Take timed practice tests on Sets, Relations and Functions for JEE Main and JEE Advanced with session-wise drills, score review, and explanation-led revision.
Six 20-question timed sessions plus one 60-question module test. Each question is original and calibrated from the uploaded material pattern without copying PDF wording.
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1. A ∪ B represents:
Explanation: Union A ∪ B = {x: x ∈ A or x ∈ B}. Intersection A ∩ B = {x: x ∈ A and x ∈ B}. Difference A − B = {x: x ∈ A and x ∉ B}.
2. (A ∪ B)' (complement of union) equals:
Explanation: De Morgan's Laws: (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'. Complement of union = intersection of complements.
3. A function f: A → B is bijective if it is:
Explanation: Bijective = one-one AND onto. Injective (one-one): f(x₁) = f(x₂) → x₁ = x₂. Surjective (onto): every element in B has a pre-image in A. Bijective functions have inverses.
4. If f(x) = 2x and g(x) = x + 1, then (f ∘ g)(x) is:
Explanation: (f ∘ g)(x) = f(g(x)) = f(x+1) = 2(x+1) = 2x + 2. Note: (g ∘ f)(x) = g(f(x)) = g(2x) = 2x + 1 ≠ f ∘ g.
5. If f(x) = 2x − 1, then f⁻¹(x) is:
Explanation: Let y = 2x − 1 → x = (y+1)/2. So f⁻¹(x) = (x+1)/2. Verify: f(f⁻¹(x)) = 2((x+1)/2) − 1 = x ✓.
6. The domain of f(x) = √(x − 2) is:
Explanation: For √(x−2) to be real: x − 2 ≥ 0 → x ≥ 2. Domain = [2, ∞). At x = 2, f(2) = 0 (included).
7. The number of subsets of a set with n elements is:
Explanation: Each element can either be included or excluded from a subset → 2 choices per element → 2ⁿ total subsets (including empty set and the set itself).
8. An equivalence relation must be:
Explanation: Equivalence relation: (1) Reflexive: aRa. (2) Symmetric: aRb → bRa. (3) Transitive: aRb and bRc → aRc. Example: equality (=), congruence modulo n.
9. The number of onto functions from a set with 3 elements to a set with 2 elements is:
Explanation: Total functions: 2³ = 8. Functions where all map to {a}: 1. All to {b}: 1. Onto = 8 − 2 = 6. Using inclusion-exclusion: 2³ − C(2,1)×1³ + C(2,2)×0³ = 8 − 2 + 0 = 6.
10. If A has 3 elements and B has 4 elements, the number of possible relations from A to B is:
Explanation: A relation from A to B is a subset of A × B. |A × B| = 3 × 4 = 12. Number of subsets = 2¹² = 4096.
11. n(A ∪ B) = n(A) + n(B) − n(A ∩ B). If n(A)=8, n(B)=6, n(A∩B)=3, then n(A∪B) is:
Explanation: n(A∪B) = 8 + 6 − 3 = 11. By inclusion-exclusion principle.
12. The number of functions from a set with m elements to a set with n elements is:
Explanation: For each of the m elements in the domain, there are n choices in the codomain → nᵐ total functions. For injections: n!/(n−m)! (if n ≥ m).