UGC NET Questions (Paper – 1)

The terms fit the polynomial rule aₙ = n⁴ + 3n³ + 2 with n starting from 1. Substituting n = 1, 2, 3, 4 and 5 into this expression yields 6, 42, 164, 450 and 1002, exactly the numbers in the series. Evaluating the same formula for n = 6 produces 1946. Hence 1946 is the only value that extends this quartic-plus-cubic pattern correctly.

Option A:
Option A, 1922, is 24 less than the value obtained from aₙ = n⁴ + 3n³ + 2 when n = 6. Accepting 1922 would require reducing the polynomial result only at the sixth term, which contradicts the behaviour of earlier entries. Therefore option A is not consistent with the established pattern.

Option B:
Option B, 1934, is still lower than the required value and does not equal the expression’s output at n = 6. It lies between the earlier predictions but fails to respect the exact algebraic rule. As a result, option B cannot be the correct continuation of the sequence.

Option C:
Option C, 1946, matches precisely the value produced by the formula when n = 6. It preserves the same contributions from the fourth-power and cubic terms together with the constant part. Because this rule explains all given terms and leads naturally to 1946, option C is the correct answer.

Option D:
Option D, 1962, is 16 greater than the polynomial value and cannot be generated by n⁴ + 3n³ + 2 at n = 6. Introducing such an extra increment would break the clean functional relationship. Hence option D is not acceptable.

Statements A, B, D and E are correct. A restates the basic simple interest rule. B is true because with annual compounding, one compounding per year means effective and nominal rates coincide. D is correct since more frequent compounding at the same nominal rate increases total interest. E is also true; at low rates and short durations, simple and compound interest often differ negligibly. C is false because more frequent compounding makes the effective annual rate higher, not lower, than the nominal rate. So A, B, D and E only are correct.

Option A:
Option A is incomplete because it omits E, which notes the practical observation that, for small rates and short periods, the difference between SI and CI can be very small.

Option B:
Option B is correct since it collects all the accurate statements about calculation bases, effective rates and compounding frequency, while excluding C, which reverses the relationship between nominal and effective rates.

Option C:
Option C is wrong because it includes C, which misstates the effect of multiple compounding periods, and therefore cannot represent the full set of correct statements.

Option D:
Option D is incorrect as it retains C (false) and omits B (true), so it both includes an error and misses a key correct statement.

The series follows the rule (a_n = n^4 + 4n^2 - 2) with n starting from 1. For n = 1, 2, 3, 4 and 5 the expression yields 3, 30, 115, 318 and 723, as in the question. For n = 6 we compute (6^4 + 4×6^2 - 2 = 1296 + 144 - 2 = 1438). Therefore 1438 is the correct next term in the sequence.

Option A:
Option A, 1414, is 24 less than the formula’s output and does not equal (6^4 + 4×6^2 - 2). It would impose an artificial reduction that the pattern does not support. Hence 1414 is not consistent with the rule.

Option B:
Option B, 1438, matches exactly the result of the expression for n = 6. It preserves the quartic and quadratic contributions in exactly the same way as for earlier terms. This alignment makes 1438 the correct answer.

Option C:
Option C, 1454, overshoots the computed value and cannot be derived from the formula for n = 6. Choosing 1454 would disrupt the precise algebraic structure of the series. Thus 1454 is not valid.

Option D:
Option D, 1470, deviates even more from 1438 and once again fails to satisfy the rule. Using 1470 would break the tight connection between index and term, so it is not correct.

D is wrong because the total probability of all simple events in a well-defined sample space must sum to exactly 1, not more than 1. Statements A, B, C and E are correct: probabilities are bounded between 0 and 1, probabilities 0 and 1 represent impossibility and certainty within the model, mutually exclusive events have additive probabilities, and NET questions often test both conceptual understanding and simple calculations. Since only D contradicts the axioms of probability, the correct answer is the option that lists D only as wrong.

Option A:
Option A is correct because it isolates D as the single statement that violates the basic rule that the total probability over a sample space equals 1. It implicitly accepts that the other statements are consistent with elementary probability theory and exam practice.

Option B:
Option B is incorrect as it also treats A as wrong, even though A correctly states the allowed numerical range of probability values. By labelling A incorrect, this option misrepresents one of the most fundamental facts about probability.

