JEE Main 2021 (Online) 27th August Morning Shift | Complex Numbers Question 42 | Mathematics

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JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :

S contains exactly two elements

S contains only one element

S is a circle in the complex plane

S is a straight line in the complex plane

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

If $${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$$, then p and q are roots of the equation :

$${x^2} - \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$

$${x^2} + \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$

$${x^2} + \left( {\sqrt 3 - 1} \right)x - \sqrt 3 = 0$$

$${x^2} - \left( {\sqrt 3 + 1} \right)x + \sqrt 3 = 0$$

JEE Main 2021 (Online) 26th August Morning Shift

MCQ (Single Correct Answer)

-1

The equation $$\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$$ represents a circle with :

centre at (0, $$-$$1) and radius $$\sqrt 2 $$

centre at (0, 1) and radius $$\sqrt 2 $$

centre (0, 0) and radius $$\sqrt 2 $$

centre at (0, 1) and radius 2

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

Let C be the set of all complex numbers. Let

S₁ = {z$$\in$$C : |z $$-$$ 2| $$\le$$ 1} and

S₂ = {z$$\in$$C : z(1 + i) + $$\overline z $$(1 $$-$$ i) $$\ge$$ 4}.

Then, the maximum value of $${\left| {z - {5 \over 2}} \right|^2}$$ for z$$\in$$S₁ $$\cap$$ S₂ is equal to :

$${{3 + 2\sqrt 2 } \over 4}$$

$${{5 + 2\sqrt 2 } \over 2}$$

$${{3 + 2\sqrt 2 } \over 2}$$

$${{5 + 2\sqrt 2 } \over 4}$$

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