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 6 of 17

1. Q101 CBSE 2025
   If ​the HCF of two ​positive ​integers $a$ and $b$ ​is 1, then their LCM ​is ​:

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

   (d) $ab$

   Step-by-step solution →
2. Q102 CBSE 2025
   The ​HCF and ​the ​LCM of 14, 21 and 77 ​respectively ​are

   1. (a)7, 77
   2. (b)14, 462
   3. (c)7, 462
   4. (d)21, 77
   Show answer

   (c) 7, 462

   Step-by-step solution →
3. Q103 CBSE 2025
   ${\left(1+\sqrt{3}\right)}^2-{\left(1-\sqrt{3}\right)}^2$ ​is:

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

   (c) a positive irrational number.

   Step-by-step solution →
4. Q104 CBSE 2025
   Let $x=a^2{b}^3{c}^n$ and $y=a^3{b}^m{c}^2$, where $a,b,c$ are ​prime ​numbers. If ​LCM of $x$ ​and $y$ is $a^3{b}^4{c}^3$, then ​the ​value of $m+n$ is

   1. (a)10
   2. (b)7
   3. (c)6
   4. (d)5
   Show answer

   (b) 7

   Step-by-step solution →
5. Q105 CBSE 2025
   Which ​of the following cannot ​be the unit digit of $8^n$, ​where $n$ is a ​natural number?

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

   (c) 0

   Step-by-step solution →
6. Q106 CBSE 2025
   The ​number $2^n$, where $n$ is a natural number, ​cannot ​end ​with ​the ​digit ​:

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

   (d) 0

   Step-by-step solution →
7. Q107 CBSE 2025
   If $x$ ​is the LCM of $4,6,8$ and $y$ ​is the ​LCM of $3,5,7$ and $p$ ​is ​the LCM of $x$ and $y$, then which of the ​following is ​true?

   1. (a)$p=35x$
   2. (b)$p=4y$
   3. (c)$p=8x$
   4. (d)$p=16y$
   Show answer

   (a) $p=35x$

   Step-by-step solution →
8. Q108 CBSE 2025
   $3^n$, ​where $n$ ​is ​a natural ​number, cannot ​end with ​the ​digit :

   1. (a)3
   2. (b)5
   3. (c)7
   4. (d)9
   Show answer

   (b) 5

   Step-by-step solution →
9. Q109 CBSE 2025
   If two ​natural ​numbers $p$ ​and $q$ can be expressed as $p=a{b}^2{c}^3$ ​and $q=a^2{b}^3{c}^2$, where $a$, $b$, $c$ ​are prime numbers, then LCM $(p,q)$ is ​equal to:

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

   (b) $a^2{b}^3{c}^3$

   Step-by-step solution →
10. Q110 CBSE 2025
    The number $3+\sqrt{2}$ is :

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

    (b) an irrational number

    Step-by-step solution →
11. Q111 CBSE 2025
    The total ​number ​of ​factors of ​the square of a prime ​number is ​:

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

    (c) 3

    Step-by-step solution →
12. Q112 CBSE 2025
    $2.\overline{35}$ is:

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

    (b) a rational number

    Step-by-step solution →
13. Q113 CBSE 2025
    For any prime number $p$, ​if $p$ divides $a^2$, ​where $a$ ​is any ​real ​number, then $p$ also divides

    1. (a)$a$
    2. (b)$a^{1/2}$
    3. (c)$a^{3/2}$
    4. (d)$a^{1/8}$
    Show answer

    (a) $a$

    Step-by-step solution →
14. Q114 CBSE 2025
    A prime number has :

    1. (a)exactly two prime factors
    2. (b)exactly one prime factor
    3. (c)at least one prime factor
    4. (d)at least two prime factors
    Show answer

    (b) exactly one prime factor

    Step-by-step solution →
15. Q115 CBSE 2025
    The ​least ​number ​which is a ​perfect square and is ​divisible by each ​of $16$, $20$ and $50$, is :

    1. (a)$1200$
    2. (b)$100$
    3. (c)$3600$
    4. (d)$2400$
    Show answer

    (c) $3600$

    Step-by-step solution →
16. Q116 CBSE 2025
    If $\mathrm{HCF}(98,28)=m$ ​and $\mathrm{LCM}(98,28)=n$, ​then the value ​of $n-7m$ ​is :

    1. (a)$0$
    2. (b)$28$
    3. (c)$98$
    4. (d)$198$
    Show answer

    (c) $98$

    Step-by-step solution →
17. Q117 CBSE 2025
    If $(-1{)}^n+(-1{)}^8=0$, ​then $n$ ​is :

    1. (a)any positive integer
    2. (b)any negative integer
    3. (c)any odd number
    4. (d)any even number
    Show answer

    (c) any odd number

    Step-by-step solution →
18. Q118 CBSE 2025
    The ​sum of ​the exponents ​of prime factors in ​the prime ​factorisation of $4004$ ​is ​:

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

    (a) $5$

    Step-by-step solution →
19. Q119 CBSE 2025
    Which ​of ​the following is a ​rational ​number ​between $\sqrt{3}$ and $\sqrt{5}$ ?

    1. (a)$1.4142387954012\dots$
    2. (b)$2.32\overline{6}$
    3. (c)$\pi$
    4. (d)$1.857142$
    Show answer

    (d) $1.857142$

    Step-by-step solution →
20. Q120 CBSE 2025
    The HCF of $40$, $110$ ​and $360$ ​is ​:

    1. (a)$40$
    2. (b)$110$
    3. (c)$360$
    4. (d)$10$
    Show answer

    (d) $10$

    Step-by-step solution →