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PracticeClass 10Chapter 01: Real Numbers
CLASS 10 · CHAPTER 01

Real Numbers
Practice Questions

20 curated NCERT & Board Exam questions to test your understanding. Click on "Show Solution & Answer" to check step-by-step working.

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Q1MCQ1 Mark

If a = x³y² and b = xy³, where x, y are prime numbers, then HCF(a, b) is:

Q2MCQ1 Mark

If p and q are co-prime positive integers, then LCM(p, q) is:

Q3MCQ1 Mark

The ratio of HCF to LCM of least composite number (4) and least prime number (2) is:

Q4MCQ1 Mark

If HCF(306, 657) = 9, then LCM(306, 657) is:

Q5Assertion-Reason1 Mark

Assertion (A): The HCF of two numbers is 5 and their product is 150, then their LCM is 30. Reason (R): For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

Q6Assertion-Reason1 Mark

Assertion (A): √3 is an irrational number. Reason (R): The square root of any prime number is always an irrational number.

Q7Short Answer2 Marks

Express 140 as a product of its prime factors.

Q8Short Answer2 Marks

Find HCF and LCM of 12, 15 and 21 using prime factorisation.

Q9Short Answer2 Marks

Check whether 6ⁿ can end with digit 0 for any natural number n.

Q10Short Answer2 Marks

Explain why 7 × 11 × 13 + 13 is a composite number.

Q11Short Answer2 Marks

Given that HCF(96, 404) = 4, find LCM(96, 404).

Q12Long Answer3 Marks

Prove that √5 is an irrational number.

Q13Long Answer3 Marks

Prove that 3 + 2√5 is irrational given √5 is irrational.

Q14Long Answer3 Marks

Find the greatest 6-digit number exactly divisible by 24, 15 and 36.

Q15Long Answer3 Marks

Three bells toll together at intervals of 9, 12, 15 minutes. When will they toll together next?

Q16Case Study4 Marks

Case Study Scenario: A seminar is conducted by an educational organization where participants in Hindi, Mathematics and Science are 60, 84 and 108. Question: Find minimum number of rooms required if in each room same number of participants are seated of same subject.

Q17Case Study4 Marks

Case Study Scenario: Sonia takes 18 minutes to drive one lap of circular track, while Ravi takes 12 minutes. Question: After how many minutes will they meet again at starting point?

Q18PYQ5 Marks

A merchant has 120L, 180L, 240L oil of 3 kinds. Find max capacity of tin to fill them equally.

Q19PYQ5 Marks

Find HCF of 65 and 117 and express it in form 65m + 117n.

Q20PYQ5 Marks

Find HCF and LCM of 408 and 1032.