JEE Mathematics - Set Theory, Relations and Mapping
Exam Duration: 60 Mins Total Questions : 50
The number of proper subsets of {1,2,3} is
- (a)
8
- (b)
7
- (c)
6
- (d)
5
If \(X=\{ { 4 }^{ n }-3n-1:n\in N\} ,\quad y=\{ 9(n-1):n\in N\} \), then
- (a)
\(X\subset Y\)
- (b)
\(Y\subset X\)
- (c)
X=Y
- (d)
none of these
Assume R and S are (non-empty) relations in a set A.Which of the following statements is false?
- (a)
If R and S are transitive then \(R\cup S\) is transitive
- (b)
If R and S are transitive then \(R\cap S\) is transitive
- (c)
If R and S are symmetric then \(R\cup S\) is symmetric
- (d)
If R and S are reflexive then \(R\cap S\) is reflexive.
If A={1,2,3}, b+{4,5}, which of the following is not a function from A to B?
- (a)
{(1,4),(2,5),(3,4)}
- (b)
{(1,4),(2,4),(3,4)}
- (c)
{(2,4),(3,5),(1,5)}
- (d)
{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)}
Let \(f:R\rightarrow R\) be defined as f(x)=cos(5x+2). Then f is
- (a)
injective
- (b)
surjective
- (c)
bijective
- (d)
none of these
If f,\(g:R:\rightarrow R\), such that \(f:x\rightarrow sin\quad x\)and \(g:x\rightarrow \)x2,then gof equals
- (a)
sin x2
- (b)
x2 six x
- (c)
sin2 x
- (d)
none of these
If \(f:R\rightarrow R\), f(x)=2x+7 then f-1(x) is
- (a)
7 +2x
- (b)
2x-7
- (c)
does not exist
- (d)
\(\frac { x-7 }{ 2 } \)
If A = {x : x is a multiple of 4 and \(x\in N\) }, then \(A\cap B\) consists of all multiples of
- (a)
16
- (b)
12
- (c)
8
- (d)
4
If A={X : X2 = 1} and B ={X : X4 =1}. then \(A\triangle B\) is equal to
- (a)
{-i, i}
- (b)
{-1, 1}
- (c)
{-1, 1, i, -i}
- (d)
None of the above
In a group of 400 people, 250 can speak Hindi and 200 can speak English. Then, people who can speak both Hindi and English are
- (a)
60
- (b)
80
- (c)
50
- (d)
45
If the relation R:A\(\rightarrow \) B, where A={1,2,3} and B={1,3,5} is defined by R={(x,y):x
- (a)
R={(1,3),(1,5),(2,3),(2,5),(3,5)}
- (b)
R={(1,1),(1,5),(2,3),(3,5)}
- (c)
R={(3,1),(5,1),(3,2),(5,3)}
- (d)
R={(1,1),(5,1),(3,2),(5,3)}
Let A={1,2,3,4,5} and R be a relation defined by \(R=\left\{ \left( x,y \right) :x,y\epsilon A,x+y=5 \right\} \) . Then, R is
- (a)
reflexive and symmetric but not transitive
- (b)
an equivalence relation
- (c)
symmetric but neither reflexive nor transitive
- (d)
neither reflexive nor symmetric but transitive
If N be the set of natural numbers and define the relation R on N by R={(1,2),(2,5),(3,10),(4,17),(5,26)}. Then, the set Builder form of R is
- (a)
\(\left\{ { \left( x,{ x }^{ 2 }+1 \right) }|{ x\epsilon N\quad and\quad x<6 } \right\} \)
- (b)
\(\left\{ { \left( x,{ x }^{ 2 }-1 \right) }|{ x\epsilon N\quad and\quad x<6 } \right\} \)
- (c)
\(\left\{ { \left( x,2x+1 \right) }|{ x\epsilon N\quad and\quad x<6 } \right\} \)
- (d)
None of the above
Let R={(2,3),(3,4)} be a relation defined in the set {2,3,4}. The minimum number of ordered pairs required to be added in R, so that enlarge relation becomes an equivalence relation is
- (a)
3
- (b)
5
- (c)
7
- (d)
9
If (x+3, 4-y)=(1,7), then (x-3, 4+y) is equal to
- (a)
(-2,-3)
- (b)
(-5,1)
- (c)
(3,4)
- (d)
(1,5)
If A={1,2,4}, B={2,4,5}, C={2,5}, then (A-C)x(B-C) is equal to
- (a)
{(1,4)}
- (b)
{(1,4),(4,4)}
- (c)
{(4,1),(4,4)}
- (d)
{(1,2)(2,5)}
Which of the following sets is a finite set?
