How many arrangements can be made using the letters of the word $CALCUTTA$?

${ }^{15} P_8 = A + 8 \cdot { }^{14} P_7 \Rightarrow A = $

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

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

$A$ car will hold $2$ persons in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

The number of integers greater than $3000$ that can be formed by using any number of digits from the set $\{0, 1, 2, 3, 4, 5\}$ without repetition is: