1
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$a,b$$ be two real numbers such that $$ab < 0$$. IF the complex number $$\frac{1+ai}{b+i}$$ is of unit modulus and $$a+ib$$ lies on the circle $$|z-1|=|2z|$$, then a possible value of $$\frac{1+[a]}{4b}$$, where $$[t]$$ is greatest integer function, is :

A
$\left(\frac{1+\sqrt{7}}{4}\right)$
B
$$\frac{1}{2}$$
C
0
D
$$-$$1
2
JEE Main 2023 (Online) 1st February Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the center and radius of the circle $$\left| {{{z - 2} \over {z - 3}}} \right| = 2$$ are respectively $$(\alpha,\beta)$$ and $$\gamma$$, then $$3(\alpha+\beta+\gamma)$$ is equal to :

A
12
B
10
C
11
D
9
3
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :
A
$\cos \frac{\pi}{12}-i \sin \frac{\pi}{12}$
B
$\sqrt{2}\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{12}\right)$
C
$\sqrt{2} i\left(\cos \frac{5 \pi}{12}-i \sin \frac{5 \pi}{12}\right)$
D
$\sqrt{2}\left(\cos \frac{5 \pi}{12}+i \sin \frac{5 \pi}{12}\right)$
4
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For all $$z \in C$$ on the curve $$C_{1}:|z|=4$$, let the locus of the point $$z+\frac{1}{z}$$ be the curve $$\mathrm{C}_{2}$$. Then :

A
the curves $$C_{1}$$ and $$C_{2}$$ intersect at 4 points
B
the curve $$C_{2}$$ lies inside $$C_{1}$$
C
the curve $$C_{1}$$ lies inside $$C_{2}$$
D
the curves $$C_{1}$$ and $$C_{2}$$ intersect at 2 points
JEE Main Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12