1
MHT CET 2021 21th September Evening Shift
+2
-0

If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$

A
$${1 \over {1 + {x^2}}}$$
B
$${1 \over {\sqrt {1 - {x^2}} }}$$
C
$$- 1$$
D
None of these
2
MHT CET 2021 21th September Morning Shift
+2
-0

If $$e^{-y} \cdot y=x$$, then $$\frac{d y}{d x}$$ is

A
$$\frac{y}{1-y}$$
B
$$\frac{1}{x y(1-y)}$$
C
$$\frac{1}{x(1-y)}$$
D
$$\frac{y}{x(1-y)}$$
3
MHT CET 2021 21th September Morning Shift
+2
-0

If $$y=\operatorname{cosec}^{-1}\left[\frac{\sqrt{x}+1}{\sqrt{x}-1}\right]+\cos ^{-1}\left[\frac{\sqrt{x}-1}{\sqrt{x}+1}\right]$$, then $$\frac{d y}{d x}=$$

A
0
B
1
C
$$\frac{2}{\sqrt{x}+1}$$
D
$$\frac{1}{2(\sqrt{x}-1)}$$
4
MHT CET 2021 21th September Morning Shift
+2
-0

The derivative of $$(\log x)^x$$ with respect to $$\log x$$ is

A
$$(\log x)^x\left[\frac{1}{\log x} \log (\log x)\right]$$
B
$$(\log x)^x\left[\log x+\frac{1}{\log (\log x)}\right]$$
C
$$x(\log x)^x\left[\frac{1}{\log x}+\log (\log x)\right]$$
D
$$x(\log x)^x\left[\log x+\frac{1}{\log (\log x)}\right]$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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