CBSE Class 10 Maths Books English Medium chapter 1 Ex 1.1 homework guffo.in

Chapter 1: Real Numbers

Example 1 : Use Euclid’s algorithm to find the HCF of 4052 and 12576.

अध्याय 1: रियल नंबर
उदाहरण 1: 4052 और 12576 के एचसीएफ को खोजने के लिए यूक्लिड के एल्गोरिदम का उपयोग करें।

Example 2 : Show that every positive even integer is of the form 2q, and that every
positive odd integer is of the form 2q + 1, where q is some integer.

Example 3 : Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where
q is some integer.

Example – A sweetseller has 420 kaju barfis and 130 badam barfis. She wants to
stack them in such a way that each stack has the same number, and they take up the
least area of the tray. What is the number of that can be placed in each stack for this
purpose?

EXERCISE 1.1
1. Use Euclid’s division algorithm to find the HCF of :

(i) 135 and 225

(ii) 196 and 38220

(iii) 867 and 255

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

Class 10 Maths Books English Medium chapter 1

3. 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?

4. Use Euclid’s division lemma to show that the square of any positive integer is either of
the form 3m or 3m + 1 for some integer m.
[Hint : Let x be any positive integer then it is of the form 3q, 3q + 1 or 3q + 2. Now square
each of these and show that they can be rewritten in the form 3m or 3m + 1.]

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