If ${}^nP_r={}^nP_{r+1}$ and ${}^nC_r={}^nC_{r-1}$, then the value of r is equal to :

JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 25 July 2021, Shift 2, Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30, Section A.

{}^nP_r={}^nP_{r+1}

and

{}^nC_r={}^nC_{r-1}

, then the value of r is equal to :

(1) $1$
(2) $2$ Official answer
(3) $3$
(4) $4$

Official answer

Option 2

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Permutations of Distinct Objects

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.