1
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

Let O be the origin and A be the point $${z_1} = 1 + 2i$$. If B is the point $${z_2}$$, $${\mathop{\rm Re}\nolimits} ({z_2}) < 0$$, such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

A
$$\arg {z_2} = \pi - {\tan ^{ - 1}}3$$
B
$$\arg ({z_1} - 2{z_2}) = - {\tan ^{ - 1}}{4 \over 3}$$
C
$$|{z_2}| = \sqrt {10}$$
D
$$|2{z_1} - {z_2}| = 5$$
2
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
$$\frac{9}{2}$$
3
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
4
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
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