Class 10

SCERT AP Board 10th Class Social Solutions 21st Lesson Social Movements in Our Times Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Social Studies Solutions 21st Lesson Social Movements in Our Times

10th Class Social Studies 21st Lesson Social Movements in Our Times Textbook Questions and Answers

Question 1.
Here are the list of items that you can use for making a table on social movements. Draw a table based on them and find out similarities and differences amongst movements:
Main area of focus of the movement; location, main demands, modes of protest, important leaders; response from the state; possible impact on society.
Answer:

Question 2.
Kanayya, Ramya and Salma have a debate. They have different expectations. Whom would you agree with and give reasons, from the context of human rights? Ramya argues it is okay to restrict the freedom of the press, etc. but ensure people do not live in poverty. Salma argues it is food alone is not important but equally important to have freedom of press because there is no other way people would know if there is violation of dignity of people in different parts of the country. Kanayya says, how will it make a difference if press belongs to the rich and powerful people, why would they cover things that ordinary people expect.
Answer:

1. I agree with Ramya.
2. She argues that food alone is not important but also to have freedom of press.
3. If we do not have freedom of press, there is no other way people would know if there is violation of dignity of people in different parts of the country.
4. Now with globalization, world has become a tiny village.
5. People are coming to know and responding quickly in social media.
6. Everyone has the right to life, liberty and security of person.
7. No one shall be subjected to inhuman or degrading treatment.
8. Protection of most human rights is important.

Question 3.
What are the basic features of social movements?
Answer:
The basic features of social movements :

1. They are based on values of justice, democracy and civil rights.
2. Protection of the cultural sphere.
3. The prevention of a change in societies structure and values.
4. Protection of livelihood and health.
5. Equal treatment in the society.
6. Protection from the consumption of alcohol and drugs.
7. Protection of the environment.
8. Protection of agricultural lands.

Question 4.
How is the role of the ordinary individuals described in the above case studies ?
Answer:

1. Without the participation of ordinary individuals any social movement cannot be a successful one.
2. They were the ones, who suffered and dejected.
3. They make their voices heard through their leaders.
4. They actively participate in marches, boycotts, processions planned by their leaders.
5. Nowadays they are making use of internet and social media to mobilise and fight for their cause.
6. They not only think of personal profits, hope for better future and sustainable environment.
7. They even oppose their own government and support the human rights of the sufferers.
8. Most movements involved them are peaceful in nature.

Question 5.
How are the rights of black people in the USA and Meira Paibi movements similar or different?
Answer:

1. The rights of black people in the USA are violated by law.
2. They are met with inhuman treatment.
3. They are discriminated in schools, transport facilities, job, housing and even in voting righ/s.
4. But they are given right to freedom of movement.
5. In Meira Paibi movements, the most suffered are women.
6. Their right to life, liberty and security of person are taken away by special protection law.
7. They are subjected to cruel and degrading treatment.
8. Their men and children are detained on no fair cause.
9. They are not even given the right to freedom of movement.
10. Government has yet to take a decision on Meira Paibi’s demands.

Question 6.
Democracies have been identified as most prominent political systems across the world.
Do you think it has been able to take care of all expectations of people. Based on the examples cited in these chapters, write a short note on ‘democracy and social movements’.
Answer:
Democracy and Social Movements :

1. Social movements are mostly the outcome of dissatisfactions in the society.
2. The ruling democracies are not able to fulfil the expectations of people.
3. Some section or the other in the society is suffering with denial of human rights or social justice.
4. Their ire is augmented and shapes into a movement.
5. When governments are after nuclear arms and not providing peace and security to people usually people resent it and movements come up.
6. When people are discriminated, they revolt against administration. Likewise, whenever there is lack of social justice and when there is a threat to environmental system also movements come out.

Question 7.
Discuss and find out how movements mobilise people from across the globe like in the above instance of campaign to protest in the context of Bhopal gas tragedy.
Answer:

1. Movements seek a vision that is different.
2. Movements mobilise people from across the globe to protest various issues.
3. Black Americans organised themselves against the segregation and discrimination they faced.
4. People of Russia fought for human rights there, when free multiparty elections were not allowed, Press freedom was not allowed.
5. Massive protests took place against the policies of the govemments, which are war mongering.
6. Greenpeace movement in the USA protested the conduct of nuclear tests under water in the USA.
7. Many such movements related to environment were taken up and people supported them.
8. There are various platforms for them like, Facebook, twitter, e-mails, Internet newspaper, etc.

10th Class Social Studies 21st Lesson Social Movements in Our Times InText Questions and Answers

10th Class Social Textbook Page No. 299

Question 1.
Try to read the famous speech of Dr King and write an essay on the ideals he set for American society and how he planned to achieve it.
Answer:
Martin Luther king set many ideals for the American society. Some of them are,
а) Justice
b) Liberty
c) Equality
d) Unalienable rights of life
e) Pursuit of happiness
f) freedom
g) Democracy etc.

He plans to achieve the ideals in the following ways:

1. Negroes should not relax until their demands are met.
2. Shaking the foundations of the government with revolt until the bright day of justice emerges.
3. The struggle should be filled with dignity and discipline.
4. By avoiding physical violence.
5. Trusting some white people who sympathize with the blacks.
6. He says that with faith all will be able to work together, pray together, struggle together, to go to jail together, to stand up for freedom together, knowing that there will be freedom one day.

10th Class Social Textbook Page No. 300

Question 2.
Make a table and list the demands of civil rights movement and possible solutions in your opinion.
Answer:

Question 3.
The USA claims to be a democracy, yet it kept certain groups of people segregated, till middle of last century. Discuss how the idea of democracy need to be more inclusive in our context.
Answer:

1. The USA claims to be a democracy.
2. It practised segregation, till the middle of last century.
3. Democracies cannot afford to alienate their subjects.
4. They cannot judge a person by the colour of the skin.
5. They cannot shy away the protection of equal rights to all subjects.
6. Democracy in this context needed to be more inclusive.
7. All the black people are to be treated on same footing with others.

Question 4.
Why do we hear different voices within a movement? Can you identify differences in them?
Answer:

1. People have differences of opinions, hence we hear different voices within a movement.
2. In American Civil Rights Movement two voices arose. They were –
   a) Many people agreed with Dr King that it was possible to achieve equality for all people through peaceful means.
   b) Many others like “Malcom X” thought that Blocks should fight for independence from white rule and for that they have to use all means including armed conflict.

Question 5.
Can you think of similarity or differences in the nature of political system in the USA and the USSR and how was their response to people’s rights?
Answer:

10th Class Social Textbook Page No. 301

Question 6.
“We Won’t Go”
America has a law which requires all able bodied citizens to enroll in the army for a short period. During the Vietnam War, thousands of citizens refused to get drafted into the army to fight in Vietnam. Let us read about one such protest refusal. This is a statement that appeared in a newspaper, Harvard Crimson:

“We, the undersigned, as American men of draftage, may be asked by our government to participate in the war in Vietnam. We have examined the history and the nature of this war, and have reached the conclusion that our participation in it would be contrary to the dictates of our consciences. We therefore declare our determination to refuse military service (all citizens are required to do so by law) while the United States is fighting in Vietnam. Our intention in signing this statement is to unite with other draftage men who share our convictions, in order to turn our personal moral rejection of this war into effective political opposition to it.”

Some thought that these people were being un-patriotic while others thought that they were justified in refusing to participate in an unjust war. Discuss the two points of view in the class and write a short note of arguments of both sides and your own viewpoint.
Answer:

1. Vietnam conflict was the outcome of the Cold War between the USA and the USSR.
2. Citizens refused to get drafted into the army to fight in Vietnam.
3. The US war with Vietnam was inhuman, hence the majority of the people opposed it.
4. People who hate “Socialistic Society” and “Communism” supported the decision of the US to continue the war with Vietnam.
5. In my opinion, I oppose the war with Vietnam as it was against democratic principles and human rights.

10th Class Social Textbook Page No. 303

Question 7.
What were the different types of responses to the weaponisation?
Answer:

1. Nuclear arms race intensified after the end of Vietnam war in 1975.
2. More and more countries competed with each other to stock pile nuclear arms.
3. Arms producing companies and governments created a war panic among the people.
4. They created war like situation.
5. People believed that war mongering and arms race made the world more unsafe.
6. It also increased the possibility of a disastrous war for all countries.
7. Massive protests took place against these policies of governments.

Question 8.
If people from different countries meet each other, there would be less chances of war, than the governments alone deciding the policy with each other. Would you agree with this statement? Give reasons for the answer.,
Answer:

1. Usually countries formulate their policies.
2. People of countries meet together and avoiding war is distant from reality.
3. Most countries in the world are democracies.
4. People vest their powers through vote to their representatives who could administer them.
5. It may be looking simple but, it definitely may not be feasible.
6. So, I cannot agree with this statement.

Question 9.
Explain how environmental issues can affect people of nations who may have no role in deciding the location of nucelar plants, polluting factories, etc. How do you deal with such situation?
Answer:

1. Usually people of the nation are suffering lot, whenever there is a nuclear tragedy.
2. They really do not have any role in deciding the nuclear plant’s location or pollution factory.
3. That will be decided by their representatives and their secretaries.
4. They decide the locations taking into consideration, a lot of things like infrastructure, raw material, technology, etc.
5. To deal with these situations the governments should take all the protective measures.
6. In case of any adversity, they should respond well in time to support the people.
7. They should see that proper care is taken about the affected and fair compensations were distributed among the suffered people.

10th Class Social Textbook Page No. 304

Question 10.
Look up the website of Greenpeace movement (http : //www.greenpeace.org/international) to find out about the issues they have been fighting for and how the methods they have used for fighting. Find out about the debates and controversies about this movement too.
Answer:
Students’ Activity.

10th Class Social Textbook Page No. 307

Question 11.
Is it impossible to build factories or mines or power plants without throwing out farmers or tribal people? What can be the alternatives? Discuss in your family and school on these issues.
Answer:

1. Most of the times it is impossible to build factories, mines or power plants without throwing out the farmers or the tribal people.
2. Because they need infrastructural facilities and raw material availability, they are to be set up like this.
3. Governments should think of alternatives.
4. Protection of the farmers and tribals is also lied with the government.
5. They should plan of no damage to these sectors of people or the minimum.
6. In case of a compulsion, they must be given compensations like land, lump sums and employment.
7. More importantly, government should concentrate on viable alternatives to protect the environment also.

