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Question 1 of 65
1. Question
Given the vectors the vector that is perpendicular to both and is given by :
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Question 2 of 65
2. Question
The value of the integral I = ∫_{C}((x – y) dx + x^{2}dy), with C the boundary of the square 0 ≤ x ≤ 2; 0 ≤ y ≤ 2, is _________
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NAT Type Question

Question 3 of 65
3. Question
Let be a unit vector that is function of the parameter t. Then
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Question 4 of 65
4. Question
The eigenvalues λ_{n} and eigenfunctions u_{n}(x) of the SturmLiouville problem 0 < x < 1; y(0) = 0, y(1) = 0 are given by :
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Question 5 of 65
5. Question
3point Gaussian integration formula is given by:
with x_{1} = 0, This formula exactly integrates
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Question 6 of 65
6. Question
Which one of the following statements is NOT true
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Question 7 of 65
7. Question
Which one of the following statements is NOT true
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Question 8 of 65
8. Question
A DE Laval nozzle is to be designed for an exit Mach number of 1.5. The reservoir conditions are given as P_{o} = 1 atm (gage) T_{o} = 20℃, γ = 1.4. Assuming shock free flow in the nozzle, the exit absolute pressure (in atm) is ________ (in three decimal places)
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NAT Type Question

Question 9 of 65
9. Question
Consider a steady one dimensional flow of a perfect gas with heat transfer in a duct. The Ts diagram (shown below) shows both the static and the stagnation conditions at two locations. A and B, in the duct, A_{t} and B_{t} denote stagnation conditions for states A and B, respectively. It is known that (∆T)_{A} = (∆T)_{B}. M_{A} and M_{B} are the Mach numbers of the flow at locations A and B.
Which of the following statements is true about the flow
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Question 10 of 65
10. Question
To ensure only the longitudinal static stability (and not the condition for equilibrium) of a low speed aircraft,, the aircraft components must be designed to satisfy which one of the following conditions:
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Question 11 of 65
11. Question
Which of the following statement(s) is/are true about the shear centre of a crosssection:
P : It is that point in the crosssection through which shear loads produce no twisting.
Q: This point is also the centre of twist of sections subjected to pure torsion.
R: The normal stress at this point is always zero.
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Question 12 of 65
12. Question
Let be respectively the nondimensional locations of the stickfixed maneuver point and stickfixed neutral point of a low speed conventional aircraft. These distances are measured with respect to the nose of the fuselage. The numerical value of
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Question 13 of 65
13. Question
The phenomenon of rudder lock in conventional low speed aircraft is primarily due to
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Question 14 of 65
14. Question
The period of revolution of earth about the sun is 365.256 days, approximately. The semimajor axis of the earth’s orbit is close to 1.4953 × 10^{11} m. The semimajor axis of the orbit of Mars is 2.2783 × 10^{11} m. The period of revolution of Mars, about the sun, is _______ Earth days (in three decimal place)
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NAT Type Question