- (a)
A = {x:x ∈ Z and x2-5x+6=0}
- (b)
B={x:x ∈Z and x2 is even}
- (c)
D = {x:x ∈ Z and x > -10}
- (d)
All of these
Which of the following sets is an infinite set?
- (a)
Set of concentric circles in a plane
- (b)
Set of all lines in a plane
- (c)
{x∊N : x<200}
- (d)
All of these
Which of the following is a finite set?
- (a)
Set of all points in a plane
- (b)
Set of all lines in plane
- (c)
{x:x ∈ R and 0 < x < 1}
- (d)
Set of all persons on the earth
Which of the following is a singleton set?
- (a)
{x:|x|=5, x∈N}
- (b)
{x:|x|=6, x∈N}
- (c)
{x:x2+x+1=0, x∈N}
- (d)
{x:x2=7, x∈N}
If P={1,2} then the set PxPxP is
- (a)
{(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)
- (b)
{(1,1,1), (1,1,2), (2,2,2), (1,2,1), (2,1,1), (2,1,2), (2,1,2), (2,2,1)}
- (c)
{(2,1,1), (2,2,2), (1,1,1)
- (d)
None of these
(AxB)U(AxC)=
- (a)
{(1,3), (1,4), (2,5), (2,6), (3,3), (3,4)}
- (b)
{(1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6)}
- (c)
{(1,3), (2,6), (3,4), (1,4), (1,5), (2,4), (2,5), (3,5)}
- (d)
None of these
If set A has 3 elements and the set B={3,4,5}, then find the number of elements in (AxB).
- (a)
8
- (b)
7
- (c)
9
- (d)
10
Let A ={1,2, 3, 4}, B={2,4,6}. Then the number of sets C such that A ∩ B ⊆ C ⊆ A ∪ B is
- (a)
6
- (b)
9
- (c)
8
- (d)
10
A relation R is defined in the set Z of integers as follows (x,y)∈R if x2+y2=9. Which of the following is false?
- (a)
R={(0,3), (0,-3), (3,0), (-3,0)}
- (b)
Domain of R={-3,0,3}
- (c)
Range of R={-3,0,3}
- (d)
None of these
Let A={x,y,z} and B={a,b,c,d}. Which one of the following is not a relation from A to B?
- (a)
{(x,a), (x,c)}
- (b)
{(y,c}, (y,d)}
- (c)
{(z,a), (z,d)}
- (d)
{(z,b), (y,b), (a,d)}
The relation R defined on the set A={1,2,3,4,5} by R={(x,y):|x2-y2|<16} is given by
- (a)
{(1,1), (2,1), (3,1), (4,1), (2,3)}
- (b)
{(2,2), (3,2), (4,2), (2,4)}
- (c)
{(3,3), (4,3), (5,4), (3,4)}
- (d)
None of these
Let A={a1, a2} and B={b1, b2}, then the number of relations from A to B is
- (a)
4
- (b)
8
- (c)
16
- (d)
2
If Y is the smallest set such that Y ∪ {1, 2} = {1, 2, 3, 5, 9}, then Y is equal to
- (a)
{1,2, 3, 5, 9}
- (b)
{3, 5, 9}
- (c)
{1, 2}
- (d)
None of these
If a relation R is defined from a set A={2,3,4,5} to a set B={3,6,7,10} as follows (x,y) ∈ R ⇔ x divides y. Expression of R-1 is represented by
- (a)
{(6,2), (10,2), (3,3), (6,3)}
- (b)
{(6,2), (3,3), (10,5), (10,2)}
- (c)
{(6,2),(10,2),(3,3), (6,3), (10,5)}
- (d)
None of these
If A={1,2,3,4}, then which of the following relations are functions from A to itself?
- (a)
f1={(x,y)∈AxA:y=x+1}
- (b)
f2={(x,y)∈AxA:x+y>4}
- (c)
f3={(x,y)∈AxA:y<x}
- (d)
f4={(x,y)∈AxA:x+y=5}
The domain of the function f(x)=\(\frac{|x+3|}{x+3}\) is
- (a)
{-3}
- (b)
R-{-3}
- (c)
R-{3}
- (d)
R
If b2 -4ac=0, a>0, then the domain of the funtion y=log(ax3+(a+b)x2+(b+c)x+c) is
- (a)
\(R-\{-\frac{b}{2a}\}\)
- (b)
\(R-\{\{-\frac{b}{2a}\}U\{x:x\ge-1\}\}\)
- (c)
\(R-\{\{-\frac{b}{2a}\}∩(-\infty,-1]\}\)
- (d)
None of these
The domain and range of the function f(x) is given by f(x)=\(\frac{x-2}{3-x}\) respectively are
- (a)
R,R-{1}
- (b)
R-{3}, R-{-1}
- (c)
R-{1}, R-{3}
- (d)
None of these
The domain of the function f(x)=log4(log5(18x-x2-77))) is
- (a)
x∈(4,5)
- (b)
x∈(0,10)
- (c)
x∈(8,10)
- (d)
x∈(8,10]
The domain of the function f(x)=\(\frac{x^2+2x+1}{x^2-8x+12}\)is
- (a)
R
- (b)
R-{1,4}
- (c)
R-{1}
- (d)
(1,4)
The domain of the function f given by f(x)=\(\frac{1}{\sqrt{x-|x|}}\) is
- (a)
R
- (b)
R+
- (c)
R-
- (d)
{ф}
If U={x:x ∈N and 2 < x < 12} A={x:x is an even prime}, B={x:x is a factor of 24}, then which of the following is not true?
