JEE Main 2020MathematicsFunctionsMediumMCQ

JEE Main 2020 — Functions Question with Solution

JEE Main 2020 (02 Sep Shift 2)

Question

Let f:R→R be a function which satisfies fx+y=fx+fy,  ∀x, y∈R . If f1=2 and gn=∑k=1n-1fk, n∈N then the value of n, for which gn=20, is

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Show full solutionCorrect option: A
Correct answer
A5

Step-by-step explanation

∵  fx+y=fx+fy

∴  fx=kx, ∀x∈R

Now f1=2  ⇒ k=2

∴  fx=2x, ∀x∈R 

gn=f1+f2+……..+fn-1

=21+2+3+……+n-1

=2·n-12n=20

⇒n2-n-20=0 

⇒n=5.

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About this question

This is a previous-year question from JEE Main 2020, covering the Functions 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.