CBSE BOARD PYQS · CHAPTER 01

Real Numbers
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Real Numbers. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

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

Q2CBSE 2023, 2019MCQ

1 Mark

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

Q3CBSE 2022, 2018MCQ

1 Mark

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

Q4CBSE 2024, 2021MCQ

1 Mark

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

Q5CBSE 2023, 2017Assertion-Reason

1 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.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

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

Q7CBSE 2024, 2020Short Answer

2 Marks

Express 140 as a product of its prime factors.

Q8CBSE 2023, 2019Short Answer

2 Marks

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

Q9CBSE 2022, 2018Short Answer

2 Marks

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

Q10CBSE 2024, 2021Short Answer

2 Marks

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

Q11CBSE 2023, 2017Short Answer

2 Marks

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

Q12CBSE 2020, 2016Long Answer

3 Marks

Prove that √5 is an irrational number.

Q13CBSE 2024, 2020Long Answer

3 Marks

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

Q14CBSE 2023, 2019Long Answer

3 Marks

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

Q15CBSE 2022, 2018Long Answer

3 Marks

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

Q16CBSE 2024, 2021Case Study

4 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.

Q17CBSE 2023, 2017Case Study

4 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?

Q18CBSE Official Board PYQPYQ

5 Marks

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

Q19CBSE Official Board PYQPYQ

5 Marks

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

Q20CBSE Official Board PYQPYQ

5 Marks

Real Numbers CBSE Most Repeated PYQs

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

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

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

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

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.

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

Express 140 as a product of its prime factors.

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

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

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

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

Prove that √5 is an irrational number.

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

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

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

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.

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?

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

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

Find HCF and LCM of 408 and 1032.

Real Numbers
CBSE Most Repeated PYQs