JEE Main 2016MathematicsSequences and SeriesHardMCQ

JEE Main 2016 — Sequences and Series Question with Solution

JEE Main 2016 (09 Apr Online)

Question

Let x, y, z be positive real numbers such that x+y+z=12 and x3y4z5=0.16003. Then x3+y3+z3 is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B216

Step-by-step explanation

x+y+z=12

A.M.≥G.M.

3x3+4y4+5z512 ≥ x33 y44 z5512 

1≥1

⇒A.M.=G.M.

⇒All the numbers are equal.

∴x3=y4=z5=k

x=3k; y=4k; z=5k

x+y+z=12

⇒3k+4k+5k=12

⇒k=1

∴ x=3; y=4; z=5

Therefore, x3+y3+z3=216.

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About this question

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.