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GATE (Graduate Aptitude Test in Engineering) Aerospace Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Aerospace Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of Main exam of GATE Aerospace Engineering. We advise candidates to solve the online GATE Aerospace Engineering mock tests to get good marks in the exam. Start practicing AerospaceGATE 2019 Mock tests here online for free

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Category: GATE Aerospace Engineering 2019

Question 1:

The maximum value of the function 𝑓(𝑥) =

x e^{- x}

(where x is real) is

A	1/e	B	$2 / e^{2}$
C	$(e^{- 1 / 2}) / 2$	D	$\infty$

Category: GATE Aerospace Engineering 2019

Question 2:

Vector

\vec{b}

is obtained by rotating

\vec{α}

= 𝑖̂+ 𝑗̂ by 900about 𝑘̂, where 𝑖̂, 𝑗̂and 𝑘̂ are unit vectors along the x, y and z axes, respectively.

\vec{b}

is given by

A	$\hat{i} - \hat{j}$	B	$- \hat{i} + \hat{j}$
C	$\hat{i} + \hat{j}$	D	$- \hat{i} - \hat{j}$

Category: GATE Aerospace Engineering 2019

Question 3:

A scalar function is given by

f (x, y) = x^{2} + y^{2} .

Take 𝑖̂ and 𝑗̂ as unit vectors along the x and y axes, respectively. At

(x, y) = (3, 4)

he direction along which 𝑓 increases the fastest is

A	$\frac{1}{5} (4 \hat{I} - 3 \hat{J})$	B	$\frac{1}{5} (3 \hat{I} - 4 \hat{J})$
C	$\frac{1}{5} (3 \hat{I} + 4 \hat{J})$	D	$\frac{1}{5} (4 \hat{I} + 3 \hat{J})$

Category: GATE Aerospace Engineering 2019

Question 4:

The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

A	$L T^{- 4}$	B	$L^{2} T^{- 1}$
C	$L T^{- 2}$	D	$L^{- 2} T$

Category: GATE Aerospace Engineering 2019

Question 5:

𝜙 (𝑥, 𝑦) represents the velocity potential of a two-dimensional flow with velocity field 𝑉 ⃗ = 𝑢(𝑥, 𝑦) 𝑖̂ + 𝑣(𝑥, 𝑦)𝑗̂, where 𝑖̂ and 𝑗̂ are unit vectors along the x and y axes, respectively. Which of the following is necessarily true?

A	∇2𝜙 = 0	B	∇ ×𝑉 ⃗= 0
C	∇ ⋅𝑉 ⃗= 0	D	𝑢 = −𝜕𝜙/𝜕𝑦, 𝑣 = 𝜕𝜙/𝜕𝑥

Category: GATE Aerospace Engineering 2019

Question 6:

F or a quasi-one-dimensional isentropic supersonic flow through a diverging duct, which of the following is true in the direction of the flow?

A	Both the Mach number and the static temperature increase.	B	The Mach number increases and the static temperature decreases.
C	The Mach number decreases and the static temperature increases	D	Both the Mach number and the static temperature decrease.

Category: GATE Aerospace Engineering 2019

Question 7:

F or a NACA2415 airfoil of chord length c, which of the following is true?

A	Maximum camber is located at 0.2c from the leading edge.	B	Maximum thickness is located at 0.15c from the leading edge.
C	Maximum camber is 0.02c.	D	Maximum thickness is 0.05c.

Category: GATE Aerospace Engineering 2019

Question 8:

When a propeller airplane in ground-roll during take-off experiences headwind, which of the following statements is FALSE?

A	The drag on the airplane increases	B	The thrust from the propellers decreases
C	The wing lift increases.	D	The ground-roll distance increases.

Category: GATE Aerospace Engineering 2019

Question 9:

Which of the following graphs represents the response of a dynamically unstable airplane?

Category: GATE Aerospace Engineering 2019

Question 10:

While flying at Mach 2.0, 11 km altitude and producing the same thrust, what is the correct order from the lowest thrust specific fuel consumption (tsfc) to the highest tsfc?

