In the expansion of `(1-x)^(30)(1+x+x^(2))^(31)` the coefficient of `x^(47)` is `(-^(30)C_(r))` then the value of `|(r)/(2)|` is

In the expansion of (3-x)/((1-x)^(2)) coefficient of x^(r) is 9 then r=

In the expansion of (1+x)^(30) the sum of the coefficients of odd powers of x is

If in the expansion of (1 + x)^(20) , the coefficients of r^(th) and (r +4)^(th) terms are equal, then the value of r,is

If C_(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value of sum_(r=0)^(n) (r + 1)^(2) C_(r) , is

Prove that he coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^(n) in the expansion of (1+x)^(2n-1)