UGC NET Questions (Paper – 1)

Statement A is correct for linear permutations. Statement B is true because circular permutations fix rotation, giving (n − 1)!. Statement C is true via the block method for adjacency. Statement E is true because extra constraints reduce valid arrangements. Statement D is false because in permutations, order matters. Thus A, B, C and E only are correct.

Option A:
Option A is correct because it includes all true statements and excludes D (false).

Option B:
Option B is incomplete as it omits E (constraints).

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

Option D:
Option D is incorrect because it includes D (false) and omits B (circular formula).

The series can be expressed by the formula aₙ = (n⁴+n²)/2 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get (1+1)/2 = 1, (16+4)/2 = 10, (81+9)/2 = 45, (256+16)/2 = 136 and (625+25)/2 = 325, matching the terms given. For n = 6 the expression gives (6⁴+6²)/2 = (1296+36)/2 = 1332/2 = 666. Thus 666 is the unique next term that fits this quartic-based sequence.

Option A:
Option A, 646, is 20 less than the computed value and does not equal (6⁴+6²)/2. It has no basis in the formula that successfully models all the earlier terms. Therefore 646 cannot serve as the correct continuation.

Option B:
Option B, 654, is still short of 666 and similarly fails to arise from the expression involving n⁴ and n². Choosing 654 would force a change in the pattern for the last term only, which is mathematically unsound. Hence it is not the right answer.

Option C:
Option C, 681, is larger than the predicted value and again does not match (6⁴+6²)/2. It represents an arbitrary modification rather than a logical extension of the rule. Thus 681 is not a valid next term.

Option D:
Option D, 666, exactly matches the output of the formula when n = 6. It preserves the structural relationship between the terms and their positions and keeps the series fully consistent. For this reason, 666 is the correct option.

Statements A, B and C correctly summarise how turns work with respect to standard compass directions. Statement E is also true because path-tracing diagrams are a common method for solving such questions. Statement D is wrong, since marking the initial position is in fact a helpful and often necessary step to keep track of the path and final position. Therefore, the only wrong statement in the list is D, and the combination identifying D only is correct.

Option A:
Option A is correct as it singles out D, which incorrectly downplays the importance of the starting point, and it does not treat any of the true statements as wrong. It cleanly matches the requirement to mark the incorrect statement or statements.

Option B:
Option B is incorrect because it claims both B and D are wrong. However, B is a correct description of turning right from North, so this option misclassifies a true statement as wrong.

Option C:
Option C is wrong since it labels A and D as wrong; A is correct because East is indeed 90 degrees clockwise from North, so this combination again mixes one false and one true statement as if both were incorrect.

Option D:
Option D is also incorrect, as it puts both C and D in the wrong category; C accurately describes a 180-degree turn from South to North, so treating it as wrong makes this option invalid.

This option is correct because 2 raised to the power 5 means multiplying 2 by itself five times. Calculating 2 × 2 × 2 × 2 × 2 gives 32. This follows the general definition of exponents as repeated multiplication. Therefore, 2⁵ is equal to 32.

Option A:
16 is the value of 2 raised to the power 4, not 5. It comes from 2 × 2 × 2 × 2, which has only four factors. Since the exponent here is 5, this option underestimates the value.

Option B:
32 is obtained by multiplying five factors of 2 together. The sequence is 2, 4, 8, 16 and finally 32, which corresponds to 2⁵. This exactly matches the requirement of the question, making this option correct.

Option C:
64 is the value of 2 raised to the power 6, which involves six factors of 2. Using 64 would correspond to 2⁶ rather than 2⁵. Hence, this option is too large for the given exponent.

Option D:
25 is the square of 5 and is unrelated to powers of 2 in this context. It does not come from repeated multiplication of 2. Therefore, this option does not answer the question correctly.

The first letters are A(1), C(3), E(5) and G(7), increasing by 2 each time. The second letters are D(4), F(6), H(8) and J(10), also increasing by 2. The next first letter is 7 + 2 = 9 (I) and the next second letter is 10 + 2 = 12 (L), forming IL. Thus IL uniquely maintains the +2 increment for both positions.

Option A:
Option A is correct because both I and L are exactly two positions ahead of G and J respectively. It preserves the parallel arithmetic progression in both components of the pair. This consistent step size is what defines the pattern, making IL the valid next term.

Option B:
Option B, IK, uses I correctly as the first letter but keeps K as the second. K is only one step ahead of J instead of two. This breaks the constant +2 difference in the second position, so IK cannot be correct.

Option C:
Option C, JL, advances the first letter by three positions from G to J while keeping the second letter L plausible. However, the first-letter sequence clearly uses steps of 2, not 3. This mismatch in the first position means JL does not follow the series rule.

Option D:
Option D, HM, shifts the first letter from G to H, which is only a single step, and moves the second letter too far to M. Both positions now violate the established +2 pattern. Consequently, HM cannot be accepted as the next term.

