Binomial Theore...

The sum of the co-efficients of all odd degree terms in the expansion of $${ \left( x+\sqrt { { x }^{ 3 }-1 }  \right)  }^{ 5 }+{ \left( x-\sqrt { { x }^{ 3 }-1 }  \right)  }^{ 5 }$$, $$\left(x>1\right)$$

If the number of terms in the expansion of $${ \left( 1-\dfrac { 2 }{ X } +\dfrac { 4 }{ { X }^{ 2 } }  \right)  }^{ n },x\neq 0,$$ is 28, then sum coefficients of all the terms in this expansion,is:

If $$\left | x \right |$$ < 1, then the coefficient of $$x^n$$ in the expansion of $$(1 + x + x^2 + x^3 + .....)^2$$ is

Number of terms which are rational in the expansion of $$(\sqrt[4]{5}+\sqrt[3]{4})^{100}$$ is 

The sum of rational terms in $$(\sqrt{2}+\sqrt[3] {3} +\sqrt[6] {5})^{10}$$

If $${ (1+x-{ 2x }^{ 2 }) }^{ 6 }=1+{ C }_{ 1 }x+{ C }_{ 2 }{ x }^{ 2 }+{ C }_{ 3 }{ x }^{ 3 }+...+{ C }_{ 12 }{ x }^{ 12 }$$, then the value of $${ C }_{ 2 }+{ C }_{ 4 }+{ C }_{ 6 }+...+{ C }_{ 12 }$$ is

The sum of the coefficients of all the even power of $$x$$ in the expansion of $${(2{x^2} - 3x + 1)^{11}}$$

The number of terms which are free from radical signs in the expansion of $$\left( \frac { 1 }{ { y }^{ 4 } } +\frac { 1 }{ { y }^{ 8 } }  \right) $$ is:

The coefficient of $${ x }^{ 49 }$$ in the expansion of $$(x-1)(x-\frac { 1 }{ 2 } )(x-\frac { 1 }{ 2^{ 2 } } ).....(x-\frac { 1 }{ 2^{ 49 } } )$$ is equal to -

If sum of the coefficient in the expression of $${ (-3{ x }^{ 2 }+\frac { 2 }{ x } ) }^{ 2n+1 }$$ is 'a' then the values of 'b' for which roots of the equation $${ x }^{ 2 }+bx+6a=0$$ are integral