UGC NET Questions (Paper – 1)

The contrapositive of a statement of the form “If p then q” is “If not q then not p,” and these two are logically equivalent. Here, p is “the number is divisible by 6” and q is “the number is divisible by 3.” The contrapositive is therefore “if a number is not divisible by 3, then it is not divisible by 6.” This preserves the logical structure of the original implication while reversing and negating its components.

Option A:
Option A negates p but not q and forms the inverse “If not p then not q,” which is not logically equivalent to the original statement in general.

Option B:
Option B correctly follows the contrapositive pattern ¬q → ¬p, matching the structure of the initial implication about divisibility. It reflects the fact that if a number is not divisible by 3, it cannot possibly be divisible by 6.

Option C:
Option C is the converse q → p, which need not be true simply because the original implication is true; many numbers are divisible by 3 but not by 6.

Option D:
Option D contradicts the original statement directly by combining p with not q, which cannot be true if the original implication holds.

Statement (1) presents a solvable linear equation, 3x + 2 = 20, which has a unique solution. Solving it gives x = 6, so statement (1) by itself fully determines the value of x. Statement (2) only tells us that x is an integer but gives no equation or relation to narrow down x further. Therefore, statement (2) alone does not allow us to find a unique x. In data sufficiency terms, (1) alone is sufficient while (2) alone is not.

Option A:
Option A correctly reflects that statement (1) yields a unique solution for x, and that statement (2) adds no new restrictive information when used alone.

Option B:
Option B reverses the roles of the statements and incorrectly claims that simply knowing x is an integer is sufficient to find a unique value, which is impossible without an equation.

Option C:
Option C assumes that neither statement can independently identify x, which is incorrect because statement (1) clearly does.

Option D:
Option D states that each statement alone is sufficient, but this overstates the power of statement (2), which does not determine any specific numerical value.

This option is correct because a syllogism is a deductive argument formed from two premises and a conclusion. Each statement in a syllogism is usually a categorical proposition involving terms and quantifiers. The conclusion follows logically from the premises if the syllogism is valid. Therefore, such a structured argument is called a syllogism.

Option A:
A proposition is an individual declarative statement that is either true or false. While syllogisms are made up of propositions, the term proposition does not describe the whole argument structure. Thus, this option is too narrow and not correct.

Option B:
A term in logic is a word or phrase that stands for an object or concept, such as the subject or predicate in a proposition. Terms are components inside propositions but not full arguments. Therefore, term is not the right label for the argument described.

Option C:
A quantifier indicates how many objects of a certain kind are being referred to, such as "all" or "some." Although quantifiers appear in categorical propositions, they are not the name of the entire argument form. Hence, quantifier is not the correct answer.

Option D:
A syllogism specifically refers to a deductive argument with exactly two premises and one conclusion, often involving categorical statements. It captures both the structure and the logical relationship described in the question. Therefore, this term correctly names the type of argument mentioned.

Let the numbers be 7x and 8x. The difference between them is 8x − 7x = x, and we are told this difference equals 15. So x = 15. Substituting back, the numbers are 7 × 15 = 105 and 8 × 15 = 120. The larger number is therefore 120.

Option A:
Option A, 105, is the smaller of the two numbers obtained from the correct solution. It correctly fits the ratio but does not match the description “larger number” in the question. Choosing 105 would therefore misinterpret which quantity is being asked for.

Option B:
Option B is correct because it corresponds to the 8x term when x = 15, which is explicitly the larger number in the ratio 7:8. Verifying, the difference 120 − 105 is indeed 15, and the ratio 105:120 simplifies to 7:8. This confirms that 120 satisfies both the ratio and difference conditions.

Option C:
Option C, 135, when paired with 120 (to keep a difference of 15), yields a ratio 120:135 = 8:9, not 7:8. If we reversed the roles, 135 and 120 would differ by 15 but still not simplify to 7:8. Thus, 135 cannot be the larger number under the stated ratio.

Option D:
Option D, 140, would require the smaller number to be 125 to maintain a difference of 15. The ratio 125:140 reduces to 25:28, which is again not equal to 7:8. Therefore, 140 is incompatible with the conditions given in the question.

Every term is a block of three consecutive letters, and the starting letter moves backward by one each time: K, J, I, H → G. Hence GHI.

Option A:
Option A is correct because it continues the −1 slide to G and keeps the 3-letter consecutive block.

Option B:
Option B repeats a previous middle term (breaks the slide).

Option C:
Option C moves forward and breaks the backward slide.

Option D:
Option D jumps the starting letter too far back (−3), not −1.

A, B and C describe good principles of reading a single graph: scale affects visual impression, legends identify categories and, within one graph, equal heights match equal values. D is wrong because equal heights on different graphs with different scales may correspond to different actual values. E is also wrong because in many data interpretation questions candidates must convert units (such as thousands to lakhs or minutes to hours). Therefore, D and E only are the incorrect statements.

