in R² whose Euclidean norms satisfy ||u|| = 2||v||. What is the value of α such that w = u + αv bisects the angle between u and v ?

(A) 2

(B) 1/2

(D) −1/2

Ans: (A)

42. Consider the following grammar:

stmt → if exp r then else expr ;stmt|0

expr → termrelop term|term

if → a|b|c

number → [0 – 9]

where relop is a relational operate (e.g <, >,….) —O refers to the empty statement, and if ,then, else are terminals.

Consider a program P following the above grammar containing ten if terminals. The number of control flows paths in P is ____________. For example the program

if e₁ then e₂ else e₃

has 2 controls flow paths e₁ → e₂ and e₁ → e₃

Ans: (1024)

43. In a database system, unique time stamps are assigned to each transaction using Lamport’s logical clock . Let TS(T₁) and TS(T₂) be the timestamps of transactions T₁ and T₂ Besides, T₁ holds a lock on the resource R, and T₂ has requested a conflicting lock on the same resource R. The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp.

if TS(T₂) < TS (T₁) then

T₁ is killed

else T₂ waits.

Assume any transactions that is not killed terminates eventually. Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks?

(A) The database system is both deadlock-free and starvation- free.

(B) The database system is deadlock- free, but not starvation-free.

(D) The database system is neither deadlock- free nor starvation-free.

Ans: (A)

44. Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A^* to B^*. We say f is computable if there exists a Turning machine M which given an input x in A^*, always halts with f(x) on its tape. Let L_f denote the language {x#f (x)| x∈A^*} .Which of the following statements is true:

(A) f if computable if and only if L_f is recursive.

(B) f is computable if and only L_f recursively enumerable.

(D) If f is computable then L_f is recursively enumerable, but not conversely.

Ans: (A)

45. Consider the expression (a – 1)^* (((b + c)/3)+d)). Let X be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture in which (i) only loads and store instructions can have memory operands and (ii) arithmetic instructions can have only register or immediate operands. The value of X is _________.

Ans: (2)

46. Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:

(I) Minimum spanning tree of G is always unique.

(II) Shortest path between any two vertices of G is always unique.

Which of the above statements is/are necessarily true?

(A) (I) only

(B) (II) only

(D) Neither (I) nor (II)

Ans: (A)

47. A multithreaded program P executes with x number of threads and uses y number of locks for ensuring mutual exclusion while operating on shared memory locations. All locks in the program are non-reentrant, i.e., if a thread holds a lock l, then it cannot re-acquire lock l without releasing it. If a thread is unable to acquire a lock, it blocks until the lock becomes available. The minimum value of x and the minimum value of y together for which execution of P can result in a deadlock are:

(A) x = 1, y = 2

(B) x = 2, y = 1

(D) x = 1, y = 1

Ans: (C)

48. The values of parameters for the Stop-and – Wait ARQ protocol are as given below:

Bit rate of the transmission channel = 1Mbps

Propagation delay from sender to receiver = 0.75 ms

Time to process a frame = 0.25ms

Number of bytes in the information frame =1980

Number of bytes in the acknowledge frame = 20

Number of overhead bytes in the information frame = 20

Assume that there are no transmission errors. Then the transmission efficiency ( expressed in percentage) of the Stop-and – Wait ARQ protocol for the above parameters is _________(correct to 2 decimal places)

Ans: (89.33)

49. A computer network uses polynomials over GF(2) for error checking with 8 bits as information bits and uses x³ + x + 1 as the generator polynomial to generate the check bits. In this network, the message 01011011 is transmitted as

(A) 01011011010

(B) 01011011011

(D) 01011011100

Ans: (C)

50. Let p, q, and r be propositions and the expression (p → q) → r be a contradiction. Then, the expression (r → p) → q is

(A) a tautology

(B) a contradiction

(D) always TRUE when q is TRUE

Ans: (D)

51. A cache memory unit with capacity of N words and block size of B words is to be designed. If it is designed as a direct mapped cache, the length of the TAG field is 10 bits. If the cache unit is now designed as a 16-way set-associative cache, the length of the TAG field is ______bits.

Ans: (14)

52. Consider the following two functions.

The output printed when fun1 (5) is called is

(A) 53423122233445

(B) 53423120112233

(D) 53423120213243

Ans: (A)

53. Consider a database that has the relation schema CR (Student Name, Course Name). An instance of the schema CR is as given below.

The following query is made on the database.

T1 → π_CourseName(σ_{StudentName = ‘SA’}(CR))

T2 ← CR ÷ T1

The number of rows in T2 is ____________.

Ans: (4)

54. Let A be n × n real valued square symmetric matrix of rank 2 with

Consider the following statements.

(I) One eigen value must be in [-5, 5]

(II) The eigen value with the largest magnitude must be strictly greater than 5.

Which of the above statements about eigen values of A is/are necessarily CORRECT?

(A) Both (I) and (II)

(B) (I) only

(D) Neither (I) nor (II)

Ans: (B)

55. Consider the context-free grammars over the alphabet {a,b,c} given below. S and T are nonterminals

G₁ : S → aSb|T, T→ cT|∈

G₂ :S → bSa|T, T → cT|∈.

The language L(G₁) ⋂ L(G₂) is

(A) Finite.

(B) Not finite but regular.

(D) Recursive but not context-free.

Ans: (B)

56. Research in the workplace reveals that people work for many reason ___________.

(A) money beside

(B) beside money

(D) besides money

Ans: (D)

57. After Rajendra chola returned from his voyage to Indonesia, he _______ to visit the temple in Thanjavur.

(A) was wishing

(B) is wishing

(D) had wished

Ans: (C)

58. Rahul Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other ?

(A) Rahul and Murali

(B) Srinivas and Arul

(D) Srinivas and Rahul

Ans: (C)

59. Find the smallest number y such that y×162 is a perfect cube.

(A) 24

(B) 27

(D) 36

Ans: (D)

60. The probability that a k-digit number does NOT contain the digits 0,5,or 9 is

(A) 0.3^k

(B) 0.6^k

(D) 0.9^k

Ans: (C)

61. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m, which of villages P,Q, R, S,T get submerged ?

(A) P, Q

(B) P, Q, T

(D) Q, R, S

Ans: (C)

62. “The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history”

Which of the following statements best reflects the author’s opinion ?

(A) Nationalists are highly imaginative.

(B) History is viewed through the filter of nationalism.

(D) Nationalism has to be both adequately and properly imagined.

Ans: (B)

63. The expression is equal to

(A) the maximum of x and y

(B) the minimum of x and y

(D) None of the above

Ans: (B)

64. Six people are seated around a circular table. There are at least two men and two women . There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

(A) 2

(B) 3

(D) Cannot be determined

Ans: (A)

65. Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of fours shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes ?

(A) 21

(B) 18

(D) 14

Ans: (D)

Gate 2017 Chemical Engineering Question Paper 12th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Chemical Engineering 12th Feb 2017

Subject Name: Chemical Engineering

Duration : 180

Total Marks: 100

1. In a venture meter, ∆P₁ and ∆P₂ are the pressure drops corresponding to volumetric flow rates Q₁ and Q₂. If equals

(A) 2

(B) 4

(D) 0.25

Ans: (B)

2. The volumetric properties of two gases M and N are described by the generalized compressibility chart which expresses the compressibility factor (Z) as a function of reduced pressure and reduced temperature only. The operating pressure (P) and temperature (T) of two gases M and N along with their critical properties (P_C, T_C) are given in the table below.

Z_M and Z_N are the compressibility factor of the gases M and N under the given operating conditions respectively.

The relation between Z_M and z_N is

(A) Z_M = 8Z_N

(B) Z_M = 3Z_N

(D) Z_M = 0.333Z_N

Ans: (C)

3. e polymerization process in Group-1 with the polymers in Group-2.

Group-1 Group-2

P) Free radical polymerization I) Nylon 6.6

Q) Ziegler Natta polymerization II) Polypropylene

R) Condensation polymerization III) Poly vinyl chloride

Choose the correct set of combinations.

(A) P − I,Q − II,R − III

(B) P − III,Q − II,R − I

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

As: (B)

4. An LVDT (Linear Variable Differential Transformer) is a transducer used for converting

(A) displacement to voltage

(B) Voltage to displacement

(D) voltage to current

Ans: (A)

5. Match the variables in Group-1 with the instruments in Group-2.

Group-1 Group-2

P) Temperature I) Capacitance probe

Q) Liquid level II) McLeod gauge

R) Vacuum III) Chromatograph

S) Concentration IV) Thermistor

Choose the correct set of combinations.

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

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

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

Ans: (C)

6. The thickness of laminar boundary layer over a flat plate varies along the distance from the leading edge of the plate. As the distance increases, the boundary layer thickness

(A) increases

(B) decreases

(D) initially decreases and then increases

Ans: (A)

7. The marks obtained by a set of students are 38, 84, 45,70, 75, 60, 48.

The mean and median marks, respectively, are

(A) 45 and 75

(B) 55 and 48

(D) 60 and 70

Ans: (C)

8. In a heat exchanger, the inner diameter of a tube is 25 mm and its outer diameter is 30 mm. The overall heat transfer coefficient based on the inner area is 360 W/m².℃. Then, the overall heat transfer coefficient based on the outer area, rounded to the nearest integer, is ___W/m².℃.

Ans: (300)

9. The cost of a new pump (including installation) is 24,000 Rupees. The pump has useful life of 10 years. Its salvage value is 4000 Rupees. Assuming straight line depreciation, the book value of the pump at the end of 4th year, rounded to the nearest integer, is ___ Rupees.

Ans: (16000)

10. A gas bubble (gas density ρ_g = 2 kg/m³; bubble diameter D = 10⁻⁴ m) is rising vertically through water (gas density ρg = 1000 kg/m³; viscosity μ = 0.001 Pa.s) Force balance on the bubble leads to the following equation,

Where n is the velocity of the bubble at any given time t. Assume that the volume of the rising bubble does not change. The value of g = 9.81 m/s².

The terminal rising velocity of the bubble (in cm/s), rounded to 2 decimal places, is ___ cm/s.

Ans: (0.54)

11. Water is heated at atmospheric pressure from 40℃ to 80℃ using two different processes. In process I, the heating is done by a source at 80℃. In process II, the water is first heated from 40℃ to 60℃ by a source at 60℃, and the then from 60℃ to 80℃ by another source at 80℃. Identify the correct statement.

(A) Enthalpy change of water in process I is greater than enthalpy change in process II

(B) Enthalpy change of water in process II is greater than enthalpy change in process I

(D) Process II is closer to reversibility

Ans: (D)

12. The DCDA (Double Contact Double Absorption) process is used the manufacture of

(A) Urea

(B) Sulphuric acid

(D) ammonia

Ans: (B)

13. The real part of 6eⁱ^π^/3 is ____.

Ans: (3)

14. Consider a first order catalytic reaction in a porous catalyst pellet.

Given R – characteristic length of the pellet: D_e – effective diffusivity; k_c – mass transfer coefficient k₁ – rate constant based on volume of the catalyst pellet; C_s – concentration of reactant on the pellet surface.

The expression for Thiele modulus is

(A)

(B)

(C)

(D)

Ans: (B)

15. Which of the following conditions are valid at the plait point?

P) Density difference between the extract and raffinate phases is zero

Q) Interfacial tension between the extract and raffinate phases is zero

R) Composition difference between the extract and raffinate phases is zero

(A) P and Q only

(B) Q and R only

(D) P, Q and R

Ans: (D)

16. The purpose of the mathanation reaction used in ammonia plants is to

(A) remove CO as it is a catalyst poison

(B) increase the amount of hydrogen

(D) utilize methane as a catalyst for ammonia synthesis

Ans: (A)

17. Which of the following is the correct sequence of equipment for size reduction of solids?

(A)

(B)

(C)

(D)

Ans: (D)

18. Let i and j be the unit vectors in the x and y directions, respectively. For the function

F(x, y) = x³ + y²

the gradient of the function i.e.. ∇F is given by

(A) 3x²i – 2yj

(B) 6x²y

(D) 2yi – 3x²j

Ans: (C)

19. Consider steady state mass transfer of a solute A from a gas phase to a liquid phase. The gas phase bulk and interface mole fractions are y_{A, G} and y_{A, i} respectively. The liquid phase bulk and interface mole fractions are x_{A, L} and x_{A, i}, respectively. The ratio is very close to zero.

The implies that mass transfer resistance is

(A) negligible in the gas phase only

(B) negligible in the liquid phase only

(D) considerable in both the phases

Ans: (B)

20. The value of

Ans: (1)

21. For a solid-catalyzed gas phase reversible reaction, which of the following statements is ALWAYS TRUE?

(A) Adsorption is rate-limiting

(B) Desorption is rate-limiting

(D) Temperature does not affect equilibrium conversion

Ans: (C)

22. The one-dimensional unsteady heat conduction equation is

Where, T – temperature, t – time, r – radial position, k – thermal conductivity, ρ- density, and C_p – specific heat.

For the cylindrical coordinate system, the value of n in the above equation is

(A) 0

(B) 1

(D) 3

Ans: (B)

23. The composition of vapour entering a tray in a distillation column is 0.47. The average composition of the vapour leaving the tray is 0.53. The equilibrium composition of the vapour corresponding to the liquid leaving this tray is 0.52. All the compositions are expressed in mole fraction of the more volatile component.

The Murphree efficiency based on the vapour phase, rounded to the nearest integer, is ___ %.

Ans: (120)

24. The number of positive roots of the function f (x) shown below in the range 0 < x < 6 is ___________.

Ans: (3)

25. The following reaction rate curve is shown for a reaction A → P. Here, (−r_A) and x_A represent reaction rate and conversion, respectively. The feed is pure A and 90% conversion is desired

Which amongst the following reactor configurations gives the lowest total volume of the reactor (s)?

