If $b + c, c + a, a + b$ are in $H.P.$,then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ are in

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 the harmonic mean between $a$ and $b$ is $H$,then $\frac{H + a}{H - a} + \frac{H + b}{H - b} = $

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 $a_n < 0$?

Let $f(x) = x + 1/2$. Then, the number of real values of $x$ for which the three unequal terms $f(x), f(2x), f(4x)$ are in $HP$ is

If $a, b, c, d$ are in $H.P.$,then $ab + bc + cd$ is equal to