UGC NET Questions (Paper – 1)

In the simple interest formula I = PRT/100, P stands for the principal, which is the original amount of money invested or borrowed. The principal is the base on which interest is calculated using the rate R and time T. Understanding the roles of P, R and T is vital for solving interest-related questions in mathematical aptitude. Therefore, identifying P as the principal is correct.

Option A:
Principal is correct because it refers to the starting sum of money before any interest is added. For example, if you deposit ₹5000 at a certain rate, that ₹5000 is the principal in the formula. Once we know P, R and T, we can compute the interest earned or payable. This clarity makes option A the appropriate choice.

Option B:
Profit is the difference between selling price and cost price in commercial transactions and is not directly represented by P in the simple interest formula. While profit can involve interest in some contexts, the formula given specifically uses P as the base amount of money, not the gain. Hence, calling P "profit" would be conceptually wrong.

Option C:
Percentage is a way of expressing a number per hundred and usually refers to the rate R in the interest formula. The letter R, not P, is associated with the percentage rate. Therefore, identifying P as percentage would confuse the roles of the variables, making this option incorrect.

Option D:
Payment is a general term for money paid, often periodically, but in the simple interest formula the symbol P has a more precise meaning. Payment may include principal plus interest, whereas P denotes just the initial principal amount. Thus, this option does not accurately capture the definition in the formula.

A prime number is an integer greater than 1 with exactly two distinct positive divisors, namely 1 and the number itself. This definition excludes 1 because it has only one positive divisor and excludes composite numbers because they have more than two divisors. In mathematical reasoning, primes are considered the building blocks of the integers. Thus, the description in the question is the standard definition of a prime number.

Option A:
Composite numbers are positive integers greater than 1 that have more than two distinct positive divisors. For example, 6 is composite because it is divisible by 1, 2, 3 and 6. Since the question clearly states "exactly two distinct positive divisors," composite numbers do not fit this requirement. Therefore, this option is incorrect.

Option B:
A multiple is a number that can be obtained by multiplying a given number by an integer, such as 12 being a multiple of 3. This term describes a relationship between numbers and does not specify how many divisors a number has. Hence, it does not answer the definition provided in the stem.

Option C:
Prime is correct because a prime has no positive divisors other than 1 and itself, satisfying the condition of exactly two distinct positive divisors. Examples include 2, 3, 5, 7 and 11. Recognising prime numbers is important in tests involving factorisation, LCM and HCF. Thus, this option directly matches the given description.

Option D:
Even numbers are those divisible by 2, but not all integers greater than 1 divisible by 2 have exactly two divisors. For example, 4 is even but has three positive divisors: 1, 2 and 4. Therefore, "even" is not equivalent to the definition provided and cannot be the correct answer.

If the average of two numbers is 20, their total sum must be 20 × 2 = 40. One of the numbers is given as 16. To find the other number, we subtract the known number from the total: 40 − 16 = 24. Therefore, the second number must be 24 so that the pair has an average of 20.

Option A:
Option A, 18, would result in a total of 34 when added to 16, which would give an average of 17, not 20. Thus, it underestimates the required second number.

Option B:
Option B, 20, would give a total of 36 and an average of 18, which again does not meet the given condition of average 20.

Option C:
Option C, 22, makes the total 38, leading to an average of 19, which is close but still not equal to 20.

Option D:
Option D maintains the correct relation: 16 + 24 = 40, and 40 ÷ 2 = 20, so the pair (16, 24) satisfies the stated average exactly.

In this series, the second letter A remains unchanged, while the first letter moves forward alphabetically: B, C, D, E. The next letter after E is F. Combining F with the constant A gives FA as the next term.

Option A:
Option A is correct because it uses F, the immediate successor of E, and retains the fixed second letter A. This respects both the constant suffix and the stepwise change in the first position. Therefore FA fits naturally as the continuation.

Option B:
Option B, GA, jumps beyond F to G, skipping one letter in the sequence. The pattern shows no evidence of skipping letters. As such, GA is too far ahead to be the next term.

Option C:
Option C, HA, moves even further away from the established progression. It disregards the requirement to use F next. This makes HA incompatible with the pattern.

