JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 July 2022, Shift 2, Maths Q65

Question 65 of 90 in this shift, Maths question 5 of 30, Section A.

The sum of all values of

n

, for which

{}^{n-1}C_4 - {}^{n-1}C_3 - \frac{5}{4}\,{}^{n-2}P_2 < 0

, is

(1)40
(2)45Official answer
(3)55
(4)56

Official answer

Option 2

NTA final key.

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

Same topic in other shifts

All Permutations and Combinations questions

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5 Apr 2026, Shift 1 · Q21Let $A = \{1, 2, 3, 4, 5, 6\}$ . The number of one-one functions $f: A \to A$ such that $f(1) \geq 3$ , $f(3) \leq 4$ and $f(2) + f(3) = 5$ ,…MediumNumerical value

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.