If the Arithmetic Mean $(AM)$ $= 16$ and the Harmonic Mean $(HM)$ $= \frac{63}{4}$ for any two numbers,what will be the Geometric Mean $(GM)$?

Given an $A.P.$ and a $G.P.$ with positive terms, where the first and second terms of both progressions are equal. If $a_n$ and $b_n$ are the $n^{\text{th}}$ terms of the $A.P.$ and $G.P.$ respectively, then:

If $a^{1/x} = b^{1/y} = c^{1/z}$ and $a, b, c$ are in $G.P.$,then $x, y, z$ will be in

The geometric mean of two numbers is $6$ and their arithmetic mean is $6.5$. The numbers are

$A$ car completes the first half of its journey with a velocity $v_1$ and the rest half with a velocity $v_2$. Then the average velocity of the car for the whole journey is

If $x, y, z$ are in Arithmetic Progression $(AP)$ and $x, y, t$ are in Geometric Progression $(GP)$,then in which progression are $x, x - y, t - z$?