Binomial Theore...

The number of rational terms in the expansion of $${ \left( 1+\sqrt { 2 } +\sqrt [ 3 ]{ 3 }  \right)  }^{ 6 }$$ is

If $${ x }^{ m }$$ occurs in the expansion of $$(x+\frac { 1 }{ { x }^{ 2 } } )^{ 2n }$$, the coefficient of $${ x }^{ m }$$, is 

The coefficient of x$$^{24}$$ in the expansion of 
(1 +3x + 6x$$^2$$ + 10x$$^3$$+ -----------+$$\infty$$)$$^{2/3}$$ =

The number of terms in the expansion of $${ \left[ { a }^{ 3 }+\dfrac { 1 }{ { a }^{ 3 } } +1 \right]  }^{ 100 }$$ is

The middle term in the expansion of $$\left(1-\dfrac{1}{x}\right)^{n}\left(1-x\right)^{n}$$ is

The coefficient of $$a^{3}b^{4}c$$ in the expansion of $$(1+a+b-c)^{9}$$ is 

If the middle term in the expansion of $$( 1 + x ) ^ { 2 n }$$ is the greatest term, then $$x$$ lies in the interval ___________________.

In the expansion of $$(\dfrac{1+x}{1-x})^2$$ , the coefficient of $$x^n$$ will be 

Coefficient of $${ t }^{ 12 }$$ in $$({ 1+t }^{ 2 }{ ) }^{ 6 }{ (1+t }^{ 6 }){ (1+t }^{ 12 })$$ is:

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