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

If $$y=x \tan y$$, then $$\frac{d y}{d x}=$$

A
$$\frac{\tan x}{x-y^2}$$
B
$$\frac{y}{x-x^2-y^2}$$
C
$$\frac{\tan x}{x-x^2-y^2}$$
D
$$\frac{\tan y}{y-x}$$
2
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

The derivative of the function $$\cot ^{-1}\left[(\cos 2 x)^{1 / 2}\right]$$ at $$x=\pi / 6$$ is

A
$$\left(\frac{1}{3}\right)^{1 / 2}$$
B
$$\left(\frac{2}{3}\right)^{1 / 2}$$
C
$$\left(\frac{3}{2}\right)^{1 / 2}$$
D
$$(3)^{1 / 2}$$
3
MHT CET 2021 23rd September Evening Shift
MCQ (Single Correct Answer)
+2
-0

For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is

A
$$\frac{1}{3}$$
B
0
C
3
D
1
4
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
$$2^x$$
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