**GATE-2020**

**AE : Aerospace Engineering**

**General Aptitude**

**Q 1 – Q5 Carry one mark each.**

1. The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.

(A) in, of

(B) from, of

(C) during, from

(D) from, from

2. He was not only accused of theft ______ of conspiracy.

(A) rather

(B) but also

(C) but even

(D) rather than

3. Select the word that fits the analogy:

Explicit : Implicit : : Express: _______

(A) Impress

(B) Repress

(C) Compress

(D) Suppress

4. The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements is English lasting 15 seconds, as opposed to informal 5 second messages in French.

The French-speaking couple were upset at ______.

(A) the in-flight announcements being made in English.

(B) the English announcements being clearer than the French ones.

(C) the English announcements being longer than the French ones.

(D) equal importance being given to English and French.

5. A superadditive function f (∙) satisfies the following property

f(x_{1} + x_{2}) ≥ f(x_{1}) + f(x_{2})

Which of the following functions is a superadditive function for x > 1?

(A) e^{x}

(B) √x

(C) 1/x

(D) e^{−}^{x}

**Q6 – Q10 carry two marks each.**

6. The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.

Which one of the following sequences shows the correct precedence as per the given passage?

(A) East Asian crisis → subprime lending crisis → banking crisis global financial crisis.

(B) Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.

(C) Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.

(D) Global financial crisis → East Asian crisis → Banking crisis → subprime lending crisis.

7. It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

(A) 0°

(B) 7.5°

(C) 15°

(D) 22.5°

8. A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a, then the area of the shaded portion is ______.

(A) πa^{2} – a^{2 }

(B) πa^{2} – √2a^{2}

(C) πa^{2} – 2a^{2}

(D) πa^{2} – 3a^{2}

9. a, b, c are real numbers. The quadratic equation ax^{2} – bx + c = 0 has equal roots, which is β, then

(A) β = b/a

(B) β^{2} = ac

(C) β^{3} = bc/(2a^{2})

(D) b^{2} ≠ 4ac

10. The following figure shows the data of students enrolled in 5 years (2014 to 2018) for two schools P and Q. During this period, the ratio of the average number of the students enrolled in school P to the average of the difference of the number of students enrolled in schools P and Q is ______ .

(A) 8 : 23

(B) 23 : 8

(C) 23 : 31

(D) 31 : 23

**AE : Aerospace Engineering**

**Q1 – Q25 Carry one mark each.**

1. for f(x) = |x|, with df/dx denoting the derivative, the mean value theorem is not applicable because

(A) f(x) is not continuous at x = 0

(B) f(x) = 0 at x = 0

(C) df/dx is not defined at x = 0

(D) df/dx = 0 at x = 0

2. For the function and σ and μ are constants, the maximum occurs at

(A) x = σ

(B) x = σ√2π

(C) x = 2σ^{2}

(D) x = μ

3. y = Ae^{mx} + Be^{−}^{mx}, where A, B and m are constants, is a solution of

(A)

(B)

(C)

(D)

4. Which of the following statements is true about the effect of increase in temperature on dynamic viscosity of water and air, at room temperature?

(A) It increases for both water and air.

(B) It increases for water and decreases for air.

(C) It decreases for water and increases for air.

(D) It decreases for both water and air.

5. Given access to the complete geometry, surface pressure and shear stress distribution over a body placed in a uniform flow, one can estimate

(A) the moment coefficient, and the force on the body.

(B) the force coefficient, and the force on the body.

(C) the moment coefficient, and the moment on the body.

(D) the force and the moment on the body.

6. A pair of infinitely long, counter-rotating line vortices of the same circulation strength Γ are situated a distance h apart in a fluid, as shown in the figure. The vortices will

(A) rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to

(B) rotate counter-clockwise about the midpoint with the tangential velocity at the line vortex equal to

(C) translate along +y direction with velocity at the line vortex equal to

(D) translate along +y direction with velocity at the line vortex equal to

7. The streamlines of a steady two dimensional flow through a channel of height 0.2 m are plotted in the figure, where Ψ is the stream function in m^{2}/s. The volumetric flow rate per unit depth is

(A) 1.0 m^{2}/s

(B) 2.0 m^{2}/s

(C) 0.5 m^{2}/s

(D) 0.1 m^{2}/s

8. Which of the following options can result in an increase in the Mach number of a supersonic flow in a duct?

(A) Increasing the length of the duct

(B) Adding heat to the flow

(C) Removing heat from the flow

(D) Inserting a convergent-divergent section with the same cross-sectional area at its inlet and exit planes

9. Which one of the following conditions needs to be satisfied for ϕ = Ax^{4} + By^{4} + Cxy^{3} to be considered as an Airy’s stress function?

