1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{f}(x)=\cos ^{-1} x, \mathrm{~g}(x)=\mathrm{e}^x$ and $\mathrm{h}(x)=\mathrm{g}(\mathrm{f}(x))$, then $\frac{\mathrm{h}^{\prime}(x)}{\mathrm{h}(x)}=$

A
$\frac{-1}{\sqrt{1-x^2}}$
B
$\frac{-(\mathrm{e})^{\left(\cos ^{-1} x\right)}}{\sqrt{1-x^2}}$
C
$\frac{-1}{\sqrt{1-x^2}} \mathrm{e}^x$
D
$-\sqrt{1-x^2}$
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\cot \left(\operatorname{cosec}^{-1} \frac{5}{3}+\tan ^{-1} \frac{2}{3}\right)$ is

A
$\frac{5}{17}$
B
$\frac{6}{17}$
C
$\frac{3}{17}$
D
$\frac{4}{17}$
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\sin \left(\cot ^{-1}(x+1)\right)=\cos \left(\tan ^{-1} x\right)$ then considering positive square roots, $x$ has the value ___________

A
0
B
$\frac{9}{4}$
C
$\frac{1}{2}$
D
$-\frac{1}{2}$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Considering only the Principal values of inverse functions, the set

$$A=\left\{x \geq 0 \left\lvert\, \tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\right.\right\}$$

A
contains two elements.
B
contains more than two elements.
C
is an empty set.
D
is a singleton set.
MHT CET Subjects
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