The rate of work of one man can be found by noting that 4 men finish the work in 12 days, so 1 man’s daily work is 1 divided by (4 × 12), which is 1/48. Similarly, 6 women finish the work in 18 days, so 1 woman’s daily work is 1 divided by (6 × 18), which is 1/108. For 2 men and 3 women together, the combined daily work is 2/48 plus 3/108. Simplifying, 2/48 is 1/24 and 3/108 is 1/36. The sum of 1/24 and 1/36 is 5/72. The total time to complete one work is 1 divided by 5/72, which equals 72/5 or 14.4 days.

Option A:
Option A, 12 days, would require the mixed group to be as effective as 4 men alone, which is not supported by the calculated rate of 5/72 per day. The combination of 2 men and 3 women is somewhat less efficient than that.

Option B:
Option B uses individual rates to compute a combined rate and then takes the reciprocal to determine total time. This standard time and work approach produces 14.4 days, which is the only option consistent with the carefully derived daily work rate.

Option C:
Option C, 15 days, is close to but not equal to 14.4 days, indicating a rounded or estimated value that does not precisely follow the computed reciprocal.

Option D:
Option D, 18 days, equates to the time taken by 6 women alone and ignores the additional contribution from the 2 men working alongside them.

The first-level differences are 9, 13, 17 and 21. These differences form an arithmetic progression with common difference 4. To continue this structure, the next difference should be 25. Adding 25 to the last term 67 gives 92, which maintains the regular growth among the differences.

Option A:
Option A gives 88, implying a difference of 21 from 67. This simply repeats the last difference rather than increasing it, so the progression of gaps 9, 13, 17, 21, 21 breaks the +4 pattern. Therefore 88 is not consistent with the rule.

Option B:
Option B gives 92, corresponding to a difference of 25. The differences become 9, 13, 17, 21, 25, which keep increasing by 4 each time. This perfect second-level arithmetic progression shows that 92 is the correct next term.

Option C:
Option C gives 96, yielding a difference of 29 from 67. The last jump among differences then becomes 8, which is double the expected 4 and disrupts the pattern. Hence 96 cannot be accepted.

Option D:
Option D gives 98, corresponding to a difference of 31 from 67. This further distorts the difference progression and makes the final step too large. Therefore 98 is not a valid continuation.

A discount of 10% on a marked price of ₹500 means that the reduction is 10% of 500. Ten percent of 500 is (10 ÷ 100) × 500 = 50. Subtracting this discount from the marked price gives a selling price of 500 − 50 = ₹450. Thus, the buyer pays ₹450 after the discount is applied.

Option A:
Option A, ₹450, follows directly from the definition of a 10% discount by subtracting ₹50 from the marked price. It respects both the percentage calculation and the link between discount and final selling price, giving a numerically consistent result.

Option B:
Option B, ₹400, would correspond to a discount of ₹100, which is 20% of 500 rather than 10%. This doubles the intended reduction and does not match the conditions given in the question.

Option C:
Option C, ₹480, would represent a discount of only ₹20, which is 4% of 500 and therefore too small compared to the required 10%. It underestimates the discount rate.

Option D:
Option D, ₹460, corresponds to a discount of ₹40, or 8%, which again does not equal the specified discount rate of 10% on the marked price.

Each term decreases by 8: 72 − 80 = −8, 64 − 72 = −8, 56 − 64 = −8 and 48 − 56 = −8. Maintaining this constant difference, we subtract 8 from 48 to get 40. Therefore, 40 is the correct next term in the series.

Option A:
Option A is 42, which is 6 less than 48 and would change the difference to −6. This contradicts the steady −8 observed earlier. Hence, 42 is not correct.

Option B:
Option B is 44, implying a difference of −4 from 48. That halves the magnitude of the step and breaks the pattern of equal decreases. Therefore, 44 cannot be accepted.

Option C:
Option C is 46, giving a difference of −2, which is far from the established −8. It would indicate a slowing decline not supported by earlier terms. Thus, 46 is not suitable.

Option D:
Option D equals 40, obtained by 48 − 8 and preserving the constant step of −8. The extended sequence 80, 72, 64, 56, 48, 40 remains a neat arithmetic progression. This confirms 40 as the correct continuation.

The differences between successive terms are 5, 10, 20 and 40, each approximately doubling the previous difference. If this pattern continues, the next difference should be 80. Adding 80 to the last term 79 gives 159. Therefore, 159 is the correct next term in the sequence.

Option A:
Option A is 120, which gives a difference of 41 from 79 and does not align with the expected 80. This breaks the doubling behaviour of the differences. Hence, 120 is not correct.

Option B:
Option B is 140, implying a difference of 61, which again fails to match the predicted 80. It does not continue the simple doubling rule. Therefore, 140 cannot be accepted.

Option C:
Option C equals 159 and produces the new difference 80, following 5, 10, 20 and 40 in a clear doubling pattern. The extended differences 5, 10, 20, 40, 80 make the structure consistent. Thus, 159 is the valid continuation.

Option D:
Option D is 180, giving a difference of 101 from 79. That has no relation to the doubling sequence of differences and therefore breaks the pattern. So, 180 is not suitable.

