Binomial Theore...

Coefficient of $$x ^ { 10 }$$ in $$\left( 1 + 2 x ^ { 4 } \right) ( 1 - x ) ^ { 8 }$$ is

The coefficient of $$x^{-2}$$ in $$(1+3x^2+x^4)\left(1+\dfrac{1}{x}\right)^8$$ is

The coefficient of $$x^2$$ in expansion of the product
(2 $$x^2$$).($$(1 + 2x + 3x^2)^6$$ + $$(1 4x^2)^6$$) is :

Coefficient of $$x^8$$ in $$(x-1)(x-2)(x-3)..(x-10)$$ is?

If $$| x | < 2 / 3$$ then the fourth term in the expansion of $$\left( 1 + \frac { 3 } { 2 } x \right) ^ { 1 / 2 }$$ is

The number of terms which are free from radical signs in the expansion of $$(y^{1/5} + x^{1/10})^{55}$$ is

Coefficient of $${ x }^{ 2009 }in(1+x+{ x }^{ 2 }+{ x }^{ 3 }+{ x }^{ 4 }{ ) }^{ 1001 }{ \left( 1-x \right)  }^{ 1002 }$$ IS...

The sum of the coefficients in the expansion (6a-5b) when n is a positive integer, is 

The number of irrational terms in the expansion of  $$\left( 5 ^ { 1 / 6 } + 2 ^ { 1 / 8 } \right) ^ { 100 }$$  is :