UGC NET Questions (Paper – 1)

The positions of these letters are Z(26), W(23), T(20), Q(17) and N(14). The difference between consecutive terms is −3 each time (26→23, 23→20, 20→17, 17→14). Continuing the same rule, the next position is 14 − 3 = 11, which is the letter K. Therefore K is the unique letter that preserves the constant backward step of 3.

Option A:
Option A, L, is at position 12, which is only 2 steps behind N at 14. This contradicts the strict pattern of subtracting 3 from the position each time. Because L does not maintain the consistent decrement, it cannot be part of the series.

Option B:
Option B, M, corresponds to position 13, giving a difference of 1 from N. There is no indication that the size of the backward step is reducing as the series progresses. Since the pattern clearly shows a constant −3, M fails to fit the rule.

Option C:
Option C, J, is at position 10, which is 4 positions behind N. This would increase the backward jump to −4, altering the original rule of the sequence. As there is no evidence of changing step sizes, J does not correctly continue the series.

Option D:
Option D is correct because K is at position 11, exactly 3 positions before N. This maintains the uniform backward movement that characterises the sequence. Keeping the decrement constant is essential for logical consistency, so K is the only valid next term.

Inductive reasoning begins with particular examples or observations and uses them to infer a broader rule or generalisation. In mathematical aptitude, students often use inductive reasoning to guess a formula or pattern from a few terms of a sequence. The conclusions of induction are probable rather than certain because they rely on limited evidence. This fits the description of moving from specific cases to a general statement.

Option A:
Deductive reasoning starts from a general rule and applies it to specific cases, which is the opposite direction of what the question describes. For example, using a known formula to solve a numerical problem is deductive, not inductive. Therefore, although important in mathematics, it does not match the process of generalising from repeated observations. Hence, this option is not correct here.

Option B:
Inductive reasoning is correct because it explicitly captures the method of drawing a general rule from specific data or examples. When we look at several terms of a number pattern and propose a general formula, we are using induction. Many discoveries in mathematics and science begin with inductive reasoning before being rigorously proven deductively. Thus, this option perfectly matches the description given in the stem.

Option C:
Analogical reasoning compares one situation with another based on similarity and then transfers knowledge from the known case to the new one. It does not necessarily require repeated observations of many particular cases. Instead, it depends on perceived resemblance, which is different from forming a general rule from multiple examples. Hence, it is not the best answer to this question.

Option D:
Statistical reasoning involves using data, averages, and measures of dispersion to make inferences, often supported by probability. While it may also use samples, it is more focused on quantitative data analysis and formal methods. The question, however, asks about a general cognitive process of moving from specific to general, which is more precisely described by inductive reasoning than by statistical reasoning.

The pattern here is given by aₙ = 3n⁴ − n² + 4 with n starting from 1. Substituting n = 1, 2, 3, 4 and 5 yields 6, 48, 238, 756 and 1854, which are exactly the numbers in the series. Applying the same expression for n = 6 gives 3856. Hence 3856 is the only value that keeps this quartic-based pattern consistent.

Option A:
Option A, 3824, is 32 less than the value obtained from aₙ = 3n⁴ − n² + 4 when n = 6. To accept 3824 we would need to subtract 32 only at the last term, which is not indicated by the earlier entries. As a result, this option does not preserve the polynomial rule and is incorrect.

Option B:
Option B, 3840, is still smaller than the required value and does not equal the output of the formula at n = 6. It represents a partial correction toward the right term but still breaks the functional relationship. Therefore option B cannot correctly continue the series.

Option C:
Option C, 3856, matches exactly the value predicted by 3n⁴ − n² + 4 for n = 6. It respects the same combination of a fourth-power term and a negative square adjustment that shapes the growth of the sequence. Because the same rule explains all the given terms and leads naturally to 3856, this option is correct.

Option D:
Option D, 3872, is 16 greater than the polynomial value and cannot be generated by the rule for the sixth position. Introducing this extra amount would break the algebraic pattern that the series follows. Thus option D is not a valid continuation.

