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Wednesday, December 29, 2010

APPLIED MATH, PAPER-I CSS PAPER 2010

FEDERAL PUBLIC SERVICE COMMISSION
COMPETITIVE EXAMINATION FOR
RECRUITMENT TO POSTS IN BPS-17 UNDER
THE FEDERAL GOVERNMENT, 2010
APPLIED MATH, PAPER-I

TIME ALLOWED: 3 HOURS MAXIMUM MARKS:100
NOTE:
(i) Attempt FIVE question in all by selecting at least TWO questions from SECTION – A
and THREE question from SECTION – B. All questions carry EQUAL marks.

(ii) Use of Scientific Calculator is allowed.
SECTION – A

Q.1. Explain the following giving examples and supported by figures: (5+5+5+5)
(a) Gradient
(b) Divergence
(c) Curl
(d) Curvilinear Coordinates
Q.2. Given that A,B,C are vectors having components along axis. Prove that: (10+10)
(a)
x y z
x y z
C C C
B B B
i j k
B x C
(b) A x B x C = Ax Bx Cx (i x k) + Ay Bx Cy (j x k)
Q.3. (a) State and prove Stokes Theorem (10)
(b) Given that V=4y i+x j + 2z k, find
( x V). nd over the hemi sphere x2+y2+z2=a2, z>=0. (10)
SECTION – B
Q.4. Discuss the following systems supported by figures/diagrams:
(a)
Equilibrium of a System coplanar forces (5)
Centre of mass of right circular solid cone of height h. (5)
(b) Centre of gravity of a rigid body of any shape. (10)
Q.5. (a) What is Simple Harmonic Motion? Discuss it in detail using Derivatives with respect time. (10)
(b) Describe the Simple Harmonic Motion of a pendulum and Calculate the time period of the
motion. (10)
Q.6. (a) Derive expression for the following:
Moment of inertia (5)
Product of inertia (5)
(b) Calculate the moment of inertia of solid sphere of mass m=37 and radius a=15.
Derive the general expression. (10)
Q.7. (a) Explain Kepler’s Laws. (10)
(b) What is Impulsive Motion? Derive its equation. (10)
Q.8. (a) Define Work, Torque, Power and energy. (10)
(b) A cricket ball is thrown vertically upwards, it attained the maximum height h after t
Seconds. Calculate its. (10)
Velocity of projection in direction vertically upward.
Acceleration when it returns to the point of projection.

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