1
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$f(x)=\operatorname{cosec}^{-1}\left[\frac{10}{6 \sin \left(2^x\right)-8 \cos \left(2^x\right)}\right]$$, then $$f^{\prime}(x)=$$

A
$$2^x \log 2$$
B
$$-1$$
C
$$\log 2$$
D
$$2^x$$
2
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\log \sqrt{\tan x}$$, then the value of $$\frac{d y}{d x}$$ at $$x=\frac{\pi}{4}$$ is

A
1
B
$$-1$$
C
$$\frac{1}{2}$$
D
0
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{x}=\mathrm{a}\left(\mathrm{t}-\frac{1}{\mathrm{t}}\right)$$ and $$\mathrm{y}=\mathrm{b}\left(\mathrm{t}+\frac{1}{\mathrm{t}}\right)$$, then $$\frac{\mathrm{dy}}{\mathrm{dx}}=$$

A
$$\frac{a^2 x}{b^2 y}$$
B
$$\frac{a^2 y}{b^2 x}$$
C
$$\frac{-b^2 x}{a^2 y}$$
D
$$\frac{b^2 x}{a^2 y}$$
4
MHT CET 2021 22th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\tan ^{-1} \sqrt{\frac{1+\cos x}{1-\cos x}}$$, then $$\frac{d y}{d x}=$$

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