1
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the volume of tetrahedron whose vertices are $A \equiv(1,-6,10), B \equiv(-1,-3,7), C \equiv(5,-1, k)$ and $D \equiv(7,-4,7)$ is 11 cu . units, then the value of $k$ is

A
7
B
5
C
3
D
1
2
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ is

A
$\frac{9}{4}$
B
$\frac{4}{9}$
C
$\frac{27}{4}$
D
$\frac{4}{27}$
3
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$$ \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)=$$

A
$\frac{1}{2 \sqrt{2}}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{1}{2}$
D
$\frac{\sqrt{3}}{2}$
4
MHT CET 2024 11th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $5 \bar{a}+4 \bar{b}$ and $\bar{a}-2 \bar{b}$ are perpendicular to each other, then the between $\bar{a}$ and $\bar{b}$ is

A
$\frac{2 \pi}{3}$
B
$\cos ^{-1}\left(\frac{2}{3}\right)$
C
$\frac{\pi}{3}$
D
$\cos ^{-1}\left(\frac{1}{3}\right)$
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