JEE MAIN - Mathematics (2021 - 27th August Morning Shift - No. 18)
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
100
Explanation
| 5 | a | b | b | a | 5 |
For divisible by 55 it shall be divisible by 11 and 5 both, for divisibility by 5 unit digit shall be 0 or 5 but as the number is six digit palindrome unit digit is 5.
A number is divisible by 11 if the difference between sum of the digits in the odd places and the sum of the digits in the even places is a multiple of 11 or zero.
Sum of the digits in the even place = a + b + 5
Sum of the digits in the odd places = a + b + 5
Difference between the two sums = (a + b + 5 ) - (a + b + 5) = 0
0 is divisible by 11.
Hence, 5abba5 is divisible by 11.
So, required number = 10 $$\times$$ 10 = 100
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