UGC NET Questions (Paper – 1)

Each term after the first is obtained by doubling the previous term and adding 2. We have 1 × 2 + 2 = 4, 4 × 2 + 2 = 10, 10 × 2 + 2 = 22, 22 × 2 + 2 = 46 and 46 × 2 + 2 = 94. Applying the same rule to 94 gives 94 × 2 + 2 = 188 + 2 = 190. This maintains a clear and consistent recursive relationship.

Option A:
Option A gives 186, which does not equal 94 × 2 + 2 and would require reducing or changing the constant term. This is not supported by any previous step. Hence, 186 is not correct.

Option B:
Option B offers 188, corresponding to 94 × 2, but misses the required addition of 2 that appears in every transition. This makes the pattern incomplete. Therefore, 188 cannot be accepted.

Option C:
Option C suggests 192, which adds 4 after doubling 94 and introduces a new constant unobserved earlier. This breaks the precise rule of "+2" at the end. Thus, 192 is not appropriate.

Option D:
Option D yields 190, exactly equal to 94 × 2 + 2, and continues the series under one stable transformation. The sequence 1, 4, 10, 22, 46, 94, 190 remains coherent. Therefore, 190 is the correct next term.

The first-level differences are 15, 25, 35 and 45. These differences themselves form an arithmetic progression with common difference 10. Thus the next difference should be 55. When 55 is added to the last term 128, we obtain 183, which continues the pattern at both the term level and the difference level.

Option A:
Option A gives 178, which would create a difference of 50 from 128. This would make the sequence of differences 15, 25, 35, 45, 50, where the last increase is 5 rather than 10. Hence 178 breaks the structure of the second-level arithmetic progression.

Option B:
Option B gives 188, corresponding to a difference of 60 from 128. That would yield differences 15, 25, 35, 45, 60, causing the final increment to jump by 15 instead of 10. Therefore 188 does not preserve the consistent behaviour among the gaps.

Option C:
Option C gives 183, leading to a difference of 55 from 128. The differences become 15, 25, 35, 45, 55, a clear arithmetic progression with constant step 10. This perfect alignment with the observed pattern makes 183 the correct next term.

Option D:
Option D gives 193, implying a difference of 65 from 128. This creates an irregular spike in the differences and abandons the neat step of 10 between them. Consequently, 193 is not a valid continuation of the series.

This series alternates between adding 3 and multiplying by 2. Starting with 5, we have 5 + 3 = 8, 8 × 2 = 16, 16 + 3 = 19, 19 × 2 = 38, 38 + 3 = 41 and 41 × 2 = 82. The next operation should be addition by 3. Thus, the next term is 82 + 3 = 85, which continues the alternating pattern exactly.

Option A:
Option A gives 83, which would require adding only 1 to 82 and introduces a new increment not used previously. This breaks the uniform "+3, then ×2" rule. Therefore, 83 is not consistent with the pattern.

Option B:
Option B offers 84, whose difference from 82 is 2, again incompatible with the fixed addition of 3 in the pattern. This makes the series irregular. Hence, 84 cannot be accepted.

Option C:
Option C suggests 87, which requires adding 5 to 82 and does not conform to the standard "+3" step seen throughout. This disrupts the structured alternation. Thus, 87 is not appropriate.

Option D:
Option D yields 85, which is exactly 82 + 3 and matches the next stage of the "+3, then ×2" cycle. The series 5, 8, 16, 19, 38, 41, 82, 85 remains coherent. Therefore, 85 is the correct next term.

The differences between the terms are 3, 6, 9 and 12. These differences form a simple arithmetic progression where each difference increases by 3. Following this logic, the next difference should be 15. Adding 15 to the last term 40 gives 55, which continues the pattern in a consistent manner.

Option A:
Option A yields 55, which is 15 greater than 40 and extends the difference sequence to 3, 6, 9, 12, 15. This smooth increase by 3 at the second level is exactly what the pattern suggests. Therefore, 55 is the correct next term in the series.

