# APPLIED MATHEMATICS. PAPER-II COMPETITIVE EXAMINATION FOR RECRUITMENT

May 19th, 2015
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Note: Attempt FIVE questions in all, including QUESTION NUMBER 8 which is COMPULSORY, select TWO questions from each SECTION. All questions carry EQUAL marks. (a) Use the method of variation of parameters to find a general solution for the differential equation y? + y = tan2 x

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FEDERAL PUBLIC SERVICE COMMISSIONCOMPETITIVE EXAMINATION FOR RECRUITMENT TO POSTSIN B.P.S.-17 UNDER THE FEDERAL GOVERNMENT, 2000.APPLIED MATHEMATICS. PAPER-IITIME ALLOWED: 3 HOURS MAXIMUM MARKS: 100 Note: Attempt FIVE questions in all, including QUESTION NUMBER 8 which is COMPULSORY, select TWO questions from each SECTION. All questions carry EQUAL marks.SECTION-I(a) Use the method of variation of parameters to find a general solution for the differential equation y? + y = tan2 x(b) Find the series solution of the differential equation y?+xy'+2y=0 withCentre of expansion at x0 =1.2. (a) Find the general solution of y?' 2y? y' + 2y = e3x(b) Define partial differential equation with examples. Solve2p+3q=1.3. (a) Use Monges method to solveq(1 +q)r(l +2q)(l +p)s+(l +p)2 t=0.(b) Find the solution of the Laplace equation in three dimensions.SECTION-II4. (a) Find the scalars that can be constructed from Cartesian tensors ofrank land 2.(b) (i) If Ai li2ir is a Cartesian tensor of rank r, then?Ai li2ir is a tensor of rank r+ 1.?x,(ii) Show that ijk ijk=65. (a) Show that Newton - Raphson is a quadratically convergent method.(b) Solve f(x) = e-x Sin [nx] =0, using Regula Falsi Method. 2 6. (a) Solve the system of equationsl0x1 + X2 + 2x3 = 44x1 + 2x2 + 10x3 = 61 2x1 +l0x2 +X3 = 51by Gauss- Seidel iterative method with an absolute convergence criterion of = = 0.0001(b) Use the Trapezoidal and simposon's rules to esti

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