# Loyola College Mathematics For Computer Science Question Papers Download

## Loyola College B.Sc. Mathematics April 2012 Mathematics For Computer Science Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

**B.Sc.** DEGREE EXAMINATION – **MATHEMATICS**

SECOND SEMESTER – **APRIL 2012**

# MT 2100 – MATHEMATICS FOR COMPUTER SCIENCE

Date : 23-04-2012 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

**PART A**

Answer **ALL** the questions: **10×2 = 20 **

- Define symmetric matrix with an example.
- Prove that.
- Remove the fractional coefficients from the equation
- Find the partial differential coefficients of .
- Evaluate.
- Evaluate
- Solve the equation = 0.
- Derive the partial differential equation by eliminating the arbitrary constants from .
- Find an iterative formula to , where N is a positive integer.
- Write Simpson’s

**PART B**

Answer any **FIVE** questions: **5×8 = 40 **

** **

- Show that the equations are consistent and solve them.
- Prove that
- Find the condition that the roots of the equation may be in geometric progression.
- Integrate with respect to
*x*. - (i) Evaluate

(ii) Prove that (**4 + 4**)

- Solve the equation
- Solve (i) (ii) (
**4 + 4**) - Determine the root of correct to three decimals using, Regula Falsi method.

**PART C**

Answer any **TWO** questions: **2×20 = 40**

- (i) Find all the characteristic roots and the associated characteristic vectors of the matrix

A =.

(ii) If then prove that (**14+6**)

- (i) Solve the equation

(ii) If , prove that . (**14+6**)

- (i) Integrate with respect to
*x*.

(ii) Solve (**6**+**14**)

- (i) Solve

(ii) Evaluate using trapezoidal rule and Simpson’s rule. (**8+12**)

## Loyola College B.Sc. Computer Science Nov 2012 Mathematics For Computer Science Question Paper PDF Download

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.

** **

** **

** **

**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)