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Lesson Posted on 06 Mar CBSE/Class 10/Mathematics CBSE/Class 11/Science/Mathematics/Unit-V: Mathematical Reasoning/Mathematical Reasoning

Suvam Banerjee

I am a B.Tech Graduate from the West Bengal University of Technology giving home tuition. I have more...

Natural Numbers: The set of counting numbers is called natural numbers. It is denoted by N, where N = {1,2,3, …..} Whole Numbers: when zero is included in the set of natural numbers, then it is a set of whole numbers. It is denoted by W, where W = {0,1,2, …..} Integers: When in the set... read more

Natural Numbers: The set of counting numbers is called **natural** numbers. It is denoted by N, where N = {1,2,3, …..}

Whole Numbers: when zero is included in the set of natural numbers, then it is a set of **whole** numbers. It is denoted by W, where W = {0,1,2, …..}

Integers: When in the set of whole numbers, natural numbers with the negative sign are included, then it becomes a set of **integers**. It is denoted by Z, where Z = {-…. , -2, -1, 0, 1, 2, …..}

Integers can be divided into negative and positive integers.

Prime Numbers: The natural numbers which have no factors other than 1 and itself are called prime numbers.

Co-prime Numbers: Two numbers that have no common factor except one are called co-prime numbers. Example: 11 and 18 etc.

Rational Numbers: The numbers that can be expressed in the form of p/q where p and q are integers and co-prime are called **rational** numbers. It is denoted by Q. Rationalnumbers can be positive or negative.

Irrational Numbers : The numbers which are not rational numbers, are called irrational numbers. or π = 3.141592 is an **irrational** number.

Real Numbers : Set of all rational numbers as well as irrational numbers are called real numbers. The square of all real numbers is positive.

Some important points on numbers :

- 2 is the only even prime number.
- Number 1 is neither divisible nor prime.
- Two consecutive odd prime numbers are called prime pair.
- All natural numbers are whole, rational, integer and real.
- Fractions are rational.
- 0 is neither negative(-) nor positive(+) number.
- Dividing any number by 0 gives infinity () whereas dividing 0 by any number gives 0.
- The sum and product of two rational numbers is always a rational number.
- The product and sum of a rational number and irrational number is always an irrational number.
- There can be infinite numer of rational and irrational numbers between two rational numbers and two irrational numbers.

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Comments Answered on 22 Mar CBSE/Class 11/Science/Mathematics/Unit-V: Mathematical Reasoning

Eduvisishta Academy

List out the formulas and theorems from all the topics you refer to; keep practising many models.

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Answers 5 Comments 1 Lesson Posted on 04 Jan CBSE/Class 11 CBSE/Class 11/Science/Biology/Unit 5: Human Physiology CBSE/Class 11/Science/Biology/Unit 5: Human Physiology/Chapter 16- Digestion and Absorption

Ramneet Singh

I make my 100%% to enrich the career of students who are the building blocks of our nation with my maximum...

The essential requirement for an organism is energy which is derived from the nutrition that it intakes. For humans, the nutrition is complicated in carbohydrates, lipids, proteins, vitamins, minerals, water and trace elements.The digestion process began from the mouth and terminated at the large intestine... read more

The essential requirement for an organism is energy which is derived from the nutrition that it intakes. For humans, the nutrition is complicated in carbohydrates, lipids, proteins, vitamins, minerals, water and trace elements.

The digestion process began from the mouth and terminated at the large intestine and occurs throughout the alimentary canal, where nervous regulation, glands and their secretions facilitate the digestion process.

Carbohydrates are the principal constituent of the diet, and most of the energy is derived from it. Lipids are known to have the highest calorific value yet forms the minor constituent for the diet. Proteins are the building blocks of muscles and genetic structure and an ultimate component of every organism's expression.

DIGESTION OF CARBOHYDRATES -

The digestion of carbohydrates begins in the mouth where the food particle is broken down into small particles by the churning of teeth. The saliva contains salivary amylase enzyme which digests about 30% of the carbohydrates. The small broken particles of food mix well with saliva and form a small ball called a bolus. The process of deglutition/peristalsis travels down by contracting and relaxing the oesophagus muscles alternatively in a wave-like motion.

This is just an introduction to the digestion method. You can join my classes to get full lectures on various topics.

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Lesson Posted on 07/12/2020 CBSE/Class 11/Science/Biology

Bidisha Ghosh

I have M.sc and b.ed. I have total 5 years experience in teaching. I have taught in various colleges,...

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Comments Lesson Posted on 07/12/2020 CBSE/Class 11/Science/Biology

Biomoleculrs-Class-11th-Biology

Bidisha Ghosh

I have M.sc and b.ed. I have total 5 years experience in teaching. I have taught in various colleges,...

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Comments Lesson Posted on 04/12/2020 CBSE/Class 11/Science/Chemistry/Some Basic Concepts of Chemistry

Rupali

I am an experienced home and online tutor working in this area from last 2 years. I worked as a subject...

To understand Fullerene, let's start with the difference between Fullerene and Graphite and finally, we will define Fullerene.In Graphite, carbon atoms form layers with a hexagonal structure, and each carbon atom is connected to three carbon atoms ( so having sp2 hybridization). Still, Fullerene having... read more

To understand Fullerene, let's start with the difference between Fullerene and Graphite and finally, we will define Fullerene.

In Graphite, carbon atoms form layers with a hexagonal structure, and each carbon atom is connected to three carbon atoms ( so having sp2 hybridization). Still, Fullerene having fused rings of carbon atoms(e.g. C60, C20, C70 etc.) well these having mixed state of hybridization depending on bonding.

A diamond which is another famous allotrope unlike Fullerene here each carbon atom is connected to another four carbon atoms( so having sp3 hybridization).

So, they are structurally different, which clarifies the definition of allotropes here. Also, we have seen they are having different types of hybridization depending on bonding.

Now we are in an excellent state to define Fullerene. Fullerene is the allotrope of Carbon having fused rings of carbon atoms connected by single and double bonds( leading to mixed hybridization) forming a closed( e.g. hollow sphere, ellipsoid) or partially closed cage (e.g. cylinder).

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Comments Answered on 25/08/2020 CBSE/Class 11/Science/Chemistry

Jayant Sardana

Online Chemistry Coaching for JEE , NEET and Boards.

Charged species are called ions. Positively charged ions are called cations, and negatively charged ions are called anions.

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Answers 166 Comments Answered on 01/11/2020 CBSE/Class 11/Science/Chemistry/States of Matter CBSE/Class 11/Science/Chemistry

Abdul

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Answers 5 Comments Answered on 17/09/2020 CBSE/Class 11/Science/Chemistry/Classification of Elements and Periodicity in Properties CBSE/Class 11/Science/Chemistry

Prashant Kumar

Chemistry, math and science with 8 year of experience in teaching school cbse board

The basic theme of the organisation in the periodic table arranges the elements in increasing order of their atomic mass but after the modern periodic table is the atomic number.

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Answered on 30/12/2020 CBSE/Class 11/Science/Physics Tuition/Class XI-XII Tuition (PUC)

Tyson

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