1
MHT CET 2023 10th May Evening Shift
+2
-0

Let $$\mathrm{S}=\left\{\mathrm{t} \in \mathrm{R} / \mathrm{f}(x)=|x-\pi|\left(\mathrm{e}^{|x|}-1\right) \sin |x|\right.$$ is not differentiable at $$\mathrm{t}\}$$, then $$\mathrm{S}$$ is

A
$$\phi$$ (an empty set)
B
$$\{0\}$$
C
$$\{\pi\}$$
D
$$\{0, \pi\}$$
2
MHT CET 2023 10th May Evening Shift
+2
-0

If $$\mathrm{f}(x)=\frac{4}{x^4}\left[1-\cos \frac{x}{2}-\cos \frac{x}{4}+\cos \frac{x}{2} \cdot \cos \frac{x}{4}\right]$$ is continuous at $$x=0$$, then $$\mathrm{f}(0)$$ is

A
$$\frac{1}{32}$$
B
$$\frac{1}{16}$$
C
$$\frac{1}{8}$$
D
$$\frac{1}{64}$$
3
MHT CET 2023 10th May Evening Shift
+2
-0

$$\lim _\limits{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}=$$

A
$$\frac{1}{3 \sqrt{3}}$$
B
$$\frac{2}{\sqrt{3}}$$
C
$$\frac{2}{3 \sqrt{3}}$$
D
$$\frac{-2}{3 \sqrt{3}}$$
4
MHT CET 2023 10th May Morning Shift
+2
-0

The value of $$\lim _\limits{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}$$ is

A
$$\frac{1}{3 \sqrt{3}}$$
B
$$\frac{2}{\sqrt{3}}$$
C
$$\frac{2}{3 \sqrt{3}}$$
D
$$\frac{4}{3 \sqrt{3}}$$
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