Option D:
Option D, IA, is also not appropriate because it continues the same mistake of skipping multiple letters. There is no indication that the series changes its step size. Consequently, IA cannot be accepted.

Let the original price be 100 units for ease of calculation. A 20% increase raises the price to 120 units. A subsequent 20% decrease is applied to this new price, so the reduction is 20% of 120, which is 24. Subtracting 24 from 120 gives 96. The final price is therefore 96, which is 4 units less than the original 100, indicating a net decrease of 4%.

Option A:
Option A, 0% change, would be correct only if an increase and an equal decrease cancelled each other exactly, but this happens only when both percentages are applied to the same base value. Here the decrease is applied to an already increased price.

Option B:
Option B, 2% decrease, underestimates the net effect and would arise from a miscalculation or an incorrect averaging of percentages without considering the changed base.

Option C:
Option C accurately tracks the price through both changes and compares the final value with the initial value. The computation demonstrates that the successive operations do not cancel out but instead yield a 4% net decrease.

Option D:
Option D, 6% decrease, overstates the net reduction and cannot be derived from the multiplicative factors 1.2 and 0.8 that represent the two changes.

A is correct since opposing motions add speeds, and B is correct as same-direction relative speed is the difference between speeds. C is true because when trains cross, they must cover the sum of their lengths relative to each other. E is also correct because the units are consistent so distance is directly in kilometres. D is false because distance is speed × time, not speed ÷ time. Hence the combination A, B, C and E only is correct.

Option A:
Option A leaves out E, failing to note the important unit consistency that allows direct interpretation of distance in kilometres. Though it includes true statements, it is not complete.

Option B:
Option B omits A and thus does not mention the case of opposite direction motion, which is central for many train problems. This makes the description insufficient.

Option C:
Option C is incomplete because it leaves out B, ignoring the same-direction relative speed rule, and so does not cover all key cases used in exam questions.

Option D:
Option D is correct, bringing together all true statements and excluding D, which misstates the basic speed–distance relation. It matches the conceptual framework required for time–speed–distance and train problems.

Let the present ages of A and B be A and B years respectively. We know A + B = 50. After 10 years, their ages will be A + 10 and B + 10, and the ratio (A + 10) : (B + 10) is given as 4 : 3. This gives the equation (A + 10) / (B + 10) = 4 / 3, which can be solved together with A + B = 50. Solving this system yields A = 30 and B = 20, so A’s present age is 30 years.

Option A:
Option A, 20 years, actually corresponds to B’s present age when the system is solved. It reverses the roles of A and B and therefore does not answer the question correctly.

Option B:
Option B, 25 years, would make the sum of their ages 50 only if B were also 25, but this would not satisfy the future ratio of 4 : 3 after 10 years.

Option C:
Option C satisfies both conditions: the present ages 30 and 20 sum to 50, and after 10 years they become 40 and 30, which indeed are in the ratio 4 : 3.

Option D:
Option D, 35 years, would require B to be 15 to keep the sum at 50, and after 10 years the ratio 45 : 25 is not equal to 4 : 3.

An even number is defined as an integer that can be written in the form 2k, where k is an integer. This means it is exactly divisible by 2 without leaving any remainder. Numbers like −4, 0, 2 and 10 are all even because they satisfy this property. Therefore, the description in the question perfectly matches the standard definition of an even number.

Option A:
Prime numbers are integers greater than 1 that have exactly two distinct positive divisors, 1 and the number itself. While some primes like 2 are even, most primes are not characterised simply by divisibility by 2. The defining property in the question is divisibility by 2 for all such numbers, which corresponds to evenness, not primality. Hence, this option is not correct.

Option B:
Odd numbers are integers that leave a remainder of 1 when divided by 2. They can be expressed as 2k+1 for some integer k. This is the opposite of being exactly divisible by 2, so odd numbers do not fit the description given in the question. Therefore, this option must be rejected.

Option C:
Even numbers are correct because they are precisely those integers that divide by 2 with no remainder. In many aptitude questions, recognising even and odd numbers quickly helps in solving problems on divisibility and parity. Knowing this definition is foundational for reasoning about number patterns and algebraic expressions. Thus, this option accurately answers the question.

