Binomial Theore...

In the expansion of $${\left( {3 - \sqrt {\frac{{17}}{4} + 3\sqrt 2 } } \right)^{15}}$$ the 11th term is a

In the expansion of $$\displaystyle \left ( 3 -\sqrt{\dfrac{17}{4} + 3\sqrt{2}} \right )^{15}$$  the $$11^{th}$$ term is a :

The coefficient of $${ x }^{ 4 }$$ in the expansion of $${ (1+x+{ x }^{ 2 }+x }^{ 3 })^{ 4 }$$ is

The coefficient of $$x^n$$ in the expansion of $$\frac{1}{{(1 - x)(3 - x)}}$$ is 

The sum of the coefficients in the expansion of $${\left( {1 + x3{x^2}} \right)^{2163}}$$ will be

The co-efficient of $$x^5$$ in the expression of $${\left( {1 + x} \right)^{21}} + {\left( {1 + x} \right)^{22}} + .......... + {\left( {1 + x} \right)^{30}}$$ is :

The coefficient of $${x^9}$$ in $$\left( {x - 1} \right)\left( {x - 4} \right)\left( {x - 9} \right)......\left( {x - 100} \right)$$ is 

If the third term in the binomial expansion of $$(1 + x)^m$$ is $$-\frac{1}{8}x^2$$, the the rational value of m is-

If $${C_0},{C_1},{C_2},.....,{C_n}$$ are the binomial coefficients, then  $$2{C_1}+{2^3}{C_3}+{2^5}{C_5} + ...$$ equals

The sum of the coefficient in the expansion of $$(1+5x-7x^2)^{3546}$$ is