# ISC Maths MCQ Relations Class-12 Semester-1 for 2021-22

ISC Maths MCQ Relations Class-12 Semester-1 for 2021-22. These MCQ  / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Physics.

## Semester-1 of 2021-22 ISC Maths MCQ Relations for Class-12

 Board ISC Class 12th (XII) Subject Maths Chapter Relations Syllabus on bifurcated syllabus (after reduction) bifurcated pattern Semester-1 Session 2021-22 Topic MCQ / Objective Type Question

### Semester-1 of 2021-22 of ISC Maths MCQ Relations for Class-12

Question :-1

#### Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b , a,b∈ T. Then R is

a) equivalence

b) reflexive but not transitive

c) transitive but not symmetric

d) none of these

Question-2

Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is
(a) reflexive and symmetric
(b) symmetric and transitive
(c) equivalence relation
(d) symmetric

Question 3.

Let R be the relation in the set (1, 2, 3, 4}, given by:
R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}.
Then:
(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation

Answer: (b) R is reflexive and transitive but not symmetric

Question :-4

If a relation R on the set {1,2,3}be defined by R={(1,2)} then R is

a) transitive

b) none of these

c) reflexive

d) symmetric

Question 5.
What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}
(a) Reflexive
(b) Transitive
(c) Symmetric
(d) None of these

Question -6.

Given triangles with sides T1 : 3, 4, 5; T2 : 5, 12, 13; T3 : 6, 8, 10; T4 : 4, 7, 9 and a relation R in set of triangles defined as R = {(Δ1, Δ2) : Δ1 is similar to Δ2}. Which triangles belong to the same equivalence class?
(a) T1 and T2
(b) T2 and T3
(c) T1 and T3
(d) T1 and T4

Question :-7.

Let R be the relation in the set N given by : R = {(a, b): a = b – 2, b > 6}. Then:
(a) (2, 4) ∈ R
(b) (3, 8) ∈ R
(c) (6, 8) ∈ R
(d) (8, 7) ∈ R.

Answer: (c) (6, 8) ∈ R

Question:-8

. R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A = {1, 2, 3}, then R is

(a) Symmetric

(b) Anti symmetric

(c) Not antisymmetric

(d) Reflexive

Question :-9

Given set A ={1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be

(a) reflexive if (1, 1) is added
(b) symmetric if (2, 3) is added
(c) transitive if (1, 1) is added
(d) symmetric if (3, 2) is added

Question :- 10

Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:
(a) 1
(b) 2
(c) 3
(d) 4

Question :-11

Let A = {1,2,3}. The number of equivalence relations containing (1,2) is

a) 2

b) 3

c) 4

d) None of these

Question :- 12
If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
(a) 12
(b) 28
(c) 61
(d) None of these

Question:-13

Given set A = {a, b, c). An identity relation in set A is
(a) R = {(a, b), (a, c)}
(b) R = {(a, a), (b, b), (c, c)}
(c) R = {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}

Answer: – (b) R = {(a, a), (b, b), (c, c)}
Question :- 14.

Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is
(a) 1
(b) 2
(c) 3
(d) 4.

Question :-15.

Let a relation T on the set R of real numbers be T = {(a, b) : 1 + ab < 0, a, ∈ R}. Then from among the ordered pairs (1, 1), (1, 2), (1, -2), (2, 2), the only pair that belongs to T is_____.​

(a) (2, 2)

(b) (1, 1)

(c) (1, -2)

(d) (1, 2)

Question :-16

#### A relation S in the set of real numbers is defined as xSy ⇒  x – y+ √3 is an irrational number, then relation S is

(a) reflexive
(b) reflexive and symmetric
(c) transitive
(d) symmetric and transitive

Question:- 17

Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is

(a) 144
(b) 12
(c) 24
(d) 64

Question:-18

If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘ x is smaller than y’. The range of R is

a) {4,6,9}

b) {1}

c) none of these

d) {1, 4,6,9}

Question-19

Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R is​

(a) R is reflexive and symmetric but not transitive.

