The terms $\log _3 2, \log _6 2, \log _{12} 2$ are in:

If $x_1, x_3$ are the roots of $A x^2 - 4 x + 1 = 0$ and $x_2, x_4$ are the roots of $B x^2 - 6 x + 1 = 0$ such that $x_1, x_2, x_3, x_4$ are in harmonic progression,then $\frac{B+A}{B-A} = $

Let $a_1, a_2, a_3, \dots$ be a harmonic progression where $a_1 = 5$ and $a_{20} = 25$. What is the smallest positive integer $n$ such that $a_n < 0$?

If $a, b, c$ are in $H.P.$,then the value of $\left( \frac{1}{b} + \frac{1}{c} - \frac{1}{a} \right) \left( \frac{1}{c} + \frac{1}{a} - \frac{1}{b} \right)$ is

If $a, b, c$ are in $H.P.$,then the value of $\left( \frac{1}{b} + \frac{1}{c} - \frac{1}{a} \right) \left( \frac{1}{c} + \frac{1}{a} - \frac{1}{b} \right)$ is

If $a, b, c$ are in a geometric progression and $a^x = b^y = c^z$,then in which progression are $x, y, z$?