A	Turbofan, Ramjet, Turbojet	B	Turbofan, Turbojet, Ramjet
C	Ramjet, Turbojet, Turbofan	D	Turbojet, Turbofan, Ramjet

Category: GATE Aerospace Engineering 2019

Question 11:

For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

A	CPR of an axial compressor > CPR of centrifugal compressor.	B	CPR of an axial compressor < CPR of centrifugal compressor.
C	CPR of an axial compressor = CPR of centrifugal compressor	D	CPR of any value can be attained with either an axial or a centrifugal compressor.

Category: GATE Aerospace Engineering 2019

Question 12:

For a beam subjected to a transverse shear load through its shear center,

A	the twist per unit length is zero.	B	the shear stress is uniform throughout the cross-section.
C	the bending stresses in the cross section are zero.	D	the shear strain is zero at the shear center.

Category: GATE Aerospace Engineering 2019

Question 13:

A function function 𝑓(𝑥) is defined by 𝑓(𝑥)

= \frac{1}{2} (x + |x|) .

The value of

\int_{- 1}^{1} f (x) d x

is _______ (round off to 1 decimal place).

0.0 to 0.0

0.0 to 0.5

0.5 to 0.5

None of these

Category: GATE Aerospace Engineering 2019

Question 14:

The value of the following limit is ________ (round off to 2 decimal places).

\lim_{0 \to 0} \frac{θ - \sin θ}{θ^{3}}

0.16 to 0.17

0.17 to 0.18

0.15 to 0.17

0.16 to 0.18

Category: GATE Aerospace Engineering 2019

Question 15:

To simulate the aerodynamic forces on a cylinder of 1 m diameter due to a uniform air flow of 1 m/s at standard temperature and pressure (STP), low-speed wind tunnel experiments at STP are conducted on a 0.1 m diameter cylinder. The free stream air speed in the wind tunnel experiments should be _______ m/s (round off to the nearest integer).

0 to 5

5 to 10

10 to 10

10 to 15

Category: GATE Aerospace Engineering 2019

Question 16:

The power-off glide range for an airplane with a maximum Lift to Drag ratio of 18, when the glide starts at an altitude of 4 km, is ______ km (round off to the nearest integer).

71 to 72

72 to 73

73 to 74

74 to 75

Category: GATE Aerospace Engineering 2019

Question 17:

For an airplane flying in a vertical plane, the angle of attack is 3o, the horizontal and vertical components of velocity in wind axis are 300 km/h and 15.72 km/h, respectively. The pitch attitude of the airplane is _______ degrees (round off to 2 decimal places).

5.92 to 5.94

5.94 to 5.96

5.96 to 5.98

5.98 to 6.00

Category: GATE Aerospace Engineering 2019

Question 18:

An airplane is in steady level flight with a true air speed of 50 m/s. The ambient air density and ambient pressure at the flight altitude are 0.91 kg/

m^{3}

and 7×

10^{4}

m^{2}

, respectively. At sea level, air density is 1.225 kg/

m^{3}

and ambient pressure is 1.01×

10^{5}

m^{2}

. The equivalent or indicated air speed of the airplane is ________ m/s (round off to 2 decimal places).

43.00 to 43.05

43.03 to 43.05

43.05 to 43.15

43.13 to 43.15

Category: GATE Aerospace Engineering 2019

Question 19:

For the complete combustion of 1 mole of ethanol

(C_{2} H_{5} O H)

, the required number of moles of oxygen is ________.

3 to 3

-3 to 0

0 to 3

-3 to 3

Category: GATE Aerospace Engineering 2019

Question 20:

One kg of diatomic gas is heated and its temperature increases from 100 K to 600 K. The energy added at constant pressure during this process is 500 kJ. The specific heat at constant volume for the gas is ____________ kJ/kgK. (round off to 2 decimal places).

0.70 to 0.72

0.72 to 0.74

0.74 to 0.76

0.76 to 0.78

Category: GATE Aerospace Engineering 2019

Question 21:

The number of independent elastic constants for a homogeneous isotropic linear elastic material is ________.

0 to 2

-2 to 2

-2 to 0

2 to 2

Category: GATE Aerospace Engineering 2019

Question 22:

A thin plate with Young’s modulus 210 GPa and Poisson’s ratio 0.3 is loaded as shown in the figure. The change in length along the y-direction is __________ mm (round off to 1 decimal place).

