If the coefficients of the three successive terms in the binomial expansion of $(1 + x)^n$ are in the ratio $1 : 7 : 42,$ then the first of these terms in the expansion is

The term independent of $x$ in the expansion of ${\left( {\sqrt {\frac{x}{3}} + \frac{3}{{2{x^2}}}} \right)^{10}}$ will be

If some three consecutive in the binomial expansion of ${\left( {x + 1} \right)^n}$ in powers of $x$ are in the ratio $2 : 15 : 70$, then the average of these three coefficient is

If for some positive integer $n,$ the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+5}$ are in the ratio $5: 10: 14,$ then the largest coefficient in this expansion is

In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$ then $5^{th}$ term from the end is :-

The coefficient of the term independent of $x$ in the expansion of ${\left( {\sqrt {\frac{x}{3}}  + \frac{3}{{2{x^2}}}} \right)^{10}}$ is