1
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The area (in sq. units), in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1, x=0$ and $x=2$, is

A
$\frac{1}{3}$
B
$\frac{2}{3}$
C
$\frac{5}{3}$
D
$\frac{8}{3}$
2
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector $\bar{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and bisects the angle between $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$. Then which one of the following gives possible values of $\alpha$ and $\beta$ ?

A
$\alpha=1, \beta=1$
B
$\alpha=2, \beta=2$
C
$\alpha=1, \beta=2$
D
$\alpha=2, \beta=1$
3
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$2 \pi-\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$ is equal to

A
$\frac{\pi}{2}$
B
$\frac{5 \pi}{4}$
C
$\frac{7 \pi}{4}$
D
$\frac{3 \pi}{2}$
4
MHT CET 2024 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$, the matrix of cofactors is

A
$\left[\begin{array}{ccc}0 & 8 & -4 \\ -1 & 3 & 2 \\ 1 & -7 & 2\end{array}\right]$
B
$\left[\begin{array}{ccc}0 & -8 & 4 \\ -1 & 3 & -2 \\ 1 & -7 & 2\end{array}\right]$
C
$\left[\begin{array}{ccc}0 & 8 & -4 \\ 1 & -3 & 2 \\ -1 & 7 & -2\end{array}\right]$
D
$\left[\begin{array}{ccc}0 & -8 & 4 \\ -1 & 3 & 2 \\ -1 & -7 & 2\end{array}\right]$
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