0.2 to 2.2

2.2 to 2.2

0.2 to 0.2

0.2 to 1.2

Category: GATE Aerospace Engineering 2019

Question 23:

For the state of stress shown in the figure, the normal stress,

σ_{n}

, on a plane inclined at 45 degrees to the x-axis is _________MPa (round off to the nearest integer).

247 to 255

256 to 264

265 to 273

274 to 282

Category: GATE Aerospace Engineering 2019

Question 24:

In the spring-mass system, shown in the figure, mass m = 3 kg and the spring stiffness k = 20 kN/m. The natural frequency of the system is _______ Hz (round off to the nearest integer).

-16 to 16

0.16 to 16

0.16 to 16.0

16 to 16

Category: GATE Aerospace Engineering 2019

Question 25:

The following system of equations 2𝑥−𝑦−𝑧=0, −𝑥+2𝑦−𝑧=0, −𝑥−𝑦+2𝑧=0

A	has no solution.	B	has a unique solution.
C	has three solutions.	D	has an infinite number of solutions

Category: GATE Aerospace Engineering 2019

Question 26:

A supersonic flow in a constant area duct at Mach number M1 encounters a ramp of angle θ1 (see Figure 1). The resulting oblique shock with shock angle β1 is then reflected from the top wall. For the reflected shock, the turn angle is andtheshock

Use the weak shock solution fromthe θ-β-M plot shown in Figure 2 to choose the correct option from the following.

A	$β_{1} > β_{2}$	B	$β_{1} < β_{2}$
C	$θ_{1} > θ_{2}$	D	$θ_{1} < θ_{2}$

Category: GATE Aerospace Engineering 2019

Question 27:

Which of the following statements about adverse yaw of an airplane is/are correct? P. It is caused by flow separation resulting from large rudder deflection. Q. It is caused by dissimilar drag forces acting on the two halves of the wing resulting from aileron deflections of same magnitude. R. It can be eliminated by ensuring that the upward deflection of one aileron is greater than the downward deflection of the opposite aileron.

A	P only	B	Q only
C	P and R	D	Q and R

Category: GATE Aerospace Engineering 2019

Question 28:

For a 1 m long simply supported beam with a concentrated vertical load of 200 N and a concentrated bending moment of 100 Nm at the center as shown in the figure, the correct bending moment diagram is:

Category: GATE Aerospace Engineering 2019

Question 29:

For real x, the number of points of intersection between the curves 𝑦=𝑥 and 𝑦=cos𝑥 is _________.

0 to 0

0 to 1

1 to 1

None of these

Category: GATE Aerospace Engineering 2019

Question 30:

One of the eigenvalues of the following matrix is 1.

(\frac{x}{- 1} \frac{2}{3})

The other eigenvalue is _______.

0 to 2

-2 to 2

-2 to -2

2 to 2

Category: GATE Aerospace Engineering 2019

Question 31:

The curve 𝑦=𝑓(𝑥) is such that its slope is equal to

y^{2}

for all real x. If the curve passes through (1, -1), the value of y at 𝑥= −2 is _______ (round off to 1 decimal place).

0.5 to 0.5

0.5 to 5.5

5.0 to 5.5

0.5 to 5.5

Category: GATE Aerospace Engineering 2019

Question 32:

The inviscid, incompressible flow field resulting from a uniform flow past a circular the cylinder of radius R centered at the origin is given by:

u_{r} = U (1 - \frac{R^{2}}{r^{2}}) \cos θ u_{θ} = (1 + \frac{R^{2}}{r^{2}}) \sin θ

where

u_{r}

and

u_{θ}

are the radial and azimuthal velocity components in polar coordinates, (r, ), as shown in the figure. U is the free stream speed. Ignore the effects of gravity. The azimuthal location (in the first quadrant) on the cylinder at which the pressure coefficient is zero is _______ degrees (round off to the nearest integer).

20 to 20

30 to 30

20 to 30

None of these

Category: GATE Aerospace Engineering 2019

Question 33:

A cylindrical container of radius R = 50 cm is filled with water up to a height ho. Upon rotating the cylinder about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaced upwards by h1 = 10 cm at r = R. The magnitude of the downward displacement h2 of the free surface at r = 0 is ________ cm (round off to the nearest integer).

