Question

A number is called a palindrome if it reads the same backward as well as forward. For example $285582$ is a six digit palindrome. The number of six digit palindromes, which are divisible by $55$, is

Answer 1

For divisible by $55,$ it is divisible by $11$ and $5$ both.
For divisibility by $5,$ unit digit is either $0$ or $5$ but as the number is six digit palindrome so unit digit is $5$.
$\therefore$ Number is of form $5ABBA5$
If the difference between the sum of the digits at the odd and even places equals $0$ or divisible by $11,$ then the number is divisible by $11.$
$\therefore$ No. of ways $=10\times 10=100$