1
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\frac{\pi}{3}$$ is

A
$$\frac{1}{2}$$
B
$$-\frac{1}{2}$$
C
$$2$$
D
$$\frac{1}{4}$$
2
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$$ then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

A
$$\frac{-x}{\sqrt{1-x^2}}$$
B
$$\frac{-2 x}{\sqrt{1-x^2}}$$
C
$$\frac{-1}{\sqrt{1-x^2}}$$
D
$$\frac{1}{\sqrt{1-x^2}}$$
3
MHT CET 2022 11th August Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y^{\frac{1}{m}}+y^{\frac{-1}{m}}=2 x, x \neq 1$$, then $$\left(x^2-1\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2$$ is equal to

A
$$m y^2$$
B
$$m^2 y$$
C
$$m^2 y^2$$
D
$$\frac{m y^2}{2}$$
4
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=1+x e^y$$, then $$\frac{d y}{d x}=$$

A
$$\frac{e^y}{2-y}$$
B
$$\frac{e^y}{2+y}$$
C
$$\frac{e^y}{1-e^y}$$
D
$$\frac{e^y}{1+e^y}$$
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