(A) CSTR followed by PFR

(B) Two CSTRs in series

(D) A single PFR

Ans: (A)

26. The total cost (C_T) of an equipment in terms of the operation variable x and y is

The optimal value of C_T, rounded to 1 decimal place, is _______.

Ans: (91.5)

27. The vapour pressure of a pure substance at a temperature T is 30bar. The actual and ideal gas values of g / RT for the saturated vapour at this temperature T and 30 bar are 7.0 and 7.7 respectively. Here, g is the molar Gibbs free energy and R is the universal gas constant. The fugacity of the saturated liquid at these conditions, rounded to 1 decimal place, is ___ bar.

Ans: (14.9)

28. The Sherwood number (Sh_L) correlation for laminar flow over a flat plate of length L is given by

Where Re_L and Sc represent Reynolds number and Schmidt number, respectively.

This correlation, expressed in the form of Chilton-Colburn j_D factor, is

(A) j_D = 0.664

(B)

(D)

Ans: (B)

29. For the initial value problem

the value of x at t = π/3, is _____.

Ans: (0.5)

30. In a counter current stripping operation using pure steam the mole ratio of a solute in the liquid stream is reduced from 0.25 to 0.05. The liquid feed flow rate, on a solute-free basis, is 3mole/s. The equilibrium line for the system is given in the figure below.

The MINIMUM flowrate of pure steam for this process, rounded to 1 decimal place, is ___mol/s.

Ans: (4)

31. The Laplace transform of a function is The initial and final values, respectively, of the function are

(A)

(B)

(C)

(D)

Ans: (B)

32. The following table provides four sets of Fanning friction factor data, for different values of Reynolds number (Re) and roughness factor

Which of the above sets of friction factor data is correct?

(A) Set I

(B) Set II

(D) Set IV

Ans: (C)

33. In a batch adsorption process, 5 g of fresh adsorbent is used to treat 1 litre of an aqueous phenol solution. The initial phenol concentration is 100 mg/litre. The equilibrium relation is given by q* = 1.3C

Where, q* is the amount of phenol adsorbed in mg of phenol per gram of adsorbent: and C is the concentration of phenol in mg/litre in the aqueous solution.

When equilibrium is attained between the adsorbent and the solution, the concentration of phenol in the solution, rounded to 1 decimal place is ___________ mg/litre.

Ans: (13.34)

34. A bond has a maturity value of 20,000 Rupees at the end of 4 years. The interest is compounded at the rate of 5% per year.

The initial investment to be made, rounded to the nearest integer, is _______ Rupees.

Ans: (16454)

35. Size analysis was carried out on a sample of gravel. The data for mass fraction (x_i) and average particle diameter (D_pi) of the fraction is given in the table below :

The mass mean diameter of the sample, to the nearest integer, is ________mm.

Ans: (13)

36. A propeller (diameter D = 15 m) rotates at N = 1 revolution per second (rps). To understand the flow around the propeller, a lab-scale model is made. Important parameters to study the flow are velocity of the propeller tip (V = πND), diameter D and acceleration due to gravity (g). The lab-scale model is 1/100^th of the size of the actual propeller.

The rotation speed of the lab-scale model, to the nearest integer, should be _________ rps.

Ans: (10.0)

37. The transfer function of a system is

For a unit step increase in the input, the fractional overshoot, rounded to 2 decimal places, is ______.

Ans: (0.37)

38. A fluid over a heated horizontal plate maintained at temperature T_w. The bulk temperature of the fluid is T_∞ . The temperature profile in the thermal boundary layer is given by:

Here, y is the vertical distance from the plate, δ_t is the thickness of the thermal boundary layer and k is the thermal conductivity of the fluid.

The local heat transfer coefficient is given by

(A)

(B)

(C)

(D)

Ans: (C)

39. The following liquid second-order reaction is carried out in an isothermal CSTR at steady state A → R (−r_A) = 0.005 C_A² mol/m³.hr

Where, C_A is the concentration of the reactant in the CSTR. The reactor volume is 2m³, the inlet flow rate is 0.5 m³/hr and the inlet concentration of the reactant is 1000 mol/m³. The fractional conversion, rounded to 2 decimal places, is _____.

Ans: (0.80)

40. Reaction A → B is carried out in a reactor operating at steady state and 1 mol/s of pure A at 425℃ enters the reactor. The outlet stream leaves the reactor at 325℃. The heat input to the reactor is 17kW. The heat of reaction at the reference temperature of 25℃ is 30kJ/mol. The specific heat capacities (in kJ/mol.K) of A and B are 0.1 and 0.15, respectively.

The molar flowrate of B leaving the reactor, rounded to 2 decimal places, is ____mol/s.

Ans: (0.6)

41. The C-curve measured during a pulse tracer experiment is shown below. In the figure, C(t) is the concentration of the tracer measured at the reactor exit in mol/liter at time t seconds.

The mean residence time in the reactor, rounded to 1 decimal place, is ______ s.

Ans: (1.0)

42. The reversible reaction of t-butyl alcohol (TBA) and ethanol (EtOH) to ethylt-butyl ether (ETBE) is

TBA + EtOH ⇌ ETBE +Water

The equilibrium constant for this reaction is K_C = 1. Initially, 74 g of TBA is mixed with 100g of aqueous solution containing 46 weight% ethanol. The molecular weights are:74g/mol for TBA. 46g/mol for EtOH, 102g/mol for ETBE, and 18 g/mol for water.

The mass of ETBE at equilibrium, rounded to 1 decimal place, is ____g.

Ans: (20.4)

43. Let I_b_λ be the spectral black body radiation intensity per unit wavelength about the wavelength λ. The blackbody radiation intensity emitted by a blackbody over all wavelengths is

(A)

(B)

(C)

(D)

Ans: (C)

44. Match the equipment in Group-1 with the process in Group-2:

Group-1

(P) Fluidized bed

(Q) Multistage adiabatic reactor with Inter-stage cooling.

(R) Fourdrinier machine

(S) Diaphragm cell

Group-2

(I) Paper-making

(II) Sodium hydroxide manufacturer

(III) SO₂ oxidation

(IV) Catalytic cracking

Choose the correct set of combinations.

(A) P − IV,Q − III,R − I,S − II

(B) P − IV,Q − III,R − II,S − I

(D) P − III,Q − IV,R − II,S − I

Ans: (A)

45. Oil is being delivered at a steady state flowrate through a circular pipe of a radius 1.25 × 10⁻² m and length 10 m. The pressure drop access the pipe is 500 Pa.

The shear stress at the pipe wall, rounded to 2 decimal places______ Pa

Ans: (0.3125)

46. Match the problem type in Group-1 with the numerical method in Group-2

Group-1 Group-2

(P) System of linear algebraic equations (I) Newton-Raphson

(Q) Non-linear algebraic equations (II) Gauss-seidel

(R) Ordinary differential equations (III) Simphson’s Rule

(S) Nemerical integrations (IV) Runge-Kutta

Choose the correct set of combinations.

(A) P − II,Q − I,R − III,S − IV

(B) P − I,Q − II,R − IV,S − III

(D) P − II,Q − I,R − IV,S − III

Ans: (D)

47. The following gas-phase reaction is carried out in a constant-volume isothermal batch reactor

A + B → R + S

The reactants A and B as well as the product S are non-condensable gases. At the operating temperature, the saturation pressure of the product R is 40 kPa.

Initially, the batch reactor contains equimolar amounts of A and B (and no products) at a total pressure of 100 kPa. The initial concentrations of the reactants are C_{A, 0} = C_{B, 0} = 12.56 mol/m³. The rate of reaction is given by (−r_A) = 0.08C_AC_B mol/m³.s.

The time at which R just starts condensing, rounded to 1 decimal place, is_____

Ans: (4)

48. The vapor phase composition and relative volatilities (with respect to n-propane) on an ideal tray of a distillation column are

The mole fraction of n-propane in the liquid phase, rounded to 2 decimal places, is ____.

Ans: (0.88)

49. The Characteristic equation of a closed-loop system is

6s³ + 11s² + 6s + (1 + k) = 0, Where k > 0

The value of K beyond which the system just becomes unstable, rounded to the nearest integer, is _____.

Ans: (10)

50. A aqueous salt-solution enters a crystallizer operating at steady state at 25℃. he feed temperature is 90℃ and the salt concentration in the feed is 40 weight%. The salt crystallizes as a pentahydrate. The crystals and the mother liquor leave the crystallizer. The molecular weight of the anhydrous salt is 135. The solubility of the salt at 25℃ is 20 weight%.

The feed flowrate required for a production rate of 100 kg/s of hydrated salt, rounded to the nearest integer, is ____ kg/s.

Ans: (200)

51. The pressure of a liquid is increased isothermally. The molar volume of the liquid decreases from 50.45 × 10⁻⁶ m³/mol to 48 × 10⁻⁶ m³/mol during this process. The isothermal compressibility of the liquid is 10⁻⁹ Pa⁻¹, which can b e assumed to be independent of pressure.

The change in the molar Gibbs free energy of liquid, rounded to nearest integer, is J/mol.

Ans: (2511.4)

52. The open loop transfer function of a process with a proportional controller (gain K_C) is

Based on the Bode criterion for closed-loop stability, the ultimate gain of the controller, rounded to 2 decimal places, is____.

Ans: (0.78)

53. In nucleate boiling, the pressure inside a bubble is higher than the pressure of the surrounding liquid. Assuming that both the liquid and vapour are saturated, the temperature of the liquid will ALWAYS be

(A) at 100℃

(B) lower than the temperature of the vapour

(D) higher than the temperature of the vapour

Ans: (B)

54. A box has 6 red balls and white balls. A ball is picked at random and replaced in the box, after which a second ball is picked.

The probability of both the balls being red, rounded to 2 decimal places, is ____.

Ans: (0.36)

55. A sparingly soluble gas (solute) is in equilibrium with a solvent at 10 bar. The mole fraction of the solvent in the gas phase is 0.01. At the operating temperature and pressure, the fugacity coefficient of the solute in the gas phase and the Henry’s law constant are 0.92 and 1000 bar, respectively. Assume that the liquid phase obeys Henry’s law.

The MOLE PERCENTAGE of the solute in the liquid phase, rounded to 2 decimal places, is _____.

Ans: (0.91)

56. Consider the following sentences:

All benches are bed is a bulb. Some bulbs are lamps.

Which of the following can be inferred?

(i) Some beds are lamps.

(ii) Some lamps are beds.

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (D)

57. The following sequence of numbers is arranged in increasing order: 1,x,x,x, y, y,9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is

(A) 5

(B) 6

(D) 8

Ans: (D)

58. The bacteria in milk are destroyed when it _________ heated to 80 degree Celsius.

(A) would be

(B) will be

(D) was

Ans: (C)

59. If the radius of a right circular cone is increased by 50%, its volume increases by

(A) 75%

(B) 100%

(D) 237.5%

Ans: (C)

60. __________ with someone else’s email account is now very serious offence.

(A) Involving

(B) Assisting

(D) Incubating

Ans: (C)

61. Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation.

Given the data below, which room will Ajit stay in?

(A) P

(B) Q

(D) S

Ans: (B)

62. The bar graph below shows the output of five carpenters over one month, each of whom made different items of furniture: Chairs, tables, and beds.

Consider the following statements.

(i) The number of beds made by carpenter C2 is exactly the same as the same as the number

of tables made by carpenter C3.

(ii) The total number of chairs made by all carpenters is less than the total number of tables.

Which one of the following is true?

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (C)

63. The last digit of (2171)⁷ + (2172)⁹ + (2173)¹¹ + (2174)¹³ is

(A) 2

(B) 4

(D) 8

Ans: (B)

64. Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects. Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

(A) 2 hours

(B) 2.5 hours

(D) 3.5 hours

Ans: (A)

65. The old concert hall was demolished because of fears that the foundation would be affected by the construction tried to mitigate the impact of pressurized air pockets created by the excavation of large amounts of soil. But even with these safeguards, it was feared that the soil below the concert hall would not be stable.

From this, one can infer that

(A) The foundations of old buildings create pressurized air pockets underground, which are difficult to handle during metro construction.

(B) Metro construction has to be done carefully considering its impact on the foundations of existing buildings.

(D) Pressurized air can be used to excavate large amounts of soil from underground areas.

Ans: (B)

Gate 2017 Civil Engineering Question Paper 12th Feb 2017 Session 2 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Civil Engineering 12th Feb 2017 Session 2

Subject Name: Civil Engineering

Duration : 180

Total Marks: 100

1. Consider a rigid retaining wall with partially submerged cohesionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine’s active earth pressure distribution against this wall?.

(A)

(B)

(C)

(D)

Ans: (B)

2. The VPI (vertical point of intersection) is 100 m away (when measured along the horizontal) from the VPC (vertical point of curvature). If the vertical curve is parabolic, the length of the curve (in meters and measured along the horizontal) is _______

Ans: (200)

3. For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________

Ans: (210)

4. Given that the scope of the construction work is well-defined with all its drawings, specifications, quantities and estimates, which one of the following types of contract would be most preferred?

(A) EPC contract

(B) Percentage rate contract

(D) Lump sum contract

Ans: (D)

5. The divergence of the vector field V = x²i + 2y³j + z⁴k at x = 1, y = 2, z = 3 is _______

Ans: (134)

6. Consider the frame shown in the figure:

If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to

(A) 5

(B) 6

(D) 8

Ans: (B)

7. As per Noise Pollution (Regulation and Control) Rules 2000 of India, the day time noise limit for a residential zone, expressed in dB (A) L_eq, is

(A) 55

(B) 65

(D) 85

Ans: (A)

8. Let G be the specific gravity of soil solids, w the water content in the soil sample, γ_w the unit weight of water, and γ_d the dry unit weight of the soil. The equation for the zero air voids line in a compaction test plot is

(A)

(B)

(C)

(D)

Ans: (A)

9. The safety within a roundabout and the efficiency of a roundabout can be increased, respectively, by

(A) increasing the entry radius and increasing the exit radius

(B) increasing the entry radius and decreasing the exit radius

(D) decreasing the entry radius and decreasing the exit radius

Ans: (C)

10. In a material under a state of plane strain, a 10×10 mm square centered at a point gets deformed as shown in the figure.

