UGC NET Questions (Paper – 1)

Statements A and B correctly define closure and commutativity for binary operations, D notes that exams introduce custom operations to test rule-following rather than standard arithmetic and E emphasises the need to use the given definition faithfully. Statement C is false because associativity means (a * b) * c = a * (b * c), not that the results are always different. Hence, the combination A, B, D and E only is correct.

Option A:
Option A is incomplete as it omits E and thus fails to stress that candidates must not revert to usual addition or multiplication when a custom rule is specified. This omission makes the description less helpful for exam strategy.

Option B:
Option B is also incomplete because it leaves out A, so it does not explicitly mention closure, the idea that combining elements of S stays within S, which is often implied when operations are defined.

Option C:
Option C is wrong since it includes C, which reverses the meaning of associativity by saying results are always different, and omits B, thereby ignoring the commutative law. This mixture of an error and an omission makes the option invalid.

Option D:
Option D is correct because it captures closure, commutativity, exam usage of custom operations and the necessity of following the definition, while excluding C, which misstates associativity. It reflects the way NET questions check conceptual clarity about operations.

Statement B is the only wrong statement in this group. A is correct because data sufficiency focuses on whether information is enough, not on computing the final number. C is true since some questions are solvable with one statement but not with the other alone. D is also correct because in some cases, even combining statements fails to give a unique answer. E is correct since we generally presume the given data are consistent unless told otherwise. B is false because two insufficient statements may remain insufficient when combined.

Option A:
Option A is incorrect as it treats both A and B as wrong, even though A accurately states the objective in data sufficiency problems. Misclassifying A makes the option invalid.

Option B:
Option B is correct because it isolates B as the sole incorrect statement, capturing the fact that insufficiency of each statement alone does not guarantee sufficiency when combined.

Option C:
Option C is wrong because it wrongly marks C as wrong as well, even though C describes a common situation where one statement alone can be sufficient.

Option D:
Option D is incorrect since it ignores B altogether and claims only C and D are wrong, even though D and C correctly describe typical sufficiency patterns and B is the problematic rule.

Statements A and B apply the multiplication principle and permutation formula correctly. A recognises that each of the 3 distinct books has 2 choices of shelf, so 2 × 2 × 2 = 2³ placements. B notes that 3 distinct books can be arranged in 3! orders on one shelf. C is false because identical books reduce the number of distinct permutations to 3!/2!, not 3!, and D is false because when counts depend on previous choices, we must adjust rather than blindly multiply m and n. E is false since choosing a student–teacher pair uses m × n, not m + n. Thus only A and B are correct.

Option A:
Option A is incomplete as it includes only statement A and omits B, thereby missing a standard example of permutations with distinct objects that is also correct.

Option B:
Option B is correct because it selects exactly the statements that correctly apply counting principles while excluding C, D and E, each of which misuses permutations or the multiplication rule. It reflects the proper reasoning expected in NET quantitative aptitude.

Option C:
Option C is wrong because it adds C, which ignores the effect of identical objects and incorrectly counts permutations as if all items were distinct.

Option D:
Option D is incorrect since it includes D and still allows the false “always m × n regardless of dependence” claim, so the combination cannot be correct.

Statements A, C and D summarise key properties of divisibility and remainders. A encodes the division algorithm representation. C is true because 6 has prime factors 2 and 3, so divisibility by 6 implies divisibility by both. D is correct since numbers with the same remainder differ by a multiple of the divisor. B is false as divisibility by 3 and 9 together does not force divisibility by 27, and E is false because a multiple of 4 need not be a multiple of 8. Therefore, A, C and D only are correct.

Option A:
Option A is correct because it collects the basic representation of numbers with remainders and two important consequences for divisibility, while excluding B and E, which overstate divisibility conditions.

Option B:
Option B is incorrect as it adds B, which wrongly claims that common divisibility by 3 and 9 forces divisibility by 27, contradicting simple counterexamples like 9 itself.

Option C:
Option C is wrong since it also incorporates E, which incorrectly asserts that multiples of 4 are automatically multiples of 8, and thus mixes false statements with true ones.

Option D:
Option D is incomplete because it drops A and only keeps C and D, leaving out the fundamental division algorithm expression that underpins the remainder concept in many NET questions.

Statements A, C and D express standard partnership principles. A is correct because profit shares are proportional to capital multiplied by duration of investment. C correctly defines a sleeping partner’s role. D is true as reducing capital during the year reduces the effective capital–time product. B is false since equal capital and time lead to a 1:1 ratio, and E is false because time is crucial when investments are made for different periods. Hence, A, C and D only are correct.

