Top 10 HOT Questions – Real Numbers (CBSE Class 10 Board Exam)
Prepare smartly for the CBSE Class 10 Maths Board Exam with these carefully selected and completely original Hot Questions from the chapter Real Numbers. These questions cover proofs, HCF-LCM, Euclid’s Algorithm, decimal expansion, and application-based problems.
Q1. Euclid’s Division Algorithm (Concept-Based)
Use Euclid’s Division Algorithm to find the HCF of 306 and 657.
Also express the HCF in the form:
657x + 306y
Q2. HCF & LCM Application
Two numbers are 135 and 225. Find their HCF and LCM.
Verify that:
HCF × LCM = Product of the two numbers
Q3. Fundamental Theorem of Arithmetic
Express 540 as a product of prime factors.
Using this, find the HCF and LCM of 540 and 630.
Q4. Irrationality Proof (Board Favourite)
Prove that 5√3 is irrational.
Q5. Advanced Irrationality Question
Prove that √7 is irrational using the contradiction method.
Q6. Decimal Expansion Concept
Without actual division, determine whether the decimal expansion of:
343 / 5000
is terminating or non-terminating. Give reason.
Q7. Higher Order Decimal Analysis
Check whether 17 / 128 has a terminating decimal expansion.
If yes, find the number of decimal places.
Q8. Euclid’s Lemma Application
Prove that if a prime number p divides a², then p divides a.
Q9. Word Problem on HCF
A school has 144 boys and 180 girls.
They are to be arranged in rows such that each row has the same number of students.
Find the maximum number of students in each row.
Q10. Mixed Concept Question
Find the greatest number that divides 306 and 657, leaving remainders 9 and 15 respectively.
⭐ Why These Questions Are Important?
- Complete coverage of the Real Numbers chapter
- Includes proof, application, and concept-based questions
- Based on CBSE board exam trends
- Perfect for revision and exam preparation
