UGC NET Questions (Paper – 1)

Statements A and B correctly describe the basis of ranking problems and the technique of using top and bottom positions to deduce total count, while D notes that composite ranking across subjects or criteria is sometimes required. Statement C is false because if someone is 5th from the top and 10th from the bottom, the total is 5 + 10 − 1 = 14, not 10. Statement E is also false since such questions do appear under mathematical reasoning and aptitude. Therefore, the combination A, B and D only is correct.

Option A:
Option A is incomplete as it omits D and therefore does not discuss the more advanced type of problems that combine rankings from different subjects or tests. Without D, the picture of ranking questions is less comprehensive.

Option B:
Option B is correct because it includes all the true statements and excludes C and E, both of which give wrong information about totals and syllabus coverage. It matches the patterns seen in NET-level ordering and ranking problems.

Option C:
Option C is wrong since it includes C, which miscomputes the total, and omits A, failing to mention the basic nature of ranking criteria such as marks or height. This mixture renders the option unsuitable.

Option D:
Option D is incorrect because it contains C and thus accepts an incorrect total, even though it includes some true statements. The presence of C makes the overall combination invalid.

This sequence is described by the rule (a_n = 5n^3 - 2n + 1) for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 4, 37, 130, 313 and 616, matching the given terms. For n = 6 we compute (5×6^3 - 2×6 + 1 = 1080 - 12 + 1 = 1069). Therefore 1069 is the correct next term.

Option A:
Option A, 1047, is smaller than the formula’s result and does not equal (5×6^3 - 2×6 + 1). It suggests a reduced value for no reason indicated by the pattern. Hence 1047 is not a valid continuation.

Option B:
Option B, 1059, is closer but still fails to match the computed value of 1069. Choosing 1059 would alter the algebraic rule only at the last step, which is inconsistent. Thus 1059 is not correct.

Option C:
Option C, 1069, coincides exactly with the output of the rule for n = 6. It preserves the combination of cubic and linear terms that generate all earlier elements. For this reason, 1069 is the correct continuation.

Option D:
Option D, 1087, overshoots the formula’s value and cannot be obtained from (5n^3 - 2n + 1) when n = 6. Adopting 1087 would destroy the precise structure of the series, so it is not appropriate.

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.

This series follows the rule (a_n = n^3 + 4) for n starting from 1. Substituting n=1,2,3,4 and 5 gives 1³+4 = 5, 2³+4 = 12, 3³+4 = 31, 4³+4 = 68 and 5³+4 = 129, which matches the given terms. For the next term, n=6, so we calculate 6³+4 = 216+4 = 220. Hence 220 is the correct next term.

Option A:
Option A, 214, does not correspond to (n^3+4) for any integer n that continues naturally after the existing values. Choosing 214 would force a change in the underlying formula. Therefore it is not compatible with the pattern.

Option B:
Option B, 218, is slightly smaller than the value produced by 6³+4 and again cannot be expressed using the same rule. This discrepancy shows that 218 does not fit the algebraic structure of the series.

Option C:
Option C equals 220, which exactly matches the value of (n^3+4) when n=6. It preserves the single formula that generates all earlier terms and therefore extends the sequence in a logically consistent manner.

Option D:
Option D, 226, is larger than the cubic prediction and does not satisfy the relation (a_n = n^3+4) for any appropriate integer n in order. As a result, 226 cannot be considered the correct continuation.

Statements A, B and C summarise fundamental rules about inequalities. A is true because “greater than” is transitive. B is correct since multiplying by a positive constant preserves the order. C is also correct because multiplying by a negative constant reverses the direction of an inequality. D is false; knowing a > b and c > d does not ensure any fixed relation between a − c and b − d. E is false since squaring can change the order when negative numbers are involved, so the correct set of statements is A, B and C only.

Option A:
Option A is incomplete as it lists only A and B and omits C, so it does not mention how multiplying by a negative constant affects the inequality, which is crucial in many exam problems. This makes the option insufficient.

Option B:
Option B is also incomplete because it includes A and C only and leaves out B, thereby ignoring the important case of multiplication by positive numbers, which must also be understood.

Option C:
Option C is incomplete since it contains only B and C and omits A, losing the basic transitivity property that is often used to chain inequalities. Without A, the rule set is not fully represented.

