UGC NET Questions (Paper – 1)

Each term is 5 more than the previous one, so the series is an arithmetic progression with common difference 5. We have 5, 10, 15 and 20 by repeatedly adding 5. Adding 5 to 20 gives 25. Therefore, 25 is the correct next term in the sequence.

Option A:
Option A preserves the pattern because 20 + 5 = 25 continues the same step used throughout. The extended series 5, 10, 15, 20, 25 remains a clean list of multiples of five. This makes the logic straightforward and exam friendly.

Option B:
Option B is 24, which is only 4 more than 20 and would change the common difference from 5 to 4. That alteration is not supported by any evidence in the earlier terms. Hence, this option is not consistent with the rule.

Option C:
Option C is 30, which would require a jump of 10 from 20 to 30, whereas all earlier jumps were 5. Introducing a larger difference at the end breaks the uniform progression. Therefore, 30 is not the correct answer.

Option D:
Option D is 22, giving a difference of 2 from 20 and severely disrupting the pattern of adding 5 each time. Such an abrupt change contradicts the clear structure of the series. Thus, this option must be rejected.

Speed measures how fast an object moves and is defined mathematically as distance travelled per unit time. This can be written as speed = distance ÷ time, which is equivalent to the ratio of distance to time. In aptitude questions, common units include km/h and m/s based on this definition. Therefore, the correct description is the ratio of distance to time.

Option A:
Time to distance would represent the inverse ratio, which tells how much time is taken per unit distance rather than how much distance is covered per unit time. While this can be useful in some contexts, it is not the standard definition of speed. Hence, this option is incorrect.

Option B:
Work to time describes the rate of doing work, usually called "work rate" or "power," not speed. This ratio is relevant in time and work problems, but it does not relate to motion along a path. Therefore, it does not fit the context of speed.

Option C:
Distance to work is not a meaningful physical ratio in basic quantitative aptitude. It does not correspond to any standard concept in time and distance or mechanics. Since the question is specifically about speed, this option is irrelevant and incorrect.

Option D:
Distance to time is correct because it captures the idea of how far an object moves in a given amount of time. For example, if a vehicle travels 60 km in 2 hours, its speed is 60 ÷ 2 = 30 km/h. This understanding is essential for solving many numerical problems in UGC NET Paper 1.

The first-level differences are 9, 19, 29 and 39. These differences themselves form an arithmetic sequence with common difference 10. To preserve this pattern, the next difference must be 49. Adding 49 to 102 gives 151 as the next term. Thus 151 is the only option that keeps the second-level pattern perfectly intact.

Option A:
Option A corresponds to adding 49 to 102, giving 151 and extending the differences to 9, 19, 29, 39, 49. This preserves the constant increase of 10 between successive differences. Because both the original series and the sequence of gaps remain consistent, 151 is the correct continuation.

Option B:
Option B would make the next difference 47, so the differences become 9, 19, 29, 39, 47. The jump from 39 to 47 is 8, not 10, so the second-level pattern breaks. Hence 149 does not follow the intended rule of steadily increasing differences by 10.

Option C:
Option C would require a difference of 51 from 102, giving differences 9, 19, 29, 39, 51. Here the increment from 39 to 51 is 12, which again violates the constant second-level difference of 10. Therefore 153 cannot be accepted as the next term.

Option D:
Option D implies a difference of 45 from 102, so the last increment in the difference sequence is only 6. This contradicts the observed +10 progression that generates 9, 19, 29 and 39. As a result, 147 is not a valid continuation of the series.

Statements A, B and C are standard algebraic identities for binomial squares and difference of squares, while D correctly results from subtracting the two square expansions and simplifies many expressions quickly. Statement E is false because these identities are widely used in aptitude problems to perform rapid simplification or mental calculation. Therefore, the set consisting of A, B, C and D only is correct.

Option A:
Option A is correct as it lists all and only the valid identities, illustrating how they combine to yield useful simplifications such as 4ab, and it rightly omits E, which denies their important role in exam problems.

Option B:
Option B is incomplete since it omits D and thus misses the composite application of the identities, which is frequently tested when candidates are asked to simplify expressions like (a + b)² − (a − b)².

