UGC NET Questions (Paper – 1)

Statements A and B correctly describe the multiplication and addition rules of counting, and D is true because many questions can be answered directly by reasoning about choices without naming permutations or combinations explicitly. Statement C is false since the multiplication rule in its simplest form assumes independence or appropriately defined conditional paths, and it cannot be applied blindly when choices are dependent. Statement E is false because counting principles are explicitly part of NET Unit 5. Thus, the combination A, B and D only is correct.

Option A:
Option A is correct as it includes the key rules and the note that problems can sometimes be solved without formal notation, while excluding C and E, which misrepresent the applicability of the multiplication rule and the syllabus.

Option B:
Option B is incomplete because it omits D, thereby failing to acknowledge that intuitive counting can sometimes bypass formal permutation or combination formulas in exam settings. Without D, the practical approach is not highlighted.

Option C:
Option C is wrong because it includes C, which incorrectly asserts that the multiplication rule applies regardless of dependence, and omits A, leaving out the fundamental statement of the rule itself.

Option D:
Option D is incorrect since it accepts C and thus endorses an overgeneralisation of the multiplication rule, even though A and D are true. The presence of C makes the overall combination logically unsound.

Statements C and E are the wrong statements here. A is correct because probabilities range from 0 to 1. B is true since probabilities of all mutually exclusive and exhaustive outcomes sum to 1. D correctly states that a certain event has probability 1. C is false because 0.7 indicates a more likely event than 0.4. E is false because P(A ∪ B) equals P(A) + P(B) only when A and B are mutually exclusive; otherwise the intersection must be subtracted. Therefore, the wrong statements are C and E only.

Option A:
Option A is incomplete because it selects only C as wrong and ignores E, which misapplies the addition rule for probabilities of unions.

Option B:
Option B is correct as it identifies both C and E as incorrect, thereby recognising that both comparative likelihood and union probabilities are mishandled in those statements.

Option C:
Option C is wrong since it mislabels A as wrong, even though A accurately describes the probability range, and still keeps C and E, mixing correct and incorrect judgments.

Option D:
Option D is incorrect because it classifies B and D as wrong despite them stating fundamental probability principles, and it omits E, which actually contains an error about unions.

Statements A, B and C express the basic axioms about range of probabilities and values for sure and impossible events. Statement D gives the general addition rule for the probability of a union of two events. Statement E is false because probabilities are never negative. Therefore, A, B, C and D only form the correct set.

Option A:
Option A is incomplete as it omits D (union/addition rule).

Option B:
Option B is incomplete because it omits B (sure event) and does not include all core axioms together.

Option C:
Option C is incomplete since it omits A (range restriction 0 ≤ P(A) ≤ 1).

Option D:
Option D is correct because it includes all true statements and excludes E, which suggests an impossible negative probability.

This series follows the Fibonacci rule, where each term is the sum of the two preceding terms. We see 1+1 = 2, 1+2 = 3, 2+3 = 5 and 3+5 = 8, which confirms the pattern. Continuing this, the next term should be 5+8 = 13. So 13 is the correct next term in the sequence.

Option A:
Option A suggests 9, which would come from adding only 1 to the previous term 8 and does not use the sum of the last two terms. This ignores the clear recursive rule that defines the series. Therefore, 9 is not correct.

Option B:
Option B is 10, which again does not arise from adding any two consecutive terms in the series. There is no pair among the last two terms that sums to 10. Hence, it breaks the Fibonacci structure.

Option C:
Option C gives 11, which would require a different rule, such as adding 3 to 8, that has not appeared earlier. Since the series has consistently used sums of the two preceding numbers, 11 cannot fit the pattern.

Option D:
Option D equals 13, which is exactly 5+8 and respects the recursive rule used throughout. Extending the series to 1, 1, 2, 3, 5, 8, 13 maintains the Fibonacci property. Thus, this option correctly represents the next term.