10th Class Social Textbook Page No. 308

Question 12.
What were the various strategies used by the social movement?
Answer:

1. Social Movements throughout the world used various strategies.
2. Civil Rights Movement in the USA used civil disobedience (Violating discriminatory laws peacefully) and boycott of discriminatory services (like buses which segregate whites and blacks)
3. Thousands of scientists and intellectuals from across the world campaigned for abolishing all nuclear weapons.
4. Volunteers in the USA setout in a smallship “Green Peace’ in protest to underwater nuclear test of the USA.
5. People used international laws to fight against the problems that factory workers and women affected in Bhopal gas disaster.
6. Women led movements for social justice and human rights.
7. People organised movements in protest to pollution, global warming and environmental degradation.

Question 13.
How do the people in movement see the process of resettlement promises?
Answer:

1. People who stood to be displaced from the project, demanded a fair compensation not just to those who own land, but all those who lived there.
2. People realised that there was actually no adequate land available to compensate for the loss.
3. They alsobelieved that it was really not possible to rehabilitate the displaced people properly.
4. People began to realise that the problem was not compensation or rehabilitation but one of faulty notion of development.
5. A development which was based on unsustainable use of natural resources, only paved way for setting up industries and commercial farms at the cost of farming and tribal communities.

10th Class Social Textbook Page No. 310

Question 14.
Find out about more recent such struggles in West Bengal (Nandigram), Odisha (Niyamagiri) and Andhra Pradesh (Polavaram, Sompeta etc). Prepare a poster explaining the main features of the struggle in each of these cases.
Answer:
Nandigram (West Bengal):

1. Nandigram is a place on the bank of Haldia and quite far from Kolkata.
2. In 2007, March the state government of West Bengal sanctioned the land there to set up Special Economic Zone by Salim Group.
3. People of Nandigram resented it and led mass processions and struggle and 14 people died.

Niyamgiri (Odisha):

1. Niyamagiri hills in Odisha state are famous for their bauxite reserves. Odisha government gave permission to British mining company Vedanta to mine bauxite from there in July 2013.
2. People resented this, especially the tribals and organised many processions and later courts involved in this matter and by January 2014 the mining was disallowed.

Sompeta, Polavaram in combined (Andhra Pradesh):

1. Sompeta was a mandal in Srikakulam district of Andhra Pradesh and government at the state permitted Nagarjuna Company Limited to set up a thermal plant there in 2010.
2. People supported by many opposition party leaders protested the decision of government and for three years there were long drawn struggles.
3. Polavaram project is to be constructed on Godavari river spreading in East, West Godavari’s and Khammam. Government obtained permissions and started it in 2004.
4. It has submerging areas and affecting, zones in Chattisgarh and Odisha also. Many conflicts were there to complete it.

Question 15.
Fill in the para and line in the section below which you think is related to the violation or are in conflict with provisions of Human rights.
Article 3: Everyone has the right to life, liberty and security of person. Para ——– line ——–.
Article 5: No one shall be subjected to torture or to cruel, inhuman or degrading treatment or punishment. Para ——– line ——–.
Article 7: All are equal before the law and are entitled without any discrimination to equal protection of the law. All are entitled to equal protection against any discrimination in violation of this Declaration and against any incitement to such discrimination. Para ——– line ——–.
Article 9: No one shall be subjected to arbitrary arrest, detention or exile. Para ——– line ——–.
Article 10: Everyone is entitled in full equality to a fair and public hearing by an independent and impartial tribunal, in the determination of his [or her]rights and obligations and of any criminal charge against him [or her]. Para ——– line ——–.
Article 12: No one shall be subjected to arbitrary interference with his [or her] privacy,family, home or correspondence, nor to attacks upon his [or her] honour and reputation. Everyone has the right to the protection of the law against such interference or attacks. Para ——– line ——–.
Articl e 13: (1) Everyone has the right to freedom of movement and residence within the borders of each state [state here means country], Para ——– line ——–.
(2) Everyone has the right to leave any country, including his own, and to return to his[or her country. Para ——– line ——–.
Answer:
Violations
Article 3: Everyone has the right to life, liberty and security of person. Para 3 line 13.
Article 5: No one shall be subjected to torture or to cruel, inhuman or degrading treatment or punishment. Para 3 line 6 and 7.
Article 9: No one shall be subjected to arbitrary arrest, detention or exile. Para 3 line 4.
Article 12: No one shall be subjected to arbitrary interference with his [or her] privacy, family, home or correspondence, nor to attacks upon his [or her]honour and reputation. Everyone has the right to the protection of the law against such interference or attacks. Para 3 line 10

AP State Board Syllabus AP SSC 10th Class Chemistry Solutions Chapter 13 Principles of Metallurgy Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Chemistry Solutions 13th Lesson Principles of Metallurgy

10th Class Chemistry 13th Lesson Principles of Metallurgy Textbook Questions and Answers

Review of Your Previous Knowledge

Question 1.
Can you mention some articles that are made up of metals?
Answer:
Jewellery, conducting wires, utensils, etc.

Question 2.
Do metals exist in nature in the form same as that we use in our daily life?
Answer:
No, they exist as ores and minerals.

Question 3.
Have you ever heard the words like ore, mineral and metallurgy?
Answer:
Yes, these words are related to extraction of metals.

Question 4.
Do you know how these metals are obtained?
Answer:
These metals are generally extracted from their ores.

Improve Your Learning

Question 1.
List three metals that are found in nature as oxide ores.
Answer:
The three metals that are found in nature as oxide ores are

1. Bauxite (Al₂O₃ 2H₂O)
2. Haematite (Fe₂O₃)
3. Zincite (ZnO).

Question 2.
List three metals that are found in nature in uncombined form.
Answer:
The three metals that are found in nature in uncombined form are

1. Gold
2. Silver
3. Platinum.

Question 3.
Write a note on dressing of ore in metallurgy.
(OR)
What is concentration of Ore? List various physical methods that are used to enrich the ore.
Answer:

• Ores that are mined from the earth are usually contaminated with large amount of impurities such as soil and sand, etc.
• Concentration or dressing means, simply getting rid of as much of the unwanted rocky material as possible from the ore. The impurities like sand and clay are called gangue.

The physical methods adopted in dressing of the ore or enriching the ore depends upon the difference between physical properties of ore and gangue.

Methods of dressing or concentration of the ore:
1. Hand picking :
If the ore particles and the impurities are different in one of the properties like colour, size, etc. using that property, the ore particles are handpicked separating them from other impurities.

2. Washing:

• We use washing method with water to separate dust from rice, dal and vegetable fruits, etc.
• Ore particles are crushed and kept on a slopy surface. They are washed with controlled flow of water. Less densive impurities are carried away by water flow, leaving the more densive ore particles behind.

3. Froth flotation:
This method is mainly useful for sulphide ores. The ore with impurities is finely powdered and kept in water taken in a flotation cell. Air under pressure is blown to produce froth in water. Froth so produced, takes the ore particles to the surface whereas impurities settle at the bottom. Froth is separated and washed to get ore particles.

4. Magnetic separation:
If the ore or impurity, one of them is magnetic substance and the other is non-magnetic substance, they are separated using electromagnets.

Question 4.
What is an ore? On what basis a mineral is chosen as an ore?
Answer:
Ore :
A mineral from which a metal can be extracted economically and conveniently is called ore.
A mineral is chosen as an ore if the mineral is economical and profitable to extract.

Example:
Aluminium is the common metal in the Earth’s crust in all sorts of minerals. It is economically feasible and profitable to extract from bauxite which contains 50-70% of aluminium oxide.

Question 5.
Write the names of any two ores of iron.
Answer:
The names of two ores of iron :

1. Haematite (Fe₂O3)
2. Magnetite (Fe₃O₄).

Question 6.
How do metals occur in nature ? Give examples to any two types of minerals.
Answer:

• The earth’s crust is the major source of metals.
• Sea water also contains some soluble salts such as sodium chloride and magnesium chloride etc.
• Some metals like gold (Au), silver (Ag) and copper (Cu) are available in nature in free state as they are least reactive.
• Other metals are found in nature in the combined form due to their more reactivity.
• The elements or compounds of the metals which occur in nature in the earth’s crust are called minerals.

Examples :
Minerals in oxide form :
Bauxite, Zincite, Magnetite, etc.

Minerals in sulphide form :
Copper iron pyretes, Galena, etc.

Question 7.
Write short notes on froth flotation process.
(OR)
Which method is useful for concentration of sulphide ore? Explain the method.
Answer:
Froth Floatation process :

• This method is mainly useful for sulphide ores which have no wetting property whereas impurities get wetted.
• The ore with impurities is finely powdered and kept in water taken in a floatation cell.

Froth floatation process for the concentration of sulphide ores

• Air under pressure is blown to produce froth in water.
• Froth so produced takes the ore particles to the surface whereas impurities settle at the bottom.
• Froth is separated and washed to get ore particles.

Question 8.
When do we use magnetic separation method for concentration of an ore? Explain with an example.
(OR)
Write the name of the method we use to separate the ore or impurity in which one of them is magnetic substance. Draw a neat diagram indicating the method.
Answer:
If the ore or impurity, one of them is magnetic substance and the other non-magnetic substance they are separated using electromagnets.
Ex :
Iron from iron ore (Fe₃O₄) is separated from its impurity by passing through a magnetic field. The field attracts magnetic ore (Iron) and repels the non-magnetic impurities.

Question 9.
Write short notes on each of the following :
i) Roasting
ii) Calcination
iii) Smelting
Answer:
i) Roasting :
Roasting is a pyrochemical process in which the ore is heated in the presence of oxygen or air, below its melting point. Generally, reverberatory furnace is used for roasting.
Ex:
Zinc blende on heating with oxygen in reverberatory furnace forms zinc oxide as solid and liberating sulphur dioxide as gas.
2Zns_(s) + 3O_2(g) → 2ZnO_(s) + 2SO_2(g)

ii) Calcination :
Calcination is a pyrochemical process in which the ore is heated in the absence of air. The ore gets generally decomposed in this process.
Ex: MgCO_3(s) → MgO_(s) + CO_2(g)

iii)Smelting:
Smelting is a pyrochemical process, in which the ore is mixed with flux and fuel, then is strongly heated.

Question 10.
What Is the difference between roasting and calcination? Give one example for each.
(OR)
Roasting and Calcination are the methods to extract crude metals from ores. What is the difference between Roasting and Calcination?
Answer:

Question 11.
Define the terms:
i) gangue
ii) slag.
Answer:
i) Gangue:
The impurity present in the ore is called gangue.
(or)
Unwanted impurity associated with ore.

ii) Slag:
The impurities found from molten metal during poling process of refining are called slag.

