For a real number $x$ let $[x]$ denote the largest number less than or equal to $x$. For $x \in R$ let $f(x)=[x] \sin \pi x$. Then,
For a real number $x$ let $[x]$ denote the largest number less than or equal to $x$. For $x \in R$ let $f(x)=[x] \sin \pi x$. Then,
- [KVPY 2014]
- A
$f$ is differentiable on $R$.
- B
$f$ is symmetric about the line $x=0$.
- C
$\int \limits_{-3}^3 f(x) d x=0$
- D
For each real $\alpha$, the equation $f(x)-\alpha=0$ has infinitely many roots.
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