UGC NET Questions (Paper – 1)

This option is correct because 50% means 50 out of 100. Writing this as a fraction gives 50/100. Dividing numerator and denominator by their greatest common divisor 50 gives 1/2. Therefore, 50% equals the fraction 1/2.

Option A:
The fraction 1/3 corresponds to approximately 33.33%, not 50%. It does not represent half of a whole. Hence, this option is not correct.

Option B:
The fraction 1/4 is equal to 25%, which is half of 50%. Therefore, 1/4 is too small to match 50%. So, this option is incorrect.

Option C:
The fraction 1/2 represents exactly half of a unit, which matches the idea of 50%. Converting back to a percentage gives 0.5 × 100 = 50%. Thus, this option correctly expresses 50% as a fraction.

Option D:
The fraction 2/3 corresponds to about 66.67%, which is greater than 50%. Therefore, it does not represent 50% and cannot be the correct answer.

This option is correct because the reciprocal of a non-zero number a is 1/a. For the number 4, its reciprocal is 1/4. Multiplying 4 by 1/4 gives 1, which verifies that they are multiplicative inverses. Therefore, 1/4 is the required reciprocal.

Option A:
The reciprocal of 4 must satisfy 4 × reciprocal = 1. If we take 4 × 4, we get 16, not 1. This shows that 4 is not the multiplicative inverse of 4. Hence, this option is incorrect.

Option B:
The fraction 1/2 multiplied by 4 gives 2, not 1. Therefore, 1/2 does not serve as the reciprocal of 4. It reduces the number but does not invert it. Thus, this option does not match the definition.

Option C:
The reciprocal of 4 is 1/4 because 4 × 1/4 = 1. This fits the standard rule that the reciprocal of a number a is 1/a. So 1/4 correctly represents the fractional reciprocal of 4.

Option D:
The number 2 multiplied by 4 equals 8, which is far from 1. As a result, 2 cannot be considered the reciprocal of 4. This option fails the basic test for a multiplicative inverse.