If the shear strain γ_xy at this point is expressed as 0.001k (in rad), the value of k is

(A) 0.50

(B) 0.25

(D) −0.50

Ans: (C)

11. The method of orientation used, when the plane table occupies a position not yet located on the map, is called as

(A) traversing

(B) radiation

(D) resection

Ans: (D)

12. If a centrifugal pump has an impeller speed of N (in rpm), discharge Q (in m³/s) and the total head H (in m), the expression for the specific speed Ns of the pump is given by

(A)

(B)

(C)

(D)

Ans: (C)

13. Following observations have been made for the elevation and temperature to ascertain the stability of the atmosphere:

The atmosphere is classified as

(A) Stable

(B) Unstable

(D) Inverse

Ans: (C)

14. During a storm event in a certain period, the rainfall intensity is 3.5 cm/hour and the Φ − index is 1.5 cm/hour. The intensity of effective rainfall (in cm/hour, up to one decimal place) for this period is ______

Ans: (2)

15. For a broad gauge railway track on a horizontal curve of radius R (in m), the equilibrium cant e required for a train moving at a speed of V (in km per hour) is

(A)

(B)

(C)

(D)

Ans: (B)

16. Consider the following simultaneous equations (with c₁ and c₂ being constants):

3x₁ + 2x₂ = c₁

4x₁ + x₂ = c₂

The characteristic equation for these simultaneous equations is

(A) λ² – 4λ – 5 = 0

(B) λ² – 4λ + 5 = 0

(D) λ² + 4λ + 5 = 0

Ans: (A)

17. A sheet pile has an embedment depth of 12 m in a homogeneous soil stratum. The coefficient of permeability of soil is 10⁻⁶ m/s. Difference in the water levels between the two sides of the sheet pile is 4 m. The flow net is constructed with five number of flow lines and eleven number of equipotential lines. The quantity of seepage (in cm³/s per m, up to one decimal place) under the sheet pile is _____

Ans: (1.6)

18. While aligning a hill road with a ruling gradient of 6 %, a horizontal curve of radius 50 m is encountered. The grade compensation (in percentage, up to two decimal places) to be provided for this case would be______

Ans: (1.5)

19. Consider the following statements related to the pore pressure parameters, A and B:

P. A always lies between 0 and 1.0

Q. A can be less than 0 or greater than 1.0

R. B always lies between 0 and 1.0

S. B can be less than 0 or greater than 1.0

For these statements, which one of the following options is correct?

(A) P and R

(B) P and S

(D) Q and S

Ans: (C)

20. Let the characteristic strength be defined as that value, below which not more than 50% of the results are expected to fall. Assuming a standard deviation of 4 MPa, the target mean strength (in MPa) to be considered in the mix design of a M25 concrete would be

(A) 18.42

(B) 21.00

(D) 31.58

Ans: (C)

21. The plate load test was conducted on a clayey strata by using a plate of 0.3m × 0.3 m dimensions, and the ultimate load per unit area for the plate was found to be 180 kPa. The ultimate bearing capacity (in kPa) of a 2 m wide square footing would be

(A) 27

(B) 180

(D) 2000

Ans: (B)

22. The infiltration capacity of a soil follows the Horton’s exponential model, f = c₁ + c₂e⁻^kt. During and experiment, the initial infiltration capacity was observed to be 200 mm/h. After a long time, the infiltration capacity was reduced to 25 mm/h. If the infiltration capacity after 1 hour was 90 mm/h, the value of the decay rate constant, k (in h⁻¹, up to two decimal places) is_______

Ans: (0.99)

23. A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be_______

Ans: (0.5)

24. The most important type of species involved in the degradation of organic matter in the case of activated sludge process is

(A) Autotrophs

(B) Heterotrophs

(D) Photo-autotrophs

Ans: (B)

25. Let w = f (x,y), where x and y are functions of t. Then, according to the chain rule, is equal to

(A)

(B)

(C)

(D)

Ans: (C)

26. Consider the portal frame shown in the figure and assume the modulus of elasticity 4 E = 2.5×10 MPa and the moment of inertial, I = 8×10⁸ mm⁴ for all the members of the frame.

The rotation (in degrees, up to one decimal place) at the rigid joint Q would be_______

Ans: (1.003)

27. The radii of relative stiffness of the rigid pavements P and Q are denoted by ℓ_p and ℓ_Q, respectively. The geometric and material properties of the concrete slab and underlying soil are given below:

The ratio (up to one decimal place) of ℓ_p/ℓ_Q is _______

Ans: (2)

28. A 1 m wide rectangular channel carries a discharge of 2m³/s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to _______

Ans: (1.069)

29. A hollow circular shaft has an outer diameter of 100 mm and inner diameter of 50 mm. If the allowable shear stress is 125 MPa, the maximum torque (in kN-m) that the shaft can resist is_______

Ans: (23.009)

30. Consider the following statements:

P. Walls of one brick thick are measured in square meters.

Q. Walls of one brick thick are measured in cubic meters.

R. No deduction in the brickwork quantity is made for openings in walls up to 0.1 m² area.

S. For the measurement of excavation from the borrow pit in a fairly uniform ground, dead men are left at suitable intervals.

For the above statements, the correct option is

(A) P-False; Q-True; R- False: S-True

(B) P-False; Q-True: R-False; S-False

(D) P-True; Q-False; R-True; S-True

Ans: (D)

31. Following are the statements related to the stress paths in a triaxial testing of soils:

P. If σ₁ = σ₃, the stress point lies at the origin of the p-q plot

Q. If σ₁ = σ₃, the stress point lies on the p-axis of the p-q plot.

R. If σ₁ > σ₃, both the stress points p and q are positive.

For the above statements, the correct combination is

(A) P − False; Q − True; R − True

(B) P − False; Q − True; R − True

(D) P − True; Q − False; R − False

Ans: (A)

32. A simply supported rectangular concrete beam of span 8m has to be prestressed with a force of 1600kN. The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity 30 kN/m. Neglecting the self-weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be________

Ans: (0.15)

33. An observer standing on the deck of a ship just sees the top of a lighthouse. The top of the lighthouse is 40 m above the sea level and the height of the observer’s eye is 5 m above the sea level. The distance (in km, up to one decimal place) of the observer form the lighthouse is _______

Ans: (33)

34. If AB^T is equal to

(A)

(B)

(C)

(D)

Ans: (A)

35. A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement (p−δ) behavior as shown in the figure.

Assume the yield stress of steel as 250 Mpa. The complementary energy (in N-mm) stored in the bar up to its linear elastic behavior will be_______

Ans: (15707, 963)

36. Two cars P and Q are moving in a racing track continuously for two hour. Assume that no other vehicles are using the track during this time. The expressions relating the distance travelled d (in km) and time t (in hour) for both the vehicles are given as

P:d = 60t

Q:d = 60t²

Within the first one hour, the maximum space headway would be

(A) 15 km at 30 minutes

(B) 15 km at 15 minutes

(D) 30 km at 15 minutes

Ans: (A)

37. Consider the following definite integral:

The value of the integral is

(A)

(B)

(C)

(D)

Ans: (A)

38. A municipal corporation is required to treat 1000 m³/day of water. It is found that an overflow rate of 20 m/day will produce a satisfactory removal of the discrete suspended particles at a depth of 3 m. The diameter (in meters, rounded to the nearest integer) of a circular settling tank designed for the removal of these particles would be______

Ans: (8)

39. For the construction of a highway. A cut is to be made as shown in the figure.

The soil exhibits c’ = 20 kPa, ϕ = 18°, and the undrained shear strength = 80 kPa. The unit weight of water is 9.81 kN/m³. The unit weights of the soil above and below the ground water table are 18 and 20 kN/m³, respectively. If the shear stress at Point A is 50 kPa, the factors of safety against the shear failure at this point, considering the undrained and drained conditions, respectively, would be

(A) 1.6 and 0.9

(B) 0.9 and 1.6

(D) 1.2 and 0.6

Ans: (A)

40. A catchment is idealized as a 25 km × 25 km square. It has five rain gauges, one at each corner and one at the center, as shown in the figure.

During a month, the precipitation at these gauges is measured as G₁ = 300 mm, G₂ = 285mm, G₃ = 272mm, G₄ = 290mmand G₅ =288mm. The average precipitation (in mm, up to one decimal place) over the catchment during this month by using the Thiessen polygon method is_______

Ans: (287.375)

41. The tangent to the curve represented by y = x ln x is required to have 45° inclination with the x-axis. The coordinates of the tangent point would be

(A) (1, 0)

(B) (0, 1)

(D) (√2, √2)

Ans: (A)

42. Water is pumped at a steady uniform flow rate of 0.01 m³/s through a horizontal smooth circular pipe of 100 mm diameter. Given that the Reynolds number is 800 and g is 9.81 m/s² , the head loss (in meters, up to one decimal place) per km length due to friction would be____

Ans: (66.67)

43. Group I given a list of test methods and test apparatus for evaluating some of the properties of ordinary Portland cement (OPC) and concrete. Group II gives the list of these properties.

Group I Group II

P. Le chatelier test 1. Soundness of OPC

Q. Vee-Bee test 2. Consistency and setting time of OPC

R. Blaine air permeability test 3. Consistency or workability of concrete

S. The Vicat apparatus 4. Fineness of OPC

The correct match of the items in Group I with the items in Group II is

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

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

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

Ans: (A)

44. The figure shows a U-tube having a 5 mm×5 mm square cross-section filled with mercury (specific gravity = 13.6) up to a height of 20 cm in each limb (open to the atmosphere).

If 5cm³ of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be______

Ans: (20.735)

45. The analysis of a water sample produces the following results:

The total hardness (in mg/L as CaCO₃) of the water sample is_____

Ans: (300)

46. Consider the three prismatic beams with the clamped supports P, Q, and R as shown in the figures.

Given that the modulus of elasticity, E is 4 2.5×10 MPa; and the moment of inertia, I is 8×10⁸ mm⁴, the correct comparison of the magnitudes of the shear forces S and the bending moment M developed at the supports is

(A) S_P < S_Q < S_R ; M_P = M_Q = M_R

(B) S_P = S_Q > S_R ; M_P = M_Q > M_R

(D) S_P < S_Q < S_R ; M_P < M_Q < M_R

Ans: (C)

47. Consider a square-shaped area ABCD on the ground with its centre at M as shown in the figure. Four concentrated vertical load of P=5000 kN are applied on this area, at each corner.

The vertical stress increment (in kPa, up to one decimal place) due to these loads according to the Boussinesq’s equation, at a point 5 m right below M, is______

Ans: (191.36)

48. For a given water sample, the ratio between BO_{5-day, 20}_℃ and the ultimate BOD is 0.68. The value of the reaction rate constant k (on base e)( in day⁻¹, up to two decimal place) is ________

Ans: (0.23)

49. Two identical concrete piles having the plan dimensions 50 cm× 50 cm are driven into a homogeneous sandy layer as shown in the figures. Consider the bearing capacity factor N_q for ϕ = 30°as24.

If Q_P1 and Q_P2 represent the ultimate point bearing resistance of the piles under dry and submerged conditions, respectively, which one of the following statements is correct ?

(A) Q_P1 > Q_P2 by about 100%

(B) Q_P1 < Q_P2 by about 100%

(D) Q_P1 < Q_P2 by about 5%

Ans: (A)

50. The culturable command area of a canal is 10,000 ha. The area grows only two crops-rice in the Kharif season and wheat in the Rabi season. The design discharge of the canal is based on the rice requirements, which has an irrigated area of 2500 ha, base period of 150 days and delta of 130 cm. The maximum permissible irrigated area (in ha) for wheat, with a base period of 120 days and delta of 50 cm, is_______

Ans: (5200)

51. The composition of a municipal solid waste sample is given below:

The difference between the energy content of the waste sample calculated on dry basis and as-discarded basis (in kJ/kg) would be______

Ans: (3870)

52. Consider the following second-order differential equation:

y”− 4y’+ 3y = 2t − 3t²

The particular solution of the differential equations is

(A) −2 – 2t – t²

(B) −2t – t²

(D) −2 – 2t – 3t²

Ans: (A)

53. Two plates of 8 mm thickness each are connected by a fillet weld of 6 mm thickness as shown in the figure.

The permissible stresses in the plate and the weld are 150 MPa and 110 MPa, respectively. Assuming the length of the weld shown in the figure to be the effective length, the permissible load P (in KN) is______

Ans: (60)

54. Two prismatic beams having the same flexural rigidity of 1000 kN-m² are shown in the figures.

If the mid-span deflections of these beams are denoted by δ₁ and δ₂ (as indicated in the figures). The correct option is

(A) δ₁ = δ₂

(B) δ₁ < δ₂

(D) δ₁ >> δ₂

Ans: (A)

55. Two towers A and B, standing vertically on a horizontal ground, appear in a vertical aerial photograph as shown in the figure.

The length of the image of the tower A on the photograph is1.5 cm and of the tower B is 2.0 cm. The distance of the top the tower A (as shown by the arrowhead) is 4.0 cm and the distance of the top of the tower B is 6.0 cm, as measured form the principal point p of the photograph. If the height of the tower B is 80 m, the height (in meters) of the tower A is ______

Ans: (90)

56. There was no doubt that their work was thorough.

Which of the words below is closest in meaning to the underlined word above?

