UGC NET Questions (Paper – 1)

This sequence follows the rule aₙ = n⁴ + 3n³ + n for n starting from 1. Evaluating for n = 1, 2, 3, 4 and 5 gives 1+3+1 = 5, 16+24+2 = 42, 81+81+3 = 165, 256+192+4 = 452 and 625+375+5 = 1005. For n = 6, we compute 6⁴+3·6³+6 = 1296+648+6 = 1950. Therefore 1950 is the unique next term that respects this quartic-plus-cubic-plus-linear pattern.

Option A:
Option A, 1950, matches exactly the result of n⁴+3n³+n when n = 6. It maintains the same combination of powers and coefficients that explain all the earlier terms. Because it arises directly from the established rule, this option correctly continues the sequence.

Option B:
Option B, 1938, is 12 less than the computed value and cannot be written as n⁴+3n³+n for n = 6. It implies a downward adjustment that does not appear anywhere in the earlier terms. Consequently, option B breaks the pattern and is incorrect.

Option C:
Option C, 1968, overshoots the correct polynomial value and likewise does not equal 6⁴+3·6³+6. Choosing 1968 would arbitrarily raise the sixth term relative to the rule. Therefore option C is not consistent with the functional relationship governing the series.

Option D:
Option D, 1980, departs even further from the formula’s output and has no basis in the given expression. Using 1980 would discard the tight connection between term position and term value, so option D cannot be correct.