JEE Main 2020MathematicsFunctionsHardMCQ

JEE Main 2020 — Functions Question with Solution

JEE Main 2020 (06 Sep Shift 1)

Question

 If f(x+y)=f(x) f(y) and Σx=1∞fx=2, x,y∈N, where N is the set of all natural numbers, then the value of f(4)f(2) is

Choose an option

Show full solutionCorrect option: D
Correct answer
D49

Step-by-step explanation

f(x)=ax satisfies the functional relation, so
Σx=1∞fx=2
⇒a+a2+a3……∞ terms =2
⇒a1-a=2

⇒a=23
⇒fx=23x
Now, f(4)f(2)=234232=49

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Functions chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.