Option D:
Composite numbers have more than two positive divisors, such as 4, 6 or 12, but the question is not about the count of divisors. Some composite numbers are even and some are odd, so "composite" is not equivalent to "divisible by 2." As the stem focuses solely on divisibility by 2, composite is not the correct term.

Statements A and B are fundamental facts about complements, D describes the multiplication rule for independent events and E is true because working with complements, like “at least one” via “1 − P(none)”, often simplifies calculations. Statement C is false because for mutually exclusive events, P(A and B) = 0, not P(A) + P(B), which is instead P(A or B) for such events. Therefore, the combination A, B, D and E only is correct.

Option A:
Option A is incomplete since it omits E and thus does not state explicitly the strategic advantage of using complementary events to simplify some NET probability questions.

Option B:
Option B is also incomplete because it leaves out D, thereby ignoring the key rule for independent events, which is central to many probability computations. Without D, the treatment of joint events is missing.

Option C:
Option C is wrong because it excludes A and consequently fails to express the basic identity P(A) + P(not A) = 1, and it still does not remove C, the incorrect equality about mutually exclusive events.

Option D:
Option D is correct as it collects all true statements and rejects C, which confuses “and” with “or” probabilities for mutually exclusive events. It represents how complementary and independent events are used in exam-level problems.

Statements A and B correctly characterise the decimal and binary systems, D describes the method of converting a binary numeral to decimal and E points out common exam tasks involving conversions and comparisons of numbers in different bases. Statement C is false because (1010)₂ equals 10 in decimal, not 5. Hence, the combination A, B, D and E only is the correct set.

Option A:
Option A is incomplete since it omits E, thereby failing to acknowledge the typical exam requirement to convert or compare numbers across bases. Without E, the link to aptitude questions is weaker.

Option B:
Option B is correct because it groups all four true statements while excluding C, which miscalculates the value of a simple binary number. It summarises both the structure and the practical use of different base systems for NET aspirants.

Option C:
Option C is wrong as it includes C, the incorrect evaluation of (1010)₂, and omits A, leaving out the definition of decimal place value. The combination of an error with an omission invalidates the option.

Option D:
Option D is incorrect because it contains C and therefore accepts a wrong binary-to-decimal conversion, even though some of its other statements are true. This makes the overall option unsuitable as a correct answer.

Each term is three times the previous one: 2×3 = 6, 6×3 = 18 and 18×3 = 54. This defines a geometric progression with common ratio 3. Multiplying the last term 54 by 3 gives 162. Thus, 162 is the next term that keeps the series consistent.

Option A:
Option A suggests 72, which is only 18 more than 54 and does not fit the multiplication-by-three rule. None of the earlier transitions involve adding a fixed number like 18. Therefore, 72 is not appropriate.

Option B:
Option B is 90, which represents 54 plus 36 and again breaks the pure multiplication pattern. The series has never used addition rules, so introducing such a change would be unjustified. Hence, 90 is incorrect.

Option C:
Option C equals 162 and results directly from 54×3, preserving the ratio of 3 between consecutive terms. The extended series 2, 6, 18, 54, 162 shows a clear and consistent geometric pattern. This makes 162 the valid next term.

Option D:
Option D is 180, which does not arise from multiplying 54 by a whole number used earlier in the sequence. Choosing 180 would produce a ratio of 10/3 with the previous term, not 3. Thus, this option does not respect the established rule.

Statements A and B correctly define speed and describe the inverse relationship between speed and time for a fixed distance. Statement E is also true because many aptitude questions demand consistent units, requiring conversions like km/h to m/s. Statement C is false since the average speed for a round trip with different speeds is given by the harmonic mean, not the simple arithmetic mean, and D is false because using consistent units, not different ones, avoids confusion. Therefore, the combination A, B and E only is correct.

Option A:
Option A is incomplete because although it includes two true statements, it omits E and thus fails to highlight the practical necessity of unit conversion in exam problems. Without E, the description of typical question features is not complete.

Option B:
Option B is correct as it collects all the true statements and rejects C and D, which misdescribe average speed and unit usage. It perfectly matches the conceptual treatment of time–speed–distance in UGC NET.

