UGC NET Questions (Paper – 1)

Statements A, C and E correctly describe blood relation terminology and strategy. A is true because maternal and paternal terms indicate sides of the family. C is correct since drawing family trees is a widely recommended method for organizing information. E accurately defines “son-in-law” as the husband of one’s daughter. B is false, as B’s gender is not specified by A being a brother of B, and D is false because siblings include both brothers and sisters. Thus A, C and E only are correct.

Option A:
Option A is correct because it includes the precise conceptual statements about terminology and problem-solving strategies while excluding B and D, which misrepresent gender implications and the definition of siblings. It reflects the conventions used in NET reasoning questions.

Option B:
Option B is incorrect as it adds B, wrongly asserting that B must be male when A is B’s brother, and therefore introduces a false assumption into the set of correct statements.

Option C:
Option C is wrong because it includes D, which incorrectly narrows “siblings” to brothers only, so the combination mixes correct and incorrect statements.

Option D:
Option D is incorrect since it omits A and adds B, losing a key distinction between maternal and paternal relations and at the same time accepting a wrong inference about B’s gender.

The consecutive differences in the series are 7, 11, 15 and 19. These differences form an arithmetic progression with common difference 4. Therefore the next difference should be 23. Adding 23 to the last term 56 gives 79, which maintains the same second-level arithmetic structure and yields a smooth continuation.

Option A:
Option A gives 79, creating differences 7, 11, 15, 19, 23. Each difference increases by 4, so the pattern among the gaps remains consistent and clear. This makes 79 the only option that fully respects the established structure of the sequence.

Option B:
Option B gives 77, corresponding to a difference of 21 from 56. The resulting difference sequence 7, 11, 15, 19, 21 would end with a step of 2 instead of 4, breaking the uniform growth in the differences. Thus 77 does not fit the rule.

Option C:
Option C gives 81, which implies a difference of 25 from 56. That produces gaps 7, 11, 15, 19, 25, where the last increment is 6 and not 4. Consequently, 81 disrupts the simple arithmetic progression among the differences.

Option D:
Option D gives 83, yielding a difference of 27 from 56. The final increment between 19 and 27 becomes 8, which sharply departs from the steady step of 4. Therefore 83 is not a valid continuation of the series.

The differences between terms are 7, 11, 15 and 19, each increasing by 4. The next difference should therefore be 23. Adding 23 to the last term 55 gives 78. Thus, 78 is the correct next term that extends the pattern of differences.

Option A:
Option A is 75, which gives a difference of 20 from 55. This does not follow the expected increase from 19 to 23. Therefore, 75 is inconsistent with the second-level pattern.

Option B:
Option B equals 78, yielding the required difference of 23. The extended sequence of differences 7, 11, 15, 19, 23 keeps the +4 rule intact. This makes 78 the valid continuation of the series.

Option C:
Option C is 80, which would create a difference of 25 from 55. That skips beyond 23 and breaks the steady increment of 4 in the differences. Hence, 80 is not appropriate.

Option D:
Option D is 82, giving a difference of 27, even further away from the expected 23. This choice would make the pattern irregular and unclear. Therefore, 82 cannot be accepted.

For a fixed distance, time is inversely proportional to speed. Let the distance between P and Q be d. The onward time is d/60 and the return time is d/40. Their ratio is (d/60):(d/40) = 1/60:1/40 = 40:60, which simplifies to 2:3. Hence, the ratio of onward time to return time is 2:3.

Option A:
Option A, 3:2, reverses the correct ratio. This would imply that the onward journey at higher speed takes more time than the return journey at lower speed, which contradicts the basic principle of inverse proportionality between time and speed for the same distance.

Option B:
Option B, 4:5, does not match the fractional comparison 1/60:1/40. If we attempted to equate 4:5 to 40:60, they would not simplify to the same reduced form. Therefore 4:5 is not aligned with the correct calculation.

Option C:
Option C is correct because it results from cancelling the common factor d and then simplifying the fraction 40:60. This ratio correctly reflects that the car spends less time on the onward trip at 60 km/h than on the return trip at 40 km/h by a factor of 2 to 3.

