With the advent of computers, the everyday tasks of human beings have become very cheap and easy. A computer can work alone like many humans. That is why the computer has many benefits in our life. Today it is used everywhere in school, college office, etc.

A high-speed computer is a fast-moving electronic machine. Through a computer, any programmer can do the work equivalent to the work done by a large number of people. Through this, a large amount of data can be processed simultaneously. The computer can accept any command within micro or nanoseconds.

While its ability to work is fast, the processed data is also 100% accurate. We will get the output as we input it, we will find the hundred percent error-free calculation inside it. The accuracy of computer results is many times better than that of humans. There is no possibility of any kind of mistake here. The work done by it is 100% pure. Attendance salary in all of school, college factory, etc., and all other accounting work are done in today’s time only through the computer.

There was a time when humans used to store all the paperwork done by them inside Almira or a very big room. And all this work could not be done from one or two rooms, for this a lot of space was required to keep these files. But today, if we store all this in computer memory, then we can store the data of files kept in thousands of acres in a system. Its memory can be easily reduced or increased. We can also transfer the data stored in one computer to another computer. We can transfer the stored data anywhere through an email or server. You should not take the above words otherwise and must know that only data like audio video images text etc. can be stored in the computer.

A computer is a non-exhausting electronic device. It does not feel tired like humans. We can use it continuously for many hours. A computer is a hard-working electronic device that keeps you working continuously for many hours without getting tired.

There is a machine that automatically keeps him working while sleeping. Whatever we give to a computer, it automatically follows it.

Through the work variety of computer, we can complete many different tasks at one time. We can work fast on many subjects or on many fields at one time. We can surf different types of web applications in different windows on our laptops or computer. In today’s era, the computer is one of the most reliable partners of human beings. We can count on computers to give accurate results. Its life is very long and it works for a long time. If there is a deficiency in any part of it, then it can be easily changed.

Any data is stored in the computer through soft copy. This means that the data that is stored in our laptop or computer, we can call it soft copy. For which we do not need any type of stationery or papers. By doing this we save a lot of money. Because here the data can be stored in an electronic medium and the work that we used to do in our files gets done in our laptop.

]]>Geomorphology derives from the Greek words Geomorphology [Geo-Earth (Earth), morphi-form (form), and logos-discourse (description)], which literally means ‘study of landforms’. Under this, the reliefs of the globe’s terraces, their constructional processes, and the interrelations between them and humans are studied.

**The following three types of reliefs are included under this science**

1. **First class relief** – It covers the continent and oceanic basin.

2. **Second class relief** – It includes the study of mountains, plateaus, plains, and lakes.

3. **Third-class relief **– Under this, the topography generated due to sarita, ocean water, groundwater, wind, glaciers, etc. is studied.

The present form of geomorphology has become possible as a result of gradual systematic developments in the last centuries. A preliminary study of *topographies in Greece*, Greece, and Egypt 500 B.C. It has started with but some basic concepts of geomorphology have been given to geomorphology, which is as follows

Several fundamental concepts related to the development of topographies have been presented in geomorphology, which has made the gradual development of geomorphology possible. Professor Thornthvette has beautifully described these concepts in his book ‘**Principles of Geomorphology**‘.

In the construction of topography, the geological processes, and rules which are active at the present time, they have been employed in the entire geological history even though their intensity has not been the same.

It is also called the principle of uniformity. It is a fundamental theory of geomorphology, first proposed by James Hutton in 1785, and later John Playfair and Sir Charles Loyal carried this concept forward. Hatten formulated the concept of uniformism by criticizing the theory of contingency prevalent in his time. He told that the history of gradual development is hidden behind the external form of nature we see today. It is not that that external form is suddenly attained. Every process that works in the land is used in the past, is also working in the present time, and will be employed in the future. By looking at the functions of the current processes or the current forms of the present, one can get information about the topography of the past.

