6.

7.

10.

11.

If the function (இ + ‏“وده‎ +i (Bx2 y-y') is analytic, the value of ‘a’ is :

bo

(A) (8) 3
(0) ‏و‎ (0) 01

Consider a function f(x)=x* in the interval 6 7,2) which may be expanded as a Fourier
series. What is the value of the following infinite series ?

1111-1

1 4 9 16
3
7

(A) नत्र (B) 27
ಸ್‌

رم چ ‎൭‏

Constraints on a simple pendulum with rigid support is :
(A) Holonomic ൯) Nonholonomic
(C) Rheonomous (1) Holonomic and Scleronomous

An electron is moving with a velocity v in an electromagnetic field of vector potential A and
scalar potential ®. The Lagrangian of the electron is :

(A) त्र (B) timo? -e®-—e(A.v)
(C) dmv? +e + e(A.v) (D) त्र

A particle is moving in an elliptical orbit under the influence a central potential V(r)= Ck)
r
The maximum and minimum distance of the particle from centre of force are r, and r,. If the

eccentricity of the elliptical path is 0.5, then what is the ratio of maximum velocity and
minimum velocity of the particle?

(A) 2 (8) 3

(0) 4 (D) 0.25
A horizontal circular platform is rotating anticlockwise about an axis passing through the
center with a constant angular velocity Q. A person seated at the centre shoots a bullet of

mass m horizontally with a speed 10m/s. The acceleration of bullet in the reference frame of
the observer will be :

(^) 20Q to his left (8) 10Q to his left
(0) 20Q to his right (0) 5Q to his right

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