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.

A is correct because with downstream speed (b + s) and upstream speed (b − s), their average is b, the still-water speed. B is correct as the stream’s speed is half the difference of downstream and upstream speeds. D is true because if stream speed is zero, upstream and downstream speeds coincide, and E applies the standard time = distance ÷ speed relation used in these problems. C is false because upstream travel is slower and hence takes more time than downstream for the same distance. Therefore, A, B, D and E only are correct.

Option A:
Option A lists A, B and D but omits E, failing to mention the basic time formula that underlies most calculations in these problems. Because it does not include all true statements, it is incomplete.

Option B:
Option B is correct as it groups all true statements and excludes C, which reverses the comparison of upstream and downstream times. It reflects how relative speed, still-water speed and stream speed are handled in aptitude questions.

Option C:
Option C wrongly includes C, which claims upstream time is always less, and omits A, failing to describe the average-speed relationship. Including C makes this option logically incorrect.

Option D:
Option D includes C as well, and therefore it too inherits the error that contradicts basic time–speed relationships, despite including some correct statements. Hence it cannot be the right answer.

Distance is the product of speed and time. In 3 hours, the slower train at 40 km/h covers 40 × 3 = 120 km. The faster train at 60 km/h covers 60 × 3 = 180 km in the same time. The difference in distances is 180 − 120 = 60 km, so the faster train travels 60 km more than the slower one.

Option A:
Option A, 40 km, would be correct if the speed difference were 40 km/h for 1 hour, but here the speed difference is 20 km/h and the time is 3 hours.

Option B:
Option B, 50 km, has no direct basis in the given speeds and time and thus reflects an incorrect computation.

Option C:
Option C, 60 km, matches the product of the speed difference (60 − 40 = 20 km/h) and the common time of 3 hours. It properly accounts for how much farther the faster train travels in the same interval.

Option D:
Option D, 80 km, overstates the difference and would require either a larger gap in speed or a longer time interval.

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. Here, the relative speed is 15 + 17 = 32 km/h. After 3 hours, the distance between them is relative speed multiplied by time, which is 32 × 3 = 96 km. This distance represents how far apart they are from the starting point after 3 hours.

Option A:
Option A, 32 km, is only the distance they would be apart after 1 hour at the relative speed of 32 km/h and fails to account for the full 3 hours of travel.

Option B:
Option B, 90 km, underestimates the separation and could come from incorrectly adding or averaging speeds, but it does not match 32 × 3.

Option C:
Option C correctly multiplies the relative speed by time, applying the standard formula distance = speed × time for relative motion. This yields 96 km as the accurate separation.

Option D:
Option D, 102 km, overstates the distance and suggests a relative speed higher than 32 km/h, which is not given.

A is correct since opposing motions add speeds, and B is correct as same-direction relative speed is the difference between speeds. C is true because when trains cross, they must cover the sum of their lengths relative to each other. E is also correct because the units are consistent so distance is directly in kilometres. D is false because distance is speed × time, not speed ÷ time. Hence the combination A, B, C and E only is correct.

Option A:
Option A leaves out E, failing to note the important unit consistency that allows direct interpretation of distance in kilometres. Though it includes true statements, it is not complete.

Option B:
Option B omits A and thus does not mention the case of opposite direction motion, which is central for many train problems. This makes the description insufficient.

Option C:
Option C is incomplete because it leaves out B, ignoring the same-direction relative speed rule, and so does not cover all key cases used in exam questions.

Option D:
Option D is correct, bringing together all true statements and excluding D, which misstates the basic speed–distance relation. It matches the conceptual framework required for time–speed–distance and train problems.

In the first hour, from 8:00 to 9:00 a.m., the first bus travels 40 km. After 9:00 a.m., the second bus starts and the relative speed between the two buses is 60 − 40 = 20 km/h. To close a gap of 40 km at a relative speed of 20 km/h, the second bus needs 40 ÷ 20 = 2 hours. Adding 2 hours to 9:00 a.m. gives 11:00 a.m. as the overtaking time.

Option A:
Option A, 10:00 a.m., would correspond to only one hour of catch-up time, which would close a distance of 20 km at a relative speed of 20 km/h, leaving 20 km still between the buses.

Option B:
Option B, 10:30 a.m., gives 1.5 hours of catch-up and would close 30 km of the gap, not the full 40 km, so the faster bus would still be behind.

Option C:
Option C, 11:00 a.m., correctly accounts for the full 2 hours needed at a relative speed of 20 km/h to cover the initial 40 km head start, exactly matching the required condition for overtaking.

Option D:
Option D, 11:30 a.m., overshoots the required catch-up time; by then, the second bus would have been ahead of the first bus for half an hour already.

Statements A, B and C give core rules for relative speed questions. A is correct because approaching objects in opposite directions effectively close the distance at the combined speed. B is true since when moving in the same direction, the faster gains on the slower at the difference of their speeds. C is also correct because when trains cross each other completely, the total length to be covered relative to one another is the sum of their lengths. D is false because inconsistent units for speed and distance must be converted before using formulas, and E is false since on a circular track the time of meeting depends on relative speed, which involves differences for same-direction motion. Thus, A, B and C only are correct.

Option A:
Option A is incomplete as it lists only A and B and omits C, thereby failing to mention the specific structure of train-crossing problems where lengths are added.

Option B:
Option B is also incomplete since it includes only A and C and omits B, so it does not explicitly state how same-direction relative speed is computed.

Option C:
Option C is incomplete as it contains only B and C and omits A, losing the rule for opposite-direction motion.

Option D:
Option D is correct because it collects all three true statements about relative speeds and excludes D and E, which misrepresent unit conversion requirements and the nature of circular-track meetings.