Option C:
Option C is also incomplete as it excludes A, failing to state the most commonly used identity for (a + b)² explicitly, even though the other identities are present. Without A, the picture is not complete.

Option D:
Option D is incorrect because it leaves out B and therefore fails to state the identity for (a − b)², which is as important as the identity for (a + b)² in exam contexts.

This sequence follows the rule aₙ = n⁴ + 6n² + 4 with n starting from 1. Evaluating the expression gives 1+6+4 = 11, 16+24+4 = 44, 81+54+4 = 139, 256+96+4 = 356 and 625+150+4 = 779, which confirms the pattern. For n = 6 we obtain 6⁴+6·6²+4 = 1296+216+4 = 1516. Hence 1516 is the only value that continues this quartic-plus-quadratic-plus-constant structure.

Option A:
Option A, 1516, equals the value given by n⁴+6n²+4 for n = 6. It preserves the same coefficients for both the quartic and quadratic terms and keeps the constant term unchanged. Because the formula explains every term including the next, this option correctly extends the series.

Option B:
Option B, 1484, is 32 less than the correct polynomial value and does not satisfy the expression for n = 6. Choosing 1484 would require an arbitrary reduction at the last term that contradicts the earlier behaviour of the sequence. Therefore option B is incorrect.

Option C:
Option C, 1532, overshoots the formula’s result by 16 and again does not arise from substituting n = 6 into the rule. It implies a modification of the constant or coefficients, which the earlier terms do not support. Hence option C is incorrect.

Option D:
Option D, 1556, deviates even more from 1516 and has no direct basis in the function aₙ = n⁴+6n²+4. Using 1556 would break the precise match between index and term that defines the series, so option D is incorrect.

The pattern can be written as a₁ = 5 and aₙ₊₁ = 4aₙ + n³ + 2 for n ≥ 1. Applying this rule gives a₂ = 4·5 + 1³ + 2 = 23, a₃ = 4·23 + 2³ + 2 = 102, a₄ = 4·102 + 3³ + 2 = 437 and a₅ = 4·437 + 4³ + 2 = 1814, all of which match the series. For n = 5 the next term is a₆ = 4·1814 + 5³ + 2 = 7256 + 125 + 2 = 7383. Thus 7383 is the only value that satisfies this recurrence and correctly continues the sequence.

Option A:
Option A, 7359, is 24 less than the recurrence output for n = 5 and cannot be written as 4a₅ + 5³ + 2. Accepting 7359 would require subtracting 24 from the correctly computed term only at the final step. This violates the consistency of the recurrence, so option A is incorrect.

Option B:
Option B, 7371, is 12 smaller than the correct value 7383 and likewise does not equal 4·1814 + 125 + 2. It provides an approximate but not exact continuation and therefore does not follow the specified rule. Consequently, option B cannot be chosen as the next term.

Option C:
Option C, 7395, is 12 greater than the correct value and again fails to match the recurrence formula. To obtain 7395 we would have to add extra units to the computed result at n = 5, altering the defined update pattern. Hence option C is not a valid extension of the sequence.

Option D:
Option D, 7383, exactly equals the value produced by the rule aₙ₊₁ = 4aₙ + n³ + 2 when n = 5. It preserves the combination of quadrupling the previous term with an added cubic and constant adjustment. Because this structure explains every step of the series, 7383 is the correct answer.

The sequence can be split into two sub-series: 2, 4, 6 and 9, 11, 13. The first sub-series 2, 4, 6 increases by 2, and the second sub-series 9, 11, 13 also increases by 2. The next term should continue the first sub-series after 6, giving 8. Therefore, 8 is the correct next term for the combined series.

Option A:
Option A fits because it extends the first subsequence 2, 4, 6 to 8 using the same +2 rule. The combined sequence becomes 2, 9, 4, 11, 6, 13, 8, which keeps both interleaved progressions intact. Hence, this option matches the alternating structure.

Option B:
Option B is 14, which would belong naturally after 13 in the second subsequence. However, in the alternating arrangement, the next position should be filled by the first subsequence. Placing 14 here would disturb the alternation order. Thus, it is not correct.

