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.

Inside each group the jumps between letters follow a fixed but asymmetric pattern, and this pattern is repeated from term to term. Comparing BILO, CJMP, DKNQ and ELOR shows that each letter in a given position moves forward by one place from one group to the next. If we shift every letter of ELOR forward by one step, E becomes F, L becomes M, O becomes P and R becomes S, giving FMPS. Since this option alone keeps both the internal spacing pattern and the uniform column wise shift, FMPS is the correct next term.

Option A:
Option A, FMPT, matches the first three letters of the true next group but changes the last letter so that the spacing from P to T differs from the spacing found in the earlier sequences. This breaks the repeated structure of the last position. Because the final jump is inconsistent with the established pattern, FMPT cannot be the correct answer.

Option B:
Option B, GMQT, shifts some letters too far ahead and does not arise from a simple one step advance from ELOR. Its second and third letters no longer align with the smooth vertical progressions in the previous groups. As it fails to respect both the column wise movement and the internal gaps, GMQT does not fit the series.

Option C:
Option C is correct because FMPS is exactly one alphabetical step ahead of ELOR in every position, while still preserving the asymmetric internal distance pattern. The starting letters E and F line up with the earlier chain from B through E, and the other columns continue similarly. This strict mechanical derivation confirms FMPS as the proper continuation.

Option D:
Option D, ENQS, keeps E and N from the last term and changes only the remaining letters, which contradicts the rule that all letters move together. The internal pattern among its letters also differs from that in the given groups. Therefore ENQS is not a valid extension of the series.

Each group is a five letter palindrome in which the first and last letters match, the second and fourth letters match and the centre letter is distinct. From APQPA to BQRQB to CRSRC to DSTSD, the outer letters move forward A, B, C, D, the inner pair moves forward P, Q, R, S and the central letter moves forward Q, R, S, T. To continue, the next outer letter should be E, the inner pair should be T and the middle letter should be U. This gives ETUTE, which maintains all three coordinated movements and the palindromic shape, making it the correct next term.

Option A:
Option A, ETUET, places T in the middle and U as the inner pair, reversing their roles compared with earlier groups. This contradicts the way the second and fourth positions move together and the middle letter moves separately. Because it changes the structure of the pattern, ETUET is not correct.

Option B:
Option B, ESVSE, keeps E at the ends but drops the inner pair back to S, which would undo the forward step from R to S already seen. The middle letter V does not follow directly from the previous T either. As it disrupts both inner and central progressions, ESVSE cannot be the answer.

Option C:
Option C, EUROE, breaks the rule that the second and fourth letters are the same by placing U and O there. The groups in the series have strictly mirrored second and fourth positions. Therefore EUROE does not follow the series structure.

Option D:
Option D is correct because ETUTE moves each of the three distinct positions forward by exactly one step from DSTSD while keeping the palindrome intact. The outer E’s, inner T’s and central U follow naturally from D, S and T respectively. This complete consistency with the multi level pattern makes ETUTE the only valid continuation.

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 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.

Each term after the first is three times the previous term plus 1. We see 1×3+1 = 4, 4×3+1 = 13 and 13×3+1 = 40, and 40×3+1 = 121. Applying the same rule gives 121×3+1 = 363+1 = 364. Therefore, 364 is the correct next term.

Option A:
Option A preserves the recursive formula exactly, producing 364 from 121×3+1. The series 1, 4, 13, 40, 121, 364 remains internally consistent with a single clear rule. Hence, this option is correct.

Option B:
Option B is 360, which would require subtracting 3 after tripling, not adding 1. This contradicts the pattern seen in earlier steps. Therefore, 360 is not suitable.

Option C:
Option C is 400, which has no direct link with the 3×n+1 structure. It appears as a round number but does not arise from the required operation. Thus, 400 cannot be accepted.

Option D:
Option D is 500, an even larger value that also fails to result from 121×3+1. Choosing 500 would completely ignore the established multiplication-plus-one pattern. Therefore, this option is incorrect.

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.

Each term after the first is obtained using the rule "multiply the previous term by 3 and subtract 1". We have 1 × 3 − 1 = 2, 2 × 3 − 1 = 5, 5 × 3 − 1 = 14, 14 × 3 − 1 = 41 and 41 × 3 − 1 = 122. Applying this rule again gives 122 × 3 − 1 = 366 − 1 = 365. This keeps the recursive structure consistent and elegant.

Option A:
Option A gives 362, which would require subtracting 4 after multiplication or using a different constant, something not present earlier in the series. As a result, 362 breaks the pattern.

Option B:
Option B offers 364, corresponding to subtracting 2 after multiplying 122 by 3, and again changes the constant part of the rule. Thus, 364 does not align with the "minus one" pattern.

