Bcs 012 0613

BCS-012
No. of Printed Pages : 4
BACHELOR OF COMPUTER
APPLICATIONS (Revised)
Term-End Examination
June, 2013
BCS-012 : BASIC MATHEMATICS
Time : 3 hours Maximum Marks : 100
Note : Question no. 1 is compulsory. Attempt any three
questions from the rest.
1. (a)
(b)
(c)
(d)
(e)
Evaluate
Show that
(c, a + b) are
For every
7"— 3" is
The sum
and their
ratio and
dy
X
2
y
2
2
2
X
3
y3 z3
the points (a,
collinear.
positive integer
divisible by
of first three
product is —1.
the terms.
ex+
b + c), (b, c +a) and
n, prove that
4.
13
terms of a G.P. is
12
Find the common
5
5
5
5
5
Find if y=
dx el— e-x
BCS-012 1 P.T.O.

(f) Evaluate J
3x2 + 13x— 10
dx 5
(g) Write the direction ratio's of the vector 5
a = i+ j — 2k and hence calculate its
direction cosines.
(h) Find a vector of magnitude 9, which is 5
perpendicular to both the vectors 4i —j +3k
and —2i+j-2k.
2. (a) Solve the following system of linear 5
equations using Cramer's Rule x+y=0,
y+z=1, z+x=3.
(b) Find x, y and z so that A = B, where 5
A= [x-2 3 21, B [ y z 6
18z y+2 6z 6y x 2y
1 0 2 1
(c) Reduce the matrix A = 2 1 3 2 to its
1 3 1 3
normal form and hence determine its rank.
3. (a) Find the sum to n terms of the A.G.P. 5
1+3x+5x2+7x3+...;x# 1.
(b) Use De Moivre's theorem to find (-,h+i)3 5
10
BCS-012 2

(c) If a, p are the roots of x2 - 4x +5=0 form 5
an equation whose roots are a2 +2, 02 +2.
(d) Solve the inequality - 2 < 1
-
5
- (4 - 3x) s 8 and 5
graph the solution set.
e
4. (a) Evaluate / /
In x_ e-x
5
x 0 x
(b) If a mothball evaporates at a rate 5
proportional to its surface area 4rrr2, show
that its radius decreases at a constant rate.
(c) Evaluate : $
d x
5
4+ 5 sin2 x
(d) Find the area enclosed by the ellipse 5
x2 y2
a b
--T + --
f- = I
5. (a) Find a unit vector perpendicular to each of 5
the. vectors a
-+13 and a
-4
-
, where
a = i + j + k, 6 = i + 2j + 3k.
(b) Find the projection of the vector 7i +j - 4k 5
on 2i + 6j +3k.
BCS-012 3 P.T.O.

(c) Solve the following LPP by graphical 10
method.
Minimize : z = 20x +10y
Subject to : x + 2y40
3x + y 30
4x +3y?.- 60
and x,
BCS-012 4

Bcs 012 0613

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