Option C:
Option C is 15, which neither continues the +2 pattern from 6 nor fits the timing of the second subsequence. It introduces an extra value that does not align with either internal progression. Therefore, 15 cannot be accepted.

Option D:
Option D is 10, which does not belong to the first subsequence 2, 4, 6 when extended by adding 2. It also does not fit the second subsequence at this position. Hence, 10 fails to respect the dual structure and is incorrect.

This series is generated by the formula (a_n = n^4 + n) for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 1+1 = 2, 16+2 = 18, 81+3 = 84, 256+4 = 260 and 625+5 = 630, which match the given terms. For n = 6 the same rule yields (6^4 + 6 = 1296 + 6 = 1302). Hence 1302 is the unique next term that respects this quartic-plus-linear pattern.

Option A:
Option A, 1286, is 16 less than the formula’s output and does not equal (6^4 + 6). It would require altering the rule arbitrarily for the last term, which is not supported by the earlier data. Therefore 1286 is not correct.

Option B:
Option B, 1294, is closer but still not equal to 1302 and fails to satisfy the expression (n^4 + n) for n = 6. Choosing 1294 would weaken the exact algebraic structure of the series. Thus 1294 is not a valid continuation.

Option C:
Option C, 1310, overshoots the correct value and again cannot be written as (6^4 + 6). Adopting 1310 would break the close correspondence between the formula and the actual terms. Therefore 1310 is not acceptable.

Option D:
Option D, 1302, equals (6^4 + 6) exactly and continues the same quartic pattern without modification. It maintains the functional relationship that has generated every earlier term, so 1302 is the correct next term.

Statements A and B are the standard counting rules for unions of finite sets, with B capturing the special case of disjoint sets. Statement D is also correct because the elements of A and A' partition the universal set, so their cardinalities add up to its size. Statement C is false; A − B means elements in A but not in B, not the other way round. Statement E is false because if A is a subset of B, then A ∩ B' can be empty. Thus only A, B and D are correct, matching option D.

Option A:
Option A is incomplete since it omits D, which connects complements to the universal set and is an important counting identity in many exam questions. Without D the set of correct statements is not complete.

Option B:
Option B is incorrect because it includes C, which reverses the direction in the definition of set difference, thereby introducing a wrong statement into the combination.

Option C:
Option C is also wrong as it adds C and D to A and B, so it contains the incorrect interpretation of A − B along with true facts, and that makes the option invalid for “select the correct statements”.

Option D:
Option D is correct because it retains only the three accurate statements about union cardinalities and complements while excluding C and E, both of which misinterpret set difference or subset relations.

Statements A, D and E correctly describe the nature of statement–argument questions and strong arguments. Statement B is wrong because emotional appeal alone does not make an argument strong if it lacks relevance or logic. Statement C is also wrong since candidates are expected to interpret and infer implied strengths or weaknesses, not just copy text. Therefore, the wrong statements are exactly B and C, which makes their combination the correct answer for this “select the wrong” question.

Option A:
Option A is incorrect because it isolates B as the only wrong statement and ignores C, even though C clearly misrepresents the need for interpretation and inference in these questions.

Option B:
Option B is also wrong because it singles out only C and overlooks B, which wrongly prioritises emotional appeal over logical relevance.

Option C:
Option C is incorrect because it wrongly treats D and E as wrong alongside B, even though D and E accurately characterise what counts as strong and how both supporting and opposing arguments are evaluated in NET exams.

Option D:
Option D is correct since it identifies B and C together as the problematic statements, while leaving A, D and E recognised as accurate descriptions of how statement–argument items work.

Statements A and B correctly identify modus ponens and modus tollens as valid argument forms, and D correctly states that denying the antecedent is invalid even though it superficially resembles a valid pattern. Statement E is also true because exam questions often depend on distinguishing valid inferences from fallacies. Statement C is false since affirming the consequent is a classic fallacy; from “if p then q” and “q” one cannot conclude “p” with certainty. Therefore, the combination A, B, D and E only is correct.

Option A:
Option A is incomplete because it omits E and therefore does not highlight the practical importance of recognising these forms when evaluating arguments in tests like UGC NET. Without E, the applied dimension of the topic is not fully expressed.

