MathsJEE Main 22 Jan 2026, Shift 2·Q19·MCQ·Easy–moderate

Sets, Relations & Functions · Functional equations

Let

f

and

g

be functions satisfying

f(x+y) = f(x)f(y)

f(1) = 7

and

g(x+y) = g(xy)

g(1) = 1

, for all

x, y \in \mathbb{N}

. If

\displaystyle\sum_{x=1}^{n}\left(\frac{f(x)}{g(x)}\right) = 19607

, then

n

is equal to:

We corrected a printing error in the original paper

Source printed “ $f(l) = 7$ ” and “ $g(l) = 1$ ” (letter l for the number 1); the missing “If” added before “ $\sum \ldots = 19607$ ”.

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