Option B:
Option B gives 53, which corresponds to a difference of 13 and does not match the expected multiple of 3. This breaks the uniform pattern of the differences. Hence, 53 cannot be considered correct.

Option C:
Option C suggests 57, which would produce a difference of 17 from 40, again not a multiple of 3 and out of step with the existing sequence of differences. Thus, 57 is not consistent with the pattern.

Option D:
Option D offers 60, which is 20 more than 40 and introduces a much larger difference than the expected 15. This disrupts the clear second-level arithmetic structure and makes the series irregular. Therefore, 60 is not an appropriate continuation.

Each term decreases by 8: 72 − 80 = −8, 64 − 72 = −8, 56 − 64 = −8 and 48 − 56 = −8. Maintaining this constant difference, we subtract 8 from 48 to get 40. Therefore, 40 is the correct next term in the series.

Option A:
Option A is 42, which is 6 less than 48 and would change the difference to −6. This contradicts the steady −8 observed earlier. Hence, 42 is not correct.

Option B:
Option B is 44, implying a difference of −4 from 48. That halves the magnitude of the step and breaks the pattern of equal decreases. Therefore, 44 cannot be accepted.

Option C:
Option C is 46, giving a difference of −2, which is far from the established −8. It would indicate a slowing decline not supported by earlier terms. Thus, 46 is not suitable.

Option D:
Option D equals 40, obtained by 48 − 8 and preserving the constant step of −8. The extended sequence 80, 72, 64, 56, 48, 40 remains a neat arithmetic progression. This confirms 40 as the correct continuation.

The differences between successive terms are 5, 10, 20 and 40, each approximately doubling the previous difference. If this pattern continues, the next difference should be 80. Adding 80 to the last term 79 gives 159. Therefore, 159 is the correct next term in the sequence.

Option A:
Option A is 120, which gives a difference of 41 from 79 and does not align with the expected 80. This breaks the doubling behaviour of the differences. Hence, 120 is not correct.

Option B:
Option B is 140, implying a difference of 61, which again fails to match the predicted 80. It does not continue the simple doubling rule. Therefore, 140 cannot be accepted.

Option C:
Option C equals 159 and produces the new difference 80, following 5, 10, 20 and 40 in a clear doubling pattern. The extended differences 5, 10, 20, 40, 80 make the structure consistent. Thus, 159 is the valid continuation.

Option D:
Option D is 180, giving a difference of 101 from 79. That has no relation to the doubling sequence of differences and therefore breaks the pattern. So, 180 is not suitable.

The nth term of this series can be expressed as (a_n = 2n^2 + 1) for n starting from 2. For n = 2, 3, 4, 5 and 6, the values are 2·4+1 = 9, 2·9+1 = 19, 2·16+1 = 33, 2·25+1 = 51 and 2·36+1 = 73, which exactly match the given sequence. For n = 7, the expression yields 2·49+1 = 99. Hence 99 is the correct continuation of the series.

Option A:
Option A, 95, does not equal 2n²+1 for any integer n that naturally follows 2 to 6 here. Using 95 would force a change in the generating rule and so is inconsistent with the polynomial pattern.

Option B:
Option B, 97, also fails to satisfy the formula 2n²+1 for the next integer n. It appears close numerically but does not arise from the same expression, so it breaks the functional relationship.

Option C:
Option C, 98, lies between 97 and 99 but again does not equal 2·49+1. Adopting 98 would mean abandoning the clear square-based rule that explains all earlier terms.

Option D:
Option D, 99, matches precisely the value predicted by the formula for n = 7. Since the same expression generates each term, 99 preserves the structure and therefore is the correct next term.

The first-level differences are 3, 7, 11, 15 and 19. These differences form an arithmetic progression with common difference 4. Following this pattern, the next difference should be 23. Adding 23 to the last term 57 gives 80, so 80 is the next term that keeps both levels of the pattern consistent.

Option A:
Option A gives 76, which corresponds to a difference of 19 from 57. This simply repeats the last difference and leads to difference values 3, 7, 11, 15, 19, 19, breaking the steady increase by 4. Therefore 76 cannot be the correct continuation.

