UGC NET Questions (Paper – 1)

A strong argument should be relevant, logical and address the purpose of the statement. Entrance tests aim to provide a common measure to compare candidates from different backgrounds. A standardized test can help identify merit and readiness for professional study. This argument connects the use of tests directly with fairness and objectivity in selection, making it strong.

Option A:
Option A highlights the core rationale behind entrance tests: fairness and standardization in assessing merit. It justifies the policy by linking it with transparent and comparable evaluation across diverse applicants, which is a central concern in admissions.

Option B:
Option B claims that tests completely remove stress, which is unrealistic and exaggerated. Tests often create some stress; this argument therefore undermines its own credibility.

Option C:
Option C rejects all testing categorically, which is extreme and does not engage with the practical need to assess suitability for professional courses.

Option D:
Option D states that professional courses do not require any ability, which is obviously false and dismisses the seriousness of such education. It cannot be considered a strong argument.

Statements A, B, C and E give standard reasoning techniques for ranking questions. A states the usual formula for total persons when one person’s ranks from top and bottom are known with no ties. B is true because ties disturb this simple formula. C is correct; it uses transitivity of “taller than” to deduce the relation between A and C. E is also correct since drawing a vertical list helps many candidates see the order clearly. D is false because equal scores can lead to shared ranks, so requiring distinct ranks is not correct. Thus, A, B, C and E only form the correct set.

Option A:
Option A is incomplete because it leaves out E, failing to mention the practical diagrammatic strategy that aids in solving ranking questions, even though A, B and C are true.

Option B:
Option B is also incomplete, as it includes only B, C and E and omits A, losing the widely used formula for computing total persons.

Option C:
Option C is correct since it brings together the numerical formula, the effect of ties, transitivity of order and the usefulness of diagrams, while excluding D, which incorrectly denies the possibility of equal ranks.

Option D:
Option D is wrong because it features D, which misstates the treatment of equal scores, and omits B, so it both includes an error and loses a critical observation about ties.

Statement A correctly defines a common version of the Fibonacci sequence using a recurrence relation. C is true because the ratio of consecutive Fibonacci numbers tends toward the golden ratio as n increases. D is also correct, as Fibonacci-type recurrences are used to model branching patterns such as rabbit populations or tree growth in idealised models. B is false since Fibonacci terms are not simply double the previous term, and E is false because Fibonacci patterns frequently appear in exam puzzles and series problems. Thus A, C and D only are correct.

Option A:
Option A is incomplete because it includes only A and C and omits D, which highlights the important application of Fibonacci recurrences to growth processes, a point often emphasised in conceptual questions.

Option B:
Option B is incorrect since it lists only C and D and leaves out A, failing to define the sequence explicitly, and it does not address the incorrect claims about doubling or exam usage. It therefore does not capture the full set of correct statements.

Option C:
Option C is correct because it unites the standard definition, the limiting ratio property and an application-related statement, while excluding the false claims in B and E. This matches the way Fibonacci numbers are treated in NET mathematical reasoning.

Option D:
Option D is wrong as it includes B, which mistakenly describes the terms as doubling, along with A, C and D. The presence of this incorrect description makes the entire combination unacceptable.

Statements A, B and C correctly describe proper fractions, terminating decimals and the fact that fraction-to-decimal conversion may yield either terminating or repeating expansions. Statement E is also true because comparison techniques such as cross-multiplication allow direct comparison of fractions without converting to decimals. Statement D is false because irrational numbers have non-terminating, non-repeating decimal expansions and cannot be expressed as terminating decimals. Thus, the combination A, B, C and E only is correct.

Option A:
Option A is incomplete as it omits E and therefore does not acknowledge the practical method of comparing fractions directly, which is an important technique in timed aptitude tests.

Option B:
Option B is also incomplete because it excludes C and thus fails to mention that fractions can produce repeating decimals as well, an important conceptual point about rational numbers.

Option C:
Option C is correct since it includes all the true statements and excludes D, which misclassifies irrational numbers. It reflects both the theory and the applied strategies involving fractions and decimals.

Option D:
Option D is wrong because it includes D, the statement that wrongly treats irrational numbers as terminating decimals, and omits B, which accurately characterises the denominators of terminating decimals. This combination cannot be accepted.

Statement A correctly defines profit when the selling price is higher than the cost price. Statement C is also correct, as profit percent in standard questions is taken on cost price unless the question says otherwise. Statement D is a direct application: 20% of 100 is 20, so the selling price becomes 120. Statement B is false because discount is subtracted from the marked price, not added, and E is false since loss happens when cost price exceeds selling price. Therefore, A, C and D only are correct, as in option D.

Option A:
Option A is incomplete because it omits D, which concretely applies the profit percentage idea, and so does not give a full set of correct statements for exam-oriented understanding.

Option B:
Option B is wrong because it adds E, which reverses the condition for loss, and therefore contains at least one false statement. Even though A and C are true, the presence of E invalidates the combination.

Option C:
Option C is incorrect since it contains only C and D and omits A, leaving out the basic definition of profit that anchors the other statements and making the set of correct facts incomplete.

