Research Scholar

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91124

120 MINUTES

1.

The value of the closed surface integral ∫r.dS where r is the radius vector and dS is an element of vector area on a spherical surface of radius R is
A)
Zero
B)
The volume of the sphere
C)
Total surface area of the sphere
D)
3 x volume of the sphere

2.

The function cot (z) has
A)
An infinite number of poles each having a residue equal to 1
B)
One pole at z = 0 and the value is 1
C)
An infinite number of poles each having residue equal to 0
D)
Exactly one pole at /2 with a residue equal to 1

3.

A good example of a vector which is solenoidal is
A)
The magnetic field vector B
B)
The electric field vector E
C)
The current density vector J
D)
The velocity vector V of an electron in an atomic orbit

4.

Consider the step function: f(t) = +1 for 0 < t < / and f(t) = -1 for -/< t < 0.
Which of the following series gives the Fourier series representation of this function? (The summations are over n = 1 to ∞).
A)
(4/) ∑ [ sin (n t) / n]
B)
(4/) ∑ [ sin {(2n+1) t} /(2 n+1)]
C)
(4/) ∑ [ cos (n t) / n]
D)
(4/) ∑ [ cos {(2n+1) t} /(2 n+1)]

5.

A and B are two arbitrary vectors. ijk is the Levi-Civita symbol in 3 dimensions.
Then what is the nature of the quantity AiBjijk?
A)
A scalar
B)
A tensor of 3rd rank
C)
A tensor of 5th rank
D)
A vector

6.

If dy/dx = (y / 2√x), and y = 1 when x = 4, then
A)
y = e√x - 2
B)
ln y = √(x - 2)
C)
y = 4√x - 8
D)
y = e√x

7.

Which of the following is not a solution of the Laplace's equation in spherical polar co-ordinates? A)
1/r
B) ar2 + b/r2
C)
ar + b/r2
D)
b/r3

8.

The Laplace transform of e-attn is
A)
n!/(s+a)n+1
C)
(s+a)n

B)
D)

n/(s+a)n asn For more materials visit www.educationobserver.com/forum

9.

The population of a city increases at a rate proportional to the population at a given time. It is seen that the