In this pattern the first and second letters gradually move forward through the alphabet while the third letter moves backward from the end. AMZ, BNY, COX and DPW show that each column increases by one step for the first two letters and decreases by one step for the last letter. Continuing this synchronized movement, A,B,C,D lead naturally to E as the next first letter, the middle letters M,N,O,P give Q as the next, and the last letters Z,Y,X,W give V. This produces EQV, which alone respects the exact motions of every position and is therefore the correct next term.

Option A:
Option A, EQW, uses the correct first two letters but keeps the last letter at W instead of moving it back to V. This breaks the clear backward march of the final letters from Z towards the middle of the alphabet. Since the last position is not updated consistently, EQW cannot be the right continuation.

Option B:
Option B, FPV, advances the first letter too far and also disturbs the coordinated step of the middle and last letters. The resulting group does not come from applying the same one step shift in each column that produced the earlier terms. Because of this mismatch, FPV does not fit the pattern.

Option C:
Option C is correct because EQV is obtained by exactly the same type of movement that takes AMZ to BNY, BNY to COX and COX to DPW. Each first letter moves one place forward, each middle letter moves one place forward and each last letter moves one place backward. This perfect alignment with the existing rule makes EQV the only consistent choice.

Option D:
Option D, ERU, moves the last letter too far back while pushing the middle letter ahead in a way that does not match the established sequences. The column wise progressions would be broken if this group were inserted. Therefore ERU cannot be considered the next term in the series.

Statement A is correct because correlation quantifies both direction and strength of linear association. Statement C is true as a value near zero indicates weak or no linear correlation. Statement D is also correct because correlation alone cannot establish cause and effect. Statement E accurately states that in negative correlation, higher values of one variable are associated with lower values of the other. Statement B is false since +1 represents perfect positive, not negative, linear relationship. Therefore, A, C, D and E only are correct.

Option A:
Option A is incomplete since it omits D (correlation is not causation).

Option B:
Option B is incomplete because it omits C and does not include the full correct set.

Option C:
Option C is incorrect because it excludes A (definition) and omits D (causation warning).

Option D:
Option D is correct as it joins all four accurate statements and excludes only B, which misstates the meaning of +1.

The terms are squares of consecutive even numbers: 2² = 4, 4² = 16, 6² = 36 and 8² = 64. The next even number in sequence is 10. Squaring 10 gives 100. Therefore, 100 is the next term that preserves this structure.

Option A:
Option A is 90, which is not a perfect square and cannot be written as k² for an integer k. It breaks the pattern of exact squares. Hence, this option is not suitable.

Option B:
Option B is 96, again not a perfect square of an integer. There is no clear way to match it with the rule based on even squares. Therefore, 96 is not correct.

Option C:
Option C equals 100, which is 10² and follows 2², 4², 6² and 8² naturally. The extended series 4, 16, 36, 64, 100 completes the pattern of consecutive even squares. This makes 100 the valid continuation.

Option D:
Option D is 108, which lies between 10² and 11² but is not itself a square. Since the rule is precisely about squares, 108 cannot be accepted.

Consecutive terms differ by 4: 2 − (−2) = 4, 6 − 2 = 4 and 10 − 6 = 4. This shows an arithmetic progression with common difference 4. Adding 4 to the last term 10 gives 14. Therefore, 14 is the correct next term in the sequence.

Option A:
Option A is 12, which is only 2 more than 10 and does not match the consistent difference of 4. Using 12 would reduce the step size at the end without justification. Hence, it cannot be correct.

Option B:
Option B equals 14, obtained by 10 + 4, which continues the established rule perfectly. The full series −2, 2, 6, 10, 14 keeps the same constant increase each time. This makes 14 the only value that preserves the pattern.

Option C:
Option C is 16, giving a difference of 6 from 10. No such difference appears earlier in the series, so this new step would break the arithmetic structure. Therefore, 16 is not the correct continuation.

