UGC NET Questions (Paper – 1)

The pattern here arises from the formula aₙ = 2n⁴−1 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 2·1⁴−1 = 1, 2·2⁴−1 = 31, 2·3⁴−1 = 161, 2·4⁴−1 = 511 and 2·5⁴−1 = 1249. For n = 6 we compute 2·6⁴−1 = 2·1296−1 = 2592−1 = 2591. Therefore 2591 is the only term that correctly extends the quartic-based pattern.

Option A:
Option A, 2511, is far below the calculated value and does not equal 2n⁴−1 for any n that continues the sequence. It ignores the rapid growth implied by the quartic expression. Thus 2511 is not a valid next term.

Option B:
Option B, 2541, is still different from 2591 and cannot be obtained from 2·6⁴−1. Choosing it would break the exact algebraic rule that explains all the previous terms. Hence 2541 cannot be the correct answer.

Option C:
Option C, 2591, matches the result of evaluating 2n⁴−1 when n = 6. It preserves the quartic dependence on n and continues the rapid increase seen in the sequence. For these reasons, 2591 is the correct continuation.

Option D:
Option D, 2651, overshoots the correct value and is not equal to 2n⁴−1 for any appropriate n in order. Adopting 2651 would distort the pattern and introduce an unjustified jump. Therefore it is not a valid option.

This sequence is defined by the rule (a_n = 3n^4 - n^2 + 2) with n starting from 1. For n = 1, 2, 3, 4 and 5 we compute 3−1+2 = 4, 48−4+2 = 46, 243−9+2 = 236, 768−16+2 = 754 and 1875−25+2 = 1852. For n = 6 we calculate (3×6^4 - 6^2 + 2 = 3888 - 36 + 2 = 3854). Therefore 3854 is the correct next term.

Option A:
Option A, 3854, is exactly the value produced by the formula for n = 6. It preserves the quartic and quadratic contributions in the same way as for the earlier terms and keeps the pattern coherent. Thus 3854 is the correct continuation of the series.

Option B:
Option B, 3818, is 36 less than the correct value and does not equal (3×6^4 - 6^2 + 2). It suggests an unwarranted reduction that is not reflected in the previous behaviour. Hence 3818 is not valid.

Option C:
Option C, 3886, overshoots the computed value and again fails to satisfy the formula. Choosing 3886 would break the algebraic structure and introduce an arbitrary jump. Therefore 3886 is not correct.

Option D:
Option D, 3922, deviates even more from 3854 and has no basis in the generating expression. Using 3922 would destroy the close match between the rule and the data, so it is not the right answer.

The given series is generated by the rule (a_n = n^3 - 2) with n starting from 2. For n=2 we get 2³−2 = 8−2 = 6, for n=3 we get 27−2 = 25, for n=4 we obtain 64−2 = 62, for n=5 we obtain 125−2 = 123 and for n=6 we obtain 216−2 = 214. The next index is n=7, giving 7³−2 = 343−2 = 341 as the next term. Hence 341 is the correct continuation of the sequence.

Option A:
Option A, 333, does not equal (n^3-2) for n=7 or for any integer n that follows in the natural order of indices. Using 333 would require modifying the clear cubic rule that currently explains every term. Thus 333 is not consistent with the pattern.

Option B:
Option B, 339, is also not of the form (7^3-2) and does not result from the same functional relation. It introduces an arbitrary deviation from the established cubic structure. Hence 339 is not a valid next term.

Option C:
Option C equals 341, which is precisely 7³−2 and continues the rule (a_n = n^3-2) seamlessly. Since this one formula accounts for all given terms and the candidate term, 341 correctly extends the series.

Option D:
Option D, 347, is larger than the value predicted by 7³−2 and fails to satisfy the same polynomial relation. Selecting 347 would break the tight algebraic pattern that unifies the sequence. Therefore 347 cannot be accepted as the next term.

The pattern here is given by aₙ = 4n²+n+3 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 4·1²+1+3 = 8, 4·2²+2+3 = 21, 4·3²+3+3 = 42, 4·4²+4+3 = 71 and 4·5²+5+3 = 108. For n = 6 we compute 4·6²+6+3 = 144+6+3 = 153. Thus 153 is the correct next term consistent with this quadratic rule.

Option A:
Option A, 153, matches exactly the value from aₙ = 4n²+n+3 when n = 6. It keeps the same combination of square, linear and constant parts used to generate all earlier terms. Because the relationship holds perfectly, 153 is the correct continuation.

