Learn CBSE with Free Lessons & Tips

No need to worry because worry will only increase ur problem instead of helping you out . Since you got ur result n it was not expected as you said so now find out where u lack out what are the major problems and minor problems don't ignore minor ones and start preparing for your jee cuz this 10 marks heet will not decide your jee numbers only your practice and practice ur mistakes n ur will to improve those mistakes will make u succeed.

Story of Pi

In math, "pi" (often written as the Greek letter π) is a number that represents the ratio of a circle's circumference (the distance around the circle) to its diameter (the distance across the circle through its center). No matter how big or small the circle is, this ratio is always the same and approximately equal to 3.14159.

To put it simply, if you take a string and wrap it once around a circle, then lay that string out straight, it would be a little more than three times the length of the circle's diameter. This "little more" is the extra decimal places of pi. Pi is an irrational number, meaning it goes on forever without repeating.

Now, what is irrational number? Will post in second lesson.

In mean while try the above and let me know.

Rational Numbers?

In simple English, "rational" means something that is logical or makes sense. In mathematics, rational numbers are related to the concept of fractions. Let's travel back and review the lesson on fractions, specifically proper and improper fractions.

Proper fractions are fractions where the numerator (the top number) is smaller than the denominator (the bottom number). For example, 3/4
is a proper fraction.
Improper fractions are fractions where the numerator is larger than or equal to the denominator. For example, 5/3
is an improper fraction.
Both proper and improper fractions are members of the rational number family. Rational numbers are numbers that can be expressed in the form a/b
, where
𝑎 and 𝑏 are integers, and 𝑏 is not zero.

Now, what happens if the denominator becomes zero? What kind of fraction is that? Is it making any sense? No, it doesn't. Dividing by zero is undefined and does not produce a valid number. Therefore, rational numbers must have a denominator that is not zero. When you divide rational numbers, you get definite decimal places that either terminate or repeat.

In summary, rational numbers are fractions where the denominator is never zero, and their decimal expansions are predictable—they either end or follow a repeating pattern.

Tips to solve numerical

1. Always read statement twice to ensure right data given in question.

2. Write data given in question .

3. Check units of given data, sign conventios and change the units if required.

eg. If data is given in cgs units then convert it to SI units.

4. Cross check formula used in numerical.

5. Do calculation carefully.

6. Checks units in which anwer has been asked.

7. Write units along with numeric value.

Practice numericals to do numerical faster. Dont be in hurry while doing numericals.

Types of Chemical Reactions

1. Combination Reaction

When two or more substances combine to form a single product, the reaction is known as a combination reaction.

For example:

In the laboratory, iron sulphide is prepared by mixing iron and sulphur.

Fe_(s) + S_(s) → FeS(s)

Formation of slaked lime by the reaction of calcium oxide with water

• Endothermic Reaction: The reactions accompanied by the absorption of heat are called endothermic reactions.
• Exothermic Reaction: The reactions accompanied by the evolution of heat are called endothermic reactions.

1.   Decomposition Reaction

A chemical reaction in which a single compound splits into two or more simple substances is called a decomposition reaction.

Correct way of heating the boiling tube containing crystals of ferrous sulphate and of smelling the odour

For example:

When mercuric oxide is heated in a crucible, the orange-red powder begins to darken and a silver mirror begins to deposit on the cooler parts of the crucible.

• Thermal Decomposition Reaction: The decomposition reactions carried out by heating are known as thermal decomposition reactions.
• Photochemical reaction: The chemical reactions which proceed with the absorption of light energy are called photochemical reactions.

2.               Displacement Reaction

Reactions in which the more reactive element displaces the less reactive element from its compound are called displacement reactions.

Iron nails dipped in copper sulphate solution

For example:

Zinc displaces copper in copper sulphate to form zinc sulphate. 

1.   Double Displacement Reaction

Reactions in which ions of the reactants exchange places to form two new compounds, are called double displacement reactions.

For example: Sodium hydroxide reacts with hydrochloric acid to form sodium chloride and water.

NaOH_(aq)          +          HCl_(aq)   →       NaCl_(aq) +          H2O_(l)

Types of Double Displacement Reactions: 

1. Precipitation 

In all of the following processes, a white material is generated that is insoluble in water. A precipitate is the insoluble substance that forms. A precipitation reaction is a reaction that results in the formation of a precipitate.

1. Neutralization 

The reactants are a base and an acid, and the products are salt and water. Neutralization is a form of double displacement reaction in which the reactants are a base and an acid, and the products are salt and water. The positive charge of the acid's hydrogen ion and the negative charge of the base's hydroxyl ions or oxide ions lose their electrical charge and form covalent water molecules. 

Na⁺OH^- + H⁺Cl^-        →      Na⁺Cl^- + H₂O

Base     Acid                   Salt    Water

Zn₂+O₂- + 2H+NO₃^- → Zn₂⁺(NO₃)₂^- + H₂O

A neutralization reaction is basically a reaction between H+ and OHions i.e., 

H⁺_(aq) + OH^-_(aq) → H₂O_(l)

2.               Oxidation - Reduction Reactions/Redox Reactions

Oxidation and reduction take place simultaneously.

Reactions which involve the addition of oxygen, or the removal of hydrogen are called oxidation reactions. For example:

Zinc displaces copper in copper sulphate to form zinc sulphate. 

1.   Double Displacement Reaction

Reactions in which ions of the reactants exchange places to form two new compounds, are called double displacement reactions.

For example: Sodium hydroxide reacts with hydrochloric acid to form sodium chloride and water.

NaOH_(aq)          +          HCl_(aq)   →       NaCl_(aq) +          H2O_(l)

Types of Double Displacement Reactions: 

1. Precipitation 

In all of the following processes, a white material is generated that is insoluble in water. A precipitate is the insoluble substance that forms. A precipitation reaction is a reaction that results in the formation of a precipitate.

1. Neutralization 

The reactants are a base and an acid, and the products are salt and water. Neutralization is a form of double displacement reaction in which the reactants are a base and an acid, and the products are salt and water. The positive charge of the acid's hydrogen ion and the negative charge of the base's hydroxyl ions or oxide ions lose their electrical charge and form covalent water molecules. 

Na⁺OH^- + H⁺Cl^-        →      Na⁺Cl^- + H₂O

Base     Acid                   Salt    Water

Zn₂+O₂- + 2H+NO₃^- → Zn₂⁺(NO₃)₂^- + H₂O

A neutralization reaction is basically a reaction between H+ and OHions i.e., 

H⁺_(aq) + OH^-_(aq) → H₂O_(l)

2.               Oxidation - Reduction Reactions/Redox Reactions

Oxidation and reduction take place simultaneously.

Reactions which involve the addition of oxygen, or the removal of hydrogen are called oxidation reactions. For example:

C_(s) + 2H_{2 (g)} → CH_{4 (g)}

Chemical reactions in which the reactants gain hydrogen are reduction reactions. For example:

·       Oxidation: Substance loses electrons or gains oxygen or loses hydrogen.

·       Reduction: Substance gains electrons or loses oxygen or gains hydrogen.

·       Oxidising agent: a substance that oxidises another substance and self-gets reduced.

·       Reducing agent: a substance that reduces another substance and self-gets oxidised.

Redox Reaction

The chemical reaction in which oxidation and reduction takes  places simultaneously is known as a redox reaction.