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In This Post we are  providing Chapter-1 PHYSICAL WORLD NCERT MOST IMPORTANT QUESTIONS for Class 11 PHYSICS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS ON PHYSICAL WORLD

Question 1.
Write the physical principle upon which the working of the gadgets mentioned in the above question is based.

Answer:
These are based on the following physical principles:

1. The boiling point rises with the increase in pressure.
2. Light is produced when the current is passed through a given resistor.
3. Light is emitted when an electric discharge is passed through the gas.
4. A rotating magnetic field is produced on passing current which notates the motor.
5. Due to evaporation of water, cooling in the air which is being forced out by the fan is produced.
6. On absorbing heat from the surroundings, compressed volatile liquid on sudden expansion causes cooling.
7. Current produces a rotating magnetic field that operates the motor.
8. Heat is produced due to the burning of L.P.G.
9. It works on the principle of heating effect of electric current.
10. Torque is produced on the coil due to the electric current passed through it, hence it rotates.
11. Current shows the heating effect when passed through the conductor.
12. It rotates due to the torque produced on the coil on passing an electric current through it.

Question 2.
Name one Scientist each from the following countries who have won Nobel Prize.

(a) Japan
Answer:
H. Yukawa

(b) England
Answer:
Janies Chadwick

(c) India
Answer:
C.V. Raman

(d) The U.S.A.
Answer:
K. Feynman

(e) Germany.
Answer:
Max. Plank.

Question 3.
How Darwin showed that scientific themes are at once simple even though phenomena in nature may be complex.

Answer:
Darwin found a simple basis for the origin of species and descent of man which is “Living things change producing descendants with different characteristics in a process that has been going on for as long as there has been life” by taking a large number of observations on the theory of evolution while onboard ship.

Question 4.
In science sometimes we observed certain phenomena experimentally but are unable to give a logical equation or theory for that sometimes, it also happens that we have a scientific theory supported by’ mathematical formulation yet are unable to test it immediately. Site one such example.

Answer:
Einstein worked to establish a relation between the energy and mass of the body. He was of the view that these are the two sides of the same coin or two facts of the same physical quantity. He succeeded when he gave his mass-energy equation E = mc². But its experimental verification came 40 years later in 1945 when the atomic bomb was exploded over Japan.

Question 5.
Why do we call physics an exact science? What is the aim of science?

Answer:
Physics is called exact science because it is based on the measurement of fundamental quantities.
The main aim of science is to find the truth behind the various processes taking place in the universe.

Question 6.
How science has helped in solving the food problem in several countries?

Answer:
Science has helped in solving food problem in the following ways:
(a) It has given improved and new agricultural implements.
(b) Science has improved the quality of seeds by genetic engineering.
(c) High-yielding hybrid varieties of grains have been developed. Some easily reaping varieties have also been developed and grown.
(d) Use of pesticides and insecticides has saved crops from being destroyed by insects and pests.
(e) Some new types of crops are also developed and are being developed to meet the requirement of society.

Question 7.
What is a scientific temperament and scientific way of doing things?

Answer:
A mindset molded in a particular set of thinking called the scientific way is known as scientific temperament. It is not only based on logic, facts but on reliable observations. The ultimate test of truth in science is experimental verification.

A scientific way of doing things involves the following steps:
(a) Identifying the problem or aim.
(b) Collecting all relevant information or data related to the problem.
(c) Hypothesising or proposing a possible theory.
(d) Taking experimental observation yielding consistent results.
(e) Predicting or making statements.

Question 8.
What is the scope of Physics?

Answer:
The scope of Physics is very wide i.e. the domain of Physics covers a very wide variety of natural phenomena.

For example, the range of distances we study in Physics varies from 10¹⁴ m (size of the nucleus) to 10²⁵ m (size of the universe).

Similarly, the range of masses included in the study of Physics varies from 10^-30 kg (mass of an electron) to 10⁵⁵ kg (mass of the universe). Also, the range of time i.e. time intervals of events we come across in the study of Physics varies from 10²² seconds (time taken by light to cross a nuclear distance) to 10^-8 seconds (lifetime of the sun).

Thus we see that the scope of Physics is really very wide. It includes; optics, electricity waves, and oscillations, heat and thermodynamics, magnetism, atomic and nuclear physics, computers, and electronics.

Question 9.
Physics is an exciting subject! Comment.

Answer:
The study of Physics is exciting in many ways, e g.:

1. Journey to the moon with controls from the grounds.
2. Lasers and their ever-increasing applications.
3. Live transmission of events thousands of kilometers away on the T: V.
4. The speed and memory of the fifth generation of computers.
5. Study of various types of forces in nature.
6. Technological advances in health science.
7. The use of robots is quite exciting.
8. Telephone calls over long distances and so on. Thus, Physics is exciting not only to the scientist but also to a layman, children, women, etc. The musical instruments, toy guns, toy trains, etc. all are constructed using simple principles of physics like collision, potential energy, and vibration, etc. Today the situation is that even our thought process and social values are affected by Physics. Thus, it is quite amazing.

Question 10 .
Write a short note on the origin and development of Physics.

Answer:
Physics as a science took roots from the days of Copernicus, i. e., nearly four centuries ago when it was not well understood and it was considered as a part of philosophy, i.e., knowledge. Later on, with the development of knowledge about nature and its various activities, the knowledge was divided into physical and biological sciences.

Some important developments like Newton’s law of gravitation, ideas about light were developed in the 18th century. The 19th century saw some of the great discoveries in Physics and at the end f the century i.e. 1889, the electromagnetic theory was developed, Fouriuatun of Einstein’s and Plank’s ideas were laid down apart from laying the basis for the industrial revolution. Physics progressed very fast in the first quarter of the 20th century.

Atomic structure, the theory of relativity, quantum theory, nuclear physics, basics of laser theory and most of the other developments took place in this period. Then came transistors, semiconductors, television, radar, and few important discoveries during World War II.

Further development in quantum mechanics, thin-film technology, computers, lasers was developed from 1950 onward. Today we have no theoretical development beyond quantum mechanics. A unified theory is not being tried yet. This is the present status with achievements in applied fields.

TEXTBOOK QUESTIONS AND ANSWER:

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Q.1 How is exchange rate determined under a flexible exchange rate regime? [6 Marks]
Or
How is foreign exchange rate determined? Explain with diagram.
Or [AI 2004; CBSE 06 q How is exchange rate determined in a foreign exchange market? Explain.[AI 2013 (Set 1)]
ANSWER:

1.  Exchange rate in a free exchange market is determined at a point, where demand for foreign exchange is equal to the supply of foreign exchange.
2.  Let us assume that there are two countries – India and U.S.A – and the exchange rate of their currencies i.e., rupee and dollar is to be determined.
   Presently, there is floating or flexible exchange regime in both India and U.S.A. Therefore, the value of currency of each country in terms of the other currency depends upon the demand for and supply of their currencies.
3. In the above diagram, the price on the vertical axis is stated in terms of domestic currency (that is, how many rupees for one US dollar). The horizontal axis measures the quantity demanded or supplied.
4. In the above diagram, the demand curve [D$] is downward sloping. This means that less foreign exchange is demanded as the exchange rate increases. This is due to the fact that the rise in price of foreign exchange increases the rupee cost of foreign goods, which make them more expensive. As a result, imports decline. Thus, the demand for foreign exchange also decreases.
   The supply curve [S$] is upward sloping which means that supply of foreign exchange increases as the exchange rate increases. This makes home country’s goods become cheaper to foreigners since rupee is depreciating in value. The demand for our exports should therefore increase as the exchange rate increases. The increased demand for our exports translates into greater supply of foreign exchange. Thus, the supply of foreign exchange increases as the exchange rate increases.
   