Option D:
Option D is 18, which would involve adding 8 to 10 and drastically changing the rate of increase. Since the series has shown only jumps of 4, this option contradicts that behaviour and must be rejected.

Statement A correctly gives the standard formula for percentage change. Statement B is also true because a negative result indicates that the new value is lower than the old one. Statement E is correct as many data interpretation graphs require reading approximate values and working with reasonable approximations. Statement C is false because changing the base (denominator) alters the percentage value, and D is false since a large absolute difference can still yield a small percentage change when the base is large. Thus, A, B and E only are correct.

Option A:
Option A is incomplete because it leaves out B, which properly explains the meaning of a negative percentage change.

Option B:
Option B is correct as it combines the correct formula, the interpretation of negative change and the realistic note about approximation, while excluding C and D.

Option C:
Option C is wrong because it includes C, which wrongly claims the base value does not matter, and it omits B.

Option D:
Option D is incorrect since it contains D (false) and omits A (formula).

This series is generated by the expression (a_n = 2n^4 - n + 3) for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 2−1+3 = 4, 32−2+3 = 33, 162−3+3 = 162, 512−4+3 = 511 and 1250−5+3 = 1248. For n = 6 we compute (2×6^4 - 6 + 3 = 2592 - 3 = 2589). Therefore 2589 is the correct next term.

Option A:
Option A, 2589, coincides with the value of (2n^4 - n + 3) when n = 6. It maintains the same combination of quartic and linear terms that explain all previous numbers. Because it fits the rule exactly, 2589 is the correct continuation.

Option B:
Option B, 2557, is 32 less than the computed value and does not satisfy the expression for n = 6. It would require a sudden drop that has no basis in the pattern, so 2557 is not valid.

Option C:
Option C, 2613, overshoots the predicted value and cannot be obtained from the generating rule. Selecting 2613 would arbitrarily increase the last term and break the algebraic structure. Thus 2613 is not correct.

Option D:
Option D, 2645, deviates even further from 2589 and is not the output of (2n^4 - n + 3) for any integer n continuing the sequence. Adopting 2645 would disrupt the pattern, so it is not the right answer.

Each group uses a sliding window of consecutive prime positions: (2,3,5)=BCE, (3,5,7)=CEG, (5,7,11)=EGK, (7,11,13)=GKM. Next is (11,13,17)=KMQ.

Option A:
Option A uses 8 which is not prime.

Option B:
Option B uses 12 which is not prime (and breaks the prime-based rule).

Option C:
Option C is correct because K(11), M(13), Q(17) are consecutive prime positions after the prior window.

Option D:
Option D starts with L(12), which is not a prime position.

Statements A, B, C and D represent correct principles for direction-sense reasoning. A is true since the four main directions are treated as perpendicular axes. B and C correctly describe standard right and left turns from given orientations. D is correct because many questions reduce movements to net north–south and east–west components, often using coordinate or vector-like thinking. E is false because “left of B” depends on B’s facing direction, not necessarily on the geographic west, so A, B, C and D only are correct.

Option A:
Option A is incomplete because although A, B and C are true, it omits D, which explains how to compute final displacement using perpendicular components, a key exam technique.

Option B:
Option B is incorrect as it includes E, which wrongly interprets “left” as fixed west, and thus mixes one false statement with true ones. This invalidates the combination.

Option C:
Option C is wrong since it drops A and includes only B, C and D, failing to mention the fundamental assumption about the four perpendicular directions that underlies most diagrams.

Option D:
Option D is correct because it collects all four true statements about directions and turning, while excluding E, which confuses relative and absolute positions. It matches how NET questions on direction sense are structured.

Using the simple interest formula I = PRT/100, we substitute I = 600, R = 10 and T = 3 to get 600 = P × 10 × 3 / 100. This simplifies to 600 = 0.3P, so P = 600 ÷ 0.3 = 2000. Therefore, the principal amount on which interest is calculated is ₹2000.

