GATE 2015 Question Paper with Answer Keys for Aerospace Engineering (AE) - Grad Plus

# GATE 2015 Question Paper with Answer Keys for Aerospace Engineering (AE)

Q. 1 – Q. 25 carry one mark each.
Q.1 The partial differential equation $latex \frac{\partial u}{\partial t}+\frac{\partial{\displaystyle\frac{u^2}2}}{\partial x}=0$ is
(A) linear and first order

(B) linear and second order

(C) non-linear and first order

(D) non-linear and second order

Ans:-(C) non-linear and first order

Q.2 The system of equations for the variables x and y
a x + b y = e
c x + d y = f
has a unique solution only if

(A) a d − b c ≠ 0

(B) a c − b d ≠ 0

(C) a + c ≠ b + d

(D) a − c ≠ b − d

Ans:-(A) a d − b c ≠ 0

Q.3 A linear mass-spring-dashpot system is over-damped. In free vibration, this system undergoes

(A) non-oscillatory motion

(B) random motion

(C) oscillatory and periodic motion

(D) oscillatory and non-periodic motion

Ans:-(A) non-oscillatory motion

Q.4 A cantilever with thin-walled channel cross section is subjected to a lateral force at its shear center. The cantilever undergoes

(A) bending without twisting

(B) bending and twisting

(C) neither bending nor twisting

(D) twisting without bending

Ans:-(A) bending without twisting

Q.5 The two non-zero principal stresses at a point in a thin plate are $latex \sigma_1= 25 M P a$ and $latex \sigma_2= -25 M P a$. The maximum shear stress (in M P a) at this point is _.

Ans:-24.99 to 25.01

Q.6 Consider the density and altitude at the base of an isothermal layer in the standard atmosphere to be \rho_1 and h_1, respectively. The density variation with altitude (ρ versus h) in that layer is governed by (R: specific gas constant, T: temperature, g_o : acceleration due to gravity at sea level)

(A) $latex \frac\rho{\rho_1}=e^{-\left\frac{g_0}{RT}\right}$

(B) $latex \frac\rho{\rho_1}=e^{-\left\frac{g_0}{RT}\right}$

(C) $latex \frac\rho{\rho_1}=e^{-\left\frac{RT}{g_0}\right}$

(D) $latex \frac\rho{\rho_1}=e^{-\left\frac{RT}{g_0}\right}$

Ans:-(A) $latex \frac\rho{\rho_1}=e^{-\left\frac{g_0}{RT}\right}$

Q.7 For constant free stream velocity and density, a change in lift for a large aspect ratio straight wing, with thin cambered airfoil section at small angles of attack, leads to

(A) a shift of the aerodynamic center and no shift of the center of pressure

(B) a shift of the center of pressure and no shift of the aerodynamic center

(C) shift of both the aerodynamic center and the center of pressure

(D) no shift either of the aerodynamic center or of the center of pressure

Ans:-(B) a shift of the center of pressure and no shift of the aerodynamic center

Q.8 Which one of the following modes of a stable aircraft has non-oscillatory response characteristics?

(A) Short period

(B) Phugoid

(C) Dutch roll

(D) Spiral

Ans:-(D) Spiral

Q.9 As a candidate for a vertical tail, which one of the following airfoil sections is appropriate?

(A) NACA 0012

(B) NACA 2312

(C) NACA 23012

(D) Clarke Y profile

Ans-(A) NACA 0012

Q.10 The primary purpose of a trailing edge flap is to

(A) avoid flow separation

(B) increase $latex C_{l,max}$

(C) reduce wave drag

(D) reduce induced drag

Ans:-(B) increase $latex C_{l,max}$

Q.11 Which one of the following aero engines has the highest propulsive efficiency?