Question 15 of 65
15. Question
Consider a system consisting of certain amount of perfect gas enclosed in a cylinder fitted with a frictionless piston. This system can undergo following processes
(i) Expansion with finite pressure difference with the surrounding.
(ii) Compression with infinitesimal pressure difference with the surrounding.
(iii) Heat transfer with finite temperature difference with the reservoir.
(iv) Heat transfer with infinitesimal temperature difference with the reservoir.
Out of these which processes are reversible?
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Question 16 of 65
16. Question
Among the following engines, which one is expected to have the maximum Specific Impulse?
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Question 17 of 65
17. Question
The maximum gas flow rate that can be handled by a multistage axial compressor at a given rotational speed is dictated by
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Question 18 of 65
18. Question
For a turbine stage, which one of the following losses occurs due to the turning of the wall boundary layer through an angle due to curved surface?
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Question 19 of 65
19. Question
In the vaneless space between the impeller and the diffuser vanes in a Centrifugal Compressor, the angular momentum varies in the following manner in the radial direction
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Question 20 of 65
20. Question
Which of the following statements about the neutral axis of a beam with unsymmetrical cross section is true:
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Question 21 of 65
21. Question
Assuming that the aircraft is flying straight, the top spar cap/flange of a wing is most likely to fail in
:
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Question 22 of 65
22. Question
A 2DOF undamped springmass system with two masses and two springs has natural frequencies ω_{1} = 0.79 rad/s and ω_{2} = 1.538 rad/s. The mode shapes for the system are given by ϕ_{1} = [0.7321]^{T} and ϕ_{2} = [−2.73]^{T}. If the first mass is displaced by 1 cm, the minimum displacement in cms to be given to the second mass to make the system vibrate in first mode alone is =_____ (in three decimal place).
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Question 23 of 65
23. Question
An aircraft landing gear can be idealized as a single degree of freedom springmassdamper system. The desirable damping characteristics of such a system is :
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Question 24 of 65
24. Question
A single degree of freedom springmass system of natural frequency 5 Hz is modified in the following manners :
Case 1 : Viscous damping with damping ratio ς = 0.2 is introduced in parallel to the spring.
Case 2 : The original undamped springmass system is moved to a surface with coefficient of friction, μ = 0.01.
The ratio of the damped natural frequency for the cases 1 and 2 is given by ______ (in three decimal places).
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Question 25 of 65
25. Question
Which of the following statements about the compatibility equations are true:
P. Strain compatibility equations must be satisfied in the solution of threedimensional problems in elasticity.
Q. Six strains are defined in terms on three displacement functions and can have arbitrary values.
R. Compatibility equations are an expression of the continuity of displacements.
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Question 26 of 65
26. Question
Matrix and Vector are given. If vector {x} is the solution to the system of equations [A] {x} = {b}, which of the following is true for {x} :
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Question 27 of 65
27. Question
Let matrix Then for any nontrivial vector which of the following is true for the value of K = {x}^{T}[A] {x}:
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Question 28 of 65
28. Question
Consider the initial value problem:
If are the Laplace transforms of y(t) and f(t) respectively, then Y(s) is given b y :
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Question 29 of 65
29. Question
Let u(x, t) denote the displacement of a point on a rod. The displacement satisfies the following equation of motion :
0 < x < 1
with u(x, 0) = 0.01 sin (10 πx), u(0, t) = 0, u(1, t) = 0. The value of u(0.25, 1) is ______ (in three decimal places).
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Question 30 of 65
30. Question
The equation has a solution y(x) that is :
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Question 31 of 65
31. Question
Consider a straight wing with rectangular planform a aspect ratio 10 and with a NACA 0012 airfoil. The span effectiveness factor for this wing is 0.95. Assume the flow to be incompressible and governed by thin airfoil theory. The lift coefficient of this wing, at an angle of attack of 6 deg, is _____ (in three decimal places)
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Question 32 of 65
32. Question
Consider an incompressible flow over a flat plate with the following approximation to the velocity profile :
where δ is the boundary layer thickness and U the freestream speed. The normalized momentum thickness (θ/δ) for this profile is ______ (in three decimal places).
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Question 33 of 65
33. Question
An idealized velocity field is given by At point (−1, 1, 0) and at t = 1, the magnitude of the material acceleration vector of the fluid element is _______
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Question 34 of 65
34. Question
A trace from the schlieren photograph of the flow around a corner reveals the edges of the expansion fan as shown below. The leading and trailing edges of the expansion fan make the angles as shown. Assuming γ = 1.4, the angle of the expansion fan (in degrees) is _______(in two decimal places)
Pandtl Meyer function is given by
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NAT Type Question

Question 35 of 65
35. Question
A strong normal shock wave, with a pressure ratio of 29 across it, is travelling into stationary air (γ = 1.4) at T = 280 K in a straight duct (see figure). The magnitude of the velocity of the air induced behind the shock wave is ________m/s. (round to nearest integer)
(Gas constant = 287 J/kg.K; Shock wave relations:
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NAT Type Question

Question 36 of 65
36. Question
In the figure below, water exits from a nozzle into atmospheric pressure of 101 kPa. If the exit velocity is V_{2} = 8 m/s and friction is neglected, the magnitude of the axial force on the flange at location 1 required to keep the nozzle attached to the pipe is _______ N (round to nearest integer).
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NAT Type Question

