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

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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

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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)

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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

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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)

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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)

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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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