The number $(49^{2}-4)(49^{3}-49)$ is divisible by (in $!$)

Two packs of $52$ cards are shuffled together. The number of ways in which a man can be dealt $26$ cards so that he does not get two cards of the same suit and same denomination is

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to

The remainder obtained when $1! + 2! + 3! + \dots + 11!$ is divided by $12$ is

If all the letters of the word $ACADEMICIAN$ are permuted in all possible ways,then the number of permutations in which no two $A$'s are together and all the consonants are together is:

If the $LCM$ of $p$ and $q$ is $r^2t^4s^2$,where $r, s,$ and $t$ are prime numbers,and $p$ and $q$ are positive integers,then the number of ordered pairs $(p, q)$ is ....