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

Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}, \alpha, \beta \in \mathbb{R}$, I is the identity matrix of order 2 , then $4(\alpha-\beta)$ is

A
$\frac{8}{3}$
B
4
C
2
D
5
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\lim _\limits{y \rightarrow 0} \frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}=$$

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

If $\overline{\mathrm{a}}$ is perpendicular to $\bar{b}$ and $\bar{c},|\bar{a}|=2$, $|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4$ and the angle between $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ is $\frac{\pi}{3}$, then $\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]=$

A
$4 \sqrt{3}$
B
$6 \sqrt{3}$
C
$24 \sqrt{3}$
D
$12 \sqrt{3}$
4
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are $2,4,10,12,14$, then the product of remaining two observations is

A
45
B
44
C
48
D
40
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