Binomial Theore...

The sum of coefficients of $$x^{2r},r=1,2,3,...,$$ in the expansion of $$(1+x)^{n}$$ is

The sum $$\displaystyle\frac{1}{2}$$ $$^{10}\textrm{C}_{0}-$$ $$^{10}\textrm{C}_{1}+$$ $$2\cdot  ^{10}\textrm{C}_{2}-$$ $$2^{2}\cdot  ^{10}\textrm{C}_{3}$$+...+$$2^{9}\cdot  ^{10}\textrm{C}_{10}$$ is equal to

The sum of coefficients of all the integral powers of  $$x$$ in the expansion of $$(1+2\sqrt{x})^{40}$$ is

The sum $$^{10}\textrm{C}_{3}+^{11}\textrm{C}_{3}+^{12}\textrm{C}_{3}+..........+^{20}\textrm{C}_{3}$$ is equal to

The sum of last ten coeffficients in the expansion of $$(1+x)^{19}$$ when expanded in ascending powers of $$x$$ is

The sum of the series $$\sum _{ r=0 }^{ 10 }{ _{  }^{ 20 }{ { C }_{ r }^{  } } } $$ is

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

The number of non-zero terms in the expansion of $${ \left( 1+3\sqrt { 2 } x \right)  }^{ 9 }+{ \left( 1-3\sqrt { 2 } x \right)  }^{ 9 }$$ is

The value of $$\displaystyle \sum_{j=1}^{n}(^{n+1}C_{j}-^{n}C_{j})$$is equal to

If $$\displaystyle C_{0},C_{1},C_{2},....C_{n}$$ are binomial coefficient in the expansion of $$\displaystyle (1+x)^{n}$$, then value of  $$\displaystyle C_{1}+C_{4}+C_{7}+...$$ equals