The number of digits required to represent the decimal number 213 in base system 5 is

Q. In the decimal system of numeration the number of 6-digit numbers in which the digit in any place is greater than the digit to the left of it is

Q. In the decimal system of numeration the number of $6$ - digits number in which the sum of the digits is divisible by $5$ is :

Q. A number of decimal system when represented in binary system then its first and last digits are same and the rest digits are also of another kind. Further this number appears to be palindrome of numerals. The number is:

Q. If u, v and w are the digits of decimal system, then the rational number represented by 0.uwuvuvuvuv......is

Q. In the numeration system with base $5$, counting is as follows : $1,2,3,4,10,11,12,13,14,20$,____. The number whose description in the decimal system is $69$, when described in the base $5$ system, is a number with: