Mechanical Engineering Gate Yearwise 


Mechanical Engineering Gate 2013 Set-4 Questions with Answer

Ques 1 GATE 2013 SET-4

In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be

A

(7.5, 5)

B

(10, 5)

C

(7.5, -5)

D

(10, -5)


(b) is the correct answer.

Ques 2 GATE 2013 SET-4

Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is

A

0.5

B

greater than zero and less than 0.5

C

greater than 0.5 and less than 1.0

D

1.0


(b) is the correct answer.

Ques 3 GATE 2013 SET-4

Choose the CORRECT set of functions, which are linearly dependent.

A

sin x, sin2x and cos2x

B

cos x, sin x and tan x

C

cos 2x, sin2x and cos2x

D

cos 2x, sin x and cos x


(c) is the correct answer.

Ques 4 GATE 2013 SET-4

The eigenvalues of a symmetric matrix are all

A

complex with non-zero positive imaginary part.

B

complex with non-zero negative imaginary part.

C

real.

D

pure imaginary.


(c) is the correct answer.

Ques 5 GATE 2013 SET-4

The partial differential equation ∂u/∂t + u(∂u/∂x) = ∂2u/∂x2 is a

A

linear equation of order 2

B

non-linear equation of order 1

C

linear equation of order 1

D

non-linear equation of order 2


(d) is the correct answer.

Ques 6 GATE 2013 SET-4

Match the CORRECT pairs.

Numerical Integration SchemeOrder of Fitting Polynomial
P. Simpson's 3/8 Rule1. First
Q. Trapezoidal Rule2. Second
R. Simpson's 1/3 Rule3. Third

A

P-2, Q-1, R-3

B

P-3, Q-2, R-1

C

P-1, Q-2, R-3

D

P-3, Q-1, R-2


(d) is the correct answer.

Ques 7 GATE 2013 SET-4

The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is

A

2/3

B

3/4

C

5/6

D

8/9


(d) is the correct answer.

Ques 8 GATE 2013 SET-4

The solution to the differential equation d2u/dx2 - k(du/dx) = 0 where k is a constant, subjected to the boundary conditions u(0)=0 and u(L)=U, is

A

u = U(x/L)

B

u = U((1-ekx)/(1-ekL))

C

u = U((1-e-kx)/(1-e-kL))

D

u = U((1+ekx)/(1+ekL))


(c) is the correct answer.

Ques 9 GATE 2013 SET-4

The value of the definite integral ∫1e √x ln(x) dx is

A

(4/9)√e3 + (2/9)

B

(2/9)√e3 - (4/9)

C

(2/9)√e3 + (4/9)

D

(4/9)√e3 - (2/9)


(c) is the correct answer.

Ques 10 GATE 2013 SET-4

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F=xi+yj+zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.
∫∫S (1/4)(F.n)dA
where S is the sphere, x2+y2+z2=1 and n is the outward unit normal vector to the sphere. The value of the surface integral is

A

π

B

2π

C

3π/4

D

4π


(a) is the correct answer.

Ques 11 GATE 2013 SET-4

The function f(t) satisfies the differential equation d2f/dt2 + f = 0 and the auxiliary conditions, f(0)=0, df/dt(0)=4. The Laplace transform of f(t) is given by

A

2/(s+1)

B

4/(s+1)

C

4/(s2+1)

D

2/(s4+1)


(c) is the correct answer.

Ques 12 GATE 2013 SET-4

A pin jointed uniform rigid rod of weight W and length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is

A

zero

B

W/4

C

W/2

D

W


(b) is the correct answer.

Ques 13 GATE 2013 SET-4

In order to have maximum power from a Pelton turbine, the bucket speed must be

A

equal to the jet speed.

B

equal to half of the jet speed.

C

equal to twice the jet speed.

D

independent of the jet speed.


(b) is the correct answer.

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