JEE-MAIN SERIES Mathematics
Complex Numbers And Quadratic Equations
53 previous year questions.
Volume: 53 Ques
Yield: High
High-Yield Trend
6
2026 1
2024 9
2023 2
2022 16
2021 1
2020 6
2019 1
2018 2
2017 2
2016 1
2015 3
2014 3
2013 Chapter Questions 53 MCQs
01
PYQ 2013
easy
mathematics ID: jee-main
Let where is any non-zero complex number. The set is equal to:
1
2
3
4
02
PYQ 2013
medium
mathematics ID: jee-main
If is a complex number of unit modulus and argument then is equal to
1
2
3
4
03
PYQ 2013
medium
mathematics ID: jee-main
If the equations and have a common root, then is
1
1:02:03
2
3:02:01
3
1:03:02
4
3:01:02
04
PYQ 2014
medium
mathematics ID: jee-main
If and are the roots of the equation, , then the equation, = 0 has roots :
1
and
2
and
3
and
4
and
05
PYQ 2014
medium
mathematics ID: jee-main
Let be any complex number such that is a purely imaginary number. Then is :
1
0
2
any non-zero real number other than 1
3
any non-zero real number
4
a purely imaginary number
06
PYQ 2014
medium
mathematics ID: jee-main
For all complex numbers z of the form 1 + i , R, if z = x + iy, then :
1
2
3
4
07
PYQ 2015
medium
mathematics ID: jee-main
A complex number is the said to be unimodular if Suppose and are
complex number such that is unimodular and is not unimodular. Then the point lies on a :
1
Straight line parallel to x-axis
2
Straight line parallel to y-axis
3
Circle of radius 2
4
Circle of radius
08
PYQ 2016
medium
mathematics ID: jee-main
The sum of all real values of satisfying the equation is
1
3
2
-4
3
6
4
5
09
PYQ 2016
medium
mathematics ID: jee-main
Let be a complex number, , such that is a real number. Then the sum is equal to :
1
2
3
4
10
PYQ 2017
medium
mathematics ID: jee-main
If, for a positive integer n, the quadratic equation, has two consecutive integral solutions, then is equal to :
1
9
2
10
3
11
4
12
11
PYQ 2017
medium
mathematics ID: jee-main
Let , the set of complex numbers. Then the equation, represents :
1
a circle with radius
2
a circle with diameter
3
an ellipse with length of major axis
4
an ellipse with length of minor axis
12
PYQ 2018
medium
mathematics ID: jee-main
If and are the roots of the quadratic equation, , then the value of is :
1
-10
2
10
3
-25
4
25
13
PYQ 2019
medium
mathematics ID: jee-main
Let and be any two non-zero complex numbers such that . If then :
1
2
3
4
14
PYQ 2019
medium
mathematics ID: jee-main
Let be a complex number such that (where i = ). Then is equal to :
1
2
3
4
15
PYQ 2019
medium
mathematics ID: jee-main
Let with Im(z) = 10 and it satisfies for some natural number .Then :
1
n = 20 and Re(z) = - 10
2
n = 20 and Re(z) = 10
3
n = 40 and Re(z) = - 10
4
n = 40 and Re(z) = 10
16
PYQ 2019
medium
mathematics ID: jee-main
If is chosen in the quadratic equation such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :
1
2
3
4
17
PYQ 2019
medium
mathematics ID: jee-main
If is a purely imaginary number and , then a value of is :
1
2
3
4
18
PYQ 2019
medium
mathematics ID: jee-main
Let be a root of the quadratic equation, . If , then arg is equal to :
1
2
3
0
4
19
PYQ 2020
medium
mathematics ID: jee-main
If be a complex number satisfying then cannot be :
1
2
3
4
20
PYQ 2021
medium
mathematics ID: jee-main
If , then p and q are roots of the equation :
1
2
3
4
21
PYQ 2021
medium
mathematics ID: jee-main
Let a complex number be w = 1 - √3 i. Let another complex number z be such that |z w| = 1 and arg(z) - arg(w) = π/2. Then the area of the triangle with vertices origin, z and w is equal to :
1
1/2
2
2
3
1/4
4
4
22
PYQ 2021
medium
mathematics ID: jee-main
Let C be the set of all complex numbers. Let
and
.
Then, the maximum value of for is equal to :
and
.
Then, the maximum value of for is equal to :
1
2
3
4
23
PYQ 2021
medium
mathematics ID: jee-main
Let and be two complex numbers such that and satisfy the equation . Then the imaginary part of is equal to _________.
24
PYQ 2021
medium
mathematics ID: jee-main
Let be in R. If and are the roots of the equation , and and are the roots of the equation , then is equal to ___________.
25
PYQ 2021
medium
mathematics ID: jee-main
The least positive integer n such that , is a positive integer, is ___________.
