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BCS - 012 o. of Printed Pages : 4 BACHELOR OF COMPUTER APPLICATIONS (Revised) Term-End Examination June, 2013 BCS-012 : BASIC MATHEMATICS Time : 3 hours aximum M arks : 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 2 2 X 3 3 3 the points a, collinear. positive integer divisible by of first three product is —1. the terms. e x + b + c), (b, c +a) and n, prove that 4. 1 3 terms of a G.P. is 12 Find the common 5 5 5 5 5 ind f y= dx l— e BCS - 012 .T.O.
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BCS
-012
o. of Printed Pages :
4
BACHELOR OF COMPUTER
APPLICATIONS
(Revised)
Term-End Examination
June, 2013
BCS-012 : BASIC MATHEMATICS
Time : 3 hours
aximum M arks : 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 2
2
X
3 3
3
the points a,
collinear.
positive integer
divisible by
of first three
product is —1.
the terms.
e
x
+
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
ind f y=
dx
l— e
BCS
-
012
.T.O.
7/21/2019 c
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(f)
Evaluate
3x
2
+ 13x— 10
dx
(g)
Write the direction ratio's of the vector
a = i+ j — 2k and hence calculate its
direction cosines.
(h)
Find a vector of
magnitude 9, which is
perpendicular to both
the vectors 4i —j +3k
and —2i+j-2k.
2.
a) Solve the following system of linear
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
A= [x 2 3 21
B
z6
18z y+2 6z
y 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.
1+3x+5x
2
+7x
3
+...;x 1.
(b) UseDe Moivre's theorem to find (-,h+i)
3
10
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(c)
If a,
p
are the roots of x
2
- 4x +5=0 form
an equation whose roots are a2 + 2,
0
2 + 2.
(d)
Solve the inequality - 2 <
1
- (4 - 3x) s 8 and 5
graph the solution set.
e
4.
a) Evaluate / /
I n _ e-x
x x
(b) If a mothball evaporates at a rate
proportional to its surface area 4rrr
2, show
that its radius decreases at a constant rate.
c)
valuate : $
d x
5
4+ 5 sin
2
x
(d) Find the area enclosed by the ellipse
x
2
y
2
ab
-T +
--f
-
=
I
5. a) Find a unit vector perpendicular to each of
the. vectors
a
1 3
and
a
4
, where
a = i + j + k, 6 = i + 2j + 3k.
(b) Find the projection of the vector 7i +j - 4k
on 2i + 6j +3k.
BCS-012
.T.O.
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(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
