Let f: \to  be a function defined by f(x)={\\begin{array}{c}x^2 \sin \\ (\\\{\pi\end\frac{array}{x^2}) , \text{ if } x \neq 0{,} ; 0{,} , \text{ if } x=0 . Then which of the following statements is TRUE? [JEE Adv 2024 P2]

Correct Answer is : f(x)=0 has more than 25 solutions in the interval (1π2,1π).

f(x)=0 has infinitely many solutions in the interval [\frac{1}{10^{10}}, \infty).

f(x)=0 has no solutions in the interval [\frac{1}{\pi}, \infty).

The set of solutions of f(x)=0 in the interval (0, \frac{1}{10^{10}}) is finite.

f(x)=0 has more than 25 solutions in the interval (\frac{1}{\pi^2}, \frac{1}{\pi}).

Limits, Continuity and Differentiability

Section: Mathematics

Question : 6 of 51

Marks: +1, -0

Let f: →  be a function defined by
f(x)={

x2sin‌(‌

)

‌ if ‌x≠0,

‌ if ‌x=0.

Then which of the following statements is TRUE?

[JEE Adv 2024 P2]

Go to Question:

Prev Question

Next Question