Machine-translated by Google. Questions are authored in English.
Top

GATE AE 2022: Aerospace Engineering

  • Paper code: AE
  • Language: English
  • 44 pages
GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 1 of 44
Page 1 of 44
Text of page 1
GATE 2022 Aerospace Engineering (AE)
GATE 2022 General Aptitude
Q.1 – Q.5 Carry ONE mark each.


Q.1        Writing too many things on the ________ while teaching could make the
           students get _________.


      (A) bored / board


      (B) board / bored


      (C) board / board


      (D) bored / bored




                                      Page 1 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 2 of 44
Page 2 of 44
Text of page 2
GATE 2022 Aerospace Engineering (AE)




Q.2         Which one of the following is a representation (not to scale and in bold) of all

            values of x satisfying the inequality 2 − 5x ≤ −          on the real number

            line?


      (A)




      (B)




      (C)




      (D)




                                         Page 2 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 3 of 44
Page 3 of 44
Text of page 3
GATE 2022 Aerospace Engineering (AE)

Q.3       If f(x) = 2 ln √e , what is the area bounded by f(x) for the interval [0, 2]
          on the x-axis?


      (A) 1
          2


      (B) 1


      (C) 2


      (D) 4




                                      Page 3 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 4 of 44
Page 4 of 44
Text of page 4
GATE 2022 Aerospace Engineering (AE)




Q.4        A person was born on the fifth Monday of February in a particular year.

           Which one of the following statements is correct based on the above
           information?


      (A) The 2nd February of that year is a Tuesday


      (B) There will be five Sundays in the month of February in that year


      (C) The 1st February of that year is a Sunday


      (D) All Mondays of February in that year have even dates




                                       Page 4 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 5 of 44
Page 5 of 44
Text of page 5
GATE 2022 Aerospace Engineering (AE)

Q.5




            Which one of the groups given below can be assembled to get the shape that is
            shown above using each piece only once without overlapping with each other?
            (rotation and translation operations may be used).


      (A)




      (B)




      (C)




      (D)




                                         Page 5 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 6 of 44
Page 6 of 44
Text of page 6
GATE 2022 Aerospace Engineering (AE)


Q. 6 – Q. 10 Carry TWO marks each.




Q.6        Fish belonging to species S in the deep sea have skins that are extremely black
           (ultra-black skin). This helps them not only to avoid predators but also sneakily
           attack their prey. However, having this extra layer of black pigment results in
           lower collagen on their skin, making their skin more fragile.

           Which one of the following is the CORRECT logical inference based on the
           information in the above passage?


      (A) Having ultra-black skin is only advantageous to species S


      (B) Species S with lower collagen in their skin are at an advantage because it helps
           them avoid predators


      (C) Having ultra-black skin has both advantages and disadvantages to species S


      (D) Having ultra-black skin is only disadvantageous to species S but advantageous
           only to their predators




                                        Page 6 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 7 of 44
Page 7 of 44
Text of page 7
GATE 2022 Aerospace Engineering (AE)


Q.7       For the past m days, the average daily production at a company was 100 units
          per day.

          If today’s production of 180 units changes the average to 110 units per day,
          what is the value of m?


      (A) 18


      (B) 10


      (C) 7


      (D) 5




                                       Page 7 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 8 of 44
Page 8 of 44
Text of page 8
GATE 2022 Aerospace Engineering (AE)



Q.8        Consider the following functions for non-zero positive integers, p and q.

           f(p, q) = p × p × p × … … … × p = p ;          f(p, 1) = p
                                terms



                                   ⫶(             )
                                 ⫶⫶
           g(p, q ) = p                               ;   g(p, 1) = p

           Which one of the following options is correct based on the above?


