### Multiple Choice Questions (MCQ) On Mathematics

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# MathematicsMultiple Choice Questions (MCQ)MCQ | Class 11 | Chapter 2RELATIONS AND FUNCTONS

• MCQ Based on the different types of Relations.
• MCQ  Based on the Domain and Range of Relations.
• MCQ Based on the Domain and Range of Functions.

### Features

• In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
• Solution Hints are also given to some difficult problems.
• Each MCQ contains four options from which one option is correct.
• On the right hand side column of the pdf Answer option is given.

### Action Plan

• First of all students should Learn and write all basic points and Formulas related to the Continuity and Differentiability.
• Start solving  the NCERT Problems with examples.
• Solve the important assignments on the Relations and Functions of  Chapter 2 Class XI.
• Then start solving the following MCQ.

# MCQ | CHAPTER 2 | CLASS 11RELATIONS AND FUNCTIONS

Q 1) IF R = {(2, 1), (4, 3), (4, 5)}, then range of the function is?
(a) Range R = {2, 4}
(b) Range R = {1, 3, 5}
(c) Range R = {2, 3, 4, 5}
(d) Range R {1, 1, 4, 5}
Ans: b

Q 2) If (x + 2, y - 3) = (5, 7) then find values of x and y.
a) x = 3 and y = 10
b) x = 3 and y = 4
c) x = 7 and y = 4
d) x = 7 and y = 10
Ans: a

Q 3) Let R be a relation on N defined by x + 2y = 8. The domain of R is
a) {2, 4, 6, 8}
b) { 1, 2, 3, 4}
c) 2, 4, 8
d) {2, 4, 6}
Ans: d

Q 4) If A, B and C are any three sets, then A × (B ∪ C) is equal to
(a) (A × B) ∪ (A × C)
(b) (A ∪ B) × (A ∪ C)
(c) None of these
(d) (A × B) ∩ (A × C)
Ans: a

Q 5) The range of the function f(x) = 3x – 2‚ is
(a) (- ∞, ∞)
(b) R – {3}
(c) (- ∞, 0)
(d) (0, – ∞)
Ans: a

Q 6) Given g(1) = 1 and g(2) = 3. If g(x) is described by the formula g(x) = ax + b then the value of a and b is
a) 2, 1
b) -2, 1
c) 2, -1
d) -2, -1
Ans: c

Q 7) Two functions f and g are said to be equal if
a) The domain of f = The domain of g
b) The co-domain of f = The co-domain of g
c) f(x) = g(x) for all x
d) All of above
Ans: d

Q 8) If the set has p elements, B has q elements then number of elements in A x B is
a) p q
b) p + q
c) p + q + 1
d) p - q
Ans:  a

Q 9) What is the domain of the logarithmic function Log x
(a) R
(b) (0, ∞)
(c ) (- ∞ , ∞ )
(d) None of these
Ans: b

Q 10) If A = { 1, 2, 3, 4} and B = { a, b, c} then what is number of relations from A to B
(a) 24
(b) 12
(c) 27
(d) 212
Ans: d

Q 11) If R is the subset of A X B relation is defined by R = {(2, 3), (3, 4), (5, 7), (2, 11), (6, 3) } then R is
(a) not a relation
(b) a function only
(c) not a function
(d) none of these
Ans: c

Q 12) What is the range of a signum function
(a) {-1, 0, 1}
(b) (-1, 1)
(c) All Real Numbers
(d) (0, ∞)
Ans: a

Q 13) How many rational and irrational numbers are possible between 0 and 1 ?
a) 0
b) Finite
c) Infinite
d) 1
Ans: c

Q 14) A relation R is defined from the set of integers to the set of real numbers as (x, y) = R if x² + y² = 16 then the domain of R is
(a) (4, 4)
(b) (- 4, 4)
(c) ( -4, - 4)
(d) None of these
Ans: b

Q 15) The domain of the function f(x) = 1/(x² – 3x + 2) is
(a) {1, 2}
(b) R
(c) R – {1, 2}
(d) R – {1, -2}
Ans: c

Q 16) Let A = {- 2, - 1, 0} and f(x) = 2x – 3 then the range of f is
(a) {7, - 5, - 3}
(b) {-7, 5, - 3}
(c) {- 7, - 5, 3}
(d) {-7, - 5, - 3}
Ans: d

Q 17) Which of the following is not a function?
a) {(1, 2), (2, 4), (3, 6)}
b) {(-1, 1), (-2, 4), (2, 4)}
c) {(1, 2), (1, 4), (2, 5), (3, 8)}
d) {(1, 1), (2, 2), (3, 3)}
Ans: c

