Javascript is required
1
JEE Main 2021 (Online) 16th March Evening Shift
+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
$$\sqrt 5$$
2
JEE Main 2021 (Online) 16th March Morning Shift
+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
3
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If $$\alpha$$, $$\beta$$ $$\in$$ R are such that 1 $$-$$ 2i (here i2 = $$-$$1) is a root of z2 + $$\alpha$$z + $$\beta$$ = 0, then ($$\alpha$$ $$-$$ $$\beta$$) is equal to :
A
$$-$$7
B
7
C
3
D
$$-$$3
4
JEE Main 2021 (Online) 25th February Morning Slot
Let the lines (2 $$-$$ i)z = (2 + i)$$\overline z$$ and (2 $$+$$ i)z + (i $$-$$ 2)$$\overline z$$ $$-$$ 4i = 0, (here i2 = $$-$$1) be normal to a circle C. If the line iz + $$\overline z$$ + 1 + i = 0 is tangent to this circle C, then its radius is :
$${3 \over {2\sqrt 2 }}$$
$$3\sqrt 2$$
$${1 \over {2\sqrt 2 }}$$
$${3 \over {\sqrt 2 }}$$