(b) R is symmetric and transitive but not reflexive.

(c) R is an equivalence relation.

(d) R is reflexive and transitive but not symmetric

Answer :- (d) R is reflexive and transitive but not symmetric.

Question: -20

The relation R = { (1,1),(2,2),(3,3)} on {1,2,3} is

a) an equivalence relation

b) transitive only

c) reflexive only

d) None of these

Question :-21.
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
(a) A = B
(b) A = C
(c) B = C
(d) A ∩ B = d

Question :- 22
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric.

Question-23

R is a relation from { 11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R−1

(a) {(8, 11), (9, 12), (10, 13)}

(b) {(11, 8), (13, 10)}

(c) {(8, 11), (10, 13)}

(d) None of these

Ans (c) {(8, 11), (10, 13)}

Question : -24

#### If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘ x is smaller than y’. The range of R is

a) {4,6,9}

b) {1}

c) none of these

d) {1, 4,6,9}

Question -25

Set A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is:
(a) 144
(b) 12
(c) 24
(d) 64

Question-26

Let C = {(a, b): a2 + b2 = 1; a, b ∈ R} a relation on R, set of real numbers. Then C is​

(a) Equivalence relation

(b) Reflexive

(c) Transitive

(d) Symmetric

Question-27

If A = {1, 2, 3, 4} and B = {1, 3, 5} and R is a relation from A to B defined by(a, b) ∈ element of R ⇔ a < b. Then, R = ?

(a) {(2, 3), (4, 5), (1, 3), (2, 5)}

(b) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

(c) {(2, 3), (4, 5), (1, 3), (2, 5), (5, 3)}

(d) {(5, 3), (3, 5), (5, 4), (4, 5)}

Answer (b) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}

Question-28

. Given the relation R = {(1, 2), (2, 3)} on eht set {1, 2, 3}, the minimum number of ordered pairs which when added to R make it an equivalence

(a) 5

(b) 6

(c) 8

(d) 7

Question-29

Let R be a relation on N, set of natural numbers such that m R n ⇔ m divides n. Then R is​

(a) Reflexive and symmetric

(b) Neither reflexive nor transitive

(c) Reflexive and transitive

(d) Symmetric and transitive

Answer : – (c) Reflexive and transitive

Question:- 30

Number of relations that can be defined on the set A = {a, b, c, d} is

(a) 24

(b) 44

(c) 16

(d) 216

Question-31

Let A = {1, 2, 3, 4, 5, 6, 7}. P = {1, 2}, Q = {3, 7}. Write the elements of the set R so that P, Q and R form a partition that results in equivalence relation.​

(a) {4, 5, 6}

(b) {0}

(c) {1, 2, 3, 4, 5, 6, 7}

(d) { }

Question-32

Which one of the following relations on set of real numbers is an equivalence relation?

(a) a R b ⇔ a ≥ b

(b) a R b ⇔ |a| = |b|

(c) a R b ⇔ a > b

(d) a R b ⇔ a < b

Solution : –(b) a R b ⇔ |a| = |b|

Question-33.

Let R be a relation on N (set of natural numbers) such that (m, n) R (p, q) mq(n + p) = np(m + q). Then, R is​

(a) An Equivalence Relation

(b) Only Reflexive

(c) Symmetric and reflexive

(d) Only Transitive

Solution : – (c) Symmetric and reflexive

Question 34
Let f: R → R be defined by f(x) = x² + 1. Then pre-images of 17 and – 3 respectively, are
(a) ø, {4,-4}
(b) {3, -3}, ø
(c) {4, -4}, ø
(d) {4, -4}, {2,-2}.

Question 35
If a ∈ R and the equation
-3(x – [x] )2 + 2 (x – [x]) + a² = 0,
where [x] denotes the greatest integer (≤ x) has no integral solution, then all possible values of a lie in the interval:
(a) (1, 2)
(b) (-2, -1)
(c) (-∞, -2) ∪(2, ∞)
(d) (-1, 0) ∪ (0, 1).