(A) Turbojet engine without afterburner

(B) Turbojet engine with afterburner

(C) Turbofan engine

(D) Ramjet engine

Ans:-(C) Turbofan engine

Q.12 The stoichiometric fuel-to-air ratio in an aircraft engine combustor varies with the compressor
pressure ratio as follows:

(A) increases linearly

(B) decreases linearly

(C) is independent

(D) increases nonlinearly

Ans-(C) is independent

Q.13 A rocket engine produces a total impulse of 112 kN.s in a burn time period of 3.5 minutes with a propellant mass flow rate of 0.25 kg/s. The effective exhaust velocity (in m/s) of gas ejecting from the engine is _.

Ans-2131.1 to 2139.1

Q.14  The function $latex y=x^3-x$  has

(A) no inflection point

(B) one inflection point

(C) two inflection points

(D) three inflection points

Ans:-(B) one inflection point

Q.15  A 0.5 kg mass is suspended vertically from a point fixed on the Earth by a spring having a stiffness of 5 N/mm. The static displacement (in mm) of the mass is _.

Ans:-0.97 to 1.01

Q.16 A slender structure is subjected to four different loading cases (I, II, III and IV) as shown below (Figures not to scale). Which pair of cases results in identical stress distribution at section S – S located far away from both ends?

(A) I and II

(B) II and III

(C) III and IV

(D) IV and I

Ans: (A) I and II

Q.17 An aircraft in level and unaccelerated flight with a velocity of $latex v_\infty=300m/s$ requires a power of $latex 9\times10^6N$. If the aircraft weighs $latex 1.5\times10^5N$ , the lift-to-drag ratio $latex L\div N$ is _.

Ans:-4.9 to 5.1

Q.18 The percentage change in the lift-off distance for a 20 % increase in aircraft weight is _.

Ans:-43.9 to 44.1

Q.19 Consider a monoplane wing and a biplane wing with identical airfoil sections, wingspans and incidence angles in identical conditions in a wind tunnel. As compared to the monoplane, the biplane experiences

(A) a higher lift and a higher drag

(B) a higher lift and a lower drag

(C) a lower lift and a lower drag

(D) a lower lift and a higher drag

Ans:-(A) a higher lift and a higher drag

Q.20 A statically stable trimmed aircraft experiences a gust and the angle of attack reduces momentarily. As a result, the center of pressure of the aircraft

(A) shifts forward

(B) shifts rearward

(C) does not shift

(D) coincides with the neutral point

Ans:-(A) shifts forward

Q.21 Consider a wing of elliptic planform, with its aspect ratio $latex AR\rightarrow\infty$. Its lift-curve slope, $latex \frac{\partial CL}{\partial\alpha}$ = _.

Ans:-6.27 to 6.29

Q.22 An ideal gas in a reservoir has a specific stagnation enthalpy of h0. The gas is isentropically expanded to a new specific stagnation enthalpy of  $latex \frac{h_0}2$ and velocity u. The flow is one-dimensional and steady. Then $latex \frac{u^2}{h_0}$ = _.

Ans:-0.99 to 1.01

Q.23 The Reynolds number, Re is defined as $latex \frac{U_\infty L}v$ where L is the length scale for a flow, $latex U_\infty$ is its reference velocity and ν is the coefficient of kinematic viscosity. In the laminar boundary layer approximation, comparison of the dimensions of the convection term $latex u\frac{\partial u}{\partial x}$ and the viscous term $latex v\frac{\partial^2u}{\partial x^2}$  leads to the following relation between the boundary layer thickness δ and Re :

(A) $latex \partial\;\alpha\;\sqrt{R_e}$

(B)$latex \partial\;\alpha\;\;\frac1{\sqrt{R_e}}$

(C)$latex \partial\;\alpha\;R_e$

(D)$latex \partial\;\alpha\;\;\frac1{R_e}$

Ans:-(B)$latex \partial\;\alpha\;\;\frac1{\sqrt{R_e}}$

Q.24 Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the following components – intake, compressor, turbine and nozzle – are denoted by ηi, ηc, ηtand ηn, respectively. Which one of the following is correct?