Option C:
Option C yields 365, exactly equal to 122 × 3 − 1, and extends the rule that has been consistently applied to all previous transitions. The sequence 1, 2, 5, 14, 41, 122, 365 is logically coherent. Hence, 365 is the correct next term.

Option D:
Option D suggests 367, which would involve adding 1 rather than subtracting 1 at the end of the operation. This is not supported by the existing steps. Therefore, 367 cannot be accepted as correct.

In this series, every group consists of four letters with the same fixed distance between consecutive letters. AEIM shows a regular pattern of positions, and BFJN, CGKO and DHLP repeat that structure with their own starting points. From one term to the next, each column increases by one letter in the alphabet. Advancing every letter of DHLP by one yields EIMQ, which keeps the constant internal spacing and extends the vertical sequences, so EIMQ is the correct next term.

Option A:
Option A, EGMR, alters the internal differences between letters and no longer keeps the equal steps that AEIM, BFJN, CGKO and DHLP share. It also does not come directly from adding one to each letter of DHLP. Because the spacing and transformation are both off, EGMR cannot be correct.

Option B:
Option B, EIFQ, begins with E and I like the true answer but changes the remaining letters so that the final gaps inside the group differ from the earlier pattern. The positions of F and Q do not fit the repeated structure. Hence EIFQ breaks the consistent internal rule of the series.

Option C:
Option C, FJNQ, moves the starting letter too far ahead and modifies multiple columns in a way that does not match the simple one step shift from DHLP. Its letters are not aligned properly with the previous vertical sequences. Therefore FJNQ does not continue the series correctly.

Option D:
Option D is correct because EIMQ is exactly one alphabetical step ahead of DHLP in each position and keeps the same spacing between successive letters. It fits neatly after the earlier groups, respecting both the constant internal step and the column wise progression. This makes EIMQ the only option that satisfies the observed pattern.

The first-level differences are 4, 8, 16, 32 and 64. Each difference is double the previous one, representing a geometric progression at the second level. The next difference should therefore be 128. Adding 128 to the last term 126 gives 254, so 254 is the value that preserves the doubling structure among the differences.

Option A:
Option A gives 250, corresponding to a difference of 124 from 126. This breaks the exact doubling rule, since 124 is not twice 64. Therefore 250 does not respect the second-level geometric behaviour.

Option B:
Option B gives 252, implying a difference of 126, which again does not equal 2×64. This leads to an inconsistent change in the pattern of differences. Hence 252 cannot be accepted.

Option C:
Option C gives 256, corresponding to a difference of 130 from 126. That would overshoot the expected difference of 128 and disrupt the doubling rule for the gaps. Thus 256 is not a valid continuation.

Option D:
Option D gives 254, which is 128 more than 126. The differences become 4, 8, 16, 32, 64, 128, perfectly doubling each time. This strong and simple structure confirms 254 as the correct next term.

Each term after the first is obtained by multiplying the previous term by 3 and adding 1. We have 1 × 3 + 1 = 4, 4 × 3 + 1 = 13, 13 × 3 + 1 = 40, 40 × 3 + 1 = 121 and 121 × 3 + 1 = 364. Applying the same rule to 364 gives 364 × 3 + 1 = 1092 + 1 = 1093. This keeps the recursion exact and transparent.

Option A:
Option A gives 1087, which cannot be expressed as 364 × 3 plus a constant of 1 and would force a different operation. This is not supported by previous steps in the series. Therefore, 1087 is not consistent with the rule.

Option B:
Option B offers 1089, which is 364 × 3, omitting the addition of 1 that has occurred at every step. This makes the pattern incomplete and inconsistent. Hence, 1089 cannot be accepted.

Option C:
Option C suggests 1091, which would correspond to adding −1 after multiplying and changes the sign of the constant term. This is not observed anywhere in the series. Thus, 1091 is not appropriate.

Option D:
Option D yields 1093, exactly equal to 364 × 3 + 1, and fully respects the recursive rule defining the sequence. The extended series remains governed by a single transformation. Therefore, 1093 is the correct next term.

Each term is obtained by multiplying the previous term by 2 and then adding 1: 10×2+1=21, 21×2+1=43, 43×2+1=87, and 87×2+1=175. Continuing the same rule gives 175×2+1 = 350+1 = 351. Therefore, 351 is the correct next term.

Option A:
Option A (300) does not satisfy the rule 175×2+1. If we apply the rule, we must reach 351, not 300. So 300 cannot be the next term.

Option B:
Option B (320) also fails the rule because the next term must be exactly 351 from 175×2+1. Any other value would break the consistent recursive operation used in every step.

Option C:
Option C (340) is not obtained from 175×2+1 and would require changing the “+1” part of the rule. Since the +1 is consistent throughout, 340 is incorrect.

Option D:
Option D (351) matches 175×2+1 exactly, so it continues the established pattern without any change. Hence, 351 is the correct next term.