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.

Statements A, B and D are correct. A states the multiplication principle for independent choices. B defines permutations as ordered arrangements. D is true because there are n! ways to arrange n distinct objects. C is false; the formula for permutations of n distinct objects taken r at a time is nPr, and E is false because identical objects reduce the number of distinct permutations below n!. Thus A, B and D only are correct.

Option A:
Option A is correct as it includes the standard counting principle, the definition of permutations and the basic n! formula, while excluding C and E, which misapply combinatorial formulas.

Option B:
Option B is incorrect since it adds C, incorrectly using nCr in place of nPr for permutations, and so combines an error with correct statements.

Option C:
Option C is wrong because it also includes E, claiming n! permutations even with identical objects, and therefore contains two incorrect statements.

Option D:
Option D is incomplete as it drops A and leaves only B, D and E, losing the foundational multiplication principle and adding E, which contradicts the effect of identical objects.