**Real Numbers NCERT Books Solutions For Class 10 Maths Chapter 1**

**NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers Mathematics** is a very important subject in school. Mathematics plays a serious role in choosing the career stream at the higher secondary level. Knowing the **CBSE Class 10th Maths** Syllabus is a prerequisite for students appearing for CBSE Board Examination. Students who are in search of **NCERT Solutions for Class 10 Maths** can check with this text.

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Below you can find the** NCERT solution for class 10 chapter 1 maths Real Numbers**. You can get a Solution for** the all-important question of “Chapter 1 Maths Class 10 Real Numbers”**

**Questions Covered In Class 10 Maths Chapter 1 Real Numbers**

**Question 1 : **Use Euclid’s division algorithm to find hcf of

(i) 135 and 225

(ii) 196 and 38220

(iii) 867 and 255

**Question 2 : **Show that any positive odd integer is of the form 6q+1 or 6q+3 or 6q+5 Where q is some integer.

**Question 3 : **An army contingent of 616 members is to march behind band of 32 members in a parade. The two groups are to march in some number of columns. What is the maximum number of columns in which they can march?

**Question 4 : **Use Euclid’s division lemma to show that square of any positive integer is either of form 3m or 3m+1 for some m.

**Question 5 : **Use Euclid’s division lemma to show that the cube of any positive integer of the form 9m, 9m+1 or 9m+8.

**Question 6 : **Express each number as product of its prime factor

(i) 140

(ii) 157

(iii) 3825

(iv) 5005

(v) 7429

**Question 7 : **Find LCM and HCF of the following pairs of integers & verify that Lcm x Hcf = product of the two numbers

(i) 26×91

(ii) 510×92

(iii) 336×54

**Question 8 : **Find the lcm and Hcf of the following integers by applying the prime factorisation method

(i) 12, 15 and 21

(ii) 17, 23 and 29

(iii) 8, 9 and 25

**Question 9 : **Given that HCF (306, 657) = 9 find Lcm.

**Question 10 : **Check whether 6n can end with the digit 0 for any natural no. n.

**Question 11 : **Explain why 7x11x 13 + 13 and 7x6x 5 x 4 x 3 x2x1 +5 are composite no.

**Question 12 : **There is a circular path around a sports field. Sonia takes 18 min to drive one round of the field, while Ravi takes 12 min for the same. Suppose they both start at the same point and at the same time, and go in the same direction. Alter how many minutes they meet again at the starting pt?

**Question 13 : **Prove that under root 5 is irrational.

**Question 14 : **Prove that 3+255 is irrational.

**Question 15 : **Prove that the following are irrationals:

(i) 1/root 2

(ii) 7 root 5

(iii) 6+root 2

**Question 16 : **Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expression on a nonterminating repeating decimal expansion:

(i) 13/3125

(ii) 17/8

(iii) 64/455

(iv) 15/1600

(v) 29/343

(vi) 23/2^3×5^2

(vii) 129/2^2×5^7×7^5

(viii) 6/15=2/5

(ix) 35/50

(x) 77/210

**Question 17 : **Write down the decimal expansions of those rational nos. in Question I above which have terminating decimal expansions.

(i) 13/3125

(ii) 17/8

(iii) 15/1600

(iv) 23/2^3×5^2

(v) 6/15

(vi) 35/50

**Question 18 : **The following real numbers have decimal expansion as given below. In each case, decide whether they are rational or not. If they are rational and of the form p/q what can you say about the prime factor of q?

(i) 43.12456789

(ii) 0.120120012000120000…

(iii) 43.123456789

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