University of Mumbai 2009-1st Sem B.Sc Information Technology (IT) Maths - I - Question Paper

Kindly obtain the attachment.

11-Dec.-Exm.-Nk-08. 92    - 20 o3 /WccShs -jz

N.B. :(1) Question No. 1 is compulsory.

(2)    Attempt any four questions from question Nos. 2 to question No. 7.

(3)    Figures to the right indicate full marks.

1. Solve :

dy

(a)    ~r = cos(x + y)

' '    dx

(b)    (x - 2e^y) dy + (y + x sin x) dx = 0

(c)    x (l-x² + (2x²- 1 j y = x³ .

(d)    (x² + y²) dx + 2xy-dy = 0.

2. (a) Find the eigen values and eigen vector for

'2-2 3 A = 1 1 1 1 3-1

(b) Find the inverse of the matrix by applying elementary row transformations

	' -4	-3	-3
A =	1	0	1
	4	4	3

3. (a) Find the n^th derivative by method of fraction :

x

^y~(x-1)(x-2)(x-3)

(b) Find n^th derivative of

x

2 2 x +a

Con. 235-TT-1020-09.

5. (a) Discuss the consistency of

3x + y + 2z = 3 2x - 3y - z = - 3 x + 2y + z = 4

(b) Find the inverse of the following matrix by finding its adjoint

1

A =

6. (a) Find the order and degree of the following :

dy 5

dx

(2)

- dx if v dx J

(b) Reduce the matrix to Echelon and find its rank

1    2 3

2    4 7

3    6 10

(c) Solve

x + y)-f+y = 0 dx

7. (a) Solve    6

(y⁴ + 2y) dx (xy³ + 2y⁴ - 4x) dy = 0.

(b)    If the temperature of air is 30 C and substance cools from 100C to 70C in 8 15 minutes. Find when the temperature will be 40C.

(c)    If z = xy + yx then show that    6

d²z

dxdy dydx

Attachment: university-of-mumbai-2009-b-sc-information-technology-51550-1.pdf

Earning:   Approval pending.