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Css Applied Mathematics 2016

css-applied-mathematics-2016 css paper

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94 views12 pages

Css Applied Mathematics 2016

css-applied-mathematics-2016 css paper

Uploaded by

shahbazbhatti372
Copyright
© © All Rights Reserved
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2% FEDERAL PUBLIC SERVICE COMMISSION ee COMPETITIVE EXAMINATION-2016 ‘RelNember 3 FOR RECRUITMENT TO POSTS IN BS-17 UNDER THE FEDERAL GOVERNMENT APPLIED MATHEMATIC TIME ALLOWED: THREE HOURS MAXIMUM MARKS = 100 NOTEXi)_Attempi ONLY FIVE questions ALL questions carry EQUAL marks Gi) All the parts (if any) of each Question must be attempted at one place instead of at different places. ‘Candidate must write Q. No. in the Answer Book in accordance with Q. No. in the Q.Paper. iv) No Page/Space be left blank between the answers. All the blank pages of Answer Book must be crossed. (vi) Extra attempt of any question or any part of the attempted question will not be considered (v) Use of Caleulator is allowed. Oy 0) (b) Verify Stokes’ theorem for spi-yz?i> tis) the upper half surface of the sphere x+y? +2 boundary Q.No.2, (=) Forces P,Q. avtata point parallel to the sides oFaiangle ABC taken in he (10) same order, Show thatthe magnitude ofthe resultant force is [PEE RT=2 QReos A-2RPcosB-2PQeose (©) Fin the distance from the cusp of the centroid ofthe region bounded by the (10) cardioid ¢ = a (1 +¢05 0) QLNo.3. (a) A partile deseribes simple harmonic motion in such a way that its velocity and (10) ‘acceleration ata point P are u and f respectively and the corresponding quantities at another point Q are v and g Find the distance PQ. (b)—_Dezive the radial and wansverse components of velocity and acceleration ofa panicle. (10) Q.No, 4, Solve the following differential equations d ‘ @ Mey «1m (b) (D’-sD+6)y = e™ (10) QNo.S. (4) Solve the diferent equation using the method of variation of parameters (10) fi a Bip-ims, eo (b) Solve the Euler - Cauchy differential equation x? y"—3 xy! + 4y (10) No.6. (a) Find the Fourier series ofthe fllowing function i) Z f-x if -n> using 0 (i) Trapezoidal rule with n= 4 Gi) Simpson's rule with ‘Also compare the results with the exact value ofthe integral (b)_ Apply the improved Euler method to solve the initial - value problem: yoxty, yO=0 by choosing h = 0.2 and computing y,.....¥s (a0) (a0) (10) (a0) FEDERAL PUBLIC SERVICE COMMISSION ‘COMPETITIVE EXAMINATION-2017 FOR RECRUITMENT TO POSTS IN BS-17 UNDER THE FEDERAL GOVERNMENT APPLIED MATHEMATICS ‘TIME ALLOWED: THREE HOURS ‘MAXIMUM MARKS = 100 NOTE} Attempt ONLY FIVE questions. ALL questions carry EQUAL marks Gi) All the parts (if any) of each Question must be atterapted at one place instead of at different places. Gil) Candidate must write Q. No. in the Answer Book in accordance with Q. No. in the Q.Paper. No Page/Space be left blank between the answers. All the blank pages of Answer Book must be crossed. (vi) Extra attempt of any question or any part of the attempted question will not be considered, (v) Use of Calculator is allowed. ar QNo.1. (qy Suppose rit) = (€ costyi+ (e'sint)j. Show that the angle between r and a0) never changes. What is the angle? 0) Using divergence theorem of Gans, Eat Jf tndy yids sendy 00) #,O0, O0, u(30)= f(a), SH g(adfattimet=0}, and O

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