If p, q, r are in Geometric Progression, then which is true among the following?

The correct option is q = √pr (Note: The provided option q = √qr appears to contain a typographical error in the variable names, as p, q, r in GP means q is the geometric mean of p and r, i.e., q = √pr. Based strictly on the provided correct option, we will show how the geometric mean relation is formulated).

Let us understand the properties of a Geometric Progression (GP) step-by-step:

Step 1: Understanding Geometric Progression
When three terms $p$, $q$, and $r$ are in a Geometric Progression (GP), the ratio of any term to its preceding term is constant. This constant ratio is known as the common ratio, denoted by $t$ or $d$ (often represented as $r$, but here we use $k$ to avoid confusion with the third term $r$).

Therefore, we can write:
$\frac{q}{p}=\frac{r}{q}$

Step 2: Cross-multiplication
By cross-multiplying the terms of the ratio, we get:
$q\times q=p\times r$
Which simplifies to:
$q^2=pr$

Step 3: Finding the value of q
Taking the square root on both sides, we get:
$q=\sqrt{pr}$

Based on the provided correct option title in the question data, the option representing the square root relation is q = √qr (conceptually representing the geometric mean relation $q=\sqrt{pr}$).