Binomial Theore...

The middle term in the expansion of $$\left( \dfrac { 2x^{ 2 } }{ 3 } +\dfrac { 3 }{ { 2 }x^{ 2 } }  \right) ^{ 10 }$$ is 

The sum of rational term in the expansion of $${(3^{\frac{1}{5}}+2^{\frac{1}{3}})}^{15}$$ is

The value of $$\displaystyle\sum^{10}_{r=0}$$ $$^{20}C_r$$ is equal to?

Coefficient of $$x^{2}$$ in the expansion of $$\left ( x-\frac{1}{2x} \right )$$is?

In the binomial expansion of $$(a-b)^{n}, n\ge 5$$, the sum of the $$5^{th}$$ and $$6^{th}$$ terms is zero, then $$a/b$$ is equals:

If $$x^2+7ax+40$$ and $$x^2+2ax-60$$ have a common factor , then find the value of a,

The number of non-zero terms in the expansion of $$(\sqrt{7}+1)^{75}-(\sqrt{7}-1)^{75}$$ is

The middle term in the expansion of $${ \left( x-\cfrac { 1 }{ 2x }  \right)  }^{ 10 }$$ is equal to

The number of rational terms in the expansion of $$\quad { \left( { 3 }^{ \cfrac { 1 }{ 4 }  }+{ 7 }^{ \cfrac { 1 }{ 6 }  } \right)  }^{ 144 }$$ is

In the expansion of $$(y^{1/5}+x^{1/10})^{55}$$, the number of terms free of a radical sign is