UGC NET Questions (Paper – 1)

Saying that something is sufficient for an outcome means that whenever that condition holds, the outcome is guaranteed. If having a ticket is sufficient to enter, then anyone with a ticket qualifies for entry, even though there might be other ways to enter in a different system. The correct conditional structure is therefore “If you have a ticket, then you can enter the hall.” This expresses that a ticket alone is enough to ensure entry under the stated rule.

Option A:
Option A reverses the implication and would make having a ticket necessary rather than sufficient, changing the logical direction.

Option B:
Option B preserves the idea that a ticket is an adequate condition that guarantees the possibility of entry today.

Option C:
Option C contradicts the original statement by saying you can enter only without a ticket, which is the opposite of what is meant.

Option D:
Option D claims ticket possession is necessary but not sufficient, which again does not match the explicit statement about sufficiency.

Statements A and B correctly define sufficient and necessary conditions by linking the holding of one property to the presence of another, and C is true because some conditions are both necessary and sufficient, forming a biconditional. Statement E is also true as many reasoning errors arise from confusing what is merely necessary with what is sufficient. Statement D is false because from “p is sufficient for q” it does not follow that q is sufficient for p; the implication generally does not reverse. Therefore, the correct combination is the one that collects A, B, C and E and excludes D.

Option A:
Option A is incomplete because it omits E and therefore does not acknowledge the common reasoning mistake of confusing necessary and sufficient conditions in practical thinking. While A, B and C are true, the set does not cover the full conceptual picture.

Option B:
Option B is also incomplete since it leaves out B, so it does not explicitly state how a necessary condition restricts the possibility of Q without P. Although A, C and E are true, missing B means the definition of necessity is not fully represented.

Option C:
Option C is correct because it gathers all true statements, including the definitional ones and the observation about everyday confusion, and it rightly rejects D, which incorrectly reverses the implication between sufficient conditions. This option best reflects the logic of conditionals.

Option D:
Option D is wrong because it includes D, which describes an invalid inference pattern, and it omits A, thereby failing to give the correct account of sufficiency. Mixing one false statement with an incomplete set of true ones makes this option unacceptable.

The statement “Some students are diligent” is an existential claim asserting that at least one member of the class of students has the property of being diligent. Its contradictory is “No student is diligent.” Therefore, if “some students are diligent” is true, then the statement “no student is diligent” must be false. Saying “It is not the case that no student is diligent” is logically equivalent to affirming that at least one diligent student exists.

Option A:
Option A is stronger than “some”; it claims that all students are diligent, which need not follow from the existence of at least one diligent student.

Option B:
Option B is the direct negation of the original statement and cannot be true if “some students are diligent” is true.

Option C:
Option C correctly denies the universal negative and is consistent with the existential affirmation about diligent students.

Option D:
Option D narrows the claim to exactly one student, which again is stronger than “some” and does not logically follow.