UGC NET Questions (Paper – 1)

Statement A correctly defines a common version of the Fibonacci sequence using a recurrence relation. C is true because the ratio of consecutive Fibonacci numbers tends toward the golden ratio as n increases. D is also correct, as Fibonacci-type recurrences are used to model branching patterns such as rabbit populations or tree growth in idealised models. B is false since Fibonacci terms are not simply double the previous term, and E is false because Fibonacci patterns frequently appear in exam puzzles and series problems. Thus A, C and D only are correct.

Option A:
Option A is incomplete because it includes only A and C and omits D, which highlights the important application of Fibonacci recurrences to growth processes, a point often emphasised in conceptual questions.

Option B:
Option B is incorrect since it lists only C and D and leaves out A, failing to define the sequence explicitly, and it does not address the incorrect claims about doubling or exam usage. It therefore does not capture the full set of correct statements.

Option C:
Option C is correct because it unites the standard definition, the limiting ratio property and an application-related statement, while excluding the false claims in B and E. This matches the way Fibonacci numbers are treated in NET mathematical reasoning.

Option D:
Option D is wrong as it includes B, which mistakenly describes the terms as doubling, along with A, C and D. The presence of this incorrect description makes the entire combination unacceptable.

This series follows the Fibonacci rule, where each term is the sum of the two preceding terms. We see 1+1 = 2, 1+2 = 3, 2+3 = 5 and 3+5 = 8, which confirms the pattern. Continuing this, the next term should be 5+8 = 13. So 13 is the correct next term in the sequence.

Option A:
Option A suggests 9, which would come from adding only 1 to the previous term 8 and does not use the sum of the last two terms. This ignores the clear recursive rule that defines the series. Therefore, 9 is not correct.

Option B:
Option B is 10, which again does not arise from adding any two consecutive terms in the series. There is no pair among the last two terms that sums to 10. Hence, it breaks the Fibonacci structure.

Option C:
Option C gives 11, which would require a different rule, such as adding 3 to 8, that has not appeared earlier. Since the series has consistently used sums of the two preceding numbers, 11 cannot fit the pattern.

Option D:
Option D equals 13, which is exactly 5+8 and respects the recursive rule used throughout. Extending the series to 1, 1, 2, 3, 5, 8, 13 maintains the Fibonacci property. Thus, this option correctly represents the next term.