Question 12.
Magnesium is an active metal if it occurs as a chloride in nature, which method of reduction is suitable for its extraction?
Answer:

• The method of reduction which is useful for chloride of magnesium which is active is electrolytic reduction.
• Fused MgCl₂ is electrolysed with steel cathode (-) and graphite anode (+). The metal (Mg) will be deposited at cathode and chlorine gas liberates at the anode.
  At cathode : Mg²⁺ + 2 e^– → Mg
  At anode : 2 Cl^– → Cl₂ + 2e^–

Question 13.
Mention two methods which produce very pure metals.
Answer:
Methods which produce very pure metals are :

1. Electrolytic Reduction
2. Smelting.

(OR)

1. Distillation
2. Poling.

Question 14.
Which method do you suggest for extraction of high reactivity metals? Why?
Answer:
1.The only method which is suitable for extraction of high reactivity metals is electrolysis of their fused compounds.

2. Other methods are not suitable due to following reasons :
a) Simple reduction methods like heating with C, CO, etc. to reduce the ores of these metals are not suitable because the temperature required for the reduction is too high and more expensive.

b) Electrolysis of their aqueous solutions are also not preferable because water in the solution would be discharged at the cathode in preference to the metal ions.

Question 15.
Suggest an experiment to prove that the presence of air and water is essential for corrosion. Explain the procedure.
(OR)
Write the experimental procedure to prove that water and air are essential for rusting of iron articles.
(OR)
How can you prove that the presence of air and humid are essential for corrosion?
(OR)
Explain in brief, an experiment to prove that the presence of air and water are essential for corrosion.
Write the precautions to be taken in the experiment to show air and water are essential for rusting iron articles and also write the experimental procedure.
Answer:
Aim :
To prove that the presence of air and water is essential for corrosion or for rusting of iron articles.

Apparatus :
3 boiled test tubes, 3 corks, boiled distilled water, anhydrous calcium chloride, clean iron nails.

Procedure :

• Take three test tubes and place clean iron nails in each of them.
• Label these test tubes A, B and C. Pour some water in test tube A and cork it.
• Pour boiled distilled water in test tube B, add about 1 ml of oil and cork it. The oil will float on water and prevent the air from dissolving in the water.
• Put some anhydrous calcium chloride in test tube C and cork it. Anhydrous calcium chloride will absorb the moisture.
• Leave these test tubes for a few days and then observe.
• We will observe that iron nails rust in test tube A, but they do not rust in test tubes B and C.

Observation :

• In test tube A, the nails are exposed to air and water. Hence, the nails rusted.
• In test tube B, the nails are exposed only to water, but not to air, because the oil float on water and prevent the air from dissolving in the water. Hence, the nails are not rusted.
• In test tube C, the nails are exposed to dry air, because anhydrous calcium chloride will absorb the moisture, if any, from the air. Hence, the nails are not rusted.

Conclusion :
From the above experiment we can prove that air and water are essential for corrosion.

Question 16.
Collect information about extraction of metals of low reactivity silver, platinum and gold and prepare a report.
(OR)
Prepare a report with the collected information about extraction of metals of low reactivity silver, platinum and gold.
Answer:
Extraction of Silver:

1. Silver can be extracted from Ag2S by using displacement from aqueous solution.
2. Ag₂S is dissolved in KCN solution to get dicyanoargentate (I) ions.
3. From these ions Ag is precipitated by treating with Zinc dust powder.
   Ag₂S + 4 CN^– → 2 [Ag(CN)₂]^– + S^2-
   2[Ag(CN)₂]^–_(aq) + Zn_(s) → [Zn(CN)₄]^2-_(aq) + 2Ag_(s)

Extraction of Gold :

1. Gold is extracted from gold ore like electrum. Impurities are separated from the gold by treating gold ore with a weak cyanide solution.
2. Zinc is added and a chemical reaction takes place which separates the gold from ore.
3. Pure gold is removed from the solution with a filter press.

Extraction of Platinum:

1. The extraction of platinum from ore is a complex process and includes milling the ore, a froth flotation process, and smelting at high temperatures.
2. This removes the base metals, notably iron and sulphur and concentrate platinum.

Question 17.
Draw the diagram showing
i) Froth flotation
ii) Magnetic separation.
(OR)
Draw a neat diagram and label the parts that shows froth floatation process for the concentration of sulphide ore.
Answer:
i)

ii)

Question 18.
Draw a neat diagram of reverberatory furnace and label it neatly.
(OR)
Draw a neat labelled diagram of a reverberatory furnace.
Answer:

Question 19.
What is activity series? How does it help in extraction of metals?
Answer:
Activity Series :
We can arrange metals in descending order of their reactivity. This series of writing metals is called activity series.

Uses of activity series the extraction of metals :

• Activity series is extremely useful in extraction of metals because we can judge the nature of metal and how it exists.
• High reactive metals like K, Na, Ca, Mg and Al are so reactive that they are never found in nature in free state.
• The moderate reactive metals like Zn, Fe, Pb, etc. are found in the earth’s crust mainly as oxides, sulphides and carbonates.
• The least reactive metals like Au, Ag, Pt are found even in free state in nature.

Question 20.
What is thermite process? Mention its applications in daily life.
Answer:
Thermite Process :

• Thermite process is the chemical reaction which takes place between metal oxides and aluminium.
• When highly reactive metals such as sodium, calcium, aluminium, etc. are used as reducing agents, they displace metals of lower reactivity from the compound.
• This reaction is highly exothermic. The amount of heat evolved is so high that the metals can he directly converted into molten state.

Applications in daily life :

• The reaction if Iron (III) oxide (Fe203) with aluminium is used to join railing of railway tracks or cracked machine parts.
  2 Al + Fe₂O₃ → Al₂O₃ + 2 Fe + Heat.
• And also used for joining of cracked metal utensils in the house.

Question 21.
Where do we use hand picking and washing methods in our daily life ? Give examples.
How do you correlate these examples with enrichment of ore?
Answer:
Daily life examples for hand picking:

• Separating mud particles from rice is an example for hand picking because the colour and size of these two are different.
• Similarly, the ore particles and the impurities are different in one of the properties like colour, size, etc. are separated by hand picking.

Daily life examples for washing :

• We can clean some vegetables like potatoes by controlled flow of water. Less densive impurities are carried away by the flow leaving the more densive potatoes.
• Similarly, ores are washed with controlled flow of water. Less densive impurities i are carried away by water flow, leaving the more densive ore particles behind.

Fill In The Blanks

1. The method is suitable to enrich the sulphide ores.
2. Arranging metals in the decreasing order of their reactivity is called
3. The method suitable for purification of low boiling metals.
4. Corrosion of iron occurs in the presence of and
5. The chemical process in which the ore is heated in the absence of air is called
Answer:

1. Froth flotation
2. activity series
3. distillation
4. air, water
5. calcination

Multiple Choice Questions

1. The impurity present in the ore is called ………………….
A) Gangue
B) Flux
C) Slag
D) Mineral
Answer:
A) Gangue

2. Which of the following is a carbonate ore?
A) Magnesite
B) Bauxite
C) Gypsum
D) Galena
Answer:
A) Magnesite

3. Which of the following is the correct formula of Gypsum?
A) CuSO₄ • 2 H₂O
B) CaSO₄ • ½ H₂O
C) CuSO₄ • 5 H₂O
D) CaSO₄ • 2 H₂O
Answer:
D) CaSO₄ • 2 H₂O

4. The oil used in the froth flotation process is
A) kerosene oil
B) pine oil
C) coconut oil
D) olive oil
Answer:
B) pine oil

5. Froth flotation is method used for the purification of ………………. ore.
A) sulphide
B) oxide
C) carbonate
D) nitrate
Answer:
A) sulphide

6. Galena is an ore of ………………..
A) Zn
B) Pb
C) Hg
D) Al
Answer:
B) Pb

7. The metal that occurs in the native form is ………………
A) Pb
B) Au
C) Fe
D) Hg
Answer:
B) Au

8. The most abundant metal in the earth’s crust is …………………
A) silver
B) aluminium
C) zinc
D) iron
Answer:
B) aluminium

9. The reducing agent in thermite process is ………………….
A) Al
B) Mg
C) Fe
D) Si
Answer:
A) Oxidise

10. The purpose of smelting an ore is to ……………….. it.
A) Oxidise
B) Reduce
C) Neutralise
D) None of these
Answer:
B) Reduce

10th Class Chemistry 13th Lesson Principles of Metallurgy InText Questions and Answers

10th Class Chemistry Textbook Page No. 238

Question 1.
How are the metals present in nature?
Answer:
Some metals like gold (Au), silver (Ag) and copper (Cu) are available in nature in free sjate. Other metals mostly are found in nature in the combined form.

10th Class Chemistry Textbook Page No. 240

Question 2.
What metals can we get from the ores mentioned in the Table – 1?
Answer:
The metals are Aluminium (Al), Copper (Cu), Magnesium (Mg), Silver (Ag), Manganese (Mn), Iron (Fe), Zinc (Zn), Sodium (Na), Mercury (Hg), Lead (Pb), Calcium (Ca).

Question 3.
Can you arrange metals in the order of their reactivity?
Answer:
The order of reactivity is like this : Ag < Cu < Pb < Mn < Fe < Zn < Al < Mg < Ca < Na.

Question 4.
What do you notice in Table – 2?
Answer:
We notice that ores of many metals are oxides and sulphides. ______

Question 5.
Can you think how we get these metals from their ores?
Answer:
We can get metals from their ores by using various extracting techniques.

Question 6.
Does the reactivity of a metal and form of its ore (oxides, sulphides, chlorides, carbonates, sulphates) has any relation with process of extraction?
Answer:
Yes, they have relation. Metals like K, Na, Ca, Mg and Al are so reactive. They exist in all forms whereas moderate reactive metals like Zn, Fe, Pb, etc. exist as oxides, sulphides and carbonates. The least reactive metals are found even in free state.

Question 7.
How are metals extracted from mineral ores?
Answer:
The extraction of a metal from its ores involves mainly in three states. They are :

1. Concentration or Dressing
2. Extraction of crude metal
3. Refining or purification of the metal.

10th Class Chemistry Textbook Page No. 248

Question 8.
Do you know why corrosion occurs?
Answer:
Corrosion occurs due to reaction of metal with both air and water.

Question 9.
What are the conditions under which iron articles rust?
Answer:
Iron articles get rust due to both air and water.

