Mathematical Reasoning & Induction · JEE Advanced previous year questions

2025 1 question

1. Q82025 · 18 May 2025 · Paper 2· One or more correct

   Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to \mathbb{R}$ be defined by $$f(x)=\{\begin{array}{ll}\frac{6x+\sin x}{2x+\sin x}& \text{if }x\ne 0,\\ \frac{7}{3}& \text{if }x=0.\end{array}$$ Then which of the following statements is (are) TRUE?

   1. A.The point $x=0$ is a point of local maxima of $f$
   2. B.The point $x=0$ is a point of local minima of $f$
   3. C.Number of points of local maxima of $f$ in the interval $[\pi ,6\pi ]$ is 3
   4. D.Number of points of local minima of $f$ in the interval $[2\pi ,4\pi ]$ is 1
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   Answer: B, C, D