If $^{2n}C_2 : ^nC_2 = 9:2$ and $^nC_r = 10$,then $r = $

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

In how many ways can $n$ books be arranged in a row so that two specified books are not together?

How many numbers lying between $500$ and $600$ can be formed with the help of the digits $1, 2, 3, 4, 5, 6$ when the digits are not to be repeated?

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $

How many words comprising of any three letters of the word $UNIVERSAL$ can be formed?