Question 37 of 65
37. Question
A football, meant to be thrown at 100 km/h in sea level air (ρ = 1.22 kg/m^{3}, μ = 1.78 × 10^{−5} Ns/m^{2}), is to be tested using a onequarter scale model in a water tunnel (ρ = 1000 kg/m^{3}, μ = 10^{−3} Ns/m^{2}). For dynamic similarity, the ratio of the model force to the prototype force is _______(round to nearest integer).
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NAT Type Question

Question 38 of 65
38. Question
An aircraft model was tested in a low speed windtunnel (Reynolds number = 2 × 10^{6} based on wing mean chord). The variation of pitching moment of coefficient (C_{m}) with angle of attack (α) for two elevator deflections (δ_{e}) as recorded during this test is presented below.
Based on the result presented in the figure above, the value of elevator control power (C_{m3e}) in per radian will be ________ (in three decimal place).
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NAT Type Question

Question 39 of 65
39. Question
A pilot was flying a single engine propeller aircraft and maintaining a steady level flight at a lift coefficient, C_{L} = 0.5 at an altitude of 500 m. Due to some emergency, at the same altitude (500 m), the pilot had to fully deploy the landing gear. If the pilot wants to maintain steady level flight at the same C_{L} = 0.5 and at the same altitude, which of the following control actions should the pilot undertake:
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Question 40 of 65
40. Question
A conventional low speed aircraft had the following aerodynamic characteristics :
C_{D0} = 0.020, e = 1.0 (Oswald efficiency).
The aircraft was flown to maintain steady level flight and for minimum thrust required, at a lift coefficient of C_{L} = 0.8. The numerical value of the aspect ratio of the wing is ______ (in three decimal places).
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NAT Type Question

Question 41 of 65
41. Question
A batch of aluminium alloy yields in uniaxial tension at the s tress of 330 MN/m^{2}. If this material is subjected to the following state of stress: σ_{x} = 140 MN/m^{2}, σ_{y} = −70 MN/m^{2}, σ_{z} = 0, τ_{xx} = χ MN/m^{2}, τ_{yz} = 0 and τ_{zx} = 0. The value of χ that would result in yielding according to the Von Mises failure criterion is _________ (in three decimal places).
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NAT Type Question

