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 2x2 + 3x +5 = 0, find 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 (D2 +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 q2 – p = y – x.
(14+6)
- (i) Solve upto 3 decimals by using Regula-flasi method.
(ii) Evaluate using Simpson’s 1/3rd rule with
(12+8)