Class 10 Maths · Chapter 1

Real Numbers

336 Class 10 Maths questions on Real Numbers from the NCERT textbook, NCERT Exemplar and CBSE board papers 2018–2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 12 of 17

1. Q221 CBSE 2023
   $(\text{HCF}\times \text{LCM})$ for ​the numbers $70$ ​and $40$ ​is ​:

   1. (a)$10$
   2. (b)$280$
   3. (c)$2800$
   4. (d)$70$
   Show answer

   (c) $2800$

   Step-by-step solution →
2. Q222 CBSE 2023
   The ​product ​of a ​non-zero ​rational ​number ​and an irrational ​number is :

   1. (a)always irrational
   2. (b)always rational
   3. (c)rational or irrational
   4. (d)always positive
   Show answer

   (a) always irrational

   Step-by-step solution →
3. Q223 CBSE 2023
   The ​number $(5-3\sqrt{5}+\sqrt{5})$ is ​:

   1. (a)an integer
   2. (b)a rational number
   3. (c)an irrational number
   4. (d)a whole number
   Show answer

   (c) an irrational number

   Step-by-step solution →
4. Q224 CBSE 2023
   If $p$ and $q$ ​are natural ​numbers and $p$ ​is the multiple ​of $q$, then what is the HCF ​of $p$ and $q$?

   1. (a)$pq$
   2. (b)$p$
   3. (c)$q$
   4. (d)$p+q$
   Show answer

   (c) $q$

   Step-by-step solution →
5. Q225 CBSE 2023
   If $\text{HCF}(72,120)=24$, ​then $\text{LCM}(72,120)$ ​is

   1. (a)$72$
   2. (b)$120$
   3. (c)$360$
   4. (d)$9640$
   Show answer

   (c) $360$

   Step-by-step solution →
6. Q226 CBSE 2023
   LCM ​of $(2^3\times 3\times 5)$ ​and $(2^4\times 5\times 7)$ is ​:

   1. (a)40
   2. (b)560
   3. (c)1680
   4. (d)1120
   Show answer

   (c) 1680

   Step-by-step solution →
7. Q227 CBSE 2023
   If the HCF of $360$ ​and $64$ ​is $8$, ​then ​their LCM ​is ​:

   1. (a)$2480$
   2. (b)$2780$
   3. (c)$512$
   4. (d)$2880$
   Show answer

   (d) $2880$

   Step-by-step solution →
8. Q228 CBSE 2023
   Which ​of ​the ​following is an irrational number?

   1. (a)${\left(2\sqrt{3}-\frac{1}{\sqrt{3}}\right)}^2$
   2. (b)$(\sqrt{2}-1{)}^2$
   3. (c)$\sqrt{2}-(2+\sqrt{2})$
   4. (d)$\frac{\sqrt{2}+5\sqrt{2}}{\sqrt{2}}$
   Show answer

   (b) $(\sqrt{2}-1{)}^2$

   Step-by-step solution →
9. Q229 CBSE 2023
   The prime factorisation ​of the ​number $2304$ ​is

   1. (a)$2^8\times 3^2$
   2. (b)$2^7\times 3^3$
   3. (c)$2^8\times 3^1$
   4. (d)$2^7\times 3^2$
   Show answer

   (a) $2^8\times 3^2$

   Step-by-step solution →
10. Q230 CBSE 2023
    If $n$ is ​a natural ​number, ​then $8^n$ cannot end with ​digit

    1. (a)$0$
    2. (b)$2$
    3. (c)$4$
    4. (d)$6$
    Show answer

    (a) $0$

    Step-by-step solution →
11. Q231 CBSE 2023
    Assertion (A): The number $5^n$ cannot end with the digit $0$, where $n$ is a natural number.

    Reason (R): Prime factorisation of $5$ has only two factors, $1$ and $5$.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

    Step-by-step solution →
12. Q232 CBSE 2023
    Directions: ​A statement of Assertion (A) ​is followed by ​a statement of Reason (R). ​Choose ​the correct option.

    Assertion (A): The perimeter of $△ABC$ is a rational number.

    Reason (R): The sum of the squares of two rational numbers is always rational.

    1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
    2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
    3. (c)Assertion (A) is true, but Reason (R) is false.
    4. (d)Assertion (A) is false, but Reason (R) is true.
    Show answer

    (d) Assertion (A) is false, but Reason (R) is true.

    Step-by-step solution →
13. Q233 CBSE 2023
    Find ​the ​HCF ​and LCM ​of $84$, $90$ and $120$ by prime ​factorization ​method.
    Show answer

    HCF $=6$, LCM $=2520$

    Step-by-step solution →
14. Q234 CBSE 2023
    Prove that $2+\sqrt{3}$ is ​an ​irrational ​number, given that $\sqrt{3}$ is ​an irrational number.
    Show answer

    Hence $2+\sqrt{3}$ is irrational.

    Step-by-step solution →
15. Q235 CBSE 2023
    Find ​LCM ​of 576 ​and ​512 by ​prime ​factorization.
    Show answer

    $\text{LCM}=4608$

    Step-by-step solution →
16. Q236 CBSE 2023
    Find ​the ​HCF and the LCM of $36$ and $60$, ​using ​the prime ​factorization ​method.
    Show answer

    $\text{HCF}=12$ and $\text{LCM}=180$

    Step-by-step solution →
17. Q237 CBSE 2023
    Two numbers are ​in the ​ratio $2:3$ and ​their LCM ​is ​180. ​What is the HCF of these numbers ?
    Show answer

    HCF $=30$

    Step-by-step solution →
18. Q238 CBSE 2023
    Show ​that $6^n$ can ​not ​end ​with digit 0 for any ​natural ​number 'n'.
    Show answer

    $6^n=2^n\times 3^n$ has no factor 5, so it is never divisible by 10 and cannot end in 0.

    Step-by-step solution →
19. Q239 CBSE 2023
    If $\sqrt{2}$ is given ​as an ​irrational ​number, ​then prove that $(5-2\sqrt{2})$ ​is ​an irrational ​number.
    Show answer

    $5-2\sqrt{2}$ is irrational (proved by contradiction).

    Step-by-step solution →
20. Q240 CBSE 2023
    Check whether $6^n$ can end with the ​digit 0 ​for ​any ​natural ​number $n$.
    Show answer

    No; $6^n$ can never end in 0 because it has no prime factor 5.

    Step-by-step solution →