These processes of erosion have always been active, they were active in the past, they will also be in the future, although the area and intensity of their work may vary. It may be that the process that is working fast today would have been less effective in the past.

The geological structure is an important controlling factor in the development of topography and is reflected in topography. The above concept implies that structure remains an important contributor to the construction of topographies.

Davis also considered structure to be an important factor in the evolution of topography along with process and condition. According to Polridge and Morgan, “The rocks, whether igneous or sedimentary, present on the one hand the handwriting of the history of the earth, on the other hand, provide the basis for contemporary scenery.” Variations in the composition and nature of rocks have a significant effect on the rate of erosion and erosion of the terrain, due to which there is a local and regional difference in the intensity of processes in different rock areas, which leads to variations in topography. For example, sandstone is a highly inaccessible rock. In contrast, the rock is an inaccessible rock. In the area of sandstone rock, most of the rainwater goes underground, so rivers are less in such areas, their tributaries are also less The valleys of the rivers are shallow. In contrast, the water flows more on the surface in the rock zone and the valleys are also deep and well-defined. Cart topography is formed due to the action of water in the limestone areas.

Metamorphic rocks are often harder and more compact than other types of rocks, due to which they do not erode easily, hence rocks like slate, nees, quercite, schist, etc. form hills, mountains, and high plateaus. Granite and fine rocks often form the dome. It is thus clear that the effect of the structure is clearly reflected in the topographies.

In the development of the landscape, there are more complexities than simple ones. It is generally believed that a particular type of process creates a specific topographic set, but in reality, it does not occur because only one process is not active in a landmass but more than one process is employed, although One process can be most effective, for example in dry or semi-arid regions, although wind erosion is a major factor, flowing rain also becomes an active factor here. In addition, the development of topography is not related to a single erosion cycle but is a byproduct of several erosion cycles. Due to the disruption caused by geomagnetic movements, more cyclic and mixed topographies are seen more than simple and single cyclic topographies.

Therefore, complexities are more common than simplifications in the development of topographies and there are two reasons for these complications – one is the operation of more than one process and the other is more than one development cycle.

*On the basis of these facts, Harburg has divided the topographies into the following five major classes.*

(i) Simple topography

(ii) Mixed topography

(iii) Acyclic topography

(iv) Multi-cyclic topography

(v) Exposed or regenerated topography

Geomorphic processes leave their own distinct mark on topography and each process forms a distinct set of topographies.

According to this concept, each process creates different topographies and has clear characteristics of topography created by a particular process and with the help of these specifications, the topography generated by one process can be distinguished from the topologies developed by other processes. . Examples

For delta, Gokhur lakes are the byproduct of flowing water, while Barkhan, Inselvarg, etc. are related to the winding process. Similarly, the Moren, Drumlin escar, U shaped valleys are topography generated by Himani.

Since each process generates distinct topographies, genetic classification of topographies can be made based on these characteristics. Keeping this fact in mind, Davis presented a genetic classification of the topographies.

By classifying various topographies in terms of their respective processes, their construction method, the sequence of development and geographical history, etc. can be easily understood. Considering the significance of the process in the development of the landscape, it emphasizes that the development of landforms does not happen in an irregular manner. Rather, there is a definite correlation of other topographies with some topographies, that is, if some topographies are found in an area, it can be estimated with the help of the relevant process which other topographies are likely to be found there.

Rocks are geological history books and fossils are its pages. By studying the present form of rocks, its history can be traced to how old this rock is and how it was built.

Wallbridge and Morgan have clarified that “rocks, whether igneous or flaky, form the handwriting of the history of the earth on one side, providing the basis for contemporary scenery on the other hand. Hatton also learned about geological history by using rocks. Have tried to do.

Similarly, the study of fossils gives an understanding of the cycle of rock development, climatic conditions, and physical conditions at the time of construction, such as the formation of coal in humid and hot climatic conditions due to vegetation being buried in deep river valleys.

