April 2022

Q1. Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429 Solution 1 Q2. 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

Q1. Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution: (i) 135 and 225 Step 1Since 225 > 135, we can apply Euclid’s division lemma to a = 225 and b = 135 to find q and r such that:225 = 135q

Q1. Prove that `sqrt{5}` is irrational. Solution 1 Q2. Prove that 3 + `2sqrt{5}` is irrational. Solution 2. Q3. Prove that the following are irrationals: (i) `frac{1}{sqrt{5}}` (ii) 7 `sqrt{5}`(iii) 6 + `sqrt{2}` Solution 3. ‹Exercise 1.2 Exercise 1.4›

Q1. 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(i) `frac{13}{3125}` (ii) `frac{17}{8}` (iii) `frac{64}{455}` (iv) `frac{15}{1600}` (v) `frac{29}{343}` (vi)`frac{23}{2^3 5^2}` (vii) `frac{129}{2^2 5^7 7^5}`(viii) `frac{6}{15}` (ix) `frac{35}{50}` (x) `frac{77}{210}` Solution 1 Q2. Write down the decimal expansions of those