Learn Class 11 with Free Lessons & Tips

Story of Pi

In math, "pi" (often written as the Greek letter π) is a number that represents the ratio of a circle's circumference (the distance around the circle) to its diameter (the distance across the circle through its center). No matter how big or small the circle is, this ratio is always the same and approximately equal to 3.14159.

To put it simply, if you take a string and wrap it once around a circle, then lay that string out straight, it would be a little more than three times the length of the circle's diameter. This "little more" is the extra decimal places of pi. Pi is an irrational number, meaning it goes on forever without repeating.

Now, what is irrational number? Will post in second lesson.

In mean while try the above and let me know.

Rational Numbers?

In simple English, "rational" means something that is logical or makes sense. In mathematics, rational numbers are related to the concept of fractions. Let's travel back and review the lesson on fractions, specifically proper and improper fractions.

Proper fractions are fractions where the numerator (the top number) is smaller than the denominator (the bottom number). For example, 3/4
is a proper fraction.
Improper fractions are fractions where the numerator is larger than or equal to the denominator. For example, 5/3
is an improper fraction.
Both proper and improper fractions are members of the rational number family. Rational numbers are numbers that can be expressed in the form a/b
, where
𝑎 and 𝑏 are integers, and 𝑏 is not zero.

Now, what happens if the denominator becomes zero? What kind of fraction is that? Is it making any sense? No, it doesn't. Dividing by zero is undefined and does not produce a valid number. Therefore, rational numbers must have a denominator that is not zero. When you divide rational numbers, you get definite decimal places that either terminate or repeat.

In summary, rational numbers are fractions where the denominator is never zero, and their decimal expansions are predictable—they either end or follow a repeating pattern.

2. Name some notable economists who estimated India’s per capita income during the colonial period.

Ans: The following economists estimated India’s per capita income during the colonial period:

1. Dadabhai Naoroji
2. R.C Desai
3. V.K.R.V. Rao
4. William Digby
5. Findlay Shirras

3. What were the main causes of India’s agricultural stagnation during the colonial period?

Ans: The reasons for the stagnation of Indian agriculture during the colonial period are as follows:

1. The British introduced the Land Revenue system in 1793. As per this system, zamindars (landowners) needed to pay a high amount of revenue to the British Government, and the source of revenue collection was the peasants. The zamindars did not focus on improving land productivity, which resulted in low agricultural growth and subsequently made the life of peasants worse.
2. Indian farmers grew food crops like rice and wheat for consumption. The British Government was forcing

Indian farmers to grow commercial crops like indigo for British Industries, which led to agriculture turning commercial and caused a shortage of food grains.

3. Lack of irrigation facilities and other important factors like the unavailability of fertilizers also impacted the agriculture industry and made it more vulnerable.

4. Name some modern industries which were in operation in our country at the time of independence.

Ans: India witnessed the growth of some industries before independence, the most prominent of which is Tata Iron and Steel Company (TISCO). India was also witnessing a growth of textile mills and ancillary products. Maharashtra, Gujarat, and Bengal were areas where cotton and jute industries were set up. Apart from these industries, some other industries that started operating are sugar, paper and cement.

Questions:

1. Define Accounting.

Ans: Accounting is defined as the systematic process of identifying, recording, classifying, summarising, interpreting and communicating information about financial transactions to the users of the accounting information, such as the owners, government, investors, creditors, etc.

It provides the following information:

• Resources available in the firm.
• The means employed to finance those resources.
• Results achieved by using those resources.

2. State the end product of financial accounting.

Ans: The end product of Financial Accounting is shown below:

Income statement: The Trading and Profit and Loss Account is part of the income statement; it determines the financial position of the business based on gross/net loss or profit.

Balance Sheet: A balance sheet is helpful in presenting the exact financial position of the business. It provides information about the assets and liabilities of a business to users of the business information.

3. Enumerate the main objectives of accounting.

Ans: The main objectives of accounting are discussed below.

1. To keep a systematic record of all financial transactions.
2. To determine the profit and loss of a business as reflected in a P & L account.
3. Making information available to users of the information (employees, shareholders, stakeholders).

To determine the financial position of the business by preparing a balance sheet.

4. Who are the users of accounting information?

Ans: There are two types of users for accounting information. They are

Internal Users: include management, employee and owners.

External Users: consist of investors, creditors, the government, the public and customers.  

5. State the nature of accounting information required by long-term lenders.

Ans: The long-term lenders seek the following accounting information:

1. Liquidity of a business
2. Profitability
3. Operating efficiency
4. Growth potential of the business
5. Ability to repay the creditors

Given, the actual path length travelled is 23 km, displacement is 10 km and the time taken is 28 min.

(a)

Average speed of the taxi is given as,

v avg = Total Path length Time

Here, s is the total path length

Substitute the values in above equation.

v avg = Total Path length Time = 23 km ( 28 min )( 1 h 60 min ) =49.3  km/h

Hence, the average speed of the taxi is 49.3  km/h .

(b)

Magnitude of the average velocity is given as,

v avg = Displacement Time

Substitute the values in the above equation.

v avg = Displacement Time = 10 km ( 28 min )( 1 h 60 min ) =21.4  km/h

(c)

From the calculation in (a) and (b), it is obtained that the average speed is not equal to the magnitude of average velocity.

(c) both an oxidizing and a reducing agent.

Hydrogen peroxide in acid solution is oxidized with KMnO₄ and reduced with KI. When H₂O₂ serves as an oxidizing agent, the oxygen is reduced to H₂O. When H₂O₂ serves as areducing agent, the oxygen is oxidized to O₂ and bubbles are noticed.