Binomial Theore...

$$9^{th}$$ term in the expansion of $$\left (\dfrac {x}{a}-\dfrac {3a}{x^2}\right )^{12}$$ is:

The middle term in the expansion of $$(x + 4)^4$$ is:

Find the term which has the exponent of x as 8 in the expansion of $$\displaystyle\left(x^{\displaystyle\frac{5}{2}}-\frac{3}{x^3\sqrt{x}}\right)^{10}$$

Find the coefficient of the term independent of x in the expansion of $$\displaystyle\left(6x^3-\frac{5}{x^6}\right)^{12}$$.

If 'p' and 'q' are the coefficients of $$x^a$$ and $$x^b$$ respectively in $$(1+x)^{a+b}$$, then

If sum of the first 3 coefficients is $$16$$ in the expansion $$\displaystyle\left(x+\frac{1}{x^3}\right)^n$$, then find n.

The value of the sum $${ \left( _{  }^{ n }{ { C }_{ 1 } } \right)  }^{ 2 }+{ \left( _{  }^{ n }{ { C }_{ 2 } } \right)  }^{ 2 }+{ \left( _{  }^{ n }{ { C }_{ 3 } } \right)  }^{ 2 }+\dots +{ \left( _{  }^{ n }{ { C }_{ n } } \right)  }^{ 2 }$$ is

The coefficient of $$x^{10}$$ in the expansion of $$1 + (1 + x) + ...............................+(1 + x)^{20}$$ is

The middle term in the expansion of $$(1 + x)^{2n}$$ is

The number of irrational terms in the binomial expansion of $$(3^{1/5}+7^{1/3})^{100}$$ is