Linear Inequalities Class 11th Notes - Free NCERT Class 11 Maths Chapter 6 notes

Linear Inequalities Class 11th Notes - Free NCERT Class 11 Maths Chapter 6 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 04:48 PM IST

Linear Inequalities refers to the 6 chapter of NCERT. The NCERT Class 11 Maths chapter 6 notes contain important formulas. Class 11 Math chapter 6 notes contain systematic explanations of topics using examples and exercises. A Class 11 Maths chapter 6 note includes FAQ’s or frequently asked questions about the chapter. Notes for Class 11 Maths chapter 6 NCERT Notes for Class 11 Maths chapter 6 is explained in a simple and understanding way that can reach students easily.

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This Story also Contains

NCERT Class 11 Maths Chapter 6 notes
Algebraic Solutions Of Linear Inequalities In One Variable And Their Graphical Representation
Graphical Solution Of Linear Inequalities In Two Variables
Significance of NCERT Class 11 Math Chapter 6 Notes
NCERT Class 11 Notes Chapter Wise.

After going through Class 11 Linear Inequalities notes

Also, students can refer,

NCERT Class 11 Maths Chapter 6 notes

Linear Inequalities

A linear inequality is defined as the expression where any two values are compared by the inequality symbol such as < > ≤ ≥

Let us take an example

Ram has Rs 120 and wants to buy some bats and balls. The cost of one register is Rs 40 and that of a pen is Rs 20. In this case, if x denotes the number of bats and y, the number of balls which Ram buys, then the total amount spent by her is Rs (40x + 20y) and we have

40x + 20y ≤ 120

Algebraic Solutions Of Linear Inequalities In One Variable And Their Graphical Representation

Equal numbers may be subtracted from or added to both sides of an inequality without affecting the inequality sign.

Example:

Solve 5x – 3 < 3x +1

when (i) x is an integer

(ii) x is a real number.

Solution:

We have,

5x –3 < 3x + 1

or 5x –3 + 3 < 3x +1 +3 (Rule 1)

or 5x < 3x +4

or 5x – 3x < 3x + 4 – 3x (Rule 1)

or 2x < 4 or x < 2 (Rule 2)

When x is an integer, the solutions of the given inequality are ...,

– 4, – 3, – 2, – 1, 0, 1

When x is a real number, the solutions of the inequality are given by x < 2, i.e., all real numbers x which are less than 2

Therefore, the solution set of the inequality is x ∈ (– ∞, 2).

Graphical Solution Of Linear Inequalities In Two Variables

We know that a line divides the cartesian plane into two parts known as half-plane.

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The region consisting of all the solutions of an inequality is called the solution region.
If inequality is of the type ax + by ≥ c or ax + by ≤ c, then the points on the line ax + by = c, are also included in the solution region. So draw a dark line in the solution region.
If inequality is of the form ax + by > c or ax + by < c, then the points on the line ax + by = c, are not to be included in the solution region. So draw a broken or dotted line in the solution region.

1647258969619

This is all about this chapter.

Significance of NCERT Class 11 Math Chapter 6 Notes

Class 11 Linear inequalities notes will help to understand the formulas, statements, rules in detail. Also, Class 11 Math chapter 6 notes also contains previous year’s questions and NCERT textbook pdf. In C lass 11 CBSE Maths Syllabuses, it contains FAQ’s or frequently asked questions along with a topic-wise explanation. Class 11 Maths chapter 6 notes pdf download can be used to download offline.

Linear inequalities Class 11 notes pdf download: link

NCERT Class 11 Notes Chapter Wise.

NCERT Class 11 Maths Chapter 1 Notes

NCERT Class 11 Maths Chapter 2 Notes

NCERT Class 11 Maths Chapter 3 Notes

NCERT Class 11 Maths Chapter 4 Notes

NCERT Class 11 Maths Chapter 5 Notes

NCERT Class 11 Maths Chapter 6 Notes

NCERT Class 11 Maths Chapter 7 Notes

NCERT Class 11 Maths Chapter 8 Notes

NCERT Class 11 Maths Chapter 9 Notes

NCERT Class 11 Maths Chapter 10 Notes

NCERT Class 11 Maths Chapter 11 Notes

NCERT Class 11 Maths Chapter 12 Notes

NCERT Class 11 Maths Chapter 13 Notes

NCERT Class 11 Maths Chapter 14 Notes

NCERT Class 11 Maths Chapter 15 Notes

NCERT Class 11 Maths Chapter 16 Notes

Subject Wise NCERT Exemplar Solutions

Subject Wise NCERT Solutions

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NCERT Books and Syllabus

NCERT Book for Class 11

NCERT Syllabus for Class 11

Also Read

NCERT Solutions for Class 11 Physics Chapter 11 Thermodynamics

NCERT Solutions for Class 11 Maths Chapter 13 Statistics

NCERT Solutions for Class 11 Maths Chapter 14 Probability

NCERT Solutions for Class 11 Maths Chapter 12 Limits and Derivatives

NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry

NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections

NCERT Exemplar Class 11 Chemistry Solutions Chapter 4 Chemical Bonding and Molecular Structure

NCERT Exemplar Class 11 Chemistry Solutions Chapter 3 Classification of Elements and Periodicity in Properties

NCERT Exemplar Class 11 Biology Solutions Chapter 7 Structural Organisation in Animals

NCERT Exemplar Class 11 Chemistry solutions Chapter 11 P-Block Elements

NCERT Exemplar Class 11 Chemistry Solutions Chapter 14 Environmental Chemistry

NCERT Exemplar Class 11 Chemistry Solutions Chapter 9 Hydrogen

NCERT Class 11 Chemistry Chapter 4 Notes Chemical Bonding and Molecular Structure - Download PDF

NCERT Class 11 Physics Chapter 6 Work, Energy and Power Notes - Download PDF

NCERT Class 11 Chemistry Chapter 3 Notes - Download PDF

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NCERT Class 11 Biology Chapter 22 Notes Chemical Coordination And Integration- Download PDF Notes

NCERT Class 11 Biology Chapter 19 Notes Excretory Products And Their Elimination- Download PDF Notes

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Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is