Relations and Functions — Class 11 MCQs with Answers

Relations and Functions — 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

   If A={1,2}, B={a,b}, then |A×B| =

   A.2

   B.4✓ Correct

   C.6

   D.8

   Answer: B. 4

   Explanation: The size of A×B is |A|×|B|: with 2 elements in A and 2 in B, that gives 2×2 = 4 ordered pairs. A common slip is adding the sizes instead of multiplying them.

2. Q2Easy

   Domain of f(x) = √x:

   A.x > 0

   B.all real x

   C.x ≥ 0✓ Correct

   D.x ≤ 0

   Answer: C. x ≥ 0

   Explanation: √x is only real when x ≥ 0, so the domain of f(x) = √x is x ≥ 0. Writing x > 0 wrongly excludes x = 0, where √0 = 0 is perfectly valid.

3. Q3Easy

   Cartesian product A × B is the set of:

   A.Unordered pairs

   B.All ordered pairs (a, b) with a ∈ A, b ∈ B✓ Correct

   C.Subsets

   D.Functions

   Answer: B. All ordered pairs (a, b) with a ∈ A, b ∈ B

   Explanation: A × B collects every ordered pair (x, y) with x taken from A and y from B — order matters, so (x, y) and (y, x) are generally different pairs.

4. Q4Easy

   A relation from A to B is:

   A.Any subset of A × B✓ Correct

   B.Same as A

   C.Same as B

   D.Function only

   Answer: A. Any subset of A × B

   Explanation: Any relation from A to B is simply a subset of A × B — it can hold as few or as many ordered pairs as chosen, unlike a function which fixes one output per input.

5. Q5Easy

   A function f from A to B is a relation where:

   A.Every element of A has exactly one image in B✓ Correct

   B.Some elements have multiple images

   C.No element has image

   D.Elements may be mapped to anything

   Answer: A. Every element of A has exactly one image in B

   Explanation: A relation is a function only when every element of A maps to exactly one image in B — mapping to two or more images, or to none, breaks the function rule.

6. Q6Easy

   If |A| = 3 and |B| = 4, then |A × B| =

   A.16

   B.7

   C.12✓ Correct

   D.9

   Answer: C. 12

   Explanation: |A × B| = |A| × |B|, so with 3 elements in A and 4 in B the product set has 3×4 = 12 ordered pairs, not 3+4 = 7.

7. Q7Medium

   Number of relations from A to B where |A| = 3, |B| = 2:

   A.32

   B.6

   C.64✓ Correct

   D.16

   Answer: C. 64

   Explanation: The number of relations from A to B is 2^(|A|·|B|), since each of the |A|·|B| possible pairs is either in or out: 2^(3×2) = 2⁶ = 64.

8. Q8Medium

   Range of f(x) = x², x ∈ R:

   A.R

   B.[0, ∞)✓ Correct

   C.(0,∞)

   D.(−∞, 0]

   Answer: B. [0, ∞)

   Explanation: For f(x) = x², squaring any real number gives a value ≥ 0, and every non-negative number is hit — so the range is [0, ∞), not all of R.

9. Q9Medium

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

   A.∅

   B.{(3,1),(3,2),(4,1),(4,2)}

   C.{1,2,3,4}

   D.{(1,3),(1,4),(2,3),(2,4)}✓ Correct

   Answer: D. {(1,3),(1,4),(2,3),(2,4)}

   Explanation: Pair each element of A = {1, 2} with each element of B = {3, 4}, keeping A's element first: (1,3), (1,4), (2,3), (2,4) — swapping the order gives a wrong set.

10. Q10Medium

    Number of functions from A to B where |A| = 3, |B| = 2:

    A.8✓ Correct

    B.6

    C.9

    D.16

    Answer: A. 8

    Explanation: The number of functions from A to B is |B| raised to |A|, since each of A's 3 elements independently picks one of B's 2 outputs: 2³ = 8.

11. Q11Medium

    If f(x)=x+1, g(x)=2x, then (f∘g)(3) =

    A.7✓ Correct

    B.6

    C.5

    D.8

    Answer: A. 7

    Explanation: (f∘g)(3) means apply g first: g(3) = 2×3 = 6, then f(6) = 6+1 = 7. Composing in the wrong order, f then g, gives a different, wrong result.

12. Q12Hard

    An equivalence relation is:

    A.Reflexive, symmetric, transitive✓ Correct

    B.Only reflexive

    C.Antisymmetric

    D.None

    Answer: A. Reflexive, symmetric, transitive

    Explanation: An equivalence relation must satisfy all three properties together — reflexive, symmetric, and transitive. Having just one or two, like symmetry alone, isn't enough.

13. Q13Hard

    f(x) = x³ on R is:

    A.Constant

    B.Many-one

    C.One-one and onto✓ Correct

    D.Not a function

    Answer: C. One-one and onto

    Explanation: f(x) = x³ is strictly increasing on R, so no two inputs share an output (one-one), and every real number has a cube root (onto) — together that's a bijection.

14. Q14Hard

    |A| = 5, |B| = 3. Number of relations from A to B:

    A.32

    B.15

    C.8

    D.2¹⁵✓ Correct

    Answer: D. 2¹⁵

    Explanation: The number of relations from A to B is 2^(|A|·|B|); with |A| = 5 and |B| = 3, that's 2^(5×3) = 2¹⁵, not 2 raised to the sum 5+3.

Relations and Functions — FAQs

More Class 11 Mathematics chapters

• 01Sets
• 03Trigonometric Functions
• 04Principle of Mathematical Induction
• 05Complex Numbers and Quadratic Equations
• 06Linear Inequalities
• 07Permutations and Combinations

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• Class 11 Biology chapters
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