10th Class Chemistry Textbook Page No. 251

Question 10.
What is the role of furnace in metallurgy?
Answer:
Furnace is used to carry out pyrochemical process in metallurgy.

Question 11.
How do furnaces bear large amounts of heat?
Answer:
Furnaces have metallic lining. So they bear large heats.

Question 12.
Do all furnaces have same structure?
Answer:
No, they have different structures.

10th Class Chemistry Textbook Page No. 239

Question 13.
Do you agree with the statement “All ores are minerals but all minerals need not be ores.? Why?
Answer:

• Yes, I agree with the statement. The elements or compounds of the metals which occur in nature in the earth’s crust are called minerals whereas ore is a mineral from which the metal is profitably extracted.
• For example, aluminium exists in two mineral forms that is clay and bauxite. But aluminium is mainly extracted from bauxite which contains 70% aluminium oxide.
• So Bauxite is an ore of aluminium whereas clay is not ore.
• So all ores are minerals but all minerals need not be ores.

10th Class Chemistry 10th Lesson Principles of Metallurgy Activities

Activity – 1
1. How do you classify ores based on their formula?
Answer:
1) Look at the following ores.

2) Identify the metal present in each ore.
3) Classification of ores as oxides, sulphides, chlorides, carbonates, and sulphates as follows :

AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets InText Questions

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets InText Questions and Answers.

10th Class Maths 2nd Lesson Sets InText Questions and Answers

Question 1.
List the teeth under each of the following type (Page No. 25)

i) Incisors
Answer:
Central incisors = 4
Lateral incisors = 4
Total incisors = 8
ii) Canines
Answer:
Total canines = 4
iii) Pre-molars
Answer:
First premolars = 4
Second premolars = 4
Total premolars = 8
iv) Molars
Answer:
First molars = 4
Second molars = 4
Third molars = 4
Total molars = 12

Question 2.
Identify and write the “common property” of the following collections. (Page No. 26)
1) 2, 4, 6, 8, …….
Answer:
All are even numbers {x : x is even}
2) 2, 3, 5, 7, 11, …….
Answer:
All are prime numbers (x : x is a prime}
3) 1, 4, 9, 16, …….
Answer:
All are perfect squares
(x : x is a perfect square}
4) January, February, March, April,…
Answer:
All are English months
{x : x is a month of the year}
5) Thumb, index finger, middle finger, ring finger, pinky.
Answer:
All are fingers of a hand
{x : x is a finger of a hand}

Question 3.
Write the following sets. (Page No. 27)
1) Set of the first five positive integers.
Answer:
{11, 2, 3, 4, 5}
2) Set of multiples of 5 which are more than 100 and less than 125.
Answer:
{105, 110, 115, 120}
3) Set of first five cubic numbers.
Answer:
{1³, 2³, 3³, 4³, 5³}
{1, 8, 27, 64, 125}
4) Set of digits in the Ramanujan number.
Answer:
Ramanujan’s number is 1729
{1, 2, 7, 9}

Question 4.
Some numbers are given below. Decide the numbers to which number sets they belong to and does not belong to and express with correct symbols. (Page No. 28)
i) 1
Answer:
1 ∈ N
ii) 0
Answer:
0 ∈ W and 0 ∉ N
iii) -4
Answer:
– 4 ∈ I and – 4 ∉ N
iv) \(\frac{5}{6}\)
Answer:
\(\frac{5}{6}\) ∈ Q and \(\frac{5}{6}\) ∉ Z
v) \(1 . \overline{3}\)
Answer:
\(1 . \overline{3}\) ∉ N and \(1 . \overline{3}\) ∉ Z
vi) √2
Answer:
√2 ∈ S and √2 ∉ Q
vii) log 2
Answer:
log 2 ∉ N
viii) 0.03
Answer:
0.03 ∉ Q
ix) π
Answer:
π ∉ Z
x) \(\sqrt{-4}\)
Answer:
\(\sqrt{-4}\) ∉ Q and \(\sqrt{-4}\) ∈ C

Question 5.
List the elements of the following sets. (Page No. 29)
i) G = {all the factors of 20}
ii) F = {the multiples of 4 between 17 and 61 which are divisible by 7}
iii) S = {x : x is a letter in the word ‘MADAM’}
iv) P = {x : x is a whole number between 3.5 and 6.7}
Answer:
i) G = {1, 2, 4, 5, 10, 20}
ii) Multiples of 4 between 17 and 61
x = {20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60}
F = {28, 56}
iii) S = {M, D, A}
iv) P = {4, 5, 6}

Question 6.
Write the following sets in the roster form.   (Page No. 29)
i) B is the set of all months in a year having 30 days.
ii) P is the set of all prime numbers smaller than 10.
iii) X is the set of the colours of the rainbow.
Answer:
i) B = {April, June, September, November}
ii) P = {2, 3, 5, 7}
iii) X = {Violet, Indigo, Blue, Green, Yellow, Orange, Red}

Question 7.
A is the set of factors of 12. Which one of the following is not a member of A?   (Page No. 29)
A) 1
B) 4
C) 5
D) 12
Answer:
[C]

Think & Discuss

Question 1.
Observe the following collections and prepare as many as generalized statements you can describing their more properties. (Page No. 26)
i) 2, 4, 6, 8,….
Answer:
a) All even natural numbers
b) All positive even integers
c) Multiples of 2

ii) 1, 4, 9, 16, …..
Answer:
a) Squares of natural numbers
b) All perfect square numbers

Question 2.
Can you write set of rational numbers listing elements in it? (Page No. 28)
Answer:
We can’t list all elements in the set of rational numbers. We know that rational numbers are infinite.

Try this

Question 1.
Write some sets of your choice, involving algebraic and geometrical ideas. (Page No. 29)
Answer:
The set of all natural numbers ‘x’ such that 4x + 9 < 50,
ii) A = {x : x is an integer and -3 ≤ x ≤ 7}
iii) B = {Equilateral triangle, Right angled triangle, Scalene triangle, Obtuse angled triangle, Acute angled triangle)
iv) C = {Rectangle, Square, Parallelogram, Rhombus, Trapezium}

Question 2.
Match roster forms with the set builder form. (Page No. 29)

Answer:
i) d
ii) c
iii) a
iv) b

Do this

Question 1.
A = {1, 2, 3, 4},
B = {2, 4},
C = {1, 2, 3, 4, 7}, ∅ = { }.
Fill in the blanks with ⊂ or ⊄.  (Page No. 33)
i) A …. B
ii) C …. A
iii) B …. A
iv)A …. C
v) B …. C
vi) ∅ …. B
Answer:
i) A ⊄ B
ii) C ⊄ A
iii) B ⊆ A
iv) A ⊆ C
v) B ⊆ C
vi) ∅ ⊆ B

Question 2.
State which of the following statements are true.    (Page No. 33)
i) { } = ∅
ii) ∅ = 0
iii) 0 = { 0 }
Answer:
i) True (T)
ii) False (F)
iii) False (F)

Question 3.
Let A = {1, 3, 7, 8} and B = [2, 4, 7, 9}.
Find A ∩ B.     (Page No. 37)
Answer:
Given sets A = (1, 3, 7, 8} and B = {2,4, 7,9}
A ∩ B = {1, 3, 7, 8} ∩ (2, 4, 7, 9} = {7}

Question 4.
If A = {6,9,11 }; ∅ = {}, find A ∪ ∅, A ∩ ∅).  (Page No. 37)
Answer:
Given sets
A = {6, 9, 11} and ∅ = { }
A ∪ ∅ = {6, 9, 11} ∪ { }
= {6, 9, 11} = A
∴ A ∪ ∅ = A
A ∩ ∅ = {6,9,11} ∩ { } = { } = ∅
∴ A ∩ ∅ = ∅

Question 5.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
B = {2, 3, 5, 7}. Find A ∩ B and show that A ∩ B = B.    (Page No. 37)
Answer:
Given sets
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 3, 5, 7}
A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ∩ {2, 3, 5, 7}
= {2, 3, 5, 7} = B
∴ A ∩ B = B

Question 6.
If A = {4, 5, 6}; B = {7, 8}, then show that A ∪ B = B ∪ A.  (Page No. 37)
Answer:
Given sets are
A = {4, 5, 6} and B = {7, 8}
A ∪ B = {4, 5, 6} ∪ {7, 8}
= {4, 5, 6, 7, 8}.
B ∪ A = {7, 8} ∪ {4, 5, 6}
= {4, 5, 6, 7, 8}
∴ A ∪ B = B ∪ A.

Question 7.
If A = {1, 2, 3, 4, 5 }; B = {4, 5, 6, 7}, then find A – B and B – A. Are they equal?  (Page No. 38)
Answer:
Given sets are
A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}
A – B = {1, 2, 3, 4, 5} – {4, 5, 6, 7}
= {1, 2, 3}
B – A = {4, 5, 6, 7} – {1, 2, 3, 4, 5}
= {6, 7}
∴ No, A – B ≠ B – A.

Question 8.
If V = {a, e, i, o, u} and B = {a, i, k, u}, find V – B and B – V.    (Page No. 38)
Answer:
Given sets are
V = {a, e, i, o, u} and B = {a, i, k, u}
V – B = {a, e, i, o, u} – {a, i, k, u}
= {e, o}
B – V = {a, i, k, u} – {a, e, i, o, u}
= {k}.

Try this

Question 1.
A = {set of quadrilaterals},
B = {square, rectangle, trapezium, rhombus}.
State whether A ⊂ B or B ⊂ A. Justify your answer.     (Page No. 33)
Answer:
A = {set of quadrilaterals} means A = {square, rectangle/trapezium, rhombus, parallelogram}
B = {square, rectangle, trapezium, rhombus}
So, B ⊂ A because A’ is having elements more than ‘B’.

Question 2.
If A = {a, b, c, d}. How many subsets does the set A have?    (Page No. 33)
A) 5 B) 6 C) 16 D) 65
Answer:
Given A = {a, b, c, d}
n(A) = 4
Number of subsets for a set, which is having ‘n’ elements is 2ⁿ.
So n(A) = 4
Number of subsets for A is 2⁴ = 16.
Answer is [C].

Question 3.
P is the set of factors of 5, Q is the set of factors of 25 and R is the set of factors of 125. Which one of the following is false?    (Page No. 33)
A) P ⊂ Q
B) Q ⊂ R
C) R ⊂ P
D) P ⊂ R
Answer: [C]

Question 4.
A is the set of prime numbers smaller than 10, B is the set of odd numbers < 10 and C is the set of even numbers < 10. How many of the following statements are true?    (Page No. 33)
i) A ⊂ B
ii) B ⊂ A
iii) A ⊂ C
iv) C ⊂ A
v) B ⊂ C
vi) C ⊂ B
Answer:
All the statements are false.

