1
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If the lines $\frac{3-x}{2}=\frac{5 y-2}{3 \lambda+1}=5-\mathrm{z}$ and $\frac{x+2}{-1}=\frac{1-3 y}{7}=\frac{4-z}{2 \mu}$ are at right angles, then $7 \lambda-10 \mu=$
A
$143$
B
$\frac{143}{3}$
C
$137$
D
$\frac{137}{5}$
2
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If the angle $\theta$ between the line $\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2 x-y+\sqrt{\lambda} z+4=0$ is such that $\sin \theta=\frac{1}{3}$, then $\lambda+1=$
A
$\frac{5}{3}$
B
$\frac{-5}{3}$
C
$\frac{8}{3}$
D
$\frac{-8}{3}$
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If the directed line makes an angle $45^{\circ}$ and $60^{\circ}$ with the X and Y -axes respectively, then the obtuse angle $\theta$ made by the line with the Z -axis is
A
$135^{\circ}$
B
$120^{\circ}$
C
$160^{\circ}$
D
$150^{\circ}$
4
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
$\left(\frac{48}{19}, \frac{-23}{19}, \frac{-13}{19}\right)$
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