Table of Contents
NWFP PUBLIC SERVICE COMMISSION
COMPETITIVE EXAMINATION FOR THE POSTS OF PROVINCIAL MANAGEMENT SERVICE (BPS-17) 2010
APPLIED MATHEMATICS PAPER-I
| MARKS: 100 | TIME: 03 Hours |
Note: Attempt any TWO questions from section A and any THREE questions from section B.
SECTION – A
Q NO 1.
Explain the gradient of scalar field and also find the Mathematical expression for it.
Explain the gradient of scalar field and also find the Mathematical expression for it.
Q NO 2.
State and prove the stoke’s theorem.
State and prove the stoke’s theorem.
Q NO 3.
What is the Centre of Gravity? Prove that potential energy of body is equal to that of a single particle with mass of body situated at its centre of gravity.
What is the Centre of Gravity? Prove that potential energy of body is equal to that of a single particle with mass of body situated at its centre of gravity.
SECTION – B
Q NO 4.
Derive the Radial and Transverse component of velocity and acceleration in terms of polar coordinate.
Derive the Radial and Transverse component of velocity and acceleration in terms of polar coordinate.
Q NO 5.
a) Prove that in conservative field of force the total energy for system of Particles remain constant through out the motion.
b) A particle is moved by a force F = 20î – 30ĵ + 15 k along a straight line from point A to the point B with positions vectors 2 î + 7 ĵ – 3 k and 5î – 3ĵ – 6 k respectively. Find the work done?
Q NO 6.
State and prove the Kepler’s first law of planetary motion.
State and prove the Kepler’s first law of planetary motion.
Q NO 7.
a) Define Rectilinear motion and derive the expression for motion of particle with variable acceleration for time dependent case only.
b) Find the distance traveled and velocity attained by a particle moving in a straight line, any time t if it starts from rest at t = 0 and subject to an acceleration t2 + sint + et?
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