UGC NET Questions (Paper – 1)

P is stated to be the father of Q, so Q is P’s child. Q is the mother of R, so R is Q’s child. This makes R the grandchild of P through Q. Since P is male, his relationship to R is that of a grandfather. The reasoning follows the generational links step by step.

Option A:
Option A correctly identifies that P stands two generations above R: P → Q → R. Being the father of R’s mother, P is the maternal grandfather of R. This matches both the gender information and the generational structure.

Option B:
Option B, father, would mean P directly parents R, but the question clearly states that Q is the mother of R, not P.

Option C:
Option C, uncle, would require P to be a sibling of R’s parent, which is not the case here because P is Q’s father, not Q’s brother.

Option D:
Option D, brother, would place P in the same generation as Q and R, which contradicts the given description that P is Q’s father.

The sequence follows the formula (a_n = n^4 + 2n + 3) with n starting from 1. For n = 1, 2, 3, 4 and 5 we compute 1+2+3 = 6, 16+4+3 = 23, 81+6+3 = 90, 256+8+3 = 267 and 625+10+3 = 638. For n = 6 the expression yields (6^4 + 12 + 3 = 1296 + 15 = 1311). Therefore 1311 is the correct next term under this quartic-plus-linear pattern.

Option A:
Option A, 1287, is 24 less than the calculated value and does not equal (6^4 + 2×6 + 3). It would require weakening the rule only at the final term, which is inconsistent. Hence 1287 is not valid.

Option B:
Option B, 1299, is still below 1311 and again cannot be written as (n^4 + 2n + 3) for n = 6. Adopting 1299 would disrupt the tight connection between index and term. Thus 1299 is not correct.

Option C:
Option C, 1311, matches exactly the output of the formula when n = 6. It preserves the same quartic and linear structure that generated all earlier values. For this reason, 1311 is the correct continuation.

Option D:
Option D, 1327, overshoots the correct value and fails to satisfy the expression for n = 6. Using 1327 would abandon the algebraic coherence of the series, so it is not a valid answer.

The differences between consecutive terms are 1, 4, 9 and 16. These are consecutive perfect squares 1², 2², 3² and 4². To continue the pattern, the next difference should be 5² = 25. Adding 25 to the last term 31 gives 31 + 25 = 56. This preserves the square-based structure of the differences and fits the logic of the series.

Option A:
Option A produces 56, which is exactly 25 more than 31 and makes the difference sequence 1, 4, 9, 16, 25. This is a neat progression of squares, showing a clear higher-level pattern. Hence, 56 is the correct next term in the number series.

Option B:
Option B gives 57, which would correspond to a difference of 26 from 31 and does not match the expected square 25. This slight mismatch is enough to break the precise square-difference rule. Therefore, 57 cannot be accepted as the correct continuation.

Option C:
Option C provides 58, which is 27 more than 31 and again deviates from the exact value of 25 required by the pattern. The differences would no longer correspond to consecutive squares. Thus, 58 is not consistent with the structure.

Option D:
Option D suggests 60, giving a difference of 29 from 31, which is far away from 25 and lacks any special square-based interpretation. Choosing 60 would destroy the elegant second-level pattern. Hence, 60 is not the right answer.

To combine the ratios A : B and B : C, we first express them with a common value for B. The ratio A : B = 2 : 3 and B : C = 4 : 5. Making the B terms equal involves scaling the first ratio by 4 and the second by 3, giving A : B = 8 : 12 and B : C = 12 : 15. Now B has the same value in both, allowing us to read off A : C as 8 : 15. This is the required compound ratio.

Option A:
Option A, 8 : 15, emerges naturally once B is expressed with the same multiplier in both original ratios. It preserves the structure of each pairwise relation and gives a consistent comparison between A and C.

Option B:
Option B, 3 : 5, retains the original A : B pattern but ignores the connection to C through the second ratio. It cannot represent A : C directly.

Option C:
Option C, 5 : 8, inverts the relationship and does not follow from any consistent scaling of the given ratios. It would imply C is relatively smaller than A in a way that contradicts the conditions.