Option B:
Option B gives 80, which implies a difference of 23 from 57. The differences become 3, 7, 11, 15, 19, 23, forming a clean arithmetic progression with step 4. Hence 80 is fully consistent with the structure of the sequence and is the correct answer.

Option C:
Option C gives 82, leading to a difference of 25 from 57. That would make the final increment between differences equal to 6 instead of 4, distorting the neat second-level pattern. Thus 82 is not suitable.

Option D:
Option D gives 84, implying a difference of 27 from 57, which makes the last step among differences equal to 8. This change is too abrupt and inconsistent with the established progression, so 84 cannot be accepted.

The differences are −5, −8, −11 and −14, which decrease by 3 each time. The next difference should therefore be −17. Adding −17 to the last term 12 gives 12 − 17 = −5. Hence, −5 is the correct next term in the series.

Option A:
Option A uses the new difference −17 and yields −5, keeping the second-level pattern of subtracting 3 from each successive difference. The extended sequence of differences −5, −8, −11, −14, −17 remains consistent. Thus, −5 correctly continues the series.

Option B:
Option B is 0, which would require subtracting 12 from 12, corresponding to a difference of −12. That does not follow the −5, −8, −11, −14 progression. Therefore, 0 is not correct.

Option C:
Option C is 2, which implies a difference of −10 from 12. This value does not arise from continuing the pattern of reducing differences by 3. Hence, 2 cannot be accepted.

Option D:
Option D is 4, yielding a difference of −8, which repeats an earlier step rather than moving further by −3. This breaks the steadily changing differences and is therefore not suitable.

Statements A, B, D and E correctly describe number and letter series questions. Such questions are built on patterns or rules, often using numerical sequences or alphabetical positions and skips, and they test a candidate's ability to recognise and extend these patterns. Series questions are explicitly designed to assess pattern recognition and prediction, and UGC NET may include series items involving numbers, letters or both. Statement C is false because the very nature of series questions is that terms follow some underlying rule rather than being completely independent. Therefore, the combination that collects A, B, D and E only is correct.

Option A:
Option A is correct because it includes all the true statements while excluding C, which wrongly denies the existence of an underlying rule in series questions. It faithfully reflects how series items are structured and used in aptitude tests.

Option B:
Option B is incorrect because it omits E, thus ignoring the explicit fact that UGC NET can include series questions involving both numbers and letters. Without E, the scope of series questions in the examination is underrepresented.

Option C:
Option C is wrong because it leaves out A, thereby failing to mention that identifying a generating rule is fundamental to solving number series questions. It gives an incomplete description even though B, D and E are true.

Option D:
Option D is incorrect because it brings in C, which incorrectly asserts that terms are always independent, and so mixes a false statement with true ones. Including C breaks the logical correctness of the combination.

The differences between consecutive terms are 11, 17, 23 and 29. These differences themselves form an arithmetic progression with common difference 6. Therefore the next difference should be 35. Adding 35 to the last term 85 gives 120, which maintains the constant step of 6 at the second level.

Option A:
Option A gives 116, implying a difference of 31 from 85. This would make the final increase between differences equal to 2 instead of 6, producing 11, 17, 23, 29, 31. Hence 116 does not preserve the consistent second-level arithmetic structure.

Option B:
Option B gives 120, implying a difference of 35 from 85. The difference sequence becomes 11, 17, 23, 29, 35, showing a uniform increment of 6 between gaps. This alignment at both levels makes 120 the correct next term.

Option C:
Option C gives 124, yielding a difference of 39 from 85. That would make the last jump among differences equal to 10, which distorts the pattern of adding 6 each time. Therefore 124 is not suitable.

Option D:
Option D gives 128, corresponding to a difference of 43 from 85. This further enlarges the final increment and deviates even more from the expected value. Thus 128 cannot be considered the correct continuation.

Each term after the first is obtained by doubling the previous term and adding 1. We have 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31 and 31 × 2 + 1 = 63. Applying the same rule again gives 63 × 2 + 1 = 127. This keeps the recursive structure consistent and explains every transition in the series.

