Binomial Theore...

The term independent of $$x$$ in the expansion of $$\left(\sqrt{\dfrac{x}{3}}+\dfrac{3}{2x^{2}}\right)^{10}$$ will be

If the fourth term in the expansion of  $$\left( p x + \dfrac { 1 } { x } \right) ^ { n }$$  is  $$\dfrac { 5 } { 2 } ,$$  then  $$n + p$$  is equal to

The sum of the coefficients of the first three terms in the expansion of  $${\left( {x - \frac{3}{{{x^2}}}} \right)^m},\,x \ne 0$$ $$m$$ being a natural number is , $$559$$. Find the term of the expansion containing $$x^3$$

$$ \binom{n}{0}+2\binom{n}{1}+2^{2}\binom{n}{2}+......++2^{n}\binom{n}{n} $$ is equal to

The coefficient of  $$x ^ { 8 }$$  in the expansion of  $$\left( 1 + x ^ { 4 } \right) ^ { 3 } ( 1 - x ) ^ { 12 }$$  is

$$\dfrac{C_0}{1} + \dfrac{C_2}{3} + \dfrac{C_4}{5} + \dfrac{C_6}{7} ..... = $$

$$C_1 +2C_2 + 3C_3 +4C_4 + ......... + {n+1} nC_n$$

$$(1+x)^{21}+(1+x)^{22}+..+(1+x)^{30}$$ in the expansion of this what is the coefficient of $$x^{5}$$ is

The sum $$^ { 20 } \mathrm { C } _ { 0 } + ^ { 20 } \mathrm { C } _ { 1 } + ^ { 20 } \mathrm { C } _ { 2 } + \ldots \ldots . ^ { 20 } \mathrm { C } _ { 10 }$$ is equal to

Coefficient of $$x^ {79}$$ in the expansion of $$\left(x+x^ {2}+x^ {4}\right)$$ is equal to-