UGC NET Questions (Paper – 1)

This series follows the rule aₙ = 2n⁴ + 5n² + 3 with n starting from 1. Substituting n = 1, 2, 3, 4 and 5 yields 2+5+3 = 10, 32+20+3 = 55, 162+45+3 = 210, 512+80+3 = 595 and 1250+125+3 = 1378, which matches the given numbers. For n = 6 we compute 2·6⁴+5·6²+3 = 2592+180+3 = 2775. Therefore 2775 is the unique next term consistent with this quartic-plus-quadratic-plus-constant structure.

Option A:
Option A, 2715, is 60 less than the formula output and does not satisfy aₙ = 2n⁴+5n²+3 for n = 6. It introduces an arbitrary downward adjustment that is not indicated by the previous terms. Hence option A is incorrect.

Option B:
Option B, 2775, equals exactly the value obtained by applying the expression to n = 6. It preserves the same coefficients and constant term that were used to generate all earlier entries in the series. Because it fits seamlessly into the algebraic rule, 2775 is the correct next term.

Option C:
Option C, 2835, overshoots the correct value by 60 and again does not arise from substituting n = 6 into the rule. Choosing 2835 would inflate the sixth term without any support from the structure of the series. Therefore option C is incorrect.

Option D:
Option D, 2895, deviates even more from the computed value and has no foundation in the expression 2n⁴+5n²+3. Using 2895 would destroy the precise link between index and term, so option D is incorrect.