Mechanical Engineering Gate Yearwise

Mechanical Engineering GATE 2013 Set-1 Questions with Answer

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Ques 1 Engineering Mathematics

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

linear equation of order 2

non-linear equation of order 1

linear equation of order 1

non-linear equation of order 2

Ques 2 Engineering Mathematics

The eigenvalues of a symmetric matrix are all

complex with non-zero positive imaginary part.

complex with non-zero negative imaginary part.

real.

pure imaginary.

Ques 3 Engineering Mathematics

Match the CORRECT pairs.

Numerical Integration Scheme	Order of Fitting Polynomial
P. Simpson's 3/8 Rule	1. First
Q. Trapezoidal Rule	2. Second
R. Simpson's 1/3 Rule	3. Third

P-2, Q-1, R-3

P-3, Q-2, R-1

P-1, Q-2, R-3

P-3, Q-1, R-2

Ques 4 Engineering Mathematics

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

0.5

greater than zero and less than 0.5

greater than 0.5 and less than 1.0

1.0

Ques 5 Engineering Mathematics

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

sin x, sin²x and cos²x

cos x, sin x and tan x

cos 2x, sin²x and cos²x

cos 2x, sin x and cos x

Ques 6 Engineering Mathematics

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

2π

3π/4

4π

Ques 7 Engineering Mathematics

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

2/(s+1)

4/(s+1)

4/(s²+1)

2/(s⁴+1)

Ques 8 Engineering Mathematics

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

2/3

3/4

5/6

8/9

Ques 9 Engineering Mathematics

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

u = U(x/L)

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

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

u = U((1+e^kx)/(1+e^kL))

Ques 10 Engineering Mathematics

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

(4/9)√e³ + (2/9)

(2/9)√e³ - (4/9)

(2/9)√e³ + (4/9)

(4/9)√e³ - (2/9)

Ques 11 General Aptitude

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

specificity

neutrality

generality

adaptation

Ques 12 General Aptitude

Were you a bird, you ________ in the sky.

would fly

shall fly

should fly

shall have flown

Ques 13 General Aptitude

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

Highest

Lowest

Medium

Integration

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