UGC NET Questions (Paper – 1)

The pair 3 and 9 is related by the operation of squaring because 3 squared is 9. To maintain the same relationship for the second pair, we should square 4. The square of 4 is 16, so x must be 16 to keep the analogy consistent. Therefore, 3 : 9 :: 4 : 16 expresses a uniform pattern based on squaring the first number.

Option A:
Option A, 8, is obtained by doubling 4, but the first pair 3 : 9 is not formed by doubling 3; it is formed by 3². Using ×2 breaks the consistent “square the first number” rule, so 8 is not suitable.

Option B:
Option B, 12, can be seen as 3 × 4, but that mixes the two numbers of the analogy rather than applying the same operation to each first term. The clearer and more consistent pattern is to square the first term (3² = 9, 4² = 16), so 12 does not fit.

Option C:
Option C, 14, does not follow any simple or symmetric rule derived from 4 that parallels 3 → 9. It would require an arbitrary operation such as “add 10”, which has no support from the first pair, so this choice breaks the analogy.

Option D:
Option D, 16, results from squaring 4 (4² = 16), exactly mirroring the relation 3² = 9. This keeps the structure of the analogy identical in both pairs, making 16 the correct value of x.

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.