Question 5.
List out some sets A and B and choose their elements such that A and B are disjoint.  (Page No. 37)
Answer:
Consider the disjoint sets
A = {1, 2, 3, 4} and B = {a, b, c}

Question 6.
If A = {2, 3, 5}, find A ∪ ∅ and ∅ ∪ A and compare.    (Page No. 37)
Answer:
Given sets A = {2, 3, 5} and ∅ = { }
A ∪ ∅ = {2,3,5} ∪ { } = {2,3,5}
∅ ∪ A = { } ∪ {2, 3, 5} = {2,3,5}
A ∪ v = ∅ ∪ A = A

Question 7.
If A = {1, 2, 3, 4}; B = {1, 2, 3, 4, 5, 6, 7, 8}, then find A ∪ B, A ∩ B. What do you notice about the result?   (Page No. 37)
Answer:
Given sets are
A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6, 7, 8}
A ∪ B = {1, 2, 3, 4} ∪ {1, 2, 3, 4, 5, 6, 7, 8} = {1, 2, 3, 4, 5, 6, 7, 8} = B
A ∩ B = {1, 2, 3, 4} ∩ {1, 2, 3, 4, 5, 6, 7, 8} = {1, 2, 3, 4} = A
If A ⊂ B, then A ∪ B = B and A ∩ B = A

Question 8.
A = {1, 2, 3, 4, 5, 6}; B = {2, 4, 6, 8, 10}. Find the intersection of A and B.     (Page No. 37)
Answer:
Given sets are
A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8, 10}
A ∩ B = {1, 2, 3, 4, 5, 6} ∩ {2, 4, 6, 8, 10} = {2, 4, 6}

Think & Discuss

Question 1.
Is empty set subset to every set?    (Page No. 34)
Answer:
‘Yes’. Empty set is subset to every set
Justify: If A ⊂ B, it means all the elements of set ‘A’ belong to set ‘B’.
In other words we can say no element of ‘A’ missed in set B.
now empty set means which has no elements, now no element of empty set can be missed in any set. So we can write empty set is subset of every set.

Question 2.
Is any set subset to itself?    (Page No. 34)
Answer:
‘Yes’. Every set is subset to itself.
Let ‘A’ is any set.
Now every element of ‘A’ definitely belongs to ‘A’.
So A ⊂ A
Hence every set is a subset to it.

Question 3.
You are given two sets such that a set is not a subset of the other. If you have to prove this, how do you prove?    (Page No. 34)
Answer:
Let the given sets are ‘A’ and ‘B’.
To prove are set (A) is not subset of other (B).
We check if all elements of ‘A’ belong to the set ‘B’ or not.
If any of the element doesn’t belong to ‘B’ then we can say ‘A’ is not subset of ‘B’. So we have to prove at least one element of ‘A’ does not belong to ‘B’.
Hence ‘A’ is not subset of ‘B’.

Question 4.
The intersection of any two disjoint sets is a null set. Justify your answer.    (Page No. 37)
Answer:
Let A and B be any two disjoint sets,
i.e., A and B have no elements in common.
∴ A ∩ B is a null set. (∵ A ∩ B is the set of all elements which are common to both A and B)

Question 5.
The sets A – B, B – A and A ∩ B are mutually disjoint sets. Use examples to observe if this is true.    (Page No. 38)
Answer:
Let the sets are A = {1, 2, 3, 4} and B = {5, 6, 7, 8}
A – B = {1, 2, 3, 4} – {5, 6, 7, 8} = {1, 2, 3, 4}
B – A = {5, 6, 7, 8} – {1, 2, 3, 4} = {5, 6, 7, 8}
A ∩ B = {1, 2, 3, 4} ∩ {5, 6, 7, 8} = { } = ∅
∴ A – B, B – A and A ∩ B are disjoint sets.

Do these

Question 1.
Which of the following are empty sets? Justify your answer.    (Page No. 44)
i) Set of integers which lie between 2 and 3 .
ii) Set of natural numbers that are smaller than 1.
iii) Set of odd numbers that leave remainder zero, when divided by 2.
Answer:
i) This is null set. We know that there is no integer that lie between 2 and 3.
ii) This is also a null set. We know that there is’ no natural number less than ‘1’.
iii) This is a null set. We know that odd numbers do not leave remainder zero when divided by 2.

Question 2.
State which of the following sets are finite and which are infinite. Give reasons for your answer.    (Page No. 44)
i) A = {x : x e N and x < 100}
ii) B = {x : x e N and x ≤ 5}
iii) C = {1² , 2², 3², ……}
iv) D = {1, 2, 3, 4}
v) {x : x is a day of the week}
Answer:
i) A = (1, 2, 3, 4, , 98, 99}
This set is finite, because there are 99 numbers possible to count.
ii) B = {1, 2, 3,  4, 5}
This set is finite because there are 5 numbers possible to count.
iii) C = {1² , 2², 3², ……}
This set is infinite because there are infinite numbers.
iv) D – {1, 2, 3, 4}
This set is finite because there are 4 numbers that are possible to count.
v) E = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
This set is finite, because there are 7 days in a week possible to count.

Question 3.
Tick the set which is infinite.      (Page No. 44)
A) The set of whole numbers < 10
B) The set of prime numbers < 10
C) The set of integers < 10
D) The set of factors of 10
Answer:
[C]
The set of integers < 10
{….., -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Try this

Question 1.
Which of the following sets are empty sets? Justify your answer.    (Page No. 44)
i) A = {x : x² = 4 and 3x = 9}.
ii) The set of all triangles in a plane having the sum of their three angles less than 180.
Answer:
i) x² = 4 ⇒ x = ± 2
3x = 9 ⇒ x = 3
The value of ‘x’ is not same in both cases, so this is a null set.
ii) This is a null set, because the sum of the three angles of a triangle is equal to 180°.

Question 2.
B = {x : x + 5 = 5} is not an empty set. Why?   (Page No. 44)
Answer:
B = {x: x + 5 = 5} is not an empty set
let x ∈ Z or x ∈ W
then for x = 0 ⇒ x + 5 = 0 + 5 = 5
So if x ∈ W, or x ∈ Z then for x = 0,
x + 5 = 5 is true.
Then the set B = {0} which is not an empty set.
Note: But if x ∈ N
We will have no ‘x’ such that x + 5 = 5
then ‘B’ will be an empty set.
But in the textbook it is not given whether x ∈ N (or) x ∈ W (or) x ∈ Z.
Hence we consider first one.

Think & Discuss

Question 1.
An empty set is a finite set. Is this statement true or false? Why?   (Page No. 44)
Answer:
Yes, it is a finite set because there is finite number i.e., ‘0’ elements it consists.

Think & Discuss

Question 1.
What is the relation between n(A), n(B), n(A ∩ B) and n(A ∪ B)?   (Page No. 45)
Answer:
n(A ∪ B) = n(A) + n(B) – n(A ∩ B). This is called Fundamental theorem of sets.

Question 2.
If A and B are disjoint sets, then how can you find n(A ∪ B)?    (Page No. 45)
Answer:
If A and B are disjoint then A ∩ B is a null set.
∴ n(A ∩ B) = 0 and it gives us n(A ∪ B) = n (A) + n(B).

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.4 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.4

10th Class Maths 2nd Lesson Sets Ex 2.4 Textbook Questions and Answers

Question 1.
State which of the following sets are empty and which are not?
i) The set of lines passing through a given point.
ii) Set of odd natural numbers divisible by 2.
iii) {x : x is a natural number, x < 5 and x > 7}
iv) {x: x is a common point to any two parallel lines}
v) Set of even prime numbers.
Answer:
i) Not empty
ii) Empty
iii) Empty
iv) Empty
v) Not empty

Question 2.
Which of the following sets are finite or infinite?
i) The set of months in a year.
ii) {1, 2, 3, …, 99, 100}
iii) The set of prime numbers smaller than 99.
Answer:
i) Finite
ii) Finite
iii) Finite

Question 3.
State whether each of the following sets is finite or infinite.
i) The set of letters in the English alphabet.
ii) The set of lines which are parallel to the X-axis.
iii) The set of numbers which are multiples of 5.
iv) The set of circles passing through the origin (0, 0).
Answer:
i) Finite
ii) Infinite
iii) Infinite
iv) Infinite

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.3 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.3

10th Class Maths 2nd Lesson Sets Ex 2.3 Textbook Questions and Answers

Question 1.
Which of the following sets are equal?
A = {x : x is a letter in the word FOLLOW}
ii) B = {x : x is a letter in the word FLOW}
iii) C = {x : x is a letter in the word WOLF}
Answer:
i) Elements in set A are {F, L, O, W}
ii) Elements in set B are {F, L, O, W}
iii) Elements in set C are {F, L, O, W} Sets A, B and C have same elements, Hence, they are equal sets.

Question 2.
Consider the following sets and fill up the blank in the statement given below with = or ≠ so as to make the statement true.
A = {1, 2, 3};
B = {The first three natural numbers};
C = {a, b, c, d};
D = {d, c, a, b};
E = {a, e, i, o, u};
F = {Set of vowels in English Alphabet}
i) A …. B
ii) A …. E
iii) C …. D
iv) D …. F
v) F …. A
vi) D …. E
vii) F …. B
Answer:
i) A = B
ii) A ≠ E
iii) C = D
iv) D ≠ F
v) F ≠ A
vi) D ≠ E
vii) F ≠ B

Question 3.
In each of the following, state whether A = B or not.
i) A = {a, b, c, d} ; B = {d, c, a, b}
ii) A = {4, 8, 12, 16} ; B = {8, 4, 16, 18}
iii) A = {2, 4, 6, 8, 10}; B = {x : x is a positive even integer and x ≤ 10}
iv) A = {x : x is a multiple of 10}; B = {10, 15, 20, 25, 30, …}
Answer:
i) A = B
ii) A ≠ B
iii) A ≠ B
iv) A ≠ B

Question 4.
State the reasons for the following :
i) {1, 2, 3, …., 10} ≠ {x : x ∈ N and 1 < x < 10}
ii) {2, 4, 6, 8, 10} ≠ {x : x = 2n+1 and x ∈ N}
iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15}
iv) {2, 3, 5, 7, 9} ≠ {x : x is a prime number}
Answer:
i) In R.H.S ‘x’ is greater than 1 and less than 10 but L.H.S is having both 1 and 10.
ii) L.H.S ≠ R.H.S
R.H.S: x = 2n + 1 is definition of odd numbers.
L.H.S: Given set is even numbers set.
iii) x is a multiple of 15.
So 5 does not exist.
iv) x is a prime number but 9 is not a prime number.