5.  The intersection of the supply and demand curves determine equilibrium exchange rate (OP$) and equilibrium quantity [OQ$] of foreign currency i.e., US [$].

Q.2 Differentiate between devaluation and depreciation. [3 Marks]
ANSWER:

Q.3 Are the concepts of demand for domestic goods and domestic demand for goods the same? [3 Marks]
ANSWER:

1. Demand for domestic goods and domestic demand for goods are two different concepts.
2. Demand for domestic goods is a demand for goods made by both domestic and foreign countries.
3. Domestic demand for goods is a demand for goods by our own country for goods ..which may be produced in foreign countries.

Q.4 Would the central bank need tointervene in a managed floating system? Explain why? [3 Marks]
ANSWER:

1.  In a managed floating system a central bank of a country has freedom to bring change in the exchange rate within certain limits.
2. A country is allowed after information to the IMF to bring a certain limited amount of change in the rate of exchange.
3.  A central bank cannot bring change in its exchange rate by more than 10%. For it, permission of IMF is necessary.

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MORE QUESTIONS SOLVED

Very Short Answer Type Questions :

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Q.1 What is foreign exchange?[CBSE AI 2011, 04]
ANSWER: Foreign exchange refers to all the currencies of the rest of the world other than the domestic currency of the country. For example, in India, US dollar is foreign exchange.

Q.2 What is meant by foreign exchange rate? [CBSE 2004,05,06,09 2011, Sample Paper 2010]
ANSWER:   The rate at which one currency is exchanged for another is called foreign exchange rate.

Q.3 What is meant by foreign exchange market?
ANSWER:  Foreign exchange market is the market where foreign currencies are bought and sold.

Q.4 Define flexible exchange rate system.[CBSE 2008]
ANSWER:   Flexible exchange rate system refers to a system in which the exchange rate of different currencies is determined by the forces of demand and supply in foreign exchange market.

Q.5The price of 1 US Dollar has fallen from Rs. 50 to Rs. 48. Has the Indian currency appreciated or depreciated?[CBSE Sample Paper 2010]
ANSWER:  Indian currency has appreciated.

Short Answer Type Questions :

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Q.1 State four sources of demand of foreign exchange.[CBSE 2004, 05, 05C, 07; A 05, 10] Or
Give three reasons why people desire to have foreign exchange.
Or [CBSE 2005]
What are the sources of demand for foreign exchange?
ANSWER:   The demand (or outflow) of foreign exchange comes from the people who need it to make payments in foreign currencies. It is demanded by the domestic residents for the following reasons:

1. Imports of Goods and Services:When India import goods and services, foreign exchange is demanded to make the payment for imports of goods and services.
2. Tourism: Foreign exchange is demanded to meet expenditure incurred in foreign tours.
3. Unilateral Transfers sent abroad: Foreign exchange is required for making unilateral transfers like sending gifts to other countries.
4. Purchase of assets in foreign countries: It is demanded to make payment for purchase of assets, like land, shares, bonds, etc. in foreign countries.

Q.2 What are the functions of a foreign exchange market?
ANSWER:

1. Transfer Function: Transfer function refers to transferring of purchasing power among countries.
2. Credit Function: It implies provision of credit in terms of foreign exchange for the export and import of goods and services across different countries of the world.
3. Hedging Function: Hedging function pertains to protecting against foreign exchange risks. Where Hedging is an activity which is designed to minimize the risk of loss.

Q.3 Why does demand for foreign exchange rise when its price falls?
Or [AI 2006, 08, 10] What are the reasons for ‘Rise in Demand’ for Foreign Currency?
ANSWER: The demand for foreign currency rises in the following situations:

1. When price of a foreign currency falls, imports from that, foreign, country become cheaper. So, imports increase and hence, the demand for foreign currency rises.
   For example, if price of 1 US dollar falls from Rs 60 to T 55, then imports from The USA will increase as American goods will become relatively cheaper. It will raise the demand for US dollar.
2. When a foreign currency becomes cheaper in terms of the domestic currency, it promotes tourism to that country. As a result, demand for foreign currency rises.
3. When price of a foreign currency falls, its demand rises as more people want to make gains from speculative activities.

Q.4 When price of a foreign currency rises, its demand falls’. Explain why?
Or [CBSE 2011]
Explain relation between foreign exchange rate and demand for it.
Or [CBSE 2004q Why demand curve of foreign exchange is downward sloping?

ANSWER:

1. Demand curve of foreign exchange slopes downwards due to inverse relationship between demand for foreign exchange and foreign exchange rate.
2. In figure, demand for foreign exchange (US dollar) and rate of foreign exchange are shown on the horizontal axis and vertical axis respectively.
3. The demand curve [US$] is downward sloping. It means that less foreign exchange is demanded as the exchange rate increases.
4. This is due to the fact that rise in the price of foreign exchange increases the rupee cost of foreign goods, which make them more expensive. As a result, imports decline. Thus, the demand for foreign exchange also decreases.

Q.5 State four sources of supply of foreign exchange.[CBSE 2004, 05, 05C, 07, 10; AI 05] Or
What are the sources for supply of foreign exchange?
ANSWER:  The supply (inflow) of foreign exchange comes from the people who receive it due to the following reasons.

1.  Exports of goods and services:Supply of foreign exchange comes through exports of goods and services.
2. Foreign investment: The amount, which foreigners invest in their home country, increases the supply of foreign exchange.
3. Remittances (unilateral transfers) from abroad: Supply of foreign exchange increases in the form of gifts and other remittances from abroad.
4. Speculation: Supply of foreign exchange comes from those who want to speculate on the value of foreign exchange.

Q.6 What are the reasons of ‘rise in supply’ of foreign currency?
Or
Why does a rise in foreign exchange rate cause a rise in foreign exchange supply? [CBSE 2006, 08]
Or
When exchange rate of a foreign currency rises, its supply also rises. How? Explain. [CBSE 2008]
ANSWER:   The supply of foreign currency rises in the following situations:

1. When price of a foreign currency rises, domestic goods become relatively cheaper. It induces the foreign country to increase their imports from the domestic country. As a result, supply of foreign currency rises. For example, if price of 1 US dollar rises from Rs 60 to Rs 65, then exports to USA will increase as Indian goods will become relatively cheaper. It will raise the supply of US dollars.
2. When price of a foreign currency rises,foreign direct investment (FDI) from rest of the world increases, which will increase the supply for foreign exchange.
3. When price of a foreign currency rises, also supply of foreign currency rises as people want to make gains from speculative activities.

