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Jee Main 2025Medium JEE math MCQ

Let \( f : [0, 3] \rightarrow A \) be defined by \( f(x) = 2x^3 - 15x^2 + 36x + 7 \) and \( g : [0, \infty) \rightarrow B \) be defined by \( g(x) = \frac{x^{2025}}{x^{2025} + 1} \). If both the functions are onto and \( S = \{ x \in \mathbb{Z} : x \in A \text{ or } x \in B \} \), then \( n(S) \) is equal to
  1. A. 29
  2. B. 30
  3. C. 31
  4. D. 36

Solution

The correct option is **B**. (B. 30)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
Let f:[0,3]A f : [0, 3] \rightarrow A be defined by f(x)=2x315x2+36x+7 f(x) = 2x^3 - 15x^2 + 36x + 7 and g:[0,)B g : [0, \infty) \rightarrow B be defined by g(x)=x2025x2025+1 g(x) = \frac{x^{2025}}{x^{2025} + 1} . If both the functions are onto and S={xZ:xA or xB} S = \{ x \in \mathbb{Z} : x \in A \text{ or } x \in B \} , then n(S) n(S) is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep