Chapter 1 · Real Numbers

NCERT Exemplar Class 10 Maths Exercise 1.1

All 10 questions of NCERT Exemplar Class 10 Maths Exercise 1.1 (Real Numbers), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   For some integer $m$, every ​even integer ​is ​of ​the ​form

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

   (c) $2m$

   Step-by-step solution →
2. Q2
   For ​some integer $q$, ​every ​odd integer ​is ​of the ​form

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

   (d) $2q+1$

   Step-by-step solution →
3. Q3
   $n^2-1$ ​is ​divisible by ​8, ​if $n$ is

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

   (c) an odd integer

   Step-by-step solution →
4. Q4
   If the HCF ​of $65$ and $117$ is ​expressible ​in ​the form $65m-117$, ​then ​the value ​of $m$ ​is

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

   (b) $2$

   Step-by-step solution →
5. Q5
   The ​largest ​number which divides $70$ and $125$, ​leaving remainders $5$ and $8$, ​respectively, is

   1. (a)$13$
   2. (b)$65$
   3. (c)$875$
   4. (d)$1750$
   Show answer

   (a) $13$

   Step-by-step solution →
6. Q6
   If two positive ​integers $a$ and $b$ are ​written as $a=x^3{y}^2$ ​and $b=x{y}^3$; $x$, $y$ ​are ​prime numbers, then ​HCF $(a,b)$ is

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

   (b) $x{y}^2$

   Step-by-step solution →
7. Q7
   If ​two positive ​integers $p$ ​and $q$ can be expressed ​as $p=a{b}^2$ and $q=a^{3}b$; $a,b$ being ​prime numbers, then ​LCM $(p,q)$ is

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

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

   Step-by-step solution →
8. Q8
   The product of ​a non-zero rational ​and an ​irrational ​number ​is

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

   (a) always irrational

   Step-by-step solution →
9. Q9
   The ​least number that ​is divisible by all the numbers from ​1 ​to 10 (both inclusive)

   1. (a)$10$
   2. (b)$100$
   3. (c)$504$
   4. (d)$2520$
   Show answer

   (d) $2520$

   Step-by-step solution →
10. Q10
    The decimal ​expansion ​of ​the rational ​number $\frac{14587}{1250}$ ​will terminate ​after:

    1. (a)one decimal place
    2. (b)two decimal places
    3. (c)three decimal places
    4. (d)four decimal places
    Show answer

    (d) four decimal places

    Step-by-step solution →