Q.7 Why supply curve of foreign exchange is upward sloping?

ANSWER:

1. Supply curve of foreign exchange slopes upwards due to positive relationship between supply for foreign exchange and foreign exchange rate, which means that supply of foreign exchange increases as the exchange rate increases.
2.  This makes home country’s goods become cheaper to foreigners since rupee is depreciating in value. The demand for our exports should therefore increase as the exchange rate increases.
3. The increased demand for our exports will translate into greater supply of foreign exchange. Thus, the supply of foreign exchange increases as the exchange rate increases.

Q.8 Explain the effect of depreciation of domestic currency on exports.
[A7 2013 (Set I), Sample Paper 2013]
ANSWER:  Depreciation of domestic currency means a fall in the price of domestic currency (say, rupee) in terms of a foreign currency (say, $). It means, with the same amount of dollars, more goods can be purchased from India, i.e., exports to USA will increase as they will become relatively cheaper.

Q.9 Explain the effect of appreciation of domestic currency on imports.
[CBSE 2013 (Set I), Sample Paper 2013)]
ANSWER: Appreciation of domestic currency means a rise in the price of domestic currency (say, rupee) in terms of a foreign currency (say, $). Now, one rupee can be exchanged for more $, i.e., with the same amount of money, more goods can be purchased from the USA. It leads to increase in imports from the USA as American goods will become relatively cheaper.

Q.10 What are the merits of fixed exchange rate system? [CBSE 2009]
ANSWER:

1. Stability: It ensures stability, in the international money market/ exchange market. Day to day fluctuations are avoided. It helps formulation of long term economic policies, particularly relating to exports and imports.
2.  Encourages international trade: Fixed exchange rate system implies low risk and low uncertainty of future payments. It encourages international trade.
3. Co-ordination of macro policies:Fixed exchange rate helps co¬ordination of macro policies across different countries of the world. Long term economic policies can be drawn in the area of international trade and bilateral trade agreements.

Q.11What are merits of flexible exchange rate system? [CBSE, AI 2009]
ANSWER:

1. No need for international reserves: Flexible exchange rate system is not to be supported with international reserves.
2. International capital movements: Flexible exchange rate system enhances movement of capital across different countries of the world. This is due to the fact that member countries are no longer required to keep huge international reserves.
3. Venture capital: Flexible exchange rate promotes venture capital in foreign exchange market. Trading in international currencies itself becomes an important economic activity.

Q.12 Differentiate between fixed exchange rate and flexible exchange rate? [AI 2015]
ANSWER:

Q.13 Explain the meaning of Managed Floating Exchange Rate? [AI 2015]
ANSWER:

1. Managed floating exchange rate is a mixture of a flexible exchange rate (the float part) and a fixed exchange rate (the Managed part).
2. In other words, it refers to a system in which foreign exchange is determined by free market forces (demand and supply forces), which can be influenced by the invention of the central bank in foreign exchange market.
3. Under this system, also called Dirty floating, central banks intervene to buy or sell foreign currencies in an attempt to stabilise exchange rate movements in case of extreme appreciation or depreciation.

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Textbook Question And Answer:

Q.1Explain why public goods must be provided by the government? [3-4 Marks]
ANSWER:

1. Public goods are those goods and services for which consumption by some individuals does not reduce the amount available to others.
2. For example parks,roads,water,bridges,national defense etc..
3. these goods are non-rival and non-excludable ones.
4. people receives benefits from public goods but do not pay for them.Such a goods can only prepared by government.

Q.2 Distinguish between revenvu expenditure and capital expenditure .
State the basis of classifying government expenditure into revenue and capital expenditure. Give an example of each.
ANSWER:

Q.3 The fiscal deficit gives the borrowing requirement of the government Elucidate. [3-4 Marks]
ANSWER:

1. Fiscal deficit is defined as excess of total expenditure over total receipts (revenue and capital receipts) excluding borrowing. In the form of an equation:
   Fiscal Deficit = Total Budget Expenditure – Total Budget Receipts (Net of borrowing)
   = Total Expenditure (Revenue
   Expenditure + Capital Expenditure) – Revenue Receipts (Tax Revenue + Non-Tax Revenue) – Non-Debt Capital Receipts (Recovery of Loans + Dis-investment Proceeds)
   = Revenue Deficit + Capital Deficit (excluding Borrowing)- Borrowing
   = Net borrowing at home + Borrowing from RBI + Borrowing from abroad
2. Fiscal deficit shows total borrowing requirements of the government from all sources.
3. As the government borrowing increases, its liability in future to repay loan with interest also increases leading to a higher revenue deficit. Therefore, fiscal deficit should be as low as possible.

Q.4 Give the relationship between revenue deficit and fiscal deficit. [3-4 Marks]
ANSWER:

1. Fiscal deficit is always a wider concept than revenue deficit.
2.  Revenue deficit is defined as the excess of government’s revenue expenditure over revenue receipts. In terms of formula:
   Revenue Deficit = Revenue Expenditures (RE) – Revenue Receipts (RR)
3.  In short, there will be revenue deficit in a government budget when revenue expenditure exceeds revenue receipts.
4. Fiscal deficit is defined as the excess for all expenditure over total receipts net of borrowings.
5. Initially, Fiscal deficit does not take into account all types of receipts. It does not take into account borrowings. But finally they have to depend on borrowing to met fiscal deficit.
   Fiscal Deficit = Revenue Deficit + Capital Deficit (Excluding Borrowing)- Borrowing
   = Net borrowing at home + Borrowing from RBI + Borrowing from abroad

Q.5 Does public (government) debt impose a burden? Explain. [3-4 Marks]
ANSWER:   Public debt is not always a blessing. Excessive use of it creates a lot of crisis in an economy; such as,

1. Hampers Economic Development of a Country: Loans are easily borrowed but it is very difficult to repay them.Generally, government imposes more taxes. It brings instability and is an obstacle in the economic development of a country.
2. Poses Threat to Political Freedom: Foreign loans and assistance lead to deep conflict among countries. The friction among countries challenges the political freedom.
3. Proves a Burden on Common Man: Loans taken for unproductive purposes, like war and armaments, are a burden on common man in the form of higher taxes.
4. Leads to Extravagant Spending: Public debt leads to unplanned spending. This provides incentive to the government to implement the schemes that require excessive expenditure.
5. Results in Drain of National Wealth: Repayment of foreign loans results in drain of wealth out of the country.

Q.6 Are fiscal deficits necessarily inflationary? [3-4 Marks]
Or
“Governments across nations are too much worried about the term fiscal deficit”. Do you think that fiscal deficit is necessarily inflationary in nature? Support your answer with valid reasons.
ANSWER:

1. Fiscal deficits are not necessarily inflationary.
2. As we know fiscal deficit shows borrowing requirement of the government.
3. If we borrow when there is a situation of underemployment in an economy i.e., in a situation of deficient demand, then it is not inflationary because in a situation of deficient demand output is held back because of lack of demand.
4. A high fiscal deficit (borrowing) is accompanied by higher demand and greater output which is not inflationary.
5. On the other hand, if we borrow at the full employment level, then it is inflationary in nature.
6. A high fiscal deficit (borrowing) is accompanied by higher prices because aggregate demand is greater than aggregate supply at the full employment level which is always inflationary.

