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NCERT Class Wise Solutions

#### Questions List of Chapter 1: Real Numbers

- Question 1 - Use Euclid’s division algorithm to find the 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 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?
- Question 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.
- Question 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.
- Question 6 - Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429
- Question 7 - Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54
- Question 8 - Find the LCM and HCF of the following integers by applying the prime factorization 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 (306, 657).
- Question 10 - Check whether 6^{n} can end with the digit 0 for any natural number n.
- Question 11 - Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers
- Question 12 - There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction.
- Question 13 - Prove that √5 is irrational
- Question 14 - Prove that 3 + 2√5 is irrational.
- Question 15 - Prove that the following are irrationals : (i) 1/√2 (ii) 7√5 (iii) 6 + √2
- Question 16 - Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
- Question 17 - The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not.

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