Guru Jambheshwar University 2006 M.C.A mathematics1 - Question Paper
M.C.A. (First Year) EXAMINATION .
(5 Years Integrated Course)
MCA-103 Mathematics--!
Time : 3 Hours Maximum Marks : 100
Note : Attempt any Five questions. All questions cany equal marks.
1. (a) Find the value of x :
x2 -7*-30 = (x + 5) - j2x2 -7x-5
(b) Solve the following equations by Cramer's rule :
- x + y>+z = 9 2x + 5v + lz " 52 2x + v -- z ~ 0
2. (a) If matrices A
4 -2]
B -
and
0
find product AB and BA. Is AB = BA ?
(b) Define transpose of a matrix and find inverse of the matrix :
1 2 3 3 1 2
A
2 3 1
3. (a) Prove that :
2 (sinD x + cos x) - 3 (sin"* x + cos4 x) + 1 = 0
(b) If 5 tan 0 = 4, find the value of
5 sin 0-3 cosG
sin 0 + 2 cosO *
Find the value of sin 15 and tan 15.
(c)
(a) If the points (x, - 1), (2, 1) and (4, 5) are on a straight -line, then find the value of x.
(b) Find the locus of a point (.v, y) which moves so that its distance from (4, 0) and j;-axis are equal
(c) Find the equation of a straight line passing through (3, 4) and having sum of intercepts as 14.
5. (a) If :
i
y - (a sin x + b cosx)
dy find ,
dx2
(b) Find /?th derivative of y-e'Mogx.
(c) Evaluate :
.....dx.
(x + 1) (x + !)
6. Solve the following differential equations :
(a) ydx - xdy - xy dx
(b) (x + y) dx + (x - y) dy- 0
2 dy
(c) cost x + v = tan x
v ; dx '
data : |
|
(b)
% (a) State and prove Baye's theorem for probability
(b) Find first two moments of Binomial distribution. Hence find mean and variance.
(c) Calculate coefficient of correlation from the following data :
a* : 1 2 3 4 5 v : 2 5 3 8 7
J-4266 5 1,600
Attachment: |
Earning: Approval pending. |