UGC NET Questions (Paper – 1)

Statements A and B correctly describe key settings in seating puzzles, including linear and circular arrangements. Statement C is also true when everyone faces the centre, because moving to the left corresponds to moving clockwise. Statement E is correct since sketching diagrams reduces errors under time pressure. Statement D is false because without specifying a reference like North, we cannot assign absolute directions such as East on a circle. Therefore, the combination A, B, C and E only includes all correct statements and excludes the false one.

Option A:
Option A is incomplete because it omits E, even though using diagrams is an important and correct strategy for such puzzles. Thus it does not list all the true statements and cannot be the right answer.

Option B:
Option B is correct since it brings together all correct points and leaves out D, which wrongly assumes that absolute directions are always meaningful in circular seating without a fixed reference.

Option C:
Option C is incorrect as it includes D, which is false, and omits A, thereby losing the description of linear arrangements while endorsing an incorrect claim about absolute directions.

Option D:
Option D is wrong because it keeps D, the faulty statement about East, and misses B and C, so it both includes a false statement and omits two true ones.

Statement B correctly negates the universal “all swans are white” by asserting that at least one swan is not white. Statement C is also correct because the negation of “no students are late” is that some students are late. Statement E summarises the general pattern for negating universal statements: replace “all” by “some” and negate the predicate. Statement A is false because “no swans are white” is stronger than the needed negation, and D is false since the negation of “some teachers are not researchers” is “all teachers are researchers”. Therefore, B, C and E only are correct, which matches option B.

Option A:
Option A is incomplete because it omits E (the general rule) and does not include all correct statements needed for the full set.

Option B:
Option B is correct as it combines the proper negations of specific universal and negative statements with the general quantifier rule, while excluding A and D, which overstate or misstate the negations.

Option C:
Option C is wrong because it includes A, which makes the negation of “all swans are white” too strong, so it contains an incorrect statement in the combination.

Option D:
Option D is incorrect since it includes D, which misnegates an existential negative statement, and it omits C, losing one of the correct concrete examples.

Statement A shows a valid chain of universals, so “All poets are creative” follows. C is valid because “No cats are dogs” is equivalent to “No dogs are cats”. E is correct provided at least one engineer exists; then at least one graduate is an engineer. B and D are invalid because they overgeneralise from particular statements. Thus A, C and E only are correct.

Option A:
Option A is incomplete because it omits E, missing the (existence-assumed) inference from “All engineers are graduates” to “Some graduates are engineers”.

Option B:
Option B is wrong because it introduces D, which wrongly generalises from “Some students are not diligent” to “No students are diligent”.

Option C:
Option C is correct because it collects exactly the valid inferences and excludes B and D, which are invalid generalisations.

Option D:
Option D is incorrect because it accepts B, which misreads a particular statement as a universal, and so includes an invalid inference.

Let the unknown number be N. If 25% of N is 60, then 0.25N = 60. Solving this equation gives N = 60 ÷ 0.25 = 240. To find 40% of this number, we compute 0.40 × 240, which equals 96. Thus, 40% of the number is 96.

Option A:
Option A, 80, corresponds to one third of 240, not 40%, and would arise from mixing up the percentage multipliers. It does not follow from the given condition.

Option B:
Option B, 90, is 37.5% of 240 and again has no direct link to the required 40% rate. It reflects an incorrect multiplication step.

Option C:
Option C is obtained by first recovering the full value of the number from the 25% information and then correctly applying the 40% factor to it. The arithmetic is consistent at each stage and produces 96.

Option D:
Option D, 100, is slightly higher than the correct value and might come from rounding or a mistaken assumption that 40% is close to half, but it is not the exact result.

The series satisfies the rule (a_n = 2n^4 - 3n + 5) with n starting from 1. For n = 1, 2, 3, 4 and 5 we get 2−3+5 = 4, 32−6+5 = 31, 162−9+5 = 158, 512−12+5 = 505 and 1250−15+5 = 1240. For n = 6 we compute (2×6^4 - 18 + 5 = 2592 - 13 = 2579). Hence 2579 is the correct next term.

Option A:
Option A, 2543, is 36 less than the value predicted by the rule and does not equal (2×6^4 - 3×6 + 5). It introduces an arbitrary shortfall not reflected earlier, so 2543 is not valid.

Option B:
Option B, 2561, is closer but still fails to match 2579 and cannot be derived from the formula for n = 6. Choosing 2561 would alter the established pattern. Thus 2561 is not correct.

Option C:
Option C, 2597, overshoots the computed value and again does not satisfy the expression for the next index. Using 2597 would inflate the term without justification and break the quartic structure. Hence 2597 is not appropriate.

Option D:
Option D, 2579, equals the exact output of (a_n = 2n^4 - 3n + 5) when n = 6. It maintains the same relationship between index and term for all entries in the series and is therefore the correct continuation.

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.

Let the two numbers be 9k and 16k. The mean proportional m between them satisfies 9k:m = m:16k. This gives m² = 9k × 16k = 144k², so m = 12k. When we cancel the common factor k, the mean proportional in terms of the ratio alone is 12. Thus, 12 is the required mean proportional for the ratio 9:16.

