Binomial Theore...

The sum of coefficient of integral powers of $$x$$ in the binomial expansion of $$(1-2\sqrt x)^{50}$$ is :

The value of $$\displaystyle \sum_{r = 1}^{15} r^{2} \left (\dfrac {^{15}C_{r}}{^{15}C_{r - 1}}\right )$$ is equal to:

Let $$(x + 10)^{50} +  (x - 10)^{50} = a_0 + a_1x + a_2x^2 + .... + a_{50} x^{50}$$, for all $$x \in R$$ then $$\dfrac{a_2}{a_0}$$ is equal to:-

The coefficient of $$x^{18}$$ in the product $$(1+x)(1-x)^{10}(1+x+x^2)^9$$ is?

Let $$s_n = 1 + q + q^2 + ................. + q^n$$ and 
$$T_n = 1 + \left(\dfrac{q + 1}{2}\right) + \left(\dfrac{q + 1}{2}\right)^2 +......... \left(\dfrac{q + 1}{2}\right)^n$$ 
 where q is a real number and q $$\neq$$ 1.
If $$^{101}C_1 + ^{101}{C_2}.S_{1} +...... + ^{101}C_{101}.S_{100} = \alpha T_{100}, then\,\,\, \alpha$$ is equal to :-

If $$(2+\dfrac {x}{3})^{55}$$ is expanded in the ascending powers of $$x$$ and the coefficients of powers of $$x$$ in two consecutive terms of the expansion are equal, then these terms are :

If the sum of odd numbered terms and the sum of even numbered terms in the expansion of $$(x + a)^{n}$$ are $$A$$ and $$B$$ respectively, then the value of $$(x^{2} - a^{2})^{n}$$ is

The coefficients of the $$ (3r)^{ th}$$ term and the $$(r + 2)^{ th}$$ term in the expansion $$(1 + x)^{2n}$$ are equal, then :

The number of rational terms in the expansion of $$(9^{1/4} + 8^{1/6})^{1000}$$ is:

In the expansion of $$(\sqrt 2+\sqrt [3]{5})^{20}$$ the number of rational terms will be: