1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\cos ^{-1} x=\alpha(0< x < 1)$ and $\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)+\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)=\frac{2 \pi}{3}$, then $\alpha$ is

A
$\frac{\pi}{2}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{4}$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the points $\mathrm{P}, \mathrm{Q}$ and R are with the position vectors $\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $-8 \hat{i}+13 \hat{j}$ respectively, then these points are

A
collinear and $Q$ lies between $P$ and $R$.
B
collinear and $R$ lies between $P$ and $Q$.
C
collinear and $P$ lies between $Q$ and $R$.
D
non-collinear.
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line makes $45^{\circ}$ angle with positive X -axis and makes equal angles with positive Y -axis ad Z-axis respectively, then the sum of the three angles which the line makes with positive X -axis, Y -axis and Z -axis is

A
$135^{\circ}$
B
$150^{\circ}$
C
$165^{\circ}$
D
$180^{\circ}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then k has the value

A
$\frac{7}{2}$
B
$\frac{3}{2}$
C
$\frac{-7}{2}$
D
$\frac{-3}{2}$
MHT CET Papers
EXAM MAP