Binomial Theore...

The number of irrational terms in the expansion of$$( \sqrt [ 8 ] { 5 } + \sqrt [ 6 ] { 2 } ) ^ { 100 } ,$$ is

The number of irrational terms in the expansion of$$( \sqrt [ 8 ] { 5 } + \sqrt [ 6 ] { 2 } ) ^ { 100 } ,$$ is

The value of m, for which the coefficients of the $$\left( {2m + 1} \right)$$ and $${\left( {4m + 5} \right)^{th}}$$ terms in the expansion $${\left( {1 + x} \right)^{10}}$$ are equal, is:

The number of terms in the expansion of $$ ( 2 x + 3 y - 4 z ) ^ { n } $$ ,is

COEFFICIENT OF $$x^k$$ IN $$(ax + b)^n$$
The coefficient if x in the expansion of $$\displaystyle (1 2x^3 + 3x^5)\left ( 1 + \dfrac{1}{x} \right )^8 $$ is 

In the expansion of $${ \left( { x }^{ 2 }+1+\frac { 1 }{ { x }^{ 2 } }  \right)  }^{ n }$$, $$n\in N$$, then

The sum of coefficients of integral powers of $$x$$ in the binomial expansion of $${\left(1-2\sqrt{x}\right)}^{-n}$$ is

The coefficient of $$x ^ { 4 }$$ in the expansion of $$\left( 1 + x + x ^ { 2 } + x ^ { 3 } \right) ^ { 11 }$$ is

In the expression of $$(1+x)^{50}$$. Let S  be the sum of coefficient of odd power of x. then S is:

If the last term in the binomial expansion of $$ (2{  }^{ \frac { 1 }{ 3 }  }-\frac { 1 }{ \sqrt { 2 }  } ){  }^{ n }\quad is\quad (\frac { 1 }{ { 3 }^{ \frac { 5 }{ 3 }  } } ){  }^{ log{  }_{ 3 }8 }$$ , then the 5th term from the beginning  is