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

The term independent of x in (1+x)^m (1+1/x)^n is

The term independent of x in (1+x)^m (1+1/x)^n 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(0 le r le 30) for which S = .^(20)C_(r).^(10)C_(0) + .^(20)C_(r-1).^(10)C_(1) + ........ + .^(20)C_(0).^(10)C_(r) is minimum can not be

If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

STATEMENT - 1 : The term independent of x in the expansion of (x+1/x+2)^(m) is ((2m) !)/((m !)^(2)) STATEMENT - 2 : The coefficient of x^(b) in the expansion of (1+x)^(n) is .^(n)C_(b) .

If a\ a n d\ b denote respectively the coefficients of x^m a n d\ x^n in the expansion of (1+x)^(m+n) , then write the relation between \ a\ a n d\ b .

If a and b are respective coefficients of x^m and x^n in the expansion of (1+ x)^(m+n) then

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: