West Bengal Institute of Technology (WBIT) 2008 B.C.A Computer Application BM101 Mathematics ( ) - Question Paper
CS/BCA/SEM- 1/BM-101/08/(09) 3
ENGINEERING & MANAGEMENT EXAMINATIONS, DECEMBER
' I Full Marks : 70
Time : 3 Hours ]
GROUP - A ( Multiple Choice Type Questions)
10 x 1 - 10
1. Choose the correct alternatives for any ten of the following :
i) If A = { 1, 2, 3, 4, 8 }, B = { 2. 4, 6, 7 }, then A A B is
a) {2, 4}
b) { 1, 2, 3, 4, 6, 7. 8 }
e) <(
d) {1, 3, 6, 7, 8}.
ii) Hm ( 1 + x)1/x is equal to
x-0
b)
d)
a) 1
c) 0 d
1
x
log ( 1/x) x log e.
b)
d)
is
b)
d)
x4
2x.
til) dx ( l0g a X ) 1S eqUal t0 a)
c) ( 1 /x) log a e
H 2 u
iv) If y = log x2, the value of \
\
|
v) The matrix A = |
|
is an |
r
a) orthogonal matrix b)
c) identity matrix d)
vi) Derivative of x4 with respect to x2 is
a) 4x3 b)
c) 2x d)
v
idempotent matrix none of these.
2x2
4.
vii) If the rocts of the equation ax2+bx+c = 0(a*0) are reed and unequal, then its discriminant D satisfies
a) D > 0 and D = a perfect square
b) D = 0
c) D > 0 and D* a perfect square
d) D < 0.
viii) If A = { 1, 2, 3}, B = {2, 3, 6}, then A U Bis
a) { 1. 2, 3} b) { 2, 3 }
c) { 1, 2, 3, 6} d) none of these.
ix) If a, p, y be the roots of x3 - 3x2 + 6x - 2 = 0, then X aP is
a) 3 b) 6
c) 2 d) none of these.
x) If / ( x) = 3 + 2x ; when x > 0 /
= - 3 - 2x ; when x < 0,
then lim f ( x) is
* -* o
a)
c)
3
0
b)
d)
none of these.
xi) If /(x) =
; when 0
= l ; when x = 0, then
a) /( x) is continuous at x = 0
b) fix) is continuous, but not differentiable at x = 0
c) ' / ( x) is discontinuous at x = 0
d) none of these.
2
xii) The value of J | x |dx is
- l
b) 5
d) none of these.
a) 3 c) 5/2
GROUP -B ( Short Answer Type Questions )
Answer any three of the following. 3x5= 15
If a, p, y be the roots of the equation, x3 + px2 + qx + r = 0, then find the value of la3.
2.
x+ y
- l
3. If u = tan
Ji+yTy
Prove that the set of even integers (including zero ) forms an additive group.
, , , 3u du l-o , then show that x + y 3y = 4 sm
jt/2
r
Vcos x
dx.
5. Evaluate
V sin x + Vcos x
| ||||||||||||||||
|
null matrix. |
, find the matrix R so that 5P + 3 Q + 2 R is a
GROUP -C (Long Answer Type Questions )
Answer any three of the following questions.
State Rolles Theorem.
a)
b)
c)
a)
b)
Differentiate n times the following equation :
( 1 + x2 ) y2 + ( 2x-1 ) y j = 0.
If y = sin ( m sin _ 1 x ) , show that
( 1-x2) yn + 2-(2n+ l)xy+1 + (m2-n2)yn =0. 4 + 5 + 6
* If pth, qth and rth terms of an A.P. are P, Q and R respectively, show that p(Q-R) + q(R-P) + r(P-9) = 0.
Show that the centroid of a triangle with vertices ( x t . y t ) . ( *2 , y 2 ) and
(*3- y3) is
y i + y 2 + y
Xj + X2 + X3
Find the equation of a straight line through the point of intersection of lines 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 and that is perpendicular to the line 6x - 7y + 8 = 0. 5 + 5 + 5
c)
a)
X K
Show that cos x>l--2~ if 0 < x < g
y 2 ,, 2
. x2 + 2*0
x + y
b) If f[x, y)
0 ,x2 + y2 = 0.
then show that f ( 0, 0 ) = fyx ( 0, 0 ) .
x2
4 + 6 + 5
dx.
Evaluate
(x2 + a2)(x2 + b2)
Reduce the following equation to its canonical form and determine the nature of the conic represented by it : .
6x2 - 5xy - 6y 2 + 14x + 5y + 4 = 0.
Find the equation of the ellipse one of whose foci is ( - 1, 1 ), eccentricity is 0-5 and the corresponding directrix is y = x + 3. 9 + 6
b)
11. a) Solve the equation by Cardans method, 2x3 + 3x2 + 3x + 1 =0.
b) Let G = {aeR/-i<a<l}. Define a binary operation on G by a b = V a, b e G. Show that ( G, 0 ) is a group.
c) Find the nature of the roots x4 + qx2 + rx - s = 0 by Descartes rule of signs (where q, r, s, being positive ). 15
12. a) If by a trnasformatkm of one rectangular axis to another with same origin the
expression ax+ by changes to a1 x' + bAy1,
2 2
prove that a2 + ba*a,+b')
oo
r dx
J ( x+ 1 ) ( x +
b) Show that I (-.T nr~2l = lo2
0
1 + 2 t + n
c) Use the method of integration to evaluate Lt ;-JTTT-- k > 0.
n -o n
15
END
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11205 (8/12)
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Attachment: |
| Earning: Approval pending. |
