1
MHT CET 2021 24th September Evening Shift
+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
$$\frac{1}{2}$$
2
MHT CET 2021 24th September Evening Shift
+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
$$\frac{-\sin ^2 y}{\sin ^2 x}$$
3
MHT CET 2021 24th September Morning Shift
+2
-0

$$\text { If } u=\cos ^3 x, v=\sin ^3 x \text {, then }\left(\frac{d v}{d u}\right)_{x=\frac{\pi}{4}} \text { is equal to }$$

A
$$-$$2
B
2
C
1
D
$$-$$1
4
MHT CET 2021 24th September Morning Shift
+2
-0

If $$y=\log _{10} x+\log _x 10+\log _x x+\log _{10} 10$$, then $$\frac{d y}{d x}=$$

A
$$\frac{1}{x \log _e 10}+\frac{1}{x \log _{10} e}$$
B
$$\frac{1}{x \log _e 10}+\frac{\log _e 10}{x\left(\log _{10} e\right)^2}$$
C
$$\frac{1}{x \log _e 10}-\frac{1}{x \log _{10} e}$$
D
$$\frac{1}{x \log _e 10}-\frac{\log _e 10}{x\left(\log _e x\right)^2}$$
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