UGC NET Questions (Paper – 1)

Statements A, B and C give core rules for relative speed questions. A is correct because approaching objects in opposite directions effectively close the distance at the combined speed. B is true since when moving in the same direction, the faster gains on the slower at the difference of their speeds. C is also correct because when trains cross each other completely, the total length to be covered relative to one another is the sum of their lengths. D is false because inconsistent units for speed and distance must be converted before using formulas, and E is false since on a circular track the time of meeting depends on relative speed, which involves differences for same-direction motion. Thus, A, B and C only are correct.

Option A:
Option A is incomplete as it lists only A and B and omits C, thereby failing to mention the specific structure of train-crossing problems where lengths are added.

Option B:
Option B is also incomplete since it includes only A and C and omits B, so it does not explicitly state how same-direction relative speed is computed.

Option C:
Option C is incomplete as it contains only B and C and omits A, losing the rule for opposite-direction motion.

Option D:
Option D is correct because it collects all three true statements about relative speeds and excludes D and E, which misrepresent unit conversion requirements and the nature of circular-track meetings.

B is correct: permutations count ordered arrangements. C is correct because nPr = nCr × r! and r! ≥ 1. D is correct since choosing 0 or all items yields one way. E is correct since choosing 1 item from n gives n ways. A is false because combinations ignore order. Hence B, C, D and E only are correct.

Option A:
Option A is incomplete because it omits D and E, which are standard special cases of combinations.

Option B:
Option B is incorrect because it omits E (true).

Option C:
Option C is incorrect because it omits C (true) even though B, D and E are true; it does not list all correct statements.

Option D:
Option D is correct because it includes all true statements and excludes A, which reverses the definition of combinations.

A is correct because conditional probability measures A given B. B is the definition formula P(A|B) = P(A ∩ B)/P(B) (when P(B) > 0). C is true because Bayes’ theorem is used to update probabilities of hypotheses/causes when evidence is known. D is true for independent events since B does not change the probability of A. E is false because P(A|B) and P(not A|B) are complementary conditional probabilities and must sum to 1, not exceed 1. Therefore, A, B, C and D only are correct.

Option A:
Option A is incomplete because it omits D, which is a key property of independent events (conditioning does not change probability).

Option B:
Option B is correct because it includes all true statements (A, B, C, D) and excludes E, which wrongly claims the sum of complementary conditional probabilities is greater than 1.

Option C:
Option C is incorrect because it includes E (false) and also omits A and D, both of which are true statements about conditional probability and independence.

Option D:
Option D is incorrect because it includes E (false) and excludes B and C, which are fundamental definitions/uses of conditional probability and Bayes’ theorem.