JEE Main 2014 (Offline) | Complex Numbers Question 107 | Mathematics

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

-1

If z is a complex number such that $$\,\left| z \right| \ge 2\,$$, then the minimum value of $$\,\,\left| {z + {1 \over 2}} \right|$$ :

is strictly greater that $${{5 \over 2}}$$

is strictly greater that $${{3 \over 2}}$$ but less than $${{5 \over 2}}$$

is equal to $${{5 \over 2}}$$

lie in the interval (1, 2)

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

If z is a complex number of unit modulus and argument $$\theta $$, then arg $$\left( {{{1 + z} \over {1 + \overline z }}} \right)$$ equals :

$$ - \theta \,\,$$

$${\pi \over 2} - \theta \,$$

$$\theta \,$$

$$\,\pi - \theta \,\,$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

If $$z \ne 1$$ and $$\,{{{z^2}} \over {z - 1}}\,$$ is real, then the point represented by the complex number z lies :

either on the real axis or a circle passing through the origin.

on a circle with centre at the origin

either on real axis or on a circle not passing through the origin.

on the imaginary axis.

AIEEE 2011

MCQ (Single Correct Answer)

-1

Let $$\alpha \,,\beta $$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots on the line Re z = 1, then it is necessary that :

$$\beta \, \in ( - 1,0)$$

$$\left| {\beta \,} \right| = 1$$

$$\beta \, \in (1,\infty )$$

$$\beta \, \in (0,1)$$

PREVIOUS NEXT

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 Magnetics Alternating Current and Electromagnetic Induction

Optics

Ray & Wave Optics

Modern Physics

Atoms and Nuclei Dual Nature of Radiation Semiconductor Communication Systems

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Structure of Atom Redox Reactions Gaseous State 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

Basics of Organic Chemistry Hydrocarbons Haloalkanes and Haloarenes Alcohols, Phenols and Ethers Aldehydes, Ketones and Carboxylic Acids Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical Organic Chemistry

Mathematics

Algebra

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

Trigonometry

Trigonometric Functions & Equations Inverse Trigonometric Functions Properties of Triangle

Coordinate Geometry

Straight Lines and Pair of Straight Lines Circle Conic Sections

Calculus

Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integrals Definite Integrals and Applications of Integrals Differential Equations