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

If $A\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ then $\left(A^2-5 A\right)^{-1}$ is

A
$\left(-\frac{1}{4}\right)\left[\begin{array}{cc}-3 & 1 \\ 7 & -1\end{array}\right]$
B
$\left(\frac{1}{4}\right)\left[\begin{array}{cc}-3 & 1 \\ 7 & -1\end{array}\right]$
C
$\left(\frac{1}{4}\right)\left[\begin{array}{ll}3 & 1 \\ 7 & 1\end{array}\right]$
D
$\left(\frac{1}{-4}\right)\left[\begin{array}{ll}3 & -1 \\ 7 & -1\end{array}\right]$
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The following statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow((\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{q})$ is

A
a fallacy.
B
equivalent to $(\sim \mathrm{p}) \rightarrow \mathrm{q}$.
C
equivalent to $\mathrm{p} \rightarrow(\sim \mathrm{q})$.
D
a tautology.
3
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\omega=-\frac{1}{2}+\mathrm{i} \frac{\sqrt{3}}{2}, \mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega^4\end{array}\right|$ is

A
$3 \omega$
B
$3 \omega(\omega-1)$
C
$3 \omega^2$
D
$3 \omega(1-\omega)$
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let f be twice differentiable function such that $\mathrm{f}^{\prime \prime}(x)=-\mathrm{f}(x), \mathrm{f}^{\prime}(x)=\mathrm{g}(x)$ and $\mathrm{h}(x)=(\mathrm{f}(x))^2+(\mathrm{g}(x))^2$. If $\mathrm{h}(5)=1$, then the value of $h(10)$ is

A
2
B
1
C
$\frac{1}{2}$
D
$-1$
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