SECTION-A
UNIT-I
1. If A= {1,2,3, 5, 7} and B : {2. q, s,9} then A - B will be :
(B) {1,3,7}
(A) {4, e}
(C) {2, 5}
@) nqne of these
2. If A : {1, 2, 3, 4\,8 = {3, 4, 5,6} and C : 14, 5, 6, 7\ then (A U B) fl'C is equal to :
(B) {3; 4,5,6,7}
(A) {4,5,6}
(c)
3'
{5,6,7}
(D) 0
In above question (A 0 B) U C will be
:
{s,6,7}
(c) 13,4,s,6,7|
(B) t2,4, s,6}
(A)
'
4.
5.
@)(r,2,3,4,s,6,7)
If A= {1,3,5,7,9, 11} andB:"(3,5,7,8\ {hencomplementofAinBwillbe:
(B) {3,5,7}
(A) {1, e,
(c) {3, s,7,
@) {8}
IfA be a frnite set consisting ofn elements then the power set F(A) contains :
(B) 2*t elements
(A) ? elements
1r}
s}
td?,,#
(c)
2'3) andB = {3'4's}
***"'r;n;f!dtr"o"""oreandBis:
{r,2,4,s}
7. IfA= {0, 1} andB :
(D) {3}
{0,-1} thenA
(A) {(0, 0), (0, 1), (-1, 0), (-1,
(C) t(-1, 1), (1,
x B willbe
1)}
:
(B) {(0, 0), (0, -1), (1, 0)' (1,
(D) none of these
-1))
-l)}
8. IfA has 32 elements,. B has 42 elemehts and A U B has 62 elements then the number of
elements in
A 0 B willbe
12
(c) 10
(B) 20
(A)
(D) 30
9, Irt S be the set ofall slraight lines in a plane. The relation R in S defined by "x is parallel y" is :
(B) Symmetric
(A) Reflexive
(C) Transitive
@) All alove
TJNIT-II
10. If (x) :
cos x
+
.6 sin x then f(%) will be equal to :
(A) I
(B) 2
(c) zJi
(D)
BCA-10512560
"2
3
--
, --.
?--<-4/==-:--.?1:-
<2)
12- rf
sinx
:]
tlr"r_cot x witl be equal to
zoze
of&e-e
:
(D;
p.zazea/,*e.r
'(3- 1f76r7--';
(A/
:
a"onffi
ts equal to;
?
(B)
{L m il
1{.
;
(D) none of these
,l-l
.,
will
be equal to :
p2
+
I
-r
I-im
(Ail 2
(cI I
fi\
7
(B) -2
(D) 0
tim *2 *bx+c
--- - is equal to :
';+:cdr- er-f
^
(B)
*
(D) 0
XrM
n
-*,1r,{l*r}:' is equal to
:
rAl
e
(B) y"
rCr
tr
(D) none of these
fr+?, ,
l-* f""t=1 4 ,
{.3-r-5 ,
x<3
x=3 is
continuous at x : 3 then the value of the l, is :
x>3
(B) 3
(D) 2
\
\hlf
3
P.TO.
Tifl
11. Iff
-+ R s.t f(")
(A) 2(x'z-l)
(C) 2x2-l
12. If
:R
?
sin
, =|
5
: 2x-1 and g : R + R s.t. g(x) - x2 then (fog) (x) is
then cot x
2(x-tf
(B)
(D) none of these
will
be equal to
:
,
:
(A);
(B)
4
;
3
(c)
13.
If
(D) none of these
+
71xy
(A)
=J; then ffiis
equal to
:
(B)
;
(c) I
14.
lim
7
5
(D) none of these
*2
-l will be equal
to :
*-1 *a
(B) -2
(D) 0
(A)
7
a
rc) e
lim
16. ,-'o(t*
D% isequal to
:
E
(A)
e
(B) %
(c)
1
(D) none of these
,
'
x<3
x=3
is continuous at x
, x>3
:
3 then the value of the
l, is :
(B) 3
(D) 2
BCA-105 t2560
3
nTo.
I
ls.
rr /(x) =lrr)t
'
:::rthen
(A) Continuous at"x
r(x) is :
(B) not continuous at x: 2
-2
(D) none of these
(C) not defined at x: 2
UNIT-III
19.
The roots of the quadratic equation2x2
- 13x +l 15:0 are
:
(B) 3,;
(D) s,;
:0 then
20. If cr, B are roots of the equation x2 -2x+ 3
t.*
wifl be equal to
:
._)
(A) ?
