UGC NET Questions (Paper – 1)

Statements A, B and D all accurately describe biconditional statements. A gives the overall truth condition: both sides must match in truth value. B shows that “if and only if” can be written as the conjunction of two implications. D restates the falsity condition: the biconditional fails when P and Q differ in truth. C is false because “P or Q” is true in more cases than “P if and only if Q”, and E is false because biconditionals are not tautologies. Hence A, B and D only are correct.

Option A:
Option A is incomplete because it omits D, so it fails to mention explicitly when the biconditional is false, which is essential for constructing its truth table.

Option B:
Option B is incorrect as it includes only B and D and omits A, losing the succinct characterisation that biconditional is true exactly when P and Q agree.

Option C:
Option C is wrong because it adds E, which incorrectly asserts that biconditionals are always true, and it therefore includes at least one false statement.

Option D:
Option D is correct as it brings together the equivalence in terms of matching truth values, the conjunction of implications and the falsity condition, while excluding C and E, which misrepresent the biconditional.

A is correct as a valid categorical syllogism uses exactly three distinct terms: major, minor and middle. B is true because the middle term must be distributed at least once to connect the extremes properly. C is correct since two negative premises provide no positive linkage, and D is true because two particular premises cannot logically support a universal conclusion. E is false because these are necessary but not sufficient conditions; a syllogism can meet them yet still be invalid for other reasons. Hence A, B, C and D only are correct.

Option A:
Option A omits D and thus fails to mention the important constraint on drawing universal conclusions from particular premises. While A, B and C are true, the omission of D makes the set incomplete.

Option B:
Option B ignores A, so it does not mention the three-term requirement; although B, C and D are true, this omission leaves out a central structural rule for syllogisms.

Option C:
Option C drops B and therefore fails to highlight the distribution requirement of the middle term, which is crucial for testing validity. Even with A, C and D present, missing B leaves the account incomplete.

Option D:
Option D is correct because it collects all the true structural rules while excluding E, which overstates their sufficiency. This matches how NET questions test necessary conditions for syllogistic validity.

This option is correct because the percentage increase is calculated as (increase ÷ original value) × 100. The increase is 120 − 100 = 20. So, (20 ÷ 100) × 100 = 20%. Therefore, the price has increased by 20%.

Option A:
The increase of ₹20 over an original price of ₹100 represents 20% of the original. This is obtained directly from the formula and matches intuitive understanding. Hence, 20% is the correct percentage increase.

Option B:
A 10% increase on ₹100 would be ₹10, giving a final price of ₹110. The actual new price is ₹120, so 10% underestimates the change. Therefore, this option is wrong.

Option C:
A 15% increase would add ₹15, resulting in a price of ₹115. This still does not reach the actual new price of ₹120. Thus, 15% is not the correct percentage increase.

Option D:
A 25% increase on ₹100 would be ₹25, leading to a price of ₹125. This overshoots the given new price, so 25% is too high. Hence, this option is incorrect.

A proportion is an equation that states that two ratios are equal, such as a:b = c:d. It indicates that the relative relationship between the first pair of quantities is the same as that between the second pair. In mathematical aptitude, many word problems use proportions to relate parts and wholes or to scale quantities. Therefore, equality of two ratios is correctly described by the term proportion.

Option A:
Variation refers to how one quantity changes in relation to another, such as direct or inverse variation, but it is not specifically about equality of two numerical ratios. While variation also deals with relationships, it does not necessarily state that two ratios are equal. Hence, this term does not match the precise condition mentioned in the question.

Option B:
Proportion is correct because it captures the idea "two ratios are equal" in a single term. For instance, if 2:3 = 4:6, we say 2, 3, 4 and 6 are in proportion. This concept is widely used in problems involving scale diagrams, recipes and map reading. Thus, option B aligns perfectly with the wording of the question.

Option C:
Inverse usually refers to inverse proportion or inverse relationship where one quantity increases while the other decreases, maintaining a constant product. It does not refer to an equality of two ratios directly. Therefore, it is not an accurate response to the specific description in the stem.

Option D:
Percentage is a way of expressing a ratio out of 100, but it is not the term used solely for equality of two ratios. You can express each ratio as a percentage, yet the fact that percentages match does not change the underlying terminology: the equality is still called a proportion. Thus, this option is not the best answer.

This series is generated by the rule aₙ = n⁴ + n! with n starting from 1. For n = 1, 2, 3, 4 and 5 we get 1⁴ + 1! = 2, 2⁴ + 2! = 18, 3⁴ + 3! = 87, 4⁴ + 4! = 280 and 5⁴ + 5! = 745, which matches the pattern exactly. For n = 6, a₆ = 6⁴ + 6! = 1296 + 720 = 2016. Therefore 2016 is the only value that continues this factorial-quartic combination correctly.

