A positive integer is called a palindrome if it reads the same forward and backwards. The number of eight-digit palindromes divisible by 5 is

For the number to be divisible by 5, the last digit must be either 0 or 5

If 0 is the last digit then the first digit must also be 0, then it will be a 7 digit number.

So the last digit can only be 5.

If the last digit is 5, then the first digit is also 5.

We have select values of second, third, fourth digits only because fifth, sixth and seventh will be same as second, third, fourth digits.

Second, third and fourth digits can have 10 possibilities.

The required number of ways = 1*10*10*10 = 1000

A is the correct answer.