Q.7 Discuss the issue of deficit reduction.[3-4 Marks]
ANSWER: The deficit in a government budget can be reduced by the following steps:

1. Taxes should be increased. Government can make a plan for rising direct taxes to increase its receipts can also be raised by increasing rates of taxes or by imposing new taxes.
2. Reduction in Government Expenditures: It can be done through making government activities more efficient through better planning of programmes and better administration.
3.  The government can raise Receipts through the sale of shares in PSUs (Public Sector Undertaking).
4. Changing the scope and role of government by withdrawing from same areas where it operated before.

Very Short Answer Type Questions :

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Q.1 Define government budget.
  ANSWER:  A government budget is an annual financial statement showing itemwise estimates of expected revenue and anticipated expenditure during a fiscal year.

Q.2 State any one obj ective of a government budget.
ANSWER:  Activities to secure a reallocation of resources

Q.3 Define a tax.
ANSWER:  A tax is a legally compulsory payment imposed by the government on income and profit of persons and companies without reference to any benefit. Tax is of two types: Direct tax and Indirect tax.

Q.4 Why is service tax an indirect tax?
ANSWER: Its impact and incidence lie on different persons.

Q.5 State any two sources of non-tax revenue receipts.
ANSWER:

1. Commercial revenue (profit and interest)
2. Administrative revenueffees, fines and penalties, escheats etc)

Q.6 Is borrowing by the government a revenue receipt?
ANSWER:  No, it is not so because it creates a liability (for the government) of repayment.

Q.7 Why is tax not a capital receipt?
ANSWER:  Tax is not a capital receipt because it leads neither to creation of liability nor to reduction in assets.

Q.8 Why is interest termed as a revenue receipt?
ANSWER:  Interest is a revenue receipt because it creates neither any liability nor causes a reduction in the assets of the government.

Q.9 Why are borrowings a capital receipt?
ANSWER:  They create a liability (in terms of repayment).

Q.10 Why are subsidies treated as revenue expenditure?
ANSWER: Subsidies are treated as revenue expenditure because they create neither any asset nor cause a reduction in any liability of the government.

Q.11 Why is repayment of loan a capital expenditure?
ANSWER: It reduces the liabilities of the government.

Q.12 Why is recovery of loans treated as a capital receipt?[CBSE All India 2005]
ANSWER: Recovery of loans is treated as a capital receipt because it reduces assets of the government.

Q.13 Why are receipts from taxes categorised as revenue receipts?
ANSWER: Receipts from taxes are categorised as revenue receipts because they create neither any liability nor cause a reduction in the assets of the government.

Q.14 What is meant by revenue deficit?
ANSWER: Revenue deficit refers to the excess of revenue expenditure of the government over its revenue receipts. Revenue Deficit = Revenue Expenditure- Revenue Receipts

Q.15 If the revenue receipts are Rs. 1,000 crore and revenue expenditure is Rs. 1,200 crore, how much will be the revenue deficit?
ANSWER:  Revenue Deficit = Revenue Expenditure – Revenue Receipts = 1,200 – 1,000 = Rs. 200 crore.

Q.16Define fiscal deficit.
ANSWER:  Fiscal deficit is defined as excess of total expenditure over total receipts (revenue and capital receipts) excluding borrowing.

Q.17 What is the meaning of primary deficit?
ANSWER:  Primary deficit refers to the difference between fiscal deficit of the current year and interest payments on the previous borrowings.

Q.18 How is primary deficit calculated?
ANSWER: Primary Deficit = Fiscal Deficit – Interest Payments

Q.19 What does zero primary deficit mean?
ANSWER:  If primary deficit is zero, fiscal deficit= interest payments. It means the government has to borrow only for its interest commitments on earlier loans.

Short Answer Type Questions : 

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Q.1 Explain objective of stability of prices of government budget. [CBSE, (F) 2010] Or
Explain the ‘economic stability’ objective of a government budget. [CBSE, AI2011] Or
Explain stabilising activities function of budget.
ANSWER:

1. Free play of market forces (or the forces of supply and demand) are bound to generate trade cycles, also called business cycles.
2. These refer to the phases of recession, depression, recovery and boom in the economy.
3. The government of a country is always committed to save the economy from business cycles. Budget is used as an important policy instrument to combat(solve) the situations of deflation and inflation.
4.  By doing it the government tries to achieve the state of economic stability.
5. Economic stability leads to more investment and increases the rate of growth and development.

Q.2 Name two sources each of non-tax revenue receipts. [CBSE 2004]
ANSWER:  Non-tax revenue refers to government revenue from all sources other than taxes called non-tax revenue. These are incomes, which the government gets by way of sale of goods and services rendered by different government departments. Its two sources are:

1. Commercial Revenue (Profit and interest): It is the revenue received by the government by selling the goods and services produced by the government agencies. For example, profit of public sector undertakings like Railways, BHEL, LIC etc. Government gives loan to State Government, union territories, private enterprises and to general public and earns interest receipts from these loans. It also includes interest and dividends on investments made by the government.
2. Administrative Revenue: The revenue that arises on account of the administrative function of the government. This includes:
   (i) Fee: Fee refers to a payment made to the government for the services that it renders to the citizens. Such services are generally in public interest and fees are paid by those, who receive such services. For example, passport fees, court fees, school fees in government schools,
   (ii) License Fee: License fee is a payment to grant a permission by a government authority. For example, registration fee for an automobile.

Q.3 Distinguish between: Revenue receipts and capital receipts. [CBSE 2005, 10]
Or
Distinguish between ‘revenue receipt’ and ‘capital receipt’ and give two examples of each. [CBSE 2007]
ANSWER:

Q.4 Distinguish between Direct tax and indirect tax.
ANSWER:

Q.5 Differentiate between Revenue Budget and Capital Budget.
ANSWER:

Q.6 Differentiate between Developmental and Non-Developmental Expenditure.
ANSWER:

Q.7 What are the implications of a large revenue deficit? Give two measures to reduce this deficit. [CBSE Sample Paper 2010]
ANSWER:

1. Revenue deficit indicates dis¬savings on government account because the government has to make up uncovered gap.
2. Revenue deficit implies that the government has to cover’this uncovered gap by drawing upon capital receipts either through borrowing or through sale of its assets.
3. Since government is using capital receipts to meet generally consumption expenditure of the government which leads to an inflationary situation in the economy.

Two measures to reduced revenue deficit are :

1. Government should reduce its unproductive or unnecessary expenditure.
2. Government should increase its receipts from various sources of tax and non-tax revenue.

