The number of words formed from the letters of the word $RAJASTHAN$ by taking all the letters at a time in which vowels are alternate is:

Three persons enter a lift at the ground floor. The lift goes up to the $10^{\text{th}}$ floor. If the lift does not stop at the $1^{\text{st}}$,$2^{\text{nd}}$,and $3^{\text{rd}}$ floors,the number of ways in which the three persons can exit the lift at three different floors is equal to . . . . . . .

How many $3$-digit even numbers can be formed using the digits $1, 2, 3, 4, 6, 7$,if no digit is repeated?

If $^mP_r - ^{m-1}P_r = a \cdot ^{m-1}P_s$,then $a - s = \dots$

The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

Each of the $10$ letters $A, H, I, M, O, T, U, V, W$ and $X$ appears the same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many $3$-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?