Option D:
Option D is correct as it gathers all three true rules and explicitly excludes D and E, both of which overgeneralise operations on inequalities. It matches the standard algebraic handling of inequalities in NET-level aptitude questions.

Statements A and B correctly describe properties of standard dice and cube rotations. Statement D is true because nets are unfolded representations of cube faces, and E is also true since such questions test spatial reasoning. Statement C is false because knowing only one pair of opposite faces does not uniquely fix the arrangement of the other four faces. Therefore, A, B, D and E only are correct.

Option A:
Option A is correct as it collects all true statements and excludes C, which overstates what can be inferred from knowing only opposite faces.

Option B:
Option B is incomplete because it omits E (purpose: 3D visualisation).

Option C:
Option C is wrong because it includes C (false), even though it has some true statements.

Option D:
Option D is wrong because it includes C (false) and omits A (a standard die property).

Each group is a block of three consecutive letters, and each new group starts one letter later than the previous one: ABC (1–3), BCD (2–4), CDE (3–5) and DEF (4–6). Following this sliding pattern, the next block should be 5–7, which is EFG. Thus EFG is the only group that continues the shifting window of three letters.

Option A:
Option A is correct because it begins at E, the letter after D, and includes the next two letters F and G. This matches the structure of overlapping three-letter blocks. EFG therefore maintains both the length and the shifting start of the groups.

Option B:
Option B, FGH, starts at F instead of E, pushing the window too far forward. This would skip the block starting with E that the pattern demands. As a result, FGH does not fit the immediate continuation of the series.

Option C:
Option C, GHI, moves even further ahead, starting at G. It ignores the systematic one-letter shift in the starting position. Because the series does not skip starting letters, GHI cannot be the next term.

Option D:
Option D, BCD, repeats an earlier block rather than providing a new one. The pattern clearly produces new overlapping groups, not repetitions. Hence BCD is not a valid continuation.

Statements A, B and C are all correct. A notes the common natural-language use of “either” as exclusive. B is true because the standard logical disjunction is inclusive and allows both A and B to be true. C correctly gives a formula for exclusive-or using OR, AND and NOT. D is false since exam questions may clarify whether the sense is inclusive or exclusive, and E is false because inclusive and exclusive or differ when both A and B are true. Hence, A, B and C only are correct.

Option A:
Option A is incomplete since it omits C, thereby failing to mention the formal definition of exclusive-or in terms of other connectives, which is important in logical reasoning.

Option B:
Option B is incorrect because it incorrectly includes D, which claims that exam usage is always exclusive, and so introduces a false constraint on interpretation.

Option C:
Option C is correct as it combines natural-language usage, the inclusive logical meaning and the formal construction of exclusive-or, while excluding D and E, which misstate exam conventions and truth-value patterns.

Option D:
Option D is wrong since it includes E, which wrongly claims that inclusive and exclusive or always agree, and it drops A, losing the important point about everyday interpretation.

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.

The series can be modelled by the recurrence a₁ = 4 and aₙ₊₁ = 2aₙ + 3n² − 1 for n ≥ 1. Applying this rule gives a₂ = 2·4+3·1²−1 = 10, a₃ = 2·10+3·2²−1 = 31, a₄ = 2·31+3·3²−1 = 88 and a₅ = 2·88+3·4²−1 = 223, which matches the given sequence. For n = 5 the next term is a₆ = 2·223+3·5²−1 = 446+75−1 = 520. Therefore 520 is the unique next term that obeys this recurrence.

Option A:
Option A, 520, is exactly the value produced by the rule aₙ₊₁ = 2aₙ+3n²−1 when applied to a₅ = 223 with n = 5. It preserves the same structure of doubling the previous term and adding a square-based correction. Since all previous terms are generated in exactly this way, 520 is the correct continuation.

Option B:
Option B, 512, is slightly smaller than the recurrence output and does not satisfy 2·223+3·5²−1. It would require subtracting 8 from the correct value only at the final step. This arbitrary change is not reflected earlier in the sequence, so option B is not consistent with the pattern.

Option C:
Option C, 528, is larger than the correctly computed value and cannot be derived from the recurrence without altering its parameters. Choosing 528 would artificially inflate the sixth term and destroy the exact match between the rule and the data. Hence option C is incorrect.

