UGC NET Questions (Paper – 1)

The word BANANA has 6 letters, with A repeated 3 times, N repeated 2 times and B appearing once. The formula for permutations of n objects with repeated groups is n! divided by the product of factorials of the counts of repeated items. Here this gives 6! ÷ (3! × 2!). Evaluating this gives 720 ÷ (6 × 2) = 720 ÷ 12 = 60. So there are 60 distinct arrangements of the letters of BANANA.

Option A:
Option A, 30, underestimates the total arrangements and would correspond to a different combination of repeats or a smaller word. It does not follow the factorial formula for this word.

Option B:
Option B, 36, arises from miscalculating either 6! or one of the factorials in the denominator. It does not equal 720 ÷ 12 and so fails to match the correct combinatorial reasoning.

Option C:
Option C, 48, again does not match the computed result and suggests partial adjustment for repetition without applying the full divisor 3! × 2!.

Option D:
Option D carefully applies the repetition-adjusted permutation formula. It fully accounts for indistinguishable arrangements caused by repeated letters and yields the correct count of 60.