UGC NET Questions (Paper – 1)

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. Here, the relative speed is 15 + 17 = 32 km/h. After 3 hours, the distance between them is relative speed multiplied by time, which is 32 × 3 = 96 km. This distance represents how far apart they are from the starting point after 3 hours.

Option A:
Option A, 32 km, is only the distance they would be apart after 1 hour at the relative speed of 32 km/h and fails to account for the full 3 hours of travel.

Option B:
Option B, 90 km, underestimates the separation and could come from incorrectly adding or averaging speeds, but it does not match 32 × 3.

Option C:
Option C correctly multiplies the relative speed by time, applying the standard formula distance = speed × time for relative motion. This yields 96 km as the accurate separation.

Option D:
Option D, 102 km, overstates the distance and suggests a relative speed higher than 32 km/h, which is not given.

A is correct because figure series often involve visual changes such as shape, shading or orientation. B is true as recognising the underlying transformation is the key to predicting the next figure. D is correct since mirror-image and water-image problems are classic non-verbal items. E is also true because such questions are often grouped under mathematical reasoning and aptitude. C is false because many non-verbal questions combine multiple types of changes, not just a single transformation. Therefore, A, B, D and E only are correct.

Option A:
Option A omits D and E, leaving out the important examples of mirror and water images and their placement in the syllabus. While it includes some true statements, it is incomplete.

Option B:
Option B includes A, B and D but omits E, so it does not mention explicitly that these questions fall within Unit 5, which is useful syllabus information for candidates.

Option C:
Option C leaves out A and so fails to cover the variety of changes involving shapes and shading, and it still omits E, thereby missing two important correct statements.

Option D:
Option D is correct as it collects all accurate statements about the nature, examples and syllabus position of non-verbal reasoning questions, and excludes C, which oversimplifies the types of changes used.

Pipe A fills 1/10 of the tank per hour, pipe B fills 1/15 per hour, and pipe C empties 1/30 per hour. The net hourly work rate when all three are open is 1/10 + 1/15 − 1/30. Using 30 as the common denominator, this becomes 3/30 + 2/30 − 1/30 = 4/30 = 2/15 of the tank per hour. The time to fill the tank is therefore 1 ÷ (2/15) = 15/2 = 7.5 hours, which matches Option B.

Option A:
Option A, 5 hours, would require a net rate of 1/5 per hour, which is much faster than the computed 2/15 and not achievable with the given pipes.

Option B:
Option B, 7.5 hours, is exactly the reciprocal of the net rate 2/15 and correctly represents the time taken to fill the tank with all three pipes open.

Option C:
Option C, 8 hours, corresponds to a net rate of 1/8 per hour, slower than 2/15, and inconsistent with the detailed rate computation.

Option D:
Option D, 10 hours, duplicates the time taken by pipe A alone and ignores the additional inflow from B and the outflow from C, so it cannot be correct.

This sequence is generated by the formula (a_n = n^3 + n^2) with n starting from 1. For n = 1, 2, 3, 4 and 5 we get 1³+1² = 2, 2³+2² = 12, 3³+3² = 36, 4³+4² = 80 and 5³+5² = 150. For n = 6 the formula gives 6³+6² = 216+36 = 252. Thus 252 maintains a single algebraic rule that explains all the terms.

Option A:
Option A, 252, matches exactly the value obtained by substituting n = 6 into the rule (a_n = n^3+n^2). Since this rule already accounts for every earlier term, extending it to 252 keeps the series perfectly consistent. Hence 252 is the correct continuation.

Option B:
Option B, 254, cannot be expressed as 6³+6² and does not result from the same expression for any natural n in order. Using 254 would break the clean connection between term position and value. Therefore it is not the right answer.

Option C:
Option C, 256, is numerically close but again does not obey the formula (n^3+n^2). It has no direct link to the pattern that generates the given sequence and so is not acceptable.

