1

IIT-JEE 2000

Subjective

+4

-0

The fourth power of the common difference of an arithmatic progression with integer entries is added to the product of any four consecutive terms of it. Prove that the resulting sum is the square of an integer.

2

IIT-JEE 1999

Subjective

+10

-0

Let a, b, c, d be real numbers in G.P. If u, v, w, satisfy the system of equations

u + 2v + 3w = 6

4u + 5v + 6w = 12

6u + 9v = 4

u + 2v + 3w = 6

4u + 5v + 6w = 12

6u + 9v = 4

then show that the roots of the equation $$\left( {{1 \over u} + {1 \over v} + {1 \over w}} \right){x^2}$$

$$ + [{(b - c)^2} + {(c - a)^2} + {(d - b)^2}]x + u + v + w = 0$$ and $$20{x^2} + 10{(a - d)^2}x - 9 = 0$$ are reciprocals of each other.

3

IIT-JEE 1996

Subjective

+3

-0

The real numbers $${x_1}$$, $${x_2}$$, $${x_3}$$ satisfying the equation $${x^3} - {x^2} + \beta x + \gamma = 0$$ are in AP. Find the intervals in which $$\beta \,\,and\,\gamma $$ lie.

4

IIT-JEE 1991

Subjective

+4

-0

Let p be the first of the n arithmetic means between two numbers and q the first of n harmonic means between the same numbers. Show that q does not lie between p and $$\,{\left( {{{n + 1} \over {n - 1}}} \right)^2}\,p$$.

Questions Asked from Sequences and Series (Subjective)

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

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
Complex Numbers

Trigonometry

Coordinate Geometry

Calculus