Mechanical Engineering Gate Yearwise
Mechanical Engineering GATE 2016 Set-1 Questions with Answer
Ques 1 CAD/CAM
The figure below represents a triangle PQR with initial coordinates of the vertices as P(1,3), Q(4,5) and R(5,3.5). The triangle is rotated in the X-Y plane about the vertex P by angle θ in clockwise direction. If sinθ = 0.6 and cosθ = 0.8, the new coordinates of the vertex Q are
Ques 2 Engineering Mathematics
The solution to the system of equations
Ques 3 Engineering Mathematics
If f(t) is a function defined for all t ≥ 0, its Laplace transform F(s) is defined as
Ques 4 Engineering Mathematics
f(z) = u(x,y) + i v(x,y) is an analytic function of complex variable z=x+iy where i=√-1. If u(x,y) = 2xy, then v(x,y) may be expressed as
Ques 5 Engineering Mathematics
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ. The standard deviation for this distribution is given by
Ques 6 Engineering Mathematics
Solve the equation x = 10cos(x) using the Newton-Raphson method. The initial guess is x = π/4. The value of the predicted root after the first iteration, up to second decimal, is ________.
1.56 is the correct answer.
Ques 7 Engineering Mathematics
Consider the function f(x) = 2x3 - 3x2 in the domain [-1, 2]. The global minimum of f(x) is ________.
-5 is the correct answer.
Ques 8 Engineering Mathematics
If y=f(x) satisfies the boundary value problem y" + 9y = 0, y(0) = 0, y(π/2) = √2, then y(π/4) is ________.
-1 is the correct answer.
Ques 9 Engineering Mathematics
The value of the integral
∫-∞∞ (sin x) / (x2+2x+2) dx
evaluated using contour integration and the residue theorem is
Ques 10 Engineering Mathematics
Gauss-Seidel method is used to solve the following equations (as per the given order):
x1 + 2x2 + 3x3 = 5
2x1 + 3x2 + x3 = 1
3x1 + 2x2 + x3 = 3
Assuming initial guess as x1 = x2 = x3 = 0, the value of x3 after the first iteration is ________.
-6 is the correct answer.
Ques 11 Engineering Mechanics
A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30° with the vertical. The magnitude of force F (in N) is ________.
57.73 is the correct answer.
Ques 12 Engineering Mechanics
A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is
Ques 13 Engineering Mechanics
A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is 0.25. The string can withstand a maximum force of 20 N. The maximum value of the mass (m) for which the string will not break and the block will be in static equilibrium is ________ kg. Take cosθ=0.8 and sinθ=0.6. Acceleration due to gravity g = 10 m/s2.
5 is the correct answer.
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