In the expansion of ${\left( {3 - \sqrt {\frac{{17}}{4} + 3\sqrt 2 } } \right)^{15}}$ the 11th term is a

The coefficient of middle term in the expansion of $(1+{x})^{40}$ is

The value of the sum $\sum _{ j=0 }^{ 8 }{8 \choose j}{ \frac { 1 }{ (j+1)(j+2) } }$ is

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

The number of terms in the expansion of $\left\{ ( \sqrt {2}x +\sqrt {3} y)^{10} - ( \sqrt {2} x - \sqrt {3} y)^{10} \right\}$ is-