Option A:
Option A captures only D as wrong and overlooks E, which incorrectly claims unit conversions are never needed. Because it fails to include all wrong statements, this option is not adequate.

Option B:
Option B treats only E as wrong and ignores the error in D regarding comparing heights across graphs with different scales. Thus it also fails to identify the complete set of wrong statements.

Option C:
Option C is correct because it selects both D and E, the two statements that mislead about cross-graph comparisons and the need for unit conversions, while leaving A, B and C intact as good interpretation practices.

Option D:
Option D incorrectly adds C to the set of wrong statements even though C is true for any single graph using a consistent scale. Including C makes this combination inaccurate.

In this series, every group consists of four letters with the same fixed distance between consecutive letters. AEIM shows a regular pattern of positions, and BFJN, CGKO and DHLP repeat that structure with their own starting points. From one term to the next, each column increases by one letter in the alphabet. Advancing every letter of DHLP by one yields EIMQ, which keeps the constant internal spacing and extends the vertical sequences, so EIMQ is the correct next term.

Option A:
Option A, EGMR, alters the internal differences between letters and no longer keeps the equal steps that AEIM, BFJN, CGKO and DHLP share. It also does not come directly from adding one to each letter of DHLP. Because the spacing and transformation are both off, EGMR cannot be correct.

Option B:
Option B, EIFQ, begins with E and I like the true answer but changes the remaining letters so that the final gaps inside the group differ from the earlier pattern. The positions of F and Q do not fit the repeated structure. Hence EIFQ breaks the consistent internal rule of the series.

Option C:
Option C, FJNQ, moves the starting letter too far ahead and modifies multiple columns in a way that does not match the simple one step shift from DHLP. Its letters are not aligned properly with the previous vertical sequences. Therefore FJNQ does not continue the series correctly.

Option D:
Option D is correct because EIMQ is exactly one alphabetical step ahead of DHLP in each position and keeps the same spacing between successive letters. It fits neatly after the earlier groups, respecting both the constant internal step and the column wise progression. This makes EIMQ the only option that satisfies the observed pattern.

If a person completes the entire work in 8 days working at a constant rate, then each day they complete 1/8 of the total work. This follows from the idea that total work is taken as 1 and is divided equally among the number of days. The daily work rate is thus the reciprocal of the total time. Therefore, 1/8 is the correct fraction of work done in one day.

Option A:
1/6 would imply that the work is fully completed in 6 days, because 6 times 1/6 equals 1. However, the question clearly states that the work is completed in 8 days. Hence, 1/6 overestimates the daily work rate and is inconsistent with the given information.

Option B:
1/4 would mean completing the work in 4 days, since four days of work at this rate would make a full unit of work. This contradicts the stated time of 8 days. Therefore, 1/4 is not compatible with the conditions of the problem.

Option C:
The fraction 1/8 is correct because multiplying it by the total number of days, 8, yields 1, representing the entire work: 8 × 1/8 = 1. This reflects the standard unitary method used in time and work questions. Recognising that the daily rate is the reciprocal of total time simplifies many such problems on competitive exams.

Option D:
2/8 simplifies to 1/4, which, as explained earlier, corresponds to finishing the work in 4 days rather than 8. Using this fraction would contradict the given total time to completion. As a result, 2/8 is not the correct fraction of work done in one day in this scenario.

The differences between terms are 3, 4, 5 and 6, which increase by 1 each time. So the next difference should be 7. Adding 7 to the last term 20 gives 27. Therefore, 27 continues the pattern of increasing differences correctly.

Option A:
Option A uses the new difference of 7, producing 20 + 7 = 27 and extending the sequence of differences to 3, 4, 5, 6, 7. This maintains a clear second-level arithmetic pattern. Hence, 27 is the correct next term.

Option B:
Option B is 26, which would give a difference of 6 from 20, repeating the previous step instead of increasing it. That breaks the systematic growth of the differences. Thus, 26 is not consistent with the rule.

Option C:
Option C is 28, implying a difference of 8 from 20, which jumps beyond the next expected difference of 7. This oversteps the gradual increase and makes the pattern irregular. Therefore, 28 cannot be correct.

Option D:
Option D is 30, which would require a difference of 10, a much larger jump than the expected 7. Such a sudden change has no support from earlier terms and spoils the structure. So, 30 is not suitable.

This series follows the Fibonacci rule, where each term is the sum of the two preceding terms. We see 1+1 = 2, 1+2 = 3, 2+3 = 5 and 3+5 = 8, which confirms the pattern. Continuing this, the next term should be 5+8 = 13. So 13 is the correct next term in the sequence.

Option A:
Option A suggests 9, which would come from adding only 1 to the previous term 8 and does not use the sum of the last two terms. This ignores the clear recursive rule that defines the series. Therefore, 9 is not correct.

Option B:
Option B is 10, which again does not arise from adding any two consecutive terms in the series. There is no pair among the last two terms that sums to 10. Hence, it breaks the Fibonacci structure.

