1

IIT-JEE 1996

Subjective

+3

-0

Let $$f\left( x \right) = \left\{ {\matrix{
{x{e^{ax}},\,\,\,\,\,\,\,x \le 0} \cr
{x + a{x^2} - {x^3},\,x > 0} \cr
} } \right.$$

Where a is a positive constant. Find the interval in which $$f'(x)$$ is increasing.

2

IIT-JEE 1996

Subjective

+5

-0

A curve $$y=f(x)$$ passes through the point $$P(1, 1)$$. The normal to the curve at $$P$$ is $$a(y-1)+(x-1)=0$$. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, determine the equation of the curve. Also obtain the area bounded by the $$y$$-axis, the curve and the normal to the curve at $$P$$.

3

IIT-JEE 1996

Subjective

+5

-0

Determine the points of maxima and minima of the function

$$f\left( x \right) = {1 \over 8}\ell n\,x - bx + {x^2},x > 0,$$ where $$b \ge 0$$ is a constant.

$$f\left( x \right) = {1 \over 8}\ell n\,x - bx + {x^2},x > 0,$$ where $$b \ge 0$$ is a constant.

4

IIT-JEE 1995

Subjective

+5

-0

Let $$(h, k)$$ be a fixed point, where $$h > 0,k > 0.$$. A straight line passing through this point cuts the possitive direction of the coordinate axes at the points $$P$$ and $$Q$$. Find the minimum area of the triangle $$OPQ$$, $$O$$ being the origin.

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

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