UGC NET Questions (Paper – 1)

Analogical reasoning involves identifying structural or functional similarity between two situations and transferring knowledge from the known situation to the new one. In mathematical aptitude, we often use analogies in number and letter series when we infer the next term by comparing to a familiar pattern. The strength of an analogy depends on the relevance and depth of the similarities, not merely superficial resemblance. This fits the description of drawing conclusions by recognising similarity between situations.

Option A:
Deductive reasoning operates by applying a general rule to a specific case rather than by comparing two similar situations. It focuses on logical implication from premises to conclusion. Since the question emphasises similarity-based reasoning, deductive reasoning does not match the required description. Therefore, this option is not correct.

Option B:
Inductive reasoning generalises from many specific instances to formulate a general rule or law. It does not primarily rely on comparing two different situations for similarity. Even though inductive reasoning might sometimes use analogies, the technical term for similarity-based inference between cases is analogical reasoning, not induction. Hence, this option is not the most appropriate.

Option C:
Analogical reasoning is correct because it is defined as reasoning that maps similarities between two domains or problems to draw new conclusions. In aptitude tests, analogies like "2:4::3:6" directly test this type of reasoning. Recognising this concept helps students approach analogy-based questions in UGC NET Paper 1 more effectively. Therefore, this option accurately represents the reasoning described in the question.

Option D:
Causal reasoning focuses on cause–effect relationships rather than on similarity between different situations. It tries to understand how one event brings about another, such as how increased study time causes better performance. The question does not mention cause and effect, but similarity, so causal reasoning is not the correct answer.

Statement B is correct because “paternal aunt” is indeed the sister of one’s father. Statement C is true as diagrams reduce confusion by showing generational levels and links. Statement D is correct since in-laws may refer to spouse’s siblings or siblings’ spouses depending on context. Statement E is also true because exam questions sometimes give clues from which gender has to be deduced. Statement A is false because “maternal uncle” is the brother of one’s mother, not the father. Hence the combination B, C, D and E only is correct.

Option A:
Option A is incomplete because, although B, C and D are true, it leaves out E, which correctly states that gender is sometimes inferred from context. Since it does not include all correct statements, it is not the right answer.

Option B:
Option B is wrong because it includes A along with B, C and D, and A incorrectly defines “maternal uncle” as the father’s brother, which contradicts standard usage. The presence of this false statement invalidates the combination.

Option C:
Option C is correct as it gathers all the true statements while excluding the incorrect definition in A. It therefore fully reflects how blood relation terms are used and tested in NET reasoning questions.

Option D:
Option D is incorrect because it omits C, the helpful recommendation about drawing family trees, and it also keeps only B, D and E, which is not the complete set of correct statements for this question.

This sequence is modelled by the rule aₙ = n! + 3n² with n starting from 1. For n = 1, 2, 3, 4 and 5 the expression gives 1! + 3·1² = 4, 2! + 3·2² = 14, 3! + 3·3² = 33, 4! + 3·4² = 72 and 5! + 3·5² = 195, which matches the given terms exactly. For n = 6 we obtain a₆ = 6! + 3·6² = 720 + 108 = 828. Hence 828 is the only value consistent with this factorial-based pattern.

Option A:
Option A, 804, is 24 less than the value from n! + 3n² at n = 6 and cannot be generated by the same formula. Choosing 804 would require subtracting 24 from the correct result only at the sixth term, which disrupts the pattern of factorial growth with a quadratic adjustment. Therefore option A is incorrect.

Option B:
Option B, 816, is 12 below the correct value 828 and does not equal 720 + 108. It represents a near approximation but still violates the exact functional relationship between n and aₙ. Consequently, option B does not correctly continue the series.

Option C:
Option C, 840, is 12 greater than the required value and likewise cannot arise from 6! + 3·6². Accepting 840 would artificially inflate the last term beyond what the rule predicts. Thus option C is not a valid continuation of the sequence.

Option D:
Option D, 828, exactly matches the value produced by the rule when n = 6. It faithfully maintains the combination of factorial growth and quadratic adjustment that governs all previous terms. Because it extends this pattern without any exception, option D is the correct answer.

