## 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

1. Define symmetric matrix with an example.
2. Prove that.
3. Remove the fractional coefficients from the equation
4. Find the partial differential coefficients of .
5. Evaluate.
6. Evaluate
7. Solve the equation = 0.
8. Derive the partial differential equation by eliminating the arbitrary constants from .
9. Find an iterative formula to , where N is a positive integer.
10. Write Simpson’s

PART B

Answer any FIVE questions:                                                                                          5×8 = 40

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

(ii) Prove that                                                                     (4 + 4)

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

PART C

Answer any TWO questions:                                                                                       2×20 = 40

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

A =.

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

1. (i) Solve the equation

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

1. (i) Integrate with respect to x.

(ii) Solve                                                             (6+14)

1. (i) Solve

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

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## 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

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)

1. 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.

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

# Part C

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

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

1. (i) Evaluate: dx

(ii) Evaluate: .

(15+5)

1. (a) Solve the equation .

(b) Solve q2 – p = y – x.

(14+6)

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

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

(12+8)

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