Option C:
Option C is wrong because it groups C with D as wrong, despite C correctly stating the addition rule for mutually exclusive events. Including a true rule alongside a false statement makes this option invalid.

Option D:
Option D is also incorrect since it adds B and C to the set of wrong statements, even though both B and C are standard properties of probability. This option rejects several correct ideas along with the one incorrect statement.

Statements A, C, D and E correctly describe statement–conclusion reasoning. A is true because a conclusion must be a reasonable inference from what is stated. C is correct in that valid syllogistic conclusions follow necessarily from premises. D is true; sometimes more than one conclusion is logically supported. E is correct because unsupported personal opinions do not qualify as conclusions based on the statement. B is false since a conclusion that contradicts the given statement is generally weak or invalid. Thus A, C, D and E only are correct.

Option A:
Option A is incomplete as it omits E, failing to emphasise that conclusions must be grounded in the statement rather than personal views, an important exam guideline.

Option B:
Option B is incorrect because it includes B, which wrongly treats contradictions as strong conclusions, and so mixes one false statement with true ones.

Option C:
Option C is wrong since it leaves out A and includes only C, D and E, thereby omitting the foundational idea of what a conclusion is in statement–conclusion questions.

Option D:
Option D is correct because it gathers all accurate points about necessity, multiplicity and support of conclusions, while excluding B, which misrepresents strong conclusions.

Statement A is correct because many letter series rely on letter positions (for example, A = 1, B = 2, etc.). Statement B is true since fixed forward or backward jumps are common. Statement D is also correct, as pairing or tripling letters often exposes a repeating cycle. Statement C is false because some series rely on reversing groups or cyclically shifting blocks, not just simple position changes. Statement E is false as NET papers do contain mixed letter–number series. Thus, the combination that includes A, B and D while excluding C and E is the only fully correct one.

Option A:
Option A is incorrect because it includes E, which wrongly claims that mixed letter–number series are never used, and therefore combines true and false statements. Even though A, B and D are correct, the presence of E makes this option invalid.

Option B:
Option B is wrong since it includes C, which falsely insists that only alphabet positions are ever used and bans reversals or rotations, and it omits D, which is a true strategy about grouping letters. This mix of one false and one missing true statement invalidates the option.

Option C:
Option C is also incorrect because it takes B, C and D together; C is false and the option leaves out A, which is an important fact about using letter positions. Including a wrong statement and omitting a true one makes the combination unsuitable.

Option D:
Option D is correct because it brings together A, B and D, all of which describe genuine features and methods for analysing letter series, while excluding the clearly false generalisations C and E.

To solve 5x + 3 = 18, we first subtract 3 from both sides to isolate the term with x. This gives 5x = 15. Dividing both sides by 5, we get x = 15 ÷ 5 = 3. Therefore, the solution of the equation is x = 3.

Option A:
Option A, 2, does not satisfy the equation because substituting x = 2 yields 5 × 2 + 3 = 13, which is not equal to 18. So this value fails to make both sides equal.

Option B:
Option B, 3, when substituted gives 5 × 3 + 3 = 15 + 3 = 18, which matches the right side and confirms that x = 3 is the correct solution.

Option C:
Option C, 4, produces 5 × 4 + 3 = 23, which is greater than 18 and so cannot be the solution.

Option D:
Option D, 5, gives 5 × 5 + 3 = 28, which again does not equal 18, and therefore cannot solve the equation.

In each group the letters are equally spaced by six positions in the alphabet. AGM uses positions 1, 7 and 13, BHN uses 2, 8 and 14, CIO uses 3, 9 and 15 and DJP uses 4, 10 and 16. The starting letter increases by one each time, so the next group should start at E and use letters at positions 5, 11 and 17, which are E, K and Q. Hence EKQ is the correct continuation.

Option A:
Option A, EKR, has the correct first two letters but ends with R, which is position 18 instead of 17. That changes the spacing of the last jump to seven rather than six. Because the sequence relies on a constant gap of six between letters in each group, EKR does not follow the pattern.

Option B:
Option B is correct because E, K and Q lie exactly six positions apart from each other, just like the letters in all previous groups. The starting letter E also continues the simple progression from A to D. This combination of consistent internal spacing and systematic movement of the first letter makes EKQ the only valid next term.

