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Question 1 of 65
1. Question
A mass m of a perfect gas at pressure p_{1} and volume V_{1} undergoes an isothermal process. The final pressure is p_{2} and volume is V_{2}. 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
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Question 2 of 65
2. Question
Which one of the following statements is TRUE for the ultrasonic machining (USM) process?
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Question 3 of 65
3. Question
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 ________
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NAT Type Question

Question 4 of 65
4. Question
The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes.
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Question 5 of 65
5. Question
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 _________
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NAT Type Question

Question 6 of 65
6. Question
The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___________
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NAT Type Question

Question 7 of 65
7. Question
Which one of the following statement is TRUE?
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Question 8 of 65
8. Question
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ____________
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Question 9 of 65
9. Question
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)
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Question 10 of 65
10. Question
It is desired to make a product having Tshaped crosssection from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?
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Question 11 of 65
11. Question
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 __________.
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NAT Type Question

Question 12 of 65
12. Question
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?
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Question 13 of 65
13. Question
For the stability of a floating body the
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Question 14 of 65
14. Question
The divergence of the vector −yi + xj __________
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NAT Type Question

Question 15 of 65
15. Question
For a loaded cantilever beam of uniform crosssection, the bending moment (in N.mm) along the length is M(x) = 5x^{2}+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 crosssection at x =10 mm is ________.
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NAT Type Question

Question 16 of 65
16. Question
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
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Question 17 of 65
17. Question
If a mass of moist air contained in a closed metallic vessel is heated, then its
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Question 18 of 65
18. Question
In a slidercrank 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 _____________
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NAT Type Question

Question 19 of 65
19. Question
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 ______
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NAT Type Question

Question 20 of 65
20. Question
The crystal structure of aluminium is
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Question 21 of 65
21. Question
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
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NAT Type Question

Question 22 of 65
22. Question
The Laplace transform of te^{t} is
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Question 23 of 65
23. Question
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 x_{2} > x_{1}, then
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Question 24 of 65
24. Question
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
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Question 25 of 65
25. Question
Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe_{3}C) is _________.
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Question 26 of 65
26. Question
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 ___________
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Question 27 of 65
27. Question
A cylindrical pin of diameter is electroplated. Plating thickness is 2.0^{±}^{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 _________.
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Question 28 of 65
28. Question
A helical compression spring made of wire of circular crosssection is subjected to a compressive load. The maximum shear stress induced in the crosssection 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 crosssection of the wire is _____.
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NAT Type Question

Question 29 of 65
29. Question
In a counterflow 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/m^{2}.K. The required heat transfer surface area (in m^{2}) is
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Question 30 of 65
30. Question
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/s^{2}. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML^{2}/12). At this instant, the magnitude of angular acceleration (in radian/s2) of the rod is ____________
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NAT Type Question

Question 31 of 65
31. Question
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.
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Question 32 of 65
32. Question
The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m^{3} 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
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Question 33 of 65
33. Question
For the laminar flow of water over a sphere, the drag coefficient C_{F} is defined as C_{F} = F/(ρU^{2}D^{2}), 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/m^{3}. 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 _____________
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Question 34 of 65
34. Question
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
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Question 35 of 65
35. Question
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 _________.
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NAT Type Question

Question 36 of 65
36. Question
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 ______
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NAT Type Question

Question 37 of 65
37. Question
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.
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Question 38 of 65
38. Question
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 m_{1} = 10kg, m_{2} = 5kg and m_{3} = 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 _________.
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NAT Type Question

Question 39 of 65
39. Question
A strip of 120 mm width and 8mm thickness is rolled between two 300 mmdiameter 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 _________.
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NAT Type Question

Question 40 of 65
40. Question
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 northwest corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (XY), in Rupees, is
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Question 41 of 65
41. Question
One kg of an ideal gas (gas constant R = 287 J/kg.K) undergoes an irreversible process from state1 (1 bar, 300 K) to state 2 (2 bar, 300 K). The change in specific entropy (s_{2} – s_{1}) of the gas (in J/kg. K) in the process is ___________
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NAT Type Question

Question 42 of 65
42. Question
A 60 mmdiameter 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/m^{3}. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________
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Question 43 of 65
43. Question
The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m^{3} flowing through a pipe. The acceleration due to gravity is 9.81 m/s^{2}. If the manometric fluid is water (density 1000 kg/m^{3}) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is ____________
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Question 44 of 65
44. Question
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/m^{2}.K and 9000kg/m^{3}, respectively. The ball temperature (in °C) after 90 seconds will be approximately.
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Question 45 of 65
45. Question
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 _________
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Question 46 of 65
46. Question
The surface integral over the surface S of the sphere x^{2} + y^{2} + z^{2} = 9, where F=(x+y) i+ (x+z) j+(y+z) k and n is the unit outward surface normal, yields ______.
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Question 47 of 65
47. Question
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/s^{2}) of point P of the block with respect to fixed point O is ________
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Question 48 of 65
48. Question
During the turning of a 20mmdiameter 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.
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Question 49 of 65
49. Question
Consider the matrix whose eigenvectors corresponding to eigenvalues λ_{1} and λ_{2} are respectively. The value of is ______
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Question 50 of 65
50. Question
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/s^{2}, the natural frequency (in radian/s) of the compound pendulum is _________.
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Question 51 of 65
51. Question
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 ______
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Question 52 of 65
52. Question
If f(z) = (x^{2} + ay^{2}) + ibxy is a complex analytic function of z = x + iy, where , then
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Question 53 of 65
53. Question
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 ______
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Question 54 of 65
54. Question
Maximize Z = 5x_{1} + 3x_{2}
Subject to
x_{1} + 2x_{12} ≤ 10,
x_{1} – x_{2} ≤ 8,
x_{1}, x_{12} ≥ 0.
In the starting Simplex tableau, x_{1} and x_{2} are nonbasic variables and the value of Z is zero. The value of Z in the next Simplex tableau is _________.
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Question 55 of 65
55. Question
The principal stresses at a point in a critical section of a machine component are σ_{1} = 60MPa, σ_{2} = 5MPa and σ_{3} = −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
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Question 56 of 65
56. Question
If you choose plan P, you will have to _______ plan Q, as these two are mutually _________.
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Question 57 of 65
57. Question
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
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Question 58 of 65
58. Question
If a and b are integers and a – b is even, which of the following must always be even?
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Question 59 of 65
59. Question
A couple has 2 children. The probability that both children are boys if the older one is a boy is
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Question 60 of 65
60. Question
The ways in which this game can be played __________ potentially infinite.
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Question 61 of 65
61. Question
“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”?
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Question 62 of 65
62. Question
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?
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Question 63 of 65
63. Question
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?
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Question 64 of 65
64. Question
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?
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Question 65 of 65
65. Question
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?
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