## Bharat Gupta is teaching live on Unacademy Plus

Base System Problems part 6

The square of (234)6 is; a. (23425)6 c. (104524)6 b. (101423)6 d. (15235)6 If (32)n * (13)n-1(198)n +4. What is the value of n +3? a. 12 d. 9 Let N E (abcde), be a 5 digit number in base A positive whole number M less than 100 is n also let M = a + b + c d + e, where a, b, c, d and e are digits. Find the smallest value oflast digit is 1, while in exactly two out of the three n such that N and M divisible by 2, 3, 4, 5 and 6 a. 60 b. 59 represented in base 2 notation, base 3 notation and base 5 notation. It is found that in all three cases the cases the leading digit is 1. Then M equals? [cat 2003] a. 31 b. 63 c. 75 d. 91 C. 61 d. 81 I take a four-digit number and subtract from it The square root of the octal number the sum of its digits. In the result I strike off 1161 is: a. (31)8 c. (29)8 b. (25)s d. (33)B one of the digits and the remaining three digits of the result are 2, 4 and 6 (not necessarily in that order). Find the digit struck off by me. b. 6 d. 9

The square of (234)6 is; a. (23425)6 b. (101423)6 c. (104524)6 d. (15235)6

The square of (234)s is; a. (23425)e c. (104524)6 d. (15235),6 (23C a 3 y 6

If (32)n* (13)n -(198)n+ 4 What is the value of n 3? a. 12 b. 11 c. 10 d. 9

If (32)n* (13)n -(198)n+ 4 What is the value of n 3? a. 12 b. 11 c. 10 d. 9 (32)n x (13.m -deg) .ry

Let N (abcde)n be a 5 digit number in base n also let M a+b+ c+d+ e, where a, b, c, d and e are digits. Find the smallest value of n such that N and M divisible by 2, 3, 4, 5 and 6. a. 60 b. 59 C. 61 d. 81

Let N (abcde)n be a 5 digit number in base n also let M a+b+ c+d+ e, where a, b, c, d and e are digits. Find the smallest value of n such that N and M divisible by 2, 3, 4, 5 and 6. a. 60 b. 59 C. 61 d. 81 chi.sibe -61

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals? [cat 2003] a. 31 b. 63 C. 75 d. 91

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals? [cat 2003] a. 31 b. 63 C. 75 d. 91 31 31 131 31 1 1011 3