Clocks: Angle & Mirror Image

A targeted practice drill on Clock reasoning problems frequently featured in Kerala PSC examinations. It covers angle calculations using the standard formula $$\theta = |30H - \frac{11}{2}M|$$, vertical mirror image times ($$11:60 - \text{time}$$), coinciding and right-angle frequencies, and relative speeds of hands.

Study Scope

• Angle Formula: $$\theta = |30H - \frac{11}{2}M|$$ and reflex angles ($$360^\circ - \theta$$)
• Mirror Reflection: Calculating reflected clock face time using $$11:60$$ or $$23:60$$
• Hand Speeds: Minute hand ($$6^\circ/\text{min}$$), hour hand ($$0.5^\circ/\text{min}$$), relative gain ($$5.5^\circ/\text{min}$$)
• Coinciding & Right Angles: $$11$$ overlaps in $$12$$ hrs, $$22$$ right angles in $$12$$ hrs

Tested Competencies

• Calculate angles between hands in seconds without arithmetic errors
• Instantly compute mirror reflections without manual clock sketching
• Recall standard frequency constants for overlaps, opposites, and right angles