Applied Mathematics Part 3-Maths-Exam Paper, Exams of Applied Mathematics

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vcore Sem WN. Com P. / /g- 9610 Aerliéd maths “T- Con. 3804-10. (REVISED COURSE) AN-3452 (3 Hours) [Tetail Marks : 100 N.B.: (1) Question no | is compulsory. (2) Attempt any four questions out of the remaining six questions (3) Figures to right indicate ful) marks. (4) Assume any suitable data whenever required and justify the same. 1 . 4. a) Find k such that 3 lost +y*)+itan™ em is analytic. & ¥ a n = b) IfA=| 4 | find cos 4. 6) t te c) Find all the basic feasible, infeasible, degenerate ,non degenerate solutions of yt 2x7 4xgtxg=7, 2x -K74t3x3+2K4=4 (5) d) Evaluate the line integral { P+ 32) dz along the straight line from(2,0) to (2,2) é and then from (2,2) to (0,2. 6) 8 -6 2 2. a) Find the eigenvalues and eigenvectors of A=|-6 7 —4] Are the eigenvectors 2 ~4 3 linearly independent? (6) 2sin 2x b) If f(z) =utiv is analytic and wty=—_—_________ (7) : e” +e” —2cos2x find f(z) in terms of z. c) Solve by simplex method Max z=x)-x2+3x3 (7) Subject to the constraints x;+x2+x3<10 2X|-X333 , 2X1-2x243x350 X1,X2,X3 20 3. -1 #1 3. a) Show that the matrix A=|~1 5 —1] is diagonalizable. Hence find the diagonal 1 -1 3 and the transforming matrix (6) b) Use Big M method to solve Max Z=x)+4x (7) Subject to the constraints 3x;+x)<3 2x143x2 <6 4xit+5x2 220 , x1X2, 20 c) State Cauchy’s residue theorem and hence evaluate (7) : z~] Hl | . ——— dz ,C:|z,=1.5 ‘ Ip +2245 Hl { Qe ii, (i docsity.com 2 5-3c0sé