26
PYQ 2021
medium
mathematics ID: jee-main
If , then :
1
S contains only one element
2
S contains exactly two elements
3
S is a straight line in the complex plane
4
S is a circle in the complex plane
27
PYQ 2021
medium
mathematics ID: jee-main
A point moves in the complex plane such that , then the minimum value of is equal to _________
28
PYQ 2021
medium
mathematics ID: jee-main
If is a complex number such that is purely imaginary, then the minimum value of is :
1
2
3
4
29
PYQ 2021
medium
mathematics ID: jee-main
If the real part of the complex number , is zero, then the value of is equal to ________.
30
PYQ 2021
medium
mathematics ID: jee-main
Let i = √-1. If , and . Then is equal to __________.
31
PYQ 2021
medium
mathematics ID: jee-main
If are such that 1 2i (here = 1) is a root of z + z+ =0, then ( ) is equal to:
1
3
2
-3
3
7
4
-7
32
PYQ 2021
medium
mathematics ID: jee-main
If the equation a|z|² + āz + a z̄ + d = 0 represents a circle where a, d are real constants, then which of the following condition is correct ?
1
|a|² - a d ≥ 0 and a ∈ R
2
|a|² - a d>0 and a ∈ R - {0}
3
|a|² - a d ≠ 0
4
α = 0, a, d ∈ R⁺
33
PYQ 2021
medium
mathematics ID: jee-main
Let z₁, z₂ be the roots of the equation z² + a z + 12 = 0 and z₁, z₂ form an equilateral triangle with origin. Then, the value of |a| is ________.
34
PYQ 2021
medium
mathematics ID: jee-main
Let C be the set of all complex numbers. Let , and . Then the number of elements in is equal to :
1
0
2
1
3
2
4
Infinite
35
PYQ 2021
medium
mathematics ID: jee-main
If the least and the largest real values of , for which the equation ( and ) has a solution, are and respectively; then is equal to _________
36
PYQ 2022
medium
mathematics ID: jee-main
The number of distinct real roots of the equation is
1
5
2
7
3
1
4
3
37
PYQ 2022
medium
mathematics ID: jee-main
Let a circle C in complex plane pass through the points , and . If is a point on C such that the line through and is perpendicular to the line through and , then is equal to:
1
2
3
4
38
PYQ 2023
medium
mathematics ID: jee-main
For if the minimum value of is , then a value of is ______
1
3
2
3
4
4
39
PYQ 2023
easy
mathematics ID: jee-main
Let and Then and are roots of the equation
1
2
3
4
40
PYQ 2023
easy
mathematics ID: jee-main
If the ellipse meets the line on the -axis and the line on the -axis, then the eccentricity of the ellipse is
1
2
3
4
41
PYQ 2023
easy
mathematics ID: jee-main
The remainder when is divided by is
1
1
2
4
3
6
4
8
42
PYQ 2023
hard
mathematics ID: jee-main
If the shortest between the lines and is , then the square of sum of all possible values of is
43
PYQ 2023
hard
mathematics ID: jee-main
If and x, y, z are non-negative integers, then find the number of integral solutions is
1
136
2
171
3
90
4
130
44
PYQ 2023
hard
mathematics ID: jee-main
Let be the roots of the equation , then is equal to:
1
-256
2
-128
3
4
45
PYQ 2023
hard
mathematics ID: jee-main
Let the complex number be such that is purely imaginary. If , then is equal to
1
2
3
4
46
PYQ 2023
medium
mathematics ID: jee-main
For two non-zero complex numbers z1 and z2, if Re(z1z2) = 0 and Re(z1 + z2), then which of the following are possible?
A. Im(z1) > 0 and Im(z2) > 0 |
B. Im(z1) < 0 and Im(z2) > 0
C. Im(z1) > 0 and Im(z2) < 0
D. Im(z1) < 0 and Im(z2) < 0
Choose the correct answer from the options given below
A. Im(z1) > 0 and Im(z2) > 0 |
B. Im(z1) < 0 and Im(z2) > 0
C. Im(z1) > 0 and Im(z2) < 0
D. Im(z1) < 0 and Im(z2) < 0
Choose the correct answer from the options given below
1
B and C
2
B and D
3
A and B
4
A and C
47
PYQ 2024
hard
mathematics ID: jee-main
The minimum value of is,
1
2
3
4
48
PYQ 2026
hard
mathematics ID: jee-main
The number of distinct real solutions of the equation
is
1
2
2
0
3
3
4
1
49
PYQ 2026
medium
mathematics ID: jee-main
Let , where . If , then is equal to
50
PYQ 2026
hard
mathematics ID: jee-main
Let and . Find the value of .
51
PYQ 2026
hard
mathematics ID: jee-main
Let and , where . If
then the value of is ___________.
52
PYQ 2026
medium
mathematics ID: jee-main
If where & then value of is ________
53
PYQ 2026
medium
mathematics ID: jee-main
If , then number of ordered pairs , where is ______.
About Complex Numbers And Quadratic Equations - JEE-MAIN
Complex Numbers And Quadratic Equations is a vital chapter for JEE-MAIN aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Complex Numbers And Quadratic Equations PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Complex Numbers And Quadratic Equations carry the most weight. Then, tackle the questions iteratively to solidify your understanding.