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Total number of all possible outcomes of a random experiment is called Exhaustive events.denoted by ‘n’. in the above examples, n = 2 & n = 6.

The number of outcomes which entail as an outcome, or number of outcomes which favours the happening of an event, denoted by ‘m’

Eg., in the above example to get H, m = 1, & to get ‘Even’ no. S ={2,4,6}, m =3.

Let S be the sample space, A be an event, then A‘ is called complementary event of A is it contains elements of S, but it does’t contain any elements of event 

Eg., S = {1,2,3,4,5,6} if A = {1,2}, then A = {3,4,5,6}.

Two or more events are said to be mutually exclusive, if no two events can occur at a time in the same trial. 

Eg, When a coin is tossed getting Head in a trial is mutually exclusive of getting Tail in the same trial.

The outcomes of a random experiment are said to be independent if the happening of an Event in the trial is independent of getting the same (or other) Event in the subsequent trials.

Eg., Getting Head in the first Toss is independent of getting Head in the second toss of a coin.

Outcomes of a random experiment are called equally likely if they have equal chance of occurrence. 

Eg. When a die is thrown, all outcomes to get 1,2,.. .6 are having equal chance to get as an outcome.

1. A compound is formed only when the constituent elements combine in a fixed proportion. 

2. The properties of a compound are different from those of its constituent elements 

3. A compound cannot be broken down by physical methods. 

4. This is because a compound is made up of different elements that are chemically combined. Sodium chloride cannot be separated by physical methods such as filtration.

5. A compound can be separated into its constituent elements by chemical methods only.

1. A compound is formed only when the constituent elements combine in a fixed proportion. 

2. The properties of a compound are different from those of its constituent elements. 

3. A compound cannot be broken down by physical methods. 

4. Compound is made up of different elements that are chemically combined. 

5. A compound can be separated into its constituent elements by chemical methods only.

(D) Dantidurga

B) more developed

After the decline of the Kushanas and Satvahanas. India was divided into a number of small kingdoms and republics. The political condition was instable.

The Pallava ruler of Kanchi form a confederacy because he realized that he could not face Samudragupta alone. So he formed a confederacy of the kings of South India under his leadership.

The frontier states of east and the west surrender to Samundragupta because the ruler of these states accepted him as their overlord and paid large sum of money as a tribute.

Akbar planned to imprison Pratap in war, in the fort of Ajmer where today museum is located and being the Shastragar of-British It is also called Magzine. Akbar made Man Singh the Senapati of this war and Asaf Khan was made his companion.

Man Singh started from Ajmer on 3 April, 1576 and encamped first in Mandalgarh after two months encamped in village Molala and hammir adjacent to Nathdwara. Pratap encamped in a narrow valley between hills of Khamner and Gogunda, named Haldighati. In this only one man can pass at a time. It was an appropriate place for soldiers of Pratap who were familier to these hills. At the end military of both confronted each other in morning on 18 June 1576 A.D. In first step attack of Rajputs become successful in the leadership of Hakim Khan. The Mihattar Khan, officer of Akbar’s reserved army spread a fake rumour that Badshah Akbar is coming himself with a big army. It encouraged Mughal army and went ahead. Rajputs also marched and confronted in “Raktatal” at the bank of river Banas. In this war battle was held between Punna and Ram Prasad, elephant from Ranas side and Gajmukta and Gajraj from Shah’s side. Due to death of Ram Prasad’s Mahawat it came in the hands of Akbar, it was veiy important for him and he named him Pir Prasad. Pratap noticed Man Singh, his horse Chetak understood him and attacked Man Singh’s elephant, Mardana’s head with his front legs. Pratap attacked on Man Singh with full power but he hid inside the “Hauda” and his bodyguard died. In the meantime with the poisonous Khanjar tied in Mardana’s trunk cut the leg of Chetak. Pratap was surrounded by the Mughal army. Jhala Manna of Badi Saddi requested Pratap to give his royal symbols to him and move away from the battle field. Jhalla died (martyred). Pratap’s loyal Chetak died while crossing a small drain located in Baleecha village. Here a Chatri is located in Baleecha village in the memoiy of Chetak. Tears were rolled down from Pratap’s eyes for his dear horse. At the meantime, he heard words ‘O! Neela Ghoda Ra Aswar’. He saw his brother Shakti Singh. He apologized for his deeds. Pratap forgave him. The information we get from the scriptures Amar Kavya Vanshawali and Raj Prashasti. It was created by Rann Chod Bhatt intellectual in Sanskrit. Some of the Historians have given it the name result less or unended war or undecided war.