Option B:
Option B, 143, is 10 less than the formula’s result and does not satisfy the expression for n = 6. It requires an unexplained reduction of the term, which is not supported by the pattern. Therefore 143 is not a valid choice.

Option C:
Option C, 147, is also different from 153 and cannot be obtained from the given formula without changing its constants. This would make the rule inconsistent at the final term. Hence 147 is not correct.

Option D:
Option D, 161, exceeds the computed value and similarly fails to equal 4n²+n+3 when n = 6. Using 161 would break the neat polynomial structure, so it is not the right answer.

This sequence is described by the formula (a_n = 2n^3 + n) with n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 3, 18, 57, 132 and 255, matching the given series exactly. For n = 6 the expression gives (2×6^3 + 6 = 432 + 6 = 438). Thus 438 is the only value that maintains this cubic-plus-linear rule.

Option A:
Option A, 430, is smaller than the computed value and does not equal (2×6^3 + 6). It would require changing the formula at the final term, which has no support from the preceding structure. Therefore 430 is not a valid continuation.

Option B:
Option B, 438, matches precisely the value produced by (a_n = 2n^3 + n) when n = 6. It preserves the same relationship between position and value that explains all earlier terms. For this reason, 438 is the correct next term in the series.

Option C:
Option C, 442, overshoots the cubic prediction and is not the output of the given expression for any suitable n after 5. Adopting 442 would arbitrarily inflate the term and break the algebraic pattern. Hence 442 cannot be accepted.

Option D:
Option D, 454, deviates even more from the expected value and similarly fails to satisfy the rule (2n^3 + n) for n = 6. Selecting 454 would destroy the clean cubic structure of the sequence, so it is not correct.

The terms satisfy the formula aₙ = n³+n+1 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 1+1+1 = 3, 8+2+1 = 11, 27+3+1 = 31, 64+4+1 = 69 and 125+5+1 = 131. For n = 6 the same rule produces 216+6+1 = 223. Consequently, 223 is the only value that continues this cubic-plus-linear pattern.

Option A:
Option A, 223, comes directly from applying aₙ = n³+n+1 with n = 6. It preserves the structure where each term combines a cubic part, the index itself and a constant. Because this formula works for all terms including the next, 223 is the correct answer.

Option B:
Option B, 213, is 10 less than the computed value and does not satisfy the generating expression. It breaks the exact algebraic pattern that has been consistent so far. Hence 213 is not a valid continuation of the series.

Option C:
Option C, 217, is closer but still not equal to 6³+6+1. Adopting 217 would mean altering the constant part or the linear component arbitrarily, which is not justified by the data. Thus 217 is not correct.

Option D:
Option D, 231, exceeds the correct value and again fails to equal n³+n+1 for n = 6. Using 231 would destroy the clean matching between the formula and the sequence, so it is not the right option.

This series is described by the formula aₙ = 5n²+n−2 for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 5·1²+1−2 = 4, 5·2²+2−2 = 20, 5·3²+3−2 = 46, 5·4²+4−2 = 82 and 5·5²+5−2 = 128. For n = 6 the same expression gives 5·6²+6−2 = 180+6−2 = 184. Therefore 184 is the correct next term under this quadratic rule.

Option A:
Option A, 174, is 10 less than the value predicted by 5n²+n−2 for n = 6. It does not fit the formula and would require arbitrarily lowering the computed term. Hence 174 is not consistent with the sequence’s structure.

Option B:
Option B, 184, exactly equals 5·6²+6−2 and so preserves the quadratic relationship between n and aₙ. It ensures that the same rule that explains all previous terms also generates the new one. For this reason, 184 is the correct continuation.

Option C:
Option C, 178, also deviates from the calculated value and does not arise from the given expression. It would amount to changing the pattern only at the last step, which is logically unsound. Thus 178 cannot be the right answer.

Option D:
Option D, 192, is larger than the formula’s result and again cannot be written as 5n²+n−2 for n = 6. Selecting 192 would break the precise connection between position and term, so it is not valid.

The series can be expressed by the formula aₙ = (n⁴+n²)/2 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get (1+1)/2 = 1, (16+4)/2 = 10, (81+9)/2 = 45, (256+16)/2 = 136 and (625+25)/2 = 325, matching the terms given. For n = 6 the expression gives (6⁴+6²)/2 = (1296+36)/2 = 1332/2 = 666. Thus 666 is the unique next term that fits this quartic-based sequence.

Option A:
Option A, 646, is 20 less than the computed value and does not equal (6⁴+6²)/2. It has no basis in the formula that successfully models all the earlier terms. Therefore 646 cannot serve as the correct continuation.

