UGC NET Questions (Paper – 1)

Statements A and B correctly capture fundamental logarithm values, D states the power rule and E refers to the change of base formula where one logarithm can be expressed as a constant multiple of another base’s logarithm. All of these are true. Statement C is false because the product rule for logarithms is logₐ(xy) = logₐ(x) + logₐ(y), not the difference. Therefore, the combination that includes A, B, D and E while excluding C is the only correct option.

Option A:
Option A is incomplete because although A, B and D are true, it leaves out E, which is an important fact about changing bases and is useful in more complex aptitude questions involving logarithms. The omission makes the set incomplete.

Option B:
Option B is also incomplete as it omits D, thereby ignoring the power rule, which is frequently used to simplify expressions like logₐ(xᵏ) in exam problems. Without D, the description of key log properties is not full.

Option C:
Option C is wrong because it excludes A and thereby omits the basic fact that logₐ(1) = 0, while still including the true D and E. Although some statements are correct, the absence of A means the option does not gather all true statements.

Option D:
Option D is correct because it retains all valid properties and discards the incorrect product rule in C, aligning with the standard set of logarithm rules that a NET candidate is expected to know.

Statements A, B, C and D summarise key facts for calendar questions. A correctly notes that 365 days leave 1 odd day beyond 52 weeks. B is true for leap years with 366 days and 2 odd days. C is correct because adding multiples of 7 days cycles the week back to the same weekday. D correctly defines odd days as leftovers after full weeks are removed. E is false since adding 7 days returns to the same weekday, not the next one. Therefore, A, B, C and D only are correct.

Option A:
Option A is incomplete as it omits D and thus fails to define odd days explicitly, even though that concept is central to computing weekday shifts.

Option B:
Option B is incomplete because it omits B and/or C and does not capture the full set of rules needed for weekday calculations.

Option C:
Option C is correct because it combines facts about year lengths, odd days and the effect of multiples of seven on weekdays, while excluding E, which misstates how adding 7 days affects the day of the week.

Option D:
Option D is wrong since it includes E (false) and omits A (true), so it both adds an error and loses a key fact.

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.

Statements A, B and D are correct. A states the multiplication principle for independent choices. B defines permutations as ordered arrangements. D is true because there are n! ways to arrange n distinct objects. C is false; the formula for permutations of n distinct objects taken r at a time is nPr, and E is false because identical objects reduce the number of distinct permutations below n!. Thus A, B and D only are correct.

Option A:
Option A is correct as it includes the standard counting principle, the definition of permutations and the basic n! formula, while excluding C and E, which misapply combinatorial formulas.

Option B:
Option B is incorrect since it adds C, incorrectly using nCr in place of nPr for permutations, and so combines an error with correct statements.

Option C:
Option C is wrong because it also includes E, claiming n! permutations even with identical objects, and therefore contains two incorrect statements.

Option D:
Option D is incomplete as it drops A and leaves only B, D and E, losing the foundational multiplication principle and adding E, which contradicts the effect of identical objects.

Statements A, B and C describe how to handle clocks that do not keep correct time. A is correct because a gaining clock runs ahead of real time. B is true since losing 5 minutes per hour over 12 hours accumulates a loss of 60 minutes, i.e. one hour. C is also correct because we treat the error per hour as a rate and compare it with a complete 60-minute error to see when the clock will be exactly one hour fast or slow and thus again coincide with the correct time on the dial. D is false because gain or loss cannot be ignored in problems about correct readings, and E is false because there is no guarantee that the error aligns perfectly at midnight. Thus A, B and C only are correct.

Option A:
Option A is incomplete as it gives only A and B and omits C, which explains the method of using the error rate to determine when the clock again shows the correct reading. Without C, the understanding of such problems is not complete.

Option B:
Option B is correct since it includes all three true statements and excludes D and E, which disregard or misdescribe the impact of gain or loss. It directly corresponds to the typical reasoning steps required in NET-level clock questions.

Option C:
Option C is wrong because it introduces D, which incorrectly claims that gain or loss can always be ignored, even though angle-based questions sometimes require perfect time. Including D mixes an error into the option.

Option D:
Option D is also incorrect as it omits A and instead lists only B and C, without clearly distinguishing faulty clock behaviour from standard angle problems, and still does not address the false ideas in D and E explicitly.

