UGC NET Questions (Paper – 1)

A percentage is a way of expressing a number as a fraction of 100, using the symbol "%". For example, 25% represents 25 out of 100, which is equivalent to 1/4. In aptitude problems, percentages are used to describe profit, loss, marks and many other comparisons. Therefore, the process of expressing a quantity as a fraction of 100 is exactly the definition of percentage.

Option A:
A fraction represents a part of a whole and can have any denominator, not necessarily 100. While every percentage can be written as a fraction, not every fraction is expressed with denominator 100. The question specifically mentions "fraction of 100," which is more precise than the general idea of a fraction. Hence, this option is not fully accurate.

Option B:
A ratio compares two quantities, but it does not require that one of them be 100. For instance, 3:5 is a ratio, yet it is not expressed per hundred. Thus, although percentages are related to ratios, the question is looking for the more specific term that involves 100 as the base.

Option C:
Percentage is correct because it directly means "per hundred," indicating how many parts out of 100 a quantity represents. Converting marks into percentages, such as 80 out of 100 being 80%, is a standard example. This concept is central to many UGC NET Paper 1 numerical questions on growth rates, scores and comparisons.

Option D:
Average is the central value of a set of numbers and is commonly found by dividing the sum of observations by the number of observations. It does not involve expressing quantities as a fraction of 100. Therefore, average is unrelated to the description in the question and cannot be the correct answer.

The series is a geometric progression with common ratio 3. Each term is obtained by multiplying the previous term by 3: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54 and 54 × 3 = 162. To continue this pattern, we multiply 162 by 3 to get 162 × 3 = 486. This maintains the constant ratio throughout the sequence.

Option A:
Option A gives 432, which would correspond to multiplying 162 by a factor less than 3 and does not follow the geometric rule. This breaks the constant ratio pattern. Hence, 432 is not correct.

Option B:
Option B offers 450, which is not 162 multiplied by any simple integer ratio used earlier in the series and appears arbitrary. Therefore, 450 cannot be accepted as consistent with the pattern.

Option C:
Option C suggests 480, which again is not equal to 162 × 3 and would require changing the ratio at the end of the series. This disrupts the geometric progression. Thus, 480 is not appropriate.

Option D:
Option D yields 486, which is exactly 162 × 3 and preserves the common ratio of 3. The expanded sequence 2, 6, 18, 54, 162, 486 is a clean geometric progression. Hence, 486 is the correct next term.

The positions of the letters are B(2), D(4), G(7), K(11) and P(16). The differences are +2, +3, +4 and +5 respectively. The pattern shows that each gap increases by 1, so the next difference should be +6. Adding 6 to 16 gives 22, which corresponds to V. Therefore V is the correct continuation.

Option A:
Option A, U, is at position 21, which is only 5 steps after P. That would repeat the last gap rather than increase it to 6. Since the pattern clearly demands a growing difference, U does not fit the rule.

Option B:
Option B, W, lies at position 23, implying a jump of 7 from P. This overshoots the expected difference and would break the smooth progression of 2, 3, 4, 5, 6. Therefore W cannot be accepted as the next term.

Option C:
Option C is correct because V occupies position 22, giving exactly the required +6 increment. It continues the trend of increasing the gap by one at each step. This strict adherence to the numerical progression of differences makes V the logical answer.

Option D:
Option D, X, at position 24, corresponds to a jump of 8 from P. Such a jump is not consistent with the incremental pattern of the series. As it would disrupt the orderly growth of the differences, X is not a valid continuation.

In propositional logic, the connective “and” corresponds to conjunction. A conjunction p and q is true only when both component statements p and q are true simultaneously. Here p says the number is even and q says it is divisible by 3. Putting them together with “and” requires both properties to hold. Thus, the combined statement means that the number must be even and divisible by 3.

Option A:
Option A uses “or” instead of “and,” which corresponds to a different connective (disjunction). It allows numbers that are only even or only divisible by 3, and hence does not capture the meaning of “p and q.”

