1

IIT-JEE 1987

Fill in the Blanks

+2

-0

The solution set of the system of equations $$X + Y = {{2\pi } \over 3},$$ $$cox\,x + cos\,y = {3 \over 2},$$ where x and y are real, is _____.

2

IIT-JEE 1987

Fill in the Blanks

+2

-0

The sides of a triangle inscribed in a given circle subtend angles $$\alpha $$, $$\beta $$ and $$\gamma $$ at the centre. The minimum value of the arithmetic mean of $$cos\left[ {\alpha + {\pi \over 2}} \right],\,\cos \left[ {\beta + {\pi \over 2}} \right]$$ and $$cos\left[ {\gamma + {\pi \over 2}} \right]$$ is equal to _______.

3

IIT-JEE 1987

Fill in the Blanks

+2

-0

The set of all $$x$$ in the interval $$\left[ {0,\,\pi } \right]$$ for which $$2\,{\sin ^2}x - 3$$ $$\sin x + 1 \ge 0,$$ is _____.

4

IIT-JEE 1981

Fill in the Blanks

+2

-0

Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an identity in x, where C

_{0}, C_{1},....C_{n}are constants, and $${C_n} \ne 0$$ , then the value of n is _____.Questions Asked from Trigonometric Functions & Equations (Fill in the Blanks)

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
Statistics
Complex Numbers

Trigonometry

Coordinate Geometry

Calculus