Q 18) Find domain of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers
Ans: a

Q 19) If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set A.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}
Ans: b

Q 20) Which function is shown in graph?

a) Constant
b) Modulus
c) Identity
d) Signum function
Ans: b

Q 21) Find range of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers
Ans: b

Q 22) f(x) = $\sqrt{9-x^{2}}$  Find the domain of the function
a) (0, 3)
b) [0, 3]
c) [-3, 3]
d) (-3, 3)
Ans: c

Q 23) f(x) = $\sqrt{9-x^{2}}$ Find the Range of the function
a) (0, 3)
b) [0, 3]
c) [-3, 3]
d) (-3, 3)
Ans: b

Q 24) If set P has 4 elements and set Q has 5 elements then find the number of elements in P X Q.
a)  9
b) 45
c) 20
d) 54
Ans:  c

Q 25) If P X Q is an empty set then which of the following is a null set?
a) only P
b) only Q
c) either P or Q
d) both P and Q
Ans: c

Q 26) If (x + 2, y - 3) = (5, 7) then find values of x and y.
a) x = 3 and y = 10
b) x = 3 and y = 4
c) x = 7 and y = 4
d) x = 7 and y = 10
Ans: a

Q 27) If P X Q has 10 elements then which is not possible?
a) n(P) = 1 and n(Q) = 10
b) n(P) = 10 and n(Q) = 1
c) n(P) = 2 and n(Q) = 5
d) n(P) = 5 and n(Q) = 4
Ans: d

Q 28) If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set A.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}
Ans: b

Q 29) If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set B.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}
Ans: d

Q 30) Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the domain.
a) {1, 2, 3, 4, 5}
b) {2, 3, 4, 5}
c) {1, 2, 3, 4}
d) {1, 2, 3, 4, 5, 6}
Ans: c

Q 31) Let A={1, 2, 3, 4, 5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the range.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}
Ans: b

Q 32) If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x = y2}. Find range of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}
Ans: b

Q 33) If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x = y2}. Find domain of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}
Ans: c

Q 34) In a function from set A to set B, every element of set A has___________ image in set B.
a) one and only one
b) different
c) same
d) many
Ans: a

Q 35) Which of the following is not a function?
a) {(1,2), (2,4), (3,6)}
b) {(-1,1), (-2,4), (2,4)}
c) {(1,2), (1,4), (2,5), (3,8)}
d) {(1,1), (2,2), (3,3)}
Ans: c

Q 36) Find domain of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers
Ans: a

Q 37) Find range of function |x|.
a) Set of real numbers
b) Set of positive real numbers
c) Set of integers
d) Set of natural numbers
Ans: b

Q 38) Domain of $\sqrt{4x-x^{2}}$  is
a) [0,4]
b) (0,4)
c) R- (0,4)
d) R- [0,4]
Ans: a

Q 39) The range of f(x) = $\frac{x-3}{3-x},\: x\neq 3$ is
a) 1
b) -1
c) {1}
d {-1}
Ans: d

Q 40) The range of the function f(x) = |x-1| is
a) (- ∞, ∞
b) (0, ∞)
c) [0, ∞)
d(-∞ , 0)
Ans: c

Q 41) Domain of $\sqrt{4x-x^{2}}$  is
a) [0,4]
b) (0,4)
c) R- (0,4)
d) R- [0,4]
Ans: a

Q 42) The domain of the function f defined by f(x) = loge (5 - 6x) is
$a)\: \: \: \left ( \frac{5}{6},\infty \right )$

$b)\: \: \: \left [ \frac{5}{6},\infty \right )$

$c)\: \: \: \left ( -\infty ,\frac{5}{6} \right ]$

$d)\: \: \: \left ( -\infty ,\frac{5}{6} \right )$

Ans: d

Q 43) If R = {(x, y) : x, y W, x2 + y2 = 169 }, then domain of R is
a) { 0, 土1, 土2, 土3, ............, 土13}
b) {0, 5, 12, 13 }
c) {0, 1, 2, 3, .........., 13 }
d)  { -13, -12, -5, 0, 5, 12, 13 }
Ans: b

Q 44) Which function is shown in graph?

a) Constant
b) Modulus
c) Identity
d) Signum function
Ans: c

Q 45) Let  A be a finite set having n elements, then the number of relations on A is
a) 2n

b) $2^{n^{2}}$
c) nn

d) n2

Ans: b

Complete PDF of MCQ

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