Question

If the number of five-digit numbers which can be read in the same way from the left and from the right is $k$ , then $\frac{k}{100}$ is equal to

Answer 1

The number will be of the form $XYZYX$ first place can’t be zero, so it can be any $1$ to $9\Rightarrow 9$ ways
$Y$ and $Z$ each can be any of $0$ and $9$ so, they can be filled in $10$ ways each.
The fourth place will be the same as second place and the last place will be the same as the first place.
So, the required number of ways $=9\times 10\times 10\times 1\times 1=900$
$\Rightarrow k=900\Rightarrow \frac{k}{100}=9.$