Question 5.
List all the subsets of the following sets.
i) B = {p, q}
ii) C = {x, y, z}
iii) D = {a, b, c, d}
iv) E = {1, 4, 9, 16}
v) F = {10, 100, 1000}
Answer:
i) Subsets of ‘B’ are {p}, {q}, {p, q}, φ
ii) Subsets of ‘C’ are {x}, {y} {z}, {x, y}, {y, z}, {z, x}, {x, y, z} and φ (2³ = 8)
iii) Subsets of ‘D’ are {a}, {b}, {c}, {d}, {a,b}, {b,c}, {c, d}, {a, c}, {a, d}, {b, d}, {a, b, c}, {b, c, d}, {a, b, d}, {a, c, d}, {a, b, c, d} and φ
iv) Subsets of ‘E’ are
φ, {1}, {4}, {9}, {16}, {1,4}, {1,9}, {1, 16}, {4, 9}, {4, 16}, (9, 16}, {1, 4, 9}, {1, 9, 16}, {4, 9, 16}, {1, 4, 16}, {1, 4, 9, 16}
v) Subsets of ‘F’ are
φ, {10}, {100}, {1000}, {10, 100}, {100, 1000}, {10, 1000}, {10, 100, 1000}.

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.2 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.2

10th Class Maths 2nd Lesson Sets Ex 2.2 Textbook Questions and Answers

Question 1.
If A = {1, 2, 3, 4}; B = {1, 2, 3, 5, 6} then find A ∩ B and B ∩ A. Are they equal ?
Answer:
Given sets are A = {1, 2, 3, 4} and B = {1,2,3, 5,6}
A ∩ B = {1,2, 3,4} ∩ {1,2, 3, 5, 6}
= {1,2,3} …… (1)
B ∩ A = {1, 2, 3, 5, 6} ∩ {1, 2, 3, 4}
= {1,2,3} …….(2)
From (1) and (2)
A ∩ B and B ∩ A are same.

Question 2.
A = {0, 2, 4}, find A ∩ φ and A ∩ A. Comment.
Answer:
Given set A = {0, 2, 4} and φ is a null set.
A ∩ φ = {0, 2, 4} ∩ { }
= { } ……. (1)
A ∩ A = {0, 2, 4} ∩ {0, 2, 4}
= {0, 2,4} …….. (2)
From (1) and (2),
We conclude that A ∩ φ = φ and A ∩ A = A

Question 3.
If A = {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}, find A – B and B – A.
Answer:
Given sets are
A {2, 4, 6, 8, 10} and B = {3, 6, 9, 12, 15}
A – B = {2, 4, 6, 8, 10} – {3, 6, 9, 12, 15}
= {2, 4, 8, 10} …… (1)
B – A = {3, 6, 9, 12, 15} – {2, 4, 6, 8, 10}
= {3, 9, 12, 15} …… (2)
From (1) and (2), A – B ≠ B – A

Question 4.
If A and B are two sets such that A ⊂ B then, what is A ∪ B?
Answer:
Let us consider A ⊂ B
Set A = {1, 2, 3} and
Set B = {1, 2, 3, 4, 5}
Now A ∪ B = {1, 2, 3} ∪ {1, 2, 3, 4, 5}
= {1, 2, 3, 4, 5} = B
∴ A ∪ B = B

Question 5.
If A = {x : x is a natural number},
B = {x : x is an even natural number},
C = {x : x is an odd natural number} and
D = {x : x is a prime number}
Find A ∩ B, A ∩ C, A ∩ D, B ∩ C, B ∩ D, C ∩ D.
Answer:
Given sets are
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ……}
B = {2, 4, 6, 8, 10, …….}
C = {1, 3, 5, 7, 9, …….}
D = {2, 3, 5, 7, 11, …….}
A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …….} ∩ {2, 4, 6, 8, 10, ……}
= {2, 4, 6, 8, 10, ……}
A ∩ C = {1, 2, 3,4, 5, 6, 7, 8, 9, 10, …} ∩ {1, 3, 5, 7, 9 }
= {1, 3, 5, 7, 9, ……}
A ∩ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …} ∩ {2, 3, -5, 7, 11,….}
= {2, 3, 5, 7, 11, ……}
B ∩ C = {2, 4, 6, 8, 10, ……} ∩ {1, 3, 5, 7, 9, …….}
= { } = φ
B ∩ D = {2, 4, 6, 8, 10, ……} ∩ {2, 3, 5, 7, 11, ……}
= {2}
C ∩ D = {1, 3, 5, 7, 9, ……} ∩ {2, 3, 5, 7, 11, 13, ……}
= {3, 5, 7, …..}

Question 6.
If A = {3, 6, 9, 12, 15, 18, 21}; B = {4, 8, 12, 16, 20}; C = {2, 4, 6, 8, 10, 12, 14, 16}; D = {5, 10, 15, 20} find
(i) A – B
(ii) A – C
(iii) A – D
(iv) B – A
(v) C – A
(vi) D – A
(vii) B – C
(viii) B – D
(ix) C – B
(x) D – B
Answer:
Given sets are A = {3, 6, 9, 12, 15, 18, 21}
B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16} and
D = {5, 10, 15, 20}
i) A – B = {3, 6, 9, 12, 15, 18, 21} – {4, 8, 12, 16, 20} = {3, 6, 9, 15, 18, 21}
ii) A – C = {3, 6, 9, 12, 15, 18, 21} – {2, 4, 6, 8, 10, 12, 14, 16} = {3,9,15,18,21}
iii) A – D = {3, 6, 9, 12, 15, 18, 21} – {5, 10, 15, 20} = {3,6,9,12,18,21}
iv) B – A = {4, 8, 12, 16, 20} – {3, 6, 9, 12, 15, 18, 21} = {4, 8, 16, 20}
v) C – A = {2, 4, 6, 8, 10, 12, 14, 16} – {3, 6, 9, 12, 15, 18, 21} = {2, 4, 8, 10, 14, 16}
vi) D – A = {5, 10, 15, 20} – {3, 6, 9, 12, 15, 18, 21} = {5, 10, 20}
vii) B – C = {4, 8, 12, 16, 20} – {2, 4, 6, 8, 10, 12, 14, 16} = {20}
viii) B – D = {4, 8, 12, 16,20} – {5, 10, 15, 20} = {4, 8, 12, 16}
ix) C – B = {2, 4, 6, 8, 10, 12, 14, 16} – {4, 8, 12, 16, 20} = {2, 6, 10, 14}
x) D – B = {5, 10, 15, 20} – {4, 8, 12, 16, 20} = {5, 10, 15}

Question 7.
State whether each of the following statement is true or false. Justify your answers.
i) {2,3,4,5} and {3,6} are disjoint sets.
ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.
iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
Answer:
i) Rule: If two sets are disjoint their intersection is null set.
= {2, 3, 4, 5} n {3, 6} = { 3 } ≠ φ
∴ Given statement is False.

ii) Given sets are
{a, e, i, o, u} and {a, b, c, d}
= {a, e, i, o, u} ∩ {a, b, c, d}
= { a } ≠ φ
∴ Given statement is False.

iii) Given sets are
{2, 6, 10, 14} and {3, 7, 11, 15}
= {2, 6, 10, 14} ∩ {3, 7, 11, 15}
= { }
∴ Given statement is True.

iv) Given sets are
{2, 6, 10} and {3, 7, 11}
= {2, 6, 10} ∩ {3, 7, 11} = { }
∴ Given statement is True.

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 2 Sets Ex 2.1 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 2nd Lesson Sets Exercise 2.1

10th Class Maths 2nd Lesson Sets Ex 2.1 Textbook Questions and Answers

Question 1.
Which of the following are sets? Justify your answer.
i) The collection of all the months of a year beginning with die letter “J”.
ii) The collection of ten most talented writers of India.
iii) A team of eleven best cricket batsmen of the world.
iv) The collection of all boys in your class.
v) The collection of all even integers.
Answer:
i) There are 3 months as January, June and July beginning with letter ‘J’. Therefore, it is a well defined collection of months and hence it is a set.
ii) The concept of talented writers of India is vague, since there is no rule given for deciding whether a particular writer is talented or not.
Hence, the given collection is not a set.
iii) A team of eleven best cricket batsmen of the world is vague, since there is no rule given for deciding whether a particular batsman is the best.
Hence, the given collection is not a set.
iv) The collection of all boys in my class is well defined. Hence, the given collection is a set.
v) The collection of all even integers i.e., (2, 4, 6, 8, ……) is well defined.
Hence, the given collection is a set.

Question 2.
If A = {0, 2, 4, 6}, B = {3, 5, 7} and C = {p, q, r} then fill the appropriate symbol, ∈ or ∉ in the blanks.
i) 0 ….. A
ii) 3 ….. C
iii) 4 ….. B
iv) 8 ….. A
v) p ….. C
vi) 7 ….. B
Answer:
i) ∈
ii) ∉
iii) ∉
iv) ∉
v) ∈
vi) ∈

Question 3.
Express the following statements using symbols.
i) The elements ‘x’ does not belong to ‘A’.
ii) ‘d’ is an element of the set ‘B’.
iii) ‘1’ belongs to the set of Natural numbers N.
iv) ‘8′ does not belong to the set of prime numbers P.
Answer:
i) x ∉ A
ii) d ∈ B
iii) 1 ∈ N
iv) 8 ∉ P

Question 4.
State whether the following statements are true or false. Justify your answer.
i) 5 ∉ set of prime numbers
ii) S = {5, 6, 7} implies 8 ∈ S.
iii) -5 ∉ W where ‘W’ is the set of whole numbers.
iv) \(\frac{8}{11}\) ∈ Z
where ‘Z’ is the set of integers.
Answer:
i) False
ii) False
iii) True
iv) False

Question 5.
Write the following sets in roster form.
i) B = {x : x is a natural number smaller than 6}.
ii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}.
iii) D = {x : x is a prime number which is a divisor of 60}.
iv) E = {x : x is an alphabet in BETTER}.
Answer:
i) B = {1, 2, 3, 4, 5}
ii) C = {17, 26, 35, 44, 53, 62, 71}
iii) D = {5, 3}
iv) E = {B, E, T, R}

