Perimeter It is the outside boundary of any closed shape. To find the perimeter we need to add all the sides of the given shape. The perimeter of a rectangle is the sum of its all sides. Its unit is same as of its length. Perimeter = 3 + 7 + 3 + 7 cm […]
Introduction to Circles There are lot many objects in our life which are round in shape. Few examples are the clock, dart board, cartwheel, ring, Vehicle wheel, Coins, etc. Circles Interior and Exterior of a Circle In a flat surface, the interior of a circle is the line whose distance from the centre is less than the radius. The exterior
Quadrilateral Any closed polygon with four sides, four angles and four vertices are called Quadrilateral. It could be regular or irregular. Angle Sum Property of a Quadrilateral The sum of the four angles of a quadrilateral is 360° If we draw a diagonal in the quadrilateral, it divides it into two triangles. And we know the
Triangle A closed figure with three sides is called a Triangle. It has three vertex, sides and Angles. Types of Triangle 1. There are three types of triangles on the basis of the length of the sides. Name of Triangle Property Image Scalene Length of all sides are different Isosceles Length of two sides are equal
Basic terms and Definitions 1. Point – A Point is that which has no component. It is represented by a dot. 2. Line – When we join two distinct points then we get a line. A line has no endpoints it can be extended infinitely. 3. Line Segment – It is the part of the line which has
Introduction Euclid was a teacher of mathematics at Alexandria in Egypt, popularly known as ‘Father of Geometry”. He introduced the method of proving mathematical results by using deductive logical reasoning and the previously proved result. He collected all his work in a book called “Elements”. This book is divided into thirteen chapters and each chapter is
Linear Equations The equation of a straight line is the linear equation. It could be in one variable or two variables. Linear Equation in One Variable The equation with one variable in it is known as a Linear Equation in One Variable. The general form is px + q = s, where p, q and s
Cartesian System If we take two number lines, one horizontal and one vertical, and then combine them in such a way that they intersect each other at their zeroes, and then they form a Cartesian Plane. Quadrants of the Cartesian Plane The Cartesian plane is dividing into four quadrants named as Quadrant I, II, III, and IV anticlockwise
Polynomial Polynomial is an algebraic expression which includes constants, variables and exponents. It is the expression in which the variables have only positive integral powers. Example 1. 4×3 + 3×2 + x +3 is a polynomial in variable x. 2. 4×2 + 3x-1 – 4 is not a polynomial as it has negative power. 3. 3×3/2 + 2x – 3 is
Natural Numbers Numbers 1, 2, 3…….∞, which are used for counting are called Natural numbers. The collection of natural numbers is denoted by N. Therefore, N = {1, 2, 3, 4, 5, ….}. Whole Numbers All natural numbers including zero are called Whole Numbers. The collection of whole numbers is denoted by W. Therefore, W =
Chapter 1: Number Systems – Important Questions with Solutions 1. Is 0 a rational number? Express it in p/q form. Solution:Yes, 0 is rational because it can be expressed as 0/1, where p = 0 and q = 1 (q ≠ 0). 2. Find six rational numbers between 3 and 4. Solution:We can find rationals
1. What is the total population of India as per Census 2011?A) 1.03 billionB) 1.21 billionC) 1.35 billionD) 1.50 billion✅ Answer: B) 1.21 billion 2. Which Indian state has the highest population according to Census 2011?A) MaharashtraB) BiharC) West BengalD) Uttar Pradesh✅ Answer: D) Uttar Pradesh 3. Which Indian state has the lowest population density?A)
1. Introduction Diversity is due to varied climate, relief, and soil conditions. 2. Factors Affecting Natural Vegetation 2.1 Relief 2.2 Climate 2.3 Ecosystem 3. Types of Vegetation in India India’s vegetation is classified into five major types: 3.1 Tropical Evergreen Forests 3.2 Tropical Deciduous Forests 3.3 Tropical Thorn Forests and Scrubs 3.4 Montane Forests 3.5
1. What type of climate does India have? A. Tropical DesertB. EquatorialC. MonsoonD. Mediterranean Answer: ✅ C. Monsoon 2. Which of the following is NOT a major control of climate? A. LatitudeB. VegetationC. Ocean currentsD. Distance from the sea Answer: ✅ B. Vegetation 3. What is the name of the hot, dry wind blowing in
