JEE Main 2023MathematicsSequences and SeriesMediumMCQ

JEE Main 2023 — Sequences and Series Question with Solution

JEE Main 2023 (11 Apr Shift 2)

Question

Let a,b,c and d be positive real numbers such that a+b+c+d=11. If the maximum value of a5b3c2d is 3750β, then the value of β is

Choose an option

Show full solutionCorrect option: A
Correct answer
A90

Step-by-step explanation

Given:

a+b+c+d=11

We know that,

AM≥GM

⇒a5+a5+a5+a5+a5+b3+b3+b3+c2+c2+d111≥a5b3c2d55332211

⇒a+b+c+d11≥a5b3c2d55332211

⇒1111≥a5b3c2d55332211

⇒a5b3c2d55332211≤1

⇒a5b3c2d≤553322

⇒a5b3c2d≤90·3750

So,

β=90

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About this question

This is a previous-year question from JEE Main 2023, covering the Sequences and Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.