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

Let $P(3,2,6)$ be a point in space and $Q$ be a point on the line $\bar{r}=\hat{i}-\hat{j}+2 \hat{k}+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which the vector $\overline{\mathrm{PQ}}$ is parallel to the plane $x-4 y+3 z=1$ is

A
$\frac{1}{4}$
B
$-\frac{1}{4}$
C
$\frac{1}{8}$
D
$-\frac{1}{8}$
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