Chapter 1: Sets Relations and Functions — Online MCQ Test
MATHS · CLASS 11th · Tamil Nadu State Board
Practice Chapter 1: Sets Relations and Functions with a free chapter-wise online MCQ test.
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....
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Chapter 1: Sets Relations and Functions — Important Questions & Answers
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.
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.
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.
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.
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.
f(f(x)) = a(ax + b) + b = a²x + ab + b. Comparing coefficients, a² = 9 implies a = 3 or a = -3.