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Limits Continuity and Differentiability question

2024 · Shift 2 · Q21

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JEE Advanced
Mathematics
Limits Continuity and Differentiability
2024 · Shift 2 · Q21

Limits Continuity and Differentiability question

2024 · Shift 2 · Q21

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMCQ+3 / −1

Let

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

be a function defined by

f(x)=\left\{\begin{array}{cc} x^2 \sin \left(\frac{\pi}{x^2}\right), & \text { if } x eq 0, \\ 0, & \text { if } x=0 . \end{array}\right.

Then which of the following statements is TRUE?

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

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