ALLIED-MATHEMATICS–I.doc-St.JosephsCollege.docVIP

CLASS: B.Sc. COMPUTER SCIENCE 13N/ 239 St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002 SEMESTER EXAMINATIONS – NOVEMBER 2013 TIME: 3 Hrs. MAXIMUM MARKS: 100 SEM SET PAPER CODE TITLE OF THE PAPER I 2013 11UCS130401 ALLIED : MATHEMATICS – I SECTION – A Answer all the questions: 20 x 1 = 20 Choose the correct answer: 1. The determinant value of the matrix is a) 0 b) 1 c) (1 d) 2 2. The complimentary function of (D2 + 5D + 6) y = ex is a) Ae(2x + Be(3x b) (A+B)e(2x c) e(2x[Acos3x + Bsin3x] d) Ae2x + Be3x 3. The geometric series is convergent if a) |x| 1 b) x ( 1 c) x = (1 d) x (1 4. The Laplace transform of t is a) 1/s b) 1/s2 c) 2/s3 d) 1 5. If the function f(x) is odd, then is a) 0 b) 1 c) 2 d) (1 Fill in the blanks: 6. The sum of the eigen values of a matrix A is equal to the sum of the elements on its _______. 7. If the auxillary equation has imaginary roots, then the solution of the DE is y = _______. 8. The sum of the series 1 + x + x2 + x3 + … + xn-1 + … is _______ if 0 x 1. 9. The Laplace transform of sin at is _______. 10. If a function f(x) is even, its Fourier expansion in ((x( contain only _______ term. State True or False: 11. The rank of a non zero matrix is greater than or equal to 1. 12. The particular integral of (aD2 + bD + c)y = X is . 13. If Sn, the sum to first ‘n’ terms of the series, tends to more than one limit, when the series is said to oscillate. 14. If L[f(t)] = f(s), then L[f(at)] = 1/a F(s/a) 15. If f(a) = f(-x), then f(x) is said to be even function. Answer in one or two sentences: 16. State Cayley Hamilton theorem. 17. Solve z = ax + by + a 18. Define divergence. 19. Find L[t2]. 20. Write down the formula for half range cosine series. SECTION – B Answer all the questions: 5 x 4 = 20 21. a. Using determinants, solve the following simultaneous equations: 5x + 3y + 3z = 48 2x + 6y – 3z = 18