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

The number of permutations of all the letters $AAAABBBC$ in which all the $A$'s appear together in a block of $4$ letters or all the $B$'s appear together in a block of $3$ letters,is-

How many words can be made from the letters of the word $BHARAT$ in which $B$ and $H$ never come together?

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first $2$ questions have $3$ choices each,the next $2$ have $4$ choices each,and the last $2$ have $5$ choices each?

The number of ways in which the letters of the word $TRIANGLE$ can be arranged such that no two vowels occur together is

There are $8$ students appearing in an examination of which $3$ have to appear in a Mathematics paper and the remaining $5$ in different subjects. In how many ways can they be made to sit in a row if the candidates in Mathematics cannot sit next to each other?