Q.8 What are implications of fiscal deficit? [A/2005; CBSE 06C, 07]
ANSWER:

1. Causes Inflation: An important component of government borrowing includes borrowing from the Reserve Bank of India. This invariably implies deficit financing or meeting deficit requirements of the government by way of printing more notes. This is a dangerous practice, though very convenient for the government. It increases circulation of money and causes inflation.
2. Increase in Foreign Dependence:Government also borrows from rest of the world. It increases our dependence on other countries. Foreign borrowing is often associated with economic and political interference by the lender countries. It increases our economic slavery.
3. Financial Burden for Future Generation: Borrowing implies accumulation of financial burdens for the future generations. It is for future generations to repay loans as well as the mounting interest thereon.
4. Deficits Multiply Borrowings:Payments of interest increases revenue expenditure of the government, causing an increase in its revenue deficit. Thus, a vicious circle set wherein deficits multiply borrowings.

Long Answer Type Question:

Q.1 Explain the role the government can play through the budget in influencing allocation of resources. [CBSE 2015] OR .
Explain the ‘allocation of resources’ objective of government budget.[CBSE 2011] OR
Explain the allocation function of agovernment budget. [CBSE AI2010]OR
Explain how government can influence allocation of resources through government budget.
ANSWER:

1. Private enterprises always desire to allocate resources to those areas of production where profits are high.
2. However, it is possible that such areas of production (like production of alcohol) may not promote social welfare.
3. Through its budgetary policy the government of a country directs ‘ the allocation of resources in a manner such that there is a balance between the goals of profit maximisation and social welfare.
4. Production of goods which are injurious to health (like cigarettes and whisky) is discouraged through heavy taxation.
5. On the other hand, production of “socially useful goods” (like electricity, ‘Khadij is encouraged through subsidies.
6.  So, finally government has to reallocate resources in accordance to social and economic considerations in case the free market fails to do or does so inefficiently.

Q.2 Explain how the government can use the budgetary policy in reducing inequalities of incomes. [AI 2015] OR
How can a government budget help in reducing inequalities of income? Explain. [CBSE 2009]OR
How can a government budget be helpful in altering distribution of income in an economy? Explain.[CBSE 2010] OR
Explain ‘redistribution of income’ objective of government budget. [CBSE2011, A/2011] OR
Reduction in income inequalities raises welfare of the people. How can government help, through government budget, in this regard? Explain? [A/2013, C (Set /)]
ANSWER:

1. Budget of a government shows its comprehensive exercise on the taxation and subsidies.
2.  A government uses fiscal instruments of taxation and subsidies with a view of improving the distribution of income and wealth in the economy.
3.  A government reduces the inequality in the distribution of income and wealth by imposing taxes on the rich and giving subsidies to the poor, or spending more on welfare of the poor.
4.  It will reduce income of the rich and raises the living standard of the poor, thus, leads to equitable distribution of income.
5. Expenditure on special anti poverty and employment schemes will be increased to bring more people above poverty line.
6. Public distribution system should be inferred so that only the poor could get foodgrains and other essential items at subsidised prices.
7. Equitable distribution of income and wealth is a sign of social justice which is as the principal objective of any welfare state in India.

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Very Short Answer Type Questions :

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Q.1. What is meant by excess demand in macroeconomics?
ANSWER: When in an economy aggregate demand exceeds “aggregate supply at full employment level”, the demand is said to be an excess demand.

Q.2 Define inflationary gap.

ANSWER:  When in an economy aggregate demand exceeds “aggregate supply at full employment level”, the demand is said to be an excess demand and the gap is called inflationary gap.

Q.3 Give the meaning of deficient demand.

ANSWER:   When in an economy aggregate demand falls short of aggregate supply at full employment level, the demand is said to be as deficient demand.

Q.4 Define deflationary gap. [CBSE 2008]
OR
Give the meaning of deflationary gap. [CBSE 2010]

ANSWER:  ” When in an economy aggregate demand falls short of aggregate supply at full employment level, the demand is said to be deficient demand and the gap is called deflationary gap.

Q.5 State two measures by which a central bank can attempt to reduce the inflationary gap.
ANSWER: 

1.  Increase in cash reserve ratio.
2.  Increase in marginal requirement.

Q.6. What is the impact of increase in margin requirements?
ANSWER:   Increase in margin requirements discourages borrowings and decreases the aggregate demand.

Q.7 Give the meaning of full employment.[CBSE 2008]
ANSWER:   Full employment equilibrium refers to the situation where aggregate demand = aggregate supply and all those who are able to work and willing to work (at the existing wage rate) are getting work.

Q.8 Give the meaning of involuntary unemployment.[CBSE 2008, 09, Sample Paper 2010]
ANSWER:   Involuntary unemployment refers to a situation in which all able and willing persons to work at existing wage-rate do not find work. They are rendered unemployed against their wish. Hence, it is termed as involuntary unemployment.

Q.9 Is it necessary that equality between AD and AS is established at the full employment level?
ANSWER:   No, it is not necessary that full employment occurs when AD = AS. Equilibrium can be achieved at full employment level, under employment level or at over full employment level.

Q.10 What is meant by full employment equilibrium?
ANSWER:  Full employment equilibrium refers to a situation when equilibrium is attained i.e., aggregate demand is equal to aggregate supply at full employment level.

Q.11 What is underemployment equilibrium?[CBSE 2008]
ANSWER:  Underemployment equilibrium refers to a situation when equilibrium is attained i.e., aggregate demand is equal to aggregate supply below full employment level or when resources are not fully employed.

Q.12 What is the meaning of over full employment equilibrium?
ANSWER:   Over full employment level refers to a situation when equilibrium is attained, i.e., aggregate demand is equal to aggregate supply beyond the full employment level.

Short Answer Type Question:

Q.1 What are the reasons or causes for excess demand?
ANSWER: The main reasons for excess demand are apparently the increase in the following components of aggregate demand:

1. Increase in household consumption demand due to rise in propensity to consume.
2. Increase in private investment demand because of rise in credit facilities.
3. Increase in public (government) expenditure.
4. Increase in export demand.
5.  Increase in money supply or increase in disposable income.

Q.2 What are impacts or effects of excess demand on price, output, employment?
ANSWER: 

1. Effect on General Price Level: Excess demand gives a rise to general price level because it arises when aggregate demand is more than aggregate supply at a full employment level. There is inflation in economy showing inflationary gap.
2. Effect on Output: Excess demand has no effect on the level of output. Economy is at full employment level and there is no idle capacity in the economy. Hence output can’t increase.
3.  Effect on Employment: There will be no change in the level of employment also. The economy is already operating at full employment equilibrium, and hence there is no unemployment.

Q.3 What are the reasons or causes for deficient demand?
ANSWER:  The main reasons for deficient demand are apparently the decrease in four components of aggregate demand:

1. Decrease in household consumption demand due to fall in propensity to consume.
2. Decrease in private investment demand because of fall in credit facilities.
3. Decrease in public (government) expenditure.
4. Decrease in export demand.
5. Decrease in money supply or decrease in disposable income.

Q.4 What are the impacts or effects of deficient demand on price (output) employment?
ANSWER: 

1. Effect on General Price Level:Deficient demand causes the general price level to fall because it arises when aggregate demand is less than aggregate supply at full employment level. There is deflation in an economy showing deflationary gap.
2. Effect on Employment: Due to deficient demand, investment level is reduced, which causes involuntary unemployment in the economy due to fall in the planned output.
3. Effect on Output: Low level of investment and employment implies low level of output.