Option A:
Option A is correct because it combines the basic rule of capital–time proportionality with the concept of sleeping partners and the effect of withdrawing capital, while excluding B and E, which misstate profit ratios and the role of time.

Option B:
Option B is incorrect because it includes B, which incorrectly fixes the profit share at 1:2 even when capital and time are equal, thus contradicting the proportional rule.

Option C:
Option C is wrong as it also includes E, wrongly claiming that time is irrelevant in partnership problems, and therefore mixes incorrect statements with correct ones.

Option D:
Option D is incomplete since it omits A and includes only C and D, failing to explicitly state the capital–time proportionality on which partnership questions are based.

A is correct because compound interest at least matches and usually exceeds simple interest for the same principal, rate and time. B correctly gives the annual compounding formula, and C is true since in simple interest interest ∝ rate × time, so halving one and doubling the other keeps the product unchanged. E is also correct because more frequent compounding at a fixed nominal rate increases the effective annual rate. D is false because changing rate and time in that way does not guarantee the same accumulated amount. Therefore, A, B, C and E only are correct.

Option A:
Option A omits E and thus fails to mention the important concept of effective rate increasing with compounding frequency. Although A, B and C are true, the combination is incomplete and so not the best answer.

Option B:
Option B is correct since it gathers all the true statements and excludes D, which wrongly suggests invariance of amount under doubling rate and halving time in compound interest. It matches the standard treatment of interest problems in aptitude tests.

Option C:
Option C wrongly includes D, which misrepresents compound interest behaviour, and omits A, underplaying the comparison between compound and simple interest. Hence it mixes a false statement with an omission.

Option D:
Option D is incorrect as it includes D and discards B and C, thereby accepting the erroneous claim and omitting correct formulas and relationships.

Statements A, B and C summarise fundamental rules about inequalities. A is true because “greater than” is transitive. B is correct since multiplying by a positive constant preserves the order. C is also correct because multiplying by a negative constant reverses the direction of an inequality. D is false; knowing a > b and c > d does not ensure any fixed relation between a − c and b − d. E is false since squaring can change the order when negative numbers are involved, so the correct set of statements is A, B and C only.

Option A:
Option A is incomplete as it lists only A and B and omits C, so it does not mention how multiplying by a negative constant affects the inequality, which is crucial in many exam problems. This makes the option insufficient.

Option B:
Option B is also incomplete because it includes A and C only and leaves out B, thereby ignoring the important case of multiplication by positive numbers, which must also be understood.

Option C:
Option C is incomplete since it contains only B and C and omits A, losing the basic transitivity property that is often used to chain inequalities. Without A, the rule set is not fully represented.

Option D:
Option D is correct as it gathers all three true rules and explicitly excludes D and E, both of which overgeneralise operations on inequalities. It matches the standard algebraic handling of inequalities in NET-level aptitude questions.

Statements A, B, C and D together give a complete and correct conceptual comparison of simple and compound interest in exam-type settings. A is correct for positive rates and more than one year because compounding on accumulated amounts cannot yield less than simple interest on principal. B and C correctly distinguish the bases on which interest is calculated in the two regimes, and D accurately contrasts the linear versus exponential-type growth patterns. Statement E is false because for exactly one year simple and compound interest coincide, so simple interest is not greater, and hence the correct combination must include A, B, C and D but exclude E.

Option A:
Option A is correct because it captures all of the true statements and omits E, which misstates the one-year comparison between simple and compound interest. It recognises that compounding over multiple periods increases or at least matches simple interest and that the two schemes use different bases for interest calculation. It also correctly reflects the different shapes of the time–amount graphs.

Option B:
Option B is incorrect because it leaves out D, the key statement about linear versus exponential-like growth, so the description of time behaviour is incomplete. Although A, B and C are true, this combination does not fully convey how amounts diverge over longer periods. For conceptual NET questions, missing such a central point makes the option inadequate.

Option C:
Option C is wrong because it includes E along with otherwise correct statements; E wrongly claims that simple interest is always greater than compound interest for one year. Including even one false statement makes the whole set incorrect in a “select correct statements” question. Therefore this combination cannot be accepted as correct.

Option D:
Option D is incorrect because it omits A and D while still containing E, the false statement. By dropping A it loses the general comparison between the two interest types, and by adding E it introduces an error about the one-year case. This mixture of omission and error makes the option invalid.

