In the expansion of the following expression $1 + (1 + x) + {(1 + x)^2} + ..... + {(1 + x)^n}$ the coefficient of ${x^k}(0 \le k \le n)$ is

The coefficient of $x^{18}$ in the product $(1+ x)(1- x)^{10} (1+ x + x^2 )^9$ is 

Find a positive value of $m$ for which the coefficient of $x^{2}$ in the expansion $(1+x)^{m}$ is $6$

The coefficient of $x^{37}$ in the expansion of $(1-x)^{30} \, (1 + x + x^2)^{29}$ is :

In the expansion of ${\left( {\frac{a}{x} + bx} \right)^{12}}$,the coefficient of $x^{-10}$ will be

The term independent of $x$ in the expansion of ${(1 + x)^n}{\left( {1 + \frac{1}{x}} \right)^n}$ is