Option A:
If the principal were ₹1500, then the interest at 10% per annum for 3 years would be 1500 × 10 × 3 / 100 = ₹450, which is less than the given interest of ₹600. Hence, this value does not satisfy the data in the problem.

Option B:
If the principal were ₹1800, simple interest at the given rate and time would be 1800 × 10 × 3 / 100 = ₹540. This again does not match the stated interest of ₹600, so this option is not correct.

Option C:
A principal of ₹2000 is correct because it produces the exact interest mentioned: 2000 × 10 × 3 / 100 = ₹600. This agreement confirms that ₹2000 is the initial amount invested or borrowed. In aptitude questions, carefully rearranging formulas like this is a common requirement.

Option D:
If the principal were ₹2200, the interest would be 2200 × 10 × 3 / 100 = ₹660, which exceeds the given value. This shows that ₹2200 cannot be the starting amount for this problem. Therefore, this option must be rejected.

If A and B share profits in the ratio 7:9, the total number of parts is 7 + 9 = 16. Each part is worth ₹1,60,000 ÷ 16 = ₹10,000. A’s share is 7 × ₹10,000 = ₹70,000 and B’s share is 9 × ₹10,000 = ₹90,000. The difference between their shares is ₹90,000 − ₹70,000 = ₹20,000.

Option A:
Option A is correct because it directly reflects the difference between 7 parts and 9 parts when each part is ₹10,000. The arithmetic shows that the financial gap between A and B is exactly two parts, which equals ₹20,000. This fits both the total profit and the specified sharing ratio.

Option B:
Option B, ₹22,000, would not correspond to an integer number of ratio parts, given that each part is ₹10,000. It would imply a difference of 2.2 parts, which contradicts the whole-number nature of the ratio 7:9 and the discrete sharing of profit.

Option C:
Option C, ₹24,000, would amount to a difference of 2.4 parts, which again is inconsistent with the ratio 7:9. Using this figure would mean the implied total profit cannot be exactly ₹1,60,000 when aligned with the ratio.

Option D:
Option D, ₹25,000, suggests an even more irregular difference and would break the connection between the ratio parts and the fixed total profit. When we reverse-calculate, no whole-number ratio 7:9 with a total of 16 parts yields a difference of ₹25,000, so this option is impossible under the given conditions.

Each term after the first is obtained by doubling the previous term and adding 2. We have 1 × 2 + 2 = 4, 4 × 2 + 2 = 10, 10 × 2 + 2 = 22, 22 × 2 + 2 = 46 and 46 × 2 + 2 = 94. Applying the same rule to 94 gives 94 × 2 + 2 = 188 + 2 = 190. This maintains a clear and consistent recursive relationship.

Option A:
Option A gives 186, which does not equal 94 × 2 + 2 and would require reducing or changing the constant term. This is not supported by any previous step. Hence, 186 is not correct.

Option B:
Option B offers 188, corresponding to 94 × 2, but misses the required addition of 2 that appears in every transition. This makes the pattern incomplete. Therefore, 188 cannot be accepted.

Option C:
Option C suggests 192, which adds 4 after doubling 94 and introduces a new constant unobserved earlier. This breaks the precise rule of "+2" at the end. Thus, 192 is not appropriate.

Option D:
Option D yields 190, exactly equal to 94 × 2 + 2, and continues the series under one stable transformation. The sequence 1, 4, 10, 22, 46, 94, 190 remains coherent. Therefore, 190 is the correct next term.

Statements A and B capture that validity is about form, not actual truth of premises. Statement C correctly defines the fallacy of affirming the consequent. Statement E is true because many reasoning questions test the distinction between validity and soundness. Statement D is false since a sound argument is valid and has true premises. Hence A, B, C and E only are correct.

Option A:
Option A is incomplete because it omits E (importance of the distinction) even though A, B, C are true.

Option B:
Option B is incomplete because it omits B (valid with false premises) and also does not include all correct statements together.

Option C:
Option C is correct because it gathers all true statements and excludes D, which reverses the condition for soundness.

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