Numbers
Practice Questions on Number System
| Q21) On dividing a number by 7, remainder obtained is 4. What will be the remainder when the square of this number is divided by 7? 1) 5 2) 4 3) 2 4) 6 Number (N) = 7Q + 4 N2 = (7Q + 4)2 = 49Q2 + 56Q + 16 = 7(7Q2 + 8Q + 2) + 2 On dividing N2 by 7, remainder obtained is 2. Hence, option 3. Q22) (1000)8/1021 1) 100 2) 10 3) 10000 4) 1000  Hence, option 4. Q23) A certain number when divided by 259 leaves a remainder 31, another number when divided by 481 leaves a remainder 53. What is the remainder when the sum of these two numbers is divided by 37? 1) 10 2) 8 3) 22 4) 30 N1 = 259a + 31, N2 = 481b + 53 N1 + N2 = (259a + 31) + (481b + 53) = 259a + 481b + 84 Remainder when N1 + N2 is divided by 37 = Remainder when 84 is divided by 37 = 10 Hence, option 1. Q24) Find the remainder when (5349 + 45) is divided by 54. 1) 0 2) 44 3) 39 4) 1 (yn + 1) is divisible by (y + 1) when n is odd. (5345 + 1) is divisible by (53 + 1) (5345 + 1) + 44 when divided by (53 + 1) will leave 44 as the remainder. Hence, option 2. |