      (A) f(2,2) = g(2,2)


      (B) f(g(2,2), 2) < f 2, g(2,2)


      (C) g(2,1) ≠ f(2,1)


      (D) f(3,2) > g(3,2)




                                        Page 8 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 9 of 44
Page 9 of 44
Text of page 9
GATE 2022 Aerospace Engineering (AE)



Q.9        Four cities P, Q, R and S are connected through one-way routes as shown in the
           figure. The travel time between any two connected cities is one hour. The boxes
           beside each city name describe the starting time of first train of the day and their
           frequency of operation. For example, from city P, the first trains of the day start
           at 8 AM with a frequency of 90 minutes to each of R and S. A person does not
           spend additional time at any city other than the waiting time for the next
           connecting train.

           If the person starts from R at 7 AM and is required to visit S and return to R,
           what is the minimum time required?




      (A) 6 hours 30 minutes


      (B) 3 hours 45 minutes


      (C) 4 hours 30 minutes


      (D) 5 hours 15 minutes




                                         Page 9 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 10 of 44
Page 10 of 44
Text of page 10
GATE 2022 Aerospace Engineering (AE)



Q.10        Equal sized circular regions are shaded in a square sheet of paper of 1 cm side
            length. Two cases, case M and case N, are considered as shown in the figures
            below. In the case M, four circles are shaded in the square sheet and in the case
            N, nine circles are shaded in the square sheet as shown.

            What is the ratio of the areas of unshaded regions of case M to that of case N?




                                     case M                 case N


       (A) 2 : 3


       (B) 1 : 1


       (C) 3 : 2


       (D) 2 : 1




                                        Page 10 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 11 of 44
Page 11 of 44
Text of page 11
GATE 2022 Aerospace Engineering (AE)
Q.11 – Q.35 Carry ONE mark Each



Q.11    The equation of the straight line representing the tangent to the curve y = x at
        the point (1,1) is


(A)     y = 2x − 2


(B)     x = 2y − 1


(C)     y − 1 = 2(x − 1)


(D)     x − 1 = 2(y − 1)




Q.12    Let ı̂, ȷ̂, and k be the unit vectors in the x, y and z directions, respectively. If the
        vector ı̂ + ȷ̂ is rotated about positive k by 135o, one gets


(A)     −ı̂


(B)     −ȷ̂


(C)           1
        −         ȷ̂
            √2

(D)     −√2ı̂




                                         Page 11 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 12 of 44
Page 12 of 44
Text of page 12
GATE 2022 Aerospace Engineering (AE)



Q.13    Let x be a real number and i = √−1. Then the real part of cos(ix) is


(A)     sinh x


(B)     cosh x


(C)     cos x


(D)     sin x




Q.14    The point of maximum entropy on a Fanno-curve in a Temperature-Entropy (T-s)
        diagram represents the


(A)     maximum flow Mach number


(B)     minimum flow Mach number


(C)     sonic Mach number


(D)     normal shock in the flow




                                      Page 12 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 13 of 44
Page 13 of 44
Text of page 13
GATE 2022 Aerospace Engineering (AE)



Q.15    Consider a two-dimensional potential flow over a cylinder. If the freestream speed
        is U , the maximum speed on the cylinder surface is


(A)     U
         2

(B)     3U
         2

(C)     2U


(D)     4U
         3




                                      Page 13 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 14 of 44
Page 14 of 44
Text of page 14
GATE 2022 Aerospace Engineering (AE)



Q.16    Consider steady, two-dimensional, incompressible flow over a non-porous flat
        plate as shown in the figure. For the control volume PQRS, the speed, u , at
        section PQ is uniform and the speed at section RS is given by u(y) = A        ,
        where n is a positive integer. The value of A for which the flow through section
        PS will vanish is:




                                                                                  n
                                            h                               y
              u                                              u ( y )  A0  
                                                                           h




(A)      u
        n+1

(B)     u (n + 1)


(C)      u
        n−1

(D)     u (n − 1)




                                      Page 14 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 15 of 44
Page 15 of 44
Text of page 15
GATE 2022 Aerospace Engineering (AE)



Q.17    Consider the velocity distribution, u(y) shown in the figure. For two adjacent fluid
        layers L1 and L2, the viscous force exerted by L1 on L2 is




