JEE Main 2025 — Functions Question with Solution
JEE Main 2025 (28 Jan Shift 2)
Question
Let A be defined by and be defined by . If both the functions are onto and or , then is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
as is onto hence is range of
$\begin{aligned}
& \text { now } \begin{array}{l}
\mathrm{f}^{\prime}(\mathrm{x})=6 \mathrm{x}^2-30 \mathrm{x}+36 \\
\quad=6(\mathrm{x}-2)(\mathrm{x}-3) \\
\quad \mathrm{f}(2)=16-60+72+7=35 \\
\mathrm{f}(3)=54-135+108+7=34 \\
\mathrm{f}(0)=7
\end{array}
\end{aligned}$
hence range
also for range of
$\begin{aligned}
& g(x)=1-\frac{1}{x^{2025}+1} \in[0,1)=B \\
& s=\{0,7,8, \ldots .35\} \text { hence } n(s)=30
\end{aligned}$
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This is a previous-year question from JEE Main 2025, 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.