1

JEE Main 2021 (Online) 18th March Morning Shift

Numerical

+4

-1

Let z

_{1}, z_{2}be the roots of the equation z^{2}+ az + 12 = 0 and z_{1}, z_{2}form an equilateral triangle with origin. Then, the value of |a| is :Your input ____

2

JEE Main 2021 (Online) 16th March Morning Shift

Numerical

+4

-1

Let z and $$\omega$$ be two complex numbers such that $$\omega = z\overline z - 2z + 2,\left| {{{z + i} \over {z - 3i}}} \right| = 1$$ and Re($$\omega$$) has minimum value. Then, the minimum value of n $$\in$$ N for which $$\omega$$

^{n}is real, is equal to ______________.Your input ____

3

JEE Main 2021 (Online) 26th February Evening Shift

Numerical

+4

-1

Let z be those complex numbers which satisfy

| z + 5 | $$ \le $$ 4 and z(1 + i) + $$\overline z $$(1 $$-$$ i) $$ \ge $$ $$-$$10, i = $$\sqrt { - 1} $$.

If the maximum value of | z + 1 |

| z + 5 | $$ \le $$ 4 and z(1 + i) + $$\overline z $$(1 $$-$$ i) $$ \ge $$ $$-$$10, i = $$\sqrt { - 1} $$.

If the maximum value of | z + 1 |

^{2}is $$\alpha$$ + $$\beta$$$$\sqrt 2 $$, then the value of ($$\alpha$$ + $$\beta$$) is ____________.Your input ____

4

JEE Main 2021 (Online) 24th February Evening Shift

Numerical

+4

-1

Let $$i = \sqrt { - 1} $$. If $${{{{\left( { - 1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 - i)}^{24}}}} + {{{{\left( {1 + i\sqrt 3 } \right)}^{21}}} \over {{{(1 + i)}^{24}}}} = k$$, and $$n = [|k|]$$ be the greatest integral part of | k |. Then $$\sum\limits_{j = 0}^{n + 5} {{{(j + 5)}^2} - \sum\limits_{j = 0}^{n + 5} {(j + 5)} } $$ is equal to _________.

Your input ____

Questions Asked from Complex Numbers (Numerical)

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2024 (Online) 9th April Morning Shift (1)
JEE Main 2024 (Online) 1st February Morning Shift (1)
JEE Main 2024 (Online) 31st January Morning Shift (1)
JEE Main 2024 (Online) 29th January Evening Shift (1)
JEE Main 2024 (Online) 29th January Morning Shift (1)
JEE Main 2024 (Online) 27th January Evening Shift (1)
JEE Main 2024 (Online) 27th January Morning Shift (1)
JEE Main 2023 (Online) 13th April Morning Shift (1)
JEE Main 2023 (Online) 11th April Evening Shift (1)
JEE Main 2023 (Online) 6th April Evening Shift (1)
JEE Main 2023 (Online) 30th January Morning Shift (1)
JEE Main 2023 (Online) 29th January Evening Shift (1)
JEE Main 2022 (Online) 28th July Evening Shift (1)
JEE Main 2022 (Online) 27th July Morning Shift (1)
JEE Main 2022 (Online) 29th June Morning Shift (1)
JEE Main 2022 (Online) 28th June Evening Shift (1)
JEE Main 2022 (Online) 28th June Morning Shift (1)
JEE Main 2022 (Online) 26th June Evening Shift (1)
JEE Main 2022 (Online) 24th June Evening Shift (1)
JEE Main 2021 (Online) 1st September Evening Shift (1)
JEE Main 2021 (Online) 31st August Morning Shift (1)
JEE Main 2021 (Online) 27th August Evening Shift (1)
JEE Main 2021 (Online) 26th August Evening Shift (1)
JEE Main 2021 (Online) 26th August Morning Shift (1)
JEE Main 2021 (Online) 27th July Evening Shift (1)
JEE Main 2021 (Online) 25th July Evening Shift (1)
JEE Main 2021 (Online) 25th July Morning Shift (1)
JEE Main 2021 (Online) 18th March Morning Shift (1)
JEE Main 2021 (Online) 16th March Morning Shift (1)
JEE Main 2021 (Online) 26th February Evening Shift (1)
JEE Main 2021 (Online) 24th February Evening Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 3rd September Morning Slot (1)

JEE Main Subjects

Physics

Mechanics

Units & Measurements Vector Algebra Motion Circular Motion Laws of Motion Work Power & Energy Center of Mass and Collision Rotational Motion Properties of Matter Heat and Thermodynamics Simple Harmonic Motion Waves Gravitation

Electricity

Electrostatics Current Electricity Capacitor Magnetic Effect of Current Magnetic Properties of Matter Electromagnetic Induction Alternating Current Electromagnetic Waves

Optics

Modern Physics

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Structure of Atom Redox Reactions Gaseous State Chemical Equilibrium Ionic Equilibrium Solutions Thermodynamics Electrochemistry Chemical Kinetics and Nuclear Chemistry Solid State Surface Chemistry

Inorganic Chemistry

Periodic Table & Periodicity Chemical Bonding & Molecular Structure Isolation of Elements Hydrogen s-Block Elements p-Block Elements d and f Block Elements Coordination Compounds Environmental Chemistry

Organic Chemistry

Mathematics

Algebra

Sets and Relations Logarithm Quadratic Equation and Inequalities Sequences and Series Mathematical Induction Binomial Theorem Matrices and Determinants Permutations and Combinations Probability Vector Algebra 3D Geometry Complex Numbers Statistics Mathematical Reasoning

Trigonometry

Trigonometric Ratio and Identites Trigonometric Equations Inverse Trigonometric Functions Properties of Triangle Height and Distance

Coordinate Geometry

Calculus