Let the positive numbers $a, b, c, d$ be in $A.P.$,then $abc, abd, acd, bcd$ are

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a harmonic progression are $u$,$v$,and $w$ respectively,then the value of $(q - r)vw + (r - p)wu + (p - q)uv$ is equal to:

If $\frac{1}{b + c}, \frac{1}{c + a}, \frac{1}{a + b}$ are in Arithmetic Progression $(AP)$,then $a^2, b^2, c^2$ are in which progression?

If $X = \sum_{n=0}^\infty a^n$,$Y = \sum_{n=0}^\infty b^n$,and $Z = \sum_{n=0}^\infty c^n$,where $a, b, c$ are in arithmetic progression and $|a| < 1, |b| < 1, |c| < 1$,then $X, Y, Z$ are in . . . . progression.

If $p, q, r$ are in harmonic progression and $p$ and $r$ are distinct and have the same sign,then what is the nature of the roots of the equation $px^2 + 2qx + r = 0$?

If $\ln(a + c)$,$\ln(c - a)$,and $\ln(a - 2b + c)$ are in $A.P.$,then