Sets — Class 11 MCQs with Answers

Sets — important questions & MCQs with answers (Class 11 Mathematics)

14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.

1. Q1Easy

   Which of the following is a well-defined set?

   A.Collection of beautiful flowers

   B.Collection of all even integers✓ Correct

   C.Collection of clever students

   D.Collection of tall people

   Answer: B. Collection of all even integers

   Explanation: A set must be well-defined — every object's membership decidable without opinion, like "even integers." "Beautiful" or "clever" depends on judgment, so those collections aren't sets at all.

2. Q2Easy

   If A = {1, 2}, the number of subsets of A is:

   A.4✓ Correct

   B.3

   C.2

   D.5

   Answer: A. 4

   Explanation: A set with n elements has 2ⁿ subsets; here n=2 gives 2²=4: ∅, {1}, {2}, {1,2}. Forgetting to count ∅ and the whole set itself is the usual undercount.

3. Q3Easy

   A set is:

   A.Any group of items

   B.A well-defined collection of distinct objects✓ Correct

   C.An ordered pair

   D.A function

   Answer: B. A well-defined collection of distinct objects

   Explanation: A set is a well-defined collection of distinct objects — membership must be decidable and repeats don't count twice. A vague "group" without a clear rule fails this test.

4. Q4Easy

   A ∪ B is the set of all elements:

   A.In A only

   B.In A and B

   C.In A or B (or both)✓ Correct

   D.In B only

   Answer: C. In A or B (or both)

   Explanation: A∪B is every element in A or in B (including those in both) — the "or" here is inclusive. Restricting it to elements in A alone misreads union as intersection.

5. Q5Easy

   If A = {1, 2, 3} and B = {3, 4}, A ∪ B is:

   A.{3}

   B.{1, 2, 3, 4}✓ Correct

   C.{1, 2}

   D.{1, 2, 3, 4, 5}

   Answer: B. {1, 2, 3, 4}

   Explanation: A∪B merges every element from either set once: {1,2,3}∪{3,4}={1,2,3,4}, with the shared 3 counted only once. Adding an extra element like 5 that appears nowhere is the trap.

6. Q6Easy

   The empty set is denoted by:

   A.0

   B.{0}

   C.∅ (or {})✓ Correct

   D.U

   Answer: C. ∅ (or {})

   Explanation: The empty set (no elements) is written ∅ or {} — never {0}, which is a set containing the element 0, so it already has one member.

7. Q7Medium

   Sets A and B are equal iff:

   A.|A| = |B|

   B.A ⊆ B and B ⊆ A✓ Correct

   C.A ⊆ B

   D.B ⊆ A

   Answer: B. A ⊆ B and B ⊆ A

   Explanation: Two sets are equal exactly when each is a subset of the other: A⊆B and B⊆A together force A=B. Checking only A⊆B alone proves containment, not equality.

8. Q8Medium

   Set of all real numbers x with 0 ≤ x < 5 is written as:

   A.[0, 5)✓ Correct

   B.(0, 5)

   C.[0, 5]

   D.(0, 5]

   Answer: A. [0, 5)

   Explanation: 0≤x<5 includes the left endpoint but excludes the right one, written [0,5) — square bracket for included, round for excluded. Using (0,5) instead wrongly excludes 0 too.

9. Q9Medium

   If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B is:

   A.{3}

   B.{1, 2}

   C.{1, 2, 3, 4, 5}✓ Correct

   D.{4, 5}

   Answer: C. {1, 2, 3, 4, 5}

   Explanation: A∪B collects every element appearing in A or B, counted once each: {1,2,3}∪{3,4,5}={1,2,3,4,5}. Listing the shared element 3 twice is the common slip.

10. Q10Medium

    For two sets: |A ∪ B| equals:

    A.|A| + |B|

    B.|A| + |B| − |A ∩ B|✓ Correct

    C.|A| × |B|

    D.|A| − |B|

    Answer: B. |A| + |B| − |A ∩ B|

    Explanation: Inclusion-exclusion for two sets: |A∪B|=|A|+|B|−|A∩B|, subtracting the overlap so it isn't counted twice. Forgetting the −|A∩B| term inflates the union's size.

11. Q11Medium

    Power set of {1, 2} is:

    A.{{1}, {2}}

    B.{1, 2}

    C.{∅, {1}, {2}, {1,2}}✓ Correct

    D.∅

    Answer: C. {∅, {1}, {2}, {1,2}}

    Explanation: The power set lists every subset, always including ∅ and the whole set: P({1,2})={∅,{1},{2},{1,2}}. Leaving out ∅ or {1,2} itself is the common omission.

12. Q12Hard

    If n(A × B) = 6 and A = {1, 2}, then n(B) is:

    A.3✓ Correct

    B.4

    C.2

    D.6

    Answer: A. 3

    Explanation: n(A × B) = n(A) × n(B), so n(B) = 6 ÷ 2 = 3.

13. Q13Hard

    If a set has 5 elements, the number of elements in its power set is:

    A.10

    B.32✓ Correct

    C.25

    D.5

    Answer: B. 32

    Explanation: |P(A)|=2ⁿ counts every subset of a set with n elements: 2⁵=32 for a 5-element set. Confusing this with n²=25 or just n=5 is the usual error.

14. Q14Hard

    Set of all positive integers x with x² ≤ 20 is:

    A.{1, 2, 3}

    B.{1, 2, 3, 4, 5}

    C.{1, 2, 3, 4}✓ Correct

    D.{0, 1, 2, 3, 4}

    Answer: C. {1, 2, 3, 4}

    Explanation: x²≤20 for positive integers holds up to x=4, since 4²=16≤20 but 5²=25 exceeds 20, giving {1,2,3,4}. Rounding √20≈4.47 up to 5 instead of down is the usual overreach.

Sets — FAQs

More Class 11 Mathematics chapters

• 02Relations and Functions
• 03Trigonometric Functions
• 04Principle of Mathematical Induction
• 05Complex Numbers and Quadratic Equations
• 06Linear Inequalities
• 07Permutations and Combinations

Class 11 — other subjects

• Class 11 Biology chapters
• Class 11 Chemistry chapters
• Class 11 Computer Science chapters
• Class 11 English chapters
• Class 11 Physics chapters