CSS Applied Mathematics Past Paper 2020

Instructions specific to this paper

• Attempt ONLY FIVE questions. ALL questions carry EQUAL marks
• Use of Calculator is allowed.
• : 3.49,4.82,5.96,7.5,8.2

Questions

1. Q. 220 marks

   A particle P of mass m slides down a frictionless inclined plane AB of an angle α with the horizontal. If it starts from rest at the top A, find (a) the acceleration (b) the velocity and (c) the distance travelled after time t.

2. Q. 310 marks

   (a) Discuss the motion of a particle moving in a straight line if it starts from rest at a distance ‘a’ from a point O and moves with an acceleration equal to k times its distance from O. (b) Find radial and transversal components of velocity and acceleration. (10) d2y (10)

3. Q. 410 marks

   (a) Solve + y = Co sec x dx 2 y − Sinx (b) Solve dy + dx = 0 x

4. Q. 510 marks

   (a) Solve the initial value problem dy x (2 + x) + 2 (1 + x) y = 1 + 3 x 2 , y (−1) = 1 dx (b) Find the general solution of the equation (10) ( D − 2 D + 1) y = 2 x − 3x + 4 x + 5 3 3 2

5. Q. 610 marks

   (a) Find the Fourier series of f:  x, 0 < x < 1 f ( x) =  0,1 < x < 2  ∂ 2u 1 ∂u (10) (b) Solve the boundary value problem = ∂x 2 k ∂t Satisfying u(o,t)=u(l,t)=0 and u(x,o)=lx-x2 APPLIED MATHEMATICS

6. Q. 710 marks

   (a) By using regular Falsi method, solve Logx – Cosx = 0 (b) Find the value of ƒ(7.5) by using Newton Gregory Backward Difference (10) Interpolation formula. X: 5, 6.1, 6.9, 8, 8.6 f (x) : 3.49,4.82,5.96,7.5,8.2

7. Q. 810 marks

   (a) Applying the Taylor series method, compute x Sin t ∫ o t dt for x = 0 (0.1)1 (b) Use fourth order RK method to solve (10) dy = t + y ; y (0) = 1 from t = 0 to t = 0.4 taking h = 0.4 dx

Standard FPSC instructions

Printed on this and every CSS paper.

• Part-II is to be attempted on the separate Answer Book.
• All the parts (if any) of each question must be attempted at one place instead of at different places.
• Write Q. No. in the Answer Book in accordance with Q. No. in the question paper.
• No page/space be left blank between the answers. All the blank pages of the Answer Book must be crossed.
• Extra attempt of any question or any part of the attempted question will not be considered.