(A)     to the right


(B)     to the left


(C)     vertically upwards


(D)     vertically downwards




                                       Page 15 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 16 of 44
Page 16 of 44
Text of page 16
GATE 2022 Aerospace Engineering (AE)

Q.18 The service ceiling of an airplane is the altitude


(A)    at which maximum rate of climb is 100 m/min


(B)    beyond which theoretically the airplane cannot sustain level flight


(C)    at which maximum power is required for flight


(D)    at which maximum rate of climb is 100 ft/min




Q.19    Regarding the horizontal tail of a conventional airplane, which one of the
        following statements is true?


(A)     It contributes to C   <0


(B)     It makes C     =0


(C)     It makes C     >0


(D)     It makes C    > 0 and C     >0




                                       Page 16 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 17 of 44
Page 17 of 44
Text of page 17
GATE 2022 Aerospace Engineering (AE)



Q.20   A beam with a symmetrical T-shaped cross-section, as shown in the figure, is
       subjected to pure bending. The maximum magnitude of the normal stress is realised:




(A)    only at the top fibres of the cross-section


(B)    only at the bottom fibres of the cross-section


(C)    both at the top and bottom fibres of the cross-section


(D)    only at the centroidal fibres of the cross-section




                                         Page 17 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 18 of 44
Page 18 of 44
Text of page 18
GATE 2022 Aerospace Engineering (AE)



Q.21 A three-member truss is simply supported at Q and R, and loaded at P by a
     horizontal force F as shown. The force in QR is




(A)   0


(B)   F (tensile)


(C)
            (compressive)
       √


(D)   √2F (tensile)




                                     Page 18 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 19 of 44
Page 19 of 44
Text of page 19
GATE 2022 Aerospace Engineering (AE)



Q.22   The closed thin-walled rectangular channel shown in figure (i) is opened by
       introducing a sharp cut at the center of the bottom edge, as shown in figure (ii).
       Which one of the following statements is correct?




(A)    Centroids of (i) and (ii) coincide while shear centers do not


(B)    Shear centers of (i) and (ii) coincide while centroids do not


(C)    Both centroids and shear centers of (i) and (ii) coincide


(D)    Neither centroids nor shear centers of (i) and (ii) coincide




Q.23    The region of highest static temperature in a rocket engine and the region of
        highest heat flux are ____________, respectively.


(A)     nozzle throat and nozzle entry


(B)     combustion chamber and nozzle throat


(C)     nozzle exit and nozzle throat


(D)     nozzle throat and combustion chamber




                                         Page 19 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 20 of 44
Page 20 of 44
Text of page 20
GATE 2022 Aerospace Engineering (AE)



Q.24    If a, b, ĉ are three mutually perpendicular unit vectors, then a ⋅ b × ĉ can take
        the value(s)


(A)     0


(B)     1


(C)     -1


(D)     ∞




Q.25    Across an oblique shock wave in a calorifically perfect gas,


(A)     the stagnation enthalpy changes


(B)     the stagnation entropy changes


(C)     the stagnation temperature changes


(D)     the speed of sound changes




                                       Page 20 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 21 of 44
Page 21 of 44
Text of page 21
GATE 2022 Aerospace Engineering (AE)



Q.26    NACA 2412 airfoil has


(A)     4% maximum camber with respect to chord


(B)     maximum camber at 40% chord


(C)     12% maximum thickness to chord ratio


(D)     maximum camber at 20% chord




Q.27    For International Standard Atmosphere (ISA) up to 11 km, which of the following
        statement(s) is/are true?