Option D:
Option D, 5:4, suggests only a mild difference between the times and in the wrong direction. It cannot be derived from the exact speeds given and leads to an incorrect relationship between the onward and return travel times.

A and B correctly give the formulas for permutations and combinations without repetition. C is true because allowing repetition means each of the r positions can be filled in n ways, giving nʳ arrangements. E is also correct since identifying whether order matters is essential to selecting the right counting approach. D is false because without repetition, r-length arrangements from n objects are counted by nPr, not rⁿ. Thus A, B, C and E only are correct.

Option A:
Option A misses E and therefore does not state the important strategic step of checking whether order is significant. Although it contains correct formulas, it is not complete as an answer.

Option B:
Option B omits A and so fails to mention the basic permutation formula, even though it includes other true statements. Leaving out A makes the set incomplete for the topic.

Option C:
Option C is correct because it collects all the true statements while excluding D, which misapplies exponent notation. It reflects the range of arrangements encountered in NET questions.

Option D:
Option D excludes B and so ignores the combination formula, and it does not correct the error in D. Consequently, it does not represent the full correct set.

The series consists of consecutive even numbers increasing by 2 each time. We move from 2 to 4, 4 to 6, 6 to 8 and 8 to 10, always adding 2. Adding 2 to 10 gives 12. Therefore, 12 is the correct next term in the sequence.

Option A:
Option A is 11, which is odd and does not fit a series of even numbers. It also breaks the uniform difference of 2. Hence, this option is not appropriate.

Option B:
Option B is 14, which is even but is 4 more than 10. That would skip 12 and change the fixed increment of 2. Thus, it cannot be the immediate next term.

Option C:
Option C equals 12 and maintains both the even nature and the step size of 2. The extended series 2, 4, 6, 8, 10, 12 remains a clean list of consecutive even integers. This makes 12 the correct answer.

Option D:
Option D is 16, which is 6 more than 10 and leaves out 12 and 14. That jump is inconsistent with the pattern of adding 2, so 16 cannot be chosen here.

Statements A, B and C give core rules for relative speed questions. A is correct because approaching objects in opposite directions effectively close the distance at the combined speed. B is true since when moving in the same direction, the faster gains on the slower at the difference of their speeds. C is also correct because when trains cross each other completely, the total length to be covered relative to one another is the sum of their lengths. D is false because inconsistent units for speed and distance must be converted before using formulas, and E is false since on a circular track the time of meeting depends on relative speed, which involves differences for same-direction motion. Thus, A, B and C only are correct.

Option A:
Option A is incomplete as it lists only A and B and omits C, thereby failing to mention the specific structure of train-crossing problems where lengths are added.

Option B:
Option B is also incomplete since it includes only A and C and omits B, so it does not explicitly state how same-direction relative speed is computed.

Option C:
Option C is incomplete as it contains only B and C and omits A, losing the rule for opposite-direction motion.

Option D:
Option D is correct because it collects all three true statements about relative speeds and excludes D and E, which misrepresent unit conversion requirements and the nature of circular-track meetings.

The nth term of this sequence is given by aₙ = 4n³+3 for n starting from 1. For n = 1, 2, 3, 4 and 5 we get 4·1³+3 = 7, 4·2³+3 = 35, 4·3³+3 = 111, 4·4³+3 = 259 and 4·5³+3 = 503. For n = 6 the same rule yields 4·6³+3 = 864+3 = 867. Hence 867 is the only number that continues the sequence according to this cubic formula.

Option A:
Option A, 867, comes directly from applying aₙ = 4n³+3 when n = 6. It maintains exactly the same relationship between the index and the term that holds for all earlier values. Because no change in the rule is needed, 867 is fully consistent with the pattern and is correct.

Option B:
Option B, 827, is significantly smaller than 867 and does not equal 4·6³+3. It would require subtracting 40 from the formula’s result with no justification from the series. Therefore 827 is not a valid next term.

Option C:
Option C, 843, is closer but still fails to match the computed value, and it is not the output of 4n³+3 for any integer following n = 5. Selecting it would disrupt the clean cubic structure of the sequence. Thus 843 cannot be the correct answer.

Option D:
Option D, 897, overshoots the value given by the formula and similarly cannot be derived from 4n³+3 for n = 6. Using 897 would destroy the exact fit between the rule and the data, so it is not appropriate.

