Relations and Functions — Class 11 MCQs with Answers

Relations and Functions — important questions & MCQs with answers (Class 11 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   If A={1,2}, B={a,b}, then |A×B| =

   A2B4C6D8
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   Answer: 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. Q2 of 6Easy

   Domain of f(x) = √x:

   Ax > 0Ball real xCx ≥ 0Dx ≤ 0
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   Answer: 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. Q3 of 6Medium

   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)}
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   Answer: {(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.

4. Q4 of 6Medium

   Assertion (A): The number of relations from A = {x, y, z} to B = {1, 2} is 64. Reason (R): If n(A) = p and n(B) = q, then the number of relations from A to B is 2^(pq).

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: Both A and R are true and R is the correct explanation of A

   Explanation: A is true: n(A × B) = 3 × 2 = 6, so the number of relations is 2⁶ = 64. R is true and it is exactly the rule used to get A.

5. Q5 of 6Hard

   f(x) = x³ on R is:

   AConstantBMany-oneCOne-one and ontoDNot a function
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   Answer: 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.

6. Q6 of 6Hard

   Assertion (A): For R = {(x, y) : y = x + 1} on A = {1, 2, 3, 4, 5, 6}, the range of R is equal to its codomain. Reason (R): The range of a relation is always a subset of its codomain.

   ABoth A and R are true and R is the correct explanation of ABBoth A and R are true but R is not the correct explanation of ACA is true but R is falseDA is false but R is true
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   Answer: A is false but R is true

   Explanation: A is false: R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}, so the range is {2, 3, 4, 5, 6} while the codomain is {1, 2, 3, 4, 5, 6}; 1 is missing. R is true: range ⊂ codomain.

Relations and Functions notes: key concepts (Class 11 Mathematics)

This chapter builds functions step by step. Ordered pairs and the Cartesian product A×B give relations as subsets of A×B, each with a domain and range. A function assigns one image to every input; the chapter surveys the standard real functions — identity, modulus, signum, greatest-integer — and the algebra of combining them.

Ordered pair

A pair (a,b) in which order matters, so (a,b)≠(b,a) unless a=b. Two ordered pairs are equal only when both corresponding components are equal.

Cartesian product

A×B is the set of all ordered pairs (a,b) with a∈A and b∈B. Then n(A×B)=n(A)·n(B), and A×B≠B×A in general.

Relation

Any subset of A×B, pairing elements of A with elements of B; on a single set it is a relation on A. There are 2^(n(A)·n(B)) possible relations.

Domain, range & codomain

The domain is the set of all first components, the range the set of all second components actually attained, and the whole target set B is the codomain.

Function

A relation in which every element of the domain has one and only one image. Written y=f(x); the vertical-line test detects it on a graph.

Identity & constant functions

The identity function f(x)=x maps every real to itself; a constant function f(x)=c sends every input to the same fixed value c.

Polynomial function

f(x)=a₀+a₁x+…+aₙxⁿ with real coefficients and whole-number powers. Its domain is all of ℝ, and its degree fixes the overall shape.

Modulus function

f(x)=|x| equals x for x≥0 and −x for x<0. Its graph is a V-shape; the domain is ℝ and the range is [0, ∞).

Signum function

sgn(x)=|x|/x for x≠0 and 0 at x=0, giving −1, 0 or 1. It records only the sign of the input; its range is {−1, 0, 1}.

Greatest-integer function

f(x)=[x] is the greatest integer not exceeding x, so [2.7]=2 and [−1.3]=−2. Its step graph has range ℤ.

Real-valued function

A function whose codomain is ℝ. Its domain is every x giving a real output — watch for division by zero or square roots of negatives.

Algebra of functions

On the common domain, (f±g)(x)=f(x)±g(x) and (fg)(x)=f(x)·g(x); the quotient (f/g)(x)=f(x)/g(x) is defined only where g(x)≠0.