Option C:
Option C is wrong because it brings in C, which wrongly uses the arithmetic mean for round trips, and therefore mixes a false statement with true ones. This mathematical error invalidates the option.

Option D:
Option D is incorrect since it includes D, the mistaken claim about using different units, and omits A, which gives the core definition of speed. This combination misleads about both concept and practice.

Statements A, B and C present the standard relationships between necessary and sufficient conditions. A is correct because sufficiency ensures Q whenever P holds. B is true since necessity means Q cannot hold without P. C is correct as “necessary and sufficient” expresses logical equivalence. D is false; sufficiency does not generally reverse, and E is false because in “if P then Q”, P is sufficient and Q is necessary. Thus, A, B and C only are correct.

Option A:
Option A is incomplete because it omits C, and therefore does not explicitly mention the important notion of equivalence when a condition is both necessary and sufficient.

Option B:
Option B is incorrect because it includes E, which reverses the roles of P and Q in the implication, so this option accepts a false description of necessary and sufficient conditions.

Option C:
Option C is correct as it collects all three accurate conceptual definitions and excludes D and E, which misrepresent the direction and roles in implications.

Option D:
Option D is wrong since it adds D, which claims sufficiency reverses, and so includes a clear logical error alongside true statements, making the combination unacceptable.

The positions of the letters are B(2), E(5), J(10), Q(17) and Z(26). The differences between consecutive positions are +3, +5, +7 and +9, forming an increasing sequence of odd numbers. The next difference should be +11, so the next position is 26 + 11 = 37, which corresponds to 37 − 26 = 11, the letter K. Thus K uniquely maintains the pattern of increasing odd-numbered jumps with wrap-around.

Option A:
Option A, J, is at position 10, which would move backward from Z instead of forward. This contradicts the established behaviour of positive jumps in position. Since all previous moves are forward and increase in size, returning to J breaks the pattern entirely.

Option B:
Option B, H, lies at position 8, again going backward from 26 to 8. There is no indication of reversal or oscillation in the sequence. Because the pattern involves steadily increasing forward gaps, H cannot be justified as the next letter.

Option C:
Option C is correct because K corresponds to position 11, which is 37 modulo 26, produced by adding 11 to 26. It keeps the next gap as the next odd number after 9 and respects the cyclic nature of the alphabet. This alignment with both the size and direction of the jump makes K the only valid continuation.

Option D:
Option D, M, is at position 13, which would imply a jump of +? that does not match the required +11 step. The position 13 cannot be obtained from 26 by adding any single odd number that fits the observed sequence. Therefore, M does not follow the underlying rule of increasing odd differences.

This series can be expressed as aₙ = n! + 2n³ + 1 with n starting from 1. Computing the values, we get for n = 1, 2, 3, 4 and 5: 1! + 2·1³ + 1 = 4, 2! + 2·2³ + 1 = 19, 3! + 2·3³ + 1 = 61, 4! + 2·4³ + 1 = 153 and 5! + 2·5³ + 1 = 371, which matches the sequence. For n = 6, a₆ = 6! + 2·6³ + 1 = 720 + 432 + 1 = 1153. Therefore 1153 is the unique number that continues this factorial-cubic pattern.

Option A:
Option A, 1153, is exactly the value obtained from 6! + 2·6³ + 1. It preserves the factorial growth together with the cubic and constant components that determine the earlier terms. Since no change to the rule is needed at the sixth term, this option correctly extends the series.

Option B:
Option B, 1129, is 24 less than the correct value and cannot be produced by n! + 2n³ + 1 at n = 6. Accepting 1129 would require reducing the computed term without any justification from the pattern. Hence option B is not a valid continuation.

Option C:
Option C, 1141, is 12 smaller than 1153 and again does not equal 720 + 432 + 1. It approximates the correct answer but does not arise from the formula. Thus option C fails to accurately follow the sequence rule.

Option D:
Option D, 1165, is 12 greater than the computed value and would demand increasing the expression’s output only at the sixth position. This breaks the exact correspondence between the formula and the data, so option D is incorrect.