1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)\left(8 x^3-\pi^3\right) \cos x}{(\pi-2 x)^4}$$

A
$\frac{\pi^2}{16}$
B
$\frac{3 \pi^2}{16}$
C
$\frac{-3 \pi^2}{16}$
D
$\frac{-\pi^2}{16}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{d x}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)}$ is equal to

A
$\frac{1}{5}\left(\frac{\pi}{4}-\tan ^{-1}\left(\frac{1}{3 \sqrt{3}}\right)\right)$
B
$\frac{1}{10}\left(\frac{\pi}{4}-\tan ^{-1}\left(\frac{1}{9 \sqrt{3}}\right)\right)$
C
$\frac{1}{20} \tan ^{-1}\left(\frac{1}{9 \sqrt{3}}\right)$
D
$\frac{\pi}{40}$
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the circle, concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the $\mathrm{X}$-axis is

A
$x^2+y^2-6 x-4 y+5=0$
B
$x^2+y^2-6 x-4 y+17=0$
C
$x^2+y^2-6 x-4 y+9=0$
D
$x^2+y^2-6 x-4 y+4=0$
4
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{f}(x)=\mathrm{e}^x, \mathrm{~g}(x)=\sin ^{-1} x$ and $\mathrm{h}(x)=\mathrm{f}(\mathrm{g}(x))$, then $\left(\frac{h^{\prime}(x)}{h(x)}\right)^2$ is equal to

A
$\frac{1}{\sqrt{1-x^2}}$
B
$\left(1-x^2\right)^2$
C
$\frac{1}{1-x^2}$
D
$\left(1-x^2\right)$
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