📘 Most Expected Questions on Real Numbers (2025–26)
CBSE Class 10 Mathematics | Chapter – Real Numbers
Here are the most important and repeatedly asked questions from CBSE Sample Question Papers and Previous Year Exams. These are highly expected for the 2025–26 board examinations.
🔢 MCQs & Numerical Based Questions
1. If two positive integers a = r y² and b = x y, where x and y are prime numbers, then the result obtained by dividing the product of the integers by LCM(a, b) is:
(a) xy
(b) ry
(c) r²y
(d) y
2. Let a = p³q² and b = p²q⁵ where p and q are prime numbers.
If HCF(a,b) = p²q² and LCM(a,b) = p³q⁵, then find (m + n)(r + s).
(a) 15
(b) 30
(c) 35
(d) 72
3. The LCM of two prime numbers p and q (p > q) is 221.
Find the value of 3p − 4q.
(a) 4
(b) 28
(c) 38
(d) 48
4. If the sum of two numbers is 1215 and their HCF is 81, then the number of possible pairs is:
(a) 2
(b) 3
(c) 4
(d) 5
5. Find the greatest 5-digit number that leaves remainder 5 when divided by 8 and 9 respectively.
(a) 99921
(b) 99931
(c) 99941
(d) 99951
6. Three alarm clocks ring after every 20 min, 25 min and 30 min.
If they ring together at 12 noon, when will they ring again together?
(a) 4:00 pm
(b) 4:30 pm
(c) 5:00 pm
(d) 5:30 pm
7. Traffic lights change after 48 sec, 72 sec and 108 sec.
If they change together at 8:00 am, at what time will they again change simultaneously?
📐 Very Important Long Answer Questions
8. Prove that √5 is an irrational number.
9. Find the smallest positive rational number by which
3/250 should be multiplied so that its decimal expansion terminates after 2 decimal places.
10. Find by prime factorisation method:
LCM of 18180 and 7575
Also find the HCF of the two numbers.
LCM of 18180 and 7575
Also find the HCF of the two numbers.
11. The HCF of 65 and 117 is expressible in the form:
65m − 117
Find m and also find the LCM using prime factorisation.
📌 Key Concepts to Revise
- Prime Factorisation
- HCF & LCM Relationship: Product of two numbers = HCF × LCM
- Decimal Expansion of Rational Numbers
- Euclid’s Division Lemma
- Proof of Irrational Numbers
- Word Problems on LCM
✅ Exam Tips for 2025–26
✔ Practice prime factorisation carefully ✔ Learn proofs step-by-step ✔ Focus on MCQs involving HCF & LCM ✔ Revise previous CBSE sample papers ✔ Memorize important formulas
📢 Bookmark this page for quick revision before exams!