Mechanical Engineering Gate 2013 Set-1 Questions with Answer

Ques 1 GATE 2013 SET-1

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

Ques 2 GATE 2013 SET-1

The eigenvalues of a symmetric matrix are all

Ques 3 GATE 2013 SET-1

Match the CORRECT pairs.

Ques 4 GATE 2013 SET-1

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

Ques 5 GATE 2013 SET-1

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

Ques 6 GATE 2013 SET-1

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

Ques 7 GATE 2013 SET-1

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

Ques 8 GATE 2013 SET-1

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

Ques 9 GATE 2013 SET-1

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

Ques 10 GATE 2013 SET-1

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

Ques 11 GATE 2013 SET-1

Complete the sentence:
Universalism is to particularism as diffuseness is to __________.

Ques 12 GATE 2013 SET-1

Were you a bird, you ________ in the sky.

Ques 13 GATE 2013 SET-1

Which one of the following options is the closest in meaning to the word given below?
Nadir