-10 to -10

-10 to 10

10 to 10

None of these

Category: GATE Aerospace Engineering 2019

Question 34:

A two-dimensional, incompressible fluid flow is described by the stream function Ψ = 𝑥𝑦3 m2/s on the Cartesian x-y plane. If the density and dynamic viscosity of the fluid are 1 kg/m3 and 0.1 kg/m-s, respectively, the magnitude of the pressure gradient in the x direction at x=1 m and y=1 m is _______ N/m3 (round off to 1 decimal place).

3.5 to 3.7

2.3 TO 2.5

3.5 to 3.7 OR 2.3 TO 2.5

None of these

Category: GATE Aerospace Engineering 2019

Question 35:

The static pressure ratio across a stationary normal shock is given by

\frac{P_{2}}{P_{1}} = 1 + \frac{2 Y}{Y + 1} (M_{1}^{2} - 1),

where M1 is the upstream Mach number. For a stationary normal shock in air (𝛾=1.4,𝑅=287 J/kg-K) with upstream flow conditions given by: speed 800 m/s, static temperature 300 K and static pressure 1 atm., the static pressure downstream of the shock is __________ atm. (round off to 2 decimal places).

5.95 to 6.10

5.96 to 6.11

5.97 to 6.12

5.98 to 6.13

Category: GATE Aerospace Engineering 2019

Question 36:

For a symmetric airfoil at an angle of attack of 10o, assuming thin airfoil theory, the magnitude of the pitching moment coefficient about the leading edge is__________ (round off to 2 decimal places).

0.25 to 0.31

0.24 to 0.30

0.23 to 0.30

0.27 to 0.30

Category: GATE Aerospace Engineering 2019

Question 37:

The span-wise distribution of circulation over a finite wing of span b = 10 m is

r (y) = {\sqrt[r_{0}]{1 - (\frac{2 y}{b})}}^{2}

If Γ0=20 𝑚2/𝑠 and the free stream density and speed are 1.2 kg/m3 and 100 m/s, respectively, the total lift is __________ kN (round off to 2 decimal places).

15.30 to 16.00

16.00 to 17.30

17.30 to 18.00

18.00 to 19.20

Category: GATE Aerospace Engineering 2019

Question 38:

The airplane shown in figure starts executing a symmetric pull-up maneuver from steady level attitude with a constant nose-up pitch acceleration of 20 deg/s2. The vertical load factor measured at this instant at the centre of gravity (CG) is 2. Given that the acceleration due to gravity is 9.81 m/s2, the vertical load factor measured at point P on the nose of the airplane, which is 2 m ahead of the CG, is _____ (round off to 2 decimal places).

2.04 to 2.06

2.06 to 2.08

2.08 to 2.10

2.10 to 2.12

Category: GATE Aerospace Engineering 2019

Question 39:

Consider an airplane with a weight of 8000 N, wing area of 16

m^{2}

, wing zero-lift drag coefficient of 0.02, Oswald’s efficiency factor of 0.8, and wing aspect ratio of 6, in steady level flight with wing lift coefficient of 0.375. Considering the same flight speed and ambient density, the ratio of the induced drag coefficient during steady level flight to that during a

30 °

climb is _______ (round off to 2 decimal places).

1.32 to 1.35

1.36 to 1.39

1.40 to 1.43

None of these

Category: GATE Aerospace Engineering 2019

Question 40:

The product of earth’s mass (M) and the universal gravitational constant (G) is GM = 3.986×

10^{14} m^{3} / s^{2}

. The radius of earth is 6371 km. The minimum increment in the velocity to be imparted to a spacecraft flying in a circular orbit around the earth at an altitude of 4000 km to make it exit earth’s gravitational field is _______ km/s (round off to 2 decimal places).

2.52 to 2.60

2.53 to 2.61

2.54 to 2.62

2.55 to 2.63

Category: GATE Aerospace Engineering 2019

Question 41:

A propeller driven airplane has a gross take-off weight of 4905 N with a wing area of 6.84

m^{2}

. Assume that the wingsareoperating at the maximum

C_{L}^{3 / 2} / C_{D} o f 13

, the propellerefficiency is 0.9 and the specific fuel consumption ofthe engine is 0.76 kg/kW-hr. Giventhat the density of air at sea level is 1.225 kg/m3 and the acceleration due to gravity is9.81m/s2, the weight of the fuel required for an endurance of 18 hours at sea level is _______N (round off to the nearest integer).