(A)     The hydrostatic/ aerostatic equation is used


(B)     The temperature lapse rate is taken as −10        K/m


(C)     The sea level conditions are taken as: pressure, p = 1.01325 × 10 Pa;
        temperature, T = 300 K; density, ρ = 1.225 kg/m


(D)     Air is treated as a perfect gas




                                          Page 21 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 22 of 44
Page 22 of 44
Text of page 22
GATE 2022 Aerospace Engineering (AE)



Q.28 Let σ and τ represent the normal stress and shear stress on a plane, respectively.
     The Mohr circle(s) that may possibly represent the state of stress at points in a beam
     of rectangular cross-section under pure bending is/are:


(A)




(B)




(C)




(D)




                                       Page 22 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 23 of 44
Page 23 of 44
Text of page 23
GATE 2022 Aerospace Engineering (AE)



Q.29    An isotropic linear elastic material point under plane strain condition in the x-y
        plane always obeys:


(A)     out-of-plane normal strain, ε   =0


(B)     out-of-plane normal stress, σ   =0


(C)     out-of-plane shear stress, τ    =0


(D)     out-of-plane shear strain,γ    =0




Q.30    A high-pressure-ratio multistage axial compressor encounters an extreme loading
        mismatch during starting. Which of the following technique(s) can be used to
        alleviate this problem?


(A)     Blade cooling


(B)     Variable angle stator vanes


(C)     Blow-off valves


(D)     Multi-spool shaft




                                        Page 23 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 24 of 44
Page 24 of 44
Text of page 24
GATE 2022 Aerospace Engineering (AE)



Q.31    The arc length of the parametric curve: x = cos θ , y = sin θ , z = θ from θ = 0
        to θ = 2π is equal to ________ (round off to one decimal place).




Q.32    An unpowered glider is flying at a glide angle of 10 degrees. Its lift-to-drag ratio
        is                  (round off to two decimal places).




Q.33    The two-dimensional plane-stress state at a point is:

                        σ    = 110 MPa; σ       = 30 MPa; τ      = 40 MPa.

        The normal stress, σ , on a plane inclined 45o as shown in the figure is ____ MPa
        (round off to the nearest integer).




                                       Page 24 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 25 of 44
Page 25 of 44
Text of page 25
GATE 2022 Aerospace Engineering (AE)



Q.34    In a static test, a turbofan engine with bypass ratio of 9 has core hot exhaust speed
        1.5 times that of fan exhaust speed. The engine is operated at a fuel to air ratio of
        f = 0.03. Both the fan and the core streams have no pressure thrust. The ratio of
        fan thrust to thrust from the core engine is _____ (round off to one decimal place).




Q.35    In a single stage turbine, the hot gases come out of stator/ nozzle at a speed of 500
        m/s and at an angle of 70 degrees with the turbine axis as shown. The design
        speed of the rotor blade is 250 m/s at the mean blade radius. The rotor blade angle,
        β, at the leading edge is ________ degrees (round off to one decimal place).




                                       Page 25 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 26 of 44
Page 26 of 44
Text of page 26
GATE 2022 Aerospace Engineering (AE)
Q.36 – Q.65 Carry TWO marks Each



Q.36    The height of a right circular cone of maximum volume that can be enclosed
        within a hollow sphere of radius R is


(A)     R


(B)     5
          R
        4

(C)     4
          R
        3

(D)     3
          R
        2



Q.37    Consider the differential equation d
                                            d2      d
                                                 − 2 d + y = 0.

        The boundary conditions are y = 0 and        = 1 at x = 0.

        Then the value of y at x = 1/2 is


(A)     0


(B)     √e


(C)     √e
        2

(D)         e
            2




                                      Page 26 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 27 of 44
Page 27 of 44
Text of page 27
GATE 2022 Aerospace Engineering (AE)



Q.38    Consider the partial differential equation     +    = 0 where x, y are real.

        If f(x, y) = a(x)b(y), where a(x) and b(y) are real functions, which one of the
        following statements can be true?


(A)     a(x) is a periodic function and b(y) is a linear function


(B)     both a(x) and b(y) are exponential functions


(C)     a(x) is a periodic function and b(y) is an exponential function


(D)     both a(x) and b(y) are periodic functions




Q.39    A cylindrical object of diameter 900 mm is designed to move axially in air at
        60 m/s. Its drag is estimated on a geometrically half-scaled model in water,
        assuming flow similarity.

