UGC NET Questions (Paper – 1)

The differences alternate between +2 and +4: 7→9 (+2), 9→13 (+4), 13→15 (+2), 15→19 (+4) and 19→21 (+2). Following this pattern, the next difference should be +4. Adding 4 to 21 gives 25. Therefore, 25 is the next term that maintains the alternating pattern.

Option A:
Option A is 23, which would add only 2 to 21 and repeat the smaller jump twice in a row. That contradicts the +2, +4 alternation visible in the earlier terms. Hence, 23 is not correct.

Option B:
Option B equals 25, obtained by 21 + 4 and continuing the established +2, +4, +2, +4, +2, +4 sequence of differences. This keeps the pattern consistent and regular. Thus, 25 is the appropriate next term.

Option C:
Option C is 27, representing a jump of 6 from 21, which has not appeared anywhere in the difference sequence. Introducing +6 here would break the simple alternation between +2 and +4. Therefore, 27 cannot be chosen.

Option D:
Option D is 29, which corresponds to an increase of 8 from 21 and departs even further from the observed pattern. As there is no justification for such a large jump, this option is not acceptable.

Statements A, B, D and E highlight the main types of patterns used in number series questions and the techniques to detect them, so they are all correct. Arithmetic and geometric patterns are common, alternating patterns occur frequently, examining differences or ratios is a standard technique and many series use squares, cubes or factorials. Statement C is false because UGC NET series questions can use a wide variety of non-uniform rules, not just simple fixed additions. Therefore, the combination that includes A, B, D and E but excludes C is the only fully correct set.

Option A:
Option A is incorrect because although A, B and D are true, this option omits E, which correctly notes that higher powers and factorials often underlie series in competitive exams. Leaving out E makes the description incomplete and therefore not the best answer.

Option B:
Option B is correct as it brings together all the true statements about typical patterns and solution strategies while excluding the restrictive and incorrect claim in C. It reflects the variety of rules that a NET aspirant should expect in number series questions.

Option C:
Option C is wrong because it includes C, which wrongly asserts that every NET series is just fixed addition, and it omits A, so it fails to state explicitly that arithmetic and geometric patterns are central. This mixture of a false statement and an omission makes the option invalid.

Option D:
Option D is incorrect since it also contains C, the false statement about fixed addition, and does not include B, ignoring alternating or multi-step patterns. By endorsing C, this option misleads students about the range of series types in exams.

This series alternates between adding 2 and adding 3. Starting with 2, we have 2 + 2 = 4, 4 + 3 = 7, 7 + 2 = 9, 9 + 3 = 12 and 12 + 2 = 14. The pattern shows that after a +2 step comes a +3 step. Therefore, the next term should be 14 + 3 = 17, which preserves this alternation.

Option A:
Option A gives 16, which would correspond to adding 2 to 14 and repeating the same increment twice in a row. This violates the established alternation between +2 and +3. Hence, 16 is not consistent with the rule.

Option B:
Option B yields 17, which is obtained by adding 3 to 14 and correctly follows the alternation pattern. The series 2, 4, 7, 9, 12, 14, 17 remains structured as a repeating cycle of +2 and +3. Therefore, 17 is the correct next term.

Option C:
Option C suggests 18, which would require adding 4 to 14 and introducing an increment not seen anywhere else in the series. This makes the pattern unclear and irregular. Thus, 18 cannot be accepted.

Option D:
Option D offers 19, which is 5 more than 14 and again breaks the consistent use of 2 and 3 as increments. Choosing 19 would destroy the simple alternating pattern. Therefore, 19 is not the right answer.