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.

NCERT exercises

Exercise 1.1 (7) Exercise 1.2 (3)

NCERT Exemplar exercises

Exercise 1.1 (10) Exercise 1.2 (10) Exercise 1.3 (14) Exercise 1.4 (5)

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 14 of 17

Q261 CBSE 2023

Prove that $3 + 72$ is an irrational number, given that $2$ is an irrational number.

Show answer

$3 + 72$ is irrational (by contradiction).

Step-by-step solution →
Q262 CBSE 2023
Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought $36$ apples and $60$ bananas and decided to distribute fruits equally among all. Based on the above information, answer the following questions.
1. (i)How many guests Khushi can invite at the most?[1]
2. (ii)How many apples and bananas will each guest get?[1]
3. (iii)(a)If Khushi decides to add $42$ mangoes, how many guests Khushi can invite at the most?[2]
4. (iii)(b)If the cost of $1$ dozen of bananas is Rs $60$ , the cost of $1$ apple is Rs $15$ and cost of $1$ mango is Rs $20$ , find the total amount spent on $60$ bananas, $36$ apples and $42$ mangoes.[2]
Show answer

(i) $12$ guests (ii) $3$ apples and $5$ bananas each (iii)(a) $6$ guests (iii)(b) Rs $1680$

Step-by-step solution →
Q263 CBSE 2023
Case Study - 3: February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Some people in India also started celebrating this day and donated the following number of books of various subjects to a public library: History = 96, Science = 240, Mathematics = 336. These books have to be arranged in minimum number of stacks such that each stack contains books of only one subject and the number of books on each stack is the same. Based on the above information, answer the following questions:
1. (i)How many books are arranged in each stack?
2. (ii)How many stacks are used to arrange all the Mathematics books? (iii)(a) Determine the total number of stacks that will be used for arranging all the books. OR (iii)(b) If the thickness of each book of History, Science and Mathematics is 1.8 cm, 2.2 cm and 2.5 cm respectively, then find the height of each stack of History, Science and Mathematics books.
Show answer

(i) 48 books per stack; (ii) 7 stacks; (iii)(a) 14 stacks total; (iii)(b) Heights 86.4 cm, 105.6 cm, 120 cm.

Step-by-step solution →
Q264 CBSE 2020
HCF of two numbers is 27 and their LCM is 162. If one of the number is 54, then the other number is
1. (a)36
2. (b)35
3. (c)9
4. (d)81
Show answer

(d) 81

Step-by-step solution →
Q265 CBSE 2020
The decimal representation of $\frac{117}{2 ^{3} 5 ^{4} 3 ^{2}}$ will
1. (a)terminate after $3$ decimal places
2. (b)terminate after $2$ decimal places
3. (c)terminate after $4$ decimal places
4. (d)not terminate
Show answer

(c) terminate after $4$ decimal places

Step-by-step solution →
Q266 CBSE 2020
What is the largest number that divides $245$ and $1029$ , leaving remainder $5$ in each?
1. (a) $15$
2. (b) $16$
3. (c) $9$
4. (d) $5$
Show answer

(b) $16$

Step-by-step solution →
Q267 CBSE 2020
HCF of 144 and 198 is
1. (a) $9$
2. (b) $18$
3. (c) $6$
4. (d) $12$
Show answer

(b) $18$

Step-by-step solution →
Q268 CBSE 2020
The sum of exponents of prime factors in the prime-factorisation of $196$ is
1. (a) $3$
2. (b) $4$
3. (c) $5$
4. (d) $2$
Show answer

(b) $4$

Step-by-step solution →
Q269 CBSE 2020
The HCF of $135$ and $225$ is
1. (a) $15$
2. (b) $75$
3. (c) $45$
4. (d) $5$
Show answer

(c) $45$

Step-by-step solution →
Q270 CBSE 2020
Given that $HCF (156, 78) = 78$ , $LCM (156, 78)$ is
1. (a) $156$
2. (b) $78$
3. (c) $156 \times 78$
4. (d) $156 \times 2$
Show answer

(a) $156$

Step-by-step solution →
Q271 CBSE 2020
The exponent of $2$ in the prime factorization of $144$ , is
1. (a) $2$
2. (b) $4$
3. (c) $1$
4. (d) $6$
Show answer

(b) $4$

Step-by-step solution →
Q272 CBSE 2020
The total number of factors of a prime number is
1. (a)1
2. (b)0
3. (c)2
4. (d)3
Show answer

(c) 2

Step-by-step solution →
Q273 CBSE 2020
Euclid's division Lemma states that for two positive integers $a$ and $b$ , there exists unique integer $q$ and $r$ satisfying $a = b q + r$ , and
1. (a) $0 < r < b$
2. (b) $0 < r \leq b$
3. (c) $0 \leq r < b$
4. (d) $0 \leq r \leq b$
Show answer

(c) $0 \leq r < b$

Step-by-step solution →
Q274 CBSE 2020
The HCF of $135$ and $225$ is:
1. (a) $9$
2. (b) $15$
3. (c) $45$
4. (d) $25$
Show answer

(c) $45$

Step-by-step solution →
Q275 CBSE 2020
225 can be expressed as
1. (a) $5 \times 3^{2}$
2. (b) $5^{2} \times 3$
3. (c) $5^{2} \times 3^{2}$
4. (d) $5^{3} \times 3$
Show answer

(c) $5^{2} \times 3^{2}$

Step-by-step solution →
Q276 CBSE 2020
The simplest form of $\frac{1095}{1168}$ is
1. (a) $\frac{17}{26}$
2. (b) $\frac{25}{26}$
3. (c) $\frac{13}{16}$
4. (d) $\frac{15}{16}$
Show answer

(d) $\frac{15}{16}$

Step-by-step solution →
Q277 CBSE 2020
$23$ 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 →
Q278 CBSE 2020
The LCM of the smallest two-digit number and the largest multiple of $6$ which is less than $50$ is
1. (a) $2$
2. (b) $48$
3. (c) $120$
4. (d) $240$
Show answer

(d) $240$

Step-by-step solution →
Q279 CBSE 2020
The HCF and the LCM of $12$ , $21$ , $15$ respectively are
1. (a) $3, 140$
2. (b) $12, 420$
3. (c) $3, 420$
4. (d) $420, 3$
Show answer

(c) $3, 420$

Step-by-step solution →
Q280 CBSE 2020
The decimal expansion of $\frac{23}{2 ^{5} \times 5 ^{2}}$ will terminate after how many places of decimal?
1. (a)2
2. (b)4
3. (c)5
4. (d)1
Show answer

(c) 5

Step-by-step solution →