Karnataka State Open University (KSOU) 2010-1st Sem B.C.A Computer Application Iester Mathematics - Question Paper

iiii mini mini    bca - 21

II Semester B.C.A. Examination, Feb./March 2010 MATHEMATICS

Time 3 Hours    Max. Marks : 80

Instructions : 1) Answer all questions in Part A, 6 out of 8 questions in Part B, and 3 out of 5 questions in Part C.

2)    Part A : Questions from 1 to 8 carry 1 mark and 9 to 14 carry 2 marks each.

3)    Part B : Each question carries 5 marks.

4)    Part C: Each question carries 10 marks.

PART - A

1.    The identity matrix of order three is of the form___

2.    Define a semi group.

3.    The section of a sphere by a plane is___

4.    The n^1h order derivative of Cos(ax + b) is _

rc/ 2

5.    The Reduction formula for J ^{sin x} dx is

0

BCA - 21    -2

10. Differentiate Sin [ Sin^-1 (x¹) ] w. r. t x

d²y

11. If x = at² and y = 2at then find 7

^J    dx²

12.    Evaluate J x tan ^-1 x dx

13.    Verify the condition for exact and hence solve (x + y + cosx) dx + sinx dy = 0.

then find A² - 5A + 13I.

PART - B

1. Find the eigen values of the matrix

	' 5	4	- 4
A =	4	5	- 4
	-1 V	-1	2 /

dx

5+4cosx

dy ^r

7. Solve : y^-x = ^a dx

¹ dx

8. Evaluate : k : 2 0I-x + x

PART - C

1. Find the eigen values and eigen vector of the matrix

1 2

2 1 - 6

2 - 2 3

2.    If A = 2i-j+31c, B=i + 2j+31c and C=3i+j-k then find A.(xC) and A x(B x C).

3.    Find the equation of the plane through the points (2, 2, 1),(1, -2, 3) and parallel to the line joining the points (2, 1, -3) and (-1, 5, -8).

4.    If y = (Sin ¹ x)² then P.T (1 - x²)y_n+2 - (2n + 1)xy_n+1 - n²y_n = 0.

5.    Solve : (y² + 2xy) dx + (2x² + 3xy) dy = 0.

1

   Find a such that the vectors

   ys ys    ys        ys    ys    ys        ys.ys.ys.

A = 2i - .j + ]k, B = i + 2j+31c and C = 3i + aj+51c are coplanar.

Attachment: karnataka-state-open-university--ksou--2010-b-c-a-computer-application-33900-1.pdf

Earning:   Approval pending.