Q1) What is the H.C.F. of 24, 36 and 72? 1) 72 2) 24 3) 144 4) 12 Hence, option 4. Q2) What is the L.C.M. of 2, 3, 4, 5, 6, 7? 1) 105 2) 840 3) 420 4) 210 Hence, option 3. Q3) Find the least number which when divided by 12 and 16 leaves 3 as the remainder. 1) 99 2) 51 3) 19 4) 15 Required Number = L.C.M.(12, 16) + 3 Hence, option 2. Q4) What is the L.C.M. of ? 1) 1/35 2) 1 3) 12 4) 12/35 Hence, option 3. Q5) Find the least number which when divided by 13 and 17 leaves 4 as the remainder but when divided by 11 leaves no remainder. 1) 1551 2) 224 3) 225 4) None of these Required number is of the form (L.C.M.(13, 17))k + 4 = 221k + 4 When this number is divided by 11, the remainder is 0 i.e.221k + 4 is divisible by 11. 221k + 4 = (11 × 20k) + (k + 4) 11 × 20k is divisible by 11 for all 'k' and k + 4 is divisible by 11 for k = 7. Required number is 221(7) + 4 = 1551 Hence, option 1. Q6) Product of two coprime numbers is 117. Then, their LCM is 1) 9 2) 13 3) 39 4) 117 LCM of two co primes is equal to their product. Hence, Option 4. Q7) For any integer n, what is HCF(22n + 7, 33n + 10) equal to? 1) 0 2) 11 3) 1 4) None of these Put n = 1 then HCF(29,43) = 1;
n = 2 then HCF(51,76) = 1;
n = 3 then HCF(73,109) = 1
So, HCF(22n + 7, 33n + 10) = 1 |