(A) A – B = 0

(B) A + B = 0

(C) A – C = 0

(D) A + C = 0

10. Consider the plane strain filed given by ε_{xx} = Ay^{2} + x, ε_{yy} = Ax^{2} + y, γ_{xy} = B x y + y . The relation between A and B needed for this strain field to satisfy the compatibility condition is

(A) B = A

(B) B = 2A

(C) B = 3A

(D) B = 4A

11. For hyperbolic trajectory of a satellite of mass m having velocity V at a distance r from the center of earth (G: gravitational constant, M: mass of earth), which one of the following relations is true?

(A)

(B)

(C)

(D)

12. For conventional airplanes, which one of the following is true regarding roll control derivative and yaw control derivative where δ_{r} is rudder deflection?

(A)

(B)

(C)

(D)

13. The ratio of exit stagnation pressure to inlet stagnation pressure across the rotating impeller of a centrifugal compressor, operating with a closed exit, is

(A) 0

(B) 1

(C) > 1

(D) 0.5

14. Which one of the following is a hypergolic propellant combination used in rocket engines?

(A) Liquid hydrogen – liquid oxygen

(B) Unsymmetrical dimethyl hydrazine – nitrogen tetroxide

(C) Rocket fuel RP-1 – liquid oxygen

(D) Liquid hydrogen – liquid fluorine

15. In aircraft engine thermodynamic cycle analysis, perfectly expanded flow in the nozzle means that the static pressure in the flow at the nozzle exit is equal to

(A) the stagnation pressure at the engine inlet.

(B) the stagnation pressure at the nozzle exit.

(C) the ambient pressure at the nozzle exit.

(D) the static pressure at the nozzle inlet.

16. Three long and slender aluminum bars of identical length are subjected to an axial tensile force. These bars have circular, triangular and rectangular cross sections. with same cross sectional area. If they yield at F_{circle}, F_{triangle} and F_{rectangle,} respectively, which one of the following is true?

(A) F_{circle} > F_{triangle } > F_{rectangle}

(B) F_{circle} < F_{triangle } < F_{rectangle}

(C) F_{triangle} > F_{circle } > F_{rectangle}

(D) F_{circle} = F_{triangle } = F_{rectangle}

17. The positive high angle-of-attack condition is obtained in a steady pull-out maneuver at the largest permissible angle-of-attack of the wing. Under this condition, at which of the following regions of the wing does the maximum tension occur?

(A) I

(B) II

(C) III

(D) IV

18. The natural frequency of the first mode of rectangular cross section contilever aluminum beam is ω rad/s. If the material and cross-section remain the same, but the length of the beam is doubled, the first mode frequency will become

(A)

(B) 4ω rad/s

(C)

(D) 16ω rad/s

19. Given the sum of squares of eigenvalues of A is

(A) tan^{2}θ

(B) 1

(C) sin^{2}θ

(D) cos^{2}θ

20. Burnout velocity of a space vehicle in a circular orbit at an angle 5 degrees above the local horizon around earth is 13.5 km/s. Tangential velocity of the space vehicle in the orbit is ________ km/s (round off to two decimal places).

21. Velocity of an airplane in the body fixed axes is given as [100 – 10 20]m/s. The sideslip angle is ______ degrees (round off to two decimal places).

22. The similarity solution for the diffusion equation, is u(x, t) = u(η), where similarity variable, _______ (round off to one decimal places).

23. Air enters the rotor of an axial compressor stage with no pre-whirl (C_{θ} = 0) and exits the rotor with whirl velocity, C_{θ} = 150 m/s. The velocity of rotor vanes, U is 200 m/s. Assuming C_{p} = 1005 J/(kg K), the stagnation temperature rise across the rotor is _______ K (round off to one decimal places).

24. A thin walled beam of constant thickness shown in the figure is subjected to a torque of 3.2 kNm. If the shear modulus is 25 GPa, the angle of twist per unit length is _____rad/m ((round off to three decimal places).

25. An airplane of mass 5000 kg is flying at a constant speed of 360 km/h at the bottom of a vertical circle with a radius of 400 m, as shown in the figure. Assuming that the acceleration due to gravity is 9.7 m/s^{2}, the load factor experienced at the center of gravity of the airplane is _______(round off to two decimal places).

