Binomial Theore...

If the expansion of $$\displaystyle\left(x^3+\frac{1}{x^2}\right)^n$$ contains a term independent of x, then the value of n can be

In the expansion of $${ \left( \dfrac { 3{ x }^{ 2 } }{ 5 } +\dfrac { 5 }{ 3{ x }^{ 2 } }  \right)  }^{ 10 }$$ mid term is

If the sum of the coefficients in the expansion of $$(l^2x^2-2lx+1)^{50}$$ vanishes then $$l$$ is equal to:

The term independent of $$x$$ in the expansion of $$\left [\sqrt {\dfrac {x}{3}} + \sqrt {\dfrac {3}{2x^{2}}} \right ]^{10}$$ is

If $$\sum _{ r=0 }^{ n-1 }{ { \left( \cfrac { { _{  }^{ n }{ C } }_{ r } }{ { _{  }^{ n }{ C } }_{ r }+{ _{  }^{ n }{ C } }_{ r+1 } }  \right)  }^{ 3 } } =\cfrac { 4 }{ 5 } $$ then $$n=$$

Sum of the last $$30$$ coefficients in the expansion of $${ \left( 1+x \right)  }^{ 59 }$$, when expanded in ascending power of $$x$$ is

If $$(1+x)^{10} = a_0 + a_1x + a_2x^2 + ..... + a_{10}x^{10}$$, then value of $$(a_0 -a_2 + a_4 - a_6 + a_8 - a_{10})^2 + (a_1 -a_3 + a_5 - a_7 + a_9)^2$$ is

The value of $$x$$ in the expression $${ \left( x+{ x }^{ \log _{ 10 }{ x }  } \right)  }^{ 5 }$$, if the third term in the expansion is $$1,000,000$$, is

If there is a term containing $$x^{2r}$$ in $$\left( x + \dfrac{1}{x^2} \right )^{n - 3}$$, then

Coefficient of $$x^n$$ in the expansion of $$\left(\displaystyle 1+\frac{x}{1!}+\frac{x^2}{2!}+...+\frac{x^n}{n!}\right)^2$$ is?