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.
Con. 235-09.
(2) Attempt any four questions from question Nos. 2 to question No. 7.
(3) Figures to the right indicate full marks.
20
1. Solve :
dy
(a) ~r = cos(x + y)
' ' dx
(b) (x - 2ey) dy + (y + x sin x) dx = 0
(c) x (l-x2 + (2x2- 1 j y = x3 .
(d) (x2 + y2) dx + 2xy-dy = 0.
10
2. (a) Find the eigen values and eigen vector for
'2-2 3 A = 1 1 1 1 3-1
10
(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 nth derivative by method of fraction :
10
10
x
y~(x-1)(x-2)(x-3)
(b) Find nth 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
10
1
A =
6. (a) Find the order and degree of the following :
dy 5
dx
- 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
d2z
dxdy dydx
Attachment: |
Earning: Approval pending. |