Option C:
Option C, ELP, does not keep a constant difference between successive letters, and its positions do not match the earlier arithmetic structure. The gaps inside ELP differ from those inside AGM, BHN, CIO and DJP. Therefore it cannot be considered a proper continuation of the series.

Option D:
Option D, FKR, breaks the pattern by starting at F instead of E and also fails to maintain the fixed six letter spacing. Both the starting position and the internal distances contradict the established rule, so FKR is not correct.

Statements A and C are correct because the contrapositive “If not q then not p” is logically equivalent to “If p then q”, and the inverse is indeed “If not p then not q”. Statement D is also true as many reasoning errors arise from confusing the converse “If q then p” with the contrapositive. Statement B is false because it mislabels the converse, and E is false because the contrapositive of a true implication is also true, not always false. Therefore, the combination A, C and D only is correct.

Option A:
Option A is correct since it gathers exactly the true statements about how converse, inverse and contrapositive are defined and how confusion among them can cause mistakes, while rejecting B and E, which misdescribe these relationships.

Option B:
Option B is incorrect as it includes B, which wrongly defines the converse, and thereby endorses a mislabelling of basic logical forms. Even though A and C are true, the presence of B ruins the option.

Option C:
Option C is wrong because it treats B, C and D as correct together, despite B being false. It also omits A, which explains the logical equivalence between an implication and its contrapositive, a central concept in NET-level logic.

Option D:
Option D is also incorrect because it includes E, which mistakenly claims that the contrapositive of a true implication is always false, and omits C, leaving out the correct statement of the inverse. This mixture makes the option unsound.

Consecutive terms differ by 7: 11 − 4 = 7, 18 − 11 = 7 and 25 − 18 = 7. This confirms an arithmetic progression with common difference 7. Adding 7 to the last term 25 gives 32. Therefore, 32 is the correct next term in the sequence.

Option A:
Option A is 29, which is only 4 greater than 25 and breaks the consistent step of 7. There is no reason in the earlier terms to reduce the difference. Hence, 29 is not correct.

Option B:
Option B equals 32, coming from 25 + 7 and preserving the constant difference of 7. The series 4, 11, 18, 25, 32 maintains a clear arithmetic structure. This makes 32 the appropriate continuation.

Option C:
Option C is 35, which is 10 more than 25 and introduces a difference of 10 not seen earlier. This would create an irregular jump at the end of the series. Therefore, 35 does not match the pattern.

Option D:
Option D is 36, giving a final difference of 11. Such a difference is unsupported by any prior step and distorts the simple structure. Thus, 36 is not the correct answer.

This sequence follows the polynomial rule aₙ = 3n⁴ + n³ + n with n starting from 1. Evaluating the expression for n = 1, 2, 3, 4 and 5 yields 5, 58, 273, 836 and 2005, matching the given terms exactly. For n = 6, we obtain a₆ = 3·6⁴ + 6³ + 6 = 3·1296 + 216 + 6 = 3888 + 222 = 4110. Therefore 4110 is the only number that fits this functional pattern and correctly continues the series.

Option A:
Option A, 4086, is 24 less than the value predicted by 3n⁴ + n³ + n when n = 6. Choosing 4086 would require reducing the correct polynomial result at this term, even though earlier values are exact. This violates the consistency of the pattern, so option A is not acceptable.

Option B:
Option B, 4098, is 12 less than the correct value and again cannot be expressed as 3·6⁴ + 6³ + 6. It provides an approximation but not the true outcome of the formula. In a high-level series problem, such a discrepancy means the option does not represent the genuine rule.

Option C:
Option C, 4122, is 12 greater than the correct term 4110 and likewise does not match the polynomial output. Accepting 4122 would introduce an unexplained upward shift at the last step. Therefore this choice cannot be considered a valid continuation of the series.

Option D:
Option D, 4110, is exactly the value obtained when n = 6 is substituted into 3n⁴ + n³ + n. It preserves the same combination of a strong quartic term, a cubic correction and a linear part that explains the earlier numbers. Because it extends the rule seamlessly, option D is the correct answer.