Option D:
Option D, 258, deviates even further from the predicted value and similarly lacks a basis in the generating rule. Selecting 258 would force an ad hoc change in the pattern, making it incorrect as the next term.

Statements A and B correctly distinguish permutations and combinations in terms of the role of order. D is true because permutations can be obtained from combinations by arranging the chosen r objects in r! ways. E is also correct since there is only one way to choose all n objects from n. Statement C is false because nPr generally exceeds nCr when 0 < r < n, so permutations and combinations are not equal in count. Thus the correct combination is A, B, D and E only. Option A: Option A is incomplete as it omits D and E, and hence does not show the quantitative relationship between permutations and combinations or the special case when all objects are chosen. It therefore does not capture the full set of correct statements. Option B: Option B is incorrect because it leaves out E and includes only A, B and D, so it does not mention the important special case nCr = 1 when r = n. This omission makes the combination incomplete. Option C: Option C is correct because it gathers the true distinctions and the exact formula relating nPr and nCr and excludes C, which wrongly claims equality of counts. It therefore matches the combinatorial facts emphasised in NET aptitude. Option D: Option D is wrong as it drops A and includes B, D and E only, failing to state explicitly that permutations take order into account while still not rejecting C. As a result, it does not provide the precise set of correct statements requested.

This option is correct because permutations count ordered arrangements of r objects chosen from n distinct objects. The standard notation for this is nPr. It takes into account both the selection and the ordering of the objects. Therefore, the correct symbol is nPr.

Option A:
nCr represents combinations, which count selections without regard to order. It does not distinguish between different arrangements of the same r objects. Since the question explicitly mentions arranging, this symbol is not appropriate.

Option B:
rPn is not the standard way of denoting arrangements of r out of n. It reverses the positions of n and r and does not correspond to any common formula in basic combinatorics. Hence, this notation is incorrect.

Option C:
The symbol nPr captures both how many objects are chosen and how they are ordered. It equals n!/(n−r)!, which counts all possible ordered selections. This matches the description of selecting and arranging r objects from n, so this option is correct.

Option D:
rCn would again reverse the roles of n and r in combination notation. It is not used to represent either permutations or combinations in standard texts. Therefore, it is not the correct symbol.

The differences between consecutive terms are 11, 17, 23 and 29. These differences themselves form an arithmetic progression with common difference 6. Therefore the next difference should be 35. Adding 35 to the last term 85 gives 120, which maintains the constant step of 6 at the second level.

Option A:
Option A gives 116, implying a difference of 31 from 85. This would make the final increase between differences equal to 2 instead of 6, producing 11, 17, 23, 29, 31. Hence 116 does not preserve the consistent second-level arithmetic structure.

Option B:
Option B gives 120, implying a difference of 35 from 85. The difference sequence becomes 11, 17, 23, 29, 35, showing a uniform increment of 6 between gaps. This alignment at both levels makes 120 the correct next term.

Option C:
Option C gives 124, yielding a difference of 39 from 85. That would make the last jump among differences equal to 10, which distorts the pattern of adding 6 each time. Therefore 124 is not suitable.

Option D:
Option D gives 128, corresponding to a difference of 43 from 85. This further enlarges the final increment and deviates even more from the expected value. Thus 128 cannot be considered the correct continuation.

This option is correct because the product of an even integer with any integer is always even. An even number can be written as 2k, and multiplying 2k by any integer m gives 2(km), which is still divisible by 2. Therefore, if at least one factor is even, the product is even.

Option A:
Even numbers are multiples of 2, and when such a number multiplies any integer, the factor of 2 remains in the result. This ensures the product is also a multiple of 2 and hence even. Thus, this option correctly states the property described.

Option B:
An odd product occurs only when both factors are odd, because then neither factor contributes a factor of 2. Here, the condition explicitly says at least one integer is even, so the product cannot be odd. Therefore, this option is wrong.

Option C:
A prime number has exactly two positive divisors, 1 and itself. The product of two integers with one even factor can be composite and need not be prime. So, prime is not guaranteed and is not the correct description.

