In the expansion of ${\left( {\frac{a}{x} + bx} \right)^{12}}$,the coefficient of $x^{-10}$ will be
$12{a^{11}}$
$12{b^{11}}a$
$12{a^{11}}b$
$12{a^{11}}{b^{11}}$
The coefficient of ${x^{39}}$ in the expansion of ${\left( {{x^4} - \frac{1}{{{x^3}}}} \right)^{15}}$ is
Number of integral tems in the expansion of $\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824}$ is equal to..................
The term independent of $x$ in the expression of $\left(1-x^{2}+3 x^{3}\right)\left(\frac{5}{2} x^{3}-\frac{1}{5 x^{2}}\right)^{11}, x \neq 0$ is
The number of integral terms in the expansion of ${({5^{1/2}} + {7^{1/6}})^{642}}$ is
The greatest coefficient in the expansion of ${(1 + x)^{2n + 1}}$ is