1
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

For $$z \in \mathbb{C}$$ if the minimum value of $$(|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)$$ is $$5 \sqrt{2}$$, then a value Question: of $$p$$ is _____________.

A
3
B
$$\frac{7}{2}$$
C
4
D
$$\frac{9}{2}$$
2
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

If $$\alpha, \beta, \gamma, \delta$$ are the roots of the equation $$x^{4}+x^{3}+x^{2}+x+1=0$$, then $$\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$$ is equal to :

A
$$-$$4
B
$$-$$1
C
1
D
4
3
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

For $$\mathrm{n} \in \mathbf{N}$$, let $$\mathrm{S}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-3+2 i|=\frac{\mathrm{n}}{4}\right\}$$ and $$\mathrm{T}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-2+3 i|=\frac{1}{\mathrm{n}}\right\}$$. Then the number of elements in the set $$\left\{n \in \mathbf{N}: S_{n} \cap T_{n}=\phi\right\}$$ is :

A
0
B
2
C
3
D
4
4
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

The real part of the complex number $${{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }}$$ is equal to :

A
$${{500} \over {13}}$$
B
$${{110} \over {13}}$$
C
$${{55} \over {6}}$$
D
$${{550} \over {13}}$$
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