(B)
T
(c) -1
(D)
;
a
J
J
zL. r
(-r,
"f:)
poldr coordinates are
be the..cartesion c6oldinates oi a point, then its
:
(B)
(D) none of these
area of this triangle will be :
22. If (4, -1), (1 ,2) and(4,-3)are vertices of artriangle thenthe
(B) 15 units
(A) 12 units
(D) 17 units
(C) 16.units
be :
23. The locus of the point whose distance from the origin is 4 will
(A) xt
-t':
(C) x, +
(B)x*Y:4
16
t' : 16
(D) none of these
points (1, 2) and (-1, 4) is given by
24. The equatiol of the line passing through the
(B)x-y-3:0
(D) x -2Y + 5 :0
(A)x+y-3:0
(C)x-Y+3:0
BCA-1O5 12s60
4
:
2s. ,,
o=l_: i
(^)[;
(c)
|.". u=[l I ;] thenA-Bis:
(',[j:t
i|
[-l z
-q]
L-+ t -tJ
i] *o
(D) none of these
'=lll
**ABis
*,[ll
il]
(D) none of these
27
.
Iirverse of the
(A)
rcl
'
r
-u,n"
t,
[]
L' ll
,
[-t :l
,Lo
r[
-rl
3 -rl
ml-o ,l
l;tan.rl it
28' a'L=*'
J '
a
.
(A) -(sin x *.cos x)
(C) sin x - cos x
d
zg. ft{"z*)
(B) cos x - sin x
(D) sin x * cos x
is :
(A) 2a*
@)
(B) ao
":
BCA-105 /2560
(D)
3
2*RTA
30.
t;
$oogrin
ax
=
(A) tan x
(C) cosec x
31.
(B) cot x
(D) none of these
i-r
rf f (x) =
fi
then
f (2) will
be equal to
:
(A) -)/
7g
(c)
32. If
4
t
y:
(A)
(D) none of these
sec
x -| tan x then
dy
dx
will be :
x (sec x - tan x)
(C) sec x (sec x + tan x)
33
(B) tan x (tan x
sec
If Y:
,12 r,
e3*
then
?
dx'
will
3i4i. If x2 + t'
be equal to
:
(B) 3e3.
(D) 9 e2.
:6x -
2ry
tben
dy_
dx
x-3
(A)F
3-x
(B) ,. ,
!-r
x*3
3-x
(D) -.,,
/1-L
(c) y*r
35. A function y (A)
(c)
f(x) will be maximum if
:
)2,,
d2v
(g) :-*<o
clx->0
s2,,
(D) none of these
clx-
==0
Function f(x)
(A)x--1
(c)
- sec x)
(D) none of these
(A) 9 e3.
(C) 6 e3.
36.
2
t
(B)
x:
:
x3
-
3x + 4 has minimum valuel:at
(B)
x:2
(D)":-2
I
BCA-10s/zsffi
:
6
UNIT-V
4
37. Jx
l'- *' dr =
(A)
_2
+2
+tosx+c
(C) togr
-t*,
2
(B)xlogx*c
(D) none of these
o'-3g. rIl+x.
(A)sec-tx*c
(C) cosec-r x
(B)tan-tx*c
(D) none of these
39. Iro*a* (A)
ea.
+c
(C) 2e2* +
c,
(B) 4ea. + s
(D)
^4x
:-+c
4
40. J,un x dx =
(A) log sin x + c
(C) log sec x + c
r1
(B) log cos x * c
(D) none of these
41. Jl;: ^ a* =
J_ ZX
(A)
\/2 -]rog1: -2x)+ c
(C)-log(3 -2x)+s
42.
(B) 2log (3 - 2x) + s
(D) none of these
l-p-' x'-16
I. ( x-a\
(A)
frog|;;J..
(cl
jr"g(#).,
43. l!-'un* o* =
", I + tan.r
(A) log (cos x sin x) + c
x * cos x) + c
,,(C) log (sin
BCA-I05 /2560
(B) log (sin x _ cos x) + c
(D) none of these
nTa
t
.
44.
l2t
x'dx =
J,
(A);
511
(C)
45.
(B)
7
-;
@) none of these
The value of the
4, ^
integal J_4(ax'+Dx+c)&
(A) c onJy
(C) a, b and
r. (a)
I
dspsnd5
6n;
@) b and c
(D) a and c
c
SEClION-B
Let R be the relation on N x N defined by (q b) R G, d), itrad = bc V (a,b)
(b)
show that R is an equivalence relation:
IfA {a,b, c, d}, B = {a, e, g} and e {e, g, m, n,
(b).
Test the continuity of the
:
:
p} then fird
(r)AUc(ts nc) Gi)(AUB)nc Gii)(AnB)uC
2. (a) Evaluate ,* lJ"'*r -"j.
| ru u-/,
f(x)_l;_n ,
following function at x
:
0,
x*o
I o , x:o
3. (a)
Find the roots of the fbllowing quadratic equation
2){+31
9
x2
+7
2x+47
t2-7
9
_z r'l
It
tt
O) If A=l 2 3| '12)lthetrshowthatA3.-6A2+25A-421=0.
L3
4. (a) Find the differential coefficient of (;-1)' *itf, *.pect to x.
(b) Find the maxima and minima of the following function2x3 - Zl* + 3Gx-20.
!. (a)
(b)
trvaluate
r2x
J7.k_2.
Evaluate -u
li.
BCA-105 t2560
*.
,*"'ni
I + cos- -r
I
eNxN,