MAH-CET 2026 — Reasoning PYQ

We can solve this problem quickly using standard visual logic or by using the standard angle formula.

Direct Visual Logic

1. A complete circle of a clock represents a total angle of $360^{\circ }$.

2. The clock dial is divided into $12$ equal hour sectors. The angle of each hour sector is:

   $$\text{Angle per hour gap}=\frac{360^{\circ }}{12}=30^{\circ }$$

3. At exactly $3:00$, the minute hand points directly at $12$ and the hour hand points directly at $3$.

4. The total number of hour gaps between $12$ and $3$ is exactly $3$ gaps ($12$ to $1$, $1$ to $2$, and $2$ to $3$).

5. Therefore, the angle $\theta$ between the hands is:

   $$\theta =3\times 30^{\circ }=90^{\circ }$$