From a:b = 2:3, b:c = 2:3 and c:d = 2:3, we can write a/b = 2/3, b/c = 2/3 and c/d = 2/3. The compound ratio a:d is obtained by multiplying these three fractions: (2/3) × (2/3) × (2/3) = 8/27. Thus, a:d = 8:27.

Option A:
Option A, 2:3, uses only one of the three ratios and ignores the repeated multiplication required to go from a to d. It would be correct if we moved only one step in the chain, but we actually move through b and c as intermediate terms, so 2:3 is incomplete.

Option B:
Option B is correct because it cubes both numerator and denominator of the base ratio 2:3, reflecting the three links in the chain from a to d. The calculation (2/3)³ = 8/27 correctly captures the effect of applying the same proportional change three times in succession.

Option C:
Option C, 4:9, corresponds to squaring the base ratio, which would be appropriate if we had only two equal steps instead of three. Since there are three equal ratios a:b, b:c and c:d, 4:9 underestimates the cumulative effect.

Option D:
Option D, 16:81, arises from raising 2:3 to the fourth power and would require four equal proportional steps, which are not present in the given information. Therefore 16:81 overstates the change and does not match the structure of the problem.

The starting letters M, P, S and V occupy positions 13, 16, 19 and 22, increasing by 3 each time. Each group is formed by three consecutive letters in forward order. Adding 3 to 22 gives 25, which is Y, and the next two letters after Y are Z and A, giving YZA with cyclic wrap around. Thus YZA is the unique group that continues the plus three pattern while respecting the cyclic nature of the alphabet.

Option A:
Option A, XYZ, starts at X, position 24, which is only 2 positions after V instead of 3. It therefore does not follow the consistent step of three seen in the starting letters. Even though XYZ is a consecutive group, it does not arise from the same generating rule.

Option B:
Option B, WXY, begins at W, position 23, just one step after V. This shrinks the required step and contradicts the established difference of three positions between starting letters. For this reason, WXY cannot be the correct continuation.

Option C:
Option C is correct because Y is position 25, exactly three positions beyond V, and YZA forms a three letter block progressing alphabetically with wrap around to A. It respects both the distance between starting letters and the internal consecutive pattern. This makes YZA the logical next term in the series.

Option D:
Option D, ZAB, starts at Z, which is four positions ahead of V when counting cyclically, not three. That would increase the gap and break the regularity of the step size. As the pattern does not show any such change, ZAB cannot be accepted.

This series is generated by the quintic rule aₙ = n⁵ − n + 1 for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 1−1+1 = 1, 32−2+1 = 31, 243−3+1 = 241, 1024−4+1 = 1021 and 3125−5+1 = 3121, exactly matching the given numbers. For n = 6 the same expression gives 6⁵−6+1 = 7776−6+1 = 7771. Therefore 7771 is the unique next term that maintains this fifth-degree pattern.

Option A:
Option A, 7729, is significantly below the computed value and does not satisfy aₙ = n⁵−n+1 for n = 6. It would require subtracting 42 from the formula’s result only at the last term. Such a deviation has no basis in the earlier behaviour of the sequence, so option A is incorrect.

Option B:
Option B, 7759, is closer but still does not equal 7771 and therefore fails to arise from applying n⁵−n+1 to n = 6. Selecting 7759 would alter the functional rule that perfectly explains all previous terms. Hence option B is not a valid continuation of the pattern.

Option C:
Option C, 7771, coincides exactly with 6⁵−6+1 and follows directly from the quintic expression. It keeps the same high-order dependence on n that produces the rapid growth observed in the sequence. Because it continues the rule without modification, 7771 is the correct next term.

Option D:
Option D, 7789, overshoots the formula’s output by 18 and cannot be expressed as n⁵−n+1 for the sixth position. Using 7789 would break the precise relationship between index and term, making option D inconsistent with the established series.

The first statement says that all rational numbers are contained within the set of real numbers. The second statement tells us that there is at least some overlap between real numbers and integers. From these premises we can be sure that the set of rationals lies inside the reals, but we are not given an explicit link between rationals and integers. It is therefore safe to say that some real numbers may be rational numbers, since rational numbers form a subset of the reals.

Option A:
Option A, “Some integers are rational numbers,” is true in standard mathematics but does not follow solely from the given premises, which never state a direct relation between integers and rationals.

