[" Let "n" and "k" be positive integers such that "n>=-n],[" The number of solutions "(x_(1),x_(2),...,x_(2))],[x_(1)>=1,x_(2)>=2...x_(2)>=k" for all integers satisfying "],[x_(1)+x_(2)+...+x_(1)=n" is "cdots]

Let n and k be positive such that n<=(k(k+1))/(2). The number of solutions (x_(1),x_(2),....x_(k)),x_(1)<=1,x_(2)<=2,......,x_(k)<=k all integers,satisfying x_(1)+x_(2)+....+x_(k)=n, is ......

Let n and k be positive integers such that n gt (k(k+1))/2 . The number of solutions (x_(1),x_(2), . ..x_(k)),x_(1) ge 1, x_(2) ge 2,, . . .x_(k) ge k for all integers satisfying x_(1)+x_(2)+ . . .+x_(k)=n is:

Let n and k be positive such that n leq (k(k+1))/2 .The number of solutions (x_1, x_2,.....x_k), x_1 leq 1, x_2 leq 2, ........,x_k leq k , all integers, satisfying x_1 +x_2+.....+x_k = n , is .......

Let n and k be positive such that n leq (k(k+1))/2 .The number of solutions (x_1, x_2,.....x_k), x_1 leq 1, x_2 leq 2, ........,x_k leq k , all integers, satisfying x_1 +x_2+.....+x_k = n , is .......

Let n and k be positive integers such that n ge K(K + 1)/2 . Find the number of solutions ( x_(1) , x_(2) , x_(3),………., x_(k) ) x_(1) ge 1, x_(2) ge 2, ……….. X_(k) ge k , all integers satisfying the condition x_(1) + x_(2) + x_(3) + ………. X_(k) = n .

Let n and k be positive integers such that n ge K(K + 1)/2 . Find the number of solutions ( x_(1) , x_(2) , x_(3),………., x_(k) ) x_(1) ge 1, x_(2) ge 2, ……….. X_(k) ge k , all integers satisfying the condition x_(1) + x_(2) + x_(3) + ………. X_(k) = n .

If N is the number of positive integral solutions of x_(1)x_(2)x_(3)x_(4)=770, then N=

The number of non-negative integral solution x_(1)+x_(2)+x_(3)+x_(4)<=n (where n is a positive integer) is:

Let n be positive integer such that, (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then a_(r) is :