1
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $0< x < 1$, then

$$\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{\frac{1}{2}}=$$

A
$\frac{x}{\sqrt{1+x^2}}$
B
$x$
C
$\sqrt{1+x^2}$
D
$x \sqrt{1+x^2}$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\tan ^{-1}\left(\frac{3+2 x}{2-3 x}\right)+\tan ^{-1}\left(\frac{3 x}{1+4 x^2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ is equal to

A
$\frac{1}{1+16 x^2}$
B
$\frac{4}{1+16 x^2}$
C
$\frac{1}{1+4 x^2}$
D
$\frac{4}{1+4 x^2}$
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

A
one
B
zero
C
two
D
infinite
4
MHT CET 2024 2nd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right)+\tan \left(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)\right)$ is

A
$\frac{2 a}{b}$
B
$\frac{2 \mathrm{~b}}{\mathrm{a}}$
C
$\frac{\mathrm{a}}{\mathrm{b}}$
D
$\frac{\mathrm{b}}{\mathrm{a}}$
MHT CET Subjects
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