Aerospace Engineering GATE 2024 Questions with Answer

Ques 40 Mathematics

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 v_o, the distance travelled by the body before coming to rest for the first time is

Ques 41 Mathematics

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).

Ques 42 Mathematics

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).

Ques 43 Mathematics

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

Ques 44 Mathematics

Given
y = e^pxsin(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

Ques 45 Mathematics

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:

Ques 46 Mathematics

Consider the function

Ques 47 Mathematics

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).

Ques 48 Solid Mechanics

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

Ques 49 Solid Mechanics

Which of the following options is/are correct?

A

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

D

The stress-strain graph for a linear elastic material is

Ques 50 Solid Mechanics

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).

Ques 51 Solid Mechanics

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

Ques 52 Solid Mechanics

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).