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

The value of $\tan ^{-1}(-\sqrt{3})-\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(\frac{-1}{2}\right)$ is

A
$\frac{-\pi}{4}$
B
$\frac{4 \pi}{3}$
C
$\frac{\pi}{12}$
D
$\frac{7 \pi}{12}$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=y \tan x-y^2 \sec x$ is

A
$\tan x=(\mathrm{c}+\sec x) y$, where c is constant of integration.
B
$\sec y=(\mathrm{c}+\tan y) x$, where c is constant of integration.
C
$\sec x=(\mathrm{c}+\tan x) y$, where c is constant of integration.
D
$\cos y=(\mathrm{c}+\tan y)$, where c is constant of integration.
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are three vectors such that $\overline{\mathrm{a}} \neq \overline{0}$ and $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=2 \overline{\mathrm{a}} \times \overline{\mathrm{c}},|\overline{\mathrm{a}}|=|\overline{\mathrm{c}}|=1,|\overline{\mathrm{~b}}|=4$ and $|\overline{\mathrm{b}} \times \overline{\mathrm{c}}|=\sqrt{15}$. If $\overline{\mathrm{b}}-2 \overline{\mathrm{c}}=\lambda \overline{\mathrm{a}}$, then $\lambda$ is

A
1
B
$-$4
C
3
D
$-$2
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Two friends A and B apply for a job in the same company. The probabilities of A getting selected is $\frac{2}{5}$ and that of B is $\frac{4}{7}$. Then the probability, that one of them is selected, is

A
$\frac{8}{35}$
B
$\frac{18}{35}$
C
$\frac{26}{35}$
D
$\frac{34}{35}$
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