General Aptitude (GA) Set-2
Q. 1 – Q. 5 carry one mark each.
1. “ The dress _________ her so well that they all immediately _________ her on her appearance.”
The words that best fill the blanks in the above sentence are
(A) complemented, complemented
(B) complimented, complemented
(C) complimented, complimented
(D) complemented, complimented
2. “ The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.”
The word that best fills the blank in the above sentence is
(A) undiminished
(B) damaged
(C) illegal
(D) uncertain
3. Find the missing group of letters in the following series: BC, FGH, LMNO, _____
(A) UVWXY
(B) TUVWX
(C) STUVW
(D) RSTUV
4. The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?
(A) The circle has the largest area.
(B) The square has the largest area.
(C) The equilateral triangle has the largest area.
(D) All the three shapes have the same area.
5. The value of the expression 
is _________.
(A) -1
(B) 0
(C) 1
(D) 3
Q. 6 – Q. 10 carry two marks each.
6. Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?
(A) 0
(B) 2
(C) 4
(D) 8
7. A wire would enclose an area of 1936 m2, if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?
(A) 1096
(B) 1111
(C) 1243
(D) 2486
8. A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?
(A) 50
(B) 89
(C) 146
(D) 175
9. A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.
i. If the house number is a multiple of 3, then it is a number from 50 to 59.
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.
What is the house number?
(A) 54
(B) 65
(C) 66
(D) 76
10. An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:
(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.
Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?
(A) Two T will occur.
(B) One H and one T will occur.
(C) Two H will occur.
(D) One H will be followed by one T.
Mechanical Engineering (Set 2)
Q. 1 – Q. 25 carry one mark each.
1. The Fourier cosine series for an even function f(x) is given by
The value of the coefficient a2 for the function f(x) = cos2(x) in [0, π] is
(A) –0.5
(B) 0.0
(C) 0.5
(D) 1.0
2. The divergence of the vector field 
(A) 0
(B) ex cosy + ex sin y
(C) 2ex cos y
(D) 2ex sin y
3. Consider a function u which depends on position x and time t. The partial differential equation
is known as the
(A) Wave equation
(B) Heat equation
(C) Laplace’s equation
(D) Elasticity equation
4. If y is the solution of the differential equation 
the value of y(–1) is
(A) −2
(B) −1
(C) 0
(D) 1
5. The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is
6. A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is
(A) 5
(B) 20
(C) 500
(D) 2000
7. In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?
(A) Transmissibility will increase.
(B) Transmissibility will decrease.
(C) Time period of free oscillations will increase.
(D) Time period of free oscillations will decrease.
8. Pre-tensioning of a bolted joint is used to
(A) strain harden the bolt head
(B) decrease stiffness of the bolted joint
(C) increase stiffness of the bolted joint
(D) prevent yielding of the thread root
9. The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 μm. If the peak wavelength of emitted radiation changes to 2.90 μm, then the temperature (in K) of the black body is
(A) 500
(B) 1000
(C) 4000
(D) 8000
10. For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (Δs) from state 1 to 2?
11. Select the correct statement for 50% reaction stage in a steam turbine.
(A) The rotor blade is symmetric.
(B) The stator blade is symmetric.
(C) The absolute inlet flow angle is equal to absolute exit flow angle.
(D) The absolute exit flow angle is equal to inlet angle of rotor blade.
12. Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by
13. During solidification of a pure molten metal, the grains in the casting near the mould wall are
(A) coarse and randomly oriented
(B) fine and randomly oriented
(C) fine and ordered
(D) coarse and ordered
14. Match the following products with the suitable manufacturing process
(A) P-4, Q-3, R-1, S-2
(B) P-2, Q-1, R-3, S-4
(C) P-4, Q-1, R-2, S-3
(D) P-1, Q-3, R-4, S-2
15. Feed rate in slab milling operation is equal to
(A) rotation per minute (rpm)
(B) product of rpm and number of teeth in the cutter
(C) product of rpm, feed per tooth and number of teeth in the cutter
(D) product of rpm, feed per tooth and number of teeth in contact
16. Metal removal in electric discharge machining takes place through
(A) ion displacement
(B) melting and vaporization
(C) corrosive reaction
(D) plastic shear
17. The preferred option for holding an odd-shaped workpiece in a centre lathe is
(A) live and dead centres
(B) three jaw chuck
(C) lathe dog
(D) four jaw chuck
18. A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic order quantity of the tyres is
(A) 64
(B) 212
(C) 300
(D) 1200
19. If 
then det(A–1) is ________(correct to two decimal places).
