1
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let S1, S2 and S3 be three sets defined as

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

S2 = {z$$\in$$C : Re((1 $$-$$ i)z) $$ \ge $$ 1}

S3 = {z$$\in$$C : Im(z) $$ \le $$ 1}

Then the set S1 $$\cap$$ S2 $$\cap$$ S3 :
A
has exactly three elements
B
is a singleton
C
has infinitely many elements
D
has exactly two elements
2
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :
A
1
B
$${1 \over 2}$$| z |2
C
$${1 \over 2}$$| z + iz |2
D
$${1 \over 2}$$
3
JEE Main 2021 (Online) 16th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
The least value of |z| where z is complex number which satisfies the inequality $$\exp \left( {{{(|z| + 3)(|z| - 1)} \over {||z| + 1|}}{{\log }_e}2} \right) \ge {\log _{\sqrt 2 }}|5\sqrt 7 + 9i|,i = \sqrt { - 1} $$, is equal to :
A
8
B
3
C
2
D
$$\sqrt 5 $$
4
JEE Main 2021 (Online) 16th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let a complex number z, |z| $$\ne$$ 1,

satisfy $${\log _{{1 \over {\sqrt 2 }}}}\left( {{{|z| + 11} \over {{{(|z| - 1)}^2}}}} \right) \le 2$$. Then, the largest value of |z| is equal to ____________.
A
5
B
8
C
6
D
7
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