Permutations combinations and arrangements – UGC NET Question

Statements A, B, D and E are all correct descriptions of the role of permutations and combinations. Permutations count ordered arrangements, combinations count unordered selections, seating arrangement problems rely heavily on order-based counting, and both concepts are frequently tested in UGC NET aptitude. Statement C is false because, for r greater than 1, nPr is larger than nCr since each combination can be arranged in several ordered ways. Thus the only option that includes all true statements while excluding the false one is the combination A, B, D and E.

Option A:
Option A is incomplete because it omits E, failing to note explicitly that both permutations and combinations are actively used in NET mathematical reasoning questions. Without E, the statement about exam relevance is missing.

Option B:
Option B is correct because it gathers A, B, D and E, which together present the conceptual distinction between order and selection and their examination usage, while rightly rejecting C, which reverses the relative sizes of permutations and combinations.

Option C:
Option C is incorrect since it leaves out A and therefore does not mention that permutations are arrangements where order matters, a central concept for the topic. Though it contains some true statements, it is not complete.

Option D:
Option D is wrong because it includes C, the false claim that nPr is always less than nCr, and thereby mixes an incorrect statement with true ones. The presence of C makes the entire combination unacceptable.