Option D:
A negative product depends on the signs of the integers, not on whether they are even or odd. An even factor does not force the product to be negative. Hence, negativity is unrelated to the parity condition in the question.

The word BANANA has 6 letters, with A repeated 3 times, N repeated 2 times and B appearing once. The formula for permutations of n objects with repeated groups is n! divided by the product of factorials of the counts of repeated items. Here this gives 6! ÷ (3! × 2!). Evaluating this gives 720 ÷ (6 × 2) = 720 ÷ 12 = 60. So there are 60 distinct arrangements of the letters of BANANA.

Option A:
Option A, 30, underestimates the total arrangements and would correspond to a different combination of repeats or a smaller word. It does not follow the factorial formula for this word.

Option B:
Option B, 36, arises from miscalculating either 6! or one of the factorials in the denominator. It does not equal 720 ÷ 12 and so fails to match the correct combinatorial reasoning.

Option C:
Option C, 48, again does not match the computed result and suggests partial adjustment for repetition without applying the full divisor 3! × 2!.

Option D:
Option D carefully applies the repetition-adjusted permutation formula. It fully accounts for indistinguishable arrangements caused by repeated letters and yields the correct count of 60.

The pattern in this series is based on increasing differences that themselves double each time. The differences between successive terms are 3, 6, 12 and 24. Each new difference is twice the previous one, giving the next difference as 48. When this difference of 48 is added to the last term 46, the next term becomes 94. Thus, 94 continues the established pattern of doubling increments.

Option A:
Option A, 88, would correspond to adding 42 to 46, which does not match the doubling pattern of 3, 6, 12 and 24. It ignores the rule that each difference is twice the previous difference.

Option B:
Option B, 90, arises if we add 44 to 46, but there is no consistent reason in the earlier terms to justify a difference of 44. It breaks the strict doubling of the gaps.

Option C:
Option C, 94, uses a difference of 48, which is double the previous difference of 24. This respects the second order structure of the series and produces a term fully consistent with the pattern.

Option D:
Option D, 98, assumes an increase of 52, again not related to the repeated doubling of the differences. It introduces a new rule that is not supported by the earlier terms.

The sequence is described by the formula aₙ = n⁴−n+2 for n starting from 1. For n = 1, 2, 3, 4 and 5, we get 1−1+2 = 2, 16−2+2 = 16, 81−3+2 = 80, 256−4+2 = 254 and 625−5+2 = 622. For n = 6 the formula gives 1296−6+2 = 1292. Thus 1292 is the correct next term in line with this quartic-minus-linear rule.

Option A:
Option A, 1252, is 40 less than the computed value and does not equal n⁴−n+2 for n = 6. It breaks the exact pattern that has held for the earlier terms. Therefore 1252 is not a valid continuation.

Option B:
Option B, 1268, is still lower than 1292 and likewise fails to come from the generating expression. Selecting 1268 would require changing the formula without any clear reason. Hence it is not correct.

Option C:
Option C, 1292, matches perfectly with 6⁴−6+2 and continues the same structural relationship between n and aₙ. It maintains both the power and linear components consistently, making 1292 the correct answer.

Option D:
Option D, 1322, overshoots the correct value and cannot be obtained by substituting n = 6 into the rule. Using 1322 would distort the pattern and undermine the algebraic coherence of the sequence. Thus it is not appropriate.

In partnership, profit is shared in proportion to the product of capital and time, so A is correct. If A’s capital is twice B’s for the same duration, A’s share becomes double B’s, making B correct. Partnership questions are naturally modelled with ratio and proportion, so E is also true. C is wrong because different times change the effective contribution, and D is wrong since a sleeping partner is still entitled to profit on capital. Thus the combination of A, B and E only is correct.

Option A:
Option A is correct because it captures the relationship of profit with both capital and time and notes the use of ratios, while excluding statements that misrepresent time dependence and sleeping partners’ shares. It fully matches how partnership questions are treated in aptitude tests.