(A) Pretty

(B) Complete

(D) Haphazard

Ans: (B)

57. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

(A) 2, Red

(B) 2, 3, Red

(D) 2, red, blue

Ans: (C)

58. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

(A) 1/9

(B) 2/9

(D) 4/9

Ans: (B)

59. What is the value of x when

(A) 1

(B) −1

(D) Cannot be determined

Ans: (B)

60. The event would have been successful if you ______ able to come.

(A) are

(B) had been

(D) would have been

Ans: (B)

61. P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats.

Which of the following must necessarily be true?

(A) P is immediately to the right of R

(B) T is immediately to the left of P

(D) U is immediately to the right of R or P is immediately to the left of T

Ans: (C)

62. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

(A) The centre operates on a first-come-first-served basis but with variable service times, depending on specific customer needs.

(B) Customers were served in an arbitrary order since they took varying amounts of time for service completion in the centre.

(C) Since some people came out within a few minutes of entering the centre. The system is likely to operate on a last-come-first-served basis.

(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Ans: (A)

63. A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri.

Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok.

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

i. Pelling is at a higher elevation than Kalimpong

ii. Kalimpong is at a lower elevation than Darjeeling

iii. Kalimpong is at a higher elevation than siliguri

iv. Siliguri is at a lower elevation than Gangtok

(A) Only ii

(B) Only ii and iii

(D) Only iii and iv

Ans: (C)

64. Budhan covers a distance of f19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

(A) 1

(B) 4

(D) 6

Ans: (D)

65. The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (D)

Gate 2017 Civil Engineering Question Paper 12th Feb 2017 Session 1 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Civil Engineering 12th Feb 2017 Session 1

Subject Name: Civil Engineering

Duration : 180

Total Marks: 100

1. The ordinates of a 2-hour unit hydrograph for a catchment are given as

The ordinate (in m³/s) of a 4-hour unit hydrograph for this catchment at the time of 3 h would be______

Ans: (15)

2. A uniformly distributed line load of 500 kN/m is acting on the ground surface. Based on Boussinesq’s theory, the ratio of vertical stress at a depth 2 m to that at 4 m, right below the line of loading, is

(A) 0.25

(B) 0.5

(D) 4.0

Ans: (C)

3. According to IS 456-2000, which one of the following statements about the depth of neutral axis χ_{u, bal} for a balanced reinforced concrete section is correct?

(A) χ_{u, bal}depends on the grade of concrete only.

(B) χ_{u, bal}depends on the grade of steel only.

(D) χ_{u, bal}does not depend on the grade of concrete and grade of steel.

Ans: (B)

4. Group I lists the type of gain or loss of strength in soils. Group II lists the property or process responsible for the loss or gain of strength in soils.

Group I Group II

P. Regain of strength with time 1. Boiling

Q. Loss of strength due to cyclic loading 2. Liquefaction

R. Loss of strength due to upward seepage 3. Thixotropy

S. Loss of strength due to remolding 4. Sensitivity

The correct match between Group I and Group II is

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

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

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

Ans: (C)

5. A runway is being constructed in a new airport as per the International Civil Aviation Organization (ICAO) recommendations. The elevation and the airport reference temperature of this airport are 535 m above the mean sea level and 22.65°C, respectively. Consider the effective gradient of runway as 1%. The length of runway required for a design-aircraft under the standard conditions is 2000 m. Within the framework of applying sequential corrections as per the ICAO recommendations, the length of runway corrected for the temperature is

(A) 2223 m

(B) 2250 m

(D) 2750 m

Ans: (C)

6. A soil sample is subjected to a hydrostatic pressure, σ. The Mohr circle for any point in the soil sample would be

(A) a circle of radius σ and center at the origin

(B) a circle of radius σ and center at a distance σ from the origin

(D) a circle of diameter σ and center at the origin

Ans: (C)

7. The figure shows a two-hinged parabolic arch of span L subjected to a uniformly distributed load of intensity q per unit length.

The maximum bending moment in the arch is equal to

(A)

(B)

(C)

(D)

8. For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation is

(A) linear with zero value at the plates

(B) linear with zero value at the center

(D) quadratic with zero value at the centre

Ans: (B)

9. An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion α, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased by T, resulting in an axial stress σ. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

(A) σ

(B) 2σ

(D) 0.25ασ

Ans: (A)

10. The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

(A) 2 and 1

(B) 1 and 2

(D) 1 and 1

Ans: (B)

11. The wastewater form a city, containing a high concentration of biodegradable organics, is being steadily discharged into a flowing river at a location S. If the rate of aeration of the river water is lower than the rate of degradation of the organics, then the dissolved oxygen of the river water

(A) is lowest at the locations S.

(B) is lowest at a point upstream of the location S.

(D) is lowest at a point downstream of the location S.

Ans: (D)

12. The reaction rate involving reactants A and B is given by –k[A]^α [B]^β. Which one of the following statements is valid for the reaction to be first –order reaction?

(A) α = 0 and β = 0

(B) α = 1 and β = 0

(D) α = 1 and β = 2

Ans: (B)

13. A strip footing is resting on the ground surface of a pure clay bed having an undrained cohesion C_u. The ultimate bearing capacity of the footing is equal to

(A) 2πC_u

(B) πC_u

(D) (π + 2)C_u

Ans: (D)

14. A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?

(A) Maximum or minimum shear force occurs where the curvature is zero.

(B) Maximum or minimum bending moment occurs where the shear force is zero.

(D) Maximum bending moment and maximum shear force occur at the same section.

Ans: (B)

15. A triangular pipe network is shown in the figure.

The head loss in each pipe is given by h_f = rQ^1.8, with the variables expressed in a consistent set of units. The value of r for the pipe AB is 1 and for the pipe BC is 2. If the discharge supplied at the point A (i.e., 100) is equally divided between the pipes AB and AC, the value of r (up to two decimal places) for the pipe AC should be_______

Ans: (0.62)

16.

Ans: (1)

17. A super-elevation e is provided on a circular horizontal curve such that a vehicle can be stopped on the curve without sliding. Assuming a design speed v and maximum coefficient of side friction f_max, which one of the following criteria should be satisfied?

(A) e ≤ f_max

(B) e > f_max

(D)

Ans: (A)

18. Which one of the following is NOT present in the acid rain?

(A) HNO₃

(B) H₂SO₄

(D) CH₃COOH

Ans: (D)

19. The accuracy of an Electronic Distance Measuring Instrument (EDMI) is specified as ±(a mm + b ppm). Which one of the following statements is correct?

(A) Both a and b remain constant, irrespective of the distance being measured.

(B) a remains constant and b varies in proportion to the distance being measured.

(D) Both a and b vary in proportion to the distance being measured.

Ans: (B)

20. Consider the following partial differential equation:

For this equation to be classified as parabolic, the value of B² must be_______

Ans: (36)

21. The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?

(A) PQ = I but QP ≠ I

(B) QP = I but PQ ≠ I

(D) PQ – QP = I

Ans: (C)

22. Vehicles arriving at an intersection from one of the approach road follow the Poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is______

Ans: (0.1354)

23. Let x be a continuous variable defined over the interval (−∞, ∞) and . The integral g(x) = ∫f(x) dx is equal to

(A)

(B)

(C)

(D)

Ans: (B)

24. The number of spectral bands in the Enhanced Thematic Mapper sensor on the remote sensing satellite Landsat-7 is

(A) 64

(B) 10

(D) 15

Ans: (C)

25. A 3 m thick clay layer is subjected to an initial uniform pore pressure of 145 kPa as shown in the figure.

For the given ground conditions, the time (in days, rounded to the nearest integer) required for 90% consolidation would be ________

Ans: (1770.833)

26. A planar truss tower structure is shown in the figure.

Consider the following statements about the external and internal determinacies of the truss.

(P) Externally Determinate

(Q) External Static Indeterminacy = 1

(R) External Static Indeterminacy = 2

(S) Internally Determinate

(T) Internal Static Indeterminacy = 1

(U) Internal Static Indeterminacy = 2

Which one of the following options is correct?

(A) P-False; Q-True; R-False; S-False; T-False; U-True

(B) P-False; Q-True; R-False; S-False: T-True; U-False

(D) P-True; Q-True; R-False; S-True; T-False; U-True

Ans: (A)

27. Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure.

Segments 1 and 2 have cross-sectional are of 100 mm² and 60 mm², Young’s modulus of 2×10⁵MPa and 3 × 10⁵ MPa, and length of 400 mm and 900 mm, respectively. The strain energy (in N-mm, up to one decimal place) in the bar due to the axial load is_____

Ans: (35)

28. Consider the beam ABCD shown in the figure.

For a moving concentrated load of 50 kN on the beam, the magnitude of the maximum bending moment (in kN-m) obtained at the support C will be equal to______

Ans: (200)

29. A column is subjected to a load through a bracket as shown in the figure.

The resultant force (in kN, up to one decimal place) in the bolt 1 is_____

Ans: (5.9 to 6.1)

30. The activity details of a project are given below:

The estimated minimum time (in days) for the completion of the project will be________

Ans: (51)

31. The value of M in the beam ABC shown in the figure is such that the joint B does not rotate.

The value of support reaction (in kN) at B should be equal to______

Ans: (60)

32. Two wastewater streams A and B, having an identical ultimate BOD are getting mixed to form the stream C. The temperature of the stream A is 20°C and the temperature of the stream C is 10°C. It is given that

• The 5-day BOD of the stream A measured at 20°C=50 mg/l

• BOD rate constant (base 10) at 20°C=0.115 per day

• Temperature coefficient = 1.135

The 5 –day BOD (in mg/l, up to one decimal place) of the stream C, calculated at 10°C, is______

Ans: (20.0 to 22.0)

33. A particle of mass 2 kg is travelling at a velocity of 1.5 m/s. A force f(t)=3t² (in N) is applied to it in the direction of motion for a duration of 2 seconds, where t denotes time in seconds. The velocity (in m/s, up to one decimal place) of the particle immediately after the removal of the force is________

Ans: (5.5)

34. The queue length (in number of vehicles) versus time (in seconds) plot for an approach to a signalized intersection with the cycle length of 96 seconds is shown in the figure (not drawn to scale).

At time t = 0, the light has just turned red. The effective green time is 36 seconds, during which vehicles discharge at the saturation flow rate, s (in vph). Vehicles arrive at a uniform rate, v (in vph), throughout the cycle. Which one of the following statements is TRUE?

(A) v = 600 vph, and for this cycle, the average stopped delay per vehicle = 30 seconds

(B) s = 1800 vph, and for this cycle, the average stopped delay per vehicle = 28.125 seconds

(D) s = 1200 vph, and for this cycle, the average stopped delay per vehicle = 28.125 seconds

Ans: (B)

35. For the function f(x) = a + bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?

(A) a = 1, b = 4

(B) a = 0.5, b = 1

(D) a = 1, b = −1

Ans: (B)

36. The infinite sand slope shown in the figure is on the verge of sliding failure. The ground water table coincides with the ground surface. Unit weight of water γ_w = 9.81 kN/m³.

The value of the effective angle of internal friction (in degrees, up to one decimal place) of the sand is ________

Ans: (34.335)

37. A sluice gate used to control the flow in a horizontal channel of unit width is shown in the figure.

It is observed that the depth of flow is 1.0 m upstream of the gate, while the depth is 0.2 m downstream of the gate. Assuming a smooth flow transition across the sluice gate, i.e., without any energy loss, and the acceleration due to gravity as 10 m/s², the discharge (in m³/s, up to two decimal places) passing under the sluice gate is_______

Ans: (0.82)

38. Group I contains three broad classes of irrigation supply canal outlets. Group II presents hydraulic performance attributes.

The correct match of the items in Group I with the items in Group II is

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

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

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

Ans: (D)

39. Consider the matrix Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

(A) Eigenvalue 3 has a multiplicity of 2, and only one independent eigenvector exists.

(B) Eigenvalue 3 has a multiplicity of 2, and two independent eigenvectors exist.

(D) Eigenvalues are 3 and -3, and two independent eigenvectors exist.

Ans: (A)

40. The laboratory test on a soil sample yields the following results: natural moisture content = 18%, liquid limit = 60%, plastic limit = 25%, percentage of clay sized fraction = 25%.

The liquidity index and activity (as per the expression proposed by skempton ) of the soil, respectively, are

(A) -0.2 and 1.4

(B) 0.2 and 1.4

(D) 1.2 and 0.714

Ans: (A)

41. The solution of the equation

(A) Q(t) = e⁻^t – 1

(B) Q(t) = 1 + e⁻^t

(D) Q(t) = 1 − e⁻^t

Ans: (D)

42. Water flows through a 90° bend in a horizontal plane as depicted in the figure.

A pressure of 140 kPa is measured at section 1-1. The inlet diameter marked at section 1-1 is while the nozzle diameter marked at section 2-2 is Assume the following:

(i) Acceleration due to gravity = 10 m/s².

(ii) Weights of both the bent pipe segment as well as water are negligible.

(iii) Friction across the bend is negligible.

The magnitude of the force (in kN, up to two decimal places) that would be required to hold the pipe section is______

Ans: (2.50 to 3.75)

43. A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm², to an initial stress of 1200 N/mm². The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______.

