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Let [t] denote the greatest integer

Question:

Let $[t]$ denote the greatest integer $\leq t$ and $\lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A$. Then the function, $\mathrm{f}(\mathrm{x})=\left[\mathrm{x}^{2}\right] \sin (\pi \mathrm{x})$ is discontinuous, when $\mathrm{x}$ is equal to :

  1. $\sqrt{\mathrm{A}+5}$

  2. $\sqrt{\mathrm{A}+1}$

  3. $\sqrt{\mathrm{A}}$

  4. $\sqrt{\mathrm{A}+21}$


Correct Option: , 2

Solution:

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