UGC NET Questions (Paper – 1)

The starting letters Q, N, K and H occupy positions 17, 14, 11 and 8, decreasing by 3 each time. Each group is a three letter block of consecutive letters in forward order. Continuing this pattern, the next starting letter is position 5, which is E, and the following letters are F and G, giving EFG. Therefore EFG fits both the minus three jump and the internal structure of the groups.

Option A:
Option A is correct because E lies exactly three positions before H and EFG continues with F and G as consecutive letters. It maintains the constant decrement in the starting letters and keeps the groups consistently formed. This alignment with both the numerical and structural aspects of the pattern makes EFG the correct answer.

Option B:
Option B, GHI, moves forward from H instead of backward, reversing the direction of the starting sequence. The series clearly shows the starting letters descending through the alphabet. As GHI would be a forward step, it does not conform to the observed rule.

Option C:
Option C, IJK, begins at I, which is only one position after H and also goes in the wrong direction. It neither preserves the backward movement nor maintains the required step size of three. Consequently, IJK cannot be the next term.

Option D:
Option D, ABC, starts at A, which is position 1, representing a jump of seven positions backward from H instead of three. This change in step size is not supported by any previous transition. As a result, ABC does not fit the pattern.

Statements A, B, D and E accurately summarise key ideas about linear equations: they have a standard form, a solution makes the equation true, a common solution satisfies each equation in a system and many word problems can be translated into such equations. Statement C is false because an equation true for all values is an identity, whereas an inconsistent equation has no solution at all. Thus, the combination A, B, D and E only is correct.

Option A:
Option A is correct as it gathers all four true statements and omits C, which confuses the notions of identity and inconsistency. It presents the conceptual framework used in NET aptitude questions about simple equations.

Option B:
Option B is incomplete since it omits E, failing to mention the important modelling role linear equations play in real-life aptitude contexts like age and mixture problems. Without E, the practical side is under-emphasised.

Option C:
Option C is wrong because it excludes A and thus lacks the canonical ax + b = 0 form that defines linear equations in one variable, while also not addressing the error in C. The combination is therefore incomplete and inaccurate.

Option D:
Option D is incorrect because it includes C, the misdefinition of inconsistent equations, even though A, D and E are true. The presence of C makes the overall set logically inconsistent.

In partnership problems, the profit is divided in the ratio of capital multiplied by time. Taking capitals as 3k, 5k and 7k for A, B and C and times as 2, 4 and 6 years, their effective investments are 3k × 2 = 6k, 5k × 4 = 20k and 7k × 6 = 42k. The ratio 6:20:42 simplifies to 3:10:21. The sum of these parts is 34, so B’s share is (10/34) of ₹1,36,000, which equals ₹40,000.

Option A:
Option A is correct because the calculation (10/34) × 1,36,000 gives exactly ₹40,000, and using 3/34 and 21/34 for A and C yields the remaining profit. The three shares add up neatly to ₹1,36,000, confirming that the ratio of effective investments has been applied correctly. Hence, ₹40,000 accurately represents B’s entitlement.

Option B:
Option B, ₹38,000, would not correspond to the fraction 10/34 of the total profit. If we assign ₹38,000 to B, the remaining amount for A and C would not then be divisible in the ratio 3:21 without leaving a remainder or altering the initial capital-time structure. Therefore, ₹38,000 is inconsistent with the proportional rule.

Option C:
Option C, ₹48,000, would represent a larger share than warranted by the 10 parts out of 34. Using ₹48,000 for B implies that B’s effective contribution outweighs that of C more than the 10:21 ratio allows. This contradicts the original investment-time data, so ₹48,000 cannot be correct.

Option D:
Option D, ₹52,000, is even higher and would require B’s share to be close to or greater than C’s share, which is not supported by the ratio 3:10:21. The necessary rebalancing of the remaining profit would distort the intended proportions. As a result, ₹52,000 does not match the proportional distribution.

Each term is 4 consecutive letters in reverse. Starting letters Z(26), V(22), R(18), N(14) decrease by −4. Next start is J(10), so the reversed block is JIHG.

Option A:
Option A is correct because J is −4 from N and J,I,H,G are consecutive in reverse order.

