UGC NET Questions (Paper – 1)

The differences between successive terms are 3, 9, 27 and 81. Each difference is obtained by multiplying the previous difference by 3, forming a geometric progression at the second level. The next difference should therefore be 81 × 3 = 243. Adding 243 to the last term 122 gives 122 + 243 = 365, which continues the pattern exactly.

Option A:
Option A gives 362, corresponding to a difference of 240 from 122, which does not match the expected value of 243. This breaks the geometric pattern in the differences. Therefore, 362 is not consistent with the rule.

Option B:
Option B offers 364, yielding a difference of 242 from 122, one less than the required 243, and again failing to preserve the exact growth in differences. Hence, 364 cannot be accepted as correct.

Option C:
Option C yields 365, which is 243 more than 122 and matches the predicted next difference in the geometric sequence 3, 9, 27, 81, 243. This keeps both the main series and the second-level pattern in harmony. Thus, 365 is the correct next term.

Option D:
Option D suggests 368, giving a difference of 246 from 122, which overshoots the expected difference and disrupts the clean factor-of-three rule. Therefore, 368 is not a valid continuation.

The differences between consecutive terms are 2, 4, 8 and 16. These are powers of two doubling at each step. To continue this pattern, the next difference should be 32. Adding 32 to the last term 31 gives 31 + 32 = 63, which extends the series in a perfectly consistent way.

Option A:
Option A gives 61, which corresponds to a difference of 30 from 31 and fails to match the next power of two. Since the previous differences are 2, 4, 8 and 16, the logical continuation is 32, not 30. Hence, 61 is not correct.

Option B:
Option B yields 63, which is 32 more than 31 and completes the power-of-two difference sequence 2, 4, 8, 16, 32. The pattern remains clean and conceptually strong. Therefore, 63 is the correct next term.

Option C:
Option C suggests 65, giving a difference of 34 from 31, which does not fit into the powers-of-two framework. Such an increment is arbitrary with respect to the earlier differences. Thus, 65 cannot be accepted.

Option D:
Option D offers 67, which is 36 greater than 31 and again unrelated to the powers-of-two idea. Using 67 would disrupt the elegant second-level pattern that defines the series. Therefore, 67 is not the right answer.

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.

The differences between the terms are 3, 6, 12, 24 and 48. Each difference is double the previous one, forming a geometric pattern at the second level. The next difference should therefore be 96. Adding 96 to the last term 100 gives 100 + 96 = 196. This continuation respects the doubling rule in the differences.

Option A:
Option A gives 184, whose difference from 100 is 84, not the expected 96. This breaks the doubling pattern governing the increments. Hence, 184 is not consistent with the series structure.

Option B:
Option B offers 188, giving a difference of 88 from 100, again not equal to 96 and incompatible with the second-level rule. Therefore, 188 cannot be accepted as correct.

Option C:
Option C suggests 192, corresponding to a difference of 92 from 100, which still fails to match the precise value 96. This makes the pattern irregular. Thus, 192 is not appropriate.

Option D:
Option D yields 196, which is 96 more than 100 and extends the difference sequence 3, 6, 12, 24, 48, 96 in a fully consistent way. This keeps the series logically sound. Therefore, 196 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.

The differences between consecutive terms are 1, 4, 9, 16 and 25. These differences are consecutive perfect squares: 1², 2², 3², 4² and 5². The next difference should therefore be 6² = 36. Adding 36 to the last term 57 gives 57 + 36 = 93, which continues the square-based pattern in the differences.

Option A:
Option A gives 88, corresponding to a difference of 31 from 57, which does not equal the next square 36. This contradicts the square structure underlying the series. Hence, 88 is not consistent with the pattern.

Option B:
Option B offers 90, whose difference from 57 is 33, again not matching 36 and making the pattern imprecise. Therefore, 90 cannot be accepted as correct.

Option C:
Option C suggests 92, which yields a difference of 35 from 57, only near but not equal to 36. This minor mismatch still breaks the strict square-difference rule. Thus, 92 is not appropriate.

Option D:
Option D yields 93, which is 36 more than 57 and extends the difference sequence 1, 4, 9, 16, 25, 36 in a perfectly regular way. This preserves the higher-level pattern. Therefore, 93 is the correct next term.

The first-level differences are 19, 35, 55 and 79. The second-level differences are 16, 20 and 24, which themselves increase by 4. Continuing this pattern, the next second-level difference should be 28, so the next first-level difference becomes 79+28 = 107. Adding 107 to 199 yields 306, which keeps both levels of the pattern coherent.

Option A:
Option A gives 300, corresponding to a difference of 101 from 199. This would make the second-level differences 16, 20, 24 and 22, breaking the rule that these grow by 4 each time. Thus 300 is not consistent with the established structure.

Option B:
Option B gives 306, implying a difference of 107 from 199. The differences become 19, 35, 55, 79, 107 and the second-level differences are 16, 20, 24, 28. This preserves the steady +4 growth at the second level, so 306 is the correct continuation.

Option C:
Option C gives 310, which corresponds to a difference of 111 from 199. That would produce a second-level jump from 79 to 111 equal to 32, not 28, making the pattern irregular. Hence 310 cannot be accepted.

Option D:
Option D gives 314, yielding a difference of 115 from 199. The last second-level step would become 36, which further disrupts the neat arithmetic progression. Therefore 314 is not a valid next term.

