1
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}$$, then $$\cos ^2 48^{\circ}-\sin ^2 12^{\circ}$$ has the value

A
$$\frac{-\sqrt{5}+1}{8}$$
B
$$\frac{\sqrt{5}-1}{8}$$
C
$$\frac{\sqrt{5}+1}{8}$$
D
$$\frac{-1-\sqrt{5}}{8}$$
2
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$A=\left[\begin{array}{cc}2 & -1 \\ -1 & 3\end{array}\right]$$, then the inverse of $$\left(2 A^2+5 A\right)$$ is

A
$$\frac{1}{95}\left[\begin{array}{ll}7 & 3 \\ 3 & 4\end{array}\right]$$
B
$$\frac{1}{95}\left[\begin{array}{cc}-7 & 3 \\ 3 & -4\end{array}\right]$$
C
$$\frac{1}{95}\left[\begin{array}{cc}-7 & -3 \\ 3 & 4\end{array}\right]$$
D
$$\frac{1}{95}\left[\begin{array}{ll}4 & 3 \\ 3 & 7\end{array}\right]$$
3
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$ I=\int \frac{\sin x+\sin ^3 x}{\cos 2 x} d x=P \cos x+Q \log \left|\frac{\sqrt{2} \cos x-1}{\sqrt{2} \cos x+1}\right| $$ (where $$c$$ is a constant of integration), then values of $$\mathrm{P}$$ and $$\mathrm{Q}$$ are respectively

A
$$\frac{1}{2}, \frac{3}{4 \sqrt{2}}$$
B
$$\frac{1}{2}, \frac{-3}{4 \sqrt{2}}$$
C
$$\frac{1}{2}, \frac{3}{2 \sqrt{2}}$$
D
$$\frac{1}{2}, \frac{-3}{2 \sqrt{2}}$$
4
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The negation of the statement $$(p \wedge q) \rightarrow(\sim p \vee r)$$ is

A
$$p \vee q \vee \sim r$$
B
$$\mathrm{p} \wedge \mathrm{q} \wedge \sim \mathrm{r}$$
C
$$\sim p \vee q \wedge r$$
D
$$ \sim p \vee \sim q \vee \sim r$$
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