Option B:
Option B starts at K (11), which is −3 from N, not −4.

Option C:
Option C starts at M (13), which is −1 from N, not −4.

Option D:
Option D moves forward to P and breaks the backward step rule.

Each group is made of four consecutive letters written in reverse order. The starting letters X, U, R and O are moving backwards through the alphabet by a fixed number of steps from one term to the next. Continuing this pattern, the next starting letter must be L and the remaining letters must step down consecutively from there. That gives LKJI, which matches both the constant backward step in starting letters and the reverse ordering inside each group, so it is the correct next term.

Option A:
Option A is correct because it begins at L, which is the next point in the backward chain after X, U, R and O, and then lists the previous three letters K, J and I in descending order. The internal structure is exactly the same as in the earlier terms. This alignment with both the starting letter sequence and the reverse block rule makes LKJI the only suitable continuation.

Option B:
Option B, MJIH, starts from M instead of L and so moves the starting letter too far back. It no longer matches the fixed step used between X, U, R and O. The letters also do not form the straightforward descending run that characterises the series, hence MJIH is not correct.

Option C:
Option C, NMLK, reverses letters but starts at N, which breaks the specific starting letter progression. It also produces a block that overlaps awkwardly with ONML rather than continuing smoothly after it. Because it does not respect the consistent backward move of the first letter, NMLK cannot be accepted.

Option D:
Option D, KJIH, uses letters that are in descending order but begins at K rather than the expected L. This would shorten the step from O to the next starting letter and contradict the constant pattern. Therefore KJIH does not fit the established rule.

This sequence is defined by a₁ = 3 and aₙ₊₁ = 5aₙ + n² for n ≥ 1. Using the rule, we get a₂ = 5·3 + 1² = 16, a₃ = 5·16 + 2² = 84, a₄ = 5·84 + 3² = 429 and a₅ = 5·429 + 4² = 2161, which matches the given terms. For n = 5 the next term is a₆ = 5·2161 + 5² = 10805 + 25 = 10830. Hence 10830 is the only number consistent with this recurrence relation.

Option A:
Option A, 10830, is precisely the value obtained from 5a₅ + 5² when a₅ = 2161. It maintains the pattern of multiplying the previous term by five and adding the square of the index. Since this mechanism generates all earlier terms correctly, 10830 is the valid continuation of the series.

Option B:
Option B, 10806, is 24 less than the computed value and cannot be produced by the recurrence at n = 5. Accepting 10806 would require subtracting 24 from the result only at this stage, which has no basis in the rule. Therefore option B is incorrect.

Option C:
Option C, 10818, is 12 less than the correct value and again fails to equal 5·2161 + 25. It is merely an approximate candidate that does not arise from the stated recurrence. As a result, option C cannot be the correct next term.

Option D:
Option D, 10842, is 12 greater than the required result and would demand increasing the formula output only for the sixth term. This contradicts the consistent pattern established by previous steps, so option D is not a valid continuation.

Initially, alcohol = (5/12) × 72 = 30 litres and water = (7/12) × 72 = 42 litres. Let x litres of water be added. Alcohol remains 30 litres, water becomes 42 + x and the new ratio is 30:(42 + x) = 5:9. Cross-multiplying gives 30 × 9 = 5(42 + x), so 270 = 210 + 5x, which leads to 5x = 60 and x = 12. Thus, 12 litres of water must be added.

Option A:
Option A, 9 litres, gives water = 51 litres and alcohol = 30 litres, yielding a ratio 30:51 which simplifies to 10:17, not 5:9. Hence, 9 litres is insufficient to reach the required proportion of water to alcohol.

Option B:
Option B, 10 litres, leads to water = 52 litres and a ratio 30:52, which reduces to 15:26. This is still not 5:9, indicating that 10 litres does not adjust the mixture to the desired composition.

Option C:
Option C, 11 litres, produces water = 53 litres and a ratio 30:53 which does not simplify to 5:9. Therefore, it also fails to create the target ratio between alcohol and water.

Option D:
Option D is correct because with water increased to 54 litres, the ratio becomes 30:54, which simplifies to 5:9 when both terms are divided by 6. This exactly matches the condition specified in the problem.