The first-level differences are 9, 13, 17 and 21. These differences form an arithmetic progression with common difference 4. To continue this structure, the next difference should be 25. Adding 25 to the last term 67 gives 92, which maintains the regular growth among the differences.

Option A:
Option A gives 88, implying a difference of 21 from 67. This simply repeats the last difference rather than increasing it, so the progression of gaps 9, 13, 17, 21, 21 breaks the +4 pattern. Therefore 88 is not consistent with the rule.

Option B:
Option B gives 92, corresponding to a difference of 25. The differences become 9, 13, 17, 21, 25, which keep increasing by 4 each time. This perfect second-level arithmetic progression shows that 92 is the correct next term.

Option C:
Option C gives 96, yielding a difference of 29 from 67. The last jump among differences then becomes 8, which is double the expected 4 and disrupts the pattern. Hence 96 cannot be accepted.

Option D:
Option D gives 98, corresponding to a difference of 31 from 67. This further distorts the difference progression and makes the final step too large. Therefore 98 is not a valid 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 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 3, 6, 9 and 12, which themselves increase by 3 each time. The next difference should therefore be 15. Adding 15 to the last term 31 gives 46. Thus, 46 is the correct next term that continues the pattern of adding multiples of 3.

Option A:
Option A is 42, which would give a difference of 11 from 31. This does not match the expected next difference of 15. Therefore, 42 is inconsistent with the difference pattern.

Option B:
Option B is 44, producing a difference of 13, which also fails to align with the +3 sequence in the differences. It introduces an odd increment without justification. Hence, 44 cannot be accepted.

Option C:
Option C equals 46 and yields a difference of 15, precisely continuing the 3, 6, 9, 12 sequence. The extended difference list 3, 6, 9, 12, 15 is fully consistent, confirming 46 as the correct answer.

Option D:
Option D is 48, which leads to a difference of 17 from 31. This value has no place in the pattern of differences and therefore breaks the structure. So, 48 is not suitable.

The differences between consecutive terms are 1, 4, 9 and 16. These are consecutive perfect squares 1², 2², 3² and 4². To continue the pattern, the next difference should be 5² = 25. Adding 25 to the last term 31 gives 31 + 25 = 56. This preserves the square-based structure of the differences and fits the logic of the series.

Option A:
Option A produces 56, which is exactly 25 more than 31 and makes the difference sequence 1, 4, 9, 16, 25. This is a neat progression of squares, showing a clear higher-level pattern. Hence, 56 is the correct next term in the number series.

Option B:
Option B gives 57, which would correspond to a difference of 26 from 31 and does not match the expected square 25. This slight mismatch is enough to break the precise square-difference rule. Therefore, 57 cannot be accepted as the correct continuation.

Option C:
Option C provides 58, which is 27 more than 31 and again deviates from the exact value of 25 required by the pattern. The differences would no longer correspond to consecutive squares. Thus, 58 is not consistent with the structure.

Option D:
Option D suggests 60, giving a difference of 29 from 31, which is far away from 25 and lacks any special square-based interpretation. Choosing 60 would destroy the elegant second-level pattern. Hence, 60 is not the right answer.

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.

The consecutive differences are 15, 25, 35 and 45. These differences form an arithmetic progression with common difference 10. Therefore the next difference should be 55. Adding 55 to the last term 124 gives 179, so 179 continues the series while preserving the same second-level arithmetic pattern.

Option A:
Option A gives 172, implying a difference of 48 from 124. This would make the final increment among differences equal to 3 instead of 10, turning the pattern 15, 25, 35, 45, 48 into an irregular sequence. Hence 172 is not appropriate.

Option B:
Option B gives 176, corresponding to a difference of 52 from 124. The second-level jump from 45 to 52 becomes 7, which again fails to match the consistent step of 10. Therefore 176 does not respect the underlying structure.

Option C:
Option C gives 179, yielding a difference of 55 from 124. The difference sequence becomes 15, 25, 35, 45, 55, showing a constant increment of 10 throughout. This strong internal cohesion means that 179 is the correct next term.

Option D:
Option D gives 184, which implies a difference of 60 from 124. The final increase among differences would then be 15, which is larger than the previous constant step and breaks the pattern. Thus 184 cannot be accepted.

The differences between the terms are 3, 6, 12, 24 and 48. Each difference is double the previous one, forming a geometric progression at the second level. The next difference should therefore be 96. Adding 96 to the last term 97 gives 97 + 96 = 193, which follows this doubling pattern exactly.

Option A:
Option A gives 187, corresponding to a difference of 90 from 97, which does not match the required next difference of 96. This breaks the doubling rule that defines the series. Hence, 187 is not consistent with the pattern.

Option B:
Option B offers 189, giving a difference of 92 from 97 and again failing to match the expected 96. This disrupts the geometric progression in the differences. Therefore, 189 cannot be accepted.

Option C:
Option C suggests 191, whose difference from 97 is 94, still not the correct doubled value of 48. This makes the second-level pattern inconsistent. Thus, 191 is not appropriate.

Option D:
Option D yields 193, which is 96 more than 97 and continues the difference sequence 3, 6, 12, 24, 48, 96 in a perfectly structured way. This maintains the integrity of the series. Hence, 193 is the correct next term.