Binomial Theore...

The coefficient of $${x^{49}}$$in the expansion of $$\left( {x - 1} \right)\left( {x - \frac{1}{2}} \right)\left( {x - \frac{1}{{{2^2}}}} \right).....\left( {x - \frac{1}{{{2^{49}}}}} \right)$$ is equal to 

Number of different terms in the sum $$ ( 1 + x ) ^ { 2009 } \cdot \left( 1 + x ^ { 2 } \right) ^ { 2008 } + \left( 1 + x ^ { 3 } \right) ^ { 2007 } , $$ is

The middle term of $$\left( { x-\cfrac { 1 }{ x }  } \right) ^{ 2n+1 }$$

Sum of coefficients of even powers of $$x$$ in expansion of $${\left( {1 + x + {x^2} + {x^3}} \right)^5}$$ is

If $$n$$ is even, then the middle term in the expansion of $$\Bigg ( x^2 + \dfrac{1}{x} \Bigg )^n$$ is $$924 x^6$$, then n is equal to 

If the second, third and fourth terms in the expansion of $${\left( {a + b} \right)^n}$$ are 135, 30 and 10/3 respectively, then the value of a is 

The number of terms in the expansion of  $$\left( x ^ { 2 } + 1 + \dfrac { 1 } { x ^ { 2 } } \right) ^ { n } , n \in  { N } ,$$  is :

The coefficient of $${ a }^{ 3 }{ b }^{ 4 }{ c }^{ 5 }$$ in the expansion of $${ (bc+ca+ab) }^{ 6 }$$ is 

If the number of terms in $$\left(x+1+\dfrac {1}{x}\right)^n (n\in I^{+})$$ is $$401$$, then $$n$$ is greater then

In the expansion of $$\left( { x }^{ 3 }-\dfrac { 1 }{ { x }^{ 2 } }  \right) ^{ n },\quad n\quad \epsilon \quad N,$$ if the sum of the coefficient of $${ x }^{ 5 }\quad and\quad { x }^{ 10 }\quad $$ is 0 then n is