1440 to 1480

1440 to 1490

1440 to 1470

None of these

Category: GATE Aerospace Engineering 2019

Question 42:

The design of an airplane is modified to increase the vertical tail area by 20% and decrease the moment arm from the aerodynamic centre of the vertical tail to the airplane centre of gravity by 20%. Assuming all other factors remain unchanged, the ratio of the modified to the original directional static stability (

(C_{N_{β}}

due to tail fin) is _______ (round off to 2decimal places).

0.00 to 0.00

0.00 to 0.96

0.96 to 0.96

None of these

Category: GATE Aerospace Engineering 2019

Question 43:

For a rocket engine, the velocity ratio r is

V_{a} / V_{e} w h e r e V_{a}

, is the vehicle velocity and Ve is the exit velocity of the exhaust gases. Assume the flow to be optimally expanded through the nozzle. For r = 2, if F is the thrust produced and 𝑚̇ is the mass flow rate of exhaust gases, then, 𝐹/(𝑚̇

V_{e}

) is ______.

-1 to -1

-1 to 1

0 to 1

1 to 1

Category: GATE Aerospace Engineering 2019

Question 44:

The specific impulse of a rocket engine is 3000 Ns/kg. The mass of the rocket at burnout is 1000 kg. The propellant consumed in the process is 720 kg. Assume all factors contributing to velocity loss to be negligible. The change in vehicle velocity Δu is _____ km/s (round off to 2 decimal places).

1.55 to 1.60

1.60 to 1.65

1.65 to 1.70

1.70 to 1.75

Category: GATE Aerospace Engineering 2019

Question 45:

The combustion products of a gas turbine engine can be assumed to be a calorically perfect gas with γ = 1.2. The pressure ratio across the turbine stage is 0.14. The measured turbine inlet and exit stagnation temperatures are 1200 K and 900 K, respectively. The total-tototal turbine efficiency is ________ % (round off to the nearest integer).

82 to 84

84 to 86

86 to 88

88 to 90

Category: GATE Aerospace Engineering 2019

Question 46:

The figure shows the velocity triangles for an axial compressor stage. The specific work input to the compressor stage is ____________ kJ/kg (round off to 2 decimal places).

2.50 to 2.60

2.55 to 2.65

2.56 to 2.65

2.55 to 2.60

Category: GATE Aerospace Engineering 2019

Question 47:

As shown in the figure, a rigid slab CD of weight W (distributed uniformly along its length) is hung from a ceiling using three cables of identical length and cross-sectional area. The central cable is made of steel (Young’s modulus = 3E) and the other two cables are made of aluminium (Young’s modulus = E). The percentage of the total weight taken by the centralcable is ______ % (round off to the nearest integer).

60 to 58

60 to 59

60 to 60

60 to 61

Category: GATE Aerospace Engineering 2019

Question 48:

All the bars in the given truss are elastic with Young’s modulus 200 GPa, and have identical cross-sections with moment of inertia 0.1 cm4. The lowest value of the load P at which the truss fails due to buckling is _______ kN (round off to the nearest integer).

550 to 570

560 to 580

555 to 575

None of these

Category: GATE Aerospace Engineering 2019

Question 49:

A solid circular shaft is designed to transmit a torque T with a factor of safety of 2. It is proposed to replace the solid shaft by a hollow shaft of the same material and identical outer radius. If the inner radius is half the outer radius, the factor of safety for the hollow shaft is _____ (round off to 1 decimal place).

1.6 to 1.7

1.8 to 1.9

2.0 to 2.1

2.2 to 2.3

Category: GATE Aerospace Engineering 2019

Question 50:

In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load along the z-direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is _____ N (round off to the nearest integer).

308 to 318

309 to 319

310 to 320

311 to 321

Category: GATE Aerospace Engineering 2019

Question 51:

A thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of T = 1 kN-m. The walls have uniform thickness t = 1 mm and shear modulus G = 26 GPa. Assume that the curved portion is semi-circular. The shear stress in the wall is _____ MPa (round off to 1 decimal place).