The differences between successive terms are 4, 6, 8 and 10. These differences form an arithmetic pattern increasing by 2 each time. The next difference should therefore be 12. Adding 12 to the last term 33 gives 33 + 12 = 45, which extends the series consistently.

Option A:
Option A gives 43, corresponding to a difference of 10 from 33, which simply repeats the last difference rather than increasing it. This breaks the second-level arithmetic progression. Hence, 43 does not follow the intended pattern.

Option B:
Option B yields 45, which is 12 more than 33 and maintains the difference sequence 4, 6, 8, 10, 12. This preserves the clear, systematic growth at the level of differences. Therefore, 45 is the correct next term in the series.

Option C:
Option C suggests 47, which would produce a difference of 14 and jump beyond the expected increment. This destroys the steady increase by 2 units in the differences. Thus, 47 is not a valid continuation.

Option D:
Option D offers 49, giving a difference of 16 from 33 and deviating even further from the planned pattern. Including 49 would make the sequence erratic. Therefore, 49 cannot be regarded as correct.

The series follows an alternating pattern of multiplying by 2 and then subtracting 2. Starting from 5, we get 5 × 2 = 10, then 10 − 2 = 8, then 8 × 2 = 16 and then 16 − 2 = 14. Continuing this pattern, the next step after 14 should be to multiply by 2, giving 14 × 2 = 28. This preserves the established alternation of operations.

Option A:
Option A, 18, could arise from adding 4 to 14, but there is no consistent rule of adding 4 in the earlier part of the series. It introduces a new pattern not supported by previous terms.

Option B:
Option B, 20, might seem plausible as adding 6 to 14, yet such an operation is not part of the alternating multiply by 2 and subtract 2 rule evident in the earlier sequence.

Option C:
Option C, 24, equals 16 + 8 or similar combinations but does not correspond to the prescribed alternation of operations applied directly to the preceding term.

Option D:
Option D directly applies the observed pattern, maintaining the multiply by 2 step after a subtract step. It ensures that the structure of alternating operations continues without disruption, making 28 the correct next term.

Statements A, B and C summarise the leap-year rule of the Gregorian calendar correctly. A states the basic rule for ordinary years divisible by 4 but not by 100. B adds the exception that years divisible by 400 are leap years even though they are century years. C notes that a century year divisible by 100 but not by 400 is not a leap year. E is also true because 366 days equal 52 weeks plus 2 days, giving two odd days. D is false since divisibility by 8 alone does not override the 100 and 400 year conditions, so A, B, C and E only are correct.

Option A:
Option A is incomplete because it omits E and thus does not connect leap years to the concept of odd days, which is often used in calendar-based reasoning questions. Without E, the relationship to day-of-week changes is not fully explained.

Option B:
Option B is also incomplete since it includes only B, C and E and omits A, failing to mention the basic divisibility-by-4 rule for non-century years. This makes the description of leap-year identification partial.

Option C:
Option C is correct because it collects all true statements, including the ordinary rule, the century-year modification and the odd-day implication, while rejecting D, which overgeneralises divisibility by 8. It reflects the treatment of leap years in NET calendar problems.

Option D:
Option D is incorrect as it introduces D, which asserts that every year divisible by 8 is leap, even though century exceptions contradict this, and it omits B. The combination therefore contains an error and cannot be considered correct.

Statements A and B correctly describe the standard structure: two premises leading to a conclusion, each with subject and predicate terms. D is also correct because syllogistic validity concerns whether the conclusion follows logically from the premises, regardless of whether those premises are actually true. C is false since the middle term appears in the premises, not the conclusion, and E is false because a valid argument can have a true conclusion even when its premises are false. Therefore A, B and D only are correct.

Option A:
Option A is correct since it includes exactly the structural and logical-form facts without importing the false claims about the middle term and truth of premises forcing truth of conclusion.

Option B:
Option B is incorrect because it includes C, which mislocates the middle term in the conclusion instead of in the premises, so it puts a wrong statement into the combination.

Option C:
Option C is wrong as it adds E, which wrongly insists that false premises force a false conclusion, and it also fails to include B, so it contains errors/omissions.

Option D:
Option D is incorrect because although B and D are true, E is false, and dropping A loses the accurate description that a categorical syllogism has two premises and one conclusion.