Option A:
Option A, 6, would result in m² = 36k², which is much smaller than 9k × 16k = 144k². The corresponding proportion 9k:6k is 3:2, but 6k:16k is 3:8, and these are not equal. Therefore 6 does not satisfy the condition for a mean proportional.

Option B:
Option B, 10, gives m² = 100k² and leads to ratios 9k:10k = 9:10 and 10k:16k = 5:8. Since 9:10 ≠ 5:8, the definition of mean proportional is not fulfilled. Thus 10 cannot be the correct answer.

Option C:
Option C, 24, is actually twice the correct value and produces m² = 576k², which corresponds to a much larger product than 9k × 16k. The resulting proportions 9k:24k and 24k:16k are not equal, so 24 fails the basic check of the definition.

Option D:
Option D is correct because m = 12k exactly satisfies m² = 9k × 16k and preserves the equality of ratios 9k:12k and 12k:16k, both simplifying to 3:4. Removing the common factor k leaves the pure numerical mean proportional as 12.

Statements A, B and C give the standard definitions and formulas for GPs. Statement E is also true because phenomena like compound interest and population growth are often modelled using GPs. Statement D is false since a GP does not have constant differences (so it is not an AP). Thus A, B, C and E only are correct.

Option A:
Option A is incomplete since it omits E (applications).

Option B:
Option B is wrong because it includes D (false).

Option C:
Option C is correct because it keeps all true statements and excludes D, which confuses multiplicative and additive patterns.

Option D:
Option D is wrong because it includes D (false) and omits A (definition).

A is correct because each element of the domain must be assigned exactly one image. B is true as many-one mappings allow different domain elements to share a common image. C correctly describes surjective functions where every codomain element is hit by at least one domain element, and D is correct that a mapping both one-one and onto is a bijection. E is false because that condition describes surjectivity; a function in general does not require every codomain element to have a pre-image. Hence A, B, C and D only are correct.

Option A:
Option A omits D and so fails to name bijection explicitly, even though the other statements are true. Because it does not list all correct statements, it is incomplete.

Option B:
Option B leaves out A and therefore does not include the basic definition of a function as a mapping with single-valued images. This omission makes the combination insufficient.

Option C:
Option C drops B and thus ignores the many-one possibility, which is an important non-injective behaviour, even though A, C and D are true. The set is therefore not fully representative.

Option D:
Option D is correct in collecting all accurate statements about functions, surjections and bijections, while excluding E, which confuses general functions with onto functions. It matches the functional concepts tested in NET.

The map scale 4 cm : 10 km means 1 cm represents 10/4 = 2.5 km. If the towns are 7.5 cm apart on the map, the actual distance is 7.5 × 2.5 km. Multiplying gives 18.75 km, so the real distance between the two towns is 18.75 kilometres.

Option A:
Option A is correct because it applies the direct proportion between map distance and real distance consistently. Converting 4 cm to 10 km first and then scaling linearly to 7.5 cm uses a single constant factor of 2.5 km per centimetre, yielding 18.75 km.

Option B:
Option B, 16.5 km, would correspond to using an incorrect scale factor or rounding at an intermediate stage. If 7.5 cm represented 16.5 km, the implied scale would not match 4 cm : 10 km, and the two ratios would conflict. Hence 16.5 km is not accurate.

Option C:
Option C, 20 km, might be guessed by assuming that 8 cm represent 20 km and then approximating 7.5 cm as 8 cm, but such estimation ignores the exact proportional relationship. When we calculate precisely using 2.5 km per centimetre, 20 km is too large.

Option D:
Option D, 22.5 km, would correspond to treating 3 cm as 10 km or some other incorrect mapping. It implies a scale factor different from 2.5 km per centimetre and cannot be derived from 4 cm : 10 km. Therefore, 22.5 km is not consistent with the given scale.

This option is correct because one of the fundamental axioms of probability states that the total probability of all outcomes in a sample space is 1. When outcomes are mutually exclusive and exhaustive, exactly one of them must occur. Therefore, adding their probabilities must give 1. This ensures that some outcome always happens.

Option A:
A total probability of 0 would mean that no outcome can occur, which contradicts the idea of running an experiment. Probabilities must be non-negative and at least one outcome must have positive probability. Thus, the sum cannot be 0 for an actual experiment.

Option B:
The value 1 represents certainty that some outcome from the sample space will occur. Since mutually exclusive and exhaustive outcomes cover all possibilities without overlap, their probabilities must add up to 1. This matches the basic probability axiom, making this option correct.

Option C:
A sum of 1/2 would imply that there is only a 50% chance that any outcome in the declared space occurs. That would mean half the probability lies outside the listed outcomes, so the set would not be exhaustive. Hence, this value cannot be correct here.

Option D:
The value 100 without the percent sign does not fit the standard probability scale from 0 to 1. Even if interpreted as a percentage, it would correspond to 1 on the probability scale, but the question expects the probability value, not the percentage number. Therefore, 100 is not the right answer.