(A) ηi    ηcη < ηn
(B) ηt   ηi <   ηc  ηn
(C) ηc   ηt<   η i ηn
(D) ηc    ηiη< ηn

Ans:-(C) ηc   ηt<   η i ηn

Q.25 A rocket nozzle is designed to produce maximum thrust at an altitude, H = 8 km from the sea level. The nozzle operates in

(A) under-expanded condition for H> 8 km

(B) under-expanded condition for H < 8 km

(C) sonic exit condition for H> 8 km

(D) unchoked condition for H<8 km

Ans:-(A) under-expanded condition forH > 8 km

Q.26 In the solution of  $latex \frac{\partial^2y}{\partial x^2}-2\frac{\partial y}{\partial x}+y=-1$, if the values of the integration constants are identical and one of the initial conditions is specified as y(0)=1, the other initial condition y'(0)=_.

Ans:-1.9 to 2.1

Q.27 For x > 0, the general solution of the differential equation  $latex \frac{\partial y}{\partial x}=1-2y$ asymptotically approaches _.

Ans:-0.49 to 0.51

Q.28 For a parabola defined by  y = ax2 + bx + c , a≠0 ,the coordinates (x,y) of the extremum are

(A)$latex \left(\frac{-b}{2a}+\frac{\sqrt{b^2-4ac}}{2a},0\right)$

(B)$latex \left(\frac{-b}{2a},\frac{-b^2+4ac}{2a}\right)$

(C)$latex \left(\frac{-b}{2a},\frac{-b^2+4ac}{4a}\right)$

(D) (0,c)

Ans:-(C)$latex \left(\frac{-b}{2a},\frac{-b^2+4ac}{4a}\right)$

Q.29 The 2-D stress state at a point P in the x-y coordinate system is  $latex \begin{bmatrix}60&50\50&-40\end{bmatrix}\;MPa$ The magnitude of the tangential stress (in MPa) on a surface normal to the x-axis at P is _.

Ans:-49.99 to 50.01

Q.30 A cube made of a linear elastic isotropic material is subjected to a uniform hydrostatic pressure of 100 N/mm^2. Under this load, the volume of the cube shrinks by 0.05%. The Young’s modulus of the material, E = 300 GPa . The Poisson’s ratio of the material is _.

Ans: 0.24 to 0.26

Q.31 A massless cantilever beam PQ has a solid square cross section (10 mm × 10 mm). This beam is subjected to a load W through a rigid massless link at the point Q, as shown below (figure not to scale). If the Young’s modulus of the material E = 200 GPa , the deflection (in mm) at point Q is _.

Ans:-5.45 to 5.60

Q.32 An aircraft, with a wing loading \frac Ws=500\;N/m^2, is gliding at (L/D) max  = 10  and C L= 0.69. Considering the free stream density \rho_\infty=0.9\;kg/m^3, the equilibrium glide speed (in m/s) is _.

Ans:-39.5 to 40.5

Q.33 For a thin flat plate at 2 degrees angle of attack, the pitching moment coefficient about the trailing edge is _.

Ans:-0.15 to 0.18

Q.34 A satellite is to be transferred from its geostationary orbit to a circular polar orbit of the same radius through a single impulse out-of-plane maneuver. The magnitude of the change in velocity required is __ times the magnitude of the escape velocity.

Ans:-0.99 to 1.01

Q.35 A planetary probe is launched at a speed of 200 km/s  and at a distance of  71,400 km from the mass center of its nearest planet of mass 1.9×1028kg . The universal gravitational constant, G = 6.67 × 10-11 m3/kg s2 . The ensuing path of the probe would be

(A) elliptic

(B) hyperbolic

(C) parabolic

(D) circular

Ans:-(B) hyperbolic

Q.36 The velocity profile of an incompressible laminar boundary layer over a flat plate developing under constant pressure is given by $latex \frac{u(y)}{U_\infty}=\frac{3y}{2\partial}-\frac12\left(\frac y\partial\right)^3$ .The freestream velocity U= 10 m/s and the dynamic viscosity of the fluid µ = 1.8× 10-5 kg/ms.At a streamwise station where the boundary layer thickness ∂ = 5mm ,the wall shear stress is _×10 -3 Pa.

