UGC NET Questions (Paper – 1)

The starting letters are Z, W, T and Q, which stand at positions 26, 23, 20 and 17, decreasing by 3 each time. Each group consists of three consecutive letters in forward alphabetical order. Continuing this rule, the next starting position is 14, corresponding to N, and the next two letters are O and P. Therefore NOP is the only group that respects both the minus three jump and the consecutive letter structure.

Option A:
Option A, OPQ, starts with O at position 15, which is only two positions below Q rather than three. This breaks the consistent backward step of three positions in the starting letters. Although OPQ is internally consecutive, it does not come from the governing position rule, so it is not correct.

Option B:
Option B, RST, moves forward from Q instead of backward, reversing the direction of the pattern. The sequence clearly shows the starting letters moving left in the alphabet by three positions. Because RST represents a forward move, it contradicts this behaviour.

Option C:
Option C, KLM, begins at K, which is position 11, giving a backward jump of 6 from Q rather than 3. This doubles the step size unexpectedly and disrupts the regular decrement. As the series does not indicate any change in the size of the backward jump, KLM cannot be accepted.

Option D:
Option D is correct because N lies exactly three positions before Q and NOP forms a block of three consecutive letters. It preserves both the direction and magnitude of the movement in the first letter, and maintains the same internal structure of the groups. This makes NOP the valid continuation of the letter group series.

The pattern in the series is that each term is obtained by doubling the previous term and adding 1. Specifically, 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31 and 31 × 2 + 1 = 63. Continuing this rule, the next term is 63 × 2 + 1 = 127. Hence, 127 is the only number that preserves the established doubling plus one pattern.

Option A:
Option A, 95, could come from adding 32 to 63, but there is no basis for adding a fixed difference when the earlier transitions are multiplicative with an extra 1. It breaks the observed rule of doubling.

Option B:
Option B applies the same operation used at every step of the series, doubling 63 and then adding 1. This keeps the structure consistent across all terms and therefore correctly predicts the next number.

Option C:
Option C, 125, is close numerically but would require adding 62, again inconsistent with the doubling plus one pattern seen earlier.

Option D:
Option D, 119, might reflect adding 56, but such a jump is not supported by any of the prior steps in the sequence.

The differences between consecutive terms are 3, 6, 9, 12 and 15. These differences increase by 3 each time, forming a simple arithmetic pattern at the second level. The next difference should therefore be 18. Adding 18 to the last term 48 gives 48 + 18 = 66, which continues the series in a consistent way.

Option A:
Option A gives 60, corresponding to a difference of 12 from 48, which repeats an earlier increment and fails to progress to 18. This disrupts the growth of the differences. Hence, 60 is not correct.

Option B:
Option B offers 63, whose difference from 48 is 15, again repeating the last difference instead of increasing it. This is not compatible with the pattern. Therefore, 63 cannot be accepted.

Option C:
Option C suggests 64, giving a difference of 16 from 48, which does not fit the multiples-of-three structure in the differences. This makes the pattern irregular. Thus, 64 is not appropriate.

Option D:
Option D yields 66, which is 18 more than 48 and extends the differences to 3, 6, 9, 12, 15, 18. This preserves the second-level arithmetic progression, so 66 is the correct next term.

The differences between consecutive terms are 9, 15, 21 and 27. These differences increase by 6 at each step, forming a simple arithmetic pattern. The next difference should therefore be 33. Adding 33 to the last term 75 gives 75 + 33 = 108, which extends the series in a consistent manner.

Option A:
Option A gives 102, which yields a difference of 27 from 75 and repeats the last difference instead of moving to 33. This breaks the steady growth by 6 in the differences. Therefore, 102 is not correct.

Option B:
Option B offers 105, whose difference from 75 is 30, not the expected 33. This slightly underestimates the predicted increment and disrupts the pattern. Hence, 105 cannot be accepted.

