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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Triangle is the simplest polygon of all the closed figures formed in a plane by three line segments. It is a closed figure formed by three line segments having six elements - three angles (i) ∠ABC or ∠B (ii) ∠ACB or ∠C (iii) ∠CAB or ∠A and three sides - (iv) AB (v) BC (vi) CA.

Two lines in a plane can either be parallel or intersecting. Three lines in a plane may (i) be parallel to each other (ii) intersect each other in exactly one point (iii) intersect each other in two points (iv) intersect each other at most in three points.

If A, B, C and D are four points in a plane such that no three of them are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, then the closed figure made up of four line segments is called a quadrilateral with vertices A, B, C and D.

A circle is a collection of all points in a plane which are at a constant distance from a fixed point.

The position of a point in a plane is fixed w.r.t. to its distances from two axes of reference, which are drawn by the two graduated number lines XOX' and YOY', at right angles to each other at O.

Mensuration is the part of geometry concerned with ascertaining lengths, areas, and volumes.

Solid figures are three-dimensional figures that include cube, cuboid, cylinder, cone, sphere and hemisphere.

Trigonometry is that branch of Mathematics which deals with the measurement of the sides and the angles of a triangle and the problems related to angles.

Statistics is a branch of Mathematics which deals with collection, presentation, analysis, interpretation of numerical data and drawing inferences and conclusions there from.

Some aspects of the data can be described quantitatively to represent certain features of the data. An average is one of such representative measures.

In day to day life, we sometimes make the statements like "It may rain today" or "Train is likely to be late". The words (may, likely, unlikely, chances, doubt) show that the event, we are talking about, is not certain to occur. It may or may not occur.

The earth is sphere in shape and its visible features can be experienced on the surface. But, huge size of earth, increasing temperature and pressure limited the direct observations. The earth has three concentric layers NIFE, SIMA and SIAL.

A landform is a feature on the Earth's surface that is part of the terrain. Mountains, hills, plateaus, and plains are the major types of landforms.

All living organisms on the earth depend on water. About 71% of the earth's surface is covered by water. The earth is the only known planet in the solar system with abundant water.

Earth is a unique planet because the life is found only on this planet because of availability of water and air. The air is a mixture of several gases. The air encompasses the earth from all sides called the atmosphere.

Air has weights and it exerts pressure which varies from place to place. These variations are specified ion pressure belts. The pressure at different location of the world also varies in different seasons. This variation causes the movement of air called winds.

The temperature, atmospheric pressure, winds and precipitation are main elements of weather have an important effect on our lives. For example the houses we construct, the clothes we wear and the food we prefer mainly depend on weather and climatic conditions.

Economics as a subject matter of social science has been treated as a science of (a) Wealth, (b) Welfare, (c) Scarcity and Choice (d) Growth and Development and (e) Sustainable Development.

Economy is a system of socially and legally acceptable ways by which people get a living. An economy is also looked at as a system of cooperation for the satisfaction of human wants.

The issue of choice arises, because a) the resources are scarce and b) the resources can be put to many alternative uses.

Production process is the process of combining inputs, utilising their services and making production of goods and services. The entrepreneur organizes the production activities for which he earns profit or bears loss.

Demand for a commodity refers to the quantity of the commodity that a buyer is willing to buy at given price at given time. Individual demand is the quantity of a commodity that an individual buyer is willing to buy at the given price at given time.

Before money was invented people used to exchange goods for goods which was called barter system. There were many problems of barter system such as absence of a common measure of value, lack of double coincidence of wants, lack of space to store goods to exchange them for other goods etc. This prompted human society to discover money.

The story of Indian economy has two distinct phases. One, the economy during British period and two, the economy after independence.

This story is set in the future when children don’t have traditional books and schools. It is set about 150 years ahead. One day, Margie, a little girl in the story, makes a diary entry - ‘Today Tommy found a real book’.

‘The Accidental Tourist’ is a humorous story. The narrator, Bill Bryson, narrates his experiences as an air traveller. There were many things that he could not do properly.

1. Who was Ausable?

Ausable was a secret agent. A very important document concerning some new missiles was under his safe custody. He didn’t look like a secret agent as we read in books or see in films. He was fat and sloppy. His office was in a small room on the sixth and top floor. Fowler was very disappointed to meet him.

1. Why was Dr. Herriot really worried about Tricki?

When Dr. Herriot saw Tricki with his mistress, he was really worried. He was shocked at his appearance. The dog had become hugely fat. His eyes were bloodshot and rheumy. His tongue lolled from his jaws. Naturally, the miserable condition of the dog made him really worried.

1. Why do you think ordinary men and woman did not generally keep records of the what they did?

The ordinary men and woman generally did not keep records of what they did as they regarded it as a part of their daily routine and not anything important.

1. What is the Mesolithic Period?

It was period between 10,000 to 8,000 BC.

1. What was Citadel?

Citadel is the west part of Harappan city. It is smaller but higher.

1. What kind of evidence from burials do archaeologists use to find out whether there were social difference amongst those who were buried?

In Brahmagiri, archaeologists located a skeleton buried with 33 gold beads, 2 stone beads, 4 copper bangles and 1 conch shell. Some other skeletons were found but with only a few pots. This helped archaeologists to find out social differences of those who were buried.

1. What are Varnas?

The priests divided into four groups called Varnas.

1. What was the original name of Lord Buddha?

Siddartha was the original name of Lord Buddha.

1. What do you mean by an empire?

Large kingdom where different types of people live in different parts of the kingdom is known as an empire.

1. What are Jatakas?

Jatakas were stories written and preserved by Buddhist monks in Sanghas.

1. What were the things for which South India was famous?

South India was famous for gold and spices, especially pepper and precious stones.

1. Name the capital of the Chalukyas.

Aihole was the capital of Chalukyas.

1. Name the God who that were worshipped in the earliest Hindus temples.

Deities such as Vishnu, Shiva and Durga were worshipped in the earliest Hindu temples.

1. List some of the technological changes associated with this period?

(a) The Persian wheel in irrigation (b) The spinning wheel in weaving (c) Firearms in combat

1. Who were the parties involved in the ‘tripartite struggle’?

Gujara - Prathihara, Rashtrakuta and Pala dynasties.

1. Which ruler first established his or her capital at Delhi?

Tomara Rajputs were the first rulers to establish their capital at Delhi.

1. What were the central provinces under the control of the Mughals?

Delhi, Agra, Awash, Allahabad, Bihar, Bengal, Gujarat, Ajmer, Lahore, Multan and Kabul.

1. What was a Shikhara?

Shikhara was the topmost portion of the building. The top of the building built during Chola rulers was called Shikhara.

1. Name three important centres of trade.

Three important centres of trade were - Surat, Hampi and Masulipatnam.

1. On what basis society was divided?

Society was divided according to the rules of Varna, prescribed by the Brahmanas.

1. How did intense devotion come in worship?

Intense devotion came into worship in 8th century and later on due to the legacy of different kinds of Bhakti and Sufi movements.

India is a diverse country with a rich cultural heritage and a multitude of regional cultures. Each region in India has its own distinct language, customs, traditions, art forms, music, dance, and cuisine.