Option D:
Option D, 10 : 9, is arbitrary and not produced by any straightforward manipulation of the initial pair of ratios.

The terms satisfy the rule (a_n = 3n^3 + 2n^2 - n + 1) for n starting from 1. For n = 1, 2, 3, 4 and 5 this expression produces 5, 31, 97, 221 and 421, matching the series. For n = 6 we compute (3×6^3 + 2×6^2 - 6 + 1 = 648 + 72 - 6 + 1 = 715). Hence 715 is the correct next term.

Option A:
Option A, 703, is 12 less than the value given by the formula and does not equal (3×6^3 + 2×6^2 - 6 + 1). It implies a pattern change that is not supported by earlier terms. Therefore 703 is not valid.

Option B:
Option B, 709, is still below 715 and cannot be obtained from the same expression for n = 6. Selecting 709 would break the algebraic rule that explains the sequence. Thus 709 is not correct.

Option C:
Option C, 721, overshoots the computed value and likewise fails to match the formula. It suggests an arbitrary increase not grounded in the pattern. Hence 721 is not appropriate.

Option D:
Option D, 715, equals the exact output of the rule for n = 6 and preserves both the cubic and quadratic contributions of the expression. For this reason, 715 is the correct continuation of the series.

This sequence uses the recurrence a₁ = 2 and aₙ₊₁ = 6aₙ + n² − 1 for n ≥ 1. With this rule we obtain a₂ = 6·2 + 1² − 1 = 12, a₃ = 6·12 + 2² − 1 = 75, a₄ = 6·75 + 3² − 1 = 458 and a₅ = 6·458 + 4² − 1 = 2763, perfectly matching the given terms. For n = 5 the next term is a₆ = 6·2763 + 5² − 1 = 16602. Therefore 16602 is the unique next term that satisfies the same recurrence.

Option A:
Option A, 16542, is 60 less than the value produced by aₙ₊₁ = 6aₙ + n² − 1 at n = 5. Selecting 16542 would require subtracting 60 from the properly computed term only at this position. Since earlier transitions obey the rule exactly, this option is inconsistent with the pattern and is incorrect.

Option B:
Option B, 16602, matches exactly the result of applying the recurrence to a₅ with n = 5. It preserves the structure of multiplying the previous term by six and then adding a quadratic correction minus one. Because this mechanism generates all earlier terms and leads straight to 16602, this option correctly continues the series.

Option C:
Option C, 16638, is 36 greater than the correct value and cannot be written as 6·2763 + 5² − 1. To obtain 16638 we would have to increase the additive part beyond n² − 1 at the sixth step, altering the rule. Thus option C does not follow the established recurrence.

Option D:
Option D, 16674, deviates even more from the computed value and similarly fails to satisfy the formula. Using 16674 would destroy the precise relationship between terms that characterises this sequence. Therefore option D is not a valid continuation.

Every group contains five letters, each separated by two positions from the next. From one group to the next, each letter shifts forward by one place: ACEGI becomes BDFHJ, then CEGIK, then DFHJL. Applying this shift again, D, F, H, J and L become E, G, I, K and M respectively. Hence EGIKM is the only group that continues the pattern.

Option A:
Option A, EGJLN, distorts the equal spacing and is not formed by adding one to each letter in DFHJL. Therefore it does not respect the structural rule.

Option B:
Option B, EGIJL, breaks the regular spacing and is not obtained by a consistent +1 transformation of DFHJL.

Option C:
Option C is correct because it advances each letter of DFHJL by exactly one position while preserving the +2 spacing inside the group.

Option D:
Option D, FGIKM, starts with F instead of E, so it does not match the +1 shift from DFHJL.

The series consists of consecutive odd numbers, each 2 greater than the previous one. We see 11, 13, 15 and 17 with differences of 2 throughout. Adding 2 to 17 gives 19. Therefore, 19 is the next consecutive odd number and fits the pattern.

Option A:
Option A is 18, which is an even number and would break the sequence of odd integers. It also changes the difference from 2 to 1, so it cannot be correct.

