Aerospace Engineering Gate Yearwise 


Aerospace Engineering Gate 2024 Questions with Answer

Ques 40 GATE 2024

The acceleration of a body travelling in a straight line is given by
a = -C1 - C2v2
, where v is the velocity, and C1, C2 are positive constants. Starting with an initial positive velocity vo, the distance travelled by the body before coming to rest for the first time is

A

1/(2C2) * ln(1 + (C2/C1) * vo2)

B

1/(2C2) * ln(1 - (C2/C1) * vo2)

C

1/(2C2) * ln(C1 + C2 * vo2)

D

1/(2C2) * ln(1 + C2 * vo2)


(a) is the correct answer.

Ques 41 GATE 2024

Two fair dice with numbered faces are rolled together. The faces are numbered from 1 to 6. The probability of getting odd numbers on both the dice is _______ (rounded off to 2 decimal places).


(1) is the correct answer.

Ques 42 GATE 2024

A particle acted upon by a constant force 4î+ĵ-3k̂ N is displaced from point A with position vector î+2ĵ+3k̂ m to point B with position vector 5î+4ĵ+k̂ m. The work done by this force is ______ J (answer in integer).


(1) is the correct answer.

Ques 43 GATE 2024

Using Trapezoidal rule with one interval, the approximate value of the definite integral:
∫12 dx/(1+x2) = _______ (rounded off to 2 decimal places).


(1) is the correct answer.

Ques 44 GATE 2024

Given
y = epxsin(qx),
where p and q are non-zero real numbers, the value of the differential expression
d2y/dx2 - 2p(dy/dx) + (p2+q2)y is

A

0

B

1

C

p2+q2

D

pq


(a) is the correct answer.

Ques 45 GATE 2024

The volume of the solid formed by a complete rotation of the shaded portion of the circle of radius R about the y-axis is kπR3. The value of k is:

A

5/12

B

5/24

C

7/12

D

7/24


(b) is the correct answer.

Ques 46 GATE 2024

Consider the function

where x is real. Which of the following statements is/are correct?

A

The function is continuous for all x

B

The derivative of the function is discontinuous at x=0

C

The derivative of the function is continuous at x=1

D

The function is discontinuous at x=0


(a) is the correct answer.

Ques 47 GATE 2024

Consider the matrix A = [[5, -4], [k, -1]] where k is a constant. If the determinant of A is 3, then the ratio of the largest eigenvalue of A to the constant k is _______ (rounded off to 1 decimal place).


(0) is the correct answer.

Ques 48 GATE 2024

The three-dimensional stress-strain relationship for an isotropic material is given as

where P, Q, and R are the three elastic constants, σ and τ represent normal and shear stresses, and ε and γ represent normal and engineering shear strains. Which one of the following options is correct?

A

R = (P - Q)/2

B

R = (Q - P)/2

C

Q = (P - R)/2

D

Q = (R - P)/2


(a) is the correct answer.

Ques 49 GATE 2024

Which of the following options is/are correct?

A

The stress-strain graph for a nonlinear elastic material is as shown in the figure

B

Material properties are independent of position in a homogeneous material

C

An isotropic material has infinitely many planes of material symmetry

D

The stress-strain graph for a linear elastic material is


(a) is the correct answer.

Ques 50 GATE 2024

A material has Poisson's ratio v=0.5 and Young's modulus E=2500 MPa. The percentage change in its volume when subjected to a hydrostatic stress of magnitude 10 MPa is _______ (answer in integer).


(a) is the correct answer.

Ques 51 GATE 2024

The figure shows plots of two yield loci for an isotropic material, where σI and σII are the principal stresses, and σY is the yield stress in uniaxial tension. Which of the following statements is/are correct?

A

Criterion P represents the von Mises criterion

B

Criterion Q represents the Tresca criterion

C

Criterion P represents the Tresca criterion

D

Criterion Q represents the von Mises criterion


(a) is the correct answer.

Ques 52 GATE 2024

The state of stress at a point is caused by two separate loading cases. One of them produces a pure uniaxial tension along the x' direction, and the other one produces a pure uniaxial compression along the y' direction, as shown in the figure. The sum of maximum and minimum principal stresses for the resultant state of stress caused by both loads acting simultaneously is _______ N/mm2 (rounded off to 1 decimal place).


(a) is the correct answer.

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