As various erosive factors are employed on the ground floor, gradual landforms, which have distinct characteristics in successive stages of development, are formed.

The topography created by any process has different characteristics at different stages of its development. Thus each stage has its own specific characteristics.

**Davis** has also emphasized in his concept of the landscape shape that topographies have successive stages of development and each stage has its own characteristic features. **Davis** has described three stages of development of topographies as puberty, maturity, and old age. Through which an elevation attains the base plane (peneplain). Although many geoscientists currently do not consider the cyclical development of topography in young, adult, and old age as suggested by Davis, Hank has emphasized the concept of timeless development of topographies.

]]>

Our family is the basis of society. The entire society is made up of families. Without family, both human and society cannot exist. There are not many families in society. We all live in a family and the family is an institution that is found in all countries. The family is a universal institution made up of a married woman, man, and child. The existence of society depends on this institution only.

The family is a biological social unit of the husband and wife and their children. The family can also be called a social institution, a society recognized by an organization that fulfills certain human needs.

Every child has the right to be brought up in the family. If the parents of many children die, then other members of the family such as grandparents, maternal grandparents and uncle Bua half take care of them.

If there are no children, then they live in an ashram which becomes their family or some family adopts them. For such children, the government and other social institutions continue to provide financial and other social assistance through various schemes from time to time. From here, the complete development of these children becomes possible. Despite not being in the family, they get their own family.

Many times children stay in the ashram and stay on the streets. The family is not made up of only males and females but children are also an integral part of it. These children can be born or adopted. Husband’s wife starts their family after marriage.

There are a variety of questions about the changing concepts of the family in today’s modern society. *How are families essential to society?* **How are families created and maintained?** Who are members of a family? **What is the role of the family in society?** What are the roles of the members of the family? *What makes a family?* What social forces have shaped our perceptions of a family?

Christmas is a global fast celebrated with pomp. Today more than 100 small and big countries across the world celebrate this festival. This festival is mainly for those who believe in Christianity, but people of all other religions also take part in this festival.

It is celebrated every year on 25 December all over the world because this day is considered to be the birthday of Jesus Christ. The prominence of this festival is increasing in many countries of the world, the main reason for this was that Jesus Christ did not accept high and low. He gave a message to the people of the entire world to live with love and brotherhood, due to which almost all the major countries of the world celebrate this festival with great pomp. In other ways, the Christmas festival also becomes very important because this day comes only a few days before the new year. You can also say that the last days of the month of December are bigger than enthusiasm.

Children especially eagerly wait for Christmas. On this day, children are eagerly waiting for the arrival of Santa Claus. As we all know Christmas is the biggest festival of Christians which is celebrated on 25 December of every year. We can also say that it is celebrated in the winter season. On this day there is a state holiday and all government schools, offices, colleges are closed.

Christmas preparations are done a long time in advance. People decorate their homes with different types of lights and stars. Very large quantities of Christmas tree Santa Claus, red and white clothes, cake gifts, etc. start appearing in the markets.

On Christmas Day i.e. December 25, people go to the nearest church and burn candles and pray to Jesus Christ and celebrate his birthday. On this day people make a very beautiful Christmas tree in their homes and also feed each other cake and congratulate them.

On this day different types of forums are decorated and comedy programs are organized. Individuals in Santa Claus dress go by giving gifts and toffees to children. The Christmas festival gives a message to everyone, big and small, to live together and to make each other feel lovingly like brotherhood and sacrifice.

Although Christmas is celebrated by people of all religions, Christmas is a major and major festival for Christians mainly. According to old beliefs, Jesus was born on December 25 at 12:00 pm. So every year this day is celebrated as the birthday of Jesus Christ or we can say that Christmas Day is celebrated. It is believed that he was born on this day in a cowshed in the city of Bethlehem.

