JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 16th March Evening ShiftQuestion 1

The least value of $|z|$ where $z$ is complex number which satisfies the inequality $\exp\left(\frac{(|z|+3)(|z|-1)}{||z|+1|}\log_e2\right)\ge\log_{\sqrt{2}}\left|5\sqrt{7}+9i\right|$, $i=\sqrt{-1}$, is equal to :

Complex Numbers

$2$$\sqrt{5}$$3$$8$

JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 2

Let the circles $C_1:|z|=r$ and $C_2:|z-3-4i|=5$, $z\in\mathbb{C}$, be such that $C_2$ lies within $C_1$. If $z_1$ moves on $C_1$, $z_2$ moves on $C_2$ and $\min|z_1-z_2|=2$, then $\max|z_1-z_2|$ is equal to :

Complex Numbers

$12$$17$$22$$24$

JEE Main 2021 (Online) 18th March Morning ShiftQuestion 3

If the equation $a|z|^{2}+\bar{\alpha}z+\alpha\bar{z}+d=0$ represents a circle where $a,d$ are real constants, then which of the following condition is correct ?

Complex Numbers

$|\alpha|^{2}-ad\ge0$ and $a\in\mathbf{R}$$|\alpha|^{2}-ad>0$ and $a\in\mathbf{R}-\{0\}$$|\alpha|^{2}-ad\neq0$$\alpha=0$, $a,d\in\mathbf{R}^{+}$

JEE Main 2023 (Online) 6th April Evening ShiftQuestion 4

Let $a\neq b$ be two non-zero real numbers. Then the number of elements in the set $X=\left\{z\in\mathbb{C}:\operatorname{Re}\left(az^{2}+bz\right)=a\text{ and }\operatorname{Re}\left(bz^{2}+az\right)=b\right\}$ is equal to

Complex Numbers

$0$$1$$2$$3$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 5

Let the lines $(2-i)z=(2+i)\bar{z}$ and $(2+i)z+(i-2)\bar{z}-4i=0$ (here $i^{2}=-1$) be normal to a circle $C$. If the line $iz+\bar{z}+1+i=0$ is tangent to this circle $C$, then its radius is :

Complex Numbers

$3\sqrt{2}$$\frac{1}{2\sqrt{2}}$$\frac{3}{2\sqrt{2}}$$\frac{3}{\sqrt{2}}$