Binomial Theore...

The coefficient x$$^2 in (1 + 2x + 3x^2 +..)^{-3/2}$$ is

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

The sum of the coefficients in the expansion of $${\left( {1 + 5x - 7{x^3}} \right)^{3165}}$$ is 

The coefficient of $$  x^{49}  $$ in the product $$ (x-1)(x-3) \dots(x-99)  $$ is

If $${x^{15}} - {x^{13}} + {x^{11}} - {x^9} + {x^7} - {x^5} + {x^3} - x = 7$$ then 

Total number of terms in the expansion of [(1+x)$$^{100}$$+(1+x$$^{2}$$)$$^{100}$$+(1+x$$^{3}$$)$$^{100}$$] is 

Coefficient of $$x^{25}$$ in $$(1+x+x^2+x^3+....x^{10})^7$$ is 

The coefficient of $$\dfrac{1}{x}$$ in the expansion of $$(1+x)^n \Bigg (1 + \dfrac{1}{x} \Bigg )^n$$ is 

The number of distinct terms in the expansion of $$\left(x + \dfrac { 1 }{ x } + x^{ 2 } + \dfrac { 1 }{ x^{ 2 } }\right)^{ 15 }$$ is/are

The coefficient of t $$ t ^ { 4 } $$ in $$ \left( \frac { 1 - t ^ { 6 } } { 1 - t } \right) ^ { 3 } $$ is