Guru Jambheshwar University 2006 M.C.A mathematics1 - Question Paper

Subject Code-4266

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 -

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

2    3 1

3. (a) Prove that :

2 (sin^D 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.

(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 :

Marks No. of Students 0~iG 3 10-20 5 20-30 7 30-40 10 40-50 12 50-60 15 60-70 12 70-80 6 80--90 2 90-100 8 oite standard deviation frc Marks No. of Students 0-10 3 10-20 16 20-30 26 3040 31 4G-50 16 50-60 8 'i. 1 4

% (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: guru-jambheshwar-university-2006-m-c-a--2197-1.pdf

Earning:   Approval pending.