# __Mathematics__

__Multiple Choice Questions (MCQ)__

MCQ | Class 11 | Chapter 2

__RELATIONS 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 11

RELATIONS 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) 2

^{4}(b) 12

(c) 2

^{7}(d) 2

^{12} 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) =

Find the domain of the function

a) (0, 3)

b) [0, 3]

c) [-3, 3]

d) (-3, 3)

Ans: c

Q 23) f(x) =

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)

4^{5}c) 20

d) 5

^{4}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 = y^{2}}. 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 = y^{2}}. 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

is

a) [0,4]

b) (0,4)

c) R- (0,4)

d) R- [0,4]

Ans: a

Q 39) The range of f(x) =

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

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) =

log_{e} (5 - 6x) is

Q 43) If R = {(x, y) : x, y ∈ W,
x^{2} + y^{2} = 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) 2^{n}

b)

c) n^{n}

d) n^{2}

Ans: b

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