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Class 11 | CBSE | MATHEMATICS
ASSERTION-REASON-1
SETS — MCQs & Assertion–Reason
Class XI | CBSE
PART A: MULTIPLE CHOICE QUESTIONS (MCQs)
MCQ 1. Which of the following collections is not a set?
- (a) Collection of vowels in English alphabet
- (b) Collection of natural numbers less than 20
- (c) Collection of most intelligent students of a class
- (d) Collection of prime numbers
Answer: (c)
MCQ 2. If
\[ A = \{1, 2, 3, 4, 5\} \]
then which of the following is true?
- (a) 6 ∈ A
- (b) 3 ∉ A
- (c) 5 ∈ A
- (d) 0 ∈ A
Answer: (c)
MCQ 3. The roster form of the set
\[ \{x : x ∈ N,\; x² < 20\} \]
Checking values:
\[ \begin{aligned} 1² &= 1 \\ 2² &= 4 \\ 3² &= 9 \\ 4² &= 16 \\ 5² &= 25 \;(\text{not allowed}) \end{aligned} \]
- (a) {1, 2, 3, 4, 5}
- (b) {1, 2, 3, 4}
- (c) {1, 4, 9, 16}
- (d) {1, 2, 3}
Answer: (b)
MCQ 4. The set
\[ \{x : x = 2n,\; n ∈ N\} \]
represents:
- (a) Odd numbers
- (b) Prime numbers
- (c) Even numbers
- (d) Natural numbers
Answer: (c)
MCQ 5. Which of the following is the correct set-builder form of
\[ \{1, 4, 9, 16\} \]
- (a) \(\{x : x = n²,\; n ∈ N,\; 1 ≤ n ≤ 4\}\)
- (b) \(\{x : x = 2n,\; n ∈ N\}\)
- (c) \(\{x : x ∈ Z,\; x² ≤ 16\}\)
- (d) \(\{x : x = n³,\; n ∈ N\}\)
Answer: (a)
MCQ 6. If
\[ A = \{a, e, i, o, u\} \]
which statement is false?
- (a) a ∈ A
- (b) b ∉ A
- (c) i ∈ A
- (d) y ∈ A
Answer: (d)
PART B: ASSERTION – REASON QUESTIONS
Directions: Choose the correct option:
- (a) Both A and R are true, and R is the correct explanation
- (b) Both A and R are true, but R is not the correct explanation
- (c) A is true, R is false
- (d) A is false, R is true
AR 1.
Assertion (A): The collection of all even integers is a set.
Reason (R): Every even integer can be clearly identified.
Answer: (a)
AR 2.
Assertion (A): The collection of best cricketers of the world is a set.
Reason (R): The word “best” depends on personal opinion.
Answer: (d)
AR 3.
Assertion (A): In roster form, the order of elements is important.
Reason (R): \(\{1, 2, 3\} ≠ \{3, 2, 1\}\)
Answer: (d)
AR 4.
Assertion (A):
\[ \{1, 2, 3\} = \{x : x ∈ N,\; x < 4\} \]
Reason (R): Both sets have exactly the same elements.
Answer: (a)
AR 5.
Assertion (A): Repetition of elements is allowed in a set.
Reason (R): A set contains only distinct elements.
Answer: (d)