Statements A, B, C and D correctly describe standard boats and streams situations. A and B give the definitions of downstream and upstream speeds. C is true because if u − v = u + v, then v must be zero. D is correct since when the stream speed is non-zero, going against the current reduces effective speed and increases travel time for the same distance. E is false because if the stream is faster than the boat in still water, the boat cannot progress upstream relative to the ground. Therefore, A, B, C and D only are correct.

Option A:
Option A is incomplete as it omits C and D, both of which provide important consequences of the definitions, one algebraic and one about time comparisons in exam problems.

Option B:
Option B is also incomplete since it excludes D, missing the key implication that upstream travel takes longer when there is a current.

Option C:
Option C is wrong because it drops A and includes only B, C and D, leaving out the basic downstream speed definition that underlies the others.

Option D:
Option D is correct because it includes all the true statements and properly excludes E, which incorrectly permits upstream motion even when the current is stronger than the boat’s still-water speed.

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.

Statements A, B and C express the basic axioms about range of probabilities and values for sure and impossible events. Statement D gives the general addition rule for the probability of a union of two events. Statement E is false because probabilities are never negative. Therefore, A, B, C and D only form the correct set.

Option A:
Option A is incomplete as it omits D (union/addition rule).

Option B:
Option B is incomplete because it omits B (sure event) and does not include all core axioms together.

Option C:
Option C is incomplete since it omits A (range restriction 0 ≤ P(A) ≤ 1).

Option D:
Option D is correct because it includes all true statements and excludes E, which suggests an impossible negative probability.

Statements A, C and D correctly summarise key properties of HCF and LCM. A gives the fundamental relationship a × b = HCF(a, b) × LCM(a, b) for positive integers. C is true because the LCM is defined as the least common multiple of the numbers. D is correct since when one number divides the other, the smaller is their HCF and the larger is their LCM. B is false because the HCF cannot exceed the smaller number, and E is false because distinct primes have HCF equal to 1, not one of them, so A, C and D only are correct.

Option A:
Option A is incomplete because it omits D, failing to mention the simple special case where one number divides the other, which is frequently used in problems. Even though it includes two true statements, it does not list all of them.

Option B:
Option B is correct as it gathers all the true properties given, including the product relationship, the multiple property of LCM and the special divisor case, while excluding the incorrect descriptions in B and E.

Option C:
Option C is wrong because it includes E, which misstates the HCF of distinct prime numbers. By adding this false statement, it makes the combination invalid.

Option D:
Option D is incomplete since it leaves out A, the central product formula linking HCF and LCM, so it does not provide the full set of correct statements among those listed.

Statement A gives the correct general definition of average speed. Statement C is the standard formula for average speed when equal distances are covered at two speeds, which equals the harmonic mean of the speeds. Statement D is also true because when equal times are spent at each speed, the average speed simplifies to the arithmetic mean. Statement B is false because the arithmetic mean does not apply for equal-distance segments, and E is false since confusing equal-distance with equal-time cases leads to wrong answers. Therefore, A, C and D only are correct, corresponding to option C.

Option A:
Option A is incomplete as it lists only A and C and omits D, failing to mention the equal-time case where the arithmetic mean does apply. This makes the description of average speed patterns incomplete.

Option B:
Option B is incorrect because it includes E, which says there is no need to distinguish between equal-distance and equal-time cases, an assertion that contradicts typical exam traps. It therefore contains a false statement.

Option C:
Option C is correct since it distinguishes the definitions for general, equal-distance and equal-time situations and explicitly excludes B and E, which misapply or trivialise the conditions.

Option D:
Option D is wrong as it contains B, the false claim about arithmetic mean for equal-distance travel, and it omits A, so it both adds an error and leaves out the basic definition of average speed.

A is correct because time = distance/speed for fixed distance, so time varies inversely with speed. C is true since distance = speed × time at constant speed. D is true because halving speed doubles time for the same distance. B is false because doubling speed at the same time doubles distance, not halves it. E is false; starting time is not forced by speed alone. Therefore A, C and D only are correct.

Option A:
Option A is correct as it captures both inverse and direct proportion relationships along with a key consequence for halving speed.

Option B:
Option B is incomplete because it excludes D, missing an explicit and important inverse-proportion consequence.

Option C:
Option C is wrong since it includes B, which misstates the effect of doubling speed at fixed time.

Option D:
Option D is incorrect because it adds E (false) and omits A (true), so it cannot be correct.