UGC NET Questions (Paper – 1)

Statements A, B, C and E correctly describe the behaviour of clock hands and the nature of related aptitude questions: the minute and hour hands have known revolution times, their relative speed determines meeting or opposite positions and questions hinge on both angular calculations and relative motion. Statement D is false because the hour also affects the angle; for example, 3:00 and 4:00 have different angles even though the minutes are zero. Hence, the combination A, B, C and E only is correct.

Option A:
Option A is correct because it includes all the true statements while excluding D, which oversimplifies angular dependence by ignoring the hour. It reflects the standard method used to model clock questions in NET exams.

Option B:
Option B is incomplete since it omits E and so does not mention that these problems blend geometry and speed concepts. Without E, the description of the skill set tested is less comprehensive.

Option C:
Option C is wrong because it includes D, which incorrectly denies the effect of the hour hand on the angle, and it also omits A, failing to mention the minute hand’s revolution time. This mix of omission and error makes the option invalid.

Option D:
Option D is incorrect as it leaves out B, and so does not state that the hour hand takes 12 hours to complete a revolution, which is important for computing relative motion. The combination is thus incomplete even though some statements in it are true.

Statements A, B and C correctly give the basic angular speeds for clock hands: 360 degrees per full rotation, 6 degrees per minute for the minute hand and 0.5 degrees per minute for the hour hand. Statement E is also true because many questions involve finding when the hands coincide or form a given angle by using relative speed. Statement D is false since at 3:00 the angle between the hands is 90 degrees, not 60. Thus A, B, C and E together form the correct set.

Option A:
Option A is incomplete as it omits E and therefore does not mention the key technique of using relative speed, which is central for higher-level clock questions in NET. This makes the option only partially accurate.

Option B:
Option B is incomplete because it omits B (minute hand speed), so it does not include all true statements even though A, C and E are correct.

Option C:
Option C is correct because it includes all true statements and excludes D, which misstates the 3:00 angle. It represents the full conceptual toolkit for handling typical clock-angle questions.

Option D:
Option D is incorrect since it includes D, the wrong value for the angle at 3:00, and it omits A, ignoring the basic 360-degree fact. This mixture of an error with an omission makes the option invalid.

At 3:30, the minute hand is at 30 minutes, which is 30 × 6 = 180 degrees from 12 o’clock, since each minute corresponds to 6 degrees. The hour hand moves 30 degrees per hour plus 0.5 degrees per minute. By 3:30 it has moved 3 × 30 = 90 degrees for three full hours and 0.5 × 30 = 15 degrees for the extra 30 minutes, totalling 105 degrees. The angle between the two hands is |180 − 105| = 75 degrees, so 75 degrees is the correct answer.

Option A:
Option A, 45 degrees, might be chosen by wrongly assuming that the hour hand stays fixed exactly at 3 when the minute hand is at 6, but in reality the hour hand has advanced halfway towards 4 by 3:30.

Option B:
Option B, 60 degrees, would correspond to some other specific times but does not result from the correct calculation of the hands’ positions at 3:30. It underestimates the actual separation once the hour hand’s extra movement is considered.

Option C:
Option C carefully computes both hands’ positions using their respective angular speeds and then subtracts to find the included angle. This process gives 75 degrees, matching the standard result for this clock-angle case.

Option D:
Option D, 90 degrees, assumes that the hands are perpendicular at 3:30, but they are exactly perpendicular at 3:00; by 3:30 the hour hand has moved ahead, so the angle is less than 90 degrees.

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.