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: 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: 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.

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.

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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 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.

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.

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.

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