Tiêu đề RELATIONS & FUNCTIONS- 1.pdf ✅

CHAPTER 2 RELATIONS AND FUNCTIONS-1 Exercise 1: NCERT Based Topic-wise MCQs 2.1 INTRODUCTION 1. Which of the following is not true? NCERT/ Page-30/N-24 (a) A relation involves pair of objects in certain order. (b) Some special relations which will quality to be functions. (c) Some functions are also called relation. (d) None of these. 2.2 CARTESIAN PRODUCTS OF SETS 2. If A = {a, b}, B = {c, d}, C = {d,e}, then {(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)} is equal to (a) A ∩ (B ∪ C) NCERT Page-32/N-25 (b) A ∪ (B ∩ C) (c) A × (B ∪ C) (d) A × (B ∩ C) 3. Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in A × B is 7 . Then p 2 + q 2 = NCERT Page-33/N-26 (a) 42 (b) 49 (c) 50 (d) 51 4. The cartesian product of A × A has 9 elements, two of which are (−1,0) and (0,1), the remaining elements of A × A is given by NCERT Page-34/N-26 (a) {(−1,1), (0,0), (−1, −1), (1, −1), (0, −1)} (b) {(−1, −1), (0,0), (−1,1), (1, −1), (1,0), (1,1), (0, −1)} (c) {(1,0), (0, −1), (0,0), (−1, −1), (1, −1), (1,1)} (d) None of these 5. Which one of the following is not true? NCERT/ Page-32/N-26 (a) A × (B − C) = (A × B) − (A × C) (b) A − (B × C) = (A − B) × (A − C) (c) A − (B × C) = A; A, B, C are subsets of U. (d) A × (B × C) ≠ (A × B) × C; A, B, C are subsets of U. 6. If A × B = {(5,5), (5,6), (5,7), (8,6), (8,7), (8,5)}, then the value A is NCERT Page-31/N-25 (a) {5} (b) {8}

15. If A = {8,9,10} and B = {1,2,3,4,5}, then the number of elements in A × A × B are NCERT Page-33/N-27 (a) 15 (b) 30 (c) 45 (d) 75 16. If A = {1,2,4}, B = {2,4,5}, C = {2,5}, then (A − C) × (B − C) is equal to NCERT Page-32/N-26 (a) {(1,4)} (b) {(1,4), (4,4)} (c) {(4,1), (4,4)} (d) {(1,2), (2,5)} 17. Let set X = {a, b, c} and Y = φ. The number of ordered pairs in X × Y are NCERT Page-32/N-26 (a) 0 (b) 1 (c) 2 (d) 3 18. If A, B and C are any three sets, then A × (B ∪ C) is equal to NCERT Page-32/N-26 (a) (A × B) ∪ (A × C) (b) (A ∪ B) × (A ∪ C) (c) (A × B) ∩ (A × C) (d) None of these 19. If A = {a, b, c}, B = {b, c, d} and C = {a, d, c}, then (A − B) × (B ∩ C) = (a) {(a, c), (a, d)} (b) {(a, b), (c, d)} (c) {(c, a), (a, d)} (d) {(a, c), (a, d), (b, d)} 20. If P = {a, b, c} and Q = {r}, then (a) P × Q = Q × P (b) P × Q ≠ Q × P (c) P × Q ⊂ Q × P (d) None of these 2.3 RELATIONS 21. The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given (a) {(1,4), (2,5), (3,6), ..... NCERT Page-31/N-28 (b) {(4,1), (5,2), (6,3), ..... (c) {(1,3), (2,6), (3,9), ..... (d) None of these 22. A relation is represented by NCERT Page-31/N-28 (a) Roster method (b) Set-builder method (c) Both (a) and (b) (d) None of these
23. If n(X) = 5 and n(Y) = 7, then the number of relations on X × Y is 2 5m. The value of ' m ' is (a) 5 NCERT Page-35/ N-29 (b) 7 (c) 6 (d) 8 24. The relation R defined on the set A = {1,2,3,4,5} by R = {(x, y): |x 2 − y 2 | < 16} is given by (a) {(1,1), (2,1), (3,1), (4,1), (2,3)} NCERT Page-34/N-29 (b) {(2,2), (3,2), (4,2), (2,4)} (c) {(3,3), (4,3), (5,4), (3,4)} (d) None of these 25. The relation R defined on set A = {x: |x| < 3, x ∈ I} by R = {(x, y): y = |x|} is NCERT Page-41/ N-28 (a) {(−2,2), (−1,1), (0,0), (1,1), (2,2)} (b) {(−2, −2), (−2,2), (−1,1), (0,0), (1, −2), (1,2), (2, −1), (2, −2)} (c) {(0,0), (1,1), (2,2)} (d) None of these 26. If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7 , then the number of relations from A to B is NCERT/ Page-35/N-29 (a) 2 9 (b) 9 2 (c) 3 2 27. Let A = {1,2}, B = {3,4}. Then, number of subsets of A × B is NCERT Page-35/N-29 (a) 4 (b) 8 (c) 18 (d) 16 28. Let A = {x, y, z} and B = {a, b, c, d}. Then, which one of the following is not a relation from A to ? (a) {(x, a), (x, c)} NCERT Page-34/N-29 (c) {(z, a), (z, d)} (b) {(y, c), (y, d)} (d) {(z, b), (y, b), (a, d)} 29. Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a − b is an integer }. Then (a) domain of R is {2,3,4,5, .... NCERT Page-35/N-29 (b) range of R is Z (c) Both (a) and (b) (d) None of the above 30. If A = {2,3,4,5} and B = {3,6,7,10}. R is a relation defined by R = {(a, b): a is relatively prime to b, a ∈ A and b ∈ B}, then domain of R is NCERT Page-35/N-29 (a) {2,3,5} (b) {3,5} (c) {2,3,4} (d) {2,3,4,5} 31. The number of elements in the domain of relation R = {(x, y): x 2 + y 2 = 16, x, y ∈ Z} is (a) 1 NCERT Page-35/N-28