1
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
$$\frac{m y^2}{2}$$
2
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
$$\frac{e^y}{1+e^y}$$
3
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x=e^t(\sin t-\cos t)$$ and $$y=e^t(\sin t+\cos t)$$, then $$\frac{d y}{d x}$$ at $$t=\frac{\pi}{3}$$ is

A
$$\sqrt{3}$$
B
$$\frac{1}{\sqrt{3}}$$
C
$$\frac{\sqrt{3}}{2}$$
D
$$\frac{1}{2}$$
4
MHT CET 2021 24th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sin ^2 x+\cos ^2 y=1$$, then $$\frac{d y}{d x}=$$

A
$$\frac{\sin ^2 x}{\sin ^2 y}$$
B
$$\frac{\sin ^2 y}{\sin 2 x}$$
C
$$\frac{\sin 2 x}{\sin 2 y}$$
D
$$\frac{-\sin ^2 y}{\sin ^2 x}$$
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