Aerospace Engineering Gate Yearwise 


Aerospace Engineering Gate 2022 Questions with Answer

Ques 40 GATE 2022

Let î, ĵ, and k̂ be the unit vectors in the x, y, and z directions, respectively. If the vector î + ĵ is rotated about positive k̂ by 135°, one gets

A

-î

B

-ĵ

C

-1/√2 ĵ

D

-√2 î


(d) is the correct answer.

Ques 41 GATE 2022

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


(b) is the correct answer.

Ques 42 GATE 2022

If â, b̂, and ĉ are three mutually perpendicular unit vectors, then â • (b̂ x ĉ) can take the value(s) _______.

A

0

B

1

C

-1

D

∞


(b,c) is the correct answer.

Ques 43 GATE 2022

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)


(8.6 to 9.1) is the correct answer.

Ques 44 GATE 2022

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

5/4 R

C

4/3 R

D

3/2 R


(c) is the correct answer.

Ques 45 GATE 2022

Consider the differential equation d2y/dx2 - 2(dy/dx) + y = 0.
The boundary conditions are y = 0 and dy/dx = 1 at x = 0. Then the value of y at x = 1/2 is _______.

A

0

B

√e

C

√e / 2

D

√(e/2)


(c) is the correct answer.

Ques 46 GATE 2022

Consider the partial differential equation ∂2f/∂x2 + ∂2f/∂y2 = 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


(b) is the correct answer.

Ques 47 GATE 2022

The real function y = sin2(|x|) is _______.

A

continuous for all x

B

differentiable for all x

C

not continuous at x = 0

D

not differentiable at x = 0


(a,d) is the correct answer.

Ques 48 GATE 2022

v⃗ = x3î + y3ĵ + z3k̂ is a vector field where î, ĵ, and k̂ 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)


(7.4 to 7.7) is the correct answer.

Ques 49 GATE 2022

The largest eigenvalue of the given matrix is _______.


(2 to 2) is the correct answer.

Ques 50 GATE 2022

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 fibers of the cross-section

B

only at the bottom fibers of the cross-section

C

both at the top and bottom fibers of the cross-section

D

only at the centroidal fibers of the cross-section


(c) is the correct answer.

Ques 51 GATE 2022

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

F/√2 (compressive)

D

√2F (tensile)


(a) is the correct answer.

Ques 52 GATE 2022

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: *[Insert Figures Here]*

A

B

C

D


(b,c) is the correct answer.

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