Option C:
Option C gives 11, which would require a different rule, such as adding 3 to 8, that has not appeared earlier. Since the series has consistently used sums of the two preceding numbers, 11 cannot fit the pattern.

Option D:
Option D equals 13, which is exactly 5+8 and respects the recursive rule used throughout. Extending the series to 1, 1, 2, 3, 5, 8, 13 maintains the Fibonacci property. Thus, this option correctly represents the next term.

The ratio 3 : 2 indicates that out of every 5 equal parts, 3 parts represent boys and 2 parts represent girls. The total number of parts is therefore 3 + 2 = 5. If 5 parts correspond to 90 students, then 1 part equals 90 ÷ 5 = 18 students. The number of boys is 3 parts, which is 3 × 18 = 54.

Option A:
Option A, 36, corresponds to 2 parts of 18 instead of 3, which would actually represent the number of girls if the same logic is applied correctly to the ratio. Hence, it mismatches the role of boys in the ratio.

Option B:
Option B, 45, is obtained if someone wrongly assumes 90 × (1/2) but that would correspond to a hypothetical 1 : 1 ratio. It does not respect the actual 3 : 2 proportion given in the question.

Option C:
Option C follows the correct ratio method: convert the total into parts, find the value of one part and then multiply by the number of parts corresponding to boys. This systematic approach yields 54, aligning with the structure of the ratio.

Option D:
Option D, 60, would imply that boys form two thirds of the class, which does not fit a 3 : 2 ratio where boys are 3/5 of the total. It clearly exceeds the value compatible with the defined proportion.

A’s one day work is 1/10 of the job and B’s one day work is 1/15 of the job. When they work together, the daily work done is the sum of their individual rates: 1/10 + 1/15. Taking the LCM of 10 and 15 gives 30, so the combined rate is (3/30 + 2/30) = 5/30 = 1/6. Thus, together they complete 1/6 of the work each day and need 6 days to finish the entire work.

Option A:
Option A, 4 days, would imply a combined rate of 1/4 per day, which is higher than what A and B can achieve together. The actual sum of their rates does not support completion in 4 days.

Option B:
Option B, 5 days, would mean they do 1/5 of the work per day, requiring a combined rate larger than 1/6. However, the calculated total rate from their individual capacities is only 1/6.

Option C:
Option C is consistent with the reciprocal method: adding 1/10 and 1/15 gives 1/6, whose reciprocal is 6 days. This uses the standard approach for time and work problems and fits the given data exactly.

Option D:
Option D, 8 days, underestimates their combined productivity and corresponds to a rate of 1/8 per day, which is lower than the actual 1/6 per day.

Statements A, B and D capture standard strategies for solving number series. A is correct because equal or regularly changing differences suggest arithmetic patterns. B is correct since regular ratios point towards geometric or multiplicative patterns. D is true because many advanced series have two or more interwoven subsequences. Statements C and E are false; series may change rules mid-way and writing differences or ratios is often very useful, so the correct combination is A, B and D only.

Option A:
Option A is correct because it includes precisely the three statements that describe genuine number series techniques while excluding C and E, which are misleading. It reflects how candidates are expected to analyse series using differences, ratios and recognition of alternating patterns.

Option B:
Option B is incorrect because it adds C, which wrongly insists on a single unchanging rule for every exam series. Including C makes the combination too restrictive and not true for many NET-style questions.

Option C:
Option C is wrong since it introduces E along with A, B and D. Statement E claims that writing differences or ratios is never useful, which contradicts common problem-solving practice, so this option cannot be fully correct.

Option D:
Option D is incorrect because it omits A and includes E. By leaving out the basic difference method and accepting the false claim that working out differences is useless, it fails to represent the correct set of statements.

Statements A, B, D and E are correct binary facts. A describes the positional value system in base 2. B is true because an odd number has last bit 1 and an even number has last bit 0. D correctly states the conversion method from binary to decimal. E is true for multiples of 4, whose binary form ends with two zeros. C is false; adding 1 flips only a block of trailing ones and the bit after that, not necessarily all bits. Therefore, A, B, D and E only are correct.

Option A:
Option A is incomplete since it omits E, thereby missing a useful rule for recognising multiples of 4 from binary patterns, which is sometimes tested in reasoning questions.

Option B:
Option B is incorrect because it includes C, wrongly claiming that adding 1 always flips all bits, which contradicts simple examples like 0010 becoming 0011.

Option C:
Option C is wrong since it leaves out A and includes only B, D and E, losing the fundamental statement about powers of 2 that underlies the entire binary system.

Option D:
Option D is correct because it gathers positional value, parity detection, conversion method and the multiple-of-4 criterion while excluding C, which misstates the effect of incrementing a binary number.

A is true because absolute value is never negative, so |x| ≥ 0 for all real x. B is true: |x| 0) means x lies within distance a of 0, i.e., −a < x a means x is outside that interval, i.e., x a. D is false because |x| > −2 is true for every real x (since |x| ≥ 0), so it does not force x to be positive. Therefore A, B and C only are correct.