JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 31 January 2024, Shift 2, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

If for some

m,n

;

{}^6C_m+2\left({}^6C_{m+1}\right)+{}^6C_{m+2}>{}^8C_3

and

{}^{n-1}P_3:{}^nP_4=1:8

, then

{}^nP_{m+1}+{}^{n+1}C_m

is equal to

(1)372Official answer
(2)376
(3)380
(4)384

Official answer

Option 1

NTA final key.

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Pascal's Rule and nCr Properties

Same idea in other shifts

Asked 3× in all

6 Apr 2024, Shift 2 · Q6Let $0\le r\le n$ . If $^{n+1}C_{r+1}:{}^{n}C_r:{}^{n-1}C_{r-1}=55:35:21$ , then $2n+5r$ is equal to :MediumSingle correct
27 Jan 2024, Shift 1 · Q5 ${}^{n-1}\mathrm{C}_r=(k^2-8)\,{}^{n}\mathrm{C}_{r+1}$ if and only if :MediumSingle correct

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.