UGC NET Questions (Paper – 1)

This option is correct because 3³ means 3 multiplied by itself three times. Calculating 3 × 3 × 3 gives 27. This follows directly from the definition of exponentiation. Therefore, 3³ equals 27.

Option A:
Squaring 3 gives 3² = 9, which is too small. The exponent 3 requires one more multiplication by 3. Hence, 9 is not the correct value for 3³.

Option B:
The result 27 comes from multiplying 3 by itself three times in succession. The sequence 3, 9 and then 27 confirms that 3³ = 27. This directly matches the required calculation, so this option is correct.

Option C:
The number 18 does not arise from any standard power of 3. It would require 3 × 6, not 3 × 3 × 3. Therefore, 18 is not correct here.

Option D:
The number 21 also does not match the cube of 3. It lies between 16 and 25 but has no connection to 3³. Thus, this option is incorrect.

This option is correct because 2 raised to the power 5 means multiplying 2 by itself five times. Calculating 2 × 2 × 2 × 2 × 2 gives 32. This follows the general definition of exponents as repeated multiplication. Therefore, 2⁵ is equal to 32.

Option A:
16 is the value of 2 raised to the power 4, not 5. It comes from 2 × 2 × 2 × 2, which has only four factors. Since the exponent here is 5, this option underestimates the value.

Option B:
32 is obtained by multiplying five factors of 2 together. The sequence is 2, 4, 8, 16 and finally 32, which corresponds to 2⁵. This exactly matches the requirement of the question, making this option correct.

Option C:
64 is the value of 2 raised to the power 6, which involves six factors of 2. Using 64 would correspond to 2⁶ rather than 2⁵. Hence, this option is too large for the given exponent.

Option D:
25 is the square of 5 and is unrelated to powers of 2 in this context. It does not come from repeated multiplication of 2. Therefore, this option does not answer the question correctly.