1.
A= { x : x ≠ x }represents
a) { 0 } b) { } c)
{ 1} d) {x}
2
Let O(A)= m ,O(B)=n.Then number
of relations from A to B is:
a) mn b)
m+n c) 2mn d)
N.O.T
3. If
A={ 1,2,3,4,5 } ,then number of proper subsets of A is:
a) 120 b)
30 c) 31 d) 32
4. If
A= { x: x is multiple of 3 } and B={ x: x is a multiple of 5} ,then A-B
is
a)
A b) B c) ¢ d) A∩Bc
5. If Na ={ an : n ÎN }
,then N6∩N8 =
a) N6 b) N8 c)
N24 d)
N44
6. If A={ x:
f(x)=0} and B={ x: g(x)=0 } ,then A∩B will be a) [ f(x)]2 +[g(x)]2
=0 b) f(x) /g(x) c) g(x)/f(x) d) N.O.T
7.
If
X={ 8n – 7n -1 : nÎN} and Y={ 49 (n-1) :
n Î N } ,then XÈY is
a) X b)
Y c) N d)
N.O.T
8. If
the sets A and B are defined as A={ (x,y): y=1/x ,0 ¹xÎR} ,
B={ (x,y): y = -x ,xÎ R} ,then
a) A∩B=A b) A∩B=B c) A∩B= ¢ d)
N.O.T
9. If A={ ¢, {¢}} ,then the power set of
A is:
a) A b) { ¢, {¢} ,A} c)
{ ¢ , {¢ },{{¢}},A} d) N.O.T
10. Let R be a relation on a set A such
that R=R-1 ,then R is
a) reflexive b) symmetric c) transitive d)
N.O.T
11. A survey shows that 63% of the Americans
like cheese whereas 76% like apples
.If x% of the Americans like both cheese and apples ,then
a) x=39 b) x=63 c)
39 ≤ x ≤ 63 d) N.O.T
12. Let R be a relation on set N of natural
numbers defined by nRm Û n is a factor of m (i.e . n çm ). Then R is:
a) reflexive and symmetric b) transitive and symmetric
c) equivalence d) reflexive
,transitive but not symmetric
13. The void relation on set A is:
a) reflexive b) symmetric
and transitive
c) reflexive and symmetric d) neither symmetric nor transitive
14. Let
L denote the set of all straight lines in a plane .Let a relation R be
defined by aRb Û a ^b, a,bÎ L ,then R is:
a) reflexive b) symmetric c) transitive d)
N.O.T
15. For real numbers x and y ,we write
xRy Ûx-y
+Ö2
is an irrational number.Then relation R is:
a) reflexive b) symmetric c) transitive d)
N.O.T
16. Relation
R on set Z of all integers defined by (x,y)ÎR Û x-y is divisible by n
(n÷x-y, n is factor of x-y)
,then relation R is :
a) symmetric b) transitive c) reflexive d)
equivalence
17. In a set A={1,2,3,4,5 } ,a relation R
is defined by R={ (x,y) ÷ x,y ÎA and x<y } .then R is:
a) reflexive b) symmetric c) transitive d)
N.O.T
- Let the A= { 1,2,3,4 } and let R={ (2,2),(3,3),(4,4),(1,2) } be a relation on
A .Then R is:
a) reflexive b) symmetric c) transitive d) N.O.T
19. If R is an equivalence relation on a
set A, then R-1 is:
a) reflexive only b)
symmetric but not transitive
c) equivalence d) N.O.T
20. If R is the relation from a set A to
set B and S is a relation from B to a set C, then the relation SoR
a) is from A to C b)
is from C to A
c) does not exist d) N.O.T
21. The domain of the function
log(x-[x]) is:
a) I b) R-I c)R d) N.O.T
22. The domain of the function f(x)=
is
is
a) R-{2} b) R-1 c)
R+ d) N.O.T
23. If
f and g be two functions with domain D1 and D2
respectively .Then which of the following statements is incorrect:
a) domain of (f ± g) =D1ÇD2 b)
domain of (f g) =D1ÇD2
c) domain of (f / g) =D1ÇD2 d) N.O.T
24. The domain of the function f(x) is
[0,1],then domain of the f(2x+3) is:
a) [0,1] b) [-3/2 ,-1] c)
[-3/2 ,1] d) N.O.T
25. The range of x /│x│ is:
a) (-1,1) b) [-1,1] c)
{1,-1} d) N.O.T
26. The range of the function is 2sin2x
+ 3cos2 x is:
a) (2,3) b) [2,3] c)
[-1,1] d) N.O.T
27. The range of the function f(x)=
P(7-x,x-3) is:
a) { 1,2,3} b) { 1,2,3,4,5,6} c)
{ 1,2,3,4} d) N.O.T
28 .The domain of the function log x +log çx ç+log[x] is:
a) x>0 b) [1,¥) c)
(-¥,¥) d) N.O.T
29. The domain of the real function f(x)=Ö log16
x2 is:
a) x>0 b) çxç >1 c)
çxç ³4 d) çxç £4
30. The domain of the function 
+
is:
+ is:
a) [4,5] b) (4,5) c)
