Coefficient of `x^m` in `(1 +x)^m+ (1+ x)^(m+1)+........ (1+ x)^n, m < n` is

The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

Statement-1 Coefficient of x^49 in (1+ x)(3 +x)(5 +x)......... (99+x) is 2500 and Statement. 2 The coefficient of x^k in (1 +x)l (2 +x)m (3 +x)n where l +m +n -k= 1 is (l+ 2m +3n).

The coefficient of x^(m) in (1+x)^(k)+(1+x)^(k+1)+....+(1+x)^(n),(k<=m<=n) ,is given by

The coefficient of x^m in the extension (1+x)^(m+n)

The coefficient of x^m in (1+x)^r+ (1+x)^(r+1)+(1+x)^(r+2)+………+(1+x)^n , rlemlen is

If m, n, r, in N then .^(m)C_(0).^(n)C_(r) + .^(m)C_(1).^(n)C_(r-1)+"…….."+.^(m)C_(r).^(n)C_(0) = coefficient of x^(r) in (1+x)^(m)(1+x)^(n) = coefficient of x^(f) in (1+x)^(m+n) The value of r for which S = .^(20)C_(r.).^(10)C_(0)+.^(20)C_(r-1).^(10)C_(1)+"........".^(20)C_(0).^(10)C_(r) is maximum can not be

If m, n, r, in N then .^(m)C_(0).^(n)C_(r) + .^(m)C_(1).^(n)C_(r-1)+"…….."+.^(m)C_(r).^(n)C_(0) = coefficient of x^(r) in (1+x)^(m)(1+x)^(n) = coefficient of x^(f) in (1+x)^(m+n) The value of r for which S = .^(20)C_(r.).^(10)C_(0)+.^(20)C_(r-1).^(10)C_(1)+"........".^(20)C_(0).^(10)C_(r) is maximum can not be

If the coefficient of x^(2) + coefficient of x in the expanssion of (1+x)^(m)(1-x)^(n),(mnen) is equal to – m, then the value of n – m is equal to: