Clock Angle General Case – UGC NET Question

At 5:40, the minute hand is at 40 minutes, corresponding to 40 × 6 = 240 degrees from the 12 o’clock position. The hour hand moves 30 degrees per hour plus 0.5 degrees per minute. By 5:40, it has moved 5 × 30 = 150 degrees for five full hours and 0.5 × 40 = 20 degrees for the extra minutes, totalling 170 degrees. The angle between the hands is 240 − 170 = 70 degrees. This is less than 180 degrees, so it is already the smaller angle between the two hands.

Option A:
Option A, 70 degrees, comes directly from the standard formulas for hand positions and the absolute difference between them, so it correctly represents the smaller angle.

Option B:
Option B, 90 degrees, would make the hands perpendicular, which they are not at 5:40 because the hour hand has moved well past the 5 while the minute hand points to 8 on the dial.

Option C:
Option C, 100 degrees, overestimates the separation and does not match the computed difference between 240 degrees and 170 degrees.

Option D:
Option D, 120 degrees, corresponds to an even wider angle and clearly contradicts the calculated positions of the hour and minute hands at 5:40.