Ans: (4.8)

44. The spherical grit particles, having a radius of 0.01mm and specific gravity of 3.0, need to be separated in a settling chamber. It is given that

• g = 9.81 m/s²

• the density of the liquid in the settling chamber = 1000 kg/m³

• the kinematic viscosity of the liquid in the settling chamber = 10⁻⁶ m²/s

Assuming laminar conditions, the settling velocity (in mm/s, up to one decimal place) is_____

Ans: (0.436)

45. The equivalent sound power level (in dB) of the four sources with the noise levels of 60 dB, 69 dB, 70 dB and 79 dB is_______

Ans: (79.9)

46. Consider the equation with u = 0 at t = 0. This is numerically solved by using the forward Euler method with a step size. ∆t = 2. The absolute error in the solution at the end of the first time step is_________

Ans: (8)

47. It is proposed to drive H-piles up to a depth of 7 m at a construction site. The average surface area of the H-pile is 3 m² per meter length. The soil at the site is homogeneous sand, having an effective friction angle of 32°. The ground water table (GWT) is at a depth of 2 m below the ground surface. The unit weights of the soil above and below the GWT are 16 kN/m³ and 19 kN/m³, respectively. Assume the earth pressure coefficient, K= 1.0, and the angle of wall friction, δ =23°. The total axial frictional resistance (in kN, up to one decimal place) mobilized on the pile against the driving is________

Ans: (385.0 to 390.0)

48. The wastewater having an organic concentration of 54 mg/l is flowing at a steady rate of 0.8m3/day through a detention tank of dimensions 2m × 4m × If the contents of the tank are well mixed and the decay constant is 0.1 per day, the outlet concentration (in mg/l, up to one decimal place) is ______

Ans: (17.9 to 18.1)

49. The radius of a horizontal circular curve on a highway is 120 m. The design speed is 60 km/hour, and the design coefficient of lateral friction between the tyre and the road surface is 0.15. The estimated value of superelevation required (if full lateral friction is assumed to develop), and the value of coefficient of friction needed (if no superelevation is provided) will, respectively, be

(A)

(B)

(C)

(D)

Ans: (C)

50. Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young’s modulus 2×10⁵ MPa, square cross-section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler’s theory, the ratio (up to one decimal place) of the buckling load of Column 2 to the buckling load of Column 1 is ________

Ans: (8)

51. The observed bearings of a traverse are given below:

The stations(s) most likely to be affected by the local attraction is/are

(A) Only R

(B) Only S

(D) P and Q

Ans: (A)

52. A 1 m wide rectangular channel has a bed slope of 0.0016 and the Manning’s roughness coefficient is 0.04. Uniform flow takes place in the channel at a flow depth of 0.5 m. At a particular section, gradually varied flow (GVF) is observed and the flow depth is measured as 0.6 m. The GVF profile at that section is classified as

(A) S₁

(B) S₂

(D) M₂

Ans: (C)

53. A consolidated undrained triaxial compression test is conducted on a normally consolidated clay at a confining pressure of 100 kPa. The deviator stress at failure is 80 kPa, and the pore-water pressure measured at failure is 50 kPa. The effective angle of internal friction (in degrees, up to one decimal place) of the soil is_________

Ans: (26.4)

54. An effective rainfall of 2-hour duration produced a flood hydrograph peak of 200 m³/s. The flood hydrograph has a base flow of 20 m³/s. If the spatial average rainfall in the watershed for the duration of storm is 2 cm and the average loss rate is 0.4 cm/hour, the peak of 2-hour unit hydrograph (in m³/s-cm, up to one decimal place) is_________

Ans: (150)

55. The following observations are made while testing aggregate for its suitability in pavement construction:

i. Mass of oven-dry aggregate in air = 1000 g

ii. Mass of saturated surface-dry aggregate in air = 1025 g

iii. Mass of saturated surface-dry aggregate under water = 625 g

Based on the above observations, the correct statement is

(A) bulk specific gravity of aggregate = 2.5 and water absorption = 2.5 %

(B) bulk specific gravity of aggregate = 2.5 and water absorption = 2.4 %

(D) apparent specific gravity of aggregate = 2.5 and water absorption = 2.4 %

Ans: (A)

56. Consider the following sentences:

All benches are beds. No bed is a bulb. Some bulbs are lamps.

Which of the following can be inferred?

i. Some beds are lamps.

ii. Some lamps are beds

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (D)

57. The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y,9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is

(A) 5

(B) 6

(D) 8

Ans: (D)

58. The bacteria in milk are destroyed when it _________ heated to 80 degree Celsius.

(A) would be

(B) will be

(D) was

Ans: (C)

59. If the radius of a right circular cone is increased by 50%, its volume increases by

(A) 75%

(B) 100%

(D) 237.5%

Ans: (C)

60. __________ with someone else’s email account is now very serious offence.

(A) Involving

(B) Assisting

(D) Incubating

Ans: (C)

Given the data below, which room will Ajit stay in?

(A) P

(B) Q

(D) S

Ans: (B)

62. The bar graph below shows the output of five carpenters over one month, each of whom made different items of furniture: Chairs, tables, and beds.

Consider the following statements.

i. The number of beds made by carpenter C2 is exactly the same as the same as the number of tables made by carpenter C3.

ii. The total number of chairs made by all carpenters is less than the total number of tables.

Which one of the following is true?

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (C)

63. The last digit (2171)⁷ + (2172)⁹ + (2173)¹¹ + (2174)¹³ is

(A) 2

(B) 4

(D) 8

Ans: (B)

64. Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects. Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

(A) 2 hours

(B) 2.5 hours

(D) 3.5 hours

Ans: (A)

From this, one can infer that

(A) The foundations of old buildings create pressurized air pockets underground, which are difficult to handle during metro construction.

(B) Metro construction has to be done carefully considering its impact on the foundations of existing buildings.

(D) Pressurized air can be used to excavate large amounts of soil from underground areas.

Ans: (B)

Gate 2017 Biotechnology Question Paper 5th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Biotechnology 5th Feb 2017

Subject Name: Biotechnology

Duration : 180

Total Marks: 100

1. Which one of the following organisms is an indicator of fecal contamination?

(A) Escherichia coli

(B) Streptococcus lactis

(D) Lactobacillus acidophilus

Ans: (A)

2. Enzyme-linked immunosorbent assay (ELISA) is used for

(A) Quantifying antibody levels in blood

(B) Determining the molecular weight of an antigen

(D) Determining the molecular weight of an anti body

Ans: (A)

3. At the transcription start site of a gene, any of the four nucleotides can occur with equal probability p. The Shannon Entropy S, given by this start site is _____.

Given data: ln(2) = 0.69

Ans: (1.36)

4. The transcription factor X binds a 10 base pair DNA stretch. In the DNA of an organism, X was found to bind at 20 distinct sites. An analysis of these 20 binding sites showed the following distribution:

What is the consensus sequence for the binding site of X?

(A) NGTCNNNTNN

(B) AGTCACNTGC

(D) ANNNACGNGC

Ans: (B)

5. Macrophages eliminate pathogenic bacteria upon activation by

(A) NK cells

(B) Basophils

(D) Plasma cells

Ans: (C)

6. A bacterium has a genome of size 6 million base pairs. If the average rate of DNA synthesis is 1000 base paris/second, the time taken (in minutes) for replication of the genome will be ___ .

Ans: (100)

7. An enzyme catalyzes a reaction by

(A) Decreasing the energy of the substrate.

(B) Decreasing the activation energy of the reaction.

(D) Increasing the activation barrier of the reaction.

Ans: (B)

8. Which one of the following techniques can be used to determine the structure of a 15 kDa globular protein at atomic resolution?

(A) Raman spectroscopy

(B) IR spectroscopy

(D) NMR spectroscopy

Ans: (D)

9. In eukaryotes, cytokinesis is inhibited by

(A) Cytochalasin D

(B) Vinblastine

(D) Colchicines

Ans: (A)

10. Which one of the following mechanisms is used by human pathogens to evade host immune responses?

(A) Somatic hypermutation

(B) Antibody production

(D) Complement activation

Ans: (C)

11. An enzyme reaction exhibits Michaelis-Menten kinetics. For this reaction, on doubling the concentration of enzyme while maintaining [S] > > [E₀].

(A) Both K_m and V_max will remain the same.

(B) K_m will remain the same but V_max will increase.

(D) Both k_m and V_max will increase.

Ans: (B)

12. The surface area (in m²) of the largest sphere that can fit into a hollow cube with edges of length 1 meter is ______ .

Given data : π = 3.14

Ans: (3.14)

13. Assertion [a]: Gram negative bacteria show staining with saffranin.

Reason [r]: Gram negative bacteria have an outer membrane with lipopolysaccharides

(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.

Ans: (A)

14. A proto-oncogene is suspected to have undergone duplication in a certain type of cancer. Of the following techniques, which one would verify the gene duplication?

(A) Northern blotting

(B) Southern blotting

(D) Western blotting

Ans: (B)

15. For y = f(x), if at x = 0, and y = 1 at x = 1, the value of y at x = 2 is _______.

Ans: (1)

16. If a protein contains four cysteine residues, the number of different ways they can simultaneously form two intra-molecular disulphide bonds is ____.

Ans: (3)

17. Natural proteins are composed primarily of 20 α − amino acids. Which one of the following statements is true for any of these amino acids in a solution of p^H5?

(A) Only the amino group is ionized.

(B) Only the carboxylic acid group is ionized.

(D) Both amino and carboxylic acid groups are neutral.

Ans: (A)

18. During protein synthesis, tRNAs are NOT involved in

(A) Charging

(B) Initiation

(D) Termination

Ans: (D)

19. A polymerase chain reaction (PCR) was set up with the following reagents: DNA template. Taq polymerase, butter, dNTPs, and Mg²⁺ . Which one of the following is missing in the reaction mixture?

(A) Helicase

(B) Single-stranded binding proteins

(D) Reverse transcriptase

Ans: (C)

20. The plant hormone indole-3-acetic acid is derived from

(A) Histidine

(B) Tyrosine

(D) Proline

Ans: (C)

21. Secretory proteins synthesized by ER-associated ribosomes traverse through

(A) Mitochondria

(B) peroxisomes

(D) the nucleus

Ans: (C)

22. A 5 liter chemostat is fed fresh medium at 0.2 litres/minute having a substrate concentration of 25 grams/liter. At steady state, the outgoing stream has substrate concentration of 2.5 grams/liter. The rate of consumption (grams/liter/minute) of the substrate in the reactor is ___.

Ans: (0.86)

23. If the nucleotide composition (%) of a viral genome is A =10, U = 20, C = 40, and G = 30, which one of the following is this genome?

(A) Double stranded RNA

(B) Single stranded RNA

(D) Double stranded DNA

Ans: (B)

24. In a thin layer chromatography experiment using a silica gel plate, a compound showed migration of 12.5 cm and the solvent front showed migration of 18 cm. The R_f value for the compound is ____ .

Ans: (0.694)

25.

Ans: (1)

26. A pedigree of an inheritable disease is shown below.

This inheritable disease is

(A) X-linked dominant

(B) X-linked recessive or Y-linked

(D) only X-linked recessive

Ans: (B)

27. A DNA strand of length 25 mm wraps diametrically around the circumference of a spherical histone-octamer once. The radius (nm) of the histone-octamer is _____ .

Given data: π = 3.14

Ans: (3.91)

28. A recombinant protein is to be expressed under the control of the lac promoter and operator in a strain of E.coli having the genotype lacl⁺ crp⁺. Even in the absence of inducer IPTG, low levels of expression of the recombinant protein are seen (leaky expression). Which one of the following should be done to minimize such leaky expression?

(A) Addition of lactose to the medium

(B) Removal of all glucose from the medium

(D) Addition of allo-lactose to the medium

Ans: (C)

29. EcoRI restriction sites on a 10kb DNA fragment are shown below.

Upon partial digestion, what are the lengths (in kb) of all the possible DNA fragments obtained?

(A) 2, 3, 4, 5, 6, 7, 8 and 10

(B) 2, 3, 4, 5, 6, and 7

(D) 2 and 3

Ans: (D)

30. A zero-order liquid phase reaction is being carried out in a batch reactor with k = 10³ mol/min. If the starting concentration of A is 0.1 moles/liter, the time (in minutes) taken by the system before A is exhausted in a 100 liter reactor is ____ .

Ans: (100)

31. The interaction energy E between two spherical particles is plotted as a function of the distance (r) between them. When r < a, where a is a constant, the net force between the spherical particles is repulsive. When r ≥ a, they attract via van der Waals attraction. Which one of the following plots correctly represents the interaction energy between the above two particles?

(A)

(B)

(C)

(D)

Ans: (D)

32. The value of c for which the following system of linear equations has an infinite number of solution is ____ .

Ans: (4)

33. Which one of the following amino acids has three ionizable groups?

(A) Glycine

(B) Leucine

(D) Lysine

Ans: (D)

34. The distribution of marks scored by a large class in an exam can be represented as a normal distribution with mean μ and standard deviation σ. In a follow-up exam in the same class, everyone scored 5 marks more than their respective score in the earlier exam. For this followup exam, the distribution of marks can be represented as a normal distribution with mean μ₂ and standard deviation σ₂ , Which one of the following is correct?

(A) μ = μ₂; σ > σ₂

(B) μ < μ₂; > σ > σ₂

(D) μ < μ₂; σ = σ₂

Ans: (D)

35. Which one of the following CANNOT be a recognition sequence for a Type II restriction enzyme?

(A) GAATTC

(B) AGCT

(D) ATGCCT

Ans: (D)

36. Match the plant hormones in Column I with functions in Column II

(A) P − 4, Q−3, R − 2, S−1

(B) P − 4, Q−2, R −3, S−1

(D) P − 2, Q−1, R − 4 S−3

Ans: (A)

37. One hundred E.Coli cells are each infected by single λ phage particle. The ratio of the number of phage particles committing to lysogeny to those committing to lysis is 4:1. Assuming that the average burst size is 80, the number of free phage particles released after one round of infection is ____ .

Ans: (1600)

38. Which one of the following organisms is responsible for crown gall disease in plants?

(A) Xamthomonas campestris

(B) Rhizobium etli

(D) Erwinia stewartii

Ans: (C)

39. The specific activity of an enzyme in a crude extract of E.coli is 9.5 units/mg of protein. The specific activity increased to 68 units/mg of protein upon ion-exchange chromatography. The fold purification is ___.

Ans: (7.20)

40. Shown below is a plasmid vector (P) and an insert (Q). The insert was cloned into the BamHI site of the vector. The recombinant plasmid was isolated and digested with BamHI or XhoL. The results from the digestion experiments are shown in (R).

