Class X Math- Real Numbers- Set 4

Class X Math - Real Numbers (Set 4)

Class X Mathematics – Chapter 1: Real Numbers (Set 4)

1. Which of the following numbers is both rational and integer?
A. √3
B. 2
C. π
D. 3/2
Answer: B. 2
Explanation: 2 is an integer and also a rational number (can be written as 2/1).
2. The prime factorization of 36 is:
A. 2 × 2 × 3
B. 2 × 3 × 3
C. 2² × 3²
D. 3 × 3 × 3
Answer: C. 2² × 3²
Explanation: 36 = 2 × 2 × 3 × 3 = 2² × 3².
3. Which of the following is the HCF of 18 and 24?
A. 6
B. 12
C. 24
D. 36
Answer: A. 6
Explanation: 6 is the highest number that divides both 18 and 24.
4. If two numbers are co-prime, then their HCF is:
A. 0
B. 1
C. Product of numbers
D. LCM of numbers
Answer: B. 1
Explanation: Co-prime numbers have no common factors other than 1.
5. The decimal expansion of 7/25 is:
A. Terminating
B. Non-terminating repeating
C. Non-terminating non-repeating
D. None of these
Answer: A. Terminating
Explanation: 7/25 = 0.28 which terminates.
6. Which of these numbers has a non-terminating repeating decimal expansion?
A. 1/4
B. 3/5
C. 2/9
D. 7/8
Answer: C. 2/9
Explanation: 2/9 = 0.222... which repeats infinitely.
7. LCM of 8 and 12 is:
A. 96
B. 24
C. 4
D. 12
Answer: B. 24
Explanation: LCM(8,12) = 24 using prime factorization.
8. Which of the following is not a real number?
A. √2
B. π
C. –1
D. √–3
Answer: D. √–3
Explanation: Square root of a negative number is not real (it's imaginary).
9. If a number is divisible by both 3 and 4, then it is also divisible by:
A. 7
B. 9
C. 12
D. 6
Answer: C. 12
Explanation: LCM of 3 and 4 is 12.
10. 0.1010010001... is:
A. Terminating
B. Rational
C. Irrational
D. Repeating
Answer: C. Irrational
Explanation: It is non-terminating and non-repeating, hence irrational.

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