Ans:-53.9 to 54.1

Q.37 The Pitot tube of an aircraft registers a pressure p0 = 54051 N/m2. The static pressure, density and the ratio of specific heats of the freestream are p= 45565 N/m 2, ρ= 0.6417 kg/m3 and γ = 1.4, respectively. The indicated airspeed (in m/s) is

(A) 157.6

(B) 162.6

(C) 172.0

(D) 182.3

Ans:-(A) 157.6

Q.38 Consider a NACA 0012 aerofoil of chord c in a freestream with velocity V at a non-zero positive angle of attack α . The average time-of-flight for a particle to move from the leading edge to the trailing edge on the suction and pressure sides are t1 and t2, respectively. Thin aerofoil theory yields the velocity perturbation to the freestream as $latex V_\infty\frac{\left(1+\cos\theta\right)\alpha}{\sin\theta}$ on the suction side and as $latex -V_\infty\frac{\left(1+\cos\theta\right)\alpha}{\sin\theta}$ on the pressure side, where θ corresponds to the chordwise position, $latex x=\frac c2\left(1-\cos\theta\right)$ .Then t2−t1 is

(A)$latex \frac{8\mathrm{παc}}{V_\infty\left(4-\mathrm\pi^2\mathrm\alpha^2\right)}\$

(B)0

(C)$latex \frac{4\mathrm{παc}}{V_\infty\left(4-\mathrm\pi^2\mathrm\alpha^2\right)}\$

(D)$latex \frac{8\mathrm{παc}}{V_\infty\left(4-\mathrm\pi^2\mathrm\alpha^2\right)}\$

Ans:-(C)$latex \frac{4\mathrm{παc}}{V_\infty\left(4-\mathrm\pi^2\mathrm\alpha^2\right)}\$

Q.39 Air enters an aircraft engine at a velocity of 180 m/s with a flow rate of 94 kg /s. The engine combustor requires 9.2 kg /s of air to burn 1 kg /s of fuel. The velocity of gas exiting from the engine is 640 m/s. The momentum thrust (in N) developed by the engine is

(A) 43241

(B) 45594

(C) 47940

(D) 49779

Ans:-(D) 49779

Q.40 A solid rocket motor is designed with a cylindrical end-burning propellant grain of length 1 m and diameter 32cm . The density of the propellant grain is 1750 kg/m 3. The specific impulse of the motor is 190 s and the acceleration due to gravity is 9.8 m/s2. If the propellant burns for a period of 150 s, then the thrust (in N ) produced by the rocket motor is __.

Ans:-1742 to 1752

Q.41- A liquid propellant rocket has the following component masses:

Mass of fuel  =470 kg
Mass of oxidizer  =1170 kg
Mass of structures  =150 kg
Mass of guidance systems =20kg

The effective exhaust velocity is 3136 m/s. The velocity increment (in km /s) of the rocket at burnout, while operating in outer space, is __.

Ans:-5.42 to 5.48

Q.42 If all the eigenvalues of a matrix are real and equal, then

(A) the matrix is diagonalizable

(B) its eigenvectors are not necessarily linearly independent

(C) its eigenvectors are linearly independent

(D) its determinant is necessarily zero

Ans:-(B) its eigenvectors are not necessarily linearly independent

Q.43 The value of the integral $latex \int_1^2\left(4x^3+3x^2+2x+1\right)\operatorname dx\$ evaluated numerically using Simpson’s rule with one step is

(A) 26.5

(B) 26

(C) 25.5

(D) 25.3

Ans:-(B) 26

Q.44 The following data is for a single degree of freedom system with viscous damping:
mass,  m= 10 ????g ;  spring stiffness, k = 2.25 N /mm;
damping coefficient,c = 0.0125 N s/mm.
The ratio of any two successive amplitudes is _.