[4,5) d) N.O.T
31. The function f(x)=sin4 x +cos4
x is symmetrical about:
a) x-axis b) y-axis c)
not symmetric d) N.O.T
32. The function f(x) =2x-2[x] is periodic
with periodicity
a) 1 b)
1/2 c) -1 d) N.O.T
33. The period of the function f(x)=2 cos[(x-p)/3] is:
a) 2p/3 b) 4p/3 c)
2p d) 4p
34. The function log(2+cos3x) is periodic
with periodicity
a) x=p/3 b) x=2p/3 c)
2p d) N.O.T
35. Function f(x)=x2 -| x | is:
a) an odd function
b) an even function
c) neither odd nor even d) N.O.T
Let
A={a,b,d} ,B={c,d,f,m} ,C={a,l,m,o},then (AÈB)ÇB=
a)
{a,l,m} b) {a,l,o} c) {a,m} d) N.O.T
2. If
n(A)=6,n(B)=3,then max(AÈB)=
a)9 b)
6 c) 3 d) N.O.T
3. If n(A)=6,n(B)=3,then min(AÈB)=
a)9 b) 6 c) 3 d) N.O.T
4. A relation R is defined from {2,3,4,5} to {3,6,7,10}by :
xRyÛx
is relatively prime to y.Then domain of R is:
a)
{2,3,5} b) {3,5} c) {2,3,4} d)
{2,3,4,5}
5. Let A={a,b,c,d} ,B={b,c,d,e}.then O[(A×B)Ç(B×A)]=
a)
3 b) 6 c) 9 d) N.O.T
6.
If R be a relation < from A={1,2,3,4} to B={1,3, 5} such that (a,b)ÎRÛa<b,then RoR-1
a)
{(1,3),(1,5),(2,3),(2,5),(3,5),(4,5)}
b)
{ (3,1),(5,1),(3,2),(5,2),(5,3),(5,4)}
c) { (3,3),(3,5),(5,3),(5,5)}
d)
{ (3,3),(3,4),(4,5)}
7. Let L denote the set of all straight lines in a
plane .Let a relation R be defined by aRb Û a êêb, a,bÎ L ,then R is:
a) reflexive b) symmetric c)
transitive d) N.O.T
8. Let R be a relation on N defined by x+2y=8.The
domain of R is:
a) { 2,4,8} c) { 2,4,6,8} c)
{ 2,4,6} d)
{1,2,3,4}
9. Let
R ={ (a,a),(b,b),(c,c),(a,b)} be a relation on a set A={a,b,c},then R is:
a) identity b) reflexive c)
symmetric d) anti-symmetric
10. Let X be a family of sets and R be a
relation on X defined by ‘A is disjoint from B’.Then R is:
a) reflexive b) symmetric c)
anti-symmetric d) transitive
11. The
minimum number of elements that must be added to the relation R={ (1,2),(2,3)}on
get N so that it is an equivalence
relation is:
a) 4 b)
7 c) 6 d) 5
12. If
A,B,C are three sets, then AÇ(BÈC) is
equal to:
a) (AÈB)Ç(AÈC) b) (AÇB)È(AÇC) c) AÇ(BÈC) d) N.O.T
13. If A
and B are any two sets,then AÇ(AÈB)=
a) A b)
B c)
Ac d)
Bc
14. If AÈ(AÇB) is
equal to:
a) A b)
B c)
Ac d)
Bc
15. Let
A and B be two finite sets having m and n elements respectively. Then the total
number of mappings from A to B is:
a) mn b) 2mn c) mn d) nm
16. If A
and B are sets, then A Ç(B-A) is:
a) f b) A c) B d) N.O.T
17. If
f:A®B
is a bijection ,then
a) n(A)>n(B) b) n(A)<n(B) c) n(A)=n(B) d) N.O.T
18. Which of the following statement is not
correct:
a) f is even ,g is even function
implies fog is even function.
b) f is odd ,g is even function
implies fog is even function.
c) f is odd ,g is odd function
implies fog is odd function.
d) N.O.T
19. f(x) is a real value decreasing function then [f(x) – f(-x)] is always is :
a) even function b) odd function c) depends upon f(x)
d) N.O.T
20. If f(x) =x-1/x
,then f(x2 )=
a) (x+1/x) f(x) b) (x-1/x)f(x) c)
x f(x) d) N.O.T
21. The function
f(x)=log(x+Öx2+1)
is:
a) an even function b) an odd function c)
periodic function
d) N.O.T
22. If f(x) is an even function ,then curve y=f(x)
is symmetric about:
a) x-axis b)
y-axis c) both the axes d) N.O.T
23. The domain of
the definition of the function f(x)= P(7-x,x-3) is:
a) [3,7] b)
{3,4,5,6,7} c) {3,4,5} d) N.O.T
24. f(x)=(x-1)(x-2)(x-3)
is:
a) one-one b)
not one-one c) bijection d) N.O.T
25. f(x)= (sin4x
+cos4x )/(x+x2 tanx) is:
a) even b)
odd c) neither odd nor
even d) N.O.T
26. The period of is
is
a) p b) 2p c) p/2 d)
N.O.T
27 .The
function f(x)=(1/2)sinx is:
a) periodic function with period p b) an odd function
c) expressible as sum of an even function
and an odd function
d) N.O.T
28.
