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)

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

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**Part B**

Answer any FIVE questions: (5 x8 = 40)

- 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*.*

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

# Part C

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

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

- (i) Evaluate:
*dx*

(ii) Evaluate: *.*

(15+5)

- (a) Solve the equation .

(b) Solve *q ^{2} – p = y – x*.

(14+6)

- (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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