**The Christmas festival** is celebrated in almost every country in the world today. On this day, people celebrate this festival with great enthusiasm. Children wear a variety of colorful costumes. In many big countries of the world, this day is declared a state holiday. This and most people who belong to Christianity mostly celebrate it. In the world today, not only those who keep Christianity but also people of other religions celebrate this festival with joy.

People cook different types of dishes in their homes. This festival took a long time to reach here and faced many obstacles. For the last nearly one and a half years, *the Christmas festival* has been held without any hindrance.

Earlier there were many differences among people in celebrating this festival.

Generally, this day i.e. 25th of December is considered to be the **birthday of Jesus Christ**, that is **why Christmas is organized on the 25th of December**, but in the beginning, even the religious people were not ready to recognize this day. Because this defeat was a festival day of the **Roman race**. On this day, the sun god was worshiped in the Roman race. According to the Roman race, it was believed that the sun was born on this day.

According to him, worshiping the sun was the official religion of the Roman emperors in those days. Later, when **Christianity** was mainly propagated, people began to worship this day by considering Isa Masih as the incarnation of the sun. But this festival could not get recognition at that time. Initially, people who followed Christianity did not organize any kind of **public festival**.

An old list of **Roman bishops** that was compiled in 354 A.D. found that the f**irst Christmas was celebrated in 336 A.D.** which is the **first recorded Christmas celebration**.

Around 360 AD, the first huge ceremony was held in a church in Rome on the birthday of Christ in which the Pope of the Christians also attended the ceremony. But even after this, there remained considerable differences regarding the date of Christmas. The Jewish religious shepherds had a tradition of celebrating the 8-day spring festival since ancient times. After preaching Christianity, the shepherds grew up to participate in this festival and started sacrificing the first child of their animals to the Messiah and also feasted in his name. But this ceremony remained only for a particular caste, which was the shepherd.

At that time, some other ceremonies were also organized these days, whose duration was often between 30 November to 2 February. In which Yule festival of Norsemen caste in which servants were given complete freedom to conduct themselves as owners. These festivals had no connection with Christianity at that time.

In the third century, celebrations on the birthday of Jesus Christ were considered very seriously, but most people refused to participate in the discussion about this festival at that time. Nevertheless, discussions were held in the Christian faith and it was decided that what should be done mainly for this festival on the day of spring. Accordingly, it was fixed on 28 March and then changed to 19 April. But this process of changing the date continued and finally, 25 December was declared as the birthday of Christ.

Although at that time, the day of 25 December was declared as the birth celebration of Jesus Christ, still it took a long time for it to come into vogue. Finally, on 25 December in Jerusalem, the **birthplace of Isa**, it was accepted as the **birth celebration of Jesus Christ** in the middle of the fifth century.

Even after this, many contradictions continued to **celebrate Christmas Day**. During the Protestant movement in the 13th century, it was felt that much of the influence of the old Pagan religion was left on him, which led to a long ban on songs of devotional songs like Christmas carols. And on 25 December 1664, a new law was made in England according to which 25 December was declared as Christmas fasting day.

This **anti-Christmas movement** also spread to other countries of the world, which resulted in the **Christmas festival** being banned in Boston, USA in 1690 AD. Later in 1836, Christmas was legally recognized in America and the day of 25 December was accepted as **Christmas Day** and this day was also declared as a public holiday. In this way, this festival got a lot of strength in other countries of the world too.

In different parts of European countries, there was an ancient tradition of decorating trees for any kind of laughter. Maybe the tradition of decorating trees on **Christmas day** is prevalent here.

Later many legends were associated with these ideologies.

In 1821, the **Queen of England** gave birth to the tradition of placing the idol of the deity in the tree for the first time in 1821 AD, by making children a **Christmas tree**. The **first Christmas card** to be greeted was first created in London in 1844 AD, later this practice spread all over the world by 1870 AD.

On **Christmas Day**, the most famous character, **Santa Claus**, was followed much later. **Saint Nicholas**, whose **birthday** was celebrated on 6 December, was a very saint of the Middle Ages. At that time, it was believed that **Saint Nicholas** brought a variety of gifts for children on his birthday. This Saint Nicholas later became **Santa Claus** and gradually became popular as Santa Claus all over the world.

Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on

(i) the same day?

(ii) consecutive days?

(iii) different days?

Solution for Ex 15.2 Class 10 Maths Question 1

**Ex 15.2 Class 10 Maths Question 2.**

A die is numbered in such a way that its faces show the number 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws:

What is the probability that the total score is at least 6?

(i) even

(ii) 6

(iii) at least 6

**Solution for Ex 15.2 Class 10 Maths Question 2**

**Ex 15.2 Class 10 Maths Question 3.**

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is doubles that of a red ball, determine the number of blue balls in the bag.

**Solution for Ex 15.2 Class 10 Maths Question 3**

**Ex 15.2 Class 10 Maths Question 4.**

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

**Solution for Ex 15.2 Class 10 Maths Question 4**

**Ex 15.2 Class 10 Maths Question 5.**

A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue balls in the jar.

**Solution for Ex 15.2 Class 10 Maths Question 5**

]]>

Complete the following statements:

(i) Probability of an event E + Probability of the event ‘not E’ = ………

(ii) The probability of an event that cannot happen is ……… Such an event is called ………

(iii) The probability of an event that is certain to happen is ………. Such an event is called ………

(iv) The sum of the probabilities of all the elementary events of an experiment is ………..

(v) The probability of an event is greater than or equal to …………. and less than or equal to ………..

Solution for Ex 15.1 Class 10 Maths Question 1

**Ex 15.1 Class 10 Maths Question 2.**

Which of the following experiments have equally likely outcomes? Explain.

(i) A driver attempts to start a car. The car starts or does not start.

(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

(iii) A trial is made to answer a true-false question. The answer is right or wrong.

(iv) A baby is born. It is a boy or a girl.

Solution for Ex 15.1 Class 10 Maths Question 2

**Ex 15.1 Class 10 Maths Question 3.**

Why is tossing a coin considered to be a fair way of deciding which team should get the bail at the beginning of a football game?

Solution for Ex 15.1 Class 10 Maths Question 3

**Ex 15.1 Class 10 Maths Question 4.**

Which of the following cannot be the probability of an event?

(A) 2/3

(B) -1.5

(C) 15%

(D) 0.7

Solution for Ex 15.1 Class 10 Maths Question 4

**Ex 15.1 Class 10 Maths Question 5.**

If P (E) = 0.05, what is the probability of ‘not E’?

Solution for Ex 15.1 Class 10 Maths Question 5

**Ex 15.1 Class 10 Maths Question 6.**

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i) an orange flavoured candy?

(ii) a lemon flavoured candy?

**Solution for Ex 15.1 Class 10 Maths Question 6**

**Ex 15.1 Class 10 Maths Question 7.**

It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

**Solution for Ex 15.1 Class 10 Maths Question 7**

**Ex 15.1 Class 10 Maths Question 8.**

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is

(i) red?

(ii) not red?

**Solution for Ex 15.1 Class 10 Maths Question 8**

**Ex 15.1 Class 10 Maths Question 9.**

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be

(i) red?

(ii) white?

(iii) not green?

**Solution for Ex 15.1 Class 10 Maths Question 9**

**Ex 15.1 Class 10 Maths Question 10.**

A piggy bank contains hundred 50 p coins, fifty Rs. 1 coins, twenty Rs. 2 coins and ten Rs. 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i) will be a 50 p coin?

(ii) will not be a Rs. 5 coin?

**Solution for Ex 15.1 Class 10 Maths Question 10**

**Ex 15.1 Class 10 Maths Question 11.**

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see figure). What is the probability that the fish taken out is a male fish?