Option B:
Option B, “Some rational numbers are integers,” is also mathematically true but again goes beyond the information explicitly stated in the premises, which only connect rationals with reals and integers with reals.

Option C:
Option C cautiously asserts a possibility: since all rationals are reals, it is entirely consistent that some real numbers may be rational. This conclusion remains within what is warranted by the premises.

Option D:
Option D, “All integers are rational numbers,” is stronger than anything that can be deduced from the given statements and is not logically enforced by them, even though it is true in standard number systems.

This series is described by the rule (a_n = 2n^4 - n^2) for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 2−1 = 1, 32−4 = 28, 162−9 = 153, 512−16 = 496 and 1250−25 = 1225, which matches the given list. For n = 6 we compute (2×6^4 - 6^2 = 2×1296 - 36 = 2592 - 36 = 2556). Therefore 2556 is the correct continuation of the quartic pattern.

Option A:
Option A, 2528, is 28 less than the formula’s output and does not equal (2×6^4 - 6^2). It would force an arbitrary downward adjustment at the last term, which is inconsistent with the rule. Hence 2528 is not a valid next term.

Option B:
Option B, 2556, matches exactly the value produced by (a_n = 2n^4 - n^2) when n = 6. It maintains the same combination of quartic and quadratic parts seen in all earlier terms. For this reason, 2556 is the correct answer.

Option C:
Option C, 2592, corresponds to (2×6^4) alone and ignores the subtraction of (6^2). That omission breaks the established formula. Thus 2592 does not correctly extend the sequence.

Option D:
Option D, 2616, is even larger and cannot be written as (2n^4 - n^2) for the next integer n. Adopting 2616 would make the pattern inconsistent, so it is not correct.

A is correct because assumptions are taken as underlying ideas that the argument depends on. C is true as implicit ideas that make the statement meaningful count as assumptions. D is also correct because many NET items ask whether a given assumption is implicit in the statement. B is false since assumptions are not always explicitly stated, and E is false because some proposed assumptions may be illogical or extreme. Therefore, A, C and D only are correct.

Option A:
Option A correctly gathers the three statements that reflect how assumptions work in reasoning questions and discards B and E, which misrepresent explicitness and logical acceptability. It fits the exam pattern for statement–assumption items.

Option B:
Option B wrongly includes B, which insists on explicit stating, contrary to the very idea of an assumption being implicit. Hence it cannot be correct even though it includes A and C.

Option C:
Option C includes B and thus inherits the same error about explicitness, even though it also includes C and D, both of which are true. Mixing a false statement with true ones invalidates the option.

Option D:
Option D is incorrect because it includes E, which incorrectly suggests all assumptions offered are sound, and omits C, ignoring the role of implicit background beliefs.

Each group uses a constant +6 jump: (1,7,13,19), (2,8,14,20), (3,9,15,21), (4,10,16,22). Next is (5,11,17,23) = EKQW.

Option A:
Option A starts at F and does not match the required positional set.

Option B:
Option B is correct because it continues both the +1 shift in the first letter and the +6 internal spacing.

Option C:
Option C breaks the fixed +6 spacing.

Option D:
Option D breaks the fixed +6 spacing (E to J is +5, not +6).

To find the LCM, we factorize the numbers into primes. The number 12 is 2² × 3 and 18 is 2 × 3². The LCM takes the highest power of each prime appearing in either factorization, giving 2² × 3². This product equals 4 × 9 = 36. Hence, 36 is the smallest number that is a multiple of both 12 and 18.

Option A:
Option A, 36, includes both enough factors of 2 and enough factors of 3 to be divisible by the two given numbers. It is also the smallest such number and so satisfies the definition of the LCM.

Option B:
Option B, 24, is divisible by 12 but not by 18 because 24 ÷ 18 is not an integer. It lacks a second factor of 3.

Option C:
Option C, 30, is divisible by neither 12 nor 18 in an exact sense, as it does not contain the required combination of prime powers.

Option D:
Option D, 42, is divisible by 6 and 7, but not by 12 or 18 without leaving a remainder. It is larger than necessary and not a common multiple in this context.

