RBSE Class 10 Mathematics MCQs (2026)
Chapter 1: Real Numbers
(Objective Type Questions | 1×20 = 20 Marks)
1. According to the Fundamental Theorem of Arithmetic, every composite number can be expressed as a
A. sum of prime numbers
B. difference of prime numbers
C. product of prime numbers uniquely
D. product of even numbers
Answer: C
2. The prime factorisation of 32760 is
A. 2³ × 3² × 5 × 7 × 13
B. 2² × 3³ × 5 × 7 × 13
C. 2³ × 3 × 5² × 7 × 13
D. 2 × 3² × 5 × 7 × 13
Answer: A
3. If p is a prime number and p divides a², then
A. p divides 2a
B. p divides a
C. p divides a³
D. p divides 4a
Answer: B
4. Which of the following numbers is irrational?
A. 0.25
B. 3/5
C. √2
D. 0.6
Answer: C
5. If HCF(6, 20) = 2, then LCM(6, 20) is
A. 20
B. 30
C. 60
D. 120
Answer: C
6. The decimal expansion of a rational number is terminating if the prime factorisation of its denominator has only
A. 2
B. 5
C. 2 and 5
D. 2, 3 and 5
Answer: C
7. The HCF of 96 and 404 is
A. 2
B. 4
C. 8
D. 16
Answer: B
8. The number √3 + 5 is
A. rational
B. irrational
C. whole number
D. natural number
Answer: B
9. If HCF(a, b) = 12 and LCM(a, b) = 180, then the value of a × b is
A. 180
B. 360
C. 2160
D. 15
Answer: C
10. Which of the following statements is true?
A. The sum of two irrational numbers is always irrational
B. The difference of a rational and an irrational number is irrational
C. The product of two rational numbers is irrational
D. The quotient of two irrational numbers is always rational
Answer: B
11. The number 6ⁿ ends with the digit zero for
A. every natural number n
B. no natural number n
C. only even values of n
D. only odd values of n
Answer: B
12. The LCM of 6, 72 and 120 is
A. 180
B. 240
C. 360
D. 720
Answer: C
13. √5 is a/an
A. rational number
B. irrational number
C. whole number
D. even number
Answer: B
14. The number 1 is not a prime number because it has
A. two factors
B. three factors
C. only one factor
D. no factors
Answer: C
15. The prime factorisation method is used to find
A. addition of numbers
B. subtraction of numbers
C. HCF and LCM
D. square roots
Answer: C
16. The irrationality of √2 is proved using
A. induction method
B. direct method
C. contradiction method
D. survey method
Answer: C
17. A rational number has a non-terminating repeating decimal expansion if its denominator has prime factors other than
A. 2
B. 5
C. 2 and 5
D. 10
Answer: C
18. The number (7 × 11 × 13 + 13) is
A. prime
B. composite
C. irrational
D. negative
Answer: B
19. Which of the following is an irrational number?
A. √9
B. √16
C. √7
D. 5
Answer: C
20. For three positive integers p, q, and r, which of the following is true?
A. HCF × LCM = p × q × r
B. HCF × LCM ≠ p × q × r
C. HCF = LCM
D. p = q = r
Answer: B