CBSE Class 11 Mathematics Relations and Functions Assignment Set 01

Case Based MCQs

Method to Find the Sets When Cartesian Product is Given For finding these two sets, we write first element of each ordered pair in first set say A and corresponding second element in second set B (say).
Number of Elements in Cartesian Product of Two Sets If there are p elements in set A and q elements in set B, then there will be pq elements in A × B i.e. if n (A) = p and n (B ) = q, then n (A × B ) = pq.

Based on the above two topic, answer the following questions.

Question. If A × B = {(a, 1), (b, 3), (a, 3), (b, 1), (a, 2), (b, 2)}. Then, A and B are
(a) {1, 3, 2}, {a,b }
(b) {a,b },{1,3}
(c) {a,b },{1,3,2}
(d) None of these
Answer : C

Question. If the set A has 3 elements and set B has 4 elements, then the number of elements in A × B is
(a) 3
(b) 4
(c) 7
(d) 12
Answer : A

Question. A and B are two sets given in such a way that A × B contains 6 elements. If three elements of A × B are (1, 3), (2, 5) and (3, 3), then A, B are
(a) {1, 2, 3}, {3, 5}
(b) {3, 5,}, {1, 2, 3}
(c) {1, 2}, {3, 5}
(d) {1, 2, 3}, {5}
Answer : A

Question. The remaining elements of A × B in (iii) is
(a) (5, 1), (3, 2), (3, 5)
(b) (1, 5), (2, 3), (3, 5)
(c) (1, 5), (3, 2), (5, 3)
(d) None of the above
Answer : D

Question. The cartesian product P × P has 16 elements among which are found (a,1) and (b, 2). Then, the set P is
(a) {a,b }
(b) {1, 2}
(c) {a,b,1,2}
(d) {a,b,1,2,4}
Answer : C

Assertion-Reasoning MCQs

Directions Each of these questions contains two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of the which is the correct answer. You have to select one of the codes (a), (b), (c) and
(d) given below.
(a) A is true, R is true; R is a correct explanation of A.
(b) A is true, R is true; R is not a correct explanation of A.
(c) A is true; R is false.
(d) A is false; R is true.

Question. Assertion (A) If (x + 1, y − 2) = (3, 1) , then x = 2 and y = 3.
Reason (R) Two ordered pairs are equal, if their corresponding elements are equal.
Answer : A

Question. Assertion (A) The cartesian product of two non-empty sets P and Q is denoted as P ×Q and P × Q = {( p, q ) : p ∈ P , q ∈ Q }.
Reason (R) If A = {red, blue} and B = {b, c , s}, then A × B = {(red, b), (red, c ), (red, s), (blue, b), (blue, c ), (blue, s)}.
Answer : A

Question. Assertion (A) If (4x + 3, y ) = (3x + 5, −2), then x = 2 and y = − 2.
Reason (R) If A = {−1, 3, 4}, then A × A is {(−1, −1), (−1, 3), (−1, 4), (3, −1), (4, −1), (3, 4)}.
Answer : C

Question. Assertion (A) If (x, 1), (y, 2) and (z , 1) are in A × B and n(A) = 3, n(B ) = 2, then A = {x, y, z } and B = {1, 2}.
Reason (R) If n(A) = 3 and n(B ) = 2, then n(A × B ) = 6 .
Answer : B

Question. Assertion (A) Let A = {1, 2} and B = {3, 4}. Then, number of relations from A to B is 16.
Reason (R) If n(A) = p and n(B ) = q, then number of relations is 2^pq .
Answer : A