UGC NET Questions (Paper – 1)

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.

Statements A and B correctly describe basic facts about directions and displacement, and D is true because right-triangle paths allow the use of Pythagoras theorem to compute straight-line distance. Statement C is false since turning right from north leads to east, not west, and E is false because direction sense can be interpreted through coordinate geometry and vector concepts, making it quite related. Therefore, the set A, B and D only is correct.

Option A:
Option A is incomplete as it omits D and thus misses the important connection between direction sense paths and right-triangle geometry, which is central in many distance questions.

Option B:
Option B is correct because it includes all three true statements and excludes C and E, both of which misstate directional relationships or conceptual links. It accurately reflects how NET-level direction questions combine basic orientation with simple geometry.

Option C:
Option C is wrong since it includes C, the incorrect turning rule, and leaves out A, failing to mention the fundamental opposition of cardinal directions. This combination is therefore not acceptable.

Option D:
Option D is incorrect because it includes C and excludes B, thereby mixing an incorrect turning direction with a partial description of displacement and Pythagorean use.