Question 6.
Write the following sets in the set – builder form.
i) {3, 6, 9, 12}
ii) {2, 4, 8, 16, 32}
iii) {5, 25, 125, 625}
iv) {1, 4, 9, 16, 25, …, 100}
Answer:
i) A = {x : x is multiple of 3 and less than 13}
ii) B = {x : x = 2^P, 0 < P < 6, P ∈ N}
iii) C = {x : x = 5^P, 0 < P < 5, P ∈ N}
iv) D = {x : x = P², 0< P < 11, P ∈ W}

Question 7.
Write the following sets in roster form.
i) A = {x: x is a natural number greater than 50 but smaller than 100}
ii) B = {x : x is an integer, x² = 4}
iii) D = {x : x is a letter in the word “LOYAL”}
Answer:
i) A = {51, 52, 53, ……. , 98, 99}
ii) B = {+2, -2}
iii) D = {L, O, Y, A}

Question 8.
Match the roster form with set builder form.
i) {1, 2, 3, 6}                       ( )      a) {x : x is a prime number and a divisor of 6}
ii) {2, 3}                              ( )      b) {x : x is an odd natural number smaller than 10}
iii) {M, A, T, H, E, I, C, S}     ( )      c) {x : x is a natural number and divisor of 6}
iv) {1, 3, 5, 7, 9}                  ( )      d) {x : x is a letter of the word MATHEMATICS}
Answer:
i) c
ii) a
iii) d
iv) b

AP State Board Syllabus AP SSC 10th Class Hindi Textbook Solutions Chapter 3 हम भारतवासी Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Hindi Solutions Chapter 3 हम भारतवासी

10th Class Hindi Chapter 3 हम भारतवासी Textbook Questions and Answers

InText Questions (Textbook Page No. 13)

प्रश्न 1.
नदियाँ किसमें विलीन होती हैं?
उत्तर:
नदियाँ समुद्र में विलीन होती हैं।

प्रश्न 2.
इसमें किस – किसको एक बताया गया है?
उत्तर:
इसमें मानव जाति, मानव धर्म तथा सारी दुनिया को एक बताया गया है।

प्रश्न 3.
‘मानव जाति एक है।’ इस पर अपने विचार बताइए।
उत्तर:
मानव जाति एक है। जिस प्रकार अनेक स्थानों से बहनेवाली नदियाँ अंत में समुद्र में मिलती हैं। उसी प्रकार अलग – अलग धर्म में जन्म लिये मनुष्य भी अंत में परमात्मा के पास पहुँचते हैं। इसलिए हम कह । सकते हैं कि मानव जाति एक है उददश्य छात्रों में कविता, गीत आदि की रचना शैली का विकास करना और उनमें देशभक्ति के साथ-साथ विश्वबंधुत्व, विश्वशांति, अहिंसा, त्याग, समर्पण आदि सद्गुणों का विकास करना तथा भारत को और भी सशक्त कर अंतर्राष्ट्रीय स्तर पर अग्रसर करने की प्रेरणा देना इस पाठ का मुख्य उद्देश्य है। विधा विशेष प्रस्तुत कविता देशभक्ति की भावना पर आधारित है। यह गेय कविता है। इसमें तुकांत शब्द प्रथम प्रेरणार्थक क्रिया व सामान्य भविष्य में हैं। यह कविता बच्चों में सत्य, अहिंसा, त्याग और | समर्पण की भावना जागृत कर, उन्हें विश्वबंधुत्व की ओर कदम बढ़ाने की प्रेरणा देती है।

InText Questions (Textbook Page No. 14)

प्रश्न 1.
ऊँच – नीच का भेद मिटाने के लिए हम क्या – क्या कर सकते हैं?
उत्तर:
ऊँच – नीच का भेद मिटाना हमारा प्रथम आशय व कर्तव्य है। इसके लिए अपनी ओर से हम भी कुछ कर सकते हैं।

• सब लोगों से मिलजुलकर रहते एकता की भावना बढानी है।
• सबसे प्रेमपूर्वक व्यवहार करते नफ़रत की भावना को छोड देना है।
• समानता का बीज बोते लोगों के दिलों में विश्वास भरना है।
• जाति, धर्म, भाषा, प्रांत, जैसे भेद भावों को छोडते लोगों की सहायता करनी है।
• सबका आदर – सम्मान करना है।
• सबकी उन्नति में समान अवसर देना है।

प्रश्न 2.
हमें अपने जीवन में कैसा पथ अपनाना चाहिए?
उत्तर:
हमें जीवन में सदा सत्य और न्यायमार्ग पर चलना है। श्रद्धा और प्रेम का उत्तम भाव दिल में रखकर दीन – दुखियों की सेवा करनी है। खुद खुश रहते सब को सुखी रखने का न्याय पथ हमें अपनाना चाहिए। अहिंसा और धर्ममार्ग को अपनाना चाहिए। त्याग भावना को अपनाना चाहिए।

प्रश्न 3.
हम भटकने वालों को राह कैसे दिखा सकते हैं?
(या)
बेराहों को राह कैसे दिखा सकते हैं?
उत्तर:
भटकने वाले लोगों को जीवन की वास्तविकता समझाने का प्रयत्न करना है। सही मार्गदर्शन करते उनको खुशियाँ पाने का ज्ञान अवगत कराना है। न्याय और सत्य मार्ग पर आगे बढने ज्ञानपूर्ण सलाह देते भटकनेवालों को राह दिखा सकते हैं।

प्रश्न 4.
सत्य, अहिंसा, त्याग और समर्पण की बगिया महकाने के लिए हम क्या – क्या कर सकते हैं?
(या)
हम खुशियों की बगिया कैसे महकायेंगे?
उत्तर:
मानव सामाजिक प्राणी है। हमारे मानव जीवन में सत्य, अहिंसा, त्याग, समर्पण, प्रेम आदि महान गुणों का विशेष महत्व है। ऐसे उत्तम गुणों की बगिया महकाने हम पहले दुनिया के सारे क्लेश मिटाने का प्रयत्न करेंगे। विश्व बंधुत्व का मूलमंत्र खुद अपनाते लोगों को श्रद्धा और प्रेम का अद्भुत दृश्य दिखायेंगे। इस तरह सत्य, अहिंसा, त्याग और समर्पण की बगिया महका सकते हैं। धरती को स्वर्ग बना सकते हैं।

अर्थग्राह्यता-प्रतिक्रिया

अ) प्रश्नों के उत्तर दीजिए।
प्रश्न 1.
यह गीत आपको कैसा लगा ? अपनी पसंद और नापसंद का कारण बताइए।
उत्तर:
“हम भारतवासी” गीत मुझे बहुत पसंद आया। यह गीत सरल, सुबोध और प्रभावशाली है। देशभक्ति भावना जगाकर, विश्वबंधुत्व की ओर हमें अग्रसर होने की प्रेरणा देनेवाला है। भारतवासियों के सत्य, अहिंसा, त्याग, समर्पण आदि गुणों का समर्थन करते हुए दुनिया को पावन धाम बनाने की महत्वाकांक्षा रखती है। सारे विश्व के लोगों के विविध क्लेशों को मिटाकर एक धर्म कुटुंब बनने की प्रेरणा देनेवाला है। भारतीय संस्कृति की गरिमा बढाने वाला है। खासकर भारतीयों के धर्म, जाति, संप्रदाय रूपी विषमताओं को भगाकर सब में अपनापन जगानेवाला है।

प्रश्न 2.
दुनिया को ‘पावन धाम’ बनाने के लिए हम क्या – क्या कर सकते हैं?
उत्तर:
दुनिया को पावन धाम बनाने के लिए

• ऊँच – नीच का भेद मिटायेंगे।
• निराशा की भावना भगाकर विश्वास जगायेंगे।
• उलझे लोगों को वास्तविकता बतायेंगे। बेराहों को राह दिखायेंगे।
• सत्य, अहिंसा, त्याग, समर्पण, विश्व बंधुत्व की भावना जगायेंगे।

आ) दिया गया पद्यांश पढ़िए और इसके मुख्य शब्द पहचान कर लिखिए।

मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखायेंगे।
सत्य, अहिंसा, त्याग, समर्पण की बगिया महकायेंगे।
जग के सारे क्लेश मिटाकर, धरती को स्वर्ग बनायेंगे।
विश्वबंधुत्व का मूल मंत्र हम, दुनिया में सरसायेंगे।

जैसे : श्रद्धा, …………………,
…………………………..,
…………………………..,
उत्तर:
प्रेम, सत्य, अहिंसा, त्याग, समर्पण, क्लेश, विश्वबंधुत्व के सहारे धरती को स्वर्ग बनाना।

इ) निम्नलिखित भाव से संबंधित कविता की पंक्तियाँ पहचानकर लिखिए।

प्रश्न 1.
संसार में व्याप्त सारे विवादों को मिटाकर, हम धरती को स्वर्ग बनायेंगे।
उत्तर:
जग के सारे क्लेश मिटाकर, धरती को स्वर्ग बनायेंगे।

प्रश्न 2.
जीवन पथ से भटके लोगों को रास्ता दिखाएँगे।
उत्तर:
भटक रहे जो जीवन पथ से, उनको राह दिखायेंगे।

प्रश्न 3.
हम भेदभाव दूर करेंगे। हम सब मिलजुलकर रहेंगे।
उत्तर:
ऊँच – नीच का भेद मिटाकर, दिल में प्यार बसायेंगे।

ई) नीचे दिया गया पद्यांश पढ़कर सही उत्तर पहचानिए।
आज़ादी अधिकार सभी का जहाँ बोलते सेनानी,
विश्व शांति के गीत सुनाती जहाँ चुनरिया ये धानी,
मेघ साँवले बरसाते हैं, जहाँ अहिंसा का पानी,
अपनी माँगें पोंछ डालती, हँसते – हँसते कल्याणी,
ऐसी भारत माँ के बेटे मान गँवाना क्या जाने,
मेरे देश के लाल हठीले शीश झुकाना क्या जानें।

1. धानी रंग की चुनरी कौन – सा गीत सुना रही है?
अ) अधिकार का
आ) आज़ादी का
इ) विश्वशांति का
ई) अहिंसा का
उत्तर:
इ) विश्वशांति का

2. भारत के लाल कैसे हैं?
अ) सजीले
आ) साँवले
इ) हठीले
ई) निराले
उत्तर:
इ) हठीले

3. सैनिक किसे सभी का अधिकार मानते हैं? ‘
अ) आज़ादी को
आ) शांति को
इ) अहिंसा को
ई) मान को
उत्तर:
अ) आज़ादी को

