POLYCET Real Numbers MCQs with Answers & Explanations 25
POLYCET Real Numbers MCQs – Preparing for the POLYCET exam requires a strong foundation in Real Numbers, one of the most important topics in Class 10 Mathematics. This set of 25 carefully designed MCQs covers key concepts such as HCF, LCM, Euclid’s Division Algorithm, irrational numbers, decimal expansions, and prime factorisation. These questions are crafted to match the latest POLYCET exam pattern, helping students improve accuracy, speed, and conceptual clarity. Whether you’re revising basics or testing your understanding, this practice set will boost your confidence and exam readiness. Each question includes a step-by-step explanation, making it ideal for self-study and quick revision.
1. The HCF of 12 and 18 is:
A) 2
B) 3
C) 6
D) 9
Answer: C
Explanation:
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18
Common highest factor = 6
2. The LCM of 8 and 12 is:
A) 12
B) 24
C) 36
D) 48
Answer: B
Explanation:
Prime factors:
8 = 2³, 12 = 2² × 3
LCM = 2³ × 3 = 24
3. If HCF = 6 and LCM = 180 for two numbers, one number is 30. The other is:
A) 36
B) 42
C) 48
D) 60
Answer: A
Explanation:
Formula:
Product of numbers = HCF × LCM
= 6 × 180 = 1080
Other number = 1080 ÷ 30 = 36
4. Euclid’s Division Algorithm states:
A) a = bq
B) a = bq + r
C) a = br
D) a = b + r
Answer: B
Explanation:
Formula:
a = bq + r, where 0 ≤ r < b
5. The decimal expansion of 1/4 is:
A) Non-terminating
B) Terminating
C) Repeating
D) Irrational
Answer: B
Explanation:
1/4 = 0.25 → finite decimal → terminating
6. Which is an irrational number?
A) 2/3
B) √4
C) √5
D) 0.75
Answer: C
Explanation:
√5 cannot be expressed as a fraction → irrational
7. The HCF of two co-prime numbers is:
A) 0
B) 1
C) Equal numbers
D) Product
Answer: B
Explanation:
Co-prime numbers have only one common factor → 1
8. The decimal expansion of 2/11 is:
A) Terminating
B) Non-terminating repeating
C) Irrational
D) Whole number
Answer: B
Explanation:
2/11 = 0.1818… → repeating decimal
9. If a number has prime factorization 2³ × 3², then total factors are:
A) 6
B) 8
C) 12
D) 16
Answer: C
Explanation:
Number of factors = (3+1)(2+1) = 4×3 = 12
10. √49 is:
A) 6
B) 7
C) 8
D) 9
Answer: B
Explanation:
√49 = 7
11. Which of the following is rational?
A) √7
B) π
C) 0.333…
D) √2
Answer: C
Explanation:
0.333… = 1/3 → rational
12. The LCM of co-prime numbers is:
A) 1
B) Sum
C) Product
D) Difference
Answer: C
Explanation:
LCM of co-primes = product of numbers
13. The decimal expansion of 7/8 is:
A) Terminating
B) Non-terminating
C) Irrational
D) Whole
Answer: A
Explanation:
7/8 = 0.875 → terminating
14. The smallest prime number is:
A) 0
B) 1
C) 2
D) 3
Answer: C
Explanation:
2 is the smallest and only even prime number
15. The product of HCF and LCM of two numbers is equal to:
A) Sum
B) Difference
C) Product of numbers
D) Square
Answer: C
Explanation:
Formula:
HCF × LCM = Product of numbers
16. Which is not a real number?
A) √2
B) 5
C) -3
D) 1/0
Answer: D
Explanation:
1/0 is undefined → not a real number
17. The decimal expansion of 1/3 is:
A) Terminating
B) Non-repeating
C) Repeating
D) Irrational
Answer: C
Explanation:
1/3 = 0.333… repeating
18. A number is divisible by 3 if:
A) Last digit is 3
B) Sum of digits divisible by 3
C) Even number
D) Prime
Answer: B
Explanation:
Divisibility rule of 3
19. If LCM = HCF, then the numbers are:
A) Co-prime
B) Equal
C) Different
D) Prime
Answer: B
Explanation:
LCM = HCF only when the numbers are equal
20. Which of the following is a terminating decimal?
A) 3/7
B) 5/6
C) 9/20
D) 2/11
Answer: C
Explanation:
Denominator = 2² × 5 → terminating
21. The prime factorisation of 36 is:
A) 2 × 18
B) 6 × 6
C) 2² × 3²
D) 3 × 12
Answer: C
Explanation:
36 = 2 × 2 × 3 × 3
22. √(2 × 8) =
A) 2
B) 4
C) 6
D) 8
Answer: B
Explanation:
√16 = 4
23. The number of irrational numbers between 1 and 2 is:
A) 1
B) 2
C) Finite
D) Infinite
Answer: D
Explanation:
Infinite irrational numbers exist between any two numbers
24. If a = bq + r and r = 0, then:
A) a < b
B) a is divisible by b
C) a > b
D) a is prime
Answer: B
Explanation:
Remainder = 0 → exact division
25. Which of the following has a non-terminating, non-repeating decimal expansion?
A) 4/5
B) 7/9
C) √3
D) 2/8
Answer: C
Explanation:
√3 is irrational → non-terminating, non-repeating
Conclusion & Student Tips
- Focus on formulas like HCF × LCM = Product
- Practice prime factorisation regularly
- Learn decimal expansion rules (terminating vs repeating)
- Revise divisibility rules
- Attempt mock tests for better speed
Consistency and practice are key to scoring high in POLYCET Mathematics!
