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. | P a g e 6. If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n 7 m is : (A) 0 (B) 28 (C) 98 (D) 198 6| P a g e 7. - (A) (B) (C) (D) 8. ABC DEF , B = E, F = C AB = 3 DE , (A) (B) (C) (D) 9. ( 1)n + ( 1)8 = 0 , n : (A) (B) (C) (D) 10. , (A) 3 (B) 5 (C)…
   Board 20251 markMCQ
2. | P a g e 18. The HCF of 40, 110 and 360 is : (A) 40 (B) 110 (C) 360 (D) 10 12| P a g e 19 20 , (A) (R) (A), (B), (C) (D) (A) (A) (R) (R), (A) (B) (A) (R) , (R), (A) (C) (A) , (R) (D) (A) , (R) 19. (A) : 5, 1, 3, 4 (R) : a1, a2, a3 n d = an an 1 20. (A) px + 3…
   Board 20251 markAssertion-Reason
3. | P a g e 14. Which of the following is a rational number between 3 and ? (A) 1·4142387954012 .... (B) (C) (D) 1·857142 10| P a g e 15. 40 72 , (A) 200 (B) 100 (C) 20 (D) 10 16. , O P - PA POB = 115 , APO : (A) 25 (B) 65 (C) 90 (D) 35 17. 150 m 30 : (A) 100 m …
   Board 20251 markMCQ
4. The sum of the exponents of prime factors in the prime factorisation of 4004 is : (A) 5 (B) 4 (C) 3 (D)
   Board 20251 markMCQ
5. (A) Prove that 5-2/3 is an irrational number. It is given that /3 is an irrational number. OR (B) Show that the number 5×11×17+3×11 is a composite number.
   Board 20242 marksshort answer
6. Find the greatest number which divides 85 and 72 leaving remainders 1 and 2 respectively.
   Board 20232 marksshort answer
7. (H$) g§»`mAm| 18180 Am¡a 7575 H$m A^mÁ` JwUZI§S>Z {d{Y Ûmam LCM kmV H$s{OE & BZ Xmo g§»`mAm| H$m HCF ^r kmV H$s{OE & AWdm (I) VrZ K§{Q>`m± 6, 12 Am¡a 18 {_ZQ>m| Ho$ A§Vamb na ~OVt h¢ & `{X `o VrZm| K§{Q>`m± EH$ gmW 6 a.m. na ~Ot hm|, Vmo CgHo$ níMmV² do VrZm| …
   Board 20233 marksshort answer
8. respectively, is: (A) 13 (B) 26 (C) 39 (D) 65 1 1. The greatest number which divides both 134 and 188, leaving remainders 4 and
   Sample paper 2026-271 markMCQ
9. Given that √3 is irrational number, prove that (2 + 3√3) is an irrational number.
   Sample paper 2026-273 marksshort answer
10. Two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R). Assertion (A): 2 is a prime number. Reason (R): The square of an…
    CBSE practice 2022-231 markAssertion-Reason
11. A number q is prime factorised as 32 × 72 × b, where b is a prime number other than 3 and 7. Based on the above information, two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose…
    CBSE practice 2023-241 markAssertion-Reason
12. The LCM of 64, 82 and k is 124 where k is a positive integer. Find the smallest value of k. Show your steps.
    CBSE practice 2022-233 marksshort answer
13. Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101. Show your steps. √
    CBSE practice 2022-232 marksshort answer
14. Prime factorisation of three numbers A, B and C is given below: A = (2r × 3p × 5q) B = (2p × 3r × 5p) C = (2q × 3q × 5p) such that, p < q < r and p, q, & r are natural numbers.. ♦ The largest number that divides A, B and C without leaving a remainder is 30. ♦ …
    CBSE practice 2023-243 marksshort answer
15. Check whether the statement below is true or false. “The square root of every composite number is rational.” Justify your answer by proving rationality or irrationality as applicable.
    CBSE practice 2023-242 marksshort answer
16. In a formula racing competition, the time taken by two racing cars A and B to complete 1 round of the track is 30 minutes and p minutes respectively. If the cars meet again at the starting point for the first time after 90 minutes and the HCF (30, p) = 15, the…
    CBSE practice 2023-241 markMCQ

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