JEE Main 2013MathematicsSequences and SeriesMediumMCQ

JEE Main 2013 — Sequences and Series Question with Solution

JEE Main 2013 (07 Apr)

Question

If x, y, z are positive numbers in A.P. and tan-1x, tan-1y and  tan-1z are also in A.P., then which of the following is correct.

Choose an option

Show full solutionCorrect option: C
Correct answer
Cx=y=z

Step-by-step explanation

Given, tan-1x, tan-1y and tan-1z are in A.P., so

2tan-1y=tan-1x+tan-1z

⇒tan-1y-tan-1x=tan-1z-tan-1y

y−x1+xy=z−y1+yz  ...i

Given x, y, z are in A.P.

i.e., 2y=x+z⇒y−x=z−y

Hence, from i

1+xy=1+yz

xy=yz either y=0  (rejected) or x=z

Hence, x = y = z.

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About this question

This is a previous-year question from JEE Main 2013, 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.