16.5 to 17.0

17.0 to 17.5

17.5 to 18.0

18.0 to 18.5

Category: GATE Aerospace Engineering 2019

Question 52:

For a damped spring-mass system, mass m = 10 kg, stiffness k = 103 N/m, and damping coefficient c = 20 kg/s. The ratio of the amplitude of oscillation of the first cycle to that of the fifth cycle is ______ (round off to 1 decimal place).

12.3 to 12.6

12.7 to 13.0

13.1 to 13.4

13.5 to 13.8

Category: GATE Aerospace Engineering 2019

Question 53:

For the system of springs and masses shown below, k = 1250 N/m and m = 10 kg. The highest natural frequency,  of the system is _______ radians/s (round off to the nearest integer).

0 to 25

-25 to 25

-25 to -25

25 to 25

Category: GATE Aerospace Engineering 2019

Question 54:

The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine

A	has larger kinetic energy lost in the exhaust jet	B	has lower thrust power
C	is not self-starting	D	has higher thrust to weight ratio

Category: GATE Aerospace Engineering 2019

Question 55:

In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine

A	decreases, as the heat input, is lower.	B	remains unchanged.
C	increases, as the compressor needs more work input from the turbine.	D	decreases, as the thrust produced is higher.

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Answered & Marked for Review (will be considered for evaluation)

Question 1:

The maximum value of the function 𝑓(𝑥) =

x e^{- x}

(where x is real) is

A	1/e	B	$2 / e^{2}$
C	$(e^{- 1 / 2}) / 2$	D	$\infty$

Correct Answer : A

Question 2:

Vector

\vec{b}

is obtained by rotating

\vec{α}

= 𝑖̂+ 𝑗̂ by 900about 𝑘̂, where 𝑖̂, 𝑗̂and 𝑘̂ are unit vectors along the x, y and z axes, respectively.

\vec{b}

is given by

A	$\hat{i} - \hat{j}$	B	$- \hat{i} + \hat{j}$
C	$\hat{i} + \hat{j}$	D	$- \hat{i} - \hat{j}$

Correct Answer : B

Question 3:

A scalar function is given by

f (x, y) = x^{2} + y^{2} .

Take 𝑖̂ and 𝑗̂ as unit vectors along the x and y axes, respectively. At

(x, y) = (3, 4)

he direction along which 𝑓 increases the fastest is

A	$\frac{1}{5} (4 \hat{I} - 3 \hat{J})$	B	$\frac{1}{5} (3 \hat{I} - 4 \hat{J})$
C	$\frac{1}{5} (3 \hat{I} + 4 \hat{J})$	D	$\frac{1}{5} (4 \hat{I} + 3 \hat{J})$

Correct Answer : C

Question 4:

The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

A	$L T^{- 4}$	B	$L^{2} T^{- 1}$
C	$L T^{- 2}$	D	$L^{- 2} T$

Correct Answer : B

Question 5:

A	∇2𝜙 = 0	B	∇ ×𝑉 ⃗= 0
C	∇ ⋅𝑉 ⃗= 0	D	𝑢 = −𝜕𝜙/𝜕𝑦, 𝑣 = 𝜕𝜙/𝜕𝑥

Correct Answer : B

Question 6:

F or a quasi-one-dimensional isentropic supersonic flow through a diverging duct, which of the following is true in the direction of the flow?

A	Both the Mach number and the static temperature increase.	B	The Mach number increases and the static temperature decreases.
C	The Mach number decreases and the static temperature increases	D	Both the Mach number and the static temperature decrease.

Correct Answer : B

Question 7:

F or a NACA2415 airfoil of chord length c, which of the following is true?

A	Maximum camber is located at 0.2c from the leading edge.	B	Maximum thickness is located at 0.15c from the leading edge.
C	Maximum camber is 0.02c.	D	Maximum thickness is 0.05c.

Correct Answer : C

Question 8:

When a propeller airplane in ground-roll during take-off experiences headwind, which of the following statements is FALSE?

A	The drag on the airplane increases	B	The thrust from the propellers decreases
C	The wing lift increases.	D	The ground-roll distance increases.