Option B:
Option B is 20, another even number, and is 3 greater than 17. This disturbs both the parity and the constant difference. Thus, it does not maintain the pattern.

Option C:
Option C is 21, which is odd but lies 4 units above 17 rather than 2. That disrupts the simple increase by 2 seen in the earlier terms. Therefore, 21 is not appropriate.

Option D:
Option D equals 19, an odd number exactly 2 more than 17. The extended series 11, 13, 15, 17, 19 keeps the same difference and parity property. Hence, this option correctly continues the sequence.

Statement A correctly defines the ad hominem fallacy as an attack on the person rather than the argument. Statement B accurately describes the straw man technique of distorting an opponent’s view. Statement C is also correct, as hasty generalisation relies on too few or biased examples to support a broad claim. Statement D is false because valid deductive arguments are structurally correct, not fallacious, and E is false since an expert authority can provide legitimate support in many contexts. Hence A, B and C only are correct, which is option C.

Option A:
Option A is incomplete since it omits C and thereby leaves out a major type of fallacy frequently tested in NET reasoning questions.

Option B:
Option B is incorrect as it includes D, which wrongly labels all valid deductions as fallacies, and it omits C, so it contains an error and misses one correct fallacy definition.

Option C:
Option C is correct because it gathers the accurate characterisations of three distinct and important fallacies, while excluding D and E, which misdescribe valid deduction and the role of authority.

Option D:
Option D is wrong since it includes E, which claims that appeal to authority is always fallacious, ignoring legitimate expert testimony, and it omits A, losing a key fallacy type.

Statement A summarises how analogy questions require transferring a discovered relation from one pair to another. Statement B notes that the relation can take many forms such as part–whole or cause–effect. Statement E is also correct because understanding the type of relation is central to answering analogies, even though word meanings are also needed. Statement C is false since in classification the odd item out is the one that does not fit the common pattern, and D is false because NET papers can mix verbal and non-verbal analogies. Thus A, B and E only are correct, matching option A.

Option A:
Option A is correct as it highlights the relational nature of analogies, the variety of possible connections and the strategic focus on identifying relationships, while excluding C and D, which misdescribe classification and exam design.

Option B:
Option B is incorrect because it includes C, which reverses the idea of an odd item out, and it omits E, so it both accepts a false statement and loses an important strategic insight.

Option C:
Option C is wrong since it includes D, which wrongly claims that verbal and non-verbal analogies never appear together, and it omits B, thereby weakening the explanation of relation types.

Option D:
Option D is incorrect because it contains C, the wrong description of the odd item, and it fails to include A, so it both introduces an error and omits a core feature of analogies.

Statement A describes a common pattern where letters are shifted forward or backward in the alphabet. Statement B acknowledges that rearranging letters, such as reversing or swapping positions, may be part of the code. Statement C is correct because within a single question, the same underlying rule is normally applied to all examples. Statement D is false; coding puzzles are designed to follow a discoverable rule, not random changes, and E is false because different words usually get different codes according to the rule. Hence A, B and C only are correct, which is option C.

Option A:
Option A is incomplete since it omits C, thereby failing to mention the crucial examination principle that a single consistent rule governs all codes in one question.

Option B:
Option B is incorrect as it adds E, which wrongly suggests that knowing one code fixes all others, ignoring the dependence on the specific letters of each word.

Option C:
Option C is correct because it brings together the main transformation techniques and the idea of rule consistency, while excluding D and E, which mischaracterise coding questions as random or uniform across all words.

Option D:
Option D is wrong since it includes D, which asserts randomness, contradicting the logic-based nature of such questions, and it omits A, thus losing a central pattern used in letter coding.

The arithmetic mean of five numbers is 18, so their total sum is 18 × 5 = 90. One of the numbers is given as 24. To find the sum of the remaining four numbers, we subtract this known value from the total: 90 − 24 = 66. Thus, the combined total of the four remaining numbers is 66.

Option A:
Option A directly applies the relationship Total = Average × Number of items and then subtracts the known element to obtain the sum of the others. This method is standard in average problems and yields 66 consistently.

