if `n! =40320` then `n`

If n! - n = n , then the value of n is :

If n! - n = n , then the value of n is :

In how many different ways can the letters of the word PUNCTUAL be arranged? (a) 64 (b) 960 (c) 20160 (d) 40320 (e) None of these

Let n_(1)

Let n_1 le n_2< n_3 < n_4< n_5 be positive integers such that n_1+n_2+n_3+n_4+n_5=20. then the number of such distinct arrangements n_1, n_2, n_3, n_4, n_5 is

If P(n) : 2n lt n! , n in N , then P(n) is true for all n gt= ………….. .

Let a_n=1000^n/(n!) for n in N , then a_n is greatest, when value of n is

If n in N and Delta_ (n) = det [[n!, (N + 1)!, (N + 2)! (N + 1)!, (N + 2)!, (N + 3)! ( n + 2)!, (n + 3)!, (n + 4)!]] then lim_ (n rarr oo) ((3 ^ (n ^ (3)) - 5) Delta_ (n)) / (Delta_ (n + 1)) equals

If f(n)=(-1)^(n-1)(n-1) and g(n)=n-f (n)AA n in N then (gog)(n)=