This series alternates between adding 2 and adding 3. Starting with 2, we have 2 + 2 = 4, 4 + 3 = 7, 7 + 2 = 9, 9 + 3 = 12 and 12 + 2 = 14. The pattern shows that after a +2 step comes a +3 step. Therefore, the next term should be 14 + 3 = 17, which preserves this alternation.

Option A:
Option A gives 16, which would correspond to adding 2 to 14 and repeating the same increment twice in a row. This violates the established alternation between +2 and +3. Hence, 16 is not consistent with the rule.

Option B:
Option B yields 17, which is obtained by adding 3 to 14 and correctly follows the alternation pattern. The series 2, 4, 7, 9, 12, 14, 17 remains structured as a repeating cycle of +2 and +3. Therefore, 17 is the correct next term.

Option C:
Option C suggests 18, which would require adding 4 to 14 and introducing an increment not seen anywhere else in the series. This makes the pattern unclear and irregular. Thus, 18 cannot be accepted.

Option D:
Option D offers 19, which is 5 more than 14 and again breaks the consistent use of 2 and 3 as increments. Choosing 19 would destroy the simple alternating pattern. Therefore, 19 is not the right answer.

A is correct because logical equivalence is defined via matching truth values in all cases. B is true as p → q is truth-functionally the same as ¬p ∨ q. D is correct since a conditional and its contrapositive always share the same truth table. C is wrong because p → q and q → p are converses and need not share truth values, and E is wrong since equivalence is about truth conditions, not syntactic identity. Therefore, C and E only are the wrong statements.

Option A:
Option A is correct because it identifies exactly C and E as the problematic statements, leaving intact the proper definitions and equivalences in A, B and D. It aligns with standard logical theory taught for NET.

Option B:
Option B considers only C as wrong and mistakenly treats E as acceptable, despite E conflating syntactic form with semantic equivalence. It therefore misses one incorrect statement.

Option C:
Option C treats only E as wrong and ignores the clear counterexamples to C where p → q and q → p differ, so it does not cover all wrong statements.

Option D:
Option D includes D among wrong statements, even though D is correct about contrapositive equivalence, and so misclassifies a true principle along with the false ones.

The terms satisfy the rule (a_n = 3n^4 + n) for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 3+1 = 4, 48+2 = 50, 243+3 = 246, 768+4 = 772 and 1875+5 = 1880. For n = 6 the expression gives (3×6^4 + 6 = 3×1296 + 6 = 3888 + 6 = 3894). Hence 3894 is the term that keeps this quartic-plus-linear pattern intact.

Option A:
Option A, 3846, is 48 less than the computed value and does not equal (3×6^4 + 6). It would require unjustified modification of the rule at the final term. Therefore 3846 is not a correct continuation.

Option B:
Option B, 3862, is closer but still fails to match 3894 and does not arise from the formula for n = 6. Choosing 3862 would weaken the exact algebraic structure that defines the sequence. Hence 3862 is not valid.

Option C:
Option C, 3894, comes directly from evaluating (a_n = 3n^4 + n) at n = 6. It preserves both the quartic and linear components exactly as before, ensuring internal consistency. For this reason, 3894 is the correct next term.

Option D:
Option D, 3950, overshoots the correct value and again cannot be written as (3n^4 + n) for the next index. Using 3950 would distort the pattern, so it is not the right answer.

In this pattern, the first letters go backward in the alphabet: Z(26), Y(25), X(24), W(23), decreasing by 1. The second letters go forward: A(1), B(2), C(3), D(4), increasing by 1. The next first letter is V(22), and the next second letter is E(5), forming VE. Therefore VE is the unique pair that preserves both movements.

Option A:
Option A, UF, uses U as the first letter, which is 2 steps before W instead of 1. It also advances the second letter to F, which is 2 steps beyond D. These larger jumps break the consistent step of 1 in both directions, making UF incorrect.

Option B:
Option B, WD, simply repeats the last term of the series. The sequence is clearly moving and does not indicate any repetition pattern. Thus WD cannot serve as the next term.

