1
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
$$\begin{aligned} & \mathrm{f}(x)=(\cos x+\mathrm{i} \sin x) \cdot(\cos 3 x+\mathrm{i} \sin 3 x) \cdots {[\cos (2 \mathrm{n}-1) x+\mathrm{i} \sin (2 \mathrm{n}-1) x] \mathrm{n} \in \mathbb{N}} \end{aligned}$$

Then $\mathrm{f}^{\prime \prime}(x)=$ _______ , (Where $\mathrm{i}=\sqrt{-1}$ )
A
$\quad \mathrm{n}^2 \mathrm{f}(x)$
B
$\quad-\mathrm{n}^4 \mathrm{f}(x)$
C
$\quad-\mathrm{n}^2 \mathrm{f}(x)$
D
$\mathrm{n}^4 \mathrm{f}(x)$
2
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The modulus of the square root of the conjugate of $-7+24 \sqrt{-1}$ is __________
A
3
B
4
C
16
D
5
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $z_1=5-2 i$ and $z_2=3+i$, where $i=\sqrt{-1}$, then $\arg \left(\frac{z_1+z_2}{z_1-z_2}\right)$ is

A
$\tan ^{-1}\left(\frac{22}{19}\right)$
B
$\tan ^{-1}\left(\frac{22}{13}\right)$
C
$\tan ^{-1}\left(\frac{21}{19}\right)$
D
$\tan ^{-1}\left(\frac{19}{22}\right)$
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{z}=x+\mathrm{i} y$ be a complex number, where $x$ and $y$ are integers and $i=\sqrt{-1}$. Then the area of the rectangle whose vertices are the roots of the equation $\overline{z z}^3+\overline{\mathrm{zz}}^3=350$ is

A
48
B
32
C
40
D
80
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