1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The projection of $\overline{\mathrm{AB}}$ on $\overline{\mathrm{CD}}$, where $A \equiv(2,-3,0), B \equiv(1,-4,-2), C \equiv(4,6,8)$ and $\mathrm{D} \equiv(7,0,10)$ is

A
$\frac{1}{\sqrt{6}}$
B
$\frac{1}{7}$
C
$\frac{4}{\sqrt{6}}$
D
$\frac{4}{7}$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of the plane through the point $(2,-1,-3)$ and parallel to the lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and $\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}$ is

A
$8 x+y-13 z+27=0$
B
$2 x+y+z=0$
C
$3 x-y-z-10=0$
D
$8 x+14 y+13 z+37=0$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $x, y, z$ are in Arithmetic Progression and $\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$ are also in Arithmetic progression, where $x, z>0$ and $x z<1, y<1$, then

A
$x=y=z$
B
$2 x=3 y=6 z$
C
$6 x=3 y=2 z$
D
$6 x=4 y=3 z$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Derivative of $\tan ^{-1} \sqrt{\frac{1-x}{1+x}}$ w.r.t. $\cos ^{-1}\left(4 x^3-3 x\right)$ is

A
$\frac{-1}{6}$
B
$\frac{2}{3}$
C
$\frac{3}{2}$
D
$\frac{1}{6}$
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