Option C:
Option C yields 108, which is 33 more than 75 and continues the difference sequence 9, 15, 21, 27, 33 as an arithmetic progression. This keeps the series logically structured. Thus, 108 is the correct next term.

Option D:
Option D suggests 111, giving a difference of 36 from 75, overshooting the required increment and making the sequence irregular. Therefore, 111 is not appropriate.

For a, b and c to be in continued proportion, we have a:b = b:c, which implies b² = ac. Given a:c = 4:25, take a = 4k and c = 25k. Then b² = 4k × 25k = 100k², so b = 10k. Hence b:a = 10k:4k = 5:2. Therefore, b:a is 5:2.

Option A:
Option A, 2:5, reverses the correct ratio and suggests that b is smaller than a. But since c is much larger than a in the ratio 4:25, b, as a geometric mean, must be larger than a, not smaller. Thus, 2:5 contradicts the expected ordering.

Option B:
Option B, 4:5, might come from confusing the ratios a:c and b:a, but if b:a were 4:5, the squared relation b² = ac would not hold when a:c = 4:25. Substituting this ratio leads to inconsistent values for c relative to a.

Option C:
Option C is correct because it comes directly from solving b² = ac with a and c in the ratio 4:25. The geometric mean b = 10k sits between 4k and 25k, and the ratio b:a simplifies cleanly to 5:2, which aligns with the structure of continued proportion.

Option D:
Option D, 25:4, mimics the given a:c ratio but in the wrong positions. Making b much larger than both a and c contradicts the notion of b being a mean between a and c. Hence 25:4 cannot represent b:a in this configuration.

Let the numbers be 4x and 7x. After adding 5 to each, they become 4x + 5 and 7x + 5, and their ratio is given as 3:5. Thus (4x + 5)/(7x + 5) = 3/5. Cross multiplying gives 5(4x + 5) = 3(7x + 5), which simplifies to 20x + 25 = 21x + 15, and hence x = 10. Therefore the numbers are 40 and 70, and the larger original number is 70.

Option A:
Option A, 40, is the smaller of the two original numbers when x = 10. It satisfies the initial ratio but does not answer the question, which specifically asks for the larger number. Moreover, choosing 40 as the larger number would contradict the ratio 4:7 where 4x must be smaller than 7x.

Option B:
Option B, 45, does not fit into any pair maintaining both the original ratio 4:7 and the new ratio 3:5 after adding 5. If we treated 45 as the larger original number, then the smaller would be 45 × (4/7), which is not an integer and fails the requirement for simple integer ratio terms. Thus 45 is an inconsistent choice.

Option C:
Option C is correct because 70 arises naturally as 7 × 10 when solving the given proportion. Substituting 40 and 70 back into the problem, we get (40 + 5):(70 + 5) = 45:75 = 3:5, which verifies the condition. This confirms that 70 is the true larger original number.

Option D:
Option D, 75, would require the smaller number to be 75 × (4/7) ≈ 42.86 to preserve the original ratio, which is not an integer and also fails to give the new ratio 3:5 after adding 5. Therefore 75 does not satisfy the structural requirements of the problem.

This option is correct because 1 hour equals 60 minutes. Therefore, 3 hours equals 3 × 60 = 180 minutes. This direct multiplication gives the correct conversion. Hence, three hours correspond to 180 minutes.

Option A:
A value of 120 minutes corresponds to only 2 hours since 120 ÷ 60 = 2. It does not represent 3 hours. Therefore, this option is not correct.

Option B:
Using 180 minutes reflects the correct multiplication of 3 by 60. This matches both the standard unit conversion and everyday experience with time. Thus, this option is accurate.

Option C:
200 minutes would be 3 hours and 20 minutes, which exceeds 3 hours. Since the question asks for exactly three hours, 200 minutes is not correct.

Option D:
240 minutes equal 4 hours, as 240 ÷ 60 = 4. This is more than 3 hours and therefore not the correct conversion.