Option C:
Option C is correct because V and E are exactly one step beyond W backward and D forward respectively. It keeps the first letter moving towards the beginning of the alphabet and the second letter moving towards the end. This symmetry ensures VE follows the established rule.

Option D:
Option D, VG, uses the correct first letter V but sends the second letter to G, two steps ahead of E. That distorts the +1 progression in the second position. As a result, VG does not properly continue the series.

Each group consists of four letters that are two positions apart inside the alphabet, for example ACEG uses positions 1, 3, 5 and 7. From one group to the next, every letter shifts one step forward: ACEG becomes BDFH, then CEGI, then DFHJ. Applying the same column wise +1 shift again, D becomes E, F becomes G, H becomes I and J becomes K, giving EGIK. Thus EGIK uniquely preserves the regular spacing and advancement.

Option A:
Option A, EFGH, destroys the spacing pattern because the letters are consecutive instead of being two steps apart. It does not arise from adding one to each letter of DFHJ. Since the series is defined by both even spacing and uniform shifting, EFGH does not fit the rule.

Option B:
Option B, EGIJ, starts correctly with E and G but changes the last two letters to I and J. The final letter J is only one step ahead of I instead of two steps ahead of G, breaking the uniform internal differences. Because it fails to keep both the +2 spacing and the consistent shift from DFHJ, EGIJ cannot be the correct answer.

Option C:
Option C, EGHJ, again loses the pattern of equal spacing. The letters E, G, H and J have mixed intervals, and this group is not produced by a simple +1 shift from DFHJ. Even though some letters look close to the expected ones, the underlying structure is not preserved.

Option D:
Option D is correct because E, G, I and K are each exactly one step ahead of D, F, H and J respectively. It keeps the difference of two positions between successive letters inside the group and maintains the same transformation that generated all earlier terms. Therefore EGIK is the logical next term in the series.

Statements A, B and C capture the standard relationships between percentages and angles in a pie chart. A correctly states that the entire circle is 100 percent. B gives the direct formula for converting a percentage to its central angle. C provides the inverse operation, dividing the angle by 3.6 to obtain the percentage. D is false because if the total value is given, absolute amounts for each sector can be calculated from percentages, and E is false since bar graphs are usually better for exact comparisons when many categories have similar sizes. Therefore, A, B and C only form the correct set.

Option A:
Option A is correct because it includes all three true statements about percentage–angle conversions and excludes D and E, which misrepresent the capabilities and comparative usefulness of pie charts. It gives exactly the relationships that candidates routinely use in NET data interpretation.

Option B:
Option B is incomplete, as it covers only A and B and ignores C, thereby failing to mention the reverse conversion from angles back to percentages. Without C, the explanation of how to read pie charts is only half finished.

Option C:
Option C is incorrect because it includes D, the false claim that absolute totals can never be deduced when totals are known, and thus mixes an error into an otherwise correct combination. Once a wrong statement is included, the option cannot be considered correct.

Option D:
Option D is wrong because it omits A and adds only B and C, not explicitly affirming that the full circle represents 100 percent, and also does not address the incorrect statements in D and E. This makes it an incomplete and therefore invalid combination.

Let the present age of the son be x years, so the father’s present age is 3x years. After 10 years, their ages will be x + 10 and 3x + 10 respectively. According to the given ratio, (3x + 10) : (x + 10) = 2 : 1, which leads to the equation 3x + 10 = 2(x + 10). Simplifying, 3x + 10 = 2x + 20 gives x = 10, so the son is presently 10 years old.

Option A:
Option A, 8 years, would make the father’s present age 24 and their ages after 10 years 18 and 34, giving a ratio of 34 : 18, which simplifies to 17 : 9, not 2 : 1. Thus, it fails the future ratio condition.

Option B:
Option B, 9 years, would give the father’s present age as 27 and future ages as 19 and 37, yielding 37 : 19, which is not 2 : 1.

Option C:
Option C satisfies both the present and future conditions: the father is 30 and son is 10 now, and after 10 years they will be 40 and 20, giving a ratio of 2 : 1. This consistency confirms 10 years as the correct present age of the son.

Option D:
Option D, 12 years, leads to a father’s present age of 36 and future ages of 22 and 46, giving the ratio 46 : 22 = 23 : 11, which again does not match the required 2 : 1.