In how many ways can $10$ true-false questions be replied?

How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?

There are $6$ multiple choice questions on an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next $3$ have $5$ each?

In how many different ways can the letters of the word '$AUCTION$' be arranged in such a way that the vowels always come together?

$n$ balls each of weight $w$ are weighed in pairs. The sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to: