In This Post we are providing Chapter-1 Relation and Function NCERT MCQ for Class 12 Math which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.
NCERT MCQ ON RELATIONS AND FUNCTIONS
1. 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
Answer: d
Explanation: (d), not reflexive, as l1 R l2
⇒ l1 ⊥ l1 Not true
Symmetric, true as l1 R l2 ⇒ l2R h
Transitive, false as l1 R l2, l2 R l3
⇒ l1 || l3 . l1 R l2.
2. 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
Answer: c
Explanation: (c), T1 and T3 are similar as their sides are proportional.
3. 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
Answer: c
Explanation: (c), here (1,2) e R, (2,1) € R, if transitive (1,1) should belong to R.
4. 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
Explanation: (b), A relation R is an identity relation in set A if for all a ∈ A, (a, a) ∈ R.
5. 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
Answer: a
Explanation:
6. 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
Answer: c
Explaination: (c), total injective mappings/functions
= 4 P3 = 4! = 24.
7. Given a function lf as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f then
(a) g(x) = 4x + 5
(b) g(x) = 54x−5
(c) g(x) = x−45
(d) g(x) = 5x – 4
Answer: c
Explaination:
8. Let Z be the set of integers and R be a relation defined in Z such that aRb if (a – b) is divisible by 5. Then R partitions the set Z into ______ pairwise disjoint subsets.
Answer:
Explaination: Five, as remainder can be 0, 1, 2, 3, 4.
9. Consider set A = {1, 2, 3 } and the relation R= {(1, 2)}, then? is a transitive relation. State true or false.
Answer:
Explaination: True, as there is no situation
(a, b) ∈ R, (b, c) ∈ R Hence, transitive. We can also say, a relation containing only one element is transitive.
10. Every relation which is symmetric and transitive is reflexive also. State true or false.
Answer:
Explaination: False,e.g.if R is arelationinset A = {2,3,4} defined as {(2, 3), (3, 2), (2, 2)} is symmetric and transitive but not reflexive.
11. Let R be a relation in set N, given by R = {(a, b): a = b – 2, b > 6} then (3, 8) ∈ R. State true or false with reason.
Answer:
Explaination: False, as in (3, 8), b = 8
⇒ a = 8 – 2
⇒ a = 6, but here a = 3.
12. Let R be a relation defined as R = {(x, x), (y, y), (z, z), (x, z)} in set A = {x, y, z} then R is (reflexive/symmetric) relation.
Answer:
Explanation: Reflexive, as for all a ∈ A, (a, a) ∈ R.
13. Let R be a relation in the set of natural numbers N defined by R = {(a, b) ∈ N × N: a < b}. Is relation R reflexive? Give a reason.
Answer:
Explanation:
Given R = {(a, b) ∈ N × N: a < b}.
Not reflexive, as for (a, a) × R
⇒ a< a, not true.
14. Let A be any non-empty set and P(A) be the power set of A. A relation R defined on P(A) by X R Y ⇔ X ∩ Y = X, X, Y ∈ P(A). Examine whether ? is symmetric.
Answer:
Explaination: X R Y ⇔ X ∩ Y = X ⇒ Y ∩ X = X ⇒ Y R X.
Hence, symmetric.
15. State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.
Answer:
Explaination: (1, 2) ∈ R, (2, 1) ∈ R, but (1, 1) ∉ R.
