Let f : R arrow R be a function defined by f(x) = begincases x^2 sin ((π)/(x^2) ), & if x ≠ 0, \ 0, & if x = 0. endcases Then which of the following statements is TRUE?

f(x) = 0 has more than 25 solutions in the interval (1/(π^2), 1/(π) ).

f(x) = 0 has infinitely many solutions in the interval [dfrac110^10, ∞ ).

f(x) = 0 has no solutions in the interval [1/(π), ∞ ).

The set of solutions of f(x) = 0 in the interval (0, dfrac110^10 ) is finite.

Let f : R arrow R be a function defined by f(x) =… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 2

Let

f : \mathbb{R} \rightarrow \mathbb{R}

be a function defined by

f(x) = \begin{cases} x^2 \sin\left(\dfrac{\pi}{x^2}\right), & \text{if } x \neq 0, \\ 0, & \text{if } x = 0. \end{cases}

Then which of the following statements is TRUE?

A.
$f(x) = 0$ has infinitely many solutions in the interval $\left[\dfrac{1}{10^{10}}, \infty\right)$ .
B.
$f(x) = 0$ has no solutions in the interval $\left[\dfrac{1}{\pi}, \infty\right)$ .
C.
The set of solutions of $f(x) = 0$ in the interval $\left(0, \dfrac{1}{10^{10}}\right)$ is finite.
D.
$f(x) = 0$ has more than 25 solutions in the interval $\left(\dfrac{1}{\pi^2}, \dfrac{1}{\pi}\right)$ .

Show answer

Correct option: D

[JEE Advanced 2024 · Paper 2]

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