Option B:
Option B is also incomplete as it leaves out A, failing to mention explicitly the widely used valid pattern of modus ponens, which is central to many logical derivations. This omission weakens the conceptual coverage.

Option C:
Option C is wrong because it includes C, which treats affirming the consequent as valid, and thereby endorses a logical fallacy. Even though A, B and D are true, the presence of C invalidates the combination.

Option D:
Option D is correct as it gathers the two standard valid forms, identifies denying the antecedent as invalid and notes the value of recognising these patterns in reasoning tasks, while excluding C, the misclassification of affirming the consequent. It matches the logic syllabus for UGC NET.

The differences between the terms are 7, 11, 15 and 19. These differences increase by 4 each time, forming an arithmetic sequence at the second level. The next difference should therefore be 23. Adding 23 to the last term 57 gives 57 + 23 = 80, which extends the pattern smoothly.

Option A:
Option A gives 76, corresponding to a difference of 19, which merely repeats the last increment and does not allow the difference to grow to 23. This disrupts the pattern. Therefore, 76 is not correct.

Option B:
Option B offers 78, whose difference from 57 is 21, still short of the expected 23. This does not match the consistent addition of 4 at the level of differences. Hence, 78 cannot be accepted.

Option C:
Option C yields 80, which is 23 more than 57 and completes the difference sequence 7, 11, 15, 19, 23. This honours the second-level arithmetic progression. Thus, 80 is the correct next term in the series.

Option D:
Option D suggests 82, giving a difference of 25 from 57, which overshoots the expected value and makes the pattern uneven. Therefore, 82 is not appropriate.

Statement A is correct because regression distinguishes a response (dependent) variable from an explanatory (independent) variable. Statement C is true as the least squares criterion minimises the sum of squared vertical residuals. Statement D is also correct since regression is widely used to predict and to analyse how variables relate. Statement B is false because the regression of Y on X is primarily used to predict Y for given X, not the other way around. Statement E is false because a horizontal line means Y is constant and does not change with X. Consequently, A, C and D only are correct.

Option A:
Option A is correct as it collects the essential properties of simple linear regression and excludes B and E.

Option B:
Option B is incorrect because it includes B (wrong predictive direction).

Option C:
Option C is wrong as it includes E (false).

Option D:
Option D is incorrect because it retains B (false) and omits A (dependent/independent distinction).

Statements A, B and D accurately reflect common coding–decoding practices. A describes a typical letter-shift pattern used in many exam questions. B explains substitution coding where fixed word–symbol mappings are used. D is correct because analysing one clear example often reveals the pattern for others. C is false because the position of a letter in the word may affect its code, and E is false since different coding questions may use different patterns within the same paper. Therefore A, B and D only are correct.

Option A:
Option A is incomplete as it ignores D and so underplays the importance of pattern discovery from a given example, which is essential in solving such questions.

Option B:
Option B is correct because it includes all the standard features of these questions—letter shifting, substitution and pattern deduction—while excluding C and E, which express unsafe assumptions about position independence and uniform patterns.

Option C:
Option C is wrong since it accepts E (false) and omits A (true), so it cannot be correct.

Option D:
Option D is incorrect because it includes E (false) and omits B (true), so it cannot be correct.

A standard deck of playing cards has 52 cards divided into 4 suits: hearts, diamonds, clubs and spades, each with 13 cards. The favorable outcomes for drawing a heart are 13. Thus, the probability is the ratio of favorable outcomes to total outcomes, which is 13/52. This fraction simplifies to 1/4. So, the probability of drawing a heart is 1/4.

Option A:
Option A, 1/4, is exactly the simplified fraction 13/52. It acknowledges that there are four equally sized suits and that hearts constitute one of the four, giving a 25% chance on a single draw.

Option B:
Option B, 1/3, would require three suits or some other distribution of cards, which is not the case in a standard deck.

Option C:
Option C, 1/13, incorrectly treats the number of ranks as the total sample space, ignoring that each suit has all 13 ranks.

Option D:
Option D, 3/13, would imply that hearts comprise nearly one-quarter of the cards, but with a different count than the actual 13 per suit. It is not supported by the structure of the deck.