# Loyola College B.Sc. Computer Science April 2003 Applicable Mathematics Question Paper PDF Download

LOYOLA COLLEGE (Autonomous), chennai – 600 034

# B.Sc.  degree examination – computer science

third semester -april 2003

## 9.00 – 12.00

PART   A                                 (10 ´ 2 = 20 Marks)

01.Show that .

1. Find the rank of the matrix .
2. Form a rational cubic equation, whose roots are 1, 3 -, 3 +.
3. If sin (A+iB) = x + iy, prove that .
4. State Euler’s theorem for a homogenous function f(x,y,z) of degree ‘n’.
5. Examine the function f(x,y) = 1+ x2-y2 for maxima and minima.
6. Evaluate .
7. Find .
8. Solve q = 2yp2.
9. Find the solution of (D2 + 2D +1) y = 0

PART B                              (5 ´ 8 = 40 Marks)

# 11.      Find the sum to infinity of the series

(OR)

Verify Cayley -Hamilton theorem for the matrix .

1. Find by Horner’s method the root of the equation x3-3x +1 = 0 which lies between 1 and 2, up to two decimal places.

(OR)

Expand sin3q cos5q inseries of sines of multiples of ‘q’.

1. Find the radius of curvature at to the curve x3 + y3 =3axy.

(OR)

Using Lagrange’s multiplier method, find the minimum of the function

u = xyz subject to xy + yz +zx = a (x >0, y>0, z >0).

1. By changing order of integration, evaluate.

(OR)

Integrate  with respect to ‘x’.

1. Solve .

(OR)

Find the solution of (D2-3D +2)y = sin 3x.

PART C                             (2 ´ 20 = 40 Marks)

1. (a) Find the eigen values and eigen vectors of the matrix.
• If tan log (x + iy) = a + ib, where a2 + b2 ¹1, show that

tan log  (x2 + y2) =.

1. (a) Solve the reciprocal equation  6x6-35x5 + 56x4-56x2 35x-6 = 0
• Investigate the maximum and minimum values of

4x2 + 6xy + 9y2 – 8x -24y + 4.

1. (a) Solve p tan x + q tan y = tan z.
• Evaluateover the positive quadrant of the circle

x2 + y2 = a2 .

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