JEE (Main) Mathematics - COMPLEX NUMBERS AND QUADRATIC EQUATIONS Multiple Choice Questions (MCQs)

1. Which of the following is a valid representation of a set containing the elements 1, 2, and 3?

• a) {1, 2, 3, 4}
• b) {1, 2, 3}
• c) {1, 2, 2, 3}
• d) {1, 2, 3, 3}

Answer: b) {1, 2, 3}

2. Which of the following sets is an example of a finite set?

• a) The set of natural numbers
• b) The set of all real numbers
• c) The set of prime numbers less than 10
• d) The set of all integers

Answer: c) The set of prime numbers less than 10

3. Which symbol is used to represent the universal set?

• a) ∅
• b) U
• c) ∩
• d) ∪

Answer: b) U

4. Which of the following sets is an example of a null set (empty set)?

• a) {1, 2, 3}
• b) {x ∈ R : x² + 1 = 0}
• c) {2, 4, 6}
• d) {a, b, c}

Answer: b) {x ∈ R : x² + 1 = 0}

5. If A = {1, 2, 3} and B = {3, 4, 5}, what is the union of sets A and B?

• a) {1, 2, 3, 4, 5}
• b) {1, 2, 4, 5}
• c) {1, 2, 3}
• d) {3}

Answer: a) {1, 2, 3, 4, 5}

6. The complement of set A, denoted by A', is defined as:

• a) All the elements of the universal set that are not in A
• b) All the elements in set A
• c) All the elements of set A
• d) The union of A and its complement

Answer: a) All the elements of the universal set that are not in A

7. Which of the following sets is the power set of the set {a, b}?

• a) {{a}, {b}, {a, b}}
• b) {a, b}
• c) {{a, b}, ∅}
• d) {{a}, {b}, ∅, {a, b}}

Answer: d) {{a}, {b}, ∅, {a, b}}

8. If A = {x ∈ N : x ≤ 4} and B = {2, 4}, which of the following is A – B?

• a) {2, 4}
• b) {1, 3}
• c) {1, 3, 5}
• d) {1, 3, 4}

Answer: b) {1, 3}

9. Which of the following represents a subset of the set {1, 2, 3}?

• a) {1, 2, 3, 4}
• b) {2, 3}
• c) {4, 5}
• d) {1, 3, 5}

Answer: b) {2, 3}

10. Which of the following is the intersection of the sets A = {1, 2, 3} and B = {2, 3, 4}?

• a) {1, 2, 3, 4}
• b) {2, 3}
• c) {1, 4}
• d) {1, 2}

Answer: b) {2, 3}

11. What is the cardinality of the set {∅, {1}, {2, 3}}?

• a) 1
• b) 3
• c) 2
• d) 4

Answer: b) 3

12. Which of the following is the correct set-builder notation for the set of all even integers?

• a) {x ∈ Z : x is even}
• b) {x ∈ N : x is even}
• c) {x ∈ Z : x is prime}
• d) {x ∈ R : x is an integer}

Answer: a) {x ∈ Z : x is even}

13. If A = {1, 2, 3} and B = {3, 4}, which of the following is the symmetric difference (A Δ B) of A and B?

• a) {1, 2, 3, 4}
• b) {1, 2, 4}
• c) {3}
• d) {1, 2}

Answer: b) {1, 2, 4}

14. The set {x ∈ N : x is a perfect square and x ≤ 25} is equal to:

• a) {1, 4, 9, 16, 25}
• b) {2, 4, 9, 16, 25}
• c) {1, 2, 3, 4, 5}
• d) {1, 3, 5, 7, 9}

Answer: a) {1, 4, 9, 16, 25}

15. Which of the following is the correct representation of the set of all integers greater than 5 and less than or equal to 10?

• a) {x ∈ Z : x > 5 and x ≤ 10}
• b) {x ∈ N : x > 5 and x ≤ 10}
• c) {6, 7, 8, 9}
• d) {5, 6, 7, 8, 9, 10}

Answer: c) {6, 7, 8, 9}