1

IIT-JEE 1984

Subjective

+2

-0

If $$a > 0,\,b > 0$$ and $$\,c > 0,$$ prove that $$\,c > 0,$$ prove that $$\left( {a + b + c} \right)\left( {{1 \over a} + {1 \over b} + {1 \over c}} \right) \ge 9$$

2

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

3

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.

4

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 ?

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

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