If ¹⁵P_r-1 : ¹⁶P_r-2 = 3 : 4 then r =

The number of odd numbers between 1000 and 10000 can be formed with the digits 1,2,3,4,5,6,7,8,9 is

The letters of word VICTORY are permuted in all possible ways and the words thus formed are arranged as in a dictionary.The rank of the word VICTORY is

If ⁽ⁿ⁺¹⁾P₅:ⁿP₆= 2: 7 then n =

The number of four digited even numbers that can be formed from the digits 0,1,2,5,7,8 is

The number of even divisors of 1600 is

If ⁿP_r =30240 and ⁿC_r=252then the ordered pair (n, r) is equal to

The sum of all possible numbers greater than 2000 formed by using the digits 2,3,4,5 is

The number of four digited numbers that can be formed from using the digits 2,4,5, 7,8 that are divisible by 4 is

A student is allowed to select atmost n books from a collection of (2n+1) books. If the total number of ways in which he can select books is 63, then n=