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JEE Advanced 2018
Paper-2 2018
Multiple correct answers - Select all that apply
Question
Let $f:(0, \pi) \rightarrow \mathrm{R}$ be a twice differentiable function such that
$ \lim _{t \rightarrow x} \frac{f(x) \sin t-f(t) \sin x}{t-x}=\sin ^2 x \text { for all } x \in(0, \pi) $
If $f\left(\frac{\pi}{6}\right)=-\frac{\pi}{12}$, then which of the following statement(s) is (are) TRUE ?
Select ALL correct options:
A
$f\left(\frac{\pi}{4}\right)=\frac{\pi}{4 \sqrt{2}}$
B
$f(x)<\frac{x^4}{6}-x^2$ for all $x \in(0, \pi)$
C
There exists $\alpha \in(0, \pi)$ such that $f^{\prime}(\alpha)=0$
D
$f^{\prime \prime}\left(\frac{\pi}{2}\right)+f\left(\frac{\pi}{2}\right)=0$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
Solution
Question Tags
JEE Advance
Mathematics
Easy
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