Coefficient of $x^3$ in the expansion of $(x^2 - x + 1)^{10} (x^2 + 1 )^{15}$ is equal to
$-360$
$-240$
$-180$
$60$
Evaluate $(\sqrt{3}+\sqrt{2})^{6}-(\sqrt{3}-\sqrt{2})^{6}$
The value of $x$, for which the 6th term in the expansion of ${\left\{ {{2^{{{\log }_2}\sqrt {({9^{x - 1}} + 7)} }} + \frac{1}{{{2^{(1/5){{\log }_2}({3^{x - 1}} + 1)}}}}} \right\}^7}$ is $84$, is equal to
The coefficients of three consecutive terms in the expansion of $(1+a)^{n}$ are in the ratio $1: 7: 42 .$ Find $n$
If the coefficients of $x^{7}$ and $x^{8}$ in the expansion of $\left(2+\frac{x}{3}\right)^{n}$ are equal, then the value of $n$ is equal to $.....$
In the expansion of ${\left( {\frac{{3{x^2}}}{2} - \frac{1}{{3x}}} \right)^9}$,the term independent of $x$ is