Statements A and B give the usual representation of individual and combined work rates in time and work problems. Statement D is also correct because increasing the number of equally efficient workers generally reduces the time for a fixed job when total work is unchanged. Statement C is false, since a faster worker takes less time, and E is false because alternate-day work patterns depend on how many days are counted and cannot always be reduced to a simple average. Hence the correct set of statements is A, B and D only, matching option B.

Option A:
Option A is incomplete as it leaves out D, thereby ignoring the inverse relation between number of workers and time, which is a standard pattern tested in exam questions.

Option B:
Option B is correct because it collects the ideas of one-day work, combined rate and inverse proportionality while excluding C and E, which misstate how speed affects time and oversimplify alternate working-day scenarios.

Option C:
Option C is wrong since it brings in E, which incorrectly claims a simple average works in all alternate-day situations, and it omits B, so it both adds an error and loses a fundamental rule.

Option D:
Option D is incorrect because it includes C, which reverses the comparison of fast and slow workers, and it omits A, dropping the basic 1/x representation of one-day work.

B gives the standard combined-rate formula. C is also correct: independent daily rates add. A is false because working together they finish faster than either alone, so the time is less than 6 days (and certainly not greater than 10). D is false because doubling workers halves time only under ideal assumptions, not “always”. E is false because different workers can have different speeds. Thus only B and C are correct.

Option A:
Option A is incomplete because it omits C, the general rate-addition rule for more than two workers.

Option B:
Option B is correct because it includes exactly the true rate principles (B and C) and excludes A, D and E, which are false generalisations.

Option C:
Option C is wrong because it includes A, which incorrectly claims the combined time is greater than 10 days.

Option D:
Option D is incorrect because it includes D, which is not universally true, even though B and C are true.

Statements A, C and E are correct: surds are indeed irrational roots, rationalising eliminates surds from denominators and simple index laws such as a⁰ = 1 are frequently used to simplify expressions in aptitude questions. Statement B is false because the rule √a × √b = √(ab) holds only when a and b are non-negative, not for all real numbers. Statement D is also false as the correct product rule is aᵐ × aⁿ = aᵐ⁺ⁿ, not aᵐ⁻ⁿ. Thus, the combination consisting of A, C and E only is correct.

Option A:
Option A is incomplete since it omits E and therefore does not mention how index laws are applied in practice to simplify complex expressions in exam questions. Without E, the connection to aptitude simplification is weaker.

Option B:
Option B is wrong because it includes D, which misstates the product law for exponents, and leaves out E, so it both accepts a wrong algebraic rule and omits a true practical fact. This combination cannot be correct.

Option C:
Option C is correct as it contains exactly those statements that align with standard definitions and simplification techniques while excluding B and D, both of which misapply or overgeneralise algebraic rules. It provides the right conceptual picture for NET-level problems.

Option D:
Option D is incorrect because it includes B, which fails to note that the square-root product rule requires non-negative radicands, and it omits E, again ignoring the exam relevance of simple index laws. This mixture makes the option unsatisfactory.

Statement A gives the fundamental relationship between HCF, LCM and the product of two positive integers. Statement C correctly defines LCM as the least positive common multiple. Statement D is also true; co-prime numbers have no common positive factor other than 1. Statement B is false because the HCF cannot exceed the numbers themselves, and E is false since if one number divides the other, the HCF is the smaller number, not necessarily 1. Thus, A, C and D only are correct, matching option A.

Option A:
Option A is correct because it combines the key algebraic relation with the proper descriptions of LCM and co-primality, while excluding B and E, which misunderstand bounds on HCF and the divisor case.

Option B:
Option B is incomplete as it includes only A and C and omits D, thereby failing to highlight the link between co-prime numbers and HCF, which is frequently tested.

Option C:
Option C is incorrect because it drops A and includes only C and D, so it loses the important multiplicative connection between HCF and LCM and provides an incomplete set of correct statements.

Option D:
Option D is wrong since it includes B, which wrongly claims that the HCF is at least as large as each number, contradicting basic number theory, and therefore the combination cannot be accepted.

Statement A matches the definition of percentage as a ratio per hundred. C is correct because a 25% profit implies selling price equals cost price plus 25% of cost, giving 125% of cost. D is true since equal ratios constitute a proportion. E is also correct; if a:b = 2:3, reversing gives b:a = 3:2. B is false, because a 20% increase followed by a 20% decrease results in a net 4% decrease. Thus A, C, D and E only form the correct set.

