UGC NET Questions (Paper – 1)

Distance is calculated using the formula Distance = Speed × Time. The given speed is 60 km/h, but the time is 30 minutes, which is half an hour or 0.5 hours. Substituting into the formula gives Distance = 60 × 0.5 = 30 km. Hence, the train covers 30 kilometres in 30 minutes at this speed.

Option A:
Option A, 20 km, would correspond to a speed of 40 km/h for 30 minutes, not the given 60 km/h. It reflects a misalignment between speed and time.

Option B:
Option B, 25 km, does not correspond to any simple fraction of 60 using half an hour and indicates an incorrect multiplication or conversion.

Option C:
Option C, 40 km, would be the distance travelled in 40 minutes at 60 km/h, or in 2/3 of an hour, not in 30 minutes. Thus, it overestimates the distance for the time given.

Option D:
Option D correctly uses 0.5 hours as the time and multiplies by 60 km/h to get 30 km. This matches both the formula and the unit conversion from minutes to hours.

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.

Statements A and B correctly define speed and describe the inverse relationship between speed and time for a fixed distance. Statement E is also true because many aptitude questions demand consistent units, requiring conversions like km/h to m/s. Statement C is false since the average speed for a round trip with different speeds is given by the harmonic mean, not the simple arithmetic mean, and D is false because using consistent units, not different ones, avoids confusion. Therefore, the combination A, B and E only is correct.

Option A:
Option A is incomplete because although it includes two true statements, it omits E and thus fails to highlight the practical necessity of unit conversion in exam problems. Without E, the description of typical question features is not complete.

Option B:
Option B is correct as it collects all the true statements and rejects C and D, which misdescribe average speed and unit usage. It perfectly matches the conceptual treatment of time–speed–distance in UGC NET.

Option C:
Option C is wrong because it brings in C, which wrongly uses the arithmetic mean for round trips, and therefore mixes a false statement with true ones. This mathematical error invalidates the option.

Option D:
Option D is incorrect since it includes D, the mistaken claim about using different units, and omits A, which gives the core definition of speed. This combination misleads about both concept and practice.