Which term of the following sequence: $\sqrt{3}, 3, 3\sqrt{3}, \ldots$ is $729$ (in $^{\text{th}}$)?

If the roots of the equation $x^3 - ax^2 + bx - c = 0$ are in $GP$,then $\frac{b^3}{a^3}$ is equal to:

If $4^{\text{th}}$,$10^{\text{th}}$,and $16^{\text{th}}$ terms of a $G$.$P$. are $x, y$,and $z$ respectively,then

Which term of the $GP$ $2, 8, 32, \ldots$ is $131072$ (in $^{\text{th}}$)?

$A$ particle starts at the origin and moves $1$ unit horizontally to the right and reaches $P_{1}$, then it moves $\frac{1}{2}$ unit vertically up and reaches $P_{2}$, then it moves $\frac{1}{4}$ unit horizontally to the right and reaches $P_{3}$, then it moves $\frac{1}{8}$ unit vertically down and reaches $P_{4}$, then it moves $\frac{1}{16}$ unit horizontally to the right and reaches $P_{5}$ and so on. Let $P_{n} = (x_{n}, y_{n})$ and $\lim_{n \rightarrow \infty} x_{n} = \alpha$ and $\lim_{n \rightarrow \infty} y_{n} = \beta$. Then, $(\alpha, \beta)$ is

If $\alpha, \beta$ are the roots of $x^2 - 3x + a = 0$ and $\gamma, \delta$ are the roots of $x^2 - 12x + b = 0$,and the numbers $\alpha, \beta, \gamma, \delta$ (in order) form an increasing $G.P.$,then: