1
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The set of all points, where the derivative of the functions $$\mathrm{f}(x)=\frac{x}{1+|x|}$$ exists, is

A
$$(-\infty, \infty)$$
B
$$[0, \infty)$$
C
$$(-\infty, 0) \cup(0, \infty)$$
D
$$(0, \infty)$$
2
MHT CET 2023 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=[(x+1)(2 x+1)(3 x+1) \ldots(\mathrm{n} x+1)]^{\frac{3}{2}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=0$$ is

A
$$\frac{3 \mathrm{n}(\mathrm{n}+1)}{4}$$
B
$$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$$
C
$$\frac{3 \mathrm{n}(\mathrm{n}+1)}{2}$$
D
$$\frac{\mathrm{n}(\mathrm{n}+1)}{4}$$
3
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\log _{\sin x} \tan x$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{x=\frac{\pi}{4}}$$ has the value

A
$$\frac{4}{\log 2}$$
B
$$-3 \log 2$$
C
$$\frac{-4}{\log 2}$$
D
$$3 \log 2$$
4
MHT CET 2023 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\mathrm{f}(x)=\log (\sin x), 0 < x < \pi$$ and $$\mathrm{g}(x)=\sin ^{-1}\left(\mathrm{e}^{-x}\right), x \geq 0$$. If $$\alpha$$ is a positive real number such that $$\mathrm{a}=(\mathrm{fog})^{\prime}(\alpha)$$ and $$\mathrm{b}=(\mathrm{fog})(\alpha)$$, then

A
$$a \alpha^2-b \alpha-a=0$$
B
$$\mathrm{a} \alpha^2-\mathrm{b} \alpha-\mathrm{a}=1$$
C
$$a \alpha^2+b \alpha-a=-2 \alpha^2$$
D
$$\mathrm{a} \alpha^2+\mathrm{b} \alpha+\mathrm{a}=0$$
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