JEE Main 2016 — Sequences And Series Question with Solution
From: JEE Main 2016 (Online) 9th April Morning Slot
Question
Let x, y, z be positive real numbers such that x + y + z = 12 and x3y4z5 = (0.1) (600)3. Then x3 + y3 + z3is equal to :
Choose an option
Show full solutionCorrect option: D
Correct answer
D216
Step-by-step explanation
As we know
AM GM
1
x3 y4 z5 33 . 44 . 55
x3 y4 z5 (0.1)(600)3
but given that,
x3 y4 z5 = (0.1) (600)3
AM GM
All the number are equal.
x 3k, y = 4k, z = 5k
given that,
x + y + z 12
3k + 4k + 5k 12
12k 12
k = 1
x 3, y 4, z 5
So, x3 + y3 + z3
33 + 43 + 53
216
AM GM
1
x3 y4 z5 33 . 44 . 55
x3 y4 z5 (0.1)(600)3
but given that,
x3 y4 z5 = (0.1) (600)3
AM GM
All the number are equal.
x 3k, y = 4k, z = 5k
given that,
x + y + z 12
3k + 4k + 5k 12
12k 12
k = 1
x 3, y 4, z 5
So, x3 + y3 + z3
33 + 43 + 53
216
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This is a previous-year question from JEE Main 2016, 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.