Option D:
Option D is correct because it collects the conceptual definition of profit, the rule for profit percentage and a worked numerical illustration, while excluding the wrong descriptions of discount and loss conditions.

A, B, C and E are all correct statements about quadratic equations and their discriminant. A states the general form with a ≠ 0, B defines the discriminant, C correctly says that Δ 0 yields two distinct real roots. D is wrong because Δ = 0 gives equal (repeated) real roots, not two distinct roots. Hence the combination containing A, B, C and E only is correct.

Option A:
Option A includes A, B and C, all of which are true, but omits E, which correctly describes the case Δ > 0. Because it misses one more true statement, this option does not capture the full set of correct statements.

Option B:
Option B adds D to A, B and C, but D is false since Δ = 0 leads to equal roots, not distinct ones. Including a false statement makes this combination incorrect even though it contains many true statements.

Option C:
Option C is correct because it lists exactly the true statements A, B, C and E and excludes D, the only incorrect one. It therefore fully reflects the standard classification of roots using the discriminant.

Option D:
Option D selects B, D and E, but by including D it wrongly treats Δ = 0 as giving distinct roots and also omits A and C, which are true. This combination is therefore both incomplete and partially wrong.

This option is correct because an odd number is defined as an integer that is not divisible by 2. When an odd number is divided by 2, it always leaves a remainder of 1. This matches exactly the condition given in the question. Therefore, an integer not divisible by 2 is called an odd number.

Option A:
An odd number has the form 2k+1 for some integer k and is not divisible by 2. Dividing any odd number by 2 leaves a remainder of 1, which fits the description in the stem. Hence, this option correctly names the type of number described.

Option B:
An even number is divisible by 2 and leaves no remainder on division by 2. The question specifies numbers that are not divisible by 2, so this property does not match. Therefore, this option is not correct here.

Option C:
A prime number is defined by having exactly two distinct positive divisors, 1 and the number itself. Some primes are odd but the concept of primality does not directly refer to divisibility by 2 alone. Hence, prime is not the specific term required by the question.

Option D:
A composite number has more than two positive divisors. It can be even or odd, and its definition is unrelated to divisibility by 2 alone. Therefore, composite is not the best term for numbers that are simply not divisible by 2.

For compound interest compounded annually, the amount A after n years is A = P(1 + R/100)^n. Substituting P = 5000, R = 10 and n = 2 gives A = 5000(1.1)^2 = 5000 × 1.21 = 6050. This includes both the principal and the accumulated interest over 2 years. Therefore, the amount after 2 years is ₹6050.

Option A:
₹6050 is correct because it reflects a 10% increase in the first year to ₹5500 and another 10% increase on ₹5500 in the second year, giving an interest of ₹550 in the second year. Adding the two years’ interest, 500 + 550 = 1050, to the principal yields 6050. This step-by-step reasoning confirms the formula-based calculation.

Option B:
₹6000 would correspond to a simple interest of ₹1000 over 2 years at 10% per annum, ignoring compounding in the second year. Compound interest, however, adds interest on both principal and accumulated interest. Therefore, 6000 underestimates the true amount.

Option C:
₹5900 is even smaller than the simple interest amount and thus significantly underestimates the effect of compound growth. It does not arise from any standard calculation with the given rate and time. Hence, this option is incorrect.

Option D:
₹6100 overestimates the compound amount at 10% per annum on ₹5000 for 2 years. It might result from an incorrect assumption of a higher effective rate. Since the exact formula yields 6050, 6100 cannot be accepted as correct.

In this series, the last two letters “AN” remain constant, while the first letter advances alphabetically. The first letters are F, G, H and I, so the next first letter should be J. Combining J with the fixed ending “AN” gives JAN. Thus JAN is the only option that maintains the simple first-letter progression.

Option A:
Option A, KAN, uses K as the first letter, which would come after J. This skips the immediate successor required by the pattern. Since the series moves one letter at a time, KAN cannot be the next term.

Option B:
Option B, IAN, repeats the last given word instead of introducing a new one. There is no indication that the pattern cycles or repeats elements. Therefore IAN is not a valid continuation here.

Option C:
Option C, GAN, is a previous term in the series. Reusing an earlier word breaks the forward movement of the first letter. Because the pattern shows steady progression, GAN cannot be the correct answer.

Option D:
Option D is correct because it uses J, the next letter after I, and keeps “AN” unchanged. It fits perfectly with the rule that only the initial letter changes step by step. Hence JAN logically completes the series.

Starting letters C(3), G(7), K(11), O(15) increase by +4. Next start is S(19), so the block is STU.

Option A:
Option A is correct because S is +4 from O and T,U follow consecutively.

Option B:
Option B starts at R(18), which is +3 from O, not +4.

Option C:
Option C starts at V(22), which is +7 from O, not +4.

Option D:
Option D starts at N(14), which goes backward and breaks the progression.

