1

IIT-JEE 1982

Subjective

+5

-0

$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$ by $$n$$, where $$m$$ and $$n$$ are natural numbers. Two squares will be called ' neighbours ' if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighbouring squares.Show that this is possible only if all the numbers used are equal.

2

IIT-JEE 1980

Subjective

+4

-0

Let $$y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}} $$

Find all the real values of $$x,$$ for which $$y$$ takes real values.

3

IIT-JEE 1980

Subjective

+4

-0

Given $${n^4} < {10^n}$$ for a fixed positive integer $$n \ge 2,$$ prove that $${\left( {n + 1} \right)^4} < {10^{n + 1}}.$$

4

IIT-JEE 1980

Subjective

+4

-0

For what values of $$m,$$ does the system of equations
$$$\matrix{
{3x + my = m} \cr
{2x - 5y = 20} \cr
} $$$

has solution satisfying the conditions $$x > 0,\,y > 0.$$

Questions Asked from Quadratic Equation and Inequalities (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

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