- (a)
A-B is an empty set
- (b)
A-B=B∩A'
- (c)
A'-B'=B-A
- (d)
(A∩B)'=A'UB'
If f:R⟶R is defined by f(x)=\(\frac{x}{x^2+1},\) find f(f(2)).
- (a)
29/9
- (b)
29/8
- (c)
29/10
- (d)
10/29
If f(x)=cos(logex), then \(f(x)f(y)-\frac{1}{2}[f(\frac{y}{x})+f(xy)]\) has the value
- (a)
1
- (b)
1/2
- (c)
-2
- (d)
0
If f and g are real functions defined by f(x)=x2+7 and g(x)=3x+5, find \(f(\frac{1}{2})\times g(14)\)
- (a)
\(\frac{1336}{5}\)
- (b)
\(\frac{1363}{4}\)
- (c)
1251
- (d)
1608
Let f(x)=√x-x and g(x)=x2 be two functions defined over the set of non-negative real numbers, then (fg)(x)=
- (a)
\(x^{\frac{2}{5}}-x^3\)
- (b)
x3-√x
- (c)
\(x^3-x^{\frac{2}{5}}\)
- (d)
\(x^{-\frac{5}{2}}-x^3\)
Let n(A)=m, n(B)=n. Then the total number of non-empty relations that can be defined from A to B is
- (a)
mn
- (b)
nm-1
- (c)
mn-1
- (d)
2mn-1
The domain and range of the real function f defined by \(f(x)=\frac{4-x}{x-4}\) is given by
- (a)
Domain=R, Range=[-1,1]
- (b)
Domain=R-{1}, Range=R
- (c)
Domain=R-{4}, Range={-1}
- (d)
Domain=R-{-4}, Range={-1,1}
Let A={1,2,3,4,5,6}. If R is the relation on A defined by {(a,b): a,b∈A,b is exactly divisible by a}.
Statement I: The relation R in Roster form is {(6,3), (6,2), (4,2)}
Statement II: The domain and range of R is {1,2,3,4,6}.
- (a)
If both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
- (b)
If both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I.
- (c)
If Statement I is true but Statement II is false
- (d)
If Statement I is false and Statement II is true.
Statement I:If \(f(x)=\frac{1}{x-2}, x\ne2\) and g(x)=(x-2)2, then (f+g)(x)=\(\frac{1+(x-2)^2}{x-2}, x\ne2\)
Statement II: If f and g are two functions, then their sum is defined by (f+g)(x)=f(x)+g(x) ∀x∈D1∩D2, where D1 and D2 are domains of f and g respectively.
- (a)
If both Statement I and Statement II are true and Statement II is the correct explanation of Statement I
- (b)
If both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I.
- (c)
If Statement I is true but Statement II is false
- (d)
If Statement I is false and Statement II is true.
In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of persons who read neither is
- (a)
210
- (b)
290
- (c)
180
- (d)
260
Let S={x|x is a positive multiple of 3 less than 100}
P={x|x is a prime number less than 20}. Then n(S)+n(P) is
- (a)
34
- (b)
41
- (c)
33
- (d)
30
Statement I: If AUB=AUC and A∩B=A∩C, then B=C
Statement II: AU(B⋂C)=(AUB)∩(AUC)
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement-I.
- (b)
If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement-I.
- (c)
If Statement-I is true but Statement-II is false.
- (d)
If Statement -I is false and Statement -II is true.
Statement-I: n(U) = 600, n(A) = 450, n(B) = 250 and n(A⋂B)=50, then given data's are correct.
Statement II: n(AUB)≤n(U)
- (a)
If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement-I.
- (b)
If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement-I.
- (c)
If Statement-I is true but Statement-II is false.
- (d)
If Statement -I is false and Statement -II is true.
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