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 9 of 17

1. Q161 CBSE 2024
   The ​exponent of $3$ ​in ​the ​prime factorisation of $243$ is:

   1. (a)$2$
   2. (b)$3$
   3. (c)$4$
   4. (d)$5$
   Show answer

   (d) $5$

   Step-by-step solution →
2. Q162 CBSE 2024
   If $a=2^7\times 3^{10}$ ​and $b=2^3\times 3^7$, ​then $\mathrm{HCF}(a,b)$ is ​:

   1. (a)$2^7\times 3^{10}$
   2. (b)$2^{10}\times 3^{17}$
   3. (c)$2^3\times 3^7$
   4. (d)$2^7\times 3^7$
   Show answer

   (c) $2^3\times 3^7$

   Step-by-step solution →
3. Q163 CBSE 2024
   The HCF of two numbers 65 and 104 is ​13. If ​LCM ​of 65 ​and 104 ​is $40x$, then the value of $x$ is ​:

   1. (a)5
   2. (b)13
   3. (c)40
   4. (d)8
   Show answer

   (b) 13

   Step-by-step solution →
4. Q164 CBSE 2024
   Prime factorisation of 424 is :

   1. (a)2 x 53 x 4
   2. (b)2 x 53 x 2
   3. (c)2^3 x 53
   4. (d)2^4 x 53
   Show answer

   (c) 2^3 x 53

   Step-by-step solution →
5. Q165 CBSE 2024
   Two ​positive integers $m$ and $n$ are expressed as $m=p^5{q}^2$ ​and $n=p^3{q}^4$, where $p$ ​and $q$ ​are prime numbers. The ​LCM ​of $m$ and $n$ ​is :

   1. (a)$p^8{q}^6$
   2. (b)$p^3{q}^2$
   3. (c)$p^5{q}^4$
   4. (d)$p^5{q}^2+p^3{q}^4$
   Show answer

   (c) $p^5{q}^4$

   Step-by-step solution →
6. Q166 CBSE 2024
   If two positive integers $p$ ​and $q$ can ​be expressed as $p=18a^2{b}^4$ ​and $q=20a^3{b}^2$, ​where $a$ ​and $b$ ​are ​prime numbers, then $\text{LCM}(p,q)$ is :

   1. (a)$2a^2{b}^2$
   2. (b)$180a^2{b}^2$
   3. (c)$12a^2{b}^2$
   4. (d)$180a^3{b}^4$
   Show answer

   (d) $180a^3{b}^4$

   Step-by-step solution →
7. Q167 CBSE 2024
   $\text{HCF}(132,77)$ is:

   1. (a)$11$
   2. (b)$77$
   3. (c)$22$
   4. (d)$44$
   Show answer

   (a) $11$

   Step-by-step solution →
8. Q168 CBSE 2024
   If $a=2^2\times 3^x$, $b=2^2\times 3\times 5$, $c=2^2\times 3\times 7$ ​and $\mathrm{LCM}(a,b,c)=3780$, ​then $x$ is ​equal ​to

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

   (c) 3

   Step-by-step solution →
9. Q169 CBSE 2024
   If ​HCF $(2520,6600)=40$ ​and LCM $(2520,6600)=252\times k$, ​then ​the ​value of $k$ ​is

   1. (a)$1650$
   2. (b)$1600$
   3. (c)$165$
   4. (d)$1625$
   Show answer

   (a) $1650$

   Step-by-step solution →
10. Q170 CBSE 2024
    If $a=2^4\times 3^3$, $b=2^3\times 3^2\times 5$, $c=3^n\times 5^2$ ​and $\mathrm{LCM}(a,b,c)=(5^2\times 3^4\times 2^4)$, ​then $n$ ​is:

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

    (d) $4$

    Step-by-step solution →
11. Q171 CBSE 2024
    If $x$ is a ​whole number, ​then $8^x$ ​ends with an even ​digit, ​except ​for which value of $x$ ​?

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

    (d) 0

    Step-by-step solution →
12. Q172 CBSE 2024
    The ​greatest number which divides $281$ ​and $1249$, ​leaving ​remainder $5$ and $7$ ​respectively, ​is :

    1. (a)$23$
    2. (b)$276$
    3. (c)$138$
    4. (d)$69$
    Show answer

    (c) $138$

    Step-by-step solution →
13. Q173 CBSE 2024
    The LCM ​of ​the smallest odd ​prime ​number and ​greatest $2$-digit ​number, is ​:

    1. (a)1
    2. (b)99
    3. (c)297
    4. (d)300
    Show answer

    (b) 99

    Step-by-step solution →
14. Q174 CBSE 2024
    Given $\mathrm{HCF}(2520,6600)=40$, $\mathrm{LCM}(2520,6600)=252\times k$, ​then ​the ​value of $k$ ​is ​:

    1. (a)1650
    2. (b)1600
    3. (c)165
    4. (d)1625
    Show answer

    (a) 1650

    Step-by-step solution →
15. Q175 CBSE 2024
    If $1080=2^x\times 3^y\times 5$, ​then $(x-y)$ ​is equal ​to :

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

    (d) 0

    Step-by-step solution →
16. Q176 CBSE 2024
    The ​LCM ​of ​three numbers $28,44,132$ ​is ​:

    1. (a)$258$
    2. (b)$231$
    3. (c)$462$
    4. (d)$924$
    Show answer

    (d) $924$

    Step-by-step solution →
17. Q177 CBSE 2024
    A pair of ​irrational ​numbers whose product ​is ​a rational number ​is :

    1. (a)$(\sqrt{16},\sqrt{4})$
    2. (b)$(\sqrt{5},\sqrt{2})$
    3. (c)$(\sqrt{3},\sqrt{27})$
    4. (d)$(\sqrt{36},\sqrt{2})$
    Show answer

    (c) $(\sqrt{3},\sqrt{27})$

    Step-by-step solution →
18. Q178 CBSE 2024
    If ​the product of two ​co-prime numbers is $553$, then their ​HCF is ​:

    1. (a)$1$
    2. (b)$553$
    3. (c)$7$
    4. (d)$79$
    Show answer

    (a) $1$

    Step-by-step solution →
19. Q179 CBSE 2024
    Assertion (A): $2+\sqrt{2}$ is an irrational number.

    Reason (R): The sum of a non-zero rational number and an irrational number is always an irrational number.

    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 →
20. Q180 CBSE 2024
    Directions: A ​statement ​of Assertion (A) is followed by ​a statement of ​Reason ​(R). Choose ​the correct option.

    Assertion (A): $\sqrt{2}(5-\sqrt{2})$ is an irrational number.

    Reason (R): Product of two irrational numbers is always irrational.

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

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

    Step-by-step solution →