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.

The movement forms a right-angled triangle with legs of 4 km east and 3 km north. The straight-line distance from the starting point to the final point is the hypotenuse of this triangle. By the Pythagoras theorem, the hypotenuse is √(4² + 3²) = √(16 + 9) = √25 = 5 km. So the person is 5 km away from the starting point.

Option A:
Option A uses the classic 3–4–5 right-angled triangle pattern, which fits perfectly with the given distances. Applying Pythagoras correctly yields 5 km, making this the exact displacement from the origin.

Option B:
Option B, 6 km, overestimates the distance and would not satisfy the squared relationship 4² + 3² = 5². It suggests a hypotenuse of √36 when the correct sum of squares is 25.

Option C:
Option C, 7 km, exaggerates the distance even more and is not supported by any computed combination of the given legs. It is much larger than the true hypotenuse.

Option D:
Option D, 4 km, simply repeats one leg of the triangle and ignores the northward movement, so it cannot represent the actual straight-line displacement.