Question 42 of 65
42. Question
The roots obtained by solving longitudinal characteristic equations of motion for a statically stable aircraft are given below :
λ_{1, 2} = −0.02 ± 0.30i, λ_{3, 4} = −2.00±2.50i, where
The undamped shortperiod longitudinal natural frequency (radians/sec) and damping ratio, in that order, are close to
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Question 43 of 65
43. Question
An aircraft is to be designed to ensure that it has enough excess power to achieve steady climb at flight path angle, γ = 10 degrees, maintaining The numerical value of the thrust to weight ratio of the complete aircraft to meet the above requirement under standard atmospheric condition will be ________ (in three decimal place).
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Question 44 of 65
44. Question
A conventional aircraft was analyzed to estimate the contribution of wing towards C_{m0} (C_{m} at α = 0) of the whole aircraft. The wing was installed with zero setting angle along the fuselage reference line. Further, the wing was laid such that and
are the nondimensional distances, from the leading edge of the wing, of the aerodynamic center of the wing and center of gravity of the aircraft respectively. The wing had the following aerodynamic characteristics:
C_{L0} = 0.20, and C_{mac} _{wing} = −0.02.
The numerical value of C_{m0, w}(contribution of the wing to C_{m0}) about the CG of the aircraft is _________ (in two decimal places).
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Question 45 of 65
45. Question
In a combustor, gaseous Octane (C_{8}H_{18}) and air are to be burned in stoichiometric proportions. If the required flowrate of air is 1 kg/s, what should be the corresponding flow rate of Octane?
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Question 46 of 65
46. Question
The given diagram represents the velocity triangles at the leading edge (1) and trailing edge (2) at the mean radius of a single stage axial compressor rotor. The stage efficiency of the compressor is 0.8. The stagnation temperature of air entering the stage is 298 K and the specific heat at constant pressure for air is 1.005 kJ/kgK. The ratio of specific heats for air is 1.4. Considering actual work in the rotor is equal to the ideal work, the pressure ratio for the stage is equal to _______ (in two decimal points).
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Question 47 of 65
47. Question
An aircraft with a turbojet engine, having an inlet area of 1 m^{2}, is flying at 270 m/s at an altitude where the atmosphere pressure is equal to 0.9 bar and the ambient temperature is equal to 290 K. The stagnation pressure and temperature at the exit of the turbine are equal to 1.6 bar and 774 K respectively. The specific heat at constant pressure of the burned gases is equal to 1.147 kJ/kgK and the ratio of specific heats is equal to 1.33. Considering ideal expansion in the nozzle with no losses, the specific thrust produced by the engine is _________ Ns/kg (in one decimal place).
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Question 48 of 65
48. Question
Air, at 450 K stagnation temperature and at a rate of 50 kg/s, enters the combustor of a turbofan engine and is burned with 1 kg/s of Aviation Kerosene (Heating value 44 MJ/kg). The specific heat at constant pressure for the incoming air and the burned products are 1.005 kJ/kgK and 1.147 kJ/kgK respectively. Considering 100% burner efficiency, the stagnation temperature at the exit of the combustor is equal to ________K. (in one decimal place).
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Question 49 of 65
49. Question
A single stage chemical rocket, having an initial mass of 10,000 kg and specific impulse of 450 s, is launched from the surface of the earth and has to reach the escape velocity (11 km/s) at burn out. Consider g_{e} = 9.8 m/s^{2}. If the atmospheric drag and the effect of gravity are to be neglected, the mass of propellant to be carried by the rocket is equal to ________ kg (in one decimal place)
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Question 50 of 65
50. Question
A centrifugal compressor requires 1800 kW of power to compress 10 kg/s of air. Consider the whirl velocity component is equal to the impeller speed (ie., no slip) and no losses in the impeller. If the impeller has to rotate at 1900 rad/s, the diameter of the impeller is to be _______ m(in two decimal place).
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Question 51 of 65
51. Question
An aircraft wing is idealized as a cantilever beam of constant width and length l with a tip mass of weight W (Newtons) and has a uniformly distributed loading of q_{o} (Newtons/m) as shown in the figure. Flexural rigidity = EI and q_{o}l = 10 W.
The upward deflection of the tip of the aircraft wing under the given loading can be expressed as :
The value of k is ________ (in three decimal places).
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Question 52 of 65
52. Question
For the state of plane stress shown in the figure, the minimum principal stress is −7 MN/m^{2}. The normal stress σ_{x} in MN/m^{2} is equal to _______ (round to nearest integer).
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Question 53 of 65
53. Question
The maximum normal stress in MN/m^{2} for the thin walled beam of square cross section of outer dimension 120 mm × 120 mm and wall thickness 1 mm under the action of moment M_{o} = 96 Nm as shown in the figure is ______ (in three decimal places).
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Question 54 of 65
54. Question
The idealized cross section of a thinwalled wing box structure shown in the figure is subjected to an anticlockwise torque of 10 kNm. The corresponding shearflow distribution under this loading condition is shown in the figure. The area of each cell is A_{1} = 300 × 10^{3} mm^{2} and A_{2} = 250 × 10^{3} mm^{2}. The ratio of the unknown x/y is given by _________ (in three decimal places).
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Question 55 of 65
55. Question
The natural frequency of the system suspended by two identical springs of stiffness k as shown in the figure is given by for small displacement. Both the springs make an angle of 45° with the horizontal. The value of a is _________(in two decimal places).
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Question 56 of 65
56. Question
The ninth and the tenth of this month are Monday and Tuesday _______.
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Question 57 of 65
57. Question
It is _______ to read this year’s textbook ______ the last year’s
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Question 58 of 65
58. Question
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?
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Question 59 of 65
59. Question
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?
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Question 60 of 65
60. Question
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?
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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 statements best reflects the author’s opinion?
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Question 62 of 65
62. Question
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?
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Question 63 of 65
63. Question
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?
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Question 64 of 65
64. Question
The number of 3digit numbers such that the digit 1 is never to the immediate right of 2 is
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Question 65 of 65
65. Question
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?
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