Q.5 Explain the role of Government expenditure and Open Market Operation in reducing AD/excess demand. [CBSE 2004C, 06, CBSE 2011; A 11]
ANSWER:  (a) Government Expenditure:

1. Government has to invest huge amount on public works like roads, buildings, irrigation works, etc.
2. During inflation, government should curtail (reduce) its expenditure on public works like roads, buildings, irrigation works thereby reducing the money income of the people and their demand for goods and services.

(b) Open Market Operation:

1. It consists of buying and selling of government securities and bonds in the open market by central bank.
2.  In a situation of excess demand leading to inflation, central bank sells government securities and bonds to commercial bank. With the sale of these securities, the power of commercial bank of giving loans decreases, which will control excess demand.

Q.6 Differentiate between full employment and underemployment equilibrium.
ANSWER: 

Q.7 What is meant by Margin Requirement? How does the Central Bank use this measure to control deflationary conditions in an economy?[CBSE Sample Paper 2016]
ANSWER: 

1. Business and traders get credit from commercial bank against the security of their goods. Bank never gives credit equal to the full value of the security. It always pays less value
   than the security.
2. So, the difference between the value of security and value of loan is called marginal requirement.
3. In a situation of deficient demand leading to deflation, central bank decreases marginal requirements. This encourages borrowing because it makes people get more credit against their securities.

Long Answer Type Question:

Q.1. Explain the concept of underemployment equilibrium with the help of a diagram. Show on the same diagram the additional investment expenditure required to reach full employment equilibrium.[CBSE 2004] OR
Explain the meaning of underemployment equilibrium. Explain two measures by which full employment equilibrium can be reached. [A/2013 (Set-7)]
ANSWER:

1. Underemployment equilibrium refers to a situation when equilibrium is attained i.e., aggregate demand is equal to aggregate supply below full employment level or when resources are not fully employed.
   
2.  In the above diagram full employment level of national income is attained at point E, but due to deficient demand, aggregate demand shifts downward from AD to AD0 and hew equilibrium is attained at point E1; which is below full employment level. The aggregate demand shifts downward because of the following reasons.
   (i) Decrease in household consumption demand due to fall in propensity to consume.
   (ii) Decrease in private investment demand because of fall in credit facilities.
   (iii) Decrease in public (government) expenditure.
   (iv) Decrease in export demand.
   (v) Decrease in money supply or decrease in disposable income.
3. In order to achieve full employment equilibrium deficiency of demand must be corrected through additional investment expenditure. In the diagram deficiency of AD = AB. Thus, AB amount of additional investment is required to reach the level of full employment.

Q.2 Differentiate between inflationary gap and deflationary gap. Show deflationary gap on a diagram. Can this gap exist at equilibrium level? Explain. [CBSE, 2004, AI 2013]
ANSWER:

Yes, deflationary gap can exist at equilibrium level of income. In the below figure equilibrium is attained at a equilibrium point E,, when deflationary gap is EB.

Q.3 Explain the concept of Inflationary Gap. Explain the role of Repo Rate in reducing this gap. [CBSE 2015] Or
What is meant by Repo Rate? How does the Central Bank use this measure to control inflationary conditions in an economy? [CBSE Sample Paper 2016]
ANSWER:

1. Inflationary gap is the gap showing excess of current aggregate demand over ‘aggregate supply at the level of full employment’. It is called inflationary because it leads to inflation (continuous rise in prices).
2. It can be explained with the help of following diagram:
   
3.  (i) Repo rate is the. rate at which commercial bank borrow money from the central bank for short period by selling their financial securities to the central bank.
   (ii) These securities are pledged as a security for the loans.
   (iii) It is called Repurchase rate as this involves commercial bank selling securities to RBI to borrow the money with an agreement to repurchase them at a later date and at a predetermined price.
   (iv) So, keeping securities and borrowing is repo rate.
   (v) In a situation of excess demand leading to inflation,
   • Central bank raises repo rate that discourages commercial banks in borrowing from central bank as it will increase the cost of borrowing of commercial bank.
   • It forces the commercial banks to increase their lending rates, which discourages borrowers from taking loans, which discourages investment.
   • Again high rate of interest induces households to increase their savings by restricting expenditure on consumption.
   • Thus, expenditure on investment and consumption is reduced, which will control the excess demand.

Q.4 Explain the concept of Deflationary Gap and the role of ‘Open Market Operations’ in reducing this gap.[CBSE 2015]
ANSWER:

1. Deflationary gap is the gap showing deficient of current aggregate demand over ‘aggregate supply at the level of full employment. It is called deflationary because it leads to deflation (continuous fall in prices).
2. It can be explained with the help of following diagram:
   
3. (i) Open Market Operation consists of buying and selling of government securities and bonds in the open market by central bank.
   (ii) In a situation of deficient demand leading to deflation,central bank purchases government securities and bonds from commercial bank. With the purchase of these securities, the power of commercial bank of giving loans increases, which will control deficient demand.

Q.5 What is ‘deficient demand’? Explain the role of ‘Bank Rate’ in removing it.[AI 2015]
ANSWER:

1. When in an economy, aggregate demand falls short of aggregate supply at full employment level, the demand is said to be a deficient demand.
2. It can be explained with the help of following diagram:
   
3. (i) Bank rate is the rate of interest at which central bank lends to commercial banks without any collateral (security for purpose of loan). The thing, which has to be remembered, is that central bank lends to commercial banks and not to general public.
   (ii) In a situation of deficient demand leading to deflation,
   • Central bank decreases bank rate that encourages commercial banks in borrowing from central bank as it will decrease the cost of borrowing of commercial bank.
   • Decrease in bank rate makes commercial bank to decrease their lending rates, which encourages borrowers from taking loans, which encourages investment.
   • Again low rate of interest induces households to decrease their savings by increasing expenditure on consumption.
   • Thus, expenditure on investment and consumption increase, which will control the deficient demand.

Q.6 What is ‘excess demand’? Explain the role of ‘Reverse Repo Rate’ in removing it. [AI 2015]
ANSWER:

1. When in an economy, aggregate demand exceeds “aggregate supply at full employment level”, the demand is said to be an excess demand.
2. It can be explained with the help of following diagram:
   
3. (i) Reverse Repo Rate is the rate at which the central bank (RBI) borrows money from commercial bank.
   (ii) In a situation of excess demand leading to inflation, Reverse repo rate is increased, it encourages the commercial bank to park their funds with the central bank to earn higher return on idle cash. It decreases the lending capability of commercial banks, which controls excess demand.

In This Post we are  providing Chapter-16 PROBABILITY NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS ON PROBABILITY

Question 1.
A coin is tossed twice, what is the probability that at least one tail occurs?