In this series, the first letters are A, E, I, M, which correspond to positions 1, 5, 9 and 13, all increasing by 4. The second letters are D, H, L, P, i.e. positions 4, 8, 12 and 16, also increasing by 4. The next first letter after M (13) is Q (17) and the next second letter after P (16) is T (20). Hence QT is the only pair that continues the uniform +4 progression in both positions.

Option A:
Option A, QS, provides the correct first letter Q but gives S as the second letter, which is only 3 steps ahead of P. The series demands a constant increase of 4 positions for the second letter as well. Since S is inconsistent with the established step size, this option disrupts the pattern and is therefore incorrect.

Option B:
Option B is correct because Q and T are exactly 4 positions ahead of M and P respectively. This keeps the uniform step size intact for both components of the pair. By preserving the same arithmetic structure as in all previous terms, QT is the only option that maintains strict logical continuity in the series.

Option C:
Option C, QU, pushes the second letter forward to U, which is 5 positions after P. This overshoots the fixed increment and changes the rule mid-series. Since the first and second letters must follow the same step of +4, QU cannot be considered a valid continuation.

Option D:
Option D, QV, again uses the correct first letter Q but moves the second letter to V, which is 6 positions ahead of P. This introduces a larger increment than used before, breaking the constant-difference pattern that defines the sequence. Therefore option D does not fit the series.

This sequence follows the rule aₙ = n³+2n for n starting from 1. For n = 1, 2, 3, 4 and 5 we obtain 1³+2 = 3, 2³+4 = 12, 3³+6 = 33, 4³+8 = 72 and 5³+10 = 135, matching the given terms. For n = 6 the formula gives 6³+12 = 216+12 = 228. Therefore 228 is the only value that continues the same cubic relationship without any adjustment.

Option A:
Option A, 218, does not equal n³+2n for n = 6 and would require subtracting 10 from the value given by the formula. This distortion breaks the clear pattern connecting each term to its index. Thus 218 cannot be regarded as the correct next term.

Option B:
Option B, 222, is still below the correct cubic value of 228 and does not satisfy the rule aₙ = n³+2n. It represents an arbitrary modification rather than a logical extension of the pattern. For this reason it is not the right answer.

Option C:
Option C, 228, is precisely the value obtained from the generating rule when n = 6. It respects the same algebraic structure used for all earlier terms and keeps the series internally consistent. Hence 228 is the correct continuation.

Option D:
Option D, 236, exceeds the formula’s prediction and has no basis in the expression n³+2n for the next index. Adopting 236 would undermine the transparent cubic pattern, so it is not a valid option.

Each term is a block of four consecutive letters written in reverse order, and the starting letter moves forward by four positions each time. The starting letters D, H, L and P have positions 4, 8, 12 and 16, all increasing by 4. The next starting letter is position 20, which is T, and writing the four letter block from T in reverse gives TSRQ. This preserves both the plus four progression and the internal reverse arrangement.

Option A:
Option A, RQPO, rearranges letters including P and O but does not start with the correct letter T. It also breaks the strict descending order that characterises each block. Since it fails to follow the formula for the starting position and the internal structure, RQPO is not consistent with the pattern.

Option B:
Option B, SRQP, begins with S instead of T, which is only three positions ahead of P, not four. This changes the size of the jump in starting letters and disrupts the regularity of the sequence. Additionally, the letter order within the block does not correspond to a straightforward reverse of four consecutive letters starting at T.

Option C:
Option C, QPON, reverses the internal order of letters found around P but again starts with Q, not T, and does not reflect the plus four movement. It also returns to letters that are two positions behind P, which contradicts the forward movement of starting positions. Because it fails on both structural and positional grounds, QPON is not the correct continuation.

Option D:
Option D is correct because T is four positions after P and TSRQ lists T, S, R and Q as consecutive letters in descending order. It exactly mirrors the format of earlier blocks, which all reverse a run of four consecutive letters. This consistent adherence to both the starting letter progression and the reverse order makes TSRQ the valid next term.

The series lists English words for natural numbers in increasing order: ONE (1), TWO (2), THREE (3) and FOUR (4). The next number in this sequence is FIVE (5). Therefore the word FIVE is the only term that preserves the numeric progression described in word form.

