Binomial Theore...

If the sum of binomial coefficient in the expansion $$(1+x)^{n}$$ is $$256$$, then $$n$$ is

The coefficient of $${ x }^{ 3 }$$ in the polynomial $$(x-1) (x-2) (x-4)$$ is

If the constants term in the expansions of $$(\sqrt{x}-\dfrac{k}{x^2})^{10}$$ is $$405$$, then what can be the value of $$k$$ ?

The middle term in $${\left( {{x^2} + \dfrac{1}{{{x^2}}} + 2} \right)^n}$$ is 

The $$5$$th term in the expansion of $$ \left(2x^2 + \dfrac{3}{x}\right)^5 $$ is

If $$n$$ is a positive integer, then the number of terms in the expansion of $$ (x+a)^n $$ is

The $$ (n+1)^{th} $$ term from the end in $$ \left(x-\dfrac{1}{x}\right)^{3n} $$ is

In any binomial expansion, the number of terms are

The $$4^{th}$$ term in the expansion of $$ \left(\sqrt{x}+\dfrac{1}{x}\right)^{12} $$ is

If $$ T_r $$ denotes the $$ r^{th} $$ term  in the expansion of $$\displaystyle \left(x + \frac{1}{x} \right)^{23} $$, then