These three bases are worthwhile to analyze the result of the war – 

(i) According to object – Akbar’s objective was to catch Pratap alive and present in his court or to kill or to assimilate his whole state in his own empire but Akbar failed these objectives.

(ii) Victory of Mughal Army is not proved because displeaseners of Akbar with Man Singh and Asaf Khan, in which their Dyodhi was closed, running of Mughal army by fear, not chasing the army of Mewar are some scenes of war which brought the result of Haldi Ghati war in Pratap’s side.

(iii) In February 1577 and October 1577 to November 1579 three continuous Mewar campaigns were efforts of Akbar to fulfill his objectives which failed. The establishment of temporary capital in Avargarh near Kamalnath Mountain of Kolyari Village by Pratap is a prove as a winner.

In Raj Garh Fort.

The stage of development when man looks for more than just fulfillment of his basic needs, is called civilisation.

Characteristics of a civilisation:

1. Surplus food production

2. Flourishing of many arts and crafts

3. Law and order exists

4. Presence of a government.

The excavations carried out at various sites prove that around 4,500 years ago highly civilized people lived in this region and gave to the world its earliest cities, its first town planning, its first architecture in stone and clay and its first example of sanitary engineering and drainage system.

The earliest civilisations grew up on the banks of rivers because of the following reasons.

1. The rivers provided abundant supply of water for various purposes all through the year.

2. The lands near the rivers were very fertile, hence good for growing crops.

3. Rivers provided means of transport and communication.

Wheat was the staple food of the Harappans.

(1) A tube of narrow bore (i.e. very small diameter) is called a capillary tube. The word capillary is derived from the Latin capillus meaning hair, capillaris in Latin means ‘like a hair’.

(2) If a capillary tube is just partially immersed in a wetting liquid the liquid rises in the capillary tube. This is called capillary rise.

If a capillary tube is just partially immersed in a non-wetting liquid, the liquid falls in the capillary tube. This is called capillary depression.

The rise of a wetting liquid and fall of a nonwetting liquid in a capillary tube is called capillarity.

Applications of capillarity:

1. A blotting paper or a cotton cloth absorbs water; ink by capillary action.

2. Oil rises up the wick of an oil lamp and sap rises up xylem tissues of a tree by capillarity.

3. Ground water rises to the open surface through the capillaries formed in the soil. In summer, the farmers plough their fields to break these capillaries and prevent excessive evaporation. 

4. Water rises up the crevices in rocks by capillary action. Expansion and contraction of this water due to daily and seasonal temperature variations cause the rocks to crumble.

[Note: The rise of sap is due to the combined action of capilarity and transpiration. The transpiration pull, is considered to be the major driving force for water transport throughout a plant.]

1. The Indus Valley Civilisation was the Earliest civilisation of India.

2. Harappa is situated in Sahiwal district in Pakistan.

3. The Indus Valley Civilisation stood on the bank of river Indus

4. The largest building discovered at Mohenjodaro is Great Granary.

5. Bronze metal was used by the people of the Indus Valley Civilisation.

6. Indus people used Burnt bricks for constructing buildings.

7. The Harappan culture came to an end by 1500 BC

There are many reasons attributed to the fall of the Indus Valley Civilisation.

1. The Harappan cities were destroyed by invaders who were probably the Aryans.

2. Natural calamities such as floods, earthquakes and epidemics might have destroyed the civilisation.

3. River Indus might have changed its course and turned the region into a desert.

The three social classes were:

1. Rich merchants and priests e. the ruling class.

2. Small merchants, artisans and craftsmen.

3. Peasants and labourers.

The phenomenon of rise or fall of a liquid in capillary tube is called capillarity.

The Harappans worshiped the pipal tree and humped bull which have been found on hundreds of seals. They also worshiped Mother Goddess which were beautifully depicted as terracotta figurines. The Harappans also worshiped ‘Shiva’ or ‘Pashupati’. A three-faced figure with horns has been found sitting in the posture of a yogi. He is surrounded by a tiger, a rhinoceros, a buffalo, and an elephant. But no temple or any other religious building has been found so far. The Harappans believed in life after death and buried the dead with his belongings.