20. A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is ________ (correct to two decimal places).
21. Fatigue life of a material for a fully reversed loading condition is estimated from
σa = 1100 N–0.15
where σa is the stress amplitude in MPa and N is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of 1 × 105 cycles under the same loading condition is ________ (correct to two decimal places).
22. The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is δL. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to δL)is ________ (correct to two decimal places).
23. An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in kJ/cycle) is ______ (correct to two decimal places).
24. The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).
25. A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in m) by the ball is __________ (correct to two decimal places).
Q. 26 – Q. 55 carry two marks each.
26. Let z be a complex variable. For a counter-clockwise integration around a unit circle C , centred at origin,
the value of A is
(A) 2/5
(B) 1/2
(C) 2
(D) 4/5
27. L et X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is
(A) exponentially distributed with mean 1/6
(B) exponentially distributed with mean 2
(C) normally distributed with mean 3/4
(D) normally distributed with mean 1/6
28. For a position vector 
the norm of the vector can be defined as 
Given a function 
29. In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180° m/s2. If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2) of point R is
(A) 8∠233°
(B) 10∠225°
(C) 10∠217°
(D) 8∠217°
30. A rigid rod of length 1 m is resting at an angle θ = 45° as shown in the figure. The end P is dragged with a velocity of 5 U m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is
(A) 5
(B) 6
(C) 8
(D) 10
31. A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment 𝑇 = 150 Nm is applied at a distance of 100 mm from end P. The torsional reactions (𝑇𝑃, 𝑇𝑄 ) in Nm at the ends P and Q respectively are
(A) (50, 100)
(B) (75, 75)
(C) (100, 50)
(D) (120, 30)
32. In a cam-follower, the follower rises by h as the cam rotates by δ (radians) at constant angular velocity ω (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period. Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is
(A) 4hω/δ
(B) hω
(C) 2hω/δ
(D) 2hω
33. A bimetallic cylindrical bar of cross sectional area 1 m2 is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10–6 in Steel bar and compressive axial strain of magnitude 10–6 in Aluminum bar, the magnitude of the required force P (in kN) along the indicated direction is
(A) 70
(B) 140
(C) 210
(D) 280
34. Air flows at the rate of 1.5 m3/s through a horizontal pipe with a gradually reducing crosssection as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2 kg/m3 and assume inviscid
incompressible flow. The change in pressure (p1 – p2) (in kPa) between sections 1 and 2 is
(A) –1.28
(B) 2.56
(C) –2.13
(D) 1.28
35. The problem of maximizing z = x1 – x2 subject to constraints x1 + x2 ≤ 10, x1 ≥ 0, x2 ≥ 0 and x2 ≤ 5 has
(A) no solution
(B) one solution
(C) two solutions
(D) more than two solutions
36. Given the ordinary differential equation
with 
the value of y(1) is _________ (correct to two decimal places).
37. A thin-walled cylindrical can with rigid end caps has a mean radius R= 100 mm and a wall thickness of t = 5. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ___________ (correct to two decimal places).
38. A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between –10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the
material is 600 MPa. The bar cross-section is square with side a. If the factor of safety is 2, the value of a (in mm), according to the modified Goodman’s criterion, is ________ (correct to two decimal places).
39. A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s2) of the centre of the disc is ________ (correct to two decimal places).