Which one of the following explains the digestion results shown in (R)?

(A) The insert did not ligate to the vector.

(B) One copy of the insert ligated to the vector.

(D) The insert ligated to the vector as two copies but not in tandem.

Ans: (C)

41. For an E.coli culture in the exponential phase of growth, optical density (OD) at 540 nm is 0.3 at hours and 0.6 at 4 hours. Assuming that the measured OD is linearly proportional to the number of E.coli cells, the growth rate (per hour) for this culture is ____.

Ans: (0.14)

42. Consider an infinite number of cylinders. The first cylinder has a radius of 1 meter and height of 1 meter. The second one has a radius of 0.5 meter and height of 0.5 meter. Every subsequent cylinder has half the radius and half the height of the preceding cylinder. The sum of the volumes (in cubic meters) of these infinite number of cylinders is ____.

Given data : π = 3.14

Ans: (3.62)

43. The concentration (in micromolar) of NADH in a solution with is ____.

Given data: Path length = 1 cm; Molar extinction coefficient of NADH ε₃₄₀ = 6220M⁻¹ cm⁻¹

Ans: (79)

44. During anaerobic growth, an organism converts glucose (P) into biomass (Q), ethanol (R) acetaldehyde (S), and glycerol (T). Every mole of carbon present in glucose gets distributed among the products as follows:

1(C – moleP) → 0.14 (C – moleQ) + 0.25(C – moleR) + 0.3(C – moles) + 0.31(C – moleT)

From 1800 grams of glucose fed to the organism, the ethanol produced (in grams) is ____.

Given data: Atomic weights (Da) of C =12, H = 1, o −16, and N =14

Ans: (345)

45. Which of the following conditions promote the development of human autoimmune disorders?

P. Inability to eliminate self-reactive lymphocytes

Q. Generation of auto-antibodies

R. Ability to eliminate self-reactive T-cells

S. Induction of regulatory T-cells in the thymus

(A) P, R

(B) Q, S

(D) R, S

Ans: (C)

46. The genome is diploid at the end of which phases of a human mitotic cell cycle?

(A) G2 & S

(B) G1 & M

(D) G1 & G2

Ans: (B)

47. Match the proteins in Group I with cellular processes in Group II.

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

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

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

Ans: (D)

48. Which one of the following graphs represents the kinetics of protein precipitation by addition of ammonium sulphate? On the Y-axis, [Protein] represents the concentration of free protein in solution.

(A)

(B)

(C)

(D)

Ans: (A)

49. Match the organisms in Column I with the characteristics in Column II

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

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

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

Ans: (D)

50. An immunocompetent person becomes infected with a pathogenic strain of bacteria. Which of the following graphs correctly depicts bacterial load in this person over time

(A)

(B)

(C)

(D)

Ans: (B)

51. For the probability density P(x) = 0.5 e^−0.5x, the integral

Ans: (1)

52. The circular dichroism spectra of three proteins P, Q and R are given below:

(A) P: α -helix, Q: β -sheet, and R: Random coil

(B) P: β -sheet, Q: α-helix , and R: Random coil

(D) P: Random coil, Q: α -helix, and R: β -sheet

Ans: (A)

53. The angle (in degrees) between the vectors

Ans: (90)

54. Growth of a microbe in a test tube is modeled as where, X is the biomass, r is the growth rate, and K is the carrying of the environment (r ≠ 0; k ≠ 0). If the value of starting biomass is which one of the following graphs qualitatively represents the growth dynamics?

(A)

(B)

(C)

(D)

Ans: (A)

55. If the chemical composition of proteins in an organism is CH₅O_0.3N_0.3S_0.004, ,the mass percentage of carbon in the proteins is ____.

Given data : Atomic weights (Da) of C = 12, H = 1, O = 16, N = 14 and S = 32.

Ans: (53)

56. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?

i. At least one bench is a table

ii. At least one shelf is a bench

iii. At least one chair is a table

iv. All benches are chairs.

(A) Only i

(B) Only ii

(D) Only iv

Ans: (B)

57. I _________________ made arrangements had I ______________ informed earlier.

(A) could have, been

(B) would have, being

(D) had been, been

Ans: (A)

58. She has a sharp tongue and it can occasionally turn_______

(A) hurtful

(B) left

(D) vital

Ans: (A)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

(A) 120

(B) 144

(D) 212

Ans: (B)

60. In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%.while other consumption increases by 70%

Which of the following statements is correct?

(A) The ratio of household to other consumption is 8/17

(B) The ratio of household to other consumption is 1/17

(D) There are errors in the official’s statement.

Ans: (D)

Here, the word ‘antagonistic’ is closest in meaning to

(A) impartial

(B) argumentative

(D) hostile

Ans: (D)

62. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

(A) 56

(B) 52

(D) 44

Ans: (A)

(A) 1440

(B) 1200

(D) 600

Ans: (A)

64. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

(A) Up-Down-Up-Down

(B) Down-Up-Down-Up

(D) Up-Down-Up

Ans: (C)

65. T.U.V.W.W.X.Y. and Z are seated around a circular table. T’s neighbours are Y and V. Z is seated third to the left of T and second to the right of S. U;s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

(A) X

(B) W

(D) T

Ans: (A)

Gate 2017 Architecture and Planning Question Paper 4th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Architecture and Planning 4th Feb 2017

Subject Name: Architecture and Planning

Duration : 180

Total Marks: 100

1. The Pritzker Architecture prize for the year 2016 has been awarded to

(A) Alejandro Aravena

(B) Frei Otto

(D) Yung Ho Chang

Ans: (A)

2. As per the CPWD Handbook on Barrier Free and Accessibility, 2014, Government of India,, the minimum length of a straight ramp in metre to raise a wheelchair to the plinth level to 600 mm, is _____

Ans: (7.2)

3. Tuscan and Composite orders are associated with

(A) Greek Architecture

(B) Islamic Architecture

(D) Roman Architecture

Ans: (D)

4. A pointed arch having two centres and radii greater than the span is known as

(A) Lancet arch

(B) Gothic arch

(D) Drop arch

Ans: (A)

5. The concepts of ‘serial vision’, ‘punctuation’ and ‘closure’ were proposed by

(A) Le Crobusier

(B) Louis Kahn

(D) Kevin Lynch

Ans: (C)

6. In one litre of paint, volume of solid pigment and volume of non-volatile binder are 400 cc and 600 cc respectively. The Pigment Volume Concentration number of the paint is ______

Ans: (0.4)

7. ‘Cold joint’ refers to the

(A) expansion joint in large span concrete members

(B) interface between an already setting concrete and a fresh batch of concrete

(D) joining of two similar metals in vacuum

Ans: (B)

8. Slenderness ratio of a column is represented as :

(A) Effective length/Cross-sectional area

(B) Effective length/Radius of gyration

(D) Actual length/Radius of gyration

Ans: (B)

9. Liquidated damage refers to the

(A) cost borne by the contractor to rectify defects within defect-liability period

(B) compensation paid on breach of contract to the affected p arty by the other party

(D) money earned by the owner from selling damaged property through auction

Ans: (B)

10. Which of the following processes is NOT used for corrosion resistance of cast iron?

(A) Painting

(B) Epoxy coating

(D) Galvanizing

Ans: (C)

11. Data on ‘households with one or more married couples sharing room with a person aged 12 years or more’, is used for computing

(A) housing density

(B) housing shortage

(D) housing affordability

Ans: (B)

12. Excellence in Design for Greater Efficiency (EDGE) programme DOES NOT focus on

(A) lower carbon emission

(B) greater resource efficiency

(D) labour safety

Ans: (D)

13. Select the right option representing strategic components arranged in ascending order of specified minimum area under Smart City Mission of Government of India.

(A) Greenfield development – Redevelopment – Retrofitting

(B) Redevelopment – Greenfield development – Retrofitting

(D) Redevelopment – Retrofitting – Greenfield development

Ans: (B)

14. The grade-separated interchange suitable for 3-legged road intersection is

(A) Trumpet

(B) Full Clover leaf

(D) Partial Clover leaf

Ans: (A)

15. The design element provided to ensure safety of a vehicle travelling at prescribed design speed along the curved segment of a highway is

(A) shoulder

(B) super-elevation

(D) footpath

Ans: (B)

16. Which of the following process is NOT adopted in solid waste management?

(A) Incineration

(B) Pyrolysis

(D) Sanitary landfill

Ans: (C)

17. The principle of Eminent Domain is the power to

(A) restrict exercise of rights in land through zoning and environmental laws

(B) control land use

(D) acquire and take possession of property in order to promote public interest

Ans: (D)

18. In which of the following models does the private partner own the revenue as well as the risk associated with the project for a limited period of time?

(A) Build, Own, Operate (BOO)

(B) Build, Own, Operate, Transfer (BOOT)

(D) Design, Bid, Build (DBB)

Ans: (B)

19. In a multi-storied building, the type of plumbing system suitable for reusing the sullage for non-potable use is

(A) single stack system

(B) partially ventilated single stack system

(D) two pipe system

Ans: (D)

20. The unit for measuring sound absorption in a room is

(A) Sabin

(B) Phon

(D) Hertz

Ans: (A)

21. In Geographic Information System, DEM represents information on

(A) vegetation cover

(B) soil type

(D) topography

Ans: (D)

22. Minimum points required for GRIHA certification is

(A) 35

(B) 40

(D) 60

Ans: (C)

23. ArchiCAD, Auto Desk Revit, Digital Project Designer (CATIA) and Vector Works Architect are examples of

(A) Statistical Analysis software

(B) GIS software

(D) Image processing software

Ans: (C)

24. The CARTOSAT 2C satellite recently launched by ISRO

(A) is a geo-synchronous satellite

(B) is a part of IRNSS GPS satellite system

(D) has high spatial resolution

Ans: (D)

25. Which of the following trees has a columnar form?

(A) Delonix regia

(B) Tamarindus indica

(D) Callistemon lanceolatus

Ans: (C)

26. Match the architectural movements in Group-I with their proponents in Group-II.

Group-I Group-II

P. Deconstruction 1. Joseph Paxton

Q. Historicism 2. Kenzo Tange

R. Metabolism 3. Walter Gropius

S. Art Nouveau 4. Victor Horta

5. Frank O. Gehry

(A) P-5, Q-1, R-2, S-4

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

(D) P-2, Q-4, R-1, S-5

Ans: (A)

27. Associate the historic buildings in Group-I with their predominant materials in Group-II.

Group-I

P. Lingaraj Temple, Bhubaneshwar, India

Q. Victoria Memorial, Kolkata, India

R. Padmanabhapuram Palace, Thuckalay, India

S. Humayun’s Tomb, Delhi, India

Group-II

1. Red sandstone

2. Timber

3. Terracotta tiles

4. Sandstone and laterite

5. Marble

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

(B) P-1, Q-4, R-3, S-5

(D) P-4, Q-5, R-2, S-1

Ans: (D)

28. Match the terminologies in Group-I with their description in Group-II.

Group-I

P. Pruning

Q. Felling

R. Hoeing

S. Mulchin

Group-II

1. Cutting of trees

2. Removing broken branches from trees for better growth

3. Maintaining moisture content in soil by a protective layer

4. Indiscriminate cutting of branches to reduce the size of a tree

5. Loosening the ground to remove weeds

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

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

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

Ans: (A)

29. A proposed housing will have HIG, MIG and LIG units on a site measuring 60,750 sq.m. The buildable area of each category of units with respect to the total buildable area will be 30%, 50% and 20% respectively. The maximum allowable FAR is 2.5, ground coverage 45% and height 15 m. The maximum buildable area in sq.m of HIG units, considering a floor height of 3 m for all categories will be _____

Ans: (41000 to 41010)

30. In 2011, the population of a town was 5,00,000 and the number of housing units were 1,00,000. Calculate the additional number of dwelling units (DU) required by 2031 so that there is no housing shortage. The assumptions are

i. 5% decadal increase in population

ii. New DU to be complete by 2021 is 10,000

iii. Number of DU which become non habitable by 2031 is 5,000

iv. Average household size is 4.5

Ans: (17495 to 17505)

31. Match the classical urban planning theories in Group-I with their proponents in Group-II.

Group-I Group-II

P. Concentric Zone Model 1. Berry and Horton

Q. Sector Model 2. Horner Hoyt

R. Multiple Nuclei Model 3. Ernest Burgess

S. Factorial Ecology 4. Shevky and Bell

5. Harris and Ullman

32. Match the distinguished housing projects in Group with their architects in Group-II.

Group-I

P. Nagakin Capsule Tower, Tokyo, Japan

Q. Tara Apartment, New Delhi, India

R. Habitat 67, Montreal, Canada

S. Byker Wall, New Castle, England

Group-II

1. Walter Gropius

2. Moshe Safdie

3. Ralph Erskine

4. Charles Correa

5. Kisho Kurokawa

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

(B) P-1, Q-3, R-4, S-5

(D) P-5, Q-4, R-2, S-1

Ans: (A)

33. Match the development scheme by Government of India in Group-I with their objectives in Group-II.

Group-I Group-II

P. PMAY 1. Housing for All

Q. AMRUT 2. Rural cluster development

R. NRuM 3. Heritage city development

S. HRIDAY 4. Urban mobility improvement

5. Urban rejuvenation

(A) P-1, Q-5, R-4, S-3

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

(D) P-4, Q-2, R-1, S-5

Ans: (B)

34. Match the international events in Group-I with their directives in Group-II.

Group-I

P. Earth Summit, Rio de Janeiro, 1992

Q. UN Framework Convention on Climate Change, New York, 1992

R. UN Sustainable Development Summit, New York, 2015

S. Habitat II, Istanbul, 1996

Group-II

1. Kyoto Protocol

2. Agenda 21

3. Heritage conservation

4. Agenda 2030

5. Housing for All

(A) P-1, Q-5, R-4, S-3

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

(D) P-2, Q-1, R-5, S-4

Ans: (C)

35. Match the planning techniques in Group-I with their salient features in Group-II.

Group-I

P. Land pooling

Q. Action Plan

R. Land sharing

S. Transfer of Development Rights

Group-II

1. Assigning specific task on a short time horizon

2. Assembling privately owned land parcels for development

3. Agreement for reallocation of land between occupiers and owners

4. Assigning specific task on a long time horizon

5. Incentive based voluntary shifting of FAR of a plot to another plot

(A) P-1, Q-5, R-4, S-3

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

(D) P-4, Q-2, R-1, S-5

Ans: (B)

36.

