Mechanical Engineering Gate 2016 Set-2 Questions with Answer

Ques 1 GATE 2016 SET-2

For the situation shown in the figure below the expression for H in terms of r, R and D is

Ques 2 GATE 2016 SET-2

The condition for which the eigenvalues of the matrix

Ques 3 GATE 2016 SET-2

The values of x for which the function
f(x) = (x² - 3x - 4) / (x² + 3x - 4)
is NOT continuous are

Ques 4 GATE 2016 SET-2

Laplace transform of cos(ωt) is

Ques 5 GATE 2016 SET-2

A function f of the complex variable z = x+iy, is given as f(x,y) = u(x,y) + i v(x,y), where u(x,y) = 2kxy and v(x,y) = x² - y². The value of k, for which the function is analytic, is ________.

Ques 6 GATE 2016 SET-2

Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

Ques 7 GATE 2016 SET-2

A scalar potential φ has the following gradient: ∇φ = yz i + xz j + xy k. Consider the integral ∫_C ∇φ.dr on the curve r = x i + y j + z k. The curve C is parameterized as follows: x=t, y=t² and z=3t² for 1 ≤ t ≤ 3. The value of the integral is ________.

Ques 8 GATE 2016 SET-2

The value of along a closed path Γ is equal to (4πi), where z=x+iy and i=√-1. The correct path Γ is

Ques 9 GATE 2016 SET-2

The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is ________.

Ques 10 GATE 2016 SET-2

The error in numerically computing the integral ∫₀^π (sin x + cos x) dx using the trapezoidal rule with three intervals of equal length between 0 and π is ________.

Ques 11 GATE 2016 SET-2

A point mass having mass M is moving with a velocity V at an angle θ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is

Ques 12 GATE 2016 SET-2

A mass of 2000 kg is currently being lowered at a velocity of 2 m/s from the drum as shown in the figure. The mass moment of inertia of the drum is 150 kg-m². On applying the brake, the mass is brought to rest in a distance of 0.5 m. The energy absorbed by the brake (in kJ) is ________.

Ques 13 GATE 2016 SET-2

A system of particles in motion has mass center G as shown in the figure. The particle i has mass m_i and its position with respect to a fixed point O is given by the position vector r_i. The position of the particle with respect to G is given by the vector ρ_i. The time rate of change of the angular momentum of the system of particles about G is (The quantity ρ̈_i indicates second derivative of ρ_i with respect to time and likewise for r_i).