Statements C and E are the wrong statements here. A is true because analogical reasoning transfers patterns from a known case to a similar new case. B is correct as only similarities in relevant features support a strong analogy. D is true because analogies often yield plausible but not absolutely certain conclusions. C is wrong since any superficial similarity does not guarantee a strong conclusion, and E is wrong because some dissimilarities may be irrelevant and do not automatically destroy the analogy. Thus the wrong statements are C and E only.

Option A:
Option A is incorrect because it claims only C is wrong and ignores E. E overstates the effect of any dissimilarity, so failing to include it makes the option incomplete.

Option B:
Option B is correct because it identifies precisely C and E as problematic: C lowers the bar on relevance too far, while E raises the bar on similarity unrealistically high.

Option C:
Option C is wrong since it marks only E as wrong and treats C as acceptable, even though C clearly exaggerates the sufficiency of any similarity.

Option D:
Option D is incorrect because it wrongly treats B as wrong, even though B is a standard requirement for a strong analogy.

The third proportional c to numbers a and b is defined by a:b = b:c. For a = 8 and b = 18, we have 8:18 = 18:c. Writing this as a fraction gives 8/18 = 18/c, so c = (18 × 18)/8 = 324/8 = 40.5. Therefore, 40.5 is the third proportional to 8 and 18 and satisfies 8:18 = 18:40.5 exactly.

Option A:
Option A, 32.4, corresponds to 324/10 and would come from dividing 324 by 10 rather than 8. Substituting 32.4 for c gives 8:18 ≠ 18:32.4, since 8/18 simplifies to 4/9 while 18/32.4 simplifies to a different value. Hence 32.4 does not fulfil the proportional condition.

Option B:
Option B, 36, gives 18:36 = 1:2, whereas 8:18 simplifies to 4:9. These are not equal ratios, so 36 cannot be the third proportional. The numerical pattern required by the definition of third proportional is not met by this value.

Option C:
Option C is correct because using c = 40.5 we get 18:40.5 = 18/(81/2) = 36/81 = 4/9, which matches 8:18 = 4:9. This equality of simplified ratios confirms that 40.5 is the unique third proportional to 8 and 18.

Option D:
Option D, 45, gives 18:45 = 2:5, which again differs from 4:9. While 45 is close numerically to 40.5, proportional relationships are sensitive to exact values, and this small change breaks the equality required by the definition. Therefore 45 is not the correct third proportional.

Starting from the origin, the person first moves 5 km north. Turning right from north leads to east, so they walk 3 km east. Turning right again from east points toward south, and walking 5 km south brings them back to the same north–south line as the starting point. Their final position is directly east of the start, at a distance of 3 km.

Option A:
Option A, 5 km East, would be correct if the eastward movement had been 5 km, but the question clearly states an eastward displacement of only 3 km. Therefore, this overestimates the actual horizontal separation.

Option B:
Option B accurately reflects that the northward and southward movements cancel each other out, leaving only the 3 km eastward shift. Thus, the net displacement is 3 km to the east of the starting point, which matches both the direction and distance required.

Option C:
Option C, 3 km West, reverses the direction of the actual displacement. Since the person walked east, not west, this option contradicts the described path.

Option D:
Option D, 5 km West, is doubly incorrect because it gives the wrong distance and direction relative to the origin. The person never moves west at all.

Each term is half of the previous one: 160÷2 = 80, 80÷2 = 40 and 40÷2 = 20. This shows a geometric progression with ratio 1/2. Halving the last term 20 gives 10. Therefore, 10 is the correct next term in the series.

Option A:
Option A is 5, which is half of 10 rather than half of 20. Using 5 directly after 20 would require dividing by 4, not by 2, and thus break the consistent ratio. Hence, 5 is not suitable.

Option B:
Option B is 12, which does not correspond to 20 divided by 2 and would introduce an inconsistent operation. There is no earlier hint of subtracting or adjusting by 8. Therefore, 12 cannot be correct.

Option C:
Option C is 15, which lies between 10 and 20 and does not represent half of the previous term. Choosing 15 would leave the ratio undefined and unclear. Thus, it does not follow the pattern.

Option D:
Option D equals 10, obtained by 20÷2 and preserving the halving process. The extended series 160, 80, 40, 20, 10 keeps the same geometric structure with ratio 1/2. This confirms that 10 is the right continuation.

Statements A, B and C state the standard time–work model: one-day work as 1/n, combined rates added and inverse relation between time and rate. Statement E is also true since many problems can be set up and solved using simple linear equations in the unknown rates. Statement D is false because if A is twice as fast as B, A will take half the time, not twice. Therefore, the combination A, B, C and E only is correct.

Option A:
Option A is incomplete because it leaves out E and thus fails to mention the useful algebraic viewpoint that rates can be handled by linear equations. Without E, the picture of modelling is not fully captured.

Option B:
Option B is correct since it collects all the true statements and excludes D, which reverses the relationship between speed and time. It reflects exactly how NET aspirants are expected to reason about time and work problems.

Option C:
Option C is incorrect because it includes D, the wrong claim about time for a faster worker, even though it also lists some true statements. Including a false statement invalidates the combination.

Option D:
Option D is also wrong as it retains D and omits A, failing to state the fundamental definition of one-day work while endorsing an incorrect comparison of times.