A number is called a palindrome if it reads t | vedclass

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(D) six-digit palindrome has the form $abc cba$. Since it is a six-digit number,$a \in \{1, 2, \dots, 9\}$ and $b, c \in \{0, 1, \dots, 9\}$.For the n

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$100$

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(D) six-digit palindrome has the form $abc cba$. Since it is a six-digit number,$a \in \{1, 2, \dots, 9\}$ and $b, c \in \{0, 1, \dots, 9\}$.For the number to be divisible by $55$,it must be divisible by both $5$ and $11$.Divisibility by $5$ implies the last digit must be $0$ or $5$. Since it is a six-digit number,the first digit $a$ cannot be $0$. Thus,$a = 5$.The number is of the form $5bc c b5$.For divisibility by $11$,the alternating sum of digits must be divisible by $11$:$(5 + c + b) - (b + c + 5) = 0$.Since $0$ is divisible by $11$,any choice of $b$ and $c$ will make the number divisible by $11$.There are $10$ possible values for $b$ ($0$ to $9$) and $10$ possible values for $c$ ($0$ to $9$).Total number of such palindromes $= 10 	imes 10 = 100$.

$A$ 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 ...... .

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