Option A:
Option A gives 127, which fits the rule "double the previous term and add one" exactly. The extended sequence 3, 7, 15, 31, 63, 127 maintains a single, simple recursive pattern. Therefore, 127 is the correct next term for this number series.

Option B:
Option B provides 125, which would correspond to subtracting 1 after doubling or using a different constant, neither of which is supported by earlier terms. This breaks the consistent "+1" part of the rule. Hence, 125 cannot be considered correct.

Option C:
Option C suggests 129, which would require adding 3 after doubling 63, changing the constant in the recursive expression. No previous step uses "+3," so this option does not follow the observed pattern. Therefore, 129 is not appropriate.

Option D:
Option D presents 130, which is 67 more than 63 and does not come from doubling and adding a fixed small constant. This makes the relationship unclear and inconsistent with the earlier rule. Thus, 130 is not the right answer.

The differences between terms are 3, 4, 5 and 6, which increase by 1 each time. So the next difference should be 7. Adding 7 to the last term 20 gives 27. Therefore, 27 continues the pattern of increasing differences correctly.

Option A:
Option A uses the new difference of 7, producing 20 + 7 = 27 and extending the sequence of differences to 3, 4, 5, 6, 7. This maintains a clear second-level arithmetic pattern. Hence, 27 is the correct next term.

Option B:
Option B is 26, which would give a difference of 6 from 20, repeating the previous step instead of increasing it. That breaks the systematic growth of the differences. Thus, 26 is not consistent with the rule.

Option C:
Option C is 28, implying a difference of 8 from 20, which jumps beyond the next expected difference of 7. This oversteps the gradual increase and makes the pattern irregular. Therefore, 28 cannot be correct.

Option D:
Option D is 30, which would require a difference of 10, a much larger jump than the expected 7. Such a sudden change has no support from earlier terms and spoils the structure. So, 30 is not suitable.

The differences between consecutive terms are 9, 13, 17 and 21. These differences form an arithmetic sequence increasing by 4 each time. Continuing this rule, the next difference should be 25. Adding 25 to the last term 65 gives 90, which fits perfectly with the established pattern. Thus, 90 is the term that correctly continues the series.

Option A:
Option A gives 90, which is 25 more than 65 and retains the difference progression 9, 13, 17, 21, 25. This keeps the second-level pattern of increasing differences completely intact. Therefore, 90 is the most appropriate choice for the next term in the series.

Option B:
Option B provides 88, which corresponds to a difference of 23 from 65 and does not match the expected increase of 4 in the difference sequence. Using 23 would break the systematic growth in the differences. Hence, 88 is not consistent with the observed pattern.

Option C:
Option C suggests 92, implying a difference of 27 from 65, which overshoots the expected next difference of 25. This disrupts the neat arithmetic progression in the differences. Therefore, 92 cannot be regarded as the correct continuation.

Option D:
Option D proposes 94, giving a difference of 29 from 65, moving even further away from the expected 25. Such a jump fails to respect the structure of the series and makes the pattern irregular. Thus, 94 is not a valid answer.

The differences between the terms are 3, 5, 7, 11 and 13. These differences are prime numbers in increasing order. The next prime after 13 is 17. Adding 17 to the last term 41 gives 58. This continues the prime-based difference pattern consistently.

Option A:
Option A gives 56, which yields a difference of 15 from 41 and is not a prime, so it conflicts with the rule that differences are prime numbers. Hence, 56 is not consistent with the underlying structure.

Option B:
Option B yields 58, whose difference from 41 is 17, the next prime expected in the pattern. The extended differences 3, 5, 7, 11, 13, 17 form a coherent prime-based second-level sequence. Therefore, 58 is the correct next term.

Option C:
Option C suggests 60, giving a difference of 19, which is a prime but would skip 17 and break the specific order in which primes are being used here. This leads to an inconsistency in how the differences evolve. Thus, 60 is not the right continuation.

Option D:
Option D offers 62, which results in a difference of 21 from 41, not a prime but a composite number. This choice would discard the key property that defines the pattern. Therefore, 62 cannot be accepted as correct.