A defines conditional probability, and B states the law of total probability for a partition. C is true because independence means conditioning on B does not change the probability of A. D is true because Bayes’ theorem updates a prior probability using likelihood/evidence. E is false: P(A∣B) + P(A∣B′) is not generally 1 (they are conditional probabilities on different conditions; their sum can be greater than 1 or less than 1). Therefore A, B, C and D only are correct.

Option A:
Option A is incorrect because it omits D, and Bayes’ theorem is a correct statement commonly paired with conditional probability concepts.

Option B:
Option B is incorrect because it omits A, which is the defining formula for conditional probability.

Option C:
Option C is correct because it includes all and only the true statements (A, B, C and D) and excludes E, which is not a valid identity in general.

Option D:
Option D is incorrect because it omits B, the law of total probability, which is true.

Statement A gives the fundamental relationship between HCF, LCM and the product of two positive integers. Statement C correctly defines LCM as the least positive common multiple. Statement D is also true; co-prime numbers have no common positive factor other than 1. Statement B is false because the HCF cannot exceed the numbers themselves, and E is false since if one number divides the other, the HCF is the smaller number, not necessarily 1. Thus, A, C and D only are correct, matching option A.

Option A:
Option A is correct because it combines the key algebraic relation with the proper descriptions of LCM and co-primality, while excluding B and E, which misunderstand bounds on HCF and the divisor case.

Option B:
Option B is incomplete as it includes only A and C and omits D, thereby failing to highlight the link between co-prime numbers and HCF, which is frequently tested.

Option C:
Option C is incorrect because it drops A and includes only C and D, so it loses the important multiplicative connection between HCF and LCM and provides an incomplete set of correct statements.

Option D:
Option D is wrong since it includes B, which wrongly claims that the HCF is at least as large as each number, contradicting basic number theory, and therefore the combination cannot be accepted.

The positions of these letters are A(1), D(4), I(9) and P(16). These correspond to 1², 2², 3² and 4². The next square number is 5² = 25, which corresponds to Y. Thus Y is the only letter that continues the pattern based on perfect squares.

Option A:
Option A, W, is at position 23, which is not a perfect square. It cannot be represented as n² for a positive integer n. Therefore W does not follow the underlying square-number rule.

Option B:
Option B, X, corresponds to position 24, which again is not a perfect square. Selecting X would abandon the clear pattern of using square positions. Hence X cannot logically follow P in this sequence.

Option C:
Option C, Z, is at position 26, also not a perfect square. While it is near 25, the pattern is exact and not approximate. Because 26 does not equal any n², Z fails to satisfy the generating rule.

Option D:
Option D is correct because Y occupies position 25, exactly 5². It extends the series of square-number positions from 1² through 4² to 5². This perfect alignment with the numerical pattern makes Y the valid next term.

Let the total work be 1 unit. A’s work rate is 1/20 per day, and A and B together work at 1/12 per day. B’s rate is the difference, 1/12 − 1/20. Taking the least common multiple of 12 and 20 as 60, we get B’s rate as (5 − 3)/60 = 2/60 = 1/30 per day. Thus, B alone would need 30 days to complete the work.

Option A:
Option A, 24 days, corresponds to a rate of 1/24, which when added to A’s rate of 1/20 would give a combined rate different from 1/12. It does not match the given completion time when working together.

Option B:
Option B, 30 days, matches a work rate of 1/30. Adding this to A’s rate 1/20 yields 1/12, which is consistent with the statement that they finish the work together in 12 days.

Option C:
Option C, 36 days, gives a rate of 1/36, and 1/20 + 1/36 does not add up to 1/12, so it contradicts the given joint time.

Option D:
Option D, 60 days, implies too slow a rate for B, and combined with A it would result in a joint time longer than 12 days.

