LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMPUTER SCI. & APPL.

FIRST SEMESTER – NOVEMBER 2012

MT 1103 – MATHEMATICS FOR COMPUTER SCIENCE

 

 

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

 

 

 

Part A

Answer ALL questions:                                                                                                              (10X2 =20)

 

1. Define Unitary Matrix.
2. Write down the expansion of in terms of cosθ.
3. If α and β are the roots of 2x² + 3x +5 = 0, find α+β and αβ.
4. Find partial differential coefficients of u = sin (ax + by + cz) with respect to x, y and z.
5. Evaluate .
6. Evaluate.
7. Solve the differential equation (D² +2D + 1)y = 0.
8. Find the complete integral of
9. Write the formula for Trapezoidal rule.
10. Write Newton’s backward difference formula for first and second order derivatives.

 

 

 

Part B

Answer any FIVE questions:                                                                                                  (5 x8 = 40)

 

 

11. Test the consistency of the following system of equations and if consistent solve

2x-y-z = 2, x+2y+z = 2, 4x-7y-5z = 2.

12. Show that
13. Solve
14. What is the radius of curvature of the curve at the point (1,1).
15. Show that .
16. Evaluate: .
17. Solve the equation.
18. Find by Newton-Raphson method, the real root of, correct to three decimal places.

 

 

Part C

 

 

Answer any TWO questions:                                                                                                (2 x 20 = 40)

 

19. Verify Cayley-Hamilton theorem for the matrix and hence find its inverse.

 

20. (i) Evaluate: dx

(ii) Evaluate: .

(15+5)

21. (a) Solve the equation .

(b) Solve q² – p = y – x.

(14+6)

 

22. (i) Solve  upto 3 decimals by using Regula-flasi method.

(ii) Evaluate  using Simpson’s 1/3^rd rule with

(12+8)

 

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