YESPYQ Start Practice
🛠️ JEE➗ Maths

Let \(f:\mathrm{ℝ}\to \mathrm{ℝ}\) be a function defined by \(f(x)=\left{\begin{matrix}{x}^{2}\sin \left(\frac{\pi }{{x}…

Q1

Let \(f:\mathrm{ℝ}\to \mathrm{ℝ}\) be a function defined by

\(f(x)=\left{\begin{matrix}{x}^{2}\sin \left(\frac{\pi }{{x}^{2}}\right), & ifx\neq 0, \\ 0, & ifx=0.\end{matrix}\right.\)

Then which of the following statements is TRUE?

a

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

b

f(x) = 0 has not solutions in the interval \([\frac{1}{\pi },\infty )\).

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 \(\left(\frac{1}{{\pi }^{2}},\frac{1}{\pi }\right)\).

🔒
Answer & explanation — PYQ Pass

Options are free to see. Unlock the correct answer and full explanation with Pass.

Unlock · ₹149
← Previous questionNext question →

Practice more JEE Maths PYQs

See every question on Trigonometric Functions, or browse the full JEE question bank.

See all questions on Trigonometric Functions →