If the roots of $x^3-k x^2+14 x-8=0$ are in geometric progression,then $k$ is equal to

If the roots of the equation $x^3-13x^2+Kx-27=0$ are in geometric progression,then $K=$

The three sides of a right-angled triangle are in $GP$ (geometric progression). If the two acute angles are $\alpha$ and $\beta$,then $\tan \alpha$ and $\tan \beta$ are

The geometric mean of $7, 7^2, 7^3, \dots, 7^n$ is .....

For a sequence $(t_n)$,if $S_n = 5(2^n - 1)$,then $t_n = \ldots$

In a certain test,there are $n$ questions. In this test,$2^{n-i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, \ldots, n$. If the total number of wrong answers given is $2047$,then $n$ is equal to: