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Jee Main 2025 — Medium JEE math MCQ

Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos \left( \frac{x}{3} - x \right) \cdot \cos \left( \frac{x}{3} + x \right) \cdot \sin 3x \cdot \cos 6x, x \in \mathbb{R} \] be \([\alpha, \beta] \). Then the distance of the point \((\alpha, \beta)\) from the line \(3x + 4y + 12 = 0\) is
  1. A. 11
  2. B. 8
  3. C. 10
  4. D. 9

Solution

The correct option is **A**. (A. 11)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let the range of the function f(x)=6+16cos⁡x⋅cos⁡(x3−x)⋅cos⁡(x3+x)⋅sin⁡3x⋅cos⁡6x,x∈R f(x) = 6 + 16 \cos x \cdot \cos \left( \frac{x}{3} - x \right) \cdot \cos \left( \frac{x}{3} + x \right) \cdot \sin 3x \cdot \cos 6x, x \in \mathbb{R} be [α,β][\alpha, \beta] . Then the distance of the point (α,β)(\alpha, \beta) from the line 3x+4y+12=03x + 4y + 12 = 0 is
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