Option B:
Option B, 654, is still short of 666 and similarly fails to arise from the expression involving n⁴ and n². Choosing 654 would force a change in the pattern for the last term only, which is mathematically unsound. Hence it is not the right answer.

Option C:
Option C, 681, is larger than the predicted value and again does not match (6⁴+6²)/2. It represents an arbitrary modification rather than a logical extension of the rule. Thus 681 is not a valid next term.

Option D:
Option D, 666, exactly matches the output of the formula when n = 6. It preserves the structural relationship between the terms and their positions and keeps the series fully consistent. For this reason, 666 is the correct option.

The sequence follows the formula (a_n = n^4 + 2n + 3) with n starting from 1. For n = 1, 2, 3, 4 and 5 we compute 1+2+3 = 6, 16+4+3 = 23, 81+6+3 = 90, 256+8+3 = 267 and 625+10+3 = 638. For n = 6 the expression yields (6^4 + 12 + 3 = 1296 + 15 = 1311). Therefore 1311 is the correct next term under this quartic-plus-linear pattern.

Option A:
Option A, 1287, is 24 less than the calculated value and does not equal (6^4 + 2×6 + 3). It would require weakening the rule only at the final term, which is inconsistent. Hence 1287 is not valid.

Option B:
Option B, 1299, is still below 1311 and again cannot be written as (n^4 + 2n + 3) for n = 6. Adopting 1299 would disrupt the tight connection between index and term. Thus 1299 is not correct.

Option C:
Option C, 1311, matches exactly the output of the formula when n = 6. It preserves the same quartic and linear structure that generated all earlier values. For this reason, 1311 is the correct continuation.

Option D:
Option D, 1327, overshoots the correct value and fails to satisfy the expression for n = 6. Using 1327 would abandon the algebraic coherence of the series, so it is not a valid answer.

The terms of this sequence satisfy the formula (a_n = 4n^3 + n^2 - 1) for n starting from 1. For n = 1, 2, 3, 4 and 5 we have 4+1−1 = 4, 32+4−1 = 35, 108+9−1 = 116, 256+16−1 = 271 and 500+25−1 = 524. For n = 6 the same expression yields (4×6^3 + 6^2 - 1 = 864 + 36 - 1 = 899). Consequently, 899 is the correct continuation of the series.

Option A:
Option A, 899, coincides with the value produced by the formula when n = 6. It keeps both the cubic and quadratic components of the pattern intact. Because it results directly from the generating rule, 899 is the correct next term.

Option B:
Option B, 887, is 12 less than the computed value and does not equal (4×6^3 + 6^2 - 1). It would require a sudden and unjustified reduction at the final step, so 887 is not valid.

Option C:
Option C, 911, overshoots the expected value and cannot be derived from the same expression for n = 6. Selecting 911 would distort the algebraic structure of the series. Hence 911 is not the right answer.

Option D:
Option D, 923, deviates even further from the formula’s output and again fails to satisfy the rule. This would destroy the strong correspondence between index and term, so 923 is not correct.

The sequence is described by the formula aₙ = n⁴−n+2 for n starting from 1. For n = 1, 2, 3, 4 and 5, we get 1−1+2 = 2, 16−2+2 = 16, 81−3+2 = 80, 256−4+2 = 254 and 625−5+2 = 622. For n = 6 the formula gives 1296−6+2 = 1292. Thus 1292 is the correct next term in line with this quartic-minus-linear rule.

Option A:
Option A, 1252, is 40 less than the computed value and does not equal n⁴−n+2 for n = 6. It breaks the exact pattern that has held for the earlier terms. Therefore 1252 is not a valid continuation.

Option B:
Option B, 1268, is still lower than 1292 and likewise fails to come from the generating expression. Selecting 1268 would require changing the formula without any clear reason. Hence it is not correct.

Option C:
Option C, 1292, matches perfectly with 6⁴−6+2 and continues the same structural relationship between n and aₙ. It maintains both the power and linear components consistently, making 1292 the correct answer.

Option D:
Option D, 1322, overshoots the correct value and cannot be obtained by substituting n = 6 into the rule. Using 1322 would distort the pattern and undermine the algebraic coherence of the sequence. Thus it is not appropriate.

The sequence follows the rule (a_n = 5n^3 + 2) for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 7, 42, 137, 322 and 627, which agree with the given terms. For n = 6 the formula gives (5×6^3 + 2 = 5×216 + 2 = 1080 + 2 = 1082). Thus 1082 is the only value that continues this cubic pattern exactly.

