Binomial Theore...

The coefficient if $$ x^6 $$ in the expansion of  $$ ( 3x^2 - \frac {1}{3x})^9 $$ is

The largest term in the expansion of $$\left(\frac{b}{2} + \frac{b}{2}\right)^{100}$$ is 

Which of the following expansion will have term containing $$x^2$$

If the second term in the expansion $$\displaystyle \lgroup ^{13}\sqrt{a} + \frac{a}{\sqrt{a^{-1}}} \rgroup^n$$ is $$\displaystyle 14a^{5/2}$$, then the value of $$\displaystyle ^nC_3/^nC_2$$ is

If $$\displaystyle ( 1+ 2x + 3x^2)^{10} = a_0 + a_1x + a_2x^2 + \dots + a_{20}x^{20}$$ then $$a_1$$equals

If the fourth term of $$\displaystyle \left(\sqrt{_x\left(\frac{1}{1 + \log_{10} x}\right)} + ^{12}\sqrt{x} \right)^6$$ is equal to 200 and x > 1, then x is equal to 

The sum of rational term in $$(\sqrt 2+\sqrt [3]{3}+\sqrt[6]{5})^{10}$$ is equal to 

The number of distinct terms in the expansion of $$\left( x+\dfrac{1}{x}+x^2+\dfrac{1}{x^2}\right)^{15}$$ is/are ( with respect to different power of $$x$$ )

The number of terms in the expansion of $$\bigg(\dfrac{a}{x}+bx\bigg)^{12}$$ are 

The general term in the expansion of $$(x + a)^n$$