Option D:
Option D, 536, deviates even more from 520 and again fails to arise from the relation aₙ₊₁ = 2aₙ+3n²−1. Using 536 would break the carefully defined index-dependent correction term, so this option is incorrect.

Statement A correctly describes qualitative data as categorical. Statement B is true for quantitative data, which involve numerical magnitudes. Statement D is also correct, since continuous data can, in principle, assume any value in an interval with arbitrary precision. Statement C is false because discrete data take countable values with gaps, while continuous data take any value in an interval. Statement E is false as understanding data type helps in choosing appropriate measures and graphs. Hence, A, B and D only are correct.

Option A:
Option A is incomplete because it omits D (continuous data).

Option B:
Option B is correct since it includes all true statements and excludes C and E.

Option C:
Option C is wrong because it includes C (false).

Option D:
Option D is incorrect because it includes C (false) and omits B.

Statements A, B, C and D together give a complete and correct conceptual comparison of simple and compound interest in exam-type settings. A is correct for positive rates and more than one year because compounding on accumulated amounts cannot yield less than simple interest on principal. B and C correctly distinguish the bases on which interest is calculated in the two regimes, and D accurately contrasts the linear versus exponential-type growth patterns. Statement E is false because for exactly one year simple and compound interest coincide, so simple interest is not greater, and hence the correct combination must include A, B, C and D but exclude E.

Option A:
Option A is correct because it captures all of the true statements and omits E, which misstates the one-year comparison between simple and compound interest. It recognises that compounding over multiple periods increases or at least matches simple interest and that the two schemes use different bases for interest calculation. It also correctly reflects the different shapes of the time–amount graphs.

Option B:
Option B is incorrect because it leaves out D, the key statement about linear versus exponential-like growth, so the description of time behaviour is incomplete. Although A, B and C are true, this combination does not fully convey how amounts diverge over longer periods. For conceptual NET questions, missing such a central point makes the option inadequate.

Option C:
Option C is wrong because it includes E along with otherwise correct statements; E wrongly claims that simple interest is always greater than compound interest for one year. Including even one false statement makes the whole set incorrect in a “select correct statements” question. Therefore this combination cannot be accepted as correct.

Option D:
Option D is incorrect because it omits A and D while still containing E, the false statement. By dropping A it loses the general comparison between the two interest types, and by adding E it introduces an error about the one-year case. This mixture of omission and error makes the option invalid.

This option is correct because combinations count the number of ways to select r objects from n distinct objects when order does not matter. The standard notation for this is nCr. It is also called the binomial coefficient and is given by n!/[r!(n−r)!]. Therefore, nCr represents the required count.

Option A:
nPr is used for permutations, where order of arrangement matters. It counts more cases than combinations because each selection can be arranged in many orders. Since the question specifies "without regard to order," nPr is not suitable.

Option B:
rCn is not the conventional way of writing combinations of r from n. It reverses the parameters and is not used in standard notation. This makes the option incorrect.

Option C:
rPn again refers to permutations but with reversed parameters compared to typical notation. It also considers ordering, which the question explicitly ignores. Thus, this symbol does not answer the question correctly.

Option D:
nCr correctly denotes the number of combinations of n objects taken r at a time. It ignores order and is widely used in probability and counting problems. This precisely matches the description given, so this option is correct.

Simple interest is calculated using the formula SI = (P × R × T) ÷ 100, where P is principal, R is rate and T is time in years. Substituting the given values, we get SI = (5000 × 8 × 2) ÷ 100. First multiply: 5000 × 8 = 40000 and 40000 × 2 = 80000. Dividing 80000 by 100 yields ₹800 as the simple interest.

Option A:
Option A, ₹600, would correspond to a lower effective rate or a shorter time than specified, so it does not match the formula outcome for the given data. It reflects an arithmetic underestimation.

Option B:
Option B correctly applies the simple interest formula, step by step, and arrives at ₹800. This value is consistent with both the principal and the specified rate and time.

Option C:
Option C, ₹900, is larger than the actual interest and suggests an error in multiplication or division, possibly treating time or rate incorrectly.

Option D:
Option D, ₹1000, further exaggerates the interest and would require either a higher rate or a longer period than 2 years at 8% per annum for ₹5000.