Answer: (d) (-1, 0) ∪ (0, 1).
Question 36

If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
(a) x² – 2
(b) 1
(c) 13 (x – 2)²
(d) None of these

Answer: (c) 13 (x – 2)²

Question 37.
The period of sin² θ is
(a) π²
(b) π
(c) 2π
(d) π/2

Question :-  38.
The domain of sin-1 (log (x/3)] is. .
(a) [1, 9]
(b) [-1, 9]
(c) [-9, 1]
(d) [-9, -1]

Question 39

What type of relation is ‘less than’ in the set of real numbers?
(a) only symmetric
(b) only transitive
(c) only reflexive
(d) equivalence

Question 40

The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5

Question 41.
Let us define a relation R in R as aRb if a ≥ b. Then R is
(a) an equivalence relation
(b) reflexive, transitive but not symmetric
(c) neither transitive nor reflexive but symmetric
(d) symmetric, transitive but not reflexive

Answer: (b) reflexive, transitive but not symmetric

Question 42
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
(a) reflexive but not symmetric
(b) reflexive-but not transitive.
(c) symmetric and transitive
(d) neither symmetric, nor transitive

Answer: (a) reflexive but not symmetric

Question 43
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
(a) 720
(b) 120
(c) 0
(d) None of these

Question 44

The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
(a) {(2, 1), (4, 2), (6, 3),….}
(b) {(1, 2), (2, 4), (3, 6),….}
(c) R-1 is not defined
(d) None of these

Answer: (b) {(1, 2), (2, 4), (3, 6),….}

Question 45.
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
(a) Reflexive but not symmetric
(b) Reflexive but not transitive
(c) Symmetric and transitive
(d) Neither symmetric nor transitive

Answer: (a) Reflexive but not symmetric

Question 46
Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) Anti-symmetric

Question 47
Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
(a) Less than n
(b) Greater than or equal to n
(c) Less than or equal to n
(d) None of these

Answer: (b) Greater than or equal to n

Question 48
For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) None of these

Question 49
Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) None of these

Question 50
Which one of the following relations on R is an equivalence relation?
(a) aR1b ⇔ |a| = |b|
(b) aR2b ⇔ a ≥ b
(c) aR3b ⇔ a divides b
(d) aR4b ⇔ a < b

Answer: (a) aR1b ⇔ |a| = |b|

Question 51
Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric

Answer: (d) Reflexive, transitive but not symmetric

Question 52

Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.
(a) 1
(b) 2
(c) 3
(d) 0
Question 53
The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5
Question 54
The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by
(a) {(2, 1), (4, 2), (6, 3),….}
(b) {(1, 2), (2, 4), (3, 6), ……..}
(c) R-1 is not defiend
(d) None of these
Answer:   (b) {(1, 2), (2, 4), (3, 6), ……..}
Question 55
Let g(x) = x2 – 4x – 5, then
(a) g is one-one on R
(b) g is not one-one on R
(c) g is bijective on R
(d) None of these
Answer: (b) g is not one-one on R

Question 56
Let A = R – {3}, B = R – {1}. Let f : A → B be defined by 𝑓(𝑥)=(𝑥2) / (𝑥3). Then,
(a) f is bijective
(b) f is one-one but not onto
(c) f is onto but not one-one
(d) None of these

Question 57
The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is
(a) one-one and onto
(b) onto but not one-one
(c) one-one but not onto
(d) neither one-one nor onto
(c) one-one but not onto

Question 58

Let f : [0, ∞) → [0, 2] be defined by 𝑓(𝑥)=2𝑥/ (1+𝑥), then f is
(a) one-one but not onto
(b) onto but not one-one
(c) both one-one and onto
(d) neither one-one nor onto
(a) one-one but not onto

Question 59
If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is
(a) one-one onto
(b) one-one into
(c) many-one onto
(d) None of these