40. A frictionless circular piston of area 10–2 m2 and mass 100 kg sinks into a cylindrical container of the same area filled with water of density 1000 kg/m3 as shown in the figure. The container has a hole of area 10–3 m2 at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is _____ (correct to three decimal places).
41. A 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is 350 K. The value of Stefan- Boltzmann constant, σ is 5.67 × 10–8 W/m2 K4. Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in W/m2) is ________ (correct to two decimalplaces).
42. Air is held inside a non-insulated cylinder using a piston (mass M=25 kg and area A=100 cm2) and stoppers (of negligible area), as shown in the figure. The initial pressure Pi and temperature Ti of air inside the cylinder are 200 kPa and 400°C, respectively. The ambient pressure P∞ and temperature T∞ are 100 kPa and 27°C, respectively. The temperature of the air inside the cylinder (°C) at which the piston will begin to move is _________ (correct to two decimal places).
43. A standard vapor compression refrigeration cycle operating with a condensing temperature of 35°C and an evaporating temperature of –10°C develops 15 kW of cooling. The p-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is 0.75, the magnitude of compressor power (in kW) is _________ (correct to two decimal places).
44. A mbient air is at a pressure of 100 kPa, dry bulb temperature of 30°C and 60% relative humidity. The saturation pressure of water at 30°C is 4.24 kPa. The specific humidity of air (in g/kg of dry air) is ________ (correct to two decimal places).
45. A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m3/s at 450 rpm. Take the water density and the acceleration due to gravity as 103 kg/m3 and 10 m/s2, respectively. Assume no losses both in model and prototype turbines. The power (in MW) of a full sized turbine while working under a head of 30 m is _______ (correct to two decimal places).
46. The true stress (in MPa) versus true strain relationship for a metal is given by
σ = 1020ε0.4
The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is 100 mm2. The cross-sectional area at the time of necking (in mm2) is ________ (correct to two decimal places)
47. A steel wire is drawn from an initial diameter (di) of 10 mm to a final diameter (df) of 7.5 mm. The half cone angle (α) of the die is 5° and the coefficient of friction (μ) between the die and the wire is 0.1. The average of the initial and final yield stress [σY)avg] is 350 MPa. The equation for drawing stress σf, (in MPa) is given as:
The drawing stress (in MPa) required to carry out this operation is _________ (correct to two decimal places).
48. Following data correspond to an orthogonal turning of a 100 mm diameter rod on a lathe. Rake angle: +15° ; Uncut chip thickness: 0.5 mm; nominal chip thickness after the cut: 1.25 mm. The shear angle (in degrees) for this process is _______ (correct to two decimal places).
49. T aylor’s tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in 20 mm thick mild steel plates. In test 1, a drill lasted 300 holes at 150 rpm while in test 2, another drill lasted 200 holes at 300 rpm. The maximum number of holes that can be made by another drill from the above batch at 200 rpm is ______ (correct to two decimal places).
50. F or sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov’s law for the estimation of the total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal places)
51. The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is _______.
52. A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The material removal rate (in mm3/min) is expressed as
4 × 104 IT–1.23
where I = 300 A and the melting point of the material, T = 1600°C . The time (in minutes) for machining this hole is ________ (correct to two decimal places)
53. A welding operation is being performed with voltage = 30 V and current = 100 A. The cross-sectional area of the weld bead is 20 mm2. The work-piece and filler are of titanium for which the specific energy of melting is 14 J/mm3. Assuming a thermal efficiency of the welding process 70%, the welding speed (in mm/s) is __________ (correct to two decimal places).
54. S team in the condenser of a thermal power plant is to be condensed at a temperature of 30°C with cooling water which enters the tubes of the condenser at 14°C and exits at 22°C. The total surface area of the tubes is 50 m2, and the overall heat transfer coefficient is 2000 W/m2 K. The heat transfer (in MW) to the condenser is ______ (correct to two decimal places).
55. A vehicle powered by a spark ignition engine follows air standard Otto cycle (γ=1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is _______ (correct to two decimal places).
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