UGC NET Questions (Paper – 1)

Average speed is defined as total distance divided by total time, not the average of the two speeds. The car travels 120 km each way, so the total distance is 240 km. The time taken in the first leg is 120 ÷ 40 = 3 hours and in the return leg is 120 ÷ 60 = 2 hours, giving a total of 5 hours. Dividing 240 by 5 yields 48 km/h as the average speed for the entire journey.

Option A:
Option A, 45 km/h, might be guessed by taking a simple average of the two speeds or by an approximate calculation, but it does not correspond to the correct total distance over total time.

Option B:
Option B uses the exact definition of average speed and calculates both distances and times explicitly. It also matches the harmonic mean formula for a round trip with equal distances, which simplifies to 2ab/(a + b).

Option C:
Option C, 50 km/h, exceeds the true average because more time is spent at the lower speed, pulling the overall average below the midpoint between 40 and 60.

Option D:
Option D, 52 km/h, is even higher and clearly inconsistent with spending a substantial part of the journey at just 40 km/h.

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.

Statement A gives the correct general definition of average speed. Statement C is the standard formula for average speed when equal distances are covered at two speeds, which equals the harmonic mean of the speeds. Statement D is also true because when equal times are spent at each speed, the average speed simplifies to the arithmetic mean. Statement B is false because the arithmetic mean does not apply for equal-distance segments, and E is false since confusing equal-distance with equal-time cases leads to wrong answers. Therefore, A, C and D only are correct, corresponding to option C.

Option A:
Option A is incomplete as it lists only A and C and omits D, failing to mention the equal-time case where the arithmetic mean does apply. This makes the description of average speed patterns incomplete.

Option B:
Option B is incorrect because it includes E, which says there is no need to distinguish between equal-distance and equal-time cases, an assertion that contradicts typical exam traps. It therefore contains a false statement.

Option C:
Option C is correct since it distinguishes the definitions for general, equal-distance and equal-time situations and explicitly excludes B and E, which misapply or trivialise the conditions.

Option D:
Option D is wrong as it contains B, the false claim about arithmetic mean for equal-distance travel, and it omits A, so it both adds an error and leaves out the basic definition of average speed.

Average speed is calculated as total distance divided by total time taken. Here, the distance is 120 km and the time is 3 hours. Dividing 120 by 3 gives 40 km/h. Therefore, the car’s average speed over the journey is 40 km/h.

Option A:
Option A is correct because the straightforward computation 120 ÷ 3 = 40 yields the average speed. This aligns with the definition of speed as distance per unit time. In exam settings, quickly identifying such basic calculations saves valuable time for more complex questions.

Option B:
An average speed of 30 km/h would correspond to travelling 90 km in 3 hours, not 120 km. Since the actual distance travelled is greater, this option underestimates the speed. Hence, it is incorrect.

Option C:
A speed of 50 km/h over 3 hours would give a distance of 150 km, which is higher than the given 120 km. This shows that 50 km/h is too high for the conditions described.

Option D:
A speed of 60 km/h for 3 hours would produce a distance of 180 km, which is much larger than 120 km. Therefore, 60 km/h does not match the data and cannot be the correct answer.