**Q26 – Q55 carry two marks each.**

26. The equation where c is a constant, represents a family of

(A) exponential curves

(B) parabolas

(C) circles

(D) hyperbolas

27. A wedge shaped airfoil is placed in a supersonic flow as shown in the figure (not to scale). The corners of the wedge are at x = X_{A}, x = X_{B}, x = X_{C}, respectively.

Which one of the following represents the correct static pressure profiles along y = Y_{I} and y = Y_{II} ?

28. The value of Poisson’s ratio at which the shear modulus of an isotropic material is equal to the bulk modulus is

(A) 1/2

(B) 1/4

(C) 1/6

(D) 1/8

29. A load P is applied to the free end of a stepped cantilever beam as shown in the figure. The Young’s modulus of the material is E, and the moments of inertia of the two sections of length 2 m and 2 m are I and 3I, respectively. Ignoring transverse shear and stress concentration effects, the deflection at the point where the load is applied at the free end of the cantilever is

(A) 23/243EI

(B) I/3EI

(C) 43/3EI

(D) 23/3EI

30. The three dimensional strain-stress relation for an isotropic material, written in a general matrix form, is

A, B and C are compliances which depend on the elastic properties of the material. Which one of the following is correct?

(A)

(B)

(C)

(D)

31. For three different airplanes A, B and C, the yawing moment coefficient (C_{n}) was measured in a wind-tunnel for three settings of sideslip angle β and tabulated as

Which one of the following statements is true regarding directional static stability of the airplanes A, B and C?

(A) All three airplanes A, B and C are stable.

(B) Only airplane C is stable, while both A and B are unstable.

(C) Airplane C is unstable, A and B are stable with A being more stable than B.

(D) Airplane C is unstable, A and B are both stable with A less stable than B.

32. A closed curve is expressed in parametric form as x = a cos θ and y = b sin θ, where a = 7 m and b = 5 m. Approximating π = 22/7, which of the following is the area enclosed by the curve?

(A) 110 m^{2}

(B) 74 m^{2}

(C) 35 m^{2}

(D) 144 m^{2}

33. An axial compressor is designed to operate at a rotor speed of 15000 rpm and an inlet stagnation temperature of 300 K. During compressor testing, the inlet stagnation temperature of the compressor measured was 280 K. What should be the rotor speed for the compressor to develop the same performance characteristics during this test as in the design condition?

(A) 14000 rpm

(B) 14491 rpm

(C) 15526 rpm

(D) 16071 rpm

34. For the state of stress shown in the figure, which one of the following represents the correct free body diagram showing the maximum shear stress and the associated normal stresses?

35. In the equation AX = B, where A is an orthogonal matrix, the sum of the unknowns, x + y +z = ______ (round off to one decimal place).

36. If is evaluated numerically using trapezoidal rule with four intervals, the difference between the numerically evaluated value and the analytical value of the integral is equal to ________ (round off to three decimal places).

37. The table shows the lift characteristics of an airfoil at low speeds. The maximum lift coefficient occurs at 16 degrees.

Using Prandtl-Glauert rule, the lift coefficient for the airfoil at the angle of attack of 6 degrees free stream Mach number of 0.6 is _______(round off to two decimal places).

38. A low speed uniform flow U_{0} is incident on an airfoil of chord c. In the figure, the velocity profile some distance downstream of the airfoil is idealized as shown for section B. The static pressure at sections A and B is the same. The drag coefficient of the airfoil is ______(round off to three decimal places).

39. An oblique shock is inclined at an angle of 35 degrees to the upstream flow of velocity 517.56 m/s. The deflection of the flow due to this shock is 5.75 degrees and the temperature downstream is 182.46 K. Assume the gas constant R = 287 J/(Kg K), specific heat ratio γ = 1.4, and specific heat at constant pressure C_{p} = 1005 J/(Kg K). Using conservation relations, the Mach number of the upstream flow can be obtained as ______(round off to ne decimal place).

40. The thickness of a laminar boundary layer (δ) over a flat plate is, where x is measured from the leading edge along the length of the plate. The velocity profile within the boundary layer is idealized as varying linearly with y. For freestream velocity of 3 m/s and kinematic viscosity of 1.5 × 10^{−}^{5} m^{2}/s, the displacement thickness at 0.5 m fro the leading edge is _______ mm (round off to two decimal places).

41. A wing of 15 m span with elliptic lift distribution is generating a lift of 80 kN at a speed of 90 m/s. The density of surrounding air is 1.2 kg/m^{3} . the induced angle of attack at this condition is ______ degrees (round off to two decimal places).

