1

IIT-JEE 1985

True or False

+1

-0

If $$P(x) = a{x^2} + bx + c\,\,and\,\,Q(x) = - a{x^2} + dx + c$$, where $$ac \ne \,0$$, then P(x) Q(x) = 0 has at least two real roots.

2

IIT-JEE 1984

True or False

+1

-0

If a < b < c < d, then the roots of the equation (x - a) (x - c) + 2 ( x - b) (x - d) = 0 are real and distinct.

3

IIT-JEE 1983

True or False

+1

-0

The equation $$2{x^2} + 3x + 1 = 0$$ has an irrational root.

4

IIT-JEE 1981

True or False

+2

-0

For every integer n > 1, the inequality $${(n!)^{1/n}} < {{n + 1} \over 2}$$ holds.

Questions Asked from Quadratic Equation and Inequalities (True of False)

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced Subjects

Physics

Mechanics

Units & Measurements Motion Laws of Motion Work Power & Energy Impulse & Momentum Rotational Motion Properties of Matter Heat and Thermodynamics Simple Harmonic Motion Waves Gravitation

Electricity

Electrostatics Current Electricity Capacitor Magnetism Electromagnetic Induction Alternating Current Electromagnetic Waves

Optics

Modern Physics

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Structure of Atom Redox Reactions Gaseous State Equilibrium Solutions States of Matter Thermodynamics Chemical Kinetics and Nuclear Chemistry Electrochemistry 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 Salt Analysis

Organic Chemistry

Mathematics

Algebra

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

Trigonometry

Coordinate Geometry

Calculus