Real Numbers: Class 10 Previous Year Questions

Real Numbers questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. (a) Prove that is an irrational number. OR (b) The factor tree of a number x is shown below : Find the values of x, y, a and b. Hence, write the product of the prime factors of the number x so obtained.
   Board 20253 marksshort answer
2. The number 3 + is : (A) a rational number (B) an irrational number (C) an integer (D) a natural number
   Board 20251 markMCQ
3. The value of (HCF LCM) for the two numbers 3 and 5 is : (A) 2 (B) 4 (C) 14 (D) 14
   Board 20251 markMCQ
4. If the HCF of two positive integers a and b is 1, then their LCM is : (A) a + b (B) a (C) b (D) ab
   Board 20251 markMCQ
5. Assertion (A) : For any two natural numbers a and b, the HCF of a and b is a factor of the LCM of a and b. Reason (R) : HCF of any two natural numbers divides both the numbers.
   Board 20251 markAssertion-Reason
6. Prove that 7 – 3 5 is an irrational number, given that 5 is an irrational number.
   Board 20243 marksshort answer
7. Find the LCM and HCF of 92 and 510, using prime factorisation.
   Board 20232 marksshort answer
8. JJJJ Page 5 6. The area of a sector of angle (in degrees) of a circle with radius R is : (a) R 2 180 (b) R 2 360 (c) 2 R 180 (d) 2 R 360 JJJJ Page 6 7. `{X 360 Am¡a 64 H$m HCF 8 h¡, Vmo BZ g§»`mAm| H$m LCM hmoJm : (a) 2480 (b) 2780 (c) 512 (d) 2880 8. 14 cm D±…
   Board 20231 markMCQ
9. If HCF (2520, 6600) 40 and LCM (2520, 6600) 252 × k, then the value of k is (A) 165 (B) 1600 (C)1625 (D)1650 1 If α and β are the Zeroes of the polynomial 2x2 − 4x − 5, the value of (α −β)𝟐 is
   Sample paper 2026-271 markMCQ

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