# NCERT Solutions for Class 10 Maths Chapter 1 Exercise 1.1

NCERT Solutions for Class 10 Maths Chapter 1 Exercise 1.1 in English Medium and Hindi Medium use online or download. Extra questions with answers based on Exercise 1.1 of Real Number are given at the end of all solutions. Solutions of Exercise 1.2, Exercise 1.3 and Exercise 1.4. Click here to go back to NCERT Solutions for Class 10 Maths Page.

## NCERT Solutions for Class 10 Maths Chapter 1 Exercise 1.1

If you need solutions in Hindi, Click for Hindi Medium solutions of 10 Maths Exercise 1.1    Exercise 1.2

Exercise 1.3

Exercise 1.4

#### 10 Maths Chapter 1 Exercise 1.1 in Hindi   Exercise 1.2

Exercise 1.3

Exercise 1.4

To get the solutions in English, Click for English Medium solutions.

##### Extra Questions for Practice based on Real Numbers Exercise 1.1
1. Write the general form of an even integer. (Answer: 2m)
2. Write the form in which every odd integer can be written taking t as variable. (Answer: 2t + 1)
3. What would be the value of n for n² – 1 divisible by 8. (Answer: An odd integer)
4. If a = 4q + r then what are the condition for a and q. What are the values that r can take? (Answer: and q are positive integers 0 ≤ r ≤ 4)
5. If n is an odd integer then show that n² – 1 is divisible by 8.
6. Use Euclid’s division algorithm to find the HCF of 16 and 28. (Answer: 4)
7. Show that square of any odd integer is of the form 4m + 1, for same integer m.
8. Show that the square of any positive integer is either of the form 4q or 4q + 1 for some integer q.
9. Show that the cube of any positive integer is of the form 4m, 4m +1 or 4m +3 for some integer m.
10. Find the HCF of 56, 96, 324 by Euclid’s algorithm. (Answer: 4)
11. Show that any positive odd integer is of the form 6q +1, 6q + 3 or 6q + 5, where q is some integer.
12. Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer, q.
13. Prove that the product of three consecutive positive integers is divisible by 6.
14. For any positive integer n, prove that n³ – n is divisible by 6.
15. Show that one and only one of n, n + 2, n +4 is divisible by 3.
16. Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.