1
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the planes $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}})=3$ and $\overline{\mathrm{r}} \cdot(4 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\mu \hat{\mathrm{k}})=5$ are parallel, then $\lambda+\mu=$

A
$\frac{1}{2}$
B
2
C
$\frac{5}{2}$
D
$\frac{7}{2}$
2
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The perimeter of a square whose two sides have equations $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{4}$ and $\frac{x}{2}=\frac{y-1}{3}=\frac{z+1}{4}$ is

A
$\frac{\sqrt{673}}{\sqrt{29}}$ units
B
$\frac{4 \sqrt{673}}{\sqrt{29}}$ units
C
$\frac{4 \sqrt{573}}{\sqrt{29}}$ units
D
$\frac{4}{\sqrt{29}}$ units
3
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the sum of the squares of the distances of a point $\mathrm{P}(x, y, z)$ from the three co-ordinate axes is 324 , then the distance of point P from the origin is ….

A
18
B
162
C
$9 \sqrt{2}$
D
324
4
MHT CET 2025 22nd April Morning Shift
MCQ (Single Correct Answer)
+2
-0

The angle between the lines $3 x=2 y=-\mathrm{z}$ and $-x=6 y=-4 z$ is

A
$\frac{\pi}{3}$
B
$\frac{\pi}{4}$
C
$\frac{\pi}{2}$
D
$\frac{\pi}{6}$
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