Correct Answer : D

Question 9:

Which of the following graphs represents the response of a dynamically unstable airplane?

Correct Answer : A

Question 10:

While flying at Mach 2.0, 11 km altitude and producing the same thrust, what is the correct order from the lowest thrust specific fuel consumption (tsfc) to the highest tsfc?

A	Turbofan, Ramjet, Turbojet	B	Turbofan, Turbojet, Ramjet
C	Ramjet, Turbojet, Turbofan	D	Turbojet, Turbofan, Ramjet

Correct Answer : B

Question 11:

For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

A	CPR of an axial compressor > CPR of centrifugal compressor.	B	CPR of an axial compressor < CPR of centrifugal compressor.
C	CPR of an axial compressor = CPR of centrifugal compressor	D	CPR of any value can be attained with either an axial or a centrifugal compressor.

Correct Answer : B

Question 12:

For a beam subjected to a transverse shear load through its shear center,

A	the twist per unit length is zero.	B	the shear stress is uniform throughout the cross-section.
C	the bending stresses in the cross section are zero.	D	the shear strain is zero at the shear center.

Correct Answer : A

Question 13:

A function function 𝑓(𝑥) is defined by 𝑓(𝑥)

= \frac{1}{2} (x + |x|) .

The value of

\int_{- 1}^{1} f (x) d x

is _______ (round off to 1 decimal place).

Correct Answer : 0.5 to 0.5

Question 14:

The value of the following limit is ________ (round off to 2 decimal places).

\lim_{0 \to 0} \frac{θ - \sin θ}{θ^{3}}

Correct Answer : 0.16 to 0.17

Question 15:

Correct Answer : 10 to 10

Question 16:

The power-off glide range for an airplane with a maximum Lift to Drag ratio of 18, when the glide starts at an altitude of 4 km, is ______ km (round off to the nearest integer).

Correct Answer : 72 to 73

Question 17:

Correct Answer : 5.98 to 6.00

Question 18:

An airplane is in steady level flight with a true air speed of 50 m/s. The ambient air density and ambient pressure at the flight altitude are 0.91 kg/

m^{3}

and 7×

10^{4}

m^{2}

, respectively. At sea level, air density is 1.225 kg/

m^{3}

and ambient pressure is 1.01×

10^{5}

m^{2}

. The equivalent or indicated air speed of the airplane is ________ m/s (round off to 2 decimal places).

Correct Answer : 43.05 to 43.15

Question 19:

For the complete combustion of 1 mole of ethanol

(C_{2} H_{5} O H)

, the required number of moles of oxygen is ________.

Correct Answer : 3 to 3

Question 20:

Correct Answer : 0.70 to 0.72

Question 21:

The number of independent elastic constants for a homogeneous isotropic linear elastic material is ________.

Correct Answer : 2 to 2

Question 22:

A thin plate with Young’s modulus 210 GPa and Poisson’s ratio 0.3 is loaded as shown in the figure. The change in length along the y-direction is __________ mm (round off to 1 decimal place).

Correct Answer : 0.2 to 0.2

Question 23:

For the state of stress shown in the figure, the normal stress,

σ_{n}

, on a plane inclined at 45 degrees to the x-axis is _________MPa (round off to the nearest integer).

Correct Answer : 247 to 255

Question 24:

In the spring-mass system, shown in the figure, mass m = 3 kg and the spring stiffness k = 20 kN/m. The natural frequency of the system is _______ Hz (round off to the nearest integer).

Correct Answer : 16 to 16

Question 25:

The following system of equations 2𝑥−𝑦−𝑧=0, −𝑥+2𝑦−𝑧=0, −𝑥−𝑦+2𝑧=0

A	has no solution.	B	has a unique solution.
C	has three solutions.	D	has an infinite number of solutions

Correct Answer : D

Question 26:

Use the weak shock solution fromthe θ-β-M plot shown in Figure 2 to choose the correct option from the following.

A	$β_{1} > β_{2}$	B	$β_{1} < β_{2}$
C	$θ_{1} > θ_{2}$	D	$θ_{1} < θ_{2}$

Correct Answer : B

Question 27:

A	P only	B	Q only
C	P and R	D	Q and R

Correct Answer : D

Question 28:

Correct Answer : A

Question 29:

For real x, the number of points of intersection between the curves 𝑦=𝑥 and 𝑦=cos𝑥 is _________.