Solution:
Let S is the sample space, then
S = {(H, H), (H, T), (T, H), (T, T)}
n(S) = 4
Let E be the event of getting at least one tail, then
E = {(H, T), (T, H), (T, T)}
∴ n(E) = 3
Hence, required probability P(E) = n(E)n(S) = 34

Question 2.
There are four men and six women on the city council. If one council member is selected for a committee at random, then how likely is it that it is a woman?

Solution:
Let S is the sample space, then
n (S) = 10
Let E be the event that woman is selected, then
n(E) = 6
Hence, required probability P(E) = n(E)n(S)
P(E) = 610 = 35

Question 3.
If 211 is the probability of an event A, then find what is the probability of the event is ‘not A’.

Solution:
Given that :
P(A) = 211
We know that,
P(A) + P(A¯) = 1
211 + P(A¯) = 1
P(A¯) = 1 – 211 = 11–211
P(A¯) = 911.

Question 4.
A box contain 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box. What is the probability that:

1. All marbles will be blue.
2. At least one marble will be green.

Solution:
In the box, there are 10 red, 20 blue and 30 green marbles.
The No. of marbles = 10 + 20 + 30 = 60
1. Total ways of choosing 5 marbles out of 60 marbles,
n(S) = ⁶⁰C₅
Let E is the event of choosing blue marbles, then
n(E) = ²⁰C₅
Probability = n(E)n(S) = 20C560C5

2. P(At least one green marble)
= 1 – P(No green)
= 1 – 30C560C5

Question 5.
4 cards are drawn from a well shuffled deck of 52 cards. What is the probability of obtaining in card of 3 diamond and one spade?

Solution:
Let S is the sample space.
Total number of selecting 4 cards out of 52 cards, n(S) = ⁵²C₄
If E is the event obtaining card of 3 diamond and 2 spade, then
n(E) = ¹³C₃ x ¹³C₁
Probability P(E) = n(E)n(S) = 13C3×13C152C4

Question 6.
Given : P(A) = 35 and P(B) = 15. If A and B are mutually exclusive events, then find P(A or B). (NCERT)

Solution:
A and B are mutually exclusive events.
∴ P (A or B) = P(A ∪ B) = P(A) + P(B)
P(A ∪ B) = 35 + 15 = 3+15 = 45

Question 7.
In a lottery, a person choose six different natural numbers at random from 1 to 20 and if there six numbers match with the six numbers already fixed by lottery committee, he wins the prize, what is the probability of winning the prize in the game? (Hint: Order of the numbers is not important)

Solution:
Let S is the sample space, then
n(S) = ²⁰C₆
= 20×19×18×17×16×156×5×4×3×2×1 = 38760
Only one prize can be win.
∴ n(E) = 1
Hence, required probability P(E) = n(E)n(S) = 13876

Question 8.
Two dice are thrown simultaneously. Find the probability of getting a sum 9 in a single throw.

Solution:
Total number of ways in which two dice may be thrown
= 6 x 6 = 36
∴ n(S) = 36
Event of getting sum 9 is A = {(3, 6), (4, 5), (5, 4), (6, 3)}
∴ n(A) = 4
∴ Required probability P(A) = n(A)n(S) = 19

Question 9.
A bag contains 8 black, 6 white and 5 red balls. Find the probability of drawing a black or a white ball from it

Solution:
Total number of balls = 8 + 6 + 5 = 19
∴ n(S) = 19
Event A of drawing 1 black or 1 white ball
n(A) = 8 + 6 = 14
∴ n(A) = 14
∴ Required probability P(A) = n(A)n(S) = 1419

Question 10.
From a pack of well shuffled cards two cards drawn simultaneously. Find the probability that both the cards are ace.

Solution:
Total number of ways of drawing two cards out of 52
= ⁵²C₂
Number of ways drawing two ace out of 4 ace
= ⁴C₂
∴ Required Probability

Question 11.
A pair of dice are thrown. Find the probability that the sum is 9 or 11.

Solution:
Let the sample space be S, then
∴ n(S) = 36
Let E be the event that sum is 9 or 11, then
E = {(5, 4), (4, 5), (6, 3), (3, 6), (6, 5), (5, 6)}
∴ n (E) = 6
The probability of getting sum 9 or 11 is
P(E) = n(E)n(S) = 636 = 16
Hence, probability that the sum is not 9 or 11 is
P(E¯) = 1 – P(E)
= 1 – 16 = 56

Question 12

A letter is selected at random from the word ‘ASSASSINATION’. Find the probability that letter is

1. a vowel
2. a consonant

Solution:
Number of letters is 13 in which there are 6 vowels and 7 consonants.
1. Let sample space is S, then
∴ n(S) = 13
E₁ is the event of choosing a vowel, then

n(E₁) = 6
Hence, required probability P(E₁) = n(E1)n(S)
P(E₁) = 613

2. E₂ is the event of choosing a consonant, then
n(E₁) = 7
Hence, required probability P(E₂) = n(E2)n(S)

Question 13.
In class XI of a school, 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Solution:
Let M and B denote the students of Mathematics and Biology respectively. Then, as given:
P(M) = 40% = 40100
= P(B) = 30% = 30100
P(M ∩ 5) = 10% = 10100
∴ P(M ∪ B) = P(M) + P(B) – P(M ∩ B)
40100 + 30100 – 10100
= 60100 = 60% = 0.6

Question 14.
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both? (NCERT)

Solution:
Let probability of passing in first examination is A and passing in the second examination is B.
P(A) = 0.8, P(B) = 0.7, P(A ∪ B) = 0.95, P(A ∩ B) = ?
We know that,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
0.95 = 0.8 + 0.7 – P(A ∩ B)
⇒ P(A ∩ B) = 1.5 – 0.95
∴ P(A ∩ B) = 0.55.

Question 15.
Check whether the following probabilities P{A) and P(B) are consistently defined:

1. P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
2. P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8.

Solution:
1. Given : P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
If P(A ∩ B) ≤ P(A) and P(A ∩ B) ≤ P(B)
Then, P(A) and P(B) are consistent.
Here

P(A) and P(B) are not consistent.

In This Post we are  providing Chapter-15 STATISTICS NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS ON STATISTICS

1. In a test with a maximum marks 25, eleven students scored 3,9,5,3,12,10,17,4,7,19,21 marks respectively. Calculate the range.

Ans. The marks can be arranged in ascending order as 3,3,4,5,7,9,10,12,17,19,21.

Range = maximum value – minimum value

=21-3

= 18

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2. Coefficient of variation of two distributions is 70 and 75, and their standard deviations are 28 and 27 respectively what are their arithmetic mean?

Ans. Given C.V (first distribution) = 70

Standard deviation = = 28

C.V 

= 

Similarly for second distribution

C.V 

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3. Write the formula for mean deviation.

Ans.MD

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4. Write the formula for variance

Ans. Variance 

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5. Find the median for the following data.

579101215

862226

Ans.

	5	7	9	10	12	15
	8	6	2	2	2	6
	8	14	16	18	20	26

Median is the average of 13^th and 14^th item, both of which lie in the c.f 14

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6. Write the formula of mean deviation about the median

Ans.

