1

IIT-JEE 1992

Subjective

+6

-0

What normal to the curve $$y = {x^2}$$ forms the shortest chord?

2

IIT-JEE 1992

Subjective

+2

-0

In this questions there are entries in columns $$I$$ and $$II$$. Each entry in column $$I$$ is related to exactly one entry in column $$II$$. Write the correct letter from column $$II$$ against the entry number in column $$I$$ in your answer book.

Let the functions defined in column $$I$$ have domain $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$

$$\,\,\,\,$$**Column $$I$$**

(A) $$x + \sin x$$

(B) $$\sec x$$

$$\,\,\,\,$$**Column $$II$$**

(p) increasing

(q) decreasing

(r) neither increasing nor decreasing

3

IIT-JEE 1991

Subjective

+4

-0

A window of perimeter $$P$$ (including the base of the arch) is in the form of a rectangle surmounded by a semi circle. The semi-circular portion is fitted with coloured glass while the rectangular part is fitted with clear glass transmits three times as such light per square meter as the coloured glass does.

What is the ratio for the sides of the rectangle so that the window transmits the maximum light ?

4

IIT-JEE 1990

Subjective

+4

-0

Show that $$2\sin x + \tan x \ge 3x$$ where $$0 \le x < {\pi \over 2}$$.

Questions Asked from Application of Derivatives (Subjective)

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2006 (1)
IIT-JEE 2005 (2)
IIT-JEE 2004 (2)
IIT-JEE 2003 (4)
IIT-JEE 2001 (1)
IIT-JEE 2000 (1)
IIT-JEE 1998 (2)
IIT-JEE 1997 (1)
IIT-JEE 1996 (3)
IIT-JEE 1995 (1)
IIT-JEE 1994 (2)
IIT-JEE 1993 (2)
IIT-JEE 1992 (3)
IIT-JEE 1991 (1)
IIT-JEE 1990 (2)
IIT-JEE 1989 (1)
IIT-JEE 1988 (1)
IIT-JEE 1987 (1)
IIT-JEE 1985 (2)
IIT-JEE 1983 (2)
IIT-JEE 1982 (2)
IIT-JEE 1981 (3)
IIT-JEE 1979 (1)

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 Chemical Equilibrium Ionic Equilibrium Solutions 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 3D Geometry Statistics Complex Numbers

Trigonometry

Coordinate Geometry

Calculus