Let `n_1ltn_2ltn_3ltn_4ltn_5` be positive integers such that `n_1+n_2+n_3+n_4+n_5="20.` then the number of distinct arrangements `n_1, n_2, n_3, n_4, n_5` is

If n_(1) , n_(2) , n_(3) ,….., n_(100) are positive real numbers such that n_(1)+n_(2)+n_(3)+…+n_(100)=20 and k=n_(1)(n_(2)+n_(3)+n_(4))(n_(5)+n_(6)+…+n_(9))(n_(10)+….+n_(16))…(…+n_(100)) , then k belongs to

If .^(n+5) P_(n +1) = ((11(n-1))/2) .^(n +3) P_(n) then the value of n are

The greatest positive integer which divides (n+1)(n+2)(n+3)...(n+r) for all ninN is

The greatest positive integer which divides n(n+1)(n+2)(n+3) for all ninN is

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of ndot

Let a_1,a_2,a_3,... be in harmonic progression with a_1=5a n da_(20)=25. The least positive integer n for which a_n<0

If n_1, n_2 are positive integers, then (1 + i)^(n_1) + ( 1 + i^3)^(n_1) + (1 + i_5)^(n_2) + (1 + i^7)^(n_2) is real if and only if :

If a_(1), a_(2) …… a_(n) = n a_(n - 1) , for all positive integer n gt= 2 , then a_(5) is equal to

Let E={1,2,3,4}a n dF={1,2}dot If N is the number of onto functions from EtoF , then the value of N//2 is

Find the number of subsets of A if A = { X : X = 4n +1, 2 lt= n lt= 5, n in NN }