UGC NET Questions (Paper – 1)

Statements A, C and D all describe standard facts from elementary number theory. Every prime greater than 2 is odd because 2 is the only even prime. Composite numbers must have at least one additional divisor besides 1 and themselves, giving at least three distinct positive divisors. There are infinitely many primes, a result known since Euclid’s proof. Statements B and E are false because 1 is neither prime nor composite and many even numbers greater than 2, such as 4, 6 and 8, are not prime, so A, C and D only are correct.

Option A:
Option A is correct because it picks exactly those statements that are true and excludes the common misconceptions in B and E. It recognises that 1 is excluded from the definition of primes and that even numbers beyond 2 are usually composite. By including C, it also captures a key structural property of composite numbers.

Option B:
Option B is incorrect as it omits D, thereby ignoring the important theorem that there are infinitely many primes. Even though it includes two true statements, it fails to include all the correct ones.

Option C:
Option C is wrong because it brings in E, which incorrectly claims that every even number greater than 2 is prime. Introducing a clearly false statement alongside A and D makes the overall combination incorrect.

Option D:
Option D is incomplete since it includes only C and D and leaves out A. While C and D are true, this option fails to capture the basic fact that primes greater than 2 are odd, so it does not list the full set of correct statements.

The series lists prime numbers in ascending order: 2, 3, 5, 7, 11, 13 and 17. The next prime after 17 is 19. Therefore, 19 is the correct next term in the sequence.

Option A:
Option A is 18, which is composite because it has divisors 1, 2, 3, 6, 9 and 18. It does not fit into a list of primes. Hence, it cannot be chosen.

Option B:
Option B equals 19, a prime number that follows 17 in the natural order of primes. Extending the series to 2, 3, 5, 7, 11, 13, 17, 19 keeps the property of primality throughout. This makes 19 the appropriate continuation.

Option C:
Option C is 21, another composite number divisible by 3 and 7. As the sequence is restricted to primes, introducing 21 would break the rule. Therefore, it is not correct.

Option D:
Option D is 23, which is prime but does not come immediately after 17. Since 19 is the first prime after 17, skipping it would not match the natural prime progression. Thus, 23 is not the correct next term here.

A prime number has exactly two distinct positive divisors, 1 and itself. The numbers 11, 13 and 17 each have no divisors other than 1 and themselves and are therefore prime. The number 15, however, is divisible by 1, 3, 5 and 15, so it has more than two divisors and is composite. Hence 15 is the odd one out in the list.

Option A:
Option A, 11, is a prime number because its only positive divisors are 1 and 11. It shares this property with 13 and 17 and therefore does not stand out in this group.

Option B:
Option B, 13, is also prime and fits the same classification as 11 and 17. It does not have additional factors that would make it different.

Option C:
Option C, 15, clearly deviates from the prime pattern, since it can be expressed as 3 × 5. Its composite nature makes it unique among the options and justifies treating it as the different number.

Option D:
Option D, 17, remains prime since no integer between 2 and 16 divides it without remainder. It aligns with 11 and 13 rather than differing from them.