Let the total quantity be T litres. Initially, milk = (5/8)T and water = (3/8)T. When 16 litres are removed from a well-mixed solution, milk removed = (5/8) × 16 = 10 litres and water removed = 6 litres. So the remaining milk is (5/8)T − 10 and the remaining water is (3/8)T − 6. After adding 16 litres of water, water becomes (3/8)T + 10. The new ratio is [(5/8)T − 10] : [(3/8)T + 10] = 5:4. Solving this proportion yields T = 144 litres.

Option A:
Option A, 96 litres, would give initial milk 60 litres and water 36 litres. After removing 16 litres and adding 16 litres of water, the final milk and water quantities would not reduce to the ratio 5:4; a detailed check shows the ratio differs from 5:4. Hence 96 litres does not satisfy the given condition.

Option B:
Option B, 128 litres, leads to initial milk 80 litres and water 48 litres. Following the same removal and replacement process, the resulting milk and water do not maintain a 5:4 ratio. The mathematical equation for the final ratio fails when T = 128, so this value is incorrect.

Option C:
Option C is correct because with T = 144 we get initial milk 90 litres and water 54 litres. Removing 16 litres removes 10 litres of milk and 6 litres of water, leaving 80 litres of milk and 48 litres of water. Adding 16 litres of water gives 80 litres of milk and 64 litres of water, giving 80:64 = 5:4. This exactly matches the new ratio stated.

Option D:
Option D, 160 litres, would create larger starting volumes but the same removal and replacement would not lead to a 5:4 ratio. Solving the final ratio equation with T = 160 gives a contradiction, meaning that this total volume cannot produce the described outcome.

This option is correct because the standard formula for the nth term of an arithmetic progression is aₙ = a + (n−1)d. Here, a is the first term and d is the constant difference between successive terms. This formula comes from adding the common difference repeatedly. Therefore, the nth term is a + (n−1)d.

Option A:
The expression a + nd adds the common difference n times, which overshoots by one step. It would correctly represent the (n+1)th term, not the nth term. Hence, this option is not correct.

Option B:
The expression a − (n−1)d would produce a decreasing sequence even if d is positive. It does not match the usual pattern for an arithmetic progression defined by adding d each time. Therefore, this option is not suitable.

Option C:
The expression nd ignores the first term a entirely and cannot generate the correct sequence unless a is zero. It fails to describe the general nth term formula. Thus, this option is incorrect.

Option D:
The formula a + (n−1)d starts from a and adds the common difference d exactly n−1 times. This accurately generates each term of the progression in order, making it the correct general term.

A is correct because compound interest at least matches and usually exceeds simple interest for the same principal, rate and time. B correctly gives the annual compounding formula, and C is true since in simple interest interest ∝ rate × time, so halving one and doubling the other keeps the product unchanged. E is also correct because more frequent compounding at a fixed nominal rate increases the effective annual rate. D is false because changing rate and time in that way does not guarantee the same accumulated amount. Therefore, A, B, C and E only are correct.

Option A:
Option A omits E and thus fails to mention the important concept of effective rate increasing with compounding frequency. Although A, B and C are true, the combination is incomplete and so not the best answer.

Option B:
Option B is correct since it gathers all the true statements and excludes D, which wrongly suggests invariance of amount under doubling rate and halving time in compound interest. It matches the standard treatment of interest problems in aptitude tests.

Option C:
Option C wrongly includes D, which misrepresents compound interest behaviour, and omits A, underplaying the comparison between compound and simple interest. Hence it mixes a false statement with an omission.

Option D:
Option D is incorrect as it includes D and discards B and C, thereby accepting the erroneous claim and omitting correct formulas and relationships.

The series can be generated using the expression 2n² + 1 for consecutive integers n. For n = 1 to 5 we obtain 2(1)² + 1 = 3, 2(2)² + 1 = 9, 2(3)² + 1 = 19, 2(4)² + 1 = 33 and 2(5)² + 1 = 51. The next integer is 6, so the next term should be 2(6)² + 1. This equals 2 × 36 + 1 = 72 + 1 = 73, which is consistent with the pattern.

Option A:
Option A gives 73, which exactly matches the formula 2n² + 1 when n = 6. The extended sequence 3, 9, 19, 33, 51, 73 is generated smoothly from one algebraic rule. This confirms that 73 is the correct continuation of the number series.

Option B:
Option B suggests 71, which does not satisfy the expression 2n² + 1 for any integer following 5 in this context. Using 71 would break the simple polynomial structure underlying the series. Therefore, 71 cannot be the correct next term.

Option C:
Option C provides 75, which also fails to match 2n² + 1 for the next integer. It introduces an inconsistent jump that is not supported by the existing values. Hence, 75 is not in harmony with the pattern of the sequence.

Option D:
Option D offers 77, which similarly does not correspond to 2n² + 1 for n = 6 or any immediate extension. Including 77 would abandon the clear quadratic rule. Thus, 77 is not the appropriate choice.