Option B:
Option B omits E and therefore ignores the explicit link with ratio–proportion techniques, even though A and B themselves are true. Because it does not include all correct statements from the list, it is incomplete.

Option C:
Option C wrongly includes C, which claims time does not matter when capital is equal, contradicting the basic formula profit ∝ capital × time. Even though it contains A and E, adding C makes the overall combination incorrect.

Option D:
Option D uses B and E but unnecessarily adds D, which misstates that sleeping partners get no profit share. Since D is false, this combination cannot be accepted as correct.

This option is correct because three consecutive integers can be written as n−1, n and n+1. Their sum is (n−1) + n + (n+1) = 3n. Dividing by 3 gives n, which is the middle integer. Therefore, the average equals the middle integer.

Option A:
The smallest integer in the set is n−1. The average of n−1, n and n+1 is n, which is larger than the smallest. Thus, the average cannot equal the smallest integer.

Option B:
The largest integer in the set is n+1. Since the average is n, which lies between n−1 and n+1, it is less than the largest value. Therefore, it is not equal to the largest integer.

Option C:
Saying the average equals the sum of the integers would ignore the division by the number of terms. The sum is 3n, while the average is 3n ÷ 3 = n. Thus, "sum of" does not describe the average correctly.

Option D:
The middle integer n is exactly the average of the three consecutive integers. It balances the smaller and larger values symmetrically. Hence, the average is always equal to the middle integer, making this option correct.

Statements B and D are wrong because they misstate how logical puzzles work and how they should be approached. Good puzzles provide consistent information that allows definite conclusions, and making tentative assumptions and revising them is in fact a standard strategy in complex puzzles. Statements A, C and E are correct: diagrams are useful, “left of” or “between” are relational clues, and many puzzles can be represented with structured diagrams or equations. Thus, the set of wrong statements consists exactly of B and D.

Option A:
Option A is incorrect since it singles out B only, ignoring that D also wrongly discourages a helpful reasoning technique. While B is indeed wrong, the omission of D means not all incorrect statements are captured.

Option B:
Option B is also wrong because it focuses only on D, treating B as acceptable, even though B incorrectly claims that puzzle information is inherently inconsistent. This does not satisfy the requirement to identify all wrong statements.

Option C:
Option C is correct because it lists both B and D as wrong while leaving the accurate descriptions in A, C and E untouched. It aligns with the practical strategies aspirants should use in NET-style logical puzzles.

Option D:
Option D is incorrect because it includes C, which is actually a correct description of relational clues, and therefore misclassifies a true statement as wrong. Mixing a true statement with the wrong ones makes the option invalid.

The positions follow the rule 2n² + 1 for n = 1 to 5: 2·1² + 1 = 3 (C), 2·2² + 1 = 9 (I), 2·3² + 1 = 19 (S), 2·4² + 1 = 33 ≡ 7 (G) and 2·5² + 1 = 51 ≡ 25 (Y) when reduced modulo 26. For n = 6, 2·6² + 1 = 73, which corresponds to position 21 (73 − 52 = 21), the letter U. Thus U is the only letter that fits the quadratic pattern with wrap-around.

Option A:
Option A, V, is at position 22 and does not satisfy the formula 2n² + 1 for any consecutive integer n after 5. It appears close numerically but does not arise from the defined rule. Therefore it cannot be accepted as the next term.

Option B:
Option B, W, corresponds to position 23, which again does not match the computed position for n = 6. While it is near in the alphabet, the underlying quadratic expression would have to change to justify W, which is not supported by the earlier terms.

Option C:
Option C, U, is correct because its position 21 is exactly what we obtain from 2·6² + 1 when considered modulo 26. It maintains the same mathematical rule that produced all previous letters. This continuity in the generating formula makes U the unique valid continuation.

Option D:
Option D, T, lies at position 20 and would correspond to a different input or rule. It does not satisfy the specific function used to generate earlier terms. As a result, T does not belong to this series as its next element.