The nth term of the series can be described by the formula (a_n = n^3 - n) with n starting from 2. Substituting n = 2, 3, 4, 5 and 6 yields 2³−2 = 6, 3³−3 = 24, 4³−4 = 60, 5³−5 = 120 and 6³−6 = 210. For n = 7, the expression gives 7³−7 = 343−7 = 336. Therefore 336 is the unique value that preserves this cubic relationship.

Option A:
Option A, 336, matches exactly the value produced by substituting n = 7 into (a_n = n^3-n). Because the same formula generates all earlier terms and 336 as well, the pattern remains perfectly intact. Hence 336 is the correct continuation of the sequence.

Option B:
Option B, 340, does not equal (7^3-7) and cannot be obtained from the same formula without altering it. Using 340 would break the neat polynomial structure that explains the given terms. Therefore 340 is not consistent with the pattern.

Option C:
Option C, 342, similarly fails to satisfy the expression (n^3-n) for an integer n following the observed order. It would require changing the rule solely for the last term, which is mathematically artificial. Hence 342 cannot be accepted.

Option D:
Option D, 346, lies even further away from the predicted value and has no direct connection with the defining cubic relation. Selecting 346 would abandon the underlying functional rule, so it is not the correct next term.

A is the standard inclusion–exclusion formula for two sets. B is a special case when A and B are disjoint (intersection is empty). C is true because an intersection cannot have more elements than either set. D is true for subset relations. E is false because inclusion–exclusion is commonly extended to three (and more) sets. Therefore, A, B, C and D only are correct.

Option A:
Option A is incomplete because it omits D, which is also a true statement about subset relations with union and intersection.

Option B:
Option B is correct because it includes all true statements (A, B, C, D) and excludes E, which is false.

Option C:
Option C is incomplete because it omits A, which is a key identity for set cardinality.

Option D:
Option D is wrong because it includes E (false), so it cannot be the correct set.

In AHO, BIP, CJQ and DKR the positions of the letters show the same wide gap between successive letters within each group. At the same time, each column increases by one letter from group to group: the first letters go A, B, C, D and the second letters H, I, J, K and the third letters O, P, Q, R. Extending these sequences gives E as the next first letter, L as the next second letter and S as the next third letter. This produces ELS, which alone satisfies both the internal spacing and the column wise progressions, making it the correct continuation.

Option A:
Option A, ELT, has the correct first two letters but pushes the third letter further ahead than the pattern demands. The jump from R to T is larger than the consistent step used in the third column earlier. Because it changes the size of the movement for the last letter, ELT does not fit the series.

Option B:
Option B, EKR, keeps E as the first letter but leaves the second and third letters aligned with the previous term rather than moving them forward. That would break the rule that all three columns advance together. Therefore EKR cannot be accepted as the next term.

Option C:
Option C is correct because ELS continues the simple A→B→C→D→E, H→I→J→K→L and O→P→Q→R→S chains and still respects the same gap inside each group. The triple is fully consistent with the way earlier terms were generated. This agreement with both dimensions of the pattern confirms ELS as the right answer.

Option D:
Option D, FLT, changes the starting letter to F and shifts the others in a way that does not match the observed sequences. The columns would no longer increase by exactly one step. As a result, FLT is not compatible with the pattern of the series.

The series alternates between multiplying by 3 and adding 1. Starting from 2, we have 2 × 3 = 6, 6 + 1 = 7, 7 × 3 = 21, 21 + 1 = 22, 22 × 3 = 66 and 66 + 1 = 67. The next operation in this alternating pattern is multiplication by 3. Thus, the next term should be 67 × 3 = 201, which maintains the established structure.

Option A:
Option A gives 200, which cannot be obtained by either multiplying by 3 or adding 1 to 67. It introduces a new operation that is not indicated by earlier transitions. Therefore, 200 is not consistent with the observed pattern.

Option B:
Option B yields 201, exactly equal to 67 × 3, and fits the repeated alternation between "×3" and "+1". The series 2, 6, 7, 21, 22, 66, 67, 201 follows one coherent rule throughout. Hence, 201 is the correct next term.

Option C:
Option C suggests 203, which is 136 greater than 67 and does not correspond to either operation used previously. This destroys the recursive clarity of the sequence. Thus, 203 is not the right continuation.

Option D:
Option D offers 205, moving even further away and requiring an even larger and unjustified jump. This is not supported by any step in the existing pattern. Therefore, 205 cannot be regarded as correct.