        Coefficients of dynamic viscosity and densities for air and water are
        1.86 × 10 Pa-s, 1.2 kg/m3 and 1.01 × 10 Pa-s, 1000 kg/m3 respectively.

        Drag measured for the model is 2280 N. Drag experienced by the full-scale object
        is ____ N (rounded off to the nearest integer).


(A)     322


(B)     644


(C)     1288


(D)     2576




                                       Page 27 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 28 of 44
Page 28 of 44
Text of page 28
GATE 2022 Aerospace Engineering (AE)

Q.40    Consider a conventional subsonic fixed-wing airplane. e is the Oswald efficiency
        factor and AR is the aspect ratio. Corresponding to the minimum     ⁄   , which of
        the following relations is true?


(A)     C     1
          =
        C   πeAR


(B)     C     4
          =
        C   3πeAR


(C)     C     1
          =
        C   πeAR


(D)     C          1
             =
         C       √πeAR




                                           Page 28 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 29 of 44
Page 29 of 44
Text of page 29
GATE 2022 Aerospace Engineering (AE)



Q.41    A horizontal load F is applied at point R on a two-member truss, as shown in the
        figure. Both the members are prismatic with cross-sectional area, A , and made of
        the same material with Young’s modulus E.

        The horizontal displacement of point R is:




(A)     0


(B)      Fl
        EA


(C)            Fl
        √2
              EA


(D)          Fl
        2
            EA




                                      Page 29 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 30 of 44
Page 30 of 44
Text of page 30
GATE 2022 Aerospace Engineering (AE)

Q.42    Which of the following is NOT always true for a combustion process taking place
        in a closed system?


(A)     Total number of atoms is conserved


(B)     Total number of molecules is conserved


(C)     Total number of atoms of each element is conserved


(D)     Total mass is conserved




Q.43    The real function y = sin (|x|) is


(A)     continuous for all x


(B)     differentiable for all x


(C)     not continuous at x = 0


(D)     not differentiable at x = 0




                                      Page 30 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 31 of 44
Page 31 of 44
Text of page 31
GATE 2022 Aerospace Engineering (AE)



Q.44    A convergent nozzle fed from a constant pressure, constant temperature reservoir,
        is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit
        (marked as Q).

        Flow through the nozzle can be assumed to be isentropic.

        If the exit area of the nozzle is increased while all the reservoir parameters and
        ambient conditions remain the same, then at steady state




(A)     the nozzle will remain choked


(B)     the nozzle will be un-choked


(C)     the Mach number at section P will increase


(D)     the Mach number at section P will decrease




                                        Page 31 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 32 of 44
Page 32 of 44
Text of page 32
GATE 2022 Aerospace Engineering (AE)

Q.45    For a conventional airplane in straight, level, constant velocity flight condition,
        which of the following condition(s) is/are possible on Euler angles (φ, θ, ψ), angle
        of attack (α) and the sideslip angle (β)?


(A)     φ = 0 ,θ = 2 ,ψ = 0 ,α = 2 ,β = 0


(B)     φ = 5 ,θ = 0 ,ψ = 0 ,α = 2 ,β = 0


(C)     φ = 0 ,θ = 3 ,ψ = 0 ,α = 3 ,β = 5


(D)     φ = 0 ,θ = 5 ,ψ = 0 ,α = 2 ,β = 5




Q.46    Consider a high Earth-orbiting satellite of angular momentum per unit mass ℎ⃗ and
        eccentricity e.

        The mass of the Earth is M and G is the universal gravitational constant.

        The distance between the satellite’s center of mass and the Earth’s center of mass
        is r, the true anomaly is θ, and the phase angle is zero.

        Which of the following statements is/are true?

