Mechanical Engineering Gate 2017 Set-1 Questions with Answer

Ques 1 GATE 2017 SET-1

The product of eigenvalues of the matrix P is

Ques 2 GATE 2017 SET-1

The value of lim_x→0 (x³ - sin(x)) / x is

Ques 3 GATE 2017 SET-1

Consider the following partial differential equation for u(x,y) with the constant c > 1:
∂u/∂y + c(∂u/∂x) = 0
Solution of this equation is

Ques 4 GATE 2017 SET-1

The differential equation d²y/dx² + 16y = 0 for y(x) with the two boundary conditions dy/dx|_x=0 = 1 and dy/dx|_x=π/2 = -1 has

Ques 5 GATE 2017 SET-1

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ________.

Ques 6 GATE 2017 SET-1

Consider the matrix
Which one of the following statements about P is INCORRECT?

Ques 7 GATE 2017 SET-1

For the vector V = 2yzi + 3xzj + 4xyk, the value of ∇.(∇ x V) is ________.

Ques 8 GATE 2017 SET-1

A parametric curve defined by x = cos(πu/2), y = sin(πu/2) in the range 0 ≤ u ≤ 1 is rotated about the X-axis by 360 degrees. Area of the surface generated is

Ques 9 GATE 2017 SET-1

P (0, 3), Q (0.5, 4), and R (1, 5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits x=0 and x=1 for the curve. The difference between the two results will be

Ques 10 GATE 2017 SET-1

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t², θ(t) = t, where t is time. The kinetic energy of the particle at time t=2 is

Ques 11 GATE 2017 SET-1

The following figure shows the velocity-time plot for a particle traveling along a straight line. The distance covered by the particle from t=0 to t=5 s is ________ m.

Ques 12 GATE 2017 SET-1

Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is

Ques 13 GATE 2017 SET-1

For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?