MAH-CET 2026 — Reasoning PYQ

Method 1: Using the Standard Formula

The absolute angle $\theta$ between the hour hand and the minute hand at any given time $H\text{ hours}$ and $M\text{ minutes}$ can be directly calculated using the standard formula:

$$\theta =\left|30H-\frac{11}{2}M\right|$$

Given time is 4:30, so:

• $H=4$

• $M=30$

Substitute these values into the formula:

$$\theta =\left|30(4)-\frac{11}{2}(30)\right|$$

$$\theta =\left|120-11(15)\right|$$

$$\theta =\left|120-165\right|$$

$$\theta =\left|-45\right|=45^{\circ }$$

Method 2: Logical / Visual Approach

1. Position of the minute hand: At 30 minutes, the minute hand points precisely at the $6$ o'clock mark.

2. Position of the hour hand: At 4:00, the hour hand is exactly at $4$. In the next 30 minutes, the hour hand moves halfway toward $5$.

   • The angle covered by an hour hand in 1 minute is $0.5^{\circ }$.

   • Movement in 30 minutes: $30\times 0.5^{\circ }=15^{\circ }$ past the $4$ o'clock mark.

3. Total separation in gaps: Each hour gap on a clock dial represents $30^{\circ }$ (since $\frac{360^{\circ }}{12}=30^{\circ }$).

   • The complete gap between $5$ and $6$ is $30^{\circ }$.

   • The remaining gap between the hour hand (halfway between $4$ and $5$) and $5$ is:

     $$30^{\circ }-15^{\circ }=15^{\circ }$$

4. Calculate total angle:

   $$\theta =15^{\circ }\text{ (from hand to 5)}+30^{\circ }\text{ (from 5 to 6)}=45^{\circ }$$

Correct Answer

The correct option is (d) 45°.