Correct Answer - Option 1 :

\(\sqrt{38}\)
__Concept:__

Let A(x1, y1, z1) and B(x2, y2, z2) be two point on a 3D plane then the distance between the points A and B is given by:\(\rm \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}\)

**Calculation:**

Given: A(1, 2, 5) and B(3, - 1, 0) are two points in a 3D plane.

As we know that, the distance between the points A(x1, y1, z1) and B(x2, y2, z2) is given by: \(\rm \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}\)

Let d be the distance between the points A and B.

\(\Rightarrow \rm d=\sqrt{(3-1)^{2}+(-1-2)^{2}+(0-5)^{2}}=\sqrt{4+9+25}=\sqrt{38}\)

Hence, the correct option is 1.