Option A:
Option A, SIX, represents the number 6, which would be two steps ahead of FOUR if FIVE is skipped. The series shows no evidence of skipping intermediate numbers. As the pattern is strictly consecutive, SIX cannot be the immediate next term.

Option B:
Option B, ONE, would restart the sequence from the beginning. There is no cyclical structure indicated; the list moves forward rather than looping. Repeating ONE therefore breaks the clear numeric ordering.

Option C:
Option C, SEVEN, represents 7 and skips both FIVE and SIX. This contradicts the strictly increasing by 1 pattern in the given sequence. Hence SEVEN cannot logically follow FOUR.

Option D:
Option D is correct because FIVE is the next integer after FOUR in the natural counting order. It continues the sequence smoothly without omissions or repetitions. As the series is clearly numerical in nature, FIVE must be the next term.

The given series increases by a constant difference of 3 between successive terms: 2 to 5, 5 to 8 and 8 to 11. To continue the same pattern, we add 3 to the last term 11. This gives 11 + 3 = 14 as the next number in the sequence. Since the rule is consistent for all previous terms, 14 uniquely fits the observed arithmetic progression.

Option A:
Option A, 13, would require a difference of 2 from 11, which breaks the established +3 pattern observed throughout the series. Choosing 13 ignores the constant increment that defines the given progression. Therefore, it is not consistent with the rule governing the sequence.

Option B:
Option B, 14, maintains the constant difference of +3 between consecutive terms, which is the key feature of this arithmetic progression. It is obtained directly by adding 3 to 11, and thus matches the pattern seen in all earlier steps. This makes 14 the logically correct continuation of the series.

Option C:
Option C, 15, would imply adding 4 to 11, which is inconsistent with the earlier differences of 3. Although close in magnitude, it does not preserve the uniform increment required in an arithmetic progression. Hence, it cannot be accepted as the next term.

Option D:
Option D, 16, would represent an even larger jump of 5, again contradicting the constant difference already established. Such a change would introduce a new pattern not supported by the original data, so it is not appropriate.

Statement A is correct because “p sufficient for q” means p guarantees q, i.e., p → q. Statement B is correct because “p necessary for q” means q cannot hold without p, i.e., q → p. Statement C is true because mixing these up is a common reasoning error. Statement D is false (they are different), and E is false (contrapositive of p → q is ¬q → ¬p). Hence A, B and C only are correct.

Option A:
Option A is incomplete because it omits C (common error point).

Option B:
Option B is incomplete because it omits A (sufficiency mapping).

Option C:
Option C is correct since it includes all true statements and excludes D and E.

Option D:
Option D is incorrect because it includes D (false) and omits B (true).

Starting letters A(1), D(4), H(8), M(13) have gaps +3, +4, +5. Next gap is +6 → S(19). Pair is ST.

Option A:
Option A starts at Q(17), which is +4 from M, not +6.

Option B:
Option B is correct because S is +6 from M and T follows S.

Option C:
Option C starts at R(18), which is +5 from M, not +6.

Option D:
Option D starts at O(15), which is +2 from M, not +6.

Statements A, B and C are correct: the behaviour of inequalities under multiplication by positive and negative numbers is standard, and solving them parallels solving equations with additional attention to sign changes. Statement D is false because solutions of inequalities are often intervals or ranges of values, not single numbers, and E is false because inequality reasoning has many practical applications and is tested in aptitude sections. Therefore the option that includes A, B and C and excludes D and E is correct.

Option A:
Option A is incomplete as it omits C and thus fails to highlight the close procedural connection between solving equations and inequalities, which is a key conceptual insight in aptitude contexts.

Option B:
Option B is also incomplete because it leaves out A, ignoring the important fact that multiplication by a positive number leaves the inequality direction unchanged. Without A, some fundamental transformation rule is missing.

Option C:
Option C is correct because it gathers all three true statements about manipulation and solution processes for inequalities, while rejecting D and E, which misrepresent the nature and usefulness of inequality solutions. It matches the conceptual level expected in UGC NET.

Option D:
Option D is wrong since it includes D, the false claim that solution sets are always single numbers, and thereby contradicts the idea of intervals. Including this misstatement makes the combination logically incorrect.