For a symmetrical two dimensional truss as shown in the above figure, vertical force in kN acting on the member PQ is _______

Ans: (0)

37.

Value of bending moment in kN-m at point C for a beam as shown in the above figure is ______

Ans: (28)

38. Fee of contractor for a project has the following provisions

• Basic fee = 15% of actual cost of work incurred

• Bonus = 20% of savings from estimated cost of work

• Penalty = 20% of cost overrun

If the estimated cost of project is Rs. 60,000, and the actual cost is Rs. 70,000, then the total fee of contractor in Rupees is _____

Ans: (8500)

39. A site has a unidirectional slope of 30° with horizontal along its longer side. The projected dimensions of the site on the horizontal plane measures 30 m × 40 m. Using cut and fill method the site has to be leveled parallel to the horizontal plane. The minimum amount of earth to be excavated in cubic metre is _______

Ans: (3463 to 3465)

40. The optimistic, most-likely and pessimistic time for developing a new product are 12 months, 15 months and 17 months, respectively. Calculate the expected time in months.

Ans: (14.00 to 15.00)

41. A circular plate inclined at an angle θ with horizontal plane generates an ellipse as top view with major axis and minor axis of 5 cm and 2.5 cm respectively. The value of θ in degrees is ______

Ans: (60)

42. Calculate the volume of cement in cubic metre required for making 10 cubic metre of M20 grade Plain Cement Concrete work, assuming the ratio of dry concrete mix to wet concrete mix as 1.52.

Ans: (2.7 to 2.9)

43. One acre of agricultural land has been given on a lease till perpetuity at an annual rent of Rs. 10,000 to be paid at the end of each year. Net Present Value of the land parcel in Rupees assuming a discount rate of 5% per annum is ________

Ans: (200000)

44. In year 2001, a district with 4,000 manufacturing jobs had a 10% share of total manufacturing jobs within the state. In year 2011, the state recorded 15% drop in manufacturing jobs whereas, share of the district in total manufacturing jobs within the state increased to 15%. Additional manufacturing jobs created in the district between year 2001 and 2011 is ______

Ans: (1100)

45. Match the parameters in Group I with their units in Group II

Group I Group II

(P) Traffic flow 1. Metre

(Q) Traffic density 2. Cycles/second

(R) Right of Way 3. Seconds

(S) Traffic signal cycle length 4. Vehicle/km

5. PCU/hr

(A) P-5, Q-4, R-1, S-2

(B) P-5, Q-4, R-1, S-3

(D) P-4, Q-5, R-1, S-3

Ans: (B)

46. Match the planning tasks in Group I with the tools of analysis in Group II

Group I

(P) Population projections

(Q) Regional resource allocation

(R) Trip distribution

(S) Design of water distribution network

Group-II

1. Input-Output Analysis

2. Hardy Cross Method

3. Cohort Analysis

4. Gravity Model

5. Moving observer method

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

(B) P-3, Q-5, R-4, S-1

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

Ans: (A)

47. Match the land use classes in Group I with the use zones in Group II

Group-I

(P) Transportation

(Q) Commercial

(R) Public and Semi-public

(S) Recreational

Group II

1. Sports complex

2. Heritage and conservation areas

3. Burial ground

4. BRT corridor

5. Service sector

(A) P-4, Q-1, R-3, S-5

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

(D) P-4, Q-5, R-3, S-1

Ans: (D)

48. Associate the structural systems in Group I with the building in Group II.

Group-I

(P) Folded plates

(Q) Shell

(R) Tensegrity

(S) Pneumatic

Group-II

1. Kurilpa Bridge, Brisbane

2. Eden Project, Cornwall

3. Riverside Museum, Glasgow

4. MIT Auditorium, Boston

5. 30, St. Mary Axe, London

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

(B) P-5, Q-4, R-3, S-1

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

Ans: (A)

49. As per National Building Code of India, 2005, the maximum number of occupants per unit exit width of a doorway is 60, where unit exit width is 500 mm. The maximum permissible occupants in a theatre having four number of 2.2 m wide doors will be _____

Ans: (960)

50. Match the instruments in Group I with the corresponding tests in Group II.

Group I

(P) Pycnometer

(Q) Brinell’s Apparatus

(R) Los Angeles Apparatus

(S) Vicat’s Apparatus

Group II

1. Initial and final setting time

2. Abrasion test

3. Surface hardness test

4. Slump test

5. Apparent Specific gravity

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

(B) P-5, Q-4, R-2, S-1

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

Ans: (A)

51. Water flows through a constricted circular pipe whose diameter at the constricted end is half of the non-constricted end. Velocity of water at the non-constricted end is 2 m/s. Velocity of water in m/s at the constricted end using the principle continuity of flow is ______

Ans: (8)

52. A drainage basin of 180 hectares comprises 40% wooded area, 45% grassed area and 15% paved area. Runoff coefficients for wooded, grassed and paved areas are 0.01, 0.02 and 0.95 respectively. The composite runoff coefficient for the drainage basin is ______

Ans: (0.2 to 0.25)

53. A fluorescent light source consumes 40 W electric power and has a luminous efficacy of 40 lm/W. Illumination in lux at a distance of 3 m from this light source is _______

Ans: (175 to 180)

54. A room measures 3 m (width) × 4 m(length) × 3 m(height). The outdoor temperature is 36℃. The volumetric specific heat of air is 1300 J/cu.m.℃. The ventilation heat flow rate in Watts required to attain an internal room temperature of 26℃ with 3 air changes per hour is _______

Ans: (390)

55. Match the equipment in Group-I with their applications in Group-II.

Group-I Group-II

P. PIR 1. Air conditioning

Q. FCU 2. Lighting

R. OLED 3. Power generation

S. BIPV 4. Motion detection

5. Daylight sensing

(A) P-4, Q-5, R-2, S-1

(B) P-1, Q-4, R-5, S-3

(D) P-4, Q-2, R-5, S-1

Ans: (C)

56. He was one of my best __________ and I felt his loss _________.

(A) friend, keenly

(B) friends, keen

(D) friends, keenly

Ans: (D)

57. As the two speakers became increasingly agitated, the debate became __________.

(A) lukewarm

(B) poetic

(D) heated

Ans: (D)

58. A right – angled cone (with base radius 5cm and height 12cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.

By what angle (in radians) about P does the cone travel?

(A)

(B)

(C)

(D)

Ans: (D)

59. In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

(A) Rs. 20,000

(B) Rs. 30,000

(D) Rs. 40,000

Ans: (B)

60. P,Q, and R talk about S’s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one Car. Only one of P, Q and R is right the number cars owned by S is.

(A) 0

(B) 1

(D) Cannot be determined

Ans: (A)

61. “Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that ‘A stronger instance than this of European prejudice with relation to this country has never come under my observations’ had no effect on his superiors.”

According to this paragraph, which of the statements below is most accurate?

(A) Stuart’s commander – in chief was moved by this demonstration of his prejudice.

(B) The Europeans were accommodating of the sepoys’ desire to weak their caste – marks.

(D) The commander– in – Chief was exempt from the European preiudice that dictated how the sepoys were to dress.

Ans: (C)

62. What is the sum of the missing digits in the subtraction problem below?

(A) 8

(B) 10

(D) Cannot be determined

Ans: (D)

63. Let S₁ be the plane figure consisting of the points (x,y) given by the inequalities |x – 1| ≤ 2 and |y + 2| ≤ Let S₂ be the plane figure given by the inequalities x – y ≥ −2, y ≥ 1, and x ≤ 3 Let S be the union of S₁ and S₂. The area of S is

(A) 26

(B) 28

(D) 34

Ans: (C)

64. Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, “There is no way you are good enough to play for your country.’’ James replied, “Maybe not, but at least I am the best player in my own family.”

Which one of the following can be inferred from this conversation?

(A) Mark was known to play better than James

(B) Steve was known to play better than Mark

(D) James played better than Steve

Ans: (B)

65. The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8(in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 litre of milk is plotted as a function of time, at two different temperatures, 25°C and 37°C.

Consider the following statements based on the data shown above:

(i) The growth in bacterial population stops earlier at 37°C as compared to 25°C

(ii) The time taken for curd formation at 25°C is twice the time taken at 37°C

Which one of the following options is correct?

(A) Only i

(B) only ii

(D) Neither i nor ii

Ans: (A)

Gate 2017 Agriculture Engineering Question Paper 4th Feb 2017 PDF Download

July 21, 2017 by M Prakash

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Agricultural Engineering 4th Feb 2017

Subject Name: Agricultural Engineering

Duration : 180

Total Marks: 100

1. Matrix is a

(A) Diagonal matrix

(B) Orthogonal matrix

(D) Skew-symmetric matrix

Ans: (D)

2. Direction cosines of the vector 3i – 2j + 6k are

(A) [3/7, −2/7, 6/7]

(B) [−3/7, 2/7, −6/7]

(D) [7/3, −7/2, 7/6]

Ans: (A)

3. Characteristic equation of the matrix with Eigen value λ is

(A) λ² + 3λ + 4 = 0

(B) λ² + 3λ – 2 = 0

(D) λ² + 3λ = 0

Ans: (C)

4. A box contains three white and four red balls. Two balls are drawn randomly in sequence. If the first draw resulted in a red ball, the probability of getting a second red ball in the next draw is

(A) 0.33

(B) 0.50

(D) 0.75

Ans: (B)

5. The probability of getting two heads and two tails from four tosses of the same coin is _____.

Ans: (0.37 to 0.38)

6. The purchase price of a tractor is R.s 5.0 lakh. Considering the constant rate of depreciation as 0.2 in declining balance method, the value of the tractor at the end of 4^th year in lakh will be ______.

Ans: (2.03 to 2.06)

7. The pump used in high pressure orchard sprayer is

(A) Centrifugal pump

(B) Rotary pump

(D) Turbine pump

Ans: (C)

8. The Reel Speed Index of a grain combine is more than 1.5, it will increase

(A) Cutter bar loss

(B) Shatter loss

(D) Straw walker loss

Ans: (B)

9. A diesel fuel has same ignition delay as that of blend of two reference fuels namely 56% n-cetane and 44% hepta-methylanonane. The cetane number of the diesel fuel is ______.

Ans: (62.6 to 62.6)

10. Air temperature at the beginning of adiabatic compression in an IC engine is 27℃ and the engine compression ratio is 16 : 1. The temperature of air at the end of the compression in ℃ will be ______.

Ans: (635 to 637)

11. In fuel property determination, Reid vapour pressure test is used for measuring

(A) Volatility

(B) Viscosity

(D) Carbon residue

Ans: (A)

12. A tractor pulls 8 kN drawbar load against 4 kN rolling resistance. If the tractor develops 57% tractive efficiency, the slip experienced by the tractor in percentage will be _______.

Ans: (14 to 15)

13. Antecedent Moisture Condition (AMC) for a soil are defined on the basis of total rainfall occurred during previous ______ days.

Ans: (5 to 5)

14. The seepage analysis in earthen dams is carried out by drawing flownet which consists of equipotential and stream lines. For a homogeneous and isotropic earthen dam, these two lines are always

(A) orthogonal to each other

(B) parallel to each other

(D) convergent to each other

Ans: (A)

15. Remedial measure generally adopted for controlling stream-bank erosion is

(A) Shelter belts

(B) Spurs

(D) Drop spillways

Ans: (B)

16. Thickness of capillary zone above the water table varies

(A) linearly with the pore-size of soil

(B) inversely with the height of water table

(D) inversely with the pore-size of soil

Ans: (D)

17. A cavity well is a tubewell which has

(A) gravel pack and a strainer

(B) a PVC strainer

(D) a bamboo strainer

Ans: (C)

18. Modified Hooghoudt’s equation for the computation of drain spacing is applicable to

(A) homogeneous soils

(B) anisotropic soils

(D) layered soils

Ans: (D)

19. The sum of ‘specific yield’ and ‘specific retention’ for an unconsolidated geologic formation is equal to its

(A) effective porosity

(B) total porosity

(D) macro-porosity

Ans: (B)

20. Sphericity of a cube with each side as L is _______.

Ans: (0.707 to 0.807)

21. A cylindrical shallow bin is filled with grains having angle of repose of 33°. The limiting height of diameter ratio of the bin is ________.

Ans: (0.64 to 0.65)

22. Length of the husking zone in a rubber roll paddy dehusker, having d as roller diameter, c as clearance between the rolls, and b as grain thickness, is

(A)

(B)

(C)

(D)

Ans: (B)

23. For a psychrometric ratio of 1003 J kg⁻¹ K⁻¹, the latent heat of vaporization at the wet bulb temperature of 35℃ is 2418.9 kJ kg⁻¹. The saturation vapour pressure is 19.7 kPa corresponding to the dry bulb temperature of 60℃. If the relative humidity of air is 20%, the saturation vapor pressure of the air at the wet bulb temperature in kPa will be ________.

Ans: (5.4 to 5.6)

24. A sphere (3.5 cm diameter) made of copper (ρ = 8954 kg m⁻³; C_p = 0.4 kJ kg⁻¹ K⁻¹; k = 375 W m⁻¹ K⁻¹) is initially at uniform temperature of 200℃. It is suddenly placed in an environment of 35℃ having convective film coefficient of 12 W m⁻² K⁻¹. After 18 minutes of exposure, the temperature of the sphere in ℃ will be______.