1. False.

Correct: The Harappan cities had well planned system.

2. False.

Correct: Farming was the main occupation of the Flarappans.

3. True.

4. True.

5. False.

Correct: The Indus Valley civilization was not governed by kings and queens

Various sites of the Indus Valley Civilisation were —The river valleys had warm and pleasant climate which favoured permanent settlement of population. Harappa, Mohenjodaro, Lothal, Kalibangan, Ropar, Alamgirpur, Banwali, Sutkagendor and others.

Trade relations with Mesopotamia have been proved with the discovery of Mesopotamian seals in the cities of the Indus Valley Civilization and Harappan seals in the ancient cities of Mesopotamia.

The main occupation of the people of the Indus Valley was farming. Farmers gr«w wheat, barley, fruits and vegetables. They also cultivated cotton. The land was fertile. The second occupation of the people of the Indus Valley was domestication of animals like goat, sheep, buffaloes, elephants, bulls, dogs and cats. The Indus Valley people were excellent potters and skilled crafts people. They made pottery of various shapes and sizes. They also made terracotta. The goldsmiths made gold and silver jewellery, copper smiths made utensils and the bronze smith made tools, weapons and metal sculptures. The people were also engaged in other crafts like brick laying, boat making, stone cutting, masonry and carpentry. Spinning and weaving were important occupations.

The Indus Valley civilization is also called the Flarappan civilizations because the things found in all the sites were very much like the articles found at Harappa.

The bronzesmiths made tools, weapons and metal sculptures such as the famous figure of the ‘dancing girl’. They were also engaged in other crafts like brick laying, boat making, stone cutting, masonry and carpentry.

The Great Granary was found at Mohenjodaro and it was the largest building discovered there. It was used for storing grains in huge quantities for lean periods. Brick platforms have been found near the granaries which were used for threshing grain. Many two-room shelters have also been found nearby which were perhaps used by labourers. Granaries were built close to river banks to facilitate easier transportation of grains during emergencies.

1. The Great Bath was a sort of modem swimming pool, discovered at Mohenjodaro. It is an example of excellent engineering’ work. It was built of burnt brick. It measures 11 - 88 x 7.01 metres

2. The lands near the rivers were very fertile, hence good for growing crops.

3. Rivers provided means of transport and communication.

4. The river valleys had warm and pleasant climate which favoured permanent settlement of population.

1. The main river of the Harappan civilization was Ravi.

2. The Great Bath is located in Mohenjodaro.

3. The main occupation of the Harappan were farming.

4. The rich wore ornaments made of gold, silver and ivoiy.

5. The Harappan seals are made of clay, soapstone and copper.

The liquids which wets the wall of the container, the value of their angle of contact is less than 90° and is called the acute angle of contact.

The Harappan cities were well-planned. The main streets ran parallel to each other, cut at right angles by smaller, streets, dividing the cities into rectangular blocks. The main roads were straight and very wide. The streets were often paved with baked bricks. Dwelling houses were building that people live in. They were in different sizes. They were made of baked bricks of very good quality. But they not used as office, trading place etc.

All the granaries were built close to the river bank so that the grains could be easily transported with the help of boats.

1. The arrangement of drains, wide roads and houses with toilets and drains attest to their sense of cleanliness. 

2. Mesopotamian seals have been found in Harappan cities and Harappan seals have been discovered in cities of ancient Mesopotamia. 

3. Big granaries and existence of towns prove the fact that they produced surplus food grains. 

4. A bronze figure of a dancing girl has been found. Several other images, weapons, utensils and tools of copper and bronze have also been found. Jewellery made of gold and silver has been found at various sites.

1. Great Granary: The Great Granary at Harappa was a large building. Historians believe that it was used to store surplus food grains. There were two rows of granaries. Each row had six granaries. 

2. Assembly Hall: The Assembly Hall was another striking building found in Mohenjodaro. It was a pillared hall with thick walls and 20 pillars made of burnt or baked bricks. This may have been and assembly hall, a prayer hall or a palace.

The pressure inside the pressure cooker is very high. This raises the boiling point of water and the temperature inside the cooker is higher them 100°C which results in faster cooking of food. At the mountains, the pressure is less, so the cooking of food is difficult.

Since nu = constant, hence 'n' decreases.