01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. If a = 2³ × 3, b = 2 × 3 × 5, c = 3ⁿ × 5 and LCM(a, b, c) = 2³ × 3² × 5, then find the value of n.
CBSE 2024 · 1 MARK
Q2. The ratio of HCF to LCM of the least composite number and the least prime number is:
(A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 1 : 3
CBSE 2024 · 2 MARKS
Q3. Find the HCF and LCM of 144 and 198 using the prime factorisation method.
CBSE 2024 · 3 MARKS
Q4. Given that √5 is an irrational number, prove that 3 + 2√5 is an irrational number.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q5. If two positive integers p and q can be expressed as p = a b² and q = a³ b, where a and b are prime numbers, then find LCM(p, q).
CBSE 2023 · 1 MARK
Q6. If p and q are two co-prime numbers, then p² and q² are:
(A) Co-prime (B) Not co-prime (C) Even (D) Odd
CBSE 2023 · 2 MARKS
Q7. Check whether 6ⁿ can end with the digit 0 for any natural number n.
CBSE 2023 · 3 MARKS
Q8. Prove that √5 is an irrational number using proof by contradiction.
CBSE 2023 · 5 MARKS
Q9. Three sets of physics, chemistry and mathematics books containing 336, 240 and 96 books respectively have to be stacked in such a way that all books are stored topic-wise and height of each stack is the same. Find the minimum number of stacks formed.
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. The prime factorisation of 3825 is expressed as:
(A) 3 × 5² × 17 (B) 3² × 5² × 17 (C) 3² × 5 × 17 (D) 3 × 5 × 17²
CBSE 2022 · 1 MARK
Q11. The greatest number which divides 70 and 125, leaving remainders 5 and 8 respectively, is:
(A) 13 (B) 65 (C) 875 (D) 1750
CBSE 2022 · 2 MARKS
Q12. Write the exponent of 2 in the prime factorisation of 144.
CBSE 2022 · 3 MARKS
Q13. Prove that √3 is an irrational number.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q14. If HCF(306, 657) = 9, find LCM(306, 657).
CBSE 2021 · 2 MARKS
Q15. Find the HCF and LCM of 72 and 120 using the prime factorisation method.
CBSE 2021 · 3 MARKS
Q16. Prove that 2 - 3√5 is an irrational number, given that √5 is irrational.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 2 MARKS
Q17. Find the largest number which divides 320 and 457 leaving remainder 5 and 7 respectively.
CBSE 2020 · 3 MARKS
Q18. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
CBSE 2020 · 5 MARKS
Q19. On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
Always solve questions on paper under timed exam conditions without looking at reference material.
02
For irrationality proofs, ensure every step ("a and b are co-prime integers", "b ≠ 0") is explicitly written.
03
Verify HCF × LCM = a × b for two numbers to double-check your arithmetic!