1

IIT-JEE 1984

Subjective

+2

-0

If $$n$$ is a natural number such that

$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p_k}{}^{{\alpha _k}}$$ and $${p_1},{p_2},\,\,......,\,{p_k}$$ are distinct primes, then show that $$In$$ $$n \ge k$$ $$in$$ 2

$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p_k}{}^{{\alpha _k}}$$ and $${p_1},{p_2},\,\,......,\,{p_k}$$ are distinct primes, then show that $$In$$ $$n \ge k$$ $$in$$ 2

2

IIT-JEE 1983

Subjective

+2

-0

Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that

(i) their sum is $$25$$

(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and

(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.

(i) their sum is $$25$$

(ii) the numbers $$2,$$ $$a, b$$ are consecutive terms of an A.P. and

(iii) the numbers $$b,c,18$$ are consecutive terms of a G.P.

3

IIT-JEE 1982

Subjective

+3

-0

Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many such progressions are possible ?

4

IIT-JEE 1980

Subjective

+3

-0

The interior angles of a polygon are in arithmetic progression. The smallest angle is $${120^ \circ }$$, and the common difference is $${5^ \circ }$$, Find the number of sides of the polygon.

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
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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

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Quadratic Equation and Inequalities
Sequences and Series
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Vector Algebra and 3D Geometry
Statistics
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Trigonometry

Coordinate Geometry

Calculus