Option B:
Option B mixes “either” with a negation in a way that is not equivalent to the original conjunction. It introduces “not divisible by 3,” which is not part of q.

Option C:
Option C reflects the standard interpretation of a logical conjunction: both conditions must be simultaneously satisfied. It directly translates “p and q” into ordinary language as “even and divisible by 3.”

Option D:
Option D makes both properties false, which would correspond to the negation of p and q, not the conjunction of p and q.

Statements A, B, C and D are all standard facts used in clock angle questions. A and B give the angular speeds of the minute and hour hands. C is correct because at 3:00 the hands are exactly 90 degrees apart. D is true since the hands overlap once between 2:00 and 3:00. E is false because the hands are perpendicular 22 times in 12 hours, not 12 times. Therefore A, B, C and D only are correct.

Option A:
Option A is incomplete since it omits D and therefore does not mention the key overlap fact used in many clock problems.

Option B:
Option B is incomplete because it drops B (the hour hand speed), which is essential for calculations.

Option C:
Option C is correct because it lists all the correct statements about hand speeds, angles and coincidences, while excluding E, which undercounts the perpendicular occurrences.

Option D:
Option D is wrong as it omits A (true) and therefore does not include all correct statements.

Statements A and B summarise the basic relationship and unit harmony. Statement C is correct (m/s → km/h multiply by 18/5). Statement D is correct (km/h → m/s multiply by 5/18). Statement E is false because inconsistent units can cause major errors even when approximating. Therefore, A, B, C and D only are correct.

Option A:
Option A is incomplete as it omits D (km/h → m/s).

Option B:
Option B is incomplete because it omits B (minutes to hours conversion) even though it includes conversion factors.

Option C:
Option C is incorrect because it omits A (distance = speed × time).

Option D:
Option D is correct since it gathers all true statements and excludes E (false).

The groups are four letter consecutive blocks where the starting letters J, L, N and P occupy positions 10, 12, 14 and 16, increasing by 2 each time. Each block then takes the next three letters in order. Continuing this rule, the next starting letter is position 18, which is R, and the block from R is RSTU. Thus RSTU uniquely keeps both the plus two starting step and the four letter structure.

Option A:
Option A, STUV, is a valid four letter block but begins at S, which is three steps after P instead of two. This changes the size of the jump in the starting letter, contradicting the constant increment of two. Therefore STUV does not align with the governing rule of the series.

Option B:
Option B, QRST, starts at Q, which is only one position after P. That reduces the step from two to one and breaks the arithmetic progression of starting positions. Because the pattern clearly shows a consistent plus two movement, QRST cannot be considered correct.

Option C:
Option C is correct because R is exactly two positions ahead of P and RSTU forms a proper four letter consecutive group. It extends the same even step difference in the starting letter and preserves the internal consecutiveness. This match with both structural aspects of the series makes RSTU the right answer.

Option D:
Option D, NOPQ, repeats an earlier block instead of moving forward. The series never reuses a previous group, and each term has a strictly increasing starting letter. As a result, NOPQ cannot be the next term.

In partnership problems, profit is divided in the ratio of “capital × time”. Taking capitals 5k, 7k and 9k for A, B and C, and times 12, 10 and 8 months, their effective investments are 5k × 12 = 60k, 7k × 10 = 70k and 9k × 8 = 72k. These are in the ratio 60:70:72. The sum of the ratio parts is 202, so C’s share is (72/202) of ₹2,02,000, which equals ₹72,000.

Option A:
Option A, ₹60,000, corresponds to 60 parts out of 202 and would be A’s share if we followed the correct method. Assigning this to C would contradict both the given investment ratio and the time periods. It undervalues C’s contribution, which is actually the largest.

Option B:
Option B is correct because it matches the 72 parts assigned to C in the 60:70:72 ratio. Multiplying the total profit by 72/202 leads exactly to ₹72,000, and the remaining profits allocate correctly to A and B when their parts are used. This ensures the distribution honours both capital and time contributions.

