1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the foot of the perpendicular from the point $(0,2,3)$ on the line $\frac{x+3}{5}=\frac{y+1}{2}=\frac{z+4}{3}$ is

A
$\left(\frac{48}{19}, \frac{23}{19}, \frac{-13}{19}\right)$
B
$\left(\frac{-48}{19}, \frac{23}{19}, \frac{-13}{19}\right)$
C
$\left(\frac{-48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$
D
$\left(\frac{48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line having direction ratios $1,-4,2$ intersects the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the points $A$ and $B$ resp., then co-ordinates of points A and B are

A
$\mathrm{A}(-8,6,-7)\qquad$ $\mathrm{B}(-6,-2,-3)$
B
$\mathrm{A}(8,6,7)\qquad$ $\mathrm{B(6,2,3)}$
C
$\mathrm{A}(8,6,7)\qquad$ $\mathrm{B}(6,-2,-3)$
D
$\mathrm{A}(7,6,8)\qquad$ $\mathrm{B}(-3,-2,6)$
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A plane makes positive intercepts of unit length on each of $X$ and $Y$ axis. If it passes through the point $(-1,1,2)$ and makes angle $\theta$ with the X -axis, then $\theta$ is

A
$\cos ^{-1}\left(\frac{2}{3}\right)$
B
$\cos ^{-1}\left(\frac{1}{3}\right)$
C
$\sin ^{-1}\left(\frac{1}{3}\right)$
D
$\sin ^{-1}\left(\frac{2}{3}\right)$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of plane through the point $(2,-1,-3)$ and parallel to 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
$8 x+14 y+13 z-37=0$
B
$8 x-14 y-13 z-34=0$
C
$8 x-14 y-13 z+37=0$
D
$8 x+14 y+13 z+37=0$
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