Let `n_(1)ltn_(2)ltn_(3)ltn_(4)ltn_(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

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 and m (ltn) are two positive integers then n(n-1)(n-2)...(n-m) =

If n be a positive integer and P(n):4^(5n)-5^(4n) If P(n) be negative value, then the value of n 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 is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n^(2) = (n)/(6)(2n+1)(7n+1)

Arrange N_(2)O_(5), N_(2)O_(3) and N_(2)O_(4) in the order of increasing acidic character .

If n is a positive integer , then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is -

If n (> 1)is a positive integer, then show that 2^(2n)- 3n - 1 is divisible by 9.

If n be a positive integer and P(n):4^(5n)-5^(4n) When n=3 then the last digit of the expression will be -

If n be a positive integer and P(n):4^(5n)-5^(4n) P(n) is divisible by -