Set A has 3 elements and set B has
4 elements.The number of injections that can be defined from A to B is:
a) 144 b) 12 c) 24 d)
N.O.T
29.
If a function f:[2,¥)®B
defined by f(x)=x2-4x+5 is a bijection ,then B=
a) R b) [1,¥) c) [4,¥) d) [5,¥)
30.
Given f(x)=log(1+x/1-x) and g(x)=3x+x3/1+3x2,then fog(x) equals:
a)
–f(x) b) 3f(x) c) [f(x)]3 d) N.O.T
31. If f(x)=ax+b and g(x)=cx+d ,then f(g(x))=g(f(x)) is equivalent to:
a) f(a)=g(c) b)
f(b)=g(b) c) f(d)=g(b) d) f(c)=g(a)
32. Let f:R®R be
a function defined by f(x)=cos(5x+2),then f is:
a) injective b)
surjective c) bijective d) N.O.T
33. Which of the
following functions from Z to itself are bijections ?
a) f(x)=x3 b) f(x)=x+2 c)
f(x)=2x+1 d) f(x)=x2+x
34. If f(x)=cos(logex),then f(x)f(y)-1/2[f(x/y)+f(xy)] equal to:
a) 0 b)
½ f(x)f(y) c) f(x+y) d) N.O.T
35. If f:R®R,defined
by f(x)=x2+1,then the value of
f-1(17) and f-1(-3) respectively are:
a) f,{4,-4} b) {3,-3},f c) {4,-4},f d)
{4,-4},{2,-2}
FILL
IN THE BLANKS
1.
The number of one-one function
from set A={1,2,3} to B={3,4} are ………
2.
The number of bijective functions
from a set A to itself where A contains 106 elements is…………………
3.
The range of the function
f(x)=cos[x] ,for -p/2
<x<p/2
is:…{cos1,-cos1,1}……………
4.
If f(x)=cos[p2]x+
cos[-p2]x
,find f(p)=…0………..
5. If f(x)=êx-2 êand
g(x)=f[f(x)],then for x>2,g’(x)=………………
6. Let A and B be two finite sets having m
and n elements respectively .Then the total number of mappings from A to B is:……….
7 The domain of the function log4log5log3(18x-x2-77)
…………….
8. The domain of the function log2log1/2{x2+4x+4}………….
9.
If f(x) is a function which is
both odd and even then f(3)-f(2) is equal to:……….
10. f(x)=sin{log(x+Öx2+1)} is an odd/even function:…………..
11.
The period of the function sin4x+cos4x=
is………………..
12. The period of the function
sin2px/3
+cospx/2
……………….
13. Let f(x)=x and g(x)=êx êfor all xÎR.Then the function f(x) satifying the equation
[f(x)-f(x)]2 +[f(x)-g(x)]2
=0,is:…………..
14. A
polynomial function f(x) satisfies the
condition f(x)f(1/x)=f(x)+f(1/x).If
f(5)=126, then f(10)=……………
15. If
f(x+2y,x-2y)=xy,then f(x,y) equals:………..
16. The range of the function
f(x)=1/(2-cos3x) is:
17. If f(x)=(x-1/x+1) ,then f(2x) in terms of
f(x) is:…………….
18. The domain of the function f(x)=sin-1(log3(x/3))
is…………..
19. The inverse of the function f(x)=(10x-10-x)/(10x+10-x)
is:……………
20. The value of the parameter a,for
which the function f(x)=1+ax,a#o is the inverse of itself , is……………….
TRUE/FALSE
1.
The period of the function f(x)=sin43x+cos43x is: p /6 (T/F)
2.
If f(x) is an odd function, then
the curve y=f(x) is symmetric about
x-axis. (T/F)
3.
Period of cos(cosx)+cos(sinx) is p. (T/F)
4.
Period of the function 1/2 { êsin x ê/cosx + sinx/ êcosx ê}is p. (T/F)
5.
Given f(x)=log(x-2)+log(x-3) and
g(x)=log(x-2)(x-3) are identical. (T/F)
6.
If f(x)=sin2x + sin2(x+p/3)+cosx
cos(x+p/3)
and g(5/4)=1,then (gof)(x) =1 (T/F)
7.
If f(x) is an odd periodic
function with period 2, then f(4)=0 (T/F)
8. Period of sin(x-[x]) is 1. (T/F)
9.
Every relation is a function. (T/F)
10. Every function is the relation. (T/F)
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