If the equation whose roots are $P$ times the roots of the equation $x^4-2 a x^3+4 b x^2+8 a x+16=0$ is a reciprocal equation, then $|P|=$

All the letters of the word 'MOTHER' are written in all possible ways and the strings of letters (with or without meaning), so formed are written as in a dictionary order. Then, the position of the word 'THROEM' is

A student is allowed to select at most $n$ books from a collection of ( $2 n+1$ ) books. If the total number of ways in which he can select at least one book is 255 , then the value of $n$ is