Not yet checked 5 of 5 questions have not yet been compared with the official paper.
Q. 1
(a)If y = sin ( k r ) r y = \frac{\sin (kr)}{r} y = r s i n ( k r ) then show that d 2 y d x 2 + κ 2 y = 0 \frac{d^2y}{dx^2} + \kappa^2 y = 0 d x 2 d 2 y + κ 2 y = 0 .
(b)Calculate the Line Integral ∫CA⋅dr , where A = − y i ^ + x j ^ A = -y \hat{i} + x \hat{j} A = − y i ^ + x j ^ and the curve C is given by the equations x2+y2=a2 and z=0 .
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(10)
Q. 2
(a)Forces of magnitude P, 2P, 3P, 4P act respectively along the sides AB, BC, CD, DA of a square ABCD, of sides a, and forces each of magnitude ( 8 2 ) P (8\sqrt{2}) P ( 8 2 ) P act along the diagonals BD, AC. Find the magnitude of the resultant force and distance of its line of action from A.
(b)A uniform ladder, of length 70 feet, rests against a vertical wall with which it makes an angle of 45∘ , the coefficient of friction between the ladder and the wall and the ground respectively being 31 and 21 .
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(10)
Q. 3
(a)A particle moves in a straight line with an acceleration k v kv k v . If its initial velocity is u , find the velocity and the time spent when the particle has travelled a distance x .
(b)Derive the Tangential and Normal components of the velocity and acceleration.
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(10)
Q. 4
(a)Solve the following Cauchy- Euler Equation: x2dx2d2y−2xdxdy−4y=0 .
(b)Convert the following Bernoulli Differential Equation into standard form and then solve: dxdy+1−x2xy=xy2 .
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(10)
Q. 7
(a)Use Newton-Raphson method to find solution accurate to within 10−4 for the non-linear equation. x3−2x2−5=0 , I = [ 1 , 4 ] I = [1,4] I = [ 1 , 4 ] .
(b)Use Lagrange Interpolating polynomial of degree two to approximate f(8.4), If f(8.1) = 16.94410, f(8.3) = 17.56492, f(8.6) = 18.50515, f(8.7)=18.82091.
The 2018 CSS Applied Mathematics paper set by the FPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.
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