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

A line with positive direction cosines passes through the point $\mathrm{P}(2,1,2)$ and makes equal angles with the coordinate axes. The line meets the plane $2 x+y+\mathrm{z}=9$ at point Q . The length of the line segment PQ equals $\qquad$ units.

A
$\frac{5}{\sqrt{3}}$
B
$2 \sqrt{3}$
C
$\frac{4}{\sqrt{3}}$
D
$4 \sqrt{3}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the tangent to the curve $x=\operatorname{acos}^3 \theta, y=\operatorname{asin}^3 \theta$ at $\theta=\frac{\pi}{4}$ is

A
$x+y=\frac{\mathrm{a}}{\sqrt{2}}$
B
$x+y=\frac{a}{2}$
C
$x+y=\frac{a}{2 \sqrt{2}}$
D
$x+y=\frac{\mathrm{a}}{8}$
3
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
$\frac{-\pi^2}{16}$
4
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
$\frac{\pi}{40}$
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