Articles

Vertical division of power among different levels of government is one of the major forms of power-sharing in modern democracies. It is most commonly referred to as federalism.

Thermodynamics is concerned with the relationship between other forms of energy and heat. It explains how thermal energy is converted from other forms of energy. The energy coming from heat is termed thermal energy. When the tiny particles within an object move, they generate heat, more amount of heat is generated, when these particles move at a faster pace.

In a democracy, all power does not rest with any one organ of the government. An intelligent sharing of power among legislature, executive and judiciary is very important to the design of a democracy.

We face a dilemma: democracy is seen to be good in principle, but felt to be not so good in its practice. This dilemma invites us to think hard about the outcomes of democracy.

A political party is a group of people who come together to contest elections and hold power in the government. They agree on some policies and programmes for the society with a view to promote the collective good. Parties reflect fundamental political divisions in a society.

The existence of social diversity does not threaten democracy. Political expression of social differences is possible and sometimes quite desirable in a democratic system. Three kinds of social differences that can take the form of social divisions and inequalities are social differences based on gender, religion and caste.

Democracy is a form of government in which the rulers are elected by the people. In a democracy the final decision-making power must rest with those elected by the people.

Rights are reasonable claims of persons recognised by society and sanctioned by law. Rights are necessary for the very sustenance of a democracy.

President is the head of the state and is the highest formal authority in the country. Prime Minister is the head of the government and actually exercises all governmental powers. He takes most of the decisions in the Cabinet meetings.

Elections take place regularly in any democracy. Elections is a mechanism by which people can choose their representatives at regular intervals and change them if they wish to do so.

The constitution of a country is a set of written rules that are accepted by all people living together in a country. Constitution is the supreme law that determines the relationship among people living in a territory (called citizens) and also the relationship between the people and government.

Three-fourth of the earth's surface is covered with water, but only a small proportion of it accounts for freshwater that can be put to use. This freshwater is mainly obtained from surface run off and ground water that is continually being renewed and recharged through the hydrological cycle.

Biodiversity or Biological Diversity is immensely rich in wildlife and cultivated species, diverse in form and function but closely integrated in a system through multiple network of interdependencies.

We use different materials and services in our daily life. Some of these are available in our immediate surroundings, while other requirements are met by bringing things from other places.

Production of goods in large quantities after processing from raw materials to more valuable products is called manufacturing.

We use different things in our daily life made from metal. Various metals are extracted from minerals after proper refinement. Minerals are an indispensable part of our lives.

1. In which hemisphere does India lie?

Northern hemisphere.

1. Why are people considered an important part of society?

People are considered an important part of society as they develop the economy and the society, make and use resources. People are both producers and consumers of the resources.

1. What is climate?

Climate refers to sum total of weather conditions over a large area for a long period of time (30 - 40 years).

1. What is a river/drainage basin?

A river/drainage basin is an area drained by a single river system.

It is difficult for us to imagine a world without printed matter. We find evidence of print everywhere around us – in books, journals, newspapers, prints of famous paintings, and also in everyday things like theatre programmes, official circulars, calendars, diaries, advertisements, cinema posters at street corners.

1. What does the geology of the peninsular plateau show?

The geology of the peninsular plateau shows that it constitutes one of the ancient landmasses on the earth’s surface. It was supposed to be one of the most stable blocks.

In 1900, a popular music publisher E.T. Paull produced a music book that had a picture on the cover page announcing the ‘Dawn of the Century’. At the centre of the picture is a goddess-like figure, the angel of progress, bearing the flag of the new century. She is gently perched on a wheel with wings, symbolising time.

In 1848, Frédéric Sorrieu, a French artist, prepared a series of four prints visualising his dream of a world made up of ‘democratic and social Republics’, as he called them. The first print of the series, shows the peoples of Europe and America - men and women of all ages and social classes - marching in a long train, and offering homage to the statue of Liberty as they pass by it.

The French Revolution opened up the possibility of creating a dramatic change in the way in which society was structured. Before the eighteenth century society was broadly divided into estates and orders and it was the aristocracy and church which controlled economic and social power.

A lot of this diversity is fast disappearing. Between 1700 and 1995, the period of industrialisation, 13.9 million sq km of forest or 9.3 per cent of the world’s total area was cleared for industrial uses, cultivation, pastures and fuelwood.

An event for an experiment is the collection of some outcomes of the experiment. The Probability of an event lies between 0 and 1 (0 and 1 inclusive).

An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.

To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical. The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate axes.

Facts or figures, collected with a definite purpose, are called data. Statistics is the area of study dealing with the presentation, analysis and interpretation of data. How data can be presented graphically in the form of bar graphs, histograms and frequency polygons.

A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.

Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure. Two congruent figures have equal areas but the converse need not be true.

Two figures are congruent, if they are of the same shape and of the same size. Two circles of the same radii are congruent. Two squares of the same sides are congruent.

When we talk of ‘globalisation’ we often refer to an economic system that has emerged since the last 50 years or so. But as you will see in this chapter, the making of the global world has a long history - of trade, of migration, of people in search of work, the movement of capital, and much else.

As you have seen, modern nationalism in Europe came to be associated with the formation of nation-states. It also meant a change in people’s understanding of who they were, and what defined their identity and sense of belonging.

In this chapter you will read about nomadic pastoralists. Nomads are people who do not live in one place but move from one area to another to earn their living. In many parts of India we can see nomadic pastoralists on the move with their herds of goats and sheep, or camels and cattle.

In the spring of 1945, a little eleven-year-old German boy called Helmuth was lying in bed when he overheard his parents discussing something in serious tones.

One type of polynomial is the quadratic polynomial of the form ax² + bx + c, a ≠ 0. When you equate this polynomial to zero, you get a quadratic equation. Quadratic equations come up when you deal with many real-life situations.

Euclid’s division algorithm, as the name suggests, has to do with divisibility of integers. Stated simply, it says any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b.

Trigonometry is one of the most ancient subjects studied by scholars all over the world. Trigonometry was invented because its need arose in astronomy. Since then the astronomers have used it, for instance, to calculate distances from the Earth to the planets and stars.

The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). trigonometry is the study of relationships between the sides and angles of a triangle.

A polynomial p(x) in one variable x is an algebraic expression in x of the form

An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables. A linear equation in two variables has infinitely many solutions.

A number r is called a rational number, if it can be written in the form p/q, where p and q are integers and q ≠ 0. A number s is called a irrational number, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.

So far, you have been dealing with figures that can be easily drawn on our notebooks or blackboards. These are called plane figures.

Sum of the

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice-versa. This property is called as the Linear pair axiom. If two lines intersect each other, then the vertically opposite angles are equal.

Much of mathematics is about finding a pattern - a recognisable link between quantities that change. In our daily life, we come across many patterns that characterise relations such as brother and sister, father and son, teacher and student.

The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle’. The subject was originally developed to solve geometric problems involving triangles.

The equation x² + 1 = 0 has no real solution as x² + 1 = 0 gives x² = -1 and square of every real number is non-negative.