Each term after the first is obtained by doubling the previous term and then adding 2. We have 4 × 2 + 2 = 10, 10 × 2 + 2 = 22, 22 × 2 + 2 = 46 and 46 × 2 + 2 = 94. Applying the same rule to 94 gives 94 × 2 + 2 = 188 + 2 = 190. This maintains a clear and consistent multiplicative pattern.

Option A:
Option A gives 188, which is simply 94 × 2 and omits the constant addition of 2 that appears at every step. This makes the pattern incomplete and inconsistent. Therefore, 188 is not the correct answer.

Option B:
Option B yields 190, produced by the operation 94 × 2 + 2, exactly as required by the recursive rule. The extended sequence 4, 10, 22, 46, 94, 190 follows the same transformation from term to term. Hence, 190 is the correct continuation of the series.

Option C:
Option C suggests 192, which would require adding 4 after doubling, changing the constant added at the end of the operation. Since all previous steps add 2, this variation is unjustified. Thus, 192 is not appropriate.

Option D:
Option D presents 196, which would involve adding 8 after doubling or some other arbitrary change, again not supported by the original rule. This disrupts the series structure. Therefore, 196 cannot be considered correct.

Statement A gives the definition of the Cartesian product using ordered pairs with components from A and B. Statement B correctly states that the number of such pairs equals the product of the set sizes when the sets are finite. Statement C is also correct since a relation is any subset of A × B, with functions being special cases. Statement D is false because many relations are not functional, and E is false because A × B and B × A generally differ as ordered pairs reverse coordinates. Therefore, A, B and C only are correct, as in option B.

Option A:
Option A is incomplete because it omits C and so fails to connect the notion of relation with the Cartesian product, which is a key conceptual bridge in discrete mathematics.

Option B:
Option B is correct since it collects the definition of A × B, the counting rule for finite sets and the identification of relations as subsets, while excluding D and E, which confuse relations with functions and swap the order of products.

Option C:
Option C is incorrect because it includes D (false: not every relation is a function) and omits B (true: the counting rule), so it neither matches the correct set nor covers all correct statements.

Option D:
Option D is wrong because it includes E (false: A × B is not always equal to B × A) and omits A (the basic definition), so it mixes errors with omissions.

In this sequence, the first letters A, B, C, D move forward by one letter each time. The second letters M, N, O, P also move forward by one letter. The next first letter after D is E, and the next second letter after P is Q, giving EQ. Thus EQ preserves the consistent +1 shift in both positions.

Option A:
Option A, ER, advances the second letter from P to R, a jump of two positions. The series, however, increases every letter by exactly one step. Since R overshoots the pattern, ER cannot be the correct continuation.

Option B:
Option B is correct because E and Q are each exactly one position ahead of D and P respectively. This keeps the relationship between terms simple and uniform. By maintaining the same step size for both letters, EQ fits the established pattern perfectly.

Option C:
Option C, FP, moves the first letter correctly from D to F only if the step were +2, which contradicts the +1 rule. It also keeps the second letter stuck at P. Because it distorts both components of the pattern, FP is not acceptable.

Option D:
Option D, FR, changes both letters with inconsistent jumps, advancing the first letter too far and the second letter by more than one step. The series shows no such uneven increments. As a result, FR does not satisfy the logical structure of the sequence.

A’s one-day work is 1/15 of the job and B’s one-day work is 1/20 of the job. Their combined daily work is 1/15 + 1/20. The least common multiple of 15 and 20 is 60, so this becomes 4/60 + 3/60 = 7/60 of the work per day. The total time to complete one whole work is therefore 1 ÷ (7/60) = 60/7 ≈ 8.57 days. Among the integer options given, 9 days is the closest approximation to 60/7, so it is the most appropriate answer.

Option A:
Option A, 8 days, underestimates the exact value of about 8.57 days; in 8 days they would complete only 8 × 7/60 = 56/60 of the work, leaving some part unfinished.

Option B:
Option B, 9 days, is the nearest whole number to 60/7 and slightly overestimates the exact time, which is why it is the best choice among the given options.

Option C:
Option C, 10 days, deviates further from the exact value and would correspond to a slower combined rate than actually calculated.

Option D:
Option D, 12 days, is much larger than 60/7 and ignores the productivity gain from having both A and B work together.

Statements A, B and C describe standard facts about implication. A gives the important equivalence p → q ≡ ¬p ∨ q. B correctly states that an implication is false only when the antecedent is true and the consequent false. C correctly identifies the contrapositive as ¬q → ¬p. D is false because ¬p → ¬q is the inverse, not the converse, and E is false since p → q is generally not equivalent to q → p. Therefore A, B and C only are correct.

Option A:
Option A is incomplete because it omits C and thus fails to mention the contrapositive, which is central to reasoning with implications in many NET questions.

Option B:
Option B is incorrect as it includes D, which mislabels the inverse as the converse and therefore misuses terminology in logic.

Option C:
Option C is wrong because it omits A and therefore drops a key equivalence used to simplify implications.

Option D:
Option D is correct since it combines the truth-table characterisation of implication, the disjunctive form and the contrapositive, while excluding D and E, which contain conceptual errors about converse and equivalence.