Option C:
Option C, ₹84,000, would represent a different fraction of the total profit and would imply that C’s effective investment is larger than 72 parts out of 202. That would disturb the precise ratio derived from 5:7:9 and the corresponding time periods. Hence ₹84,000 does not reflect the correct proportional sharing.

Option D:
Option D, ₹90,000, exceeds even Option C and would require a much stronger claim for C’s investment than is supported by the data. If we tried to back-calculate the implied ratio, the figures would no longer match the product of capital and time given in the question. Thus, ₹90,000 cannot be C’s correct share.

This option is correct because the symbol '→' represents the logical conditional and is read as "implies." The statement "P → Q" is pronounced "P implies Q." It conveys that whenever P is true, Q must also be true. Therefore, the correct connective word is "implies."

Option A:
The phrase "P causes Q" suggests a causal relationship rather than a logical one. Logical implication does not necessarily assert any physical cause-and-effect link. Thus, "causes" is not the standard reading of the connective.

Option B:
In "P implies Q," "implies" is the accepted wording for the conditional statement. It indicates that truth of P guarantees truth of Q under the logical system. This matches the conventional reading of the symbol '→', so this option is correct.

Option C:
The phrase "P equals Q" refers to equality, which is represented by a different symbol, usually '='. It does not describe a conditional relation where one statement leads to another. Hence, this option is not appropriate.

Option D:
"P contradicts Q" would mean that P and Q cannot both be true, relating to negation rather than implication. That idea is closer to exclusive or or inconsistency, not the ordinary conditional statement. Therefore, this option is incorrect.

Statements A, B and C provide the standard classification of formulas into tautology, contradiction and contingency. Statement E is also true because truth tables are a systematic way to test which of these categories a formula falls into. Statement D is false because the existence of contingencies means there is indeed a third kind of formula. Therefore, A, B, C and E only make up the correct set.

Option A:
Option A is incomplete as it omits E and thus does not mention the main procedural tool, the truth table, which is central to exam questions on this topic.

Option B:
Option B is wrong since it includes D, which denies the existence of contingencies, contradicting statement C.

Option C:
Option C is correct because it captures all true statements and excludes D, which misclassifies propositional forms.

Option D:
Option D is incorrect as it retains D and omits A, losing the definition of tautology while including a false generalisation about all formulas.

Each term is obtained by doubling the previous term and adding 3. We have 2 × 2 + 3 = 7, 7 × 2 + 3 = 17, 17 × 2 + 3 = 37 and 37 × 2 + 3 = 77. Applying the same rule to 77 gives 77 × 2 + 3 = 154 + 3 = 157. This keeps the recursive pattern uniform across all steps.

Option A:
Option A gives 155, which would require adding only 1 after doubling or using a different operation, neither of which is seen earlier. Thus, 155 is not compatible with the pattern.

Option B:
Option B offers 156, which corresponds to adding 2 after doubling 77 and again changes the constant part of the rule. This violates the consistency of "plus 3." Therefore, 156 cannot be accepted as correct.

Option C:
Option C yields 157, exactly equal to 77 × 2 + 3, and perfectly aligns with the transformation applied to each term. The sequence 2, 7, 17, 37, 77, 157 remains governed by a single simple rule. Hence, 157 is the correct next term.

Option D:
Option D suggests 159, which is 82 more than 77 and does not arise from the rule "double then add three." This introduces an arbitrary jump into the series. Therefore, 159 is not appropriate.

The sequence is generated by aₙ = n⁴ + n³ + 3n² + 2 for n starting from 1. For n = 1, 2, 3, 4 and 5 we calculate 1+1+3+2 = 7, 16+8+12+2 = 38, 81+27+27+2 = 137, 256+64+48+2 = 370 and 625+125+75+2 = 827, matching the given terms exactly. For n = 6 this formula yields 6⁴+6³+3·6²+2 = 1296+216+108+2 = 1622. Thus 1622 is the only value that continues this specific quartic-plus-cubic-plus-quadratic pattern.

