UGC NET Questions (Paper – 1)

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.

This option is correct because the square root of a number is a value which, when squared, gives the original number. Here, 9 × 9 = 81. The positive value that satisfies this is 9. Therefore, the positive square root of 81 is 9.

Option A:
If we square 7, we get 49, which is less than 81. Thus, 7 is not the square root of 81. It does not satisfy the required condition.

Option B:
Squaring 8 gives 64, which is still less than 81. Hence, 8 is not the number whose square equals 81 and cannot be the correct answer.

Option C:
The number 9 squared gives exactly 81, so 9 is the positive square root of 81. The question asks specifically for the positive square root, so we choose 9 and not −9. Therefore, this option is correct.

Option D:
81 is the original number itself and would be the square of 9, not its square root. Squaring 81 gives a much larger number, 6561. Thus, 81 cannot be the square root of 81.

The given terms are 1², 2², 3², 4² and 5², showing a sequence of consecutive perfect squares. Following this pattern, the next square should be 6². Computing 6² gives 36, so 36 must be the next term. This preserves the structure of consecutive squares.

Option A:
Option A is 30, which is not a perfect square of any integer. It does not follow from squaring the next whole number after 5. Thus, it fails to continue the pattern correctly.

Option B:
Option B is 32, which lies between 5² and 6² but is not itself a square of an integer. Because the rule involves exact squares in order, 32 cannot be accepted.

Option C:
Option C equals 36, which is 6² and follows naturally after 5² = 25. The extended series 1, 4, 9, 16, 25, 36 clearly shows consecutive squares of 1, 2, 3, 4, 5 and 6. Therefore, this choice correctly matches the pattern.

Option D:
Option D is 34, which again is not a perfect square and has no special relation to the square sequence here. Including 34 would break the logical connection between terms. Hence, it is not the correct answer.