Option A:
Option A is incomplete; while A and C are true, omitting D and E ignores important proportional and inverse ratio relationships frequently examined in NET aptitude questions.

Option B:
Option B is wrong as it includes B, which misstates the effect of successive percentage changes, and so mixes a false statement with correct ones.

Option C:
Option C is correct because it collects the accurate definitions and interpretations of percentage, profit, proportion and inverse ratio, while excluding B, which leads to a typical exam trap.

Option D:
Option D is incorrect because it includes B, allowing a false claim about successive percentage operations into the option, even though C, D and E are correct.

Statements A, B, D and E are correct. A restates the basic simple interest rule. B is true because with annual compounding, one compounding per year means effective and nominal rates coincide. D is correct since more frequent compounding at the same nominal rate increases total interest. E is also true; at low rates and short durations, simple and compound interest often differ negligibly. C is false because more frequent compounding makes the effective annual rate higher, not lower, than the nominal rate. So A, B, D and E only are correct.

Option A:
Option A is incomplete because it omits E, which notes the practical observation that, for small rates and short periods, the difference between SI and CI can be very small.

Option B:
Option B is correct since it collects all the accurate statements about calculation bases, effective rates and compounding frequency, while excluding C, which reverses the relationship between nominal and effective rates.

Option C:
Option C is wrong because it includes C, which misstates the effect of multiple compounding periods, and therefore cannot represent the full set of correct statements.

Option D:
Option D is incorrect as it retains C (false) and omits B (true), so it both includes an error and misses a key correct statement.

Statements A and C both capture the cross-multiplication property of equal ratios in a proportion. Statement B is a direct algebraic consequence of A when all terms are non-zero. Statement D is correct because multiplying or dividing each term by the same non-zero factor leaves the ratio unchanged. Statement E is false, since if a:b = 2:3, then b:a should be 3:2, not 3:4. Therefore, A, B, C and D only form the correct set, which is option D.

Option A:
Option A is incomplete as it has only A, B and C and omits D, thereby ignoring the important rule about scaling ratios, which is frequently used in simplifying or comparing them.

Option B:
Option B is incorrect because it omits B (true) and so fails to include the fraction form a/c = b/d implied by a:b = c:d.

Option C:
Option C is incomplete since it excludes A; without stating ad = bc explicitly, the key proportionality check is missing even though some other statements are true.

Option D:
Option D is correct because it gathers all the fundamental properties of proportions and ratio scaling while excluding E, which misstates the inverse ratio of 2:3.

Statement A correctly describes the overall concentration as a weighted average of component concentrations. Statement B is a special case for equal quantities, where the weights are equal and the average is arithmetic. Statement C states the classical alligation rule connecting mixing ratio to the differences from the mean. Statement D is false because adding pure water does not change the solute amount, and E is false since diluting with water lowers concentration but does not decrease the amount of solute. Hence A, B and C only are correct, which corresponds to option A.

Option A:
Option A is correct because it includes the general weighted-average idea, its equal-quantity special case and the alligation rule, while excluding D and E, which misunderstand how solute amount changes under dilution.

Option B:
Option B is incorrect since it includes D, which wrongly asserts that adding pure water increases solute amount, mixing an error with accurate statements.

Option C:
Option C is wrong because it includes E (false: adding water alone does not reduce solute amount) and omits B (true equal-quantity averaging), so it does not match the true set.

Option D:
Option D is incorrect as it contains D (false) and omits A (the key weighted-average principle), making it both incorrect and incomplete.

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, B and C are standard algebraic identities for binomial squares and difference of squares, while D correctly results from subtracting the two square expansions and simplifies many expressions quickly. Statement E is false because these identities are widely used in aptitude problems to perform rapid simplification or mental calculation. Therefore, the set consisting of A, B, C and D only is correct.

Option A:
Option A is correct as it lists all and only the valid identities, illustrating how they combine to yield useful simplifications such as 4ab, and it rightly omits E, which denies their important role in exam problems.

Option B:
Option B is incomplete since it omits D and thus misses the composite application of the identities, which is frequently tested when candidates are asked to simplify expressions like (a + b)² − (a − b)².

Option C:
Option C is also incomplete as it excludes A, failing to state the most commonly used identity for (a + b)² explicitly, even though the other identities are present. Without A, the picture is not complete.

Option D:
Option D is incorrect because it leaves out B and therefore fails to state the identity for (a − b)², which is as important as the identity for (a + b)² in exam contexts.