Option A:
Option A, 1622, matches perfectly the value obtained from n⁴+n³+3n²+2 when n = 6. It preserves all components of the expression and continues the same growth trend seen in the previous terms. Because no modification of the coefficients or constant is required, 1622 is the correct continuation of the series.

Option B:
Option B, 1606, is 16 less than the formula’s output and does not satisfy the rule for n = 6. Choosing 1606 would require reducing the term without any structural change in the function, which contradicts the exact fit observed earlier. Hence option B is incorrect.

Option C:
Option C, 1640, overshoots the correct value by 18 and again cannot be written as n⁴+n³+3n²+2 for n = 6. It represents an arbitrary increase that is not indicated by the previous behaviour of the series. Therefore option C is incorrect.

Option D:
Option D, 1664, deviates even more from the computed value and has no basis in the established expression. Using 1664 would break the precise mapping between index and term that defines this number series, so option D is incorrect.

The first letters are C(3), G(7), K(11) and O(15), each increasing by 4. The second letters are F(6), J(10), N(14) and R(18), also increasing by 4. Therefore, the next first letter is 15 + 4 = 19 (S) and the next second letter is 18 + 4 = 22 (V). Hence SV is the only pair that continues the uniform +4 progression in both positions.

Option A:
Option A, SV, is correct because it places S (19) after O (15) by +4 and V (22) after R (18) by +4. It preserves the same arithmetic step used in every previous pair. Therefore SV is the correct continuation.

Option B:
Option B, SW, keeps S correct but changes the second letter to W (23), which is +5 from R, not +4. This breaks the constant increment rule in the second position. Hence SW is incorrect.

Option C:
Option C, SX, keeps S correct but takes X (24), which is +6 from R. This increases the step size without any basis in the series. Therefore SX does not fit the pattern.

Option D:
Option D, TX, changes the first letter to T (20), which is +5 from O instead of +4. Since the first position must also increase by exactly 4, TX cannot be the correct next term.

At 5:40, the minute hand is at 40 minutes, corresponding to 40 × 6 = 240 degrees from the 12 o’clock position. The hour hand moves 30 degrees per hour plus 0.5 degrees per minute. By 5:40, it has moved 5 × 30 = 150 degrees for five full hours and 0.5 × 40 = 20 degrees for the extra minutes, totalling 170 degrees. The angle between the hands is 240 − 170 = 70 degrees. This is less than 180 degrees, so it is already the smaller angle between the two hands.

Option A:
Option A, 70 degrees, comes directly from the standard formulas for hand positions and the absolute difference between them, so it correctly represents the smaller angle.

Option B:
Option B, 90 degrees, would make the hands perpendicular, which they are not at 5:40 because the hour hand has moved well past the 5 while the minute hand points to 8 on the dial.

Option C:
Option C, 100 degrees, overestimates the separation and does not match the computed difference between 240 degrees and 170 degrees.

Option D:
Option D, 120 degrees, corresponds to an even wider angle and clearly contradicts the calculated positions of the hour and minute hands at 5:40.

This series is governed by the formula aₙ = n⁴+n³ for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 1+1 = 2, 16+8 = 24, 81+27 = 108, 256+64 = 320 and 625+125 = 750. For n = 6 the expression gives 1296+216 = 1512. Therefore 1512 is the only value that maintains the quartic-plus-cubic structure of the sequence.

Option A:
Option A, 1432, is 80 less than the correct value and does not equal n⁴+n³ for n = 6. It breaks the clear algebraic rule that generates the previous terms. Thus 1432 cannot be the correct continuation.

Option B:
Option B, 1512, is exactly the sum of 6⁴ and 6³ and follows directly from the rule aₙ = n⁴+n³. It preserves both the degree and the coefficients of the terms in the expression. For these reasons, 1512 is the correct next term.

Option C:
Option C, 1462, also fails to satisfy the formula for n = 6 and would require altering the mathematical relationship. This inconsistency makes 1462 an invalid choice.

Option D:
Option D, 1572, overshoots the predicted value and again cannot be obtained from n⁴+n³ for the next index. Choosing 1572 would abandon the tight functional fit, so it is not correct.