4. “मान” शब्द का विलोमार्थक है
अ) निरमान
आ) दुरमान
इ) अपमान
ई) स्वमान
उत्तर:
इ) अपमान

5. भारत माँ के बेटे क्या गाँवाना नहीं चाहते हैं?
अ) आज़ादी
आ) मान
इ) शीश
ई) अधिकार
उत्तर:
आ) मान

अभिव्यक्ति – सृजनात्मकता

अ) इन प्रश्नों के उत्तर तीन – चार पंक्तियों में लिखिए।

प्रश्न 1.
उलझनों से बचे रहने के लिए हमें कैसी सावधानियाँ लेनी चाहिए?
उत्तर:
उलझनों से बचे रहने के लिए

• धार्मिक भेद – भाव न रखना चाहिए।
• उत्तम मानवीय मूल्यों को बनाये रखना है।
• पारस्परिक सहयोग की भावना होना है।
• हमेशा सतर्क, जागरूक रहना है।
• बौद्धिक विकास करना चाहिए।

प्रश्न 2.
निराशावादी और आशावादी के स्वभाव में क्या अंतर होता है?
उत्तर:
निराशावादी में निराशा की भावना होती है। वह निष्क्रिय होता है। जीवन दुखद होता है। उलझा रहता है। आशावादी में आशा की भावना होती है। वह सक्रिय होता है। जागरूक रहता है। सत्य, अहिंसा, त्याग समर्पण होती है।

आ) गीत में ‘धरती को स्वर्ग’ बनाने की बात कही गयी है। हम इसमें क्या सहयोग दे सकते हैं?
(या)
पूरे विश्व को स्वर्ग का धाम कैसे बना सकते हैं?
उत्तर:
कविता का नाम : हम भारतवासी
कवि का नाम : आर.पी.निशंक
हिंदी के विख्यात कवि हैं आर.पी. निशंक| इस कविता के ज़रिये कवि छात्रों में देश भक्ति, विश्वबंधुत्व, विश्वशांति, सत्य, अहिंसा, त्याग, समर्पण आदि महान सद्गुणों का विकास करना चाहते हैं।

“हम भारतवासी” कविता में धरती को स्वर्ग बनाने की बात पर प्रकाश डाला गया है। सच्चे भारतीय होने के कारण हम भी अपना पूरा सहयोग दे सकते हैं।

• हम मानवों में भरे जाति – धर्म, वर्ग – वर्ण, ऊँच – नीच, अमीर – गरीब जैसे भेदभावों को दूर कर
• सकते हैं। इससे एकता की भावना बढकर सब लोग प्रेम से रह सकते हैं।
• सत्य, अहिंसा, सेवा, त्याग, प्रेम आदि का महत्व समझाकर विश्व बंधुत्व की भावना जगा सकते हैं।
• स्वार्थ भाव से भरे लोगों को स्वार्थरहित, पक्षपात रहित और सहनशील बनाकर देश प्रेमी बना सकते हैं।
• दुःख में धीरज धर लेने का आत्मविश्वास उनमें भरकर निराशावाद दूर भगाकर आशावादी बना सकते हैं।
• जीवन पथ से भटके लोगों को मार्गदर्शन करके उन्हें सक्रिय मार्ग पर लगा सकते हैं।
• हर्ष – विषाद आपस में बाँटकर अपनापन बढा सकते हैं। – एक दूसरे के प्रति आदर का भाव रखते, प्रेमालू बना सकते हैं।

एक बात में कहे तो वसुदैक कुटुंबकम बना सकते हैं। ऐसा करके हम भी धरती को स्वर्ग बनाने में अपना पूरा सहयोग दे सकते हैं।

विशेषता : इस कविता में देश भक्ति और नैतिक मूल्य बताये गये हैं।

इ) विश्वशांति की राह में समर्पित किस महान व्यक्ति का साक्षात्कार आप लेना चाहेंगे? साक्षात्कार में उनसे पूछे जाने वाले प्रश्नों की एक सूची तैयार कीजिए।
उत्तर:
विख्यात नेता से साक्षात्कार लेने के लिए मैं निम्न लिखित इस प्रश्नावली को तैयार करूँगा।
वे प्रश्न इस प्रकार हैं –

• महोदय। विश्वशांति के लिए आप अविरल प्रयत्न कर रहे हैं। क्या आप यह बता सकते हैं कि विश्वशाँति माने क्या है? उसकी क्या आवश्यकता है?
• आपको इस महत्वपूर्ण कार्य में पदार्पण करने का विचार क्यों और कैसे आया? इसके क्या कारण हो सकते हैं?
• आपके इस पवित्र यज्ञ में किन-किन सज्जनों ने आपका सहयोग दिया ?
• अपनी संकल्प सिद्धि के इस पावन काम में आपने कौनसे त्याग किये ? वे कहाँ तक फलदायी हुये हैं?
• आपको इस काम में कहाँ तक सफलता मिली है?
• आपके इस पुण्य कार्य में कौन-सी अडचनों का सामना करना पड़ा?
• आगे आनेवाली पीढी को आपका संदेश क्या है?
• सुना है कि इस विश्वशांति के पावन यज्ञ में सफल हुए व्यक्ति को नोबेल पुरस्कार से सम्मानित करते हैं। आपको यह पुरस्कार मिले तो आप कैसा अनुभव करते ?

ई) सत्य, अहिंसा, त्याग आदि भावनाओं का हमारे जीवन में क्या महत्व है?
उत्तर:
हमारे जीवन में सच्चाई से बढ़कर कोई तपस्या नहीं होती। सत्य से जीवन सुखद बनता है। इसके आचरण से सच्चरित्र और महान बनता है। समाज में वंदनीय और पूजनीय बनता है।

किसी को क्षमा करना और हर प्राणी पर दया करना मनुष्य का कर्तव्य होना चाहिए। अहिंसा से दया और भाईचारे का जन्म होता है।

त्याग भावना से प्रेम और भाईचारा भाव बढ़ता है। चारों ओर संतोष होता है। भोग से त्याग श्रेयस्कर होता है।

भाषा की बात

अ) कोष्ठक में दी गयी सूचना पढ़िए और उसके अनुसार कीजिए।

प्रश्न 1.
दुनिया, अमृत, पावन (वाक्य प्रयोग कीजिए। पर्याय शब्द लिखिए।)
(जैसे – यह दुनिया बड़ी निराली है। विश्व, जग, संसार)
उत्तर:
वाक्य प्रयोग
अमृत : देव जाति के लोगों ने अमृत का पान किया है।
पावन : बापूजी का यह पावन उदेदश्य आदर्शनीय है।

पर्याय शब्द
अमृत – सुधा, पीयूष
पावन – पवित्र, पुनीत

प्रश्न 2.
निराशा, त्याग, प्यार (विलोम शब्द लिखिए। उससे वाक्य प्रयोग कीजिए।)
(जैसे – निराशा × आशा, हमें जीवन में आशा बढानी चाहिए।)
उत्तर:
विलोम शब्द
त्याग × स्वार्थ
प्यार × घृणा

वाक्य प्रयोग
त्याग : त्याग भावना उत्तम है, स्वार्थ भावना अधम है।
प्यार : प्यार से रहना चाहिए। ईर्ष्या या घृणा पाप है।

प्रश्न 3.
खुशी, बगीचा, भावना (वचन बदलिए। वाक्य प्रयोग कीजिए।)
(जैसे – खुशी – खुशियाँ, बच्चों को खेलों से बहुत सारी खुशियाँ मिलती हैं।)
वचन वाक्य प्रयोग
उत्तर:
खुशी – खुशियाँ : वे सब मिलकर खुशियाँ मना रहे हैं।

बगीचा – बगीचे : बैगलूर में कई सुंदर बगीचे हैं।
भावना – भावनाएँ : हमें अपने दिलों में सदा अच्छी भावनाएँ रखनी हैं।

आ) सूचना पढ़िए और उसके अनुसार कीजिए।

प्रश्न 1.
पवन, पावन, निराशा (संधि विच्छेद कीजिए।)
उत्तर:
संधि विच्छेद
पवन = पो + अन
पावन = पौ + अन
निराशा = निः + आशा

प्रश्न 2.
भारतवासी, जीवनज्योत (समास पहचानिए।)
उत्तर:
भारतवासी : → तत्पुरुष समास (भारत के वासी)
जीवनज्योत → कर्मधारय समास(जीवन रूपी ज्योत)

इ) इन्हें समझिए और वाक्य प्रयोग कीजिए।
1. खुशी
2. खुशियाँ
3. खुशियों में
उत्तर:

1. वह खुशी मनाती है। यह खुशी संज्ञा शब्द है।
2. त्यौहार के दिन लोग खुशियाँ मनाते हैं। खुशी का बहुवचन खुशियाँ हैं।
3. अच्छे लोग सदा खुशियों की दुनिया में रहते हैं। संबंध बोध कारक हैं।

ई)1. नीचे दिया गया उदाहरण समझिए। उसके अनुसार दिये गये वाक्य बदलिए।

उत्तर:

2. कविता में आये मुहावरे पहचानिए और अर्थ लिखिकर वाक्य प्रयोग कीजिए।
उत्तर:
1. पावन धाम बनाना = पवित्र स्थल बनाना
हमें दुनिया को पावन धाम बनाना चाहिए।

2. अमृत रस सरसाना = प्रेम भावना जगाना
भारतवासी सभी लोगों के दिलों में अमृत रस सरसायेंगे।

3. विश्वास जगाना = यकीन दिलाना
निराशावादी लोगों में विश्वास जगाने की आवश्यकता है।

4. राह दिखाना = सही रास्ता दिखाना
अध्यापक छात्रों को राह दिखाते हैं।

5. दिल में प्यार बसाना = एकता बनाना
नेता लोगों के दिल में प्यार बसाते हैं।

6. तथ्य दीप समझाना = यथार्थ / वास्तव बताना
तथ्य दीप समझाने से अहित कार्य नहीं होते।

7. कुहासा तोडना = स्पष्ट करना
मन में व्याप्त कुहासा तोडने से सुखी रह सकते हैं ।

परियोजना कार्य

शांति के पथ पर समर्पित किसी महान व्यक्ति के बारे में जानकारी इकट्ठा कर कक्षा में प्रस्तुत कीजिए।
उत्तर:
जिम्मी कार्टर जिम्मी कार्टर का पूरा नाम जेम्स अर्ल कार्टर जूनियर है। (जन्म अक्तूबर 1, 1924) एक अमेरिकी राजनेता हैं जो 1976 से 