In the expansion of ${(1 + x)^n}$ the coefficient of $p^{th}$ and ${(p + 1)^{th}}$ terms are respectively $p$ and $q$. Then $p + q = $
$n + 3$
$n + 1$
$n + 2$
$n$
In the expansion of ${\left( {{x^2} - 2x} \right)^{10}}$, the coefficient of ${x^{16}}$ 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
If $7^{th}$ term from beginning in the binomial expansion ${\left( {\frac{3}{{{{\left( {84} \right)}^{\frac{1}{3}}}}} + \sqrt 3 \ln \,x} \right)^9},\,x > 0$ is equal to $729$ , then possible value of $x$ is
Write the general term in the expansion of $\left(x^{2}-y x\right)^{12}, x \neq 0$
The coefficient of $x ^7$ in $\left(1-x+2 x^3\right)^{10}$ is $........$.