**Solution for Ex 15.1 Class 10 Maths Question 11**

**Ex 15.1 Class 10 Maths Question 12.**

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure.), and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

**Solution for Ex 15.1 Class 10 Maths Question 12**

**Ex 15.1 Class 10 Maths Question 13.**

A die is thrown once. Find the probability of getting

(i) a prime number

(ii) a number lying between 2 and 6

(ill) an odd number

**Solution for Ex 15.1 Class 10 Maths Question 13**

**Ex 15.1 Class 10 Maths Question 14.**

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

**Solution for Ex 15.1 Class 10 Maths Question 14**

**Ex 15.1 Class 10 Maths Question 15.**

Five cards – the ten, jack, queen, king and ace of diamonds, are well shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is

(a) an ace?

(b) a queen?

**Solution for Ex 15.1 Class 10 Maths Question 15**

**Ex 15.1 Class 10 Maths Question 16.**

12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

**Solution for Ex 15.1 Class 10 Maths Question 16**

**Ex 15.1 Class 10 Maths Question 17.**

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

**Solution for Ex 15.1 Class 10 Maths Question 17**

**Ex 15.1 Class 10 Maths Question 18.**

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i) a two digit number.

(ii) a perfect square number.

(iii) a number divisible by 5.

**Solution for Ex 15.1 Class 10 Maths Question 18**

**Ex 15.1 Class 10 Maths Question 19.**

A child has a die whose six faces show the letters as given below:

The die is thrown once. What is the probability of getting

(i) A?

(ii) D?

**Solution for Ex 15.1 Class 10 Maths Question 19**

**Ex 15.1 Class 10 Maths Question 20.**

Suppose you drop a die at random on the rectangular region shown in figure. What is the probability that it will land inside the circle with diameter 1 m?

**Solution for Ex 15.1 Class 10 Maths Question 20**

**Ex 15.1 Class 10 Maths Question 21.**

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that

(i) she will buy it?

(ii) she will not buy it?

**Solution for Ex 15.1 Class 10 Maths Question 21**

**Ex 15.1 Class 10 Maths Question 22.**

Two dice, one blue and one grey, are thrown at the same time. Now

(i) Complete the following table:

(ii) A student argues that-there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability 1/11. Do you agree with this argument? Justify your answer.

**Solution for Ex 15.1 Class 10 Maths Question 22**

**Ex 15.1 Class 10 Maths Question 23.**

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e. three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

**Solution for Ex 15.1 Class 10 Maths Question 23**

**Ex 15.1 Class 10 Maths Question 24.**

A die is thrown twice. What is the probability that

(i) 5 will not come up either time?

(ii) 5 will come up at least once?

[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment.

**Solution for Ex 15.1 Class 10 Maths Question 24**

**Ex 15.1 Class 10 Maths Question 25.**

Which of the following arguments are correct and which are not correct? Give reasons for your answer.

(i) If two coins are tossed simultaneously there are three possible outcomes- two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3.

(ii) If a die is thrown, there are two possible outcomes- an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.

**Solution for Ex 15.1 Class 10 Maths Question 25**

The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

**Solution for Ex 14.4 Class 10 Maths Question 1**

**Ex 14.4 Class 10 Maths Question 2.**

During the medical check-up of 35 students of a class, their weights were recorded as follows:

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

**Solution for Ex 14.4 Class 10 Maths Question 2**

**Ex 14.4 Class 10 Maths Question 3.**

The following table gives production yield per hectare of wheat of 100 farms of a village.

Change the distribution to a more than type distribution, and draw its ogive.

**Solution for Ex 14.4 Class 10 Maths Question 3**

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

**Solution for Ex 14.3 Class 10 Maths Question 1**

**Ex 14.3 Class 10 Maths Question 2.**

If the median of the distribution given below is 28.5, find the values of x and y.

**Solution for Ex 14.3 Class 10 Maths Question 2**

**Ex 14.3 Class 10 Maths Question 3.**

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

**Solution for Ex 14.3 Class 10 Maths Question 3**

**Ex 14.3 Class 10 Maths Question 4.**

The lengths of 40 leaves of a plant are measured correct to nearest millimetre, and the data obtained is represented in the following table:

Find the median length of the leaves.

