UGC NET Questions (Paper – 1)

Statements A and B apply the multiplication principle and permutation formula correctly. A recognises that each of the 3 distinct books has 2 choices of shelf, so 2 × 2 × 2 = 2³ placements. B notes that 3 distinct books can be arranged in 3! orders on one shelf. C is false because identical books reduce the number of distinct permutations to 3!/2!, not 3!, and D is false because when counts depend on previous choices, we must adjust rather than blindly multiply m and n. E is false since choosing a student–teacher pair uses m × n, not m + n. Thus only A and B are correct.

Option A:
Option A is incomplete as it includes only statement A and omits B, thereby missing a standard example of permutations with distinct objects that is also correct.

Option B:
Option B is correct because it selects exactly the statements that correctly apply counting principles while excluding C, D and E, each of which misuses permutations or the multiplication rule. It reflects the proper reasoning expected in NET quantitative aptitude.

Option C:
Option C is wrong because it adds C, which ignores the effect of identical objects and incorrectly counts permutations as if all items were distinct.

Option D:
Option D is incorrect since it includes D and still allows the false “always m × n regardless of dependence” claim, so the combination cannot be correct.