1. Introduction India’s climate is monsoonal, influenced by multiple factors like location, relief, winds, and the Himalayas. 2. Factors Affecting Climate of India India’s climate is controlled by a complex set of factors: 2.1 Latitude 2.2 Altitude 2.3 Pressure and Wind Systems Important wind systems: 2.4 Distance from the Sea 2.5 Ocean Currents 2.6 Relief
1. Which river is known as the ‘Dakshin Ganga’? A. KrishnaB. MahanadiC. Godavari ✅D. Kaveri 2. The Ganga originates from which glacier? A. SiachenB. ZemuC. Gangotri ✅D. Yamunotri 3. The Brahmaputra River is called Tsangpo in which country? A. IndiaB. Tibet ✅C. BangladeshD. Nepal 4. Which is the longest river in India? A. BrahmaputraB. Ganga
Introduction The drainage system of India is controlled by: 1. Drainage Patterns Rivers form different patterns depending on slope, rock structure, and topography: 2. The Himalayan Rivers 2.1 Characteristics 2.2 Major Himalayan River Systems (A) The Indus River System (B) The Ganga River System (C) The Brahmaputra River System 3. The Peninsular Rivers 3.1 Characteristics
Introduction India’s landmass shows great physical diversity. India’s physical features are broadly grouped into six major divisions: 1. Geological Structure of India India’s physical features are a result of plate tectonics. Thus, India’s relief reflects both old and young landforms. 2. The Himalayan Mountains 2.1 General Features 2.2 Longitudinal Divisions 2.3 Regional Divisions of Himalayas
Introduction India, one of the world’s oldest civilizations, is a land of diverse geography, culture, and history. Its size and location have always shaped its destiny.Situated in the south-central part of Asia, India is unique in many ways – its massive area, large population, rich resources, and strategic geographical position make it significant not only
1. The Himalayas were formed due to the collision of which two plates? A. Eurasian Plate and Pacific PlateB. Indo-Australian Plate and Eurasian Plate ✅C. Indian Plate and Arabian PlateD. Pacific Plate and African Plate 2. Which is the highest mountain peak in India? A. Mount EverestB. Kanchenjunga ✅C. Nanda DeviD. Dhaulagiri 3. The Northern
1. Democratic Rights 2. Why Democratic Rights Are Important 3. Types of Democratic Rights in India India’s Constitution provides six main rights, often referred to as Fundamental Rights: 3.1 Right to Equality (Articles 14–18) Importance: Ensures social justice and removes discrimination. 3.2 Right to Freedom (Articles 19–22) Importance: Guarantees individual liberty and political participation. 3.3
1. Political Institutions 2. Main Democratic Institutions in India 2.1 Legislature (Parliament) 2.2 Executive 2.3 Judiciary 2.4 Political Parties 2.5 Media and Civil Society 3. How Institutions Work Together 4. Challenges in the Working of Institutions 5. Importance of Working Institutions 6. Conclusion Quick Revision Points
1. Elections Key Idea: 2. Why Elections Are Important 3. Key Features of Elections in India 4. Political Parties 4.1 Functions of Political Parties 4.2 Types of Political Parties 5. How Elections Work in India 5.1 Electoral System 5.2 Steps in an Election 6. Challenges in Electoral Politics 7. Importance of Political Awareness 8. Reforms
1. What is Constitution? 2. Why Do We Need a Constitution? 3. Making of the Indian Constitution 3.1 Historical Background 3.2 Constituent Assembly 3.3 Adoption 3.4 Leadership 4. Guiding Values of the Indian Constitution 4.1 Experiences of Struggle 4.2 Influence of World Events 4.3 Objective Resolution (1946) 5. The Preamble The Preamble is the introduction
1. Democracy 2. Meaning of Democracy 3. Key Features of Democracy 4. Arguments Against Non-Democracy Such systems lack accountability, transparency, and equality. 5. Why Democracy? (Merits) 6. Limitations of Democracy Even though democracy has limitations, it is still better than all other forms of government because it ensures people’s participation. 7. Broader Meaning of Democracy
1. Food Security Key Idea: 2. What is Food Security? 3. Importance of Food Security 4. Food Production in India 5. Challenges to Food Security in India 5.1 Poverty 5.2 Unequal Distribution 5.3 Malnutrition 5.4 Natural Calamities 5.5 Population Growth 5.6 Storage and Wastage 6. Measures to Ensure Food Security 6.1 Public Distribution System (PDS)
