Mechanical Engineering Gate Yearwise
Mechanical Engineering GATE 2016 Set-2 Questions with Answer
Ques 1 Engineering Drawing
For the situation shown in the figure below the expression for H in terms of r, R and D is
Ques 2 Engineering Mathematics
The condition for which the eigenvalues of the matrix
Ques 3 Engineering Mathematics
The values of x for which the function
f(x) = (x2 - 3x - 4) / (x2 + 3x - 4)
is NOT continuous are
Ques 4 Engineering Mathematics
Laplace transform of cos(ωt) is
Ques 5 Engineering Mathematics
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 ________.
-1 is the correct answer.
Ques 6 Engineering Mathematics
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
Ques 7 Engineering Mathematics
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 ________.
726 is the correct answer.
Ques 8 Engineering Mathematics
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 Engineering Mathematics
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 ________.
0.41 is the correct answer.
Ques 10 Engineering Mathematics
The error in numerically computing the integral ∫0π (sin x + cos x) dx using the trapezoidal rule with three intervals of equal length between 0 and π is ________.
0.186 is the correct answer.
Ques 11 Engineering Mechanics
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 Engineering Mechanics
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 ________.
14.2 is the correct answer.
Ques 13 Engineering Mechanics
A system of particles in motion has mass center G as shown in the figure. The particle i has mass mi and its position with respect to a fixed point O is given by the position vector ri. The position of the particle with respect to G is given by the vector ρi. The time rate of change of the angular momentum of the system of particles about G is (The quantity ρ̈i indicates second derivative of ρi with respect to time and likewise for ri).
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