Chapter Exam

Chapter 1: Sets Relations and Functions — Online MCQ Test

Q: If a set A has 3 elements and a set B has 2 elements, the number of elements in the Cartesian product A × B is:

Answer: B. 6 — The number of elements in A × B is the product of the number of elements in set A and set B, which is 3 × 2 = 6.

Q: Which of the following is the definition of an empty set?

Answer: C. A set containing no elements — An empty set or null set is a set that contains no elements at all.

Q: If A = {1, 2} and B = {3, 4}, how many relations are there from A to B?

Answer: C. 16 — The number of relations is 2^(n(A)×n(B)). Here, n(A)=2 and n(B)=2, so 2^(2×2) = 2^4 = 16.

Q: Which of the following statements about the function f(x) = sin(x) is false?

Answer: D. The function is injective on its domain — The sine function is not injective on the set of real numbers because sin(0) = sin(π) = 0.

Q: If f(x) = ax + b and f(f(x)) = 9x + 8, what are the possible values of a?

Answer: C. 3 or -3 — f(f(x)) = a(ax + b) + b = a²x + ab + b. Comparing coefficients, a² = 9 implies a = 3 or a = -3.

MATHS · CLASS 11th · Tamil Nadu State Board

Practice Chapter 1: Sets Relations and Functions with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 11th MATHS. This chapter covers: This chapter covers set operations cartesian products intervals neighborhoods relations and function concepts. Students study function transformations types domain range and graphi.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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

Frequently asked questions from Tamil Nadu State Board CLASS 11th MATHS — Chapter 1: Sets Relations and Functions, with answers and explanations. These are sample questions; the exam has its own separate question set.

If a set A has 3 elements and a set B has 2 elements, the number of elements in the Cartesian product A × B is:

A. 5
B. 6 ✓
C. 9
D. 8

Answer: B. 6
The number of elements in A × B is the product of the number of elements in set A and set B, which is 3 × 2 = 6.

Which of the following is the definition of an empty set?

A. A set with one element
B. A set that is equal to its universal set
C. A set containing no elements ✓
D. A set with infinite elements

Answer: C. A set containing no elements
An empty set or null set is a set that contains no elements at all.

If A = {1, 2} and B = {3, 4}, how many relations are there from A to B?

A. 4
B. 8
C. 16 ✓
D. 32

Answer: C. 16
The number of relations is 2^(n(A)×n(B)). Here, n(A)=2 and n(B)=2, so 2^(2×2) = 2^4 = 16.

Which of the following statements about the function f(x) = sin(x) is false?

A. The domain is ℝ
B. The range is [-1, 1]
C. The function is periodic
D. The function is injective on its domain ✓

Answer: D. The function is injective on its domain
The sine function is not injective on the set of real numbers because sin(0) = sin(π) = 0.

If f(x) = ax + b and f(f(x)) = 9x + 8, what are the possible values of a?

A. 3 only
B. -3 only
C. 3 or -3 ✓
D. 9 or -9

Answer: C. 3 or -3
f(f(x)) = a(ax + b) + b = a²x + ab + b. Comparing coefficients, a² = 9 implies a = 3 or a = -3.

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