                                                       ⃗
(A)     The trajectory equation is r = r(θ) =     (        )


(B)                                                    ⃗
        The trajectory equation is r = r(θ) =     (        )



(C)     ℎ⃗ is conserved


(D)     The sum of potential energy and kinetic energy of the satellite is conserved




                                       Page 32 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 33 of 44
Page 33 of 44
Text of page 33
GATE 2022 Aerospace Engineering (AE)



Q.47    A rocket operates at an absolute chamber pressure of 20 bar to produce thrust, F .

        The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a
        convergent-divergent nozzle with exit to throat area ratio    of 3.5 and thrust
        coefficient, C , =1.42.

        The same rocket when operated at an absolute chamber pressure of 50 bar
        produces thrust F and the thrust coefficient is C , .

        Which of the following statement(s) is/are correct?


(A)     F
          = 2.5
        F


(B)     F
          > 2.5
        F


(C)     C ,
            =1
        C ,


(D)     C ,
            >1
        C ,




Q.48    v⃗ = x ı̂ + y ȷ̂ + z k is a vector field where ı̂, ȷ̂, k are the base vectors of a
        cartesian coordinate system.

        Using the Gauss divergence theorem, the value of the outward flux of the vector
        field over the surface of a sphere of unit radius centered at the origin is________
        (rounded off to one decimal place).




                                         Page 33 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 34 of 44
Page 34 of 44
Text of page 34
GATE 2022 Aerospace Engineering (AE)



Q.49    The largest eigenvalue of the given matrix is _____.

                                               0 1       1
                                               1 0       1
                                               1 1       0




                                                               
Q.50    A rotational velocity field in an air flow is given as V  ayiˆ  bxjˆ , with a = 10 s-1,
        b = 20 s-1.

        The air density is 1.0 kg/m3 and the pressure at (x, y) = (0 m, 0 m) is 100 kPa.

        Neglecting gravity, the pressure at (x, y) = (6 m, 8 m) is _____ kPa (rounded off
        to nearest integer).




Q.51    Consider a circulation distribution over a finite wing given by the equation below.

                                                2y                       b
                                         Γ 1−            if     0≤y≤
                              Γ(y) =             b                       2
                                                2y              b
                                         Γ   1+          if −     ≤y≤0
                                                 b              2
        The wingspan b is 10 m, the maximum circulation Γ is 20 m2/s, density of air is
        1.2 kg/m3 and the free stream speed is 80 m/s.

        The lift over the wing is ______N (rounded off to the nearest integer).




                                         Page 34 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 35 of 44
Page 35 of 44
Text of page 35
GATE 2022 Aerospace Engineering (AE)



Q.52    Consider a solid cylinder housed inside another cylinder as shown in the figure.
        Radius of the inner cylinder is 1 m and its height is 2 m. The gap between the
        cylinders is 5 mm and is filled with a fluid of viscosity 10-4 Pa-s.

        The inner cylinder is rotating at a constant angular speed of 5 rad/s while the outer
        cylinder is stationary. Friction at the bottom surfaces can be ignored. Velocity
        profile in the vertical gap between the cylinders can be assumed to be linear.

        The driving moment required for the rotating motion of the inner cylinder is
        ____________ Nm (rounded off to two decimal places).




                                       Page 35 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 36 of 44
Page 36 of 44
Text of page 36
GATE 2022 Aerospace Engineering (AE)



Q.53    In a converging duct, area and velocity at section P are 1 m2 and 15 m/s,
        respectively. The temperature of the fluid is 300 K.

        Air flow through the nozzle can be assumed to be inviscid and isothermal.
        Characteristic gas constant is 287 J/(kg-K) and ratio of specific heats is for air.

        To ensure that the air flow remains incompressible (Mach number, M ≤ 0.3) in the
        duct, the minimum area required at section Q is _____ m2 (rounded off to two
        decimal places).




Q.54    Consider a thin symmetric airfoil at 2 degree angle of attack in a uniform flow at
        50 m/s. The pitching moment coefficient about its leading edge is _____ (rounded
        off to three decimal places).




