JEE Main 2017MathematicsSequences and SeriesMediumMCQ

JEE Main 2017 — Sequences and Series Question with Solution

JEE Main 2017 (08 Apr Online)

Question

If the arithmetic mean of two numbers a and b, a>b>0 , is five times their geometric mean, then a+ba-b is equal to:

Choose an option

Show full solutionCorrect option: D
Correct answer
D5612

Step-by-step explanation

Arithmetic Mean =a+b2
Geometric Mean =ab

⇒a+b2=5ab
⇒a+b=10ab

⇒(a+b)2=100ab

⇒(a-b)2=(a+b)2-4ab=96ab

Now,

⇒a+ba-b=(a+b)2(a-b)2=10096

=5612

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About this question

This is a previous-year question from JEE Main 2017, 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.