**Solution for Ex 14.3 Class 10 Maths Question 4**

**Ex 14.3 Class 10 Maths Question 5.**

The following table gives the distribution of the lifetime of 400 neon lamps:

Find the median lifetime of a lamp.

**Solution for Ex 14.3 Class 10 Maths Question 5**

**Ex 14.3 Class 10 Maths Question 6.**

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows:

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

**Solution for Ex 14.3 Class 10 Maths Question 6**

**Ex 14.3 Class 10 Maths Question 7.**

The distribution below gives the weight of 30 students of a class. Find the median weight of the students.

**Solution for Ex 14.3 Class 10 Maths Question 7**

]]>

As we have learned in the previous class, in the tests given the polymer is the great one which has come the most frequently i.e. the observation which has the highest frequency. In **CBSE NCERT chapter 14 ex 14.2** we will find the **polymer of classified data**. In this exercise, we will learn that there is more than one assuming that there is only one maximum frequency. We will limit the **ex 14.2 maths class 10** to problems with only one polymer. We will try to explain this to you through example number 4. As shown in example number 4, how the number of levers in 10 cricket matches has been given by Akash whose polymer we will extract. **ex 14.2 Example 4** gives the number of wickets and the number of cricket matches. You can take the **polymer formula** from your textbook where all the alphabets used in the formula are explained differently. Which is like this

h = measure of the square interval

l = lowest number of polymer class

f0 = frequency number of the square just before the polymer square

f1 = frequency number of polymer class

f2 = Frequency number of square coming right after polymer square

The following table shows the ages of the patients admitted to a hospital for a year.

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

The following data gives information on the observed lifetimes (in hours) of 225 electrical components:

Determine the modal lifetimes of the components.

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Find the mode of the data.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:

]]>

As we have learned in the previous class, to get the mean of the classified data, we need the sum of the figures and the number of figures. As an example, we try to understand it. Suppose the marks obtained by a class of 30 students in a mathematics paper out of 100 are shown through the table given below. Now we have to find the mean of the marks obtained by these students here. The medium that we also call average. Here we will learn in-depth about

You can see the table depicted on

**Ex 14.1 Class 10 Maths Question 1.**

A survey was conducted by a group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Which method did you use for finding the mean, and why?

Solution for Ex 14.1 Class 10 Maths Question 1

**Ex 14.1 Class 10 Maths Question 2.**

Consider the following distribution of daily wages of 50 workers of a factory.

Find the mean daily wages of the workers of the factory by using an appropriate method.

**Solution for Ex 14.1 Class 10 Maths Question 2**

**Ex 14.1 Class 10 Maths Question 3.**

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is ₹ 18. Find the missing frequency f.

**Solution for Ex 14.1 Class 10 Maths Question 3**

**Ex 14.1 Class 10 Maths Question 4.**

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method

**Solution for Ex 14.1 Class 10 Maths Question 4**

**Ex 14.1 Class 10 Maths Question 5.**

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

**Solution for Ex 14.1 Class 10 Maths Question 5**

**Ex 14.1 Class 10 Maths Question 6.**

The table below shows the daily expenditure on food of 25 households in a locality.

Find the mean daily expenditure on food by a suitable method.

**Solution for Ex 14.1 Class 10 Maths Question 6**

**Ex 14.1 Class 10 Maths Question 7.**

To find out the concentration of in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented below:

Find the mean concentration of in the air.

**Solution for Ex 14.1 Class 10 Maths Question 7**

**Ex 14.1 Class 10 Maths Question 8.**

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

**Solution for Ex 14.1 Class 10 Maths Question 8**

**Ex 14.1 Class 10 Maths Question 9.**

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

**Solution for Ex 14.1 Class 10 Maths Question 9**

]]>