UGC NET Questions (Paper – 1)

This option is correct because a prime number is greater than 1 and has exactly two distinct positive divisors. The number 2 is divisible only by 1 and 2, satisfying this definition. It is also the smallest number with this property. Therefore, 2 is the smallest prime number.

Option A:
The number 1 has only one positive divisor, namely itself. Because primes must have exactly two distinct positive divisors, 1 is not considered a prime number. Hence, this option is incorrect.

Option B:
The number 2 is the first integer greater than 1 that has exactly two positive divisors. It is divisible by 1 and itself and no other positive integer. This makes 2 the smallest prime number as required in the question.

Option C:
The number 3 is prime, but it is not the smallest prime. Since 2 is smaller than 3 and already satisfies the definition of a prime, 3 cannot be the correct answer. Therefore, this option is not appropriate.

Option D:
The number 0 is divisible by every non-zero integer and does not fit the standard definition of prime numbers. It is not even positive in the usual sense of positive integers. Thus, 0 cannot be the smallest prime.