XE Engineering Science- 2013 GATE Paper (Practice Test) - GATE MCQ

Which of the above underlined parts of the sentence is not appropriate?

Select the pair that best expresses a relationship similar to that expressed in the pair:
water: pipe::

Q. 6 to Q. 10 carry two marks each

Q.

Velocity of an object fired directly in upward direction is given by V = 80 − 32 t, where t (time)
is in seconds. When will the velocity be between 32 m/sec and 64 m/sec?

In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents
respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a
randomly drawn autocomponent from the combined lot is found defective, what is the probability
that it was manufactured by M2?

Following table gives data on tourists from different countries visiting India in the year 2011.

Which two countries contributed to the one third of the total number of tourists who visited India in
2011?

If |−2x + 9| = 3 then the possible value of |−x| − x² would be:

All professors are researchers
Some scientists are professors
Which of the given conclusions is logically valid and is inferred from the above arguments:

Q. 11 – Q. 17 carry one mark each.

Q.

The value of the integral 

Which one of the following partial differential equations CAN NOT be reduced to two
ordinary differential equations by the method of separation of variables?

The Fourier series of the periodic function

is given by

Using the above, the sum of the infinite series  

Consider the function   the function f

The integral  along the contour C: |z − (1 + i)| = 2, oriented anticlockwise,
is equal to

The integral equals

If the mean and variance of a binomial distribution are 6 and 2 respectively, then the
probability of two failures is

Q. 18 - Q. 21 carry two marks each.

Q

For the matrix   consider the following statements

(P) The characteristic equation of λ is λ³ − λ = 0.
(Q) M^-1 does not exist.
(R) The matrix M is diagonalizable.
Which of the above statements are true?

The work done by the force in moving a particle once
along the triangle with vertices (0,0), (1,0) and (0,1) in the anti-clockwise direction is

The general solution of the differential equation

is

Using Euler’s method to solve the differential equation

with step-size h = 0.25, the value of y(0.5) is

Q. 22 – Q. 30 carry one mark each.

Q.

The gauge pressure inside a soap bubble of radius R, with σ denoting the surface tension between the soap solution and air, is.

Let M, B and G represent respectively the metacentre, centre of buoyancy and the centre of
mass of a floating buoy. Which of the following statements is correct?

A reservoir connected to a pipe line is being filled with water, as shown in the Figure. At
any time t, the free surface level in the reservoir is h. Find the time in seconds for the
reservoir to get filled up to a height of 1 m, if the initial level is 0.2 m. _________

(Important : you should answer only the numeric value)

Bernoulli’s equation is valid for the following type of flow:

If A is the area of a circle of radius r enclosing a plane forced vortex flow, with origin at
the centre of the vortex and if ω is the angular velocity, ζ is the vorticity, is the velocity
vector, then the circulation around the contour of the circle is given by

Flow past a circular cylinder can be produced by superposition of the following elementary
potential flows:

Let δ, δ1 and δ2 denote respectively the boundary-layer thickness, displacement thickness
and the momentum thickness for laminar boundary layer flow of an incompressible fluid
over a flat plate. The correct relation among these quantities is

In the hydrodynamic entry region of a circular duct, the pressure forces balance the sum of

Bodies with various cross-sectional shapes subjected to cross-flow of air are shown in the
following figures. The characteristic dimension of all the shapes is the same. The crosssectional
shape with the largest coefficient of drag (i.e. sum of the pressure and skinfriction
drags), at any moderately large Reynolds number, is