Binomial Theore...

After simplification, the total number of terms in the expansion of $$ ( x + \sqrt { 2 } ) ^ { 4 } + ( x - \sqrt { 2 })^4 $$ is-

The number of integral terms in expansion $$(\sqrt [2]{3} + \sqrt [ 8 ]{ 5 } )^{256}$$ is 

If x=1/3, then the greatest term in the expansion of $$(1+4x)^{8}$$ is

The coefficient of the term independent of $$x$$ in the expansion of $$(1 - x)^2 \cdot \left(x + \dfrac{1}{x}\right)^{10}$$ is

$$\left (5^{\dfrac {1}{2}} + 7^{\dfrac {1}{6}}\right )^{642}$$ contains $$n$$ integral terms then $$n$$ is

Number of irrational terms in the expansion of $$\left( \sqrt { 2 } +\sqrt { 3 }  \right) ^{ 15 }\quad are$$

The coefficient of $${ x }^{ 4y }\quad in\quad the\quad expansion\quad of\quad (x-1)\left( x-\frac { 1 }{ 2 }  \right) \left( x-\frac { 1 }{ { 2 }^{ 2 } }  \right) ......\left( x-\frac { 1 }{ { 2 }^{ 49 } }  \right) $$ is equal to

The coefficient of  $$x ^ { 15 }$$  in the product of  $$( 1 - x )( 1 - 2 x ) \left( 1 - 2 ^ { 2 } x \right) \dots \ldots \ldots \ldots \left( 1 - 2 ^ { 15 } x \right)$$  is equal to

In the expansion of $${ x }^{ 2 }{ \left( \sqrt { x } +\frac { \lambda  }{ { x }^{ 2 } }  \right)  }^{ 10 }$$. The coefficient of $${ x }^{ 2 }$$ is $$720$$ then $$\lambda $$ is

The number of integral terms in the expansion of $$\displaystyle (5^ \frac{1}{2}+7^\frac {1}{6})^ {642}$$ is?