Ans:-1.27 to 1.32

Q.45 Determine the correctness or otherwise of the following assertion [a] and reason [r]:

Assertion [a]: Aircraft directional static stability can be improved by moving the vertical tail rearward.

Reason [r]: Moving the vertical tail rearward increases the moment arm from the tail aerodynamic center to the aircraft center of gravity.

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(C) Both [a] and [r] are false

(D) [a] is true and [r] is false

Ans:-(A) Both [a] and [r] are true and [r] is the correct reason for [a]

Q.46 Consider a 2-D blunt body in an incompressible fluid stream. The flow is irrotational and can be modeled as a linear combination of a uniform flow and a line source (Rankine half body) as shown below. Let s be the distance of the line source from the front stagnation point. Let d be the upstream distance from the stagnation point to the streamwise location (labeled below as P) where the oncoming stream reaches 90% of its undisturbed velocity. Then d/s= _.

Ans:-8.9 to 9.1

Q.47 Following are the operational parameters of an axial compressor stage:
Air mass flow rate  = 24 kg /s
Static temperature of air at the rotor inlet  = 278 k
Velocity of air at the rotor inlet (zero whirl velocity)  = 140 m/s
Work done on the compressor rotor  = 734 kJ
Isentropic efficiency of the compressor stage = 0.86
Ratio of specific heats = 1.4
Specific heat at constant pressure  = 1.005 kJ/kgK

The stagnation pressure ratio across the axial compressor stage is __.

Ans:-1.33 to 1.40

Q.48 The thin rectangular tube shown below is made of a material with shear modulus, G = 80 GPa . The shear flow is calculated based on the mid-thickness dimensions. If the free end is allowed to twist no more than 0.0727 rad, then the maximum torque (in Nm) which the tube can be subjected to at its free end is _.

Ans:-990 to 1020

Q.49 A 200 mm long simply-supported column has a 5 mm × 10 mm rectangular cross section. The Young’s modulus of the material, E= 200 GPa . Assuming a factor of safety of 2.5 corresponding to the buckling load, the maximum load (in N) the column can support in compression is _.

Ans:-2046 to 2075

Q.50 For a level flight at cruise altitude,  CD = 0.018  with drag coefficient at zero lift, C D,0 = 0.015. For a 30° climb at the same altitude and speed,  CD = _ ×10 -3.

Ans:-17.2 to 17.3

Q.51 An aircraft is flying with inertial ground and wind speeds of $latex \overrightarrow{v_g}^b$ =(100,5,5)m/s and $latex \overrightarrow{v_w}^b$ = (0,-5,-10) m/s , respectively, as expressed in the body frame. The corresponding sideslip angle (in degrees) is

(A) 0

(B) 5.65

(C) 8.49

(D) 9.54

Ans:-(B) 5.65

Q.53 For a normal shock, the relation between the upstream Mach number(M1) and the downstream Mach number(M 2) is given by $latex M_2^2=\frac{\left(\gamma-1\right)M_1^2+2}{2\gamma M_1^2+1-\gamma}$. For an ideal gas with γ=1.4, the asymptotic value of the downstream Mach number is _.

Ans:-0.37 to 0.39

Q.54 A centrifugal air compressor is operating at the following conditions:
Inlet stagnation temperature   =288K
Inlet stagnation pressure  =1.15 bar
Exit stagnation temperature  =454 K
Exit stagnation pressure = 4.8 bar
The energy loss due to non-isentropic compression per unit mass of flowing air (ratio of specific heats, γ=1.4and specific heat at constant pressure, CP=1.005 kJ/kgk) is __ kJ/kg.

Ans:- 20.5 to 21.3

Q.55 Hot gas (ratio of specific heats, γ=1.33) at a temperature of 1450K  enters into an axial turbine and expands isentropically. Assume that the kinetic energy of the gas across the turbine is negligible. If the ratio of inlet to outlet pressures of the turbine is 9.5, then the temperature (in K) of gas exiting the turbine is _.

Ans:-824.0 to 832.1

End of Question Paper

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