Maths · Algebra · chapter 6 of 14

Class 11 Maths Chapter 6: Permutations and Combinations Assertion-reason questions with answers

2 assertion-reason questions on Permutations and Combinations, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.

Question 1
Assertion (A): The number of ways of choosing 3 balls from 5 balls of different colours is 60. Reason (R): ⁿPr = ⁿCr × r!, 0 < r ≤ n.
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Answer: (d) A is false, but R is true.

A is false: a choice has no order, ⁵C₃ = 10; 60 is ⁵P₃. R is Theorem 5 and is true: each choice of 3 gives 3! = 6 arrangements, 10 × 6 = 60.

Question 2
Assertion (A): ¹²C₅ + ¹²C₄ = ¹³C₅. Reason (R): ⁿCr + ⁿCr − 1 = ⁿ⁺¹Cr for 1 ≤ r ≤ n.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.

R is Theorem 6. With n = 12 and r = 5 it gives ¹²C₅ + ¹²C₄ = ¹³C₅ (792 + 495 = 1287), so R explains A.

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