Option B:
Option B, 72, would correspond to a larger total of 96 if 24 were added back, which would produce an average of 19.2 instead of 18. This contradicts the given mean.

Option C:
Option C, 80, similarly gives a total of 104 when 24 is added back, leading to an average of 20.8, which is inconsistent with the initial information.

Option D:
Option D, 84, implies a total of 108 for five numbers, resulting in an average of 21.6, again conflicting with the given average of 18.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio. Here, 6÷3=2, 12÷6=2 and 24÷12=2, so the ratio between consecutive terms is consistently 2. This confirms that the common ratio is 2. Hence, option B correctly identifies the multiplier generating this sequence.

Option A:
The common ratio is 2, meaning each term is double the previous term. Starting from 3, multiplying by 2 gives 6, then 12, then 24, which matches the sequence given. In mathematical reasoning, recognising this multiplicative pattern helps to predict future terms and solve related problems. Therefore, 2 is the precise value that fits the definition of common ratio in this context.

Option B:
A common ratio of 3 would require that each term be three times the previous term, producing 3, 9, 27, 81 and so on. This does not match the actual sequence where the next term is only double the previous one. Since the ratios 6÷3, 12÷6 and 24÷12 are all 2, not 3, this option is incorrect.

Option C:
A common ratio of 4 would produce 3, 12, 48, 192, which is very different from the given numbers. None of the consecutive quotients in the sequence equals 4. Therefore, 4 cannot describe how the terms are generated, making this option wrong.

Option D:
A common ratio of 1.5 would create terms like 3, 4.5, 6.75, 10.125, which again do not appear in the question. The actual sequence remains strictly integer and doubles each time, unlike the fractional increase implied by 1.5. Hence, 1.5 is not suitable for this pattern.

The tap fills 1/12 of the tank per hour, while the leakage empties 1/18 of the tank per hour. When both operate together, the net filled amount per hour is 1/12 − 1/18. Taking the least common multiple of 12 and 18 as 36, we get the net rate as 3/36 − 2/36 = 1/36 of the tank per hour. Thus, the tank will be completely filled in 36 hours.

Option A:
Option A, 9 hours, would imply a net rate of 1/9 per hour, which is much faster than 1/36 and cannot be achieved under the given rates of filling and emptying. This ignores the slowing effect of the leakage.

Option B:
Option B, 12 hours, equals the time taken by the tap alone without any leakage. Since the leakage reduces the effective filling rate, the actual time must be longer than 12 hours.

Option C:
Option C, 18 hours, still underestimates the combined effect because the leakage continuously counters the filling tap. The computed net rate clearly shows that an even longer period is needed.

Option D:
Option D aligns with the net rate of 1/36 per hour obtained by subtracting the emptying rate from the filling rate. It is the only option that respects the mathematical relationship between the two processes.

The terms of this sequence satisfy the formula (a_n = 4n^3 + n^2 - 1) for n starting from 1. For n = 1, 2, 3, 4 and 5 we have 4+1−1 = 4, 32+4−1 = 35, 108+9−1 = 116, 256+16−1 = 271 and 500+25−1 = 524. For n = 6 the same expression yields (4×6^3 + 6^2 - 1 = 864 + 36 - 1 = 899). Consequently, 899 is the correct continuation of the series.

Option A:
Option A, 899, coincides with the value produced by the formula when n = 6. It keeps both the cubic and quadratic components of the pattern intact. Because it results directly from the generating rule, 899 is the correct next term.

Option B:
Option B, 887, is 12 less than the computed value and does not equal (4×6^3 + 6^2 - 1). It would require a sudden and unjustified reduction at the final step, so 887 is not valid.

Option C:
Option C, 911, overshoots the expected value and cannot be derived from the same expression for n = 6. Selecting 911 would distort the algebraic structure of the series. Hence 911 is not the right answer.

Option D:
Option D, 923, deviates even further from the formula’s output and again fails to satisfy the rule. This would destroy the strong correspondence between index and term, so 923 is not correct.