Ans: (123 to 124)

25. The reaction rate for destruction of Clostridium botulimum increases 11 times for temperature rise of 10℃ from 121.1℃. The decimal reductioni time of this organism is 5.7 s at 121.1℃. The minimum sterilization time in seconds at 135℃, for eight log cycle reduction of the organism, is

(A) 0.20

(B) 0.31

(D) 2.49

Ans: (C)

26. The areas of seven horizontal cross-sections of a water reservoir at intervals of 9 m are 210, 250, 320, 350, 290, 230 and 170 m². The estimated volume of the reservoir in m³ using Simpson’s rule is ______.

Ans: (14760 to 14760)

27. Divergence value of a function (x²y)i – (z³ – 3x)j + (4y²) k at x = 1, y = 2 and z = 3 is _______.

Ans: (4 to 4)

28. Differentiation of gives

(A)

(B)

(C)

(D)

Ans: (D)

29.

(A)

(B)

(C)

(D)

Ans: (D)

30. A subsoiler operating at 400 mm depth requires 15 kW peak drawbar power at 3 km h⁻¹ The standard is rigidly fixed vertically on the main frame. The resultant soil resistance acts horizontally at a vertical distance of 450 mm from the main frame. The standard has rectangular cross-section with width of thickness ratio of 4:1, and it fails due to bending. If the allowable bending stress is 90 N mm⁻², the width of the standard in mm will be ______.

Ans: (128 to 130)

31. A 9-row fluted roller type speed drill with 400 mm ground wheel diameter is used for sowing wheat at 200 mm row spacing. Each fluted roller discharges 6500 mm³ volume of seeds per revolution. The ratio of ground wheel rpm to fluted roller shaft rpm is 2:1. If the bulk density of wheat is 850 kg m⁻³, the seed rate in kg ha⁻¹ will be ______.

Ans: (108.5 to 110.5)

32. The diameter of feed rollers of a conveyor type power chaff cutter is 100 mm and they are rotating at 90 rpm for cutting the dry fodder. The effective length of each feed roller is 250 mm and the average clearance between them is 15 mm. The compressed density of the material while passing through the feed roller s is 250 kg m⁻³. The throughout capacity of the chaff cutter in ton h⁻¹ is ______.

Ans: (1.55 to 1.65)

33. The horizontal component of resultant soil thrust (T) acting on each gang of a single acting disc harrow is 1650 N. The resultant downward load (W) acting on each gang is 2500 N. The perpendicular distance of T from the gang axis is 200 mm. In order to get a uniform depth of cut, the distance between the line of action of W and the centre of gang in mm will be _______.

Ans: (131 to 133)

34. A cylindrical parabolic solar collector is designed to heat a fluid that enters the absorber at 140℃ at a flow rate of 5 kg min⁻¹. The specific heat capacity of the fluid is 1.5 kJ kg⁻¹℃⁻¹ and its outlet temperature is 180℃. If the incident beam radiation on the plane of aperture is 3000 kJ h⁻¹ m⁻² and useful projected area of the reflector is 2 m × 10 m, the efficiency of the collector in percentage will be ______.

Ans: (30 to 30)

35. A load of 3 kN is acting on a tyre having 150 mm nominal width. The effective friction coefficient of tyre and ground interaction is 0.6 and the kingpin offset is 10 mm. Assuming the tyre impression on ground as circle of diameter same as the tyre nominal width, the kingpin torque of the tyre in N m will be ______.

Ans: (96 to 98)

36. In a tractor power transmission, the input pinion (24 teeth) is in mesh with a gear (46 teeth) on counter shaft and another gear (20 teeth) of counter shaft is in mesh with main shaft gear (50 teeth). The engine is running at 1800 rpm, differential gear ratio is 3.5:1 and final drive ratio is 4 : 1. If the tractor is fitted with 1.2 m diameter rear wheels, the forward speed of the tractor in kmh⁻¹ is _______.

Ans: (5.5 to 6.5)

37. A hydraulic system comprising of a pump and a single acting cylinder lifts 11 kN road. The pump flow rate is 25 L min⁻¹ and its overall efficiency is 80%. The cylinder diameter is 80 mm and its efficiency is 90%. If the pressure drop in the hydraulic circuit is 500 kPa, the power required to drive the pump in kW will be ________.

Ans: (1.4 to 1.7)

38. A tractor of 19.5 kN weight and 1.8 m wheel base has 70% static weight on the rear axle. It pulls 8 kN drawbar load parallel to the ground through a hitch point located 450 mm above the ground. The dynamic weight on the rear axle of the tractor under operating condition in kN will be ________.

Ans: (15 to 17)

39. A six-stage centrifugal pump delivers 120 L s⁻¹ against a total head of 510 m. If the design speed of this pump is 1450 rpm, the specific speed of the pump will be _______.

Ans: (565 to 570)

40. A watershed of 100 km² is underlain by an unconfined aquifer having hydraulic conductivity of 15 m day⁻¹ and specific yield of 0.20. If 30 million m³ of water is pumped from this aquifer through uniformly distributed wells, the average drop of water table over the watershed in meter will be

(A) 1.50

(B) 0.75

(D) 6.00

Ans: (A)

41. Match the following items between Column-I and Column-II with the most appropriate combinations.

Column-I Column-II

(1) Neutron Probe (P) Open channel flow

(2) Pressure Plate Apparatus (Q) Deep percolation

(3) Tipping Bucket (R) Aquifer parameters

(4) Current Meter (S) Soil moisture

(5) Pumping Test (T) Rainfall intensity

(6) Lysimeter (U) Soil-moisture characteristic curve

(A) 1-Q, 2-P, 3-T, 4-S, 5-R, 6-U

(B) 1-S, 2-U, 3-T, 4-P, 5-R, 6-Q

(D) 1-P, 2-U, 3-S,, 4-T, 5-R, 6-Q

Ans: (B)

42. Graded furrows of 80 m length and 0.75 spacing are used for irrigating a field with an initial furrow stream of 100 L min⁻¹. The initial furrow stream flow reaches the lower end of the field in 40 min. Thereafter, the furrow stream flow is reduced to 30 L min⁻¹ and the cutback stream flow is continued for 1 hour. The average depth of irrigation over the field in cm will be _______.

Ans: (9.65 to 9.75)

43. The soil of a cropped field has field capacity of 25% and wilting point of 13% on weight basis. The effective root-zone depth of the crop is 0.70 m and the consumptive use of water by the crop is 5 mm day⁻¹. Apparent specific gravity of the soil is 1.50. If the allowable soil moisture depletion is 40%, the permissible moisture depletion between irrigations and the frequency of irrigation are

(A) 5 cm; 10 days

(B) 10 cm; 7 days

(D) 4 cm; 8 days

Ans: (A)

44. A watershed of 4.8 km² generates 4.3 cm runoff from a rain storm of 4-hour duration. The measured rainfall intensities for this storm in successive 30-minute durations are given below:

The value of Φ-index for the watershed in cm h⁻¹ will be

(A) 6.5

(B) 5.3

(D) 2.1

Ans: (C)

45. Bunds are to be constructed to conserve rainwater in a farm having 6% slope. If the horizontal interval between two bunds is 30 m and there is no loss of water, the required height of the bund to store rainwater from an 18 cm rainfall event with 10 years of return period in cm will be _______.

Ans: (80 to 81)

46. A rectangular channel having bed slope of 0.05% and Manning’s roughness coefficient of 0.01 carries a discharge of 5 m³ s⁻¹. If the channel is designed as the most economical section, the width of the channel in meter will be _______.

Ans: (2.45 to 2.50)

47. A trapezoidal notch, placed over an emergency spillway, has the following details:

Top width = 2 m

Bottom width = 1 m

Height = 0.5 m

Coefficient of discharge for the triangular portion = 0.65

Coefficient of discharge for the rectangular portion = 0.68

For a flow head of 0.4 m over the notch, the discharge in Ls⁻¹ will be about

(A) 155

(B) 353

(D) 663

Ans: (D)

48. In a vertical tube single effect evaporator, the boiling film coefficient inside the tubes is 1350 W m⁻² K⁻¹. Steam condensation film coefficient outside is 7500 W m⁻² K⁻¹. Thermal conductivity of 20 tubes make of SS 304 is 16 W m⁻¹ K⁻¹. The vertical tubes are 4.3 m long and are of 25 mm ID and 27 mm OD, maintaining a steady 15℃ temperature difference across the tube walls. Assume no boiling point rise, no heat losses, the feed enters the evaporator at the boiling point and the latent heat of vaporization of water is 2346.3 kJ kg⁻¹. Total water evaporation rate from the evaporator bundle of tubes in kg h⁻¹ will be _______.

Ans: (168 to 169)

49. Hot water at 95℃ is sent through a countercurrent tube-in-tube heat exchange with cold water entering at 25℃. Hot/cold water specific heat capacity is 4.2 kJ kg⁻¹ K⁻¹. Flow rates of hot and cold water are 2.7 and 4.1 kg min⁻¹,, respectively. Overall heat transfer coefficient is 55 W m⁻² K⁻¹ and the area of heat transfer is 5 m². Cold water outlet temperature from the heat exchanger in ℃ will be ________.

Ans: (55 to 56)

50. In a cold storage, 10 metric ton of potato is to be brought down from 30 to 80℃ storage temperature in 6 hours of air blast at the evaporator temperature of −10℃. Specific heat capacity of potato is 3.2 kJ kg⁻¹ K⁻¹. COP of the refrigeration cycle deployed is 4.2 with evaporator load extraction capacity of 210 kJ kg⁻¹. Neglecting the respiration load of potato, the refrigerant flow rate and compressor power requirement will be

(A) 3.9 kg min⁻¹; 7.76 kW

(B) 9.3 kg min⁻¹l; 8.50 kW

(D) 3.9 kg min⁻¹; 8.50 kW

Ans: (C)

51. Steam (h_f = 632.2, h_fg = 2113.2, h_g = 2745.4 kJ kg⁻¹) at 150℃ is used to sterilize milk by direct stream injection. Milk is initially at 90℃ and after sterilization, the blend of resultant milk and condensed steam (h_f = 567.6, h_fg = 2159.1, h_g = 2726.7 kJ kg⁻¹) are at 135℃. Specific heat capacity of milk is 3.8 kJ kg⁻¹ K⁻¹. Assuming no energy loss, the amount of milk (in kg) sterilized per kg steam supplied is

(A) 21.57

(B) 12.74

(D) 4.48

Ans: (B)

52. A batch of 1000 kg of apples containing 6.2% bruised apples is sorted by an electronic colour sorter. The sorted apples contain 927.3 kg red apples and 17.4 kg bruised apples. Remaining red and bruised apples are delivered at the rejection outlet of the sorter. Overall effectiveness of the sorter is _______.

Ans: (0.70 to 0.72)

53. Spherical dust particles of 50 μm are settling under gravity in air at 21℃ and normal atmospheric pressure. Density of particles is 1250 kg m⁻³ and density of air is 1.2 kg m⁻³. Considering viscosity of air as 1.81 × 10⁻⁵ Pa s, the settling velocity of dust in mm s⁻¹ will be _______.

Ans: (94 to 94)

54. India’s annual paddy production is 160 million ton (clean paddy basis). Average husk content of paddy is 22.4% and milled rice yield is 70%. Considering 18% oil content in bran fraction and calorific value of 12 MJ kg⁻¹ of husk, the oil potential of bran and energy potential of husk will respectively be

(A) 2.19 × 10⁶ ton; 430080 × 10¹² J

(B) 2.19 × 10⁶ ton; 210450 × 10¹² J

(D) 4.76 × 10⁶ ton; 430080 × 10¹² J

Ans: (A)

55. A cylindrical silo, 3 m in diameter and 20 m high, is filled with barley having bulk density of 625 kg m⁻³. Coefficient of friction between grain and the bin wall is 0.45 and the ratio of lateral pressure to vertical pressure is 0.4. The lateral pressure at the base of the bin in kPa will be __________.

Ans: (10.1 to 10.2)

56. The ways in which this game can be played ______ potentially infinite.

(A) is

(B) is being

(D) are being

Ans: (C)

57. If you choose plan P, you will have to _____ plan Q, as these two are mutually______.

(A) forgo, exclusive

(B) forget, inclusive

(D) adopt, intrusive

Ans: (A)

58. If a and b are integers and a – b is even, which of the following must always be even?

(A) ab

(B) a² + b² + 1

(D) ab – b

Ans: (D)

59. A couple has 2 children. The probability that both children are boys if the older one is a boy is

(A) 1/4

(B) 1/3

(D) 1

Ans: (C)

60. P looks at Q while Q looks at R. P is married, R is not. The number of pairs of people in which a married person is looking at an unmarried person is

(A) 0

(B) 1

(D) Cannot be determined

Ans: (B)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lives too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following is closest in meaning to ‘cleaving’?

(A) deteriorating

(B) arguing

(D) splitting

Ans: (D)

62. X bullocks and Y tractors take 8 days to plough a field. If we halve the number bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take X bullocks alone to plough the field?

(A) 30

(B) 35

(D) 45

Ans: (A)

63. There are 4 women P, Q, R, S and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how many ways can 4 such pairs be formed?

(A) 74

(B) 76

(D) 80

Ans: (C)

64. All people in a certain island are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identify. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

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

(A) Both P and Q are knights

(B) P is a knight; Q is a knave

(D) The identities of P, Q cannot be determined

Ans: (D)

65. In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10℃) and a month is summer (average temperature 30℃)

Consider the following statements based on the data shown above :

i. Over the given months, the difference between the maximum and the minimum pollutants concentrations is the same in both winter and summer.

Which one of the following options is correct?

(A) Only i

(B) Only ii

(D) Neither i nor ii

Ans: (B)