Here, we are providing the NCERT solutions for Class 10 Mathematics chapter 15, Real Numbers. Our subject experts have reviewed these NCERT solutions to provide you the error free content which will make it easy for you to make an effective preparation for the board exams.

Main topics discussed in Class 10 Mathematics chapter - Real Numbers are:

• Basics concepts related to real numbers

• Euclid's Division Lemma,

• Fundamental Theorem of Arithmetic

• Revisiting irrational numbers

• Revisiting rational numbers and their decimal expansions and

Students may download all the NCERT Solutions for CBSE Class 10 Mathematics chapter – Real Numbers, in the form of PDF.

**Some of the questions and their solutions from NCERT Solutions for Class 10 Maths: Real Numbers, are as follows:**

**Q. **Show that any positive odd integer is of the form 6*q *+ 1, or 6*q *+ 3, or 6*q *+ 5, where *q *is some integer.

**Sol.**

By Euclid’s algorithm,

* a* = 6*q* + *r*, and *r* = 0, 1, 2, 3, 4, 5

Hence, *a* = 6*q* or 6*q* + 1 or 6*q* + 2 or 6*q + *3 or 6*q* + 4 or 6*q* + 5

Clearly, 6*q* + 1, 6*q* + 3, 6*q* + 5 are of the form 2*k* + 1, where *k* is an integer.

Therefore, 6*q* + 1, 6*q* + 3, 6*q* + 5 are not exactly divisible by 2.

Hence, these numbers are odd numbers.

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

**Sol.**

Euclid’s algorithm

616 = 32 × 19 + 8

32 = 8 × 4 + 0

The HCF (616, 32) is 8.

Therefore, they can march in 8 columns each.

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NCERT books offer a number of problems for students to practice for self-assessment and exam preparations. Practicing a variety of questions helps to strengthen the fundamentals of a topic which makes students efficient in solving different questions asked in exams based on that particular topic. Therefore, students are suggested to solve all the NCERT questions and learn to write perfect solutions which will help them score good marks in exams.

For all the questions given in CBSE Class 10 Mathematics NCERT book, we have collated detailed and accurate answers that will help students find the right approach to solve different questions.

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