Option A:
Option A, 1992, is 24 less than the value produced by n⁴ + n! at n = 6. Selecting 1992 would require lowering the term below what the formula prescribes only at this index. Such a change contradicts the exact fit observed in earlier terms, so option A is not correct.

Option B:
Option B, 2004, is 12 smaller than the correct value 2016 and again cannot be written as 1296 + 720. It approximates but does not equal the output of the expression for n = 6. Consequently, option B is not a legitimate continuation of the pattern.

Option C:
Option C, 2016, exactly matches the result obtained from the rule for n = 6. It maintains the same contribution from both the quartic term and the factorial term that gave rise to the earlier numbers. Because it extends this combined pattern consistently, option C is the correct answer.

Option D:
Option D, 2028, is 12 greater than the computed value and cannot arise from the expression n⁴ + n! at n = 6. Adopting 2028 would artificially inflate the last term, disrupting the precise relationship between n and aₙ. Hence option D is not a valid continuation.

The pattern is a 5-letter palindrome: 1st=5th and 2nd=4th. Outer letters go A,B,C,D→E. The 2nd/4th letters go Z,Y,X,W→V. The middle letter goes Y,X,W,V→U. So the next term is EVUVE.

Option A:
Option A collapses the middle and inner-pair logic by repeating V in three positions, not matching the observed centre shift.

Option B:
Option B swaps the inner-pair and the middle behaviour (inner becomes U and centre becomes V), which is inconsistent with the series.

Option C:
Option C keeps W in the inner pair instead of moving to V, breaking the step.

Option D:
Option D is correct because it advances the outer letter to E, moves the inner pair to V, and shifts the centre from V to U while preserving the palindrome.

The terms are generated by aₙ = 4n⁴ − n² + 3 with n starting at 1. Substituting n = 1, 2, 3, 4 and 5 gives 6, 63, 318, 1011 and 2478, which matches the series. For n = 6 we obtain a₆ = 4·6⁴ − 6² + 3 = 4·1296 − 36 + 3 = 5184 − 33 = 5151. Thus 5151 is the only term consistent with this quartic pattern.

Option A:
Option A, 5127, is 24 less than the value predicted by 4n⁴ − n² + 3 at n = 6. Adopting 5127 would mean arbitrarily reducing the correct polynomial result at the final step. Since earlier values fit the rule exactly, this modification is unjustified, so option A is incorrect.

Option B:
Option B, 5139, is 12 less than the correct value 5151 and cannot be obtained from 4·6⁴ − 6² + 3. It suggests a slight downward deviation that does not follow from the formula. Therefore this option fails to provide a mathematically sound continuation of the series.

Option C:
Option C, 5151, is precisely the number produced when n = 6 is substituted into 4n⁴ − n² + 3. It maintains the same balance between the quartic term and the subtractive quadratic component that governs the earlier terms. Because it extends the pattern without any alteration, this option is correct.

Option D:
Option D, 5163, is 12 greater than the polynomial value and likewise cannot be generated by the rule at n = 6. Introducing such an increase at only one term would break the consistent algebraic structure. Hence option D is not a valid continuation.

Statements A, B, C and D together summarise the standard relationships between mutually exclusive and independent events. A correctly defines mutual exclusivity as events that cannot happen simultaneously. B properly describes independence in terms of unchanged probabilities. C follows because if two non-trivial events are mutually exclusive, their joint probability is zero and cannot equal the product of positive probabilities, so they are not independent. D restates the formal definition of independence using the product rule. E is false since mutual exclusivity and independence are distinct concepts, so the correct set is A, B, C and D only.

Option A:
Option A is incomplete because it omits D and thus fails to express the formal product definition of independence, even though A, B and C are true. The absence of D makes the description of independence less precise.

Option B:
Option B is correct as it combines the basic definitions and implications about mutual exclusivity and independence and excludes E, which wrongly equates the two. It matches the conceptual treatment of events found in NET-level probability questions.

Option C:
Option C is incorrect because it includes E, the false claim that mutual exclusivity and independence mean the same thing, and leaves out B, which is a core statement about independence. This mixture of error and omission invalidates the option.

Option D:
Option D is wrong as it drops A and includes only B, C and D, leaving out the explicit definition of mutual exclusivity while still not rejecting E. It therefore does not provide the complete and correct set of statements.

From a:b = 2:3, let a = 2k and b = 3k. From b:c = 4:5, let b = 4m and c = 5m. Equating b gives 3k = 4m, so we choose k = 4 and m = 3 to get a = 8, b = 12 and c = 15. Then (a + b) = 20 and (b + c) = 27, so the required ratio is 20:27. This ratio is unique after we bring the two given ratios to a common middle term.

Option A:
Option A, 14:19, does not arise from any consistent choice of a, b and c that satisfies both 2:3 and 4:5 as the given ratios. If we attempt to back-calculate from 14:19, the implied values of a, b and c will violate at least one of the original relationships. Hence 14:19 is not compatible with the data.