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7. Find the rang of the following series 6,7,10,12,13,4,8,12

Ans. Range = maximum value – minimum value

= 113-4

=9

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8. Find the mean of the following data 3,6,11,12,18

Ans. Mean = 

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9. Express in the form of a + ib (3i-7) + (7-4i) – (6+3i) + i²³

Ans. Let

Z = 

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10. Find the conjugate of 

Ans.

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11. Solve for x and y, 3x + (2x-y) i= 6 – 3i

Ans.3x = 6

x = 2

2x – y = – 3

2 × 2 – y = – 3

– y = – 3 – 4

y = 7

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12. Find the value of 1+i² + i⁴ + i⁶ + i⁸ + —- + i²⁰

Ans.

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13. Multiply 3-2i by its conjugate.

Ans. Let z = 3 – 2i

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14. Find the multiplicative inverse 4 – 3i.

Ans. Let z = 4 – 3i

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15. Express in term of a + ib 

Ans.

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In This Post we are  providing Chapter- 14 MATHEMATICAL REASONING NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS ON MATHEMATICAL REASONING

Question 1.

Give three examples of sentences which are not statements. Give reasons for the answers.

Ans. (i) The sentence “Rani is a beautiful girl” is not a statement. To some Rani may look beautiful and to other she may not look beautiful. We cannot say on logic whether or not this sentence is true.

(ii) The sentence ‘shut the door’ is not a statement. It is only an imperative sentence giving a direction to someone. There is no question of it being true or false.

(iii) The sentence ‘yesterday was Friday’ is not a statement. It is an ambiguous sentence which is true if spoken on Saturday and false if spoken on other days. Truth or false hood of the sentence depends on the time at which it is spoken and not on mathematical reasoning.

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Question 2.

Write the negation of the following statements

(i) Chennai is the capital of Tamil Nadu.

(ii) Every natural number is an integer.

Ans. (i) Chennai is not the capital of Tamil Nadu.

(ii) Every natural number is not an integer.

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Question-3

Ans.

 Question-4

Ans.

Question-5

Ans.

 Question-6

Ans.

 Question-7

Ans.

NCERT Solutions for Class 11 Maths Chapter 14 Exercise.14.3

Question-6

Ans.

 Question-7

Ans.

 Question-8

Ans.

 Question-9

Ans.

Question-10

Ans.

 Question-11

Ans.

Question-12

Ans.

 Question-11

Ans.

Question-12

Ans.

 Question-13

Ans.

 Question-14

Ans.

 Question-15

Ans.

In This Post we are  providing Chapter-13 LIMITS AND DERIVATIVES NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS LIMITS AND DERIVATIVES

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1. Find the derivative of at 

Ans. 

At 

=

=

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2. Find the derivative of with respect to using product rule

Ans. let

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3. Find the derivative of with respect to 

Ans. let

=

=

=

=

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4. Find 

when 

Ans. 

We know that 

L. H. L. 

R. H. L. 

L. H. L. R. H. L does not exist

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5. Find the derivative of the function at Also show that 

Ans. 

At 

 Hence proved

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6. Evaluate 

Ans. 

=

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7. Find derivative of  by first principle

Ans. 

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8. Evaluate 

Ans. 

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9. Evaluate (if it exist)

Ans. 

---

Ans.

For all real number exist

For 

 all integral values of exist

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10. Differentiate the function with respect to 

Ans. 

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11. Find 

Ans. 

12. Find 

Ans. 

13. Find derivative of by first principle

Ans. 

14. Find derivative of 

Ans. 

15. Find derivative of 
Ans. 

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In This Post we are  providing Chapter-12 INTRODUCTION TO THREE DIMENSIONAL GEOMETRY NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

Question 1:

Ans:

 Question 2:

Ans:

 Question 3:

Ans:

 Question 4:

Ans:

 Question 5:

Ans:

Question 6:

Ans:

Question 7:

Ans:

 Question 8:

Ans:


 Question 9:

Ans:

Question 10:

Ans:

Question 11:

Ans:

 Question 12:

Ans:

 Question 13:

Ans:

Question 14:

Ans:

 Question 15:

Ans:

In This Post we are  providing Chapter- 11 CONIC SECTIONS NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS CONIC SECTIONS

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1.Find the equation of an ellipse whose foci are & the eccentricity is ?

Ans. Let the required equation of the ellipse be 

let the foci be &

Now 

Hence equation is 

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2.Find the equation of an ellipse whose vertices are & 

Ans. Let equation be 

& its vertices are 

Let 

Then 

Now 

Hence the equation is 

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3.Find the equation of hyperbola whose length of latus rectum is 36 & foci are 

Ans. Clearly C = 12

Length of cat us rectum 

Now 

This 

Hence, 

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4.Find the equation of a circle drawn on the diagonal of the rectangle as its diameter, whose sides are 

Ans. Let ABCD be the given rectangle & 

Then 

So the equation of the circle with AC as diameter is given as

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5.Find the coordinates of the focus & vertex, the equations of the diretrix & the axis & length of latus rectum of the parabola 

Ans.

& 

So, 

So it is case of downward parabola

o, foci is 

Its vertex is 

So, 

Its axis is y – axis, whose equation is length of lotus centum

units.

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6.Show that the equation represents a circle. Also find its centre & radius.

Ans.

So 

Where, 

Hence, centre of circle &

Radius of circle 

units

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7.Find the equation of the parabola with focus at & directrix is 

Ans.Focus lies to the right hand side of the origin

So, it is right hand parabola.

Let the required equation be

So, 

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8.Find the equation of the hyperbola with centre at the origin, length of the transverse axis 18 & one focus at (0,4)

Ans.Let its equation be 

Clearly, C = 4.

length of the transverse axis 

Also, 

So, 

So, equation is 

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9.Find the equation of an ellipse whose vertices are  the foci are 

Ans.Let the equation be 

& a = 13

Let its foci be  then 

So, 

So, equation be 

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10.Find the equation of the ellipse whose foci are & length of whose major axis is 10

Ans. Let the required equation be 

Let 

Its foci are 

Also, a = length of the semi- major axis = 

Now, 

Then, 

Hence the required equation is 

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11.Find the equation of the hyperbola with centre at the origin, length of the transverse axis 8 & one focus at (0,6)

Ans. Let its equation by 

Clearly, C = 6

& length of the transverse axis  

Also, 

So, 

Hence, the required equation is 

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12.Find the equation of the hyperbola whose foci are at & the length of whose conjugate axis is 

Ans. Let it equation be 

Let it foci be 

Length of conjugate axis 

Also, 

Hence, required equation is 

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13.Find the equation of the hyperbola whose vertices are & foci are 

Ans. The vertices are 

But it is given that the vertices are

Let its foci be 

But it is given that the foci are 

Now 

Then 

Hence the required equation is 

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14.Find the equation of the ellipse for which & whose vertices are 

Ans. Its vertices are therefore a =10

Let 

Then, 

Now,

Hence the required equation is 

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15.Find the equation of the ellipse, the ends of whose major axis are & the ends of whose minor axis are 

Ans. Its vertices are & therefore, a = 5 ends of the minor axis are

 i.e length of minor axis = 25 units

Now, 

Hence, the required equation 

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