Correct Answer : 1 to 1

Question 30:

One of the eigenvalues of the following matrix is 1.

(\frac{x}{- 1} \frac{2}{3})

The other eigenvalue is _______.

Correct Answer : 2 to 2

Question 31:

The curve 𝑦=𝑓(𝑥) is such that its slope is equal to

y^{2}

for all real x. If the curve passes through (1, -1), the value of y at 𝑥= −2 is _______ (round off to 1 decimal place).

Correct Answer : 0.5 to 0.5

Question 32:

The inviscid, incompressible flow field resulting from a uniform flow past a circular the cylinder of radius R centered at the origin is given by:

u_{r} = U (1 - \frac{R^{2}}{r^{2}}) \cos θ u_{θ} = (1 + \frac{R^{2}}{r^{2}}) \sin θ

where

u_{r}

and

u_{θ}

Correct Answer : 30 to 30

Question 33:

Correct Answer : 10 to 10

Question 34:

Correct Answer : 3.5 to 3.7 OR 2.3 TO 2.5

Question 35:

The static pressure ratio across a stationary normal shock is given by

\frac{P_{2}}{P_{1}} = 1 + \frac{2 Y}{Y + 1} (M_{1}^{2} - 1),

Correct Answer : 5.95 to 6.10

Question 36:

Correct Answer : 0.24 to 0.30

Question 37:

The span-wise distribution of circulation over a finite wing of span b = 10 m is

r (y) = {\sqrt[r_{0}]{1 - (\frac{2 y}{b})}}^{2}

If Γ0=20 𝑚2/𝑠 and the free stream density and speed are 1.2 kg/m3 and 100 m/s, respectively, the total lift is __________ kN (round off to 2 decimal places).

Correct Answer : 18.00 to 19.20

Question 38:

Correct Answer : 2.06 to 2.08

Question 39:

Consider an airplane with a weight of 8000 N, wing area of 16

m^{2}

30 °

climb is _______ (round off to 2 decimal places).

Correct Answer : 1.32 to 1.35

Question 40:

The product of earth’s mass (M) and the universal gravitational constant (G) is GM = 3.986×

10^{14} m^{3} / s^{2}

Correct Answer : 2.54 to 2.62

Question 41:

A propeller driven airplane has a gross take-off weight of 4905 N with a wing area of 6.84

m^{2}

. Assume that the wingsareoperating at the maximum

C_{L}^{3 / 2} / C_{D} o f 13

Correct Answer : 1440 to 1490

Question 42:

(C_{N_{β}}

due to tail fin) is _______ (round off to 2decimal places).

Correct Answer : 0.96 to 0.96

Question 43:

For a rocket engine, the velocity ratio r is

V_{a} / V_{e} w h e r e V_{a}

V_{e}

) is ______.

Correct Answer : 1 to 1

Question 44:

Correct Answer : 1.55 to 1.60

Question 45:

Correct Answer : 88 to 90

Question 46:

The figure shows the velocity triangles for an axial compressor stage. The specific work input to the compressor stage is ____________ kJ/kg (round off to 2 decimal places).

Correct Answer : 2.50 to 2.60

Question 47:

Correct Answer : 60 to 60

Question 48:

Correct Answer : 550 to 570

Question 49:

Correct Answer : 1.8 to 1.9

Question 50:

Correct Answer : 310 to 320

Question 51:

Correct Answer : 17.0 to 17.5

Question 52:

Correct Answer : 12.3 to 12.6

Question 53:

For the system of springs and masses shown below, k = 1250 N/m and m = 10 kg. The highest natural frequency,  of the system is _______ radians/s (round off to the nearest integer).

Correct Answer : 25 to 25

Question 54:

The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine

A	has larger kinetic energy lost in the exhaust jet	B	has lower thrust power
C	is not self-starting	D	has higher thrust to weight ratio

Correct Answer : A

Question 55:

A	decreases, as the heat input, is lower.	B	remains unchanged.
C	increases, as the compressor needs more work input from the turbine.	D	decreases, as the thrust produced is higher.

Correct Answer : C

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