UGCNET Questions

The given series consists of perfect squares of natural numbers. Specifically, 1² = 1, 2² = 4, 3² = 9, 4² = 16 and 5² = 25. The next term should therefore be 6², which is 36. This continues the clear pattern of successive squares.

Option A:
Option A, 30, does not correspond to any perfect square and breaks the pattern of square numbers. It would require a different rule that is not evident in the series.

Option B:
Option B, 32, is also not a perfect square and falls between 25 and 36 without a clear basis from squaring integers.

Option C:
Option C, 35, is again not a perfect square and therefore cannot follow the pattern of 1², 2², 3², 4² and 5².

Option D:
Option D, 36, is 6² and naturally follows 5² = 25 in the sequence of square numbers. It maintains the structure of the series and is therefore the correct next term.

The rule states that each letter is replaced by the next letter in the alphabet. For the word NET, N is followed by O, E is followed by F and T is followed by U. Replacing each letter accordingly, N becomes O, E becomes F and T becomes U, giving the code OFU. This maintains the same pattern that was used to convert WORD into XPSE.

Option A:
Option A correctly shifts every letter of NET forward by one position, providing O from N, F from E and U from T. It applies the coding rule consistently to all positions and thus matches the example given.

Option B:
Option B, OEU, shifts only some letters correctly and uses E instead of F for the second position. This breaks the uniform next-letter rule for the middle letter.

Option C:
Option C, MFS, shifts N backwards to M instead of forwards and only partially follows the pattern. It does not consistently apply the specified direction of shift.

Option D:
Option D, NEU, keeps N unchanged, which contradicts the rule that each letter must be replaced by its immediate successor in the alphabet.

The letters in the series correspond to positions in the English alphabet with a constant skip of one letter in between. A is 1, C is 3, E is 5 and G is 7, so the sequence follows 1, 3, 5, 7. The next alphabet position should therefore be 9, which corresponds to the letter I. This consistent pattern of adding 2 to position numbers confirms I as the correct continuation.

Option A:
Option A, H, corresponds to position 8, which would result from adding 1 to G. That would break the established pattern of skipping one letter between terms. Therefore, H does not fit the rule observed in the given series.

Option B:
Option B, J, is position 10, which is two steps after I and would mean the series suddenly jumps by 3 from G’s position 7. There is no evidence of such a change in increment, so J is not appropriate.

Option C:
Option C, I, is position 9, obtained by adding 2 to 7, which aligns exactly with the pattern used to generate all previous letters. The series consistently increases by two positions each time, so I is the only choice that respects the underlying rule.

Option D:
Option D, K, corresponds to position 11, implying a jump of 4 from position 7, which is inconsistent with the fixed increment of 2. Choosing K would ignore the observed regularity of the series.

The given series multiplies each term by a constant factor to obtain the next one. Specifically, 9 ÷ 3 = 3, 27 ÷ 9 = 3 and 81 ÷ 27 = 3, so the common ratio is 3. To continue the pattern, we multiply 81 by 3 to obtain the next term. This gives 81 × 3 = 243, which preserves the geometric progression.

Option A:
Option A, 162, arises if someone incorrectly multiplies by 2 instead of 3, giving 81 × 2. However, this contradicts the established common ratio of 3 used in all previous steps.

Option B:
Option B, 200, does not correspond to any simple multiple of 81 consistent with the progression and seems unrelated to the pattern.

Option C:
Option C, 225, is 15² and may be chosen due to familiarity with square numbers, but it does not follow from multiplying 81 by the common ratio 3.

Option D:
Option D maintains the constant ratio of 3 between consecutive terms. By applying 81 × 3, we get 243, which is the only option that respects the geometric structure of the series.

The rule is that a number n maps to n² + 4. For n = 2, we get 2² + 4 = 4 + 4 = 8, and for n = 3, we get 3² + 4 = 9 + 4 = 13, matching the given examples. Applying the same rule to n = 5 yields 5² + 4 = 25 + 4 = 29. Hence, 5 maps to 29 under this square-plus-four rule.

Option A:
Option A, 21, could arise from a different linear rule like 4n + 13, but it does not agree with the n² + 4 pattern shown by the examples.

Option B:
Option B, 29, is exactly 5² + 4 and therefore fits the defined function rule for this analogy.

Option C:
Option C, 31, would correspond to 5² + 6, which changes the constant term and breaks the consistency of the mapping.

Option D:
Option D, 35, is even further from 29 and does not follow from squaring and then adding a fixed constant.

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.