42. A solid circular shaft, made of ductile material with yield stress σ_{Y} = 280 MPa, is subjected to a torque of 10 kNm. Using the Tresca failure theory, the smallest radius of the shaft to avoid failure is _______ cm (round off to two decimal places).

43. The ratio of tangential velocities of a planet at the perihelion and the aphelion from the sun is 1.0339. Assuming that the planet’s orbit around the sun is planar and elliptic, the value of eccentricity of the orbit is _________(round off to three decimal places).

44. The eigenvalues for phugoid mode of a general aviation airplane at a stable cruise flight condition at low angle of attack are λ_{1, 2} = −02 ± 0.25. If the acceleration due to gravity is 9.8 m/s^{2}, the equilibrium speed of the airplane is ________m/s (round off to two decimal places).

45. For a general aviation airplane with tail efficiency η = 0.95, horizontal tail volume ratio V_{H} = 0.453, downwash angle slope dε/dα = 0.35, wing lift curve slope horizontal tail lift curve slope shift in neutral point location as a percentage of mean aerodynamic chord is ______(round off to two decimal places).

46. A single engine, propeller driven, general aviation airplane is flying in cruise at sea-level condition (density of air at sea-level is 1.225 kg/m^{3}) with speed to cover maximum range. For drag coefficient C_{D} = 0.025 + 0.049 C_{L}^{2} and wing loading W/S = 9844 N/m^{2}, the speed of the airplane is ______m/s (round off to one decimal place).

47. The design flight Mach number of an ideal ramjet engine is 2.8. The stagnation temperature of air at the exit of the combustor is 2400 K. Assuming the specific heat ratio of 1.4 and gas constant of 287 J/(kg K), the velocity of air at the exit of the engine is _______ m/s (round off to one decimal place).

48. The operating conditions of an aircraft engine combustor are as follows.

The rat of total enthalpy of air entering the combustor = 28.94 MJ/s

The rate of total enthalpy of air leaving the combustor = 115.42 MJ/s.

Mass flow rate of air = 32 kg/s.

Air to fuel mass ratio = 15.6.

Lower heating value of the fuel = 46 MJ/kg.

The efficiency of the combustor is _______% (round off to two decimal places.)

49. The figure shows the T-S diagram for an axial turbine stage.

Assuming specific heat ratio of 1.33 for the hot gas, the isentropic efficiency of the turbine stage is ______% (round off to two decimal places).

50. A rocket engine has a sea level specific impulse of 210 s and a nozzle throat area of 0.005 m^{2}. While testing at sea level conditions, the characteristic velocity and pressure for the thrust chamber are 1900 m/s and 50 bar, respectively. Assume the acceleration due to gravity to be 9.8 m/s^{2}. The thrust produced by the rocket engine is _______kN (round off to one decimal place).

51. A critically damped single degree of freedom spring-mass-damper system used in a door closing mechanism becomes overdamped due to softening of the spring with extended use. If the new damping ratio (ξ_{new}) for overdamped condition is 1.2, the ratio of the original spring stiffness to the new spring stiffness (k_{org}/k_{new}), assuming that the other parameters remain unchanged, is _______(round off to two decimal places).

52. The two masses of the two degree of freedom system shown in the figure are given initial displacement of 2 cm (x_{1}) and 1.24 cm (x_{2}). The system starts to vibrate in the first mode. The first mode shape of this system is ϕ_{1} = [1 a]^{T}, where a = _______(round off to two decimal places).

53. As shown in the figure, a beam of length 1 m is rigidly supported at one end and simply supported at the other. Under the action of a uniformly distributed load of 10 N/m, the magnitude of the normal reaction force at the simply supported end is _______N (round off to two decimal places).

54. An airplane of mass 4000 kg and wing reference area 25 m^{2} flying at sea level has a maximum lift coefficient of 1.65. Assume density of air as 1.225 kg/m^{3} and acceleration due to gravity as 9.8 m/s^{2}. Using a factor of safety of 1.25 to account for additional unsteady lift during a sudden pull-up, the speed at which the airplane reaches a load factor of 3.2 is _________m/s (round off to two decimal places).

55. A Pitot tube mounted on the wing tip of an airplane flying at an altitude of 3 k measures a pressure of 0.72 bar, and the outside air temperature is 268.66 K. Take the sea level condition as, pressure = 1.01 bar, temperature = 288.16 K, and density = 1.225 kg/m^{3}. The acceleration due to gravity is 9.8 m/s^{2} and the gas constant is 287 J/(kg K). Assuming standard atmosphere, the equivalent airspeed for this airplane is _____m/s (round off to two decimal place).

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