Class 11th Maths – RD Sharma Chapter 2 : Relation Multiple Choice Questions (MCQs) Solution

   MULTIPLE CHOICE QUESTIONS (MCQs)

  Mark the correct alternative in each of the following:

1. 1. If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is
      (a) {(1, 2), (1, 5), (2, 5)}
      (b) {(1, 4)}
      (c) (1, 4)
      (d) none of these. Watch Solution
   2. If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⇔ y = 3x, then R =
      (a) {(3, 1), (6, 2), (8, 2), (9, 3)}
      (b) {(3, 1), (6, 2), (9, 3)}
      (c) {(3, 1), (2, 6), (3, 9)}
      (d) none of these. Watch Solution
   3. Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by R = {(1, 3), (2, 5), (3, 3)}. Then, R⁻¹ is
      (a) {(3, 1), (3, 1), (5, 2)}
      (b) {(1, 3), (2, 5), (3, 3)}
      (c) {(1, 3), (5, 2)}
      (d) none of these. Watch Solution
   4. If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by ‘x is greater than y’. The range of R is
      (a) {1, 4, 6, 9}
      (b) {4, 6, 9}
      (c) {1}
      (d) none of these. Watch Solution
   5. If R = {(x, y) : x, y ∈ Z, x² + y² ≤ 4} is a relation on Z, then domain of R is
      (a) {0, 1, 2}
      (b) {0, −1, −2}
      (c) {−2, −1, 0, 1, 2}
      (d) none of these. Watch Solution
   6. A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y ⇔ x is relatively prime to y. Then, domain of R is
      (a) {2, 3, 5}
      (b) {3, 5}
      (c) {2, 3, 4}
      (d) {2, 3, 4, 5}. Watch Solution
   7. A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
      (a) (2 + 3i) ϕ 13
      (b) 3 ϕ (−3)
      (c) (1 + i) ϕ 2
      (d) i ϕ 1.Watch Solution
   8. Let R be a relation on N defined by x + 2y = 8. The domain of R is
      (a) {2, 4, 8}
      (b) {2, 4, 6, 8}
      (c) {2, 4, 6}
      (d) {1, 2, 3, 4}. Watch Solution
   9. R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R⁻¹ is
      (a) {(8, 11), (10, 13)}
      (b) {(11, 8), (13, 10)}
      (c) {(10, 13), (8, 11), (12, 10)}
      (d) none of these. Watch Solution
   10. If the set A has p elements, B has q elements, then the number of elements in A × B is
       (a) p + q
       (b) p + q + 1
       (c) pq
       (d) p² Watch Solution
   11. Let R be a relation from a set A to a set B, then
       (a) R = A ∪ B
       (b) R = A ∩ B
       (c) R ⊆ A × B
       (d) R ⊆ B × A. Watch Solution
   12. If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
       (a) 2mn
       (b) 2mn − 1
       (c) 2mn
       (d) mn Watch Solution
   13. If R is a relation on a finite set having n elements, then the number of relations on A is
       (a) 2ⁿ
       (b) 2ⁿ²
       (c) n²
       (d) nⁿ Watch Solution
   14. Let n(A) = m and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is
       (a) mⁿ
       (b) nᵐ − 1
       (c) mn − 1
       (d) 2mn − 1 Watch Solution