                                        Page 36 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 37 of 44
Page 37 of 44
Text of page 37
GATE 2022 Aerospace Engineering (AE)



Q.55    A convergent-divergent nozzle with adiabatic walls is designed for an exit Mach
        number of 2.3. It is discharging air to atmosphere under the conditions indicated in
        the figure.

        Flow through the nozzle is inviscid, the characteristic gas constant for air is 287
        J/(kg-K), and γ =1.4.

        When the reservoir pressure is 25 bar (absolute), and temperature is 300 K, Prandtl-
        Meyer expansion waves appear at the nozzle exit as shown.

        The minimum percentage change in the reservoir pressure required to eliminate the
        wave system at the nozzle exit under steady state is _______%.




Q.56    A conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at a
        constant speed of 100 m/s at sea level.

        Taking the acceleration due to gravity as 10 m/s2, the bank angle of the airplane is
                          degrees.




                                       Page 37 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 38 of 44
Page 38 of 44
Text of page 38
GATE 2022 Aerospace Engineering (AE)



Q.57    Given: The tip deflection and tip slope for a tip loaded cantilever of length L are:
            and     , respectively, where N is the tip force and EI is the flexural rigidity.

        A cantilever PQ of rectangular cross-section is subjected to transverse load, F, at
        its mid-point. Two cases are considered as shown in the figure. In Case I, the end
        Q is free and in Case II, Q is simply supported.

        The ratio of the magnitude of the maximum bending stress at P in Case I to that in
        Case II is ________ (rounded off to one decimal place).




Q.58    A simply supported Aluminium column of length 1 m and rectangular cross-
        section w × t with t ≤ w, is subjected to axial compressive loading.

        Young’s modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa.

        The value of t at which the failure load for yielding and buckling coincide is
        _______mm.




                                       Page 38 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 39 of 44
Page 39 of 44
Text of page 39
GATE 2022 Aerospace Engineering (AE)



Q.59    A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an
        axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the
        figure.

        The allowable stress under uniaxial tension is 100 MPa.

        Using maximum principal stress criterion, the minimum thickness, t, of the shaft
        so that it does not fail is _____ mm (rounded off to the nearest integer).




Q.60    A 10 kN axial load is applied eccentrically on a rod of square cross-section (1 cm
        × 1 cm) as shown in the figure.

        The strains measured by the two strain gages attached to the top and bottom
        surfaces at a distance of 0.5 m from the tip are ε = 0.0016 and ε = 0.0004,
        respectively.

        The eccentricity in loading, e is _________mm.




                                       Page 39 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 40 of 44
Page 40 of 44
Text of page 40
GATE 2022 Aerospace Engineering (AE)



Q.61    For a thin-walled I section, the width of the two flanges as well as the web height
        are the same, i.e., 2b = 20 mm. Thickness is 0.6 mm.

        The second moment of area about a horizontal axis passing through the centroid is
        ______ mm4.




Q.62    A damper with damping coefficient, c, is attached to a mass of 5 kg and spring of
        stiffness 5 kN/m as shown in figure. The system undergoes under-damped
        oscillations.

        If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value
        of c is ____ Ns/m (rounded off to the nearest integer).




                                        Page 40 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 41 of 44
Page 41 of 44
Text of page 41
GATE 2022 Aerospace Engineering (AE)



Q.63    A uniform rigid prismatic bar of total mass m is suspended from a ceiling by two
        identical springs as shown in figure.

        Let ω and ω be the natural frequencies of mode I and mode II respectively
        (ω < ω ).

        The value of ω /ω is _________ (rounded off to one decimal place).




Q.64    An ideal ramjet is to operate with exhaust gases optimally expanded to ambient
        pressure at an altitude where temperature is 220 K. The exhaust speed at the nozzle
        exit is 1200 m/s at a temperature of 1100 K.

        Given: γ = 1.4 at 220 K; R = 287 J/(kg-K) for air
              γ = 1.33 at 1100 K; R = 287 J/(kg-K) for exhaust gases.

        The cruise speed of this ramjet is ________ m/s (rounded off to nearest integer).




