Chapter Exam

Chapter 1: Relations and Functions — Online MCQ Test

Q: If two ordered pairs (a, b) and (c, d) are equal, then which statement is true?

Answer: A. a = c and b = d — Two ordered pairs are equal only when their corresponding first and second components are equal.

Q: The Cartesian product A × B is the set of all ordered pairs of the form:

Answer: A. (a, b), where a ∈ A and b ∈ B — By definition, A × B contains all ordered pairs whose first element is from A and second element is from B.

Q: If n(A) = 3 and n(B) = 4, then n(A × B) is:

Answer: B. 12 — The number of elements in A × B is n(A) × n(B) = 3 × 4 = 12.

Q: For the relation R = {(1, 2), (2, 4), (3, 6)}, the domain is:

Answer: B. {1, 2, 3} — The domain of a relation is the set of all first components of the ordered pairs.

Q: Let A = {1, 2, 3} and B = {2, 3, 4, 5}. If R = {(x, y) : y = x + 1, x ∈ A, y ∈ B}, then R is:

Answer: A. {(1, 2), (2, 3), (3, 4)} — Substituting x = 1, 2, 3 gives y = 2, 3, 4 respectively.

Q: For f : R → R defined by f(x) = x², which statement is true?

Answer: D. f is neither one-one nor onto — Since f(1) = f(-1), it is not one-one. Also negative real numbers are not images, so it is not onto R.

Q: For f : Z → Z defined by f(n) = n + 2, the function is:

Answer: A. one-one and onto — Different integers give different images, and every integer k has a preimage k - 2. Hence the function is one-one and onto.

Q: If n(A) = 3 and n(B) = 5, then the number of one-one functions from A to B is:

Answer: C. 60 — For a one-one function, the 3 elements of A must get distinct images from 5 elements of B. The number is 5 × 4 × 3 = 60.

Q: Let f : R → R be f(x) = ax + b, where a ≠ 0. For which condition is f⁻¹ = f?

Answer: B. a = -1 with any real b, or a = 1 and b = 0 — For f⁻¹ = f, we need f(f(x)) = x for all x. This gives a² = 1 and b(a + 1) = 0, so a = -1 with any b, or a = 1 and b = 0.

MATHS · CLASS 10th · Tamil Nadu State Board

Practice Chapter 1: Relations and Functions with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 10th MATHS. This chapter covers: Ordered pairs Cartesian product Relations Functions Domain Range Codomain One one function Many one function Onto function Into function Composite function Inverse function Represe.... AI-generated questions from basic to board-exam level, with instant results and explanations.

Questions

20m

Time Limit

Attempts Left

10 random questions from this chapter (mixed difficulty)
Questions you've seen before won't repeat until the pool resets
You have 20 minutes — exam auto-submits when time is up
Maximum 3 attempts per chapter
Results and explanations shown immediately after submission

New here? Register free — includes 3 free chapter exams.

Chapter 1: Relations and Functions — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 10th MATHS — Chapter 1: Relations and Functions, with answers and explanations. These are sample questions; the exam has its own separate question set.

If two ordered pairs (a, b) and (c, d) are equal, then which statement is true?

A. a = c and b = d ✓
B. a = d and b = c
C. a + b = c + d only
D. a = b and c = d

Answer: A. a = c and b = d
Two ordered pairs are equal only when their corresponding first and second components are equal.

The Cartesian product A × B is the set of all ordered pairs of the form:

A. (a, b), where a ∈ A and b ∈ B ✓
B. (b, a), where a ∈ A and b ∈ B
C. (a, a), where a ∈ A only
D. (b, b), where b ∈ B only

Answer: A. (a, b), where a ∈ A and b ∈ B
By definition, A × B contains all ordered pairs whose first element is from A and second element is from B.

If n(A) = 3 and n(B) = 4, then n(A × B) is:

A. 7
B. 12 ✓
C. 1
D. 34

Answer: B. 12
The number of elements in A × B is n(A) × n(B) = 3 × 4 = 12.

For the relation R = {(1, 2), (2, 4), (3, 6)}, the domain is:

A. {2, 4, 6}
B. {1, 2, 3} ✓
C. {1, 2, 3, 4, 6}
D. {(1, 2), (2, 4), (3, 6)}

Answer: B. {1, 2, 3}
The domain of a relation is the set of all first components of the ordered pairs.

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

A. {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)} ✓
B. {(3, 1), (4, 1), (5, 1), (3, 2), (4, 2), (5, 2)}
C. {(1, 2), (3, 4), (4, 5)}
D. {1, 2, 3, 4, 5}

Answer: A. {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
A × B contains all ordered pairs with first element from A and second element from B.

Let A = {1, 2, 3} and B = {2, 3, 4, 5}. If R = {(x, y) : y = x + 1, x ∈ A, y ∈ B}, then R is:

A. {(1, 2), (2, 3), (3, 4)} ✓
B. {(2, 1), (3, 2), (4, 3)}
C. {(1, 3), (2, 4), (3, 5)}
D. {(1, 1), (2, 2), (3, 3)}

Answer: A. {(1, 2), (2, 3), (3, 4)}
Substituting x = 1, 2, 3 gives y = 2, 3, 4 respectively.

For f : R → R defined by f(x) = x², which statement is true?

A. f is one-one and onto
B. f is one-one but not onto
C. f is onto but not one-one
D. f is neither one-one nor onto ✓

Answer: D. f is neither one-one nor onto
Since f(1) = f(-1), it is not one-one. Also negative real numbers are not images, so it is not onto R.

For f : Z → Z defined by f(n) = n + 2, the function is:

A. one-one and onto ✓
B. many-one and onto
C. one-one but not onto
D. neither one-one nor onto

Answer: A. one-one and onto
Different integers give different images, and every integer k has a preimage k - 2. Hence the function is one-one and onto.

If n(A) = 3 and n(B) = 5, then the number of one-one functions from A to B is:

A. 15
B. 25
C. 60 ✓
D. 125

Answer: C. 60
For a one-one function, the 3 elements of A must get distinct images from 5 elements of B. The number is 5 × 4 × 3 = 60.

Let f : R → R be f(x) = ax + b, where a ≠ 0. For which condition is f⁻¹ = f?

A. a = 1 and b can be any real number
B. a = -1 with any real b, or a = 1 and b = 0 ✓
C. a = 0 and b = 1
D. a = 2 and b = 0

Answer: B. a = -1 with any real b, or a = 1 and b = 0
For f⁻¹ = f, we need f(f(x)) = x for all x. This gives a² = 1 and b(a + 1) = 0, so a = -1 with any b, or a = 1 and b = 0.

Next Chapter →

Chapter 2: Numbers and Sequences