1
MHT CET 2023 11th May Morning Shift
+2
-0

$$\lim _\limits{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x^3-3 x^2+2 x}\right]$$ is equal to

A
$$\frac{2}{3}$$
B
$$\frac{-2}{3}$$
C
$$\frac{3}{2}$$
D
$$\frac{-3}{2}$$
2
MHT CET 2023 11th May Morning Shift
+2
-0

The left-hand derivative of $$\mathrm{f}(x)=[x] \sin (\pi x)$$, at $$x=\mathrm{k}, \mathrm{k}$$ is an integer and [.] is the greatest integer function, is

A
$$(-1)^{\mathrm{k}}(\mathrm{k}-1) \pi$$
B
$$(-1)^{\mathrm{k}-1}(\mathrm{k}-1) \pi$$
C
$$(-1)^{\mathrm{k}} \mathrm{k} \pi$$
D
$$(-1)^{\mathrm{k}-\mathrm{l}} \mathrm{k} \pi$$
3
MHT CET 2023 11th May Morning Shift
+2
-0

If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+\mathrm{m} x}-\sqrt{1-\mathrm{m} x}}{x}, & -1 \leq x < 0 \\ \frac{2 x+1}{x-2} & , 0 \leq x \leq 1\end{array}\right.$$ is continuous in the interval $$[-1,1]$$, then $$\mathrm{m}$$ is equal to

A
$$\frac{1}{2}$$
B
$$-\frac{1}{2}$$
C
$$-1$$
D
$$-\frac{1}{4}$$
4
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
$$\{0, \pi\}$$
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