Option B:
Option B is correct because it is computed after properly equalising the middle term b in both ratios. The method ensures that b plays the same role in both proportional relationships before forming (a + b) and (b + c). This leads precisely to 20:27 as the resulting ratio of the sums.

Option C:
Option C, 7:9, looks like a simplified ratio but does not match the actual numerical values 20 and 27 obtained from solving. Any attempt to assign a, b and c consistent with 7:9 will contradict the starting ratios 2:3 and 4:5. Therefore 7:9 cannot represent (a + b):(b + c).

Option D:
Option D, 3:4, is unrelated to the sums and instead resembles a typical simple ratio. When we compute (a + b) and (b + c) using the correct method, their ratio is not reducible to 3:4. Thus, 3:4 is not the correct resultant ratio.

The volume of a sphere is proportional to the cube of its radius. If the radii are in the ratio 5:7, then the volumes are in the ratio 5³:7³ = 125:343. Cubing both terms of the radius ratio correctly scales the measure from a linear dimension to a three-dimensional one. Therefore, the ratio of the volumes is 125:343.

Option A:
Option A, 5:7, simply repeats the ratio of the radii and ignores the fact that volume is a three-dimensional measure. Using this ratio would be correct if we were comparing lengths, not volumes, so it is too small a difference for the situation described.

Option B:
Option B, 25:49, is obtained by squaring the radius ratio and is appropriate for comparing surface areas, not volumes. This reflects a two-dimensional rather than a three-dimensional relationship, so 25:49 does not apply here.

Option C:
Option C, 125:196, mixes a cubed numerator with a squared denominator, which has no geometric justification. Such a mismatch does not correspond to any standard dimensional comparison and cannot represent the ratio of volumes.

Option D:
Option D is correct because it cubes both terms of the radius ratio consistently, giving 5³:7³ = 125:343. This matches the known formula V ∝ r³ and correctly captures how volume scales with changes in radius.

Statements A, B, C and E correctly summarise how pie charts work. A states that sector angles reflect relative shares. B is true because a full circle corresponds to 360 degrees. C is correct as pie charts emphasise contribution to a whole rather than precise comparisons between many categories. E is true since the total proportion is fixed at 100%, so increasing one share must reduce some other share. D is false because if the total quantity is known, one can estimate or compute numeric values from the percentages shown. Hence A, B, C and E only are correct.

Option A:
Option A is correct because it includes all the valid properties of pie charts and excludes D, which overstates the limitation of estimating values from them.

Option B:
Option B is incomplete as it omits E and thus fails to stress the compensating changes between categories when one sector grows, which is central to understanding proportions.

Option C:
Option C is wrong because it leaves out A and therefore misses the fundamental encoding rule (angles proportional to shares).

Option D:
Option D is incorrect because it omits B and does not include all the true statements together, so it cannot be correct.

The given series is generated by the rule (a_n = n^3 - 2) with n starting from 2. For n=2 we get 2³−2 = 8−2 = 6, for n=3 we get 27−2 = 25, for n=4 we obtain 64−2 = 62, for n=5 we obtain 125−2 = 123 and for n=6 we obtain 216−2 = 214. The next index is n=7, giving 7³−2 = 343−2 = 341 as the next term. Hence 341 is the correct continuation of the sequence.

Option A:
Option A, 333, does not equal (n^3-2) for n=7 or for any integer n that follows in the natural order of indices. Using 333 would require modifying the clear cubic rule that currently explains every term. Thus 333 is not consistent with the pattern.

Option B:
Option B, 339, is also not of the form (7^3-2) and does not result from the same functional relation. It introduces an arbitrary deviation from the established cubic structure. Hence 339 is not a valid next term.

Option C:
Option C equals 341, which is precisely 7³−2 and continues the rule (a_n = n^3-2) seamlessly. Since this one formula accounts for all given terms and the candidate term, 341 correctly extends the series.

Option D:
Option D, 347, is larger than the value predicted by 7³−2 and fails to satisfy the same polynomial relation. Selecting 347 would break the tight algebraic pattern that unifies the sequence. Therefore 347 cannot be accepted as the next term.

Each term is 5 consecutive letters in reverse. Starting letters E(5), J(10), O(15), T(20) increase by +5. Next start is Y(25), giving YXWVU.

Option A:
Option A is correct because it starts at Y (+5 from T) and lists Y,X,W,V,U in reverse order.

Option B:
Option B starts at Z (+6 from T), breaking the +5 rule.

Option C:
Option C starts at W, not Y, and breaks the starting-letter progression.

Option D:
Option D repeats the last term.

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.

Outer letters remain M. Middle letters move A, B, C, D → next E. So the next group is MEM.

Option A:
Option A is correct because it keeps M on both sides and advances the middle letter to E.

Option B:
Option B breaks the symmetry rule because last letter is not M.

Option C:
Option C skips E and jumps to F.

Option D:
Option D jumps further to G and breaks the +1 pattern.