The pattern here is aₙ = 2n⁴ + n² + 2 with n starting from 1. Substituting n = 1, 2, 3, 4 and 5 gives 2·1⁴+1²+2 = 5, 2·2⁴+2²+2 = 38, 2·3⁴+3²+2 = 173, 2·4⁴+4²+2 = 530 and 2·5⁴+5²+2 = 1277, which confirms the rule. For n = 6 we have 2·6⁴+6²+2 = 2·1296+36+2 = 2592+38 = 2630. Hence 2630 is the only value that continues this quartic-plus-quadratic-plus-constant pattern.

Option A:
Option A, 2598, is 32 less than the formula’s outcome and does not satisfy aₙ = 2n⁴+n²+2 for n = 6. It would introduce an arbitrary drop at the sixth term that is not suggested by the earlier values. Thus option A is not consistent with the sequence.

Option B:
Option B, 2614, is closer but still fails to match the value 2630 predicted by the rule. Choosing 2614 would mean altering the pattern only at the final step, which is logically unjustified. Therefore option B cannot be correct.

Option C:
Option C, 2622, also differs from the formula’s result and cannot be obtained from substituting n = 6 into 2n⁴+n²+2. It represents a partial correction but still does not maintain the exact algebraic structure. As a result, option C is not a valid continuation.

Option D:
Option D, 2630, matches exactly the computed value for n = 6. It preserves the dependence on n⁴ and n², as well as the constant term, in exactly the same way as the earlier terms. Because the same rule explains every entry including the next, 2630 is the correct answer.

The letters in LOGIC correspond to positions: L is 12, O is 15, G is 7, I is 9 and C is 3. Adding these positions gives 12 + 15 + 7 + 9 + 3 = 46. Therefore, the sum of the code numbers for LOGIC is 46.

Option A:
Option A exactly matches the sum of the letter positions and correctly applies the coding rule to every letter in the word.

Option B:
Option B, 49, is 3 more than the correct total and indicates an error in adding one or more of the letter values.

Option C:
Option C, 51, overshoots the correct sum by 5 and could result from misreading one of the letter positions.

Option D:
Option D, 52, is even farther from the true total and cannot be obtained by any correct application of the given mapping.

Each term is obtained by multiplying the previous term by 2 and then adding 1: 10×2+1=21, 21×2+1=43, 43×2+1=87, and 87×2+1=175. Continuing the same rule gives 175×2+1 = 350+1 = 351. Therefore, 351 is the correct next term.

Option A:
Option A (300) does not satisfy the rule 175×2+1. If we apply the rule, we must reach 351, not 300. So 300 cannot be the next term.

Option B:
Option B (320) also fails the rule because the next term must be exactly 351 from 175×2+1. Any other value would break the consistent recursive operation used in every step.

Option C:
Option C (340) is not obtained from 175×2+1 and would require changing the “+1” part of the rule. Since the +1 is consistent throughout, 340 is incorrect.

Option D:
Option D (351) matches 175×2+1 exactly, so it continues the established pattern without any change. Hence, 351 is the correct next term.

Profit is the difference between selling price and cost price. Here, the profit equals ₹920 − ₹800 = ₹120. The profit percentage is calculated on cost price, so it is (profit ÷ cost price) × 100 = (120 ÷ 800) × 100. This simplifies to (12 ÷ 80) × 100 = 0.15 × 100 = 15%. Therefore, the profit made is 15% of the cost price.

Option A:
Option A reflects the correct application of the profit percentage formula, using cost price as the base. The computation carefully converts the absolute profit into a relative percentage, yielding 15%, which accurately quantifies the gain.

Option B:
Option B, 12%, may result from mistakenly using the profit amount directly without proper division by the cost price. It underestimates the true rate of return on the investment.

Option C:
Option C, 10%, is even smaller and could emerge from misreading the difference or misplacing zeros, but does not match the actual ratio of 120 to 800.

Option D:
Option D, 18%, overstates the profit rate and cannot be derived from the given selling and cost prices using the standard formula.