Mechanical Engineering Gate Yearwise
Mechanical Engineering GATE 2016 Set-3 Questions with Answer
Ques 1 Engineering Mathematics
A real square matrix A is called skew-symmetric if
Ques 2 Engineering Mathematics
Ltx→0 (loge(1+4x)) / (e3x-1) is equal to
Ques 3 Engineering Mathematics
Solutions of Laplace's equation having continuous second-order partial derivatives are called
Ques 4 Engineering Mathematics
The area (in percentage) under standard normal distribution curve of random variable Z within limits from -3 to +3 is ________.
99.7 is the correct answer.
Ques 5 Engineering Mathematics
The root of the function f(x) = x3 + x - 1 obtained after first iteration on application of Newton-Raphson scheme using an initial guess of x0 = 1 is
Ques 6 Engineering Mathematics
The number of linearly independent eigenvectors of matrix
is ________.
2 is the correct answer.
Ques 7 Engineering Mathematics
The value of the line integral ∮C F.T ds, where C is a circle of radius 4/√π units is ________. Here, F(x,y) = y i + 2x j and T is the UNIT tangent vector on the curve C at an arc length s from a reference point on the curve. i and j are the basis vectors in the x-y Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
16 is the correct answer.
Ques 8 Engineering Mathematics
limx→∞ √(x2+x-1) - x is
Ques 9 Engineering Mathematics
Three cards were drawn from a pack of 52 cards. The probability that they are a king, a queen, and a jack is
Ques 10 Engineering Mechanics
A force F is acting on a bent bar which is clamped at one end as shown in the figure.
Ques 11 Engineering Mechanics
An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is ________.
133.33 is the correct answer.
Ques 12 Engineering Mechanics
A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed v of the disc when it reaches position B is ________ m/s. Acceleration due to gravity g = 10 m/s2.
20 is the correct answer.
Ques 13 Fluid Mechanics
A channel of width 450 mm branches into two sub-channels having width 300 mm and 200 mm as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is 0.9 m3/s and the velocity in the sub-channel of width 200 mm is 3 m/s, the velocity in the sub-channel of width 300 mm is ________ m/s. Assume both inlet and outlet to be at the same elevation.
1 is the correct answer.
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