                                      Page 41 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 42 of 44
Page 42 of 44
Text of page 42
GATE 2022 Aerospace Engineering (AE)



Q.65    A multistage axial compressor takes in air at 1 atm, 300 K and compresses it to a
        minimum of 5 atm.
                                                               ∆
        The mean blade speed is 245 m/s and work coefficient,    is 0.55 for each stage.
        For air, use C =1005 J/(kg-K), R = 287 J/(kg-K) and γ = 1.4.

        If the compression is isentropic, the number of stages required is ___________
        (rounded off to the next higher integer).




                                      Page 42 of 42

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 43 of 44
Page 43 of 44
Text of page 43
Q. No.   Session Question   Subject   Key/Range      Mark
                 Type       Name
1        8       MCQ        GA        B              1
2        8       MCQ        GA        C              1
3        8       MCQ        GA        C              1
4        8       MCQ        GA        A              1
5        8       MCQ        GA        B OR C         1
6        8       MCQ        GA        C              2
7        8       MCQ        GA        C              2
8        8       MCQ        GA        A              2
9        8       MCQ        GA        A              2
10       8       MCQ        GA        B              2
11       8       MCQ        AE        C              1
12       8       MCQ        AE        D              1
13       8       MCQ        AE        B              1
14       8       MCQ        AE        C              1
15       8       MCQ        AE        C              1
16       8       MCQ        AE        B              1
17       8       MCQ        AE        B              1
18       8       MCQ        AE        D              1
19       8       MCQ        AE        A              1
20       8       MCQ        AE        B              1
21       8       MCQ        AE        B              1
22       8       MCQ        AE        A              1
23       8       MCQ        AE        B              1
24       8       MSQ        AE        B, C           1
25       8       MSQ        AE        B, D           1
26       8       MSQ        AE        B, C           1
27       8       MSQ        AE        A, D           1
28       8       MSQ        AE        B, C           1
29       8       MSQ        AE        A, C, D        1
30       8       MSQ        AE        B, C, D        1
31       8       NAT        AE        8.6 to 9.1     1
32       8       NAT        AE        5.55 to 5.80   1
33       8       NAT        AE        109 to 111     1
34       8       NAT        AE        5.7 to 6.0     1
35       8       NAT        AE        51.5 to 52.6   1
36       8       MCQ        AE        C              2
37       8       MCQ        AE        C              2
38       8       MCQ        AE        C              2
39       8       MCQ        AE        B              2
40       8       MCQ        AE        B              2
41       8       MCQ        AE        C              2
42       8       MCQ        AE        B              2
43       8       MSQ        AE        A, B           2
44       8       MSQ        AE        A, C           2

GATE AE 2022 question paper, GATE 2022, Aerospace Engineering, page 44 of 44
Page 44 of 44
Text of page 44
45   8   MSQ   AE   A                        2
46   8   MSQ   AE   B, C, D                  2
47   8   MSQ   AE   B, D                     2
48   8   NAT   AE   7.4 to 7.7               2
49   8   NAT   AE   2 to 2                   2
50   8   NAT   AE   88 to 91                 2
51   8   NAT   AE   9500 to 9800             2
52   8   NAT   AE   1.24 to 1.28             2
53   8   NAT   AE   0.14 to 0.15             2
54   8   NAT   AE   -0.057 to -0.053         2
55   8   NAT   AE   49 to 51 OR -51 to -49   2
56   8   NAT   AE   44 to 46                 2
57   8   NAT   AE   2.6 to 2.7               2
58   8   NAT   AE   43 to 48                 2
59   8   NAT   AE   1 to 1                   2
60   8   NAT   AE   0.95 to 1.05             2
61   8   NAT   AE   2700 to 2960             2
62   8   NAT   AE   19 to 21                 2
63   8   NAT   AE   1.7 to 1.8               2
64   8   NAT   AE   545 to 555               2
65   8   NAT   AE   6 or greater than 6      2

Page 1 of 44

Source: GATE. Question paper published by GATE.