Binomial Theore...

The total number of rational terms in the expansion of $$\left(7^{\frac 13} + 11^{\frac 19}\right)^{6561}$$ is

If the coefficient of $$x^7$$ in $$\displaystyle \left [ ax^2 + \left ( \dfrac{1}{bx} \right ) \right ]^{11}$$ equals the coefficient of $$x^{-7}$$ in $$\displaystyle \left [ ax - \left ( \dfrac{1}{bx^2} \right ) \right ]^{11}$$, then $$a$$ and $$b$$ satisfy the relation

If the coefficients of $$2^{nd}, 3^{rd}, 4^{th}$$ terms of $$(1+x)^n$$ are in A.P., then $$n=$$

If the middle term in the expansion of $$({ { x }^{ 2 } }+\dfrac{1}{x} )^{ n }$$ is $$924\,{ x }^{ 6 }$$, then find the value of $$n$$

The middle term in the expansion of $$\left (\dfrac{x}{y}+\dfrac{y}{x}  \right )^{8}$$ is.

If the coefficient of (2r + 4)th term is equal to the coefficient of (r - 2)th term in the expansion of $$(1+x)^{18}$$ then r$$=$$

The coefficient of the middle term in the binomial expansion in powers of x of $$(1+\alpha x)^4$$ and of $$(1+\alpha x)^6$$ is the same if $$\alpha =$$ 

The coefficient of $$x^4$$ in the expansion of $$\displaystyle \frac{(1-3x)^2}{(1-2x)}$$ is

The numerically greatest term in the expansion of $$(3-2x)^{9}$$ when $$x=1 $$ is

If the coefficients of $$5^{th}, 6^{th}, 7^{th}$$ terms of $$(1+x)^n$$ are in A.P., then $$n=$$