Option A:
Option A, 1082, is exactly the value produced by (a_n = 5n^3 + 2) when n = 6. It keeps the same coefficient and constant term that explain all previous terms. Because it arises naturally from the rule, 1082 is the correct next term in the series.

Option B:
Option B, 1066, is 16 less than the computed value and does not satisfy the cubic expression. It would suggest a sudden decrease not supported by the pattern. Hence 1066 is not a valid continuation.

Option C:
Option C, 1094, overshoots the formula’s output and cannot be obtained from (5n^3 + 2) for the next index. Selecting 1094 would arbitrarily increase the term and disrupt the algebraic structure. Therefore 1094 is not correct.

Option D:
Option D, 1106, is even further away from the expected value and similarly fails to equal (5×6^3 + 2). Using 1106 would break the strong consistency of the sequence, so it is not acceptable.

This sequence is given by the formula (a_n = n^4 + n^3 + n) for n starting from 1. For n = 1, 2, 3, 4 and 5 we compute 1+1+1 = 3, 16+8+2 = 26, 81+27+3 = 111, 256+64+4 = 324 and 625+125+5 = 755. For n = 6 we obtain (6^4 + 6^3 + 6 = 1296 + 216 + 6 = 1518). Therefore 1518 is the correct next term.

Option A:
Option A, 1494, is smaller than the formula’s output and does not equal (6^4 + 6^3 + 6). It would impose an unjustified reduction at the last step, so 1494 is not a valid continuation.

Option B:
Option B, 1506, is still below 1518 and fails to satisfy the expression for n = 6. Choosing 1506 would break the quartic-plus-cubic structure of the sequence. Thus 1506 is not correct.

Option C:
Option C, 1518, matches exactly the value produced by the rule when n = 6. It preserves the same combination of quartic and cubic terms that generated all the earlier numbers and hence is the correct next term.

Option D:
Option D, 1530, overshoots the computed value and cannot be written as (n^4 + n^3 + n) for the next index. Using 1530 would distort the carefully balanced pattern, so it is not appropriate.

The sequence is generated by the rule aₙ = n⁴−n²+2 for n starting from 1. For n = 1, 2, 3, 4 and 5 we compute 1−1+2 = 2, 16−4+2 = 14, 81−9+2 = 74, 256−16+2 = 242 and 625−25+2 = 602. For n = 6 the expression gives 1296−36+2 = 1262. Hence 1262 is the term that preserves this quartic-minus-square pattern.

Option A:
Option A, 1222, is 40 less than the value predicted by n⁴−n²+2 for n = 6. It does not satisfy the formula and would require adjusting the result in a way that is not supported by the earlier data. Therefore 1222 is not the correct continuation.

Option B:
Option B, 1238, also fails to match 1296−36+2 and breaks the tight link between index and term. It represents a partial correction but still does not arise from the generating rule. Thus 1238 cannot be accepted.

Option C:
Option C, 1292, overshoots the correct value and cannot be written as n⁴−n²+2 for n = 6. Adopting 1292 would abandon the exact quartic pattern that fits the sequence so well. Hence it is not valid.

Option D:
Option D, 1262, exactly equals 6⁴−6²+2 and therefore continues the same polynomial relationship. It keeps the structure of the series fully consistent from the first term to the next one. For this reason, 1262 is the correct next term.

The terms can be generated by the formula aₙ = n³−n+2 with n starting from 1. For n = 1, 2, 3, 4 and 5 we have 1³−1+2 = 2, 2³−2+2 = 8, 3³−3+2 = 26, 4³−4+2 = 62 and 5³−5+2 = 122, which matches the sequence. For n = 6 we get 6³−6+2 = 216−6+2 = 212. Thus 212 is the unique next term that preserves this cubic-minus-linear pattern.

Option A:
Option A, 202, is 10 less than the value predicted by the formula for n = 6. It is not equal to 6³−6+2 and therefore cannot be justified by the same rule. Choosing 202 would disrupt the precise algebraic structure of the sequence.

Option B:
Option B, 206, also differs from 212 and does not satisfy the relationship aₙ = n³−n+2 for the next index. It would amount to an arbitrary adjustment with no support from the earlier terms. Hence 206 is not the correct continuation.

Option C:
Option C, 220, is larger than the correct cubic value and similarly fails to equal 6³−6+2. Using 220 would break the pattern that neatly connects all the preceding terms to their positions. For this reason, 220 is not a valid choice.

Option D:
Option D, 212, is exactly the result of applying the formula with n = 6. It continues the same rule without any modification and keeps the entire series logically coherent. Therefore this option is the correct next term.