Binomial Theore...

In the expansion of $$\left (x+ \sqrt{x^{2}-1}\right )^{6}$$+ $$\left (x- \sqrt{x^{2}-1}\right )^{6}$$,the number of terms is

If $$\left ( 1+x \right )\left ( 1+x^{2} \right )\left ( 1+x^{4} \right )...\left ( 1+x^{128} \right )=\sum_{r=0}^{n}x^{r}$$ then $$n$$ is

The number of terms with integral coefficients in the expansion of$$\left ( 7^{1/3}+5^{1/2}.x \right )^{600}$$ is

The sum of coefficients in the binomial expansion of $$\displaystyle \left ( \frac{1}{x}+2x \right )^{n}$$is equal to $$6561$$.The constant term in the expansion is

The coefficient of $$x^{49}$$ in the product $$(x-1)(x-3)\dots(x-99)$$ is

If the $$4th$$ term in the expansion is of $$ \left (px+x^{-1} \right )^{m}$$ is $$2.5$$ for all $$x\epsilon R$$ then

The number of real negative terms in the binomial expansion of $$\left ( 1+ix \right )^{4n-2},$$ $$n\epsilon N,$$ $$x>0,$$ is

The number of terms whose values depends on $$x$$ in the expansion of $$\displaystyle\left (  x^{2}-2+\frac{1}{x^{2}}\right )^{n}$$ is

The absolute value of middle term in the expansion of $$\displaystyle \left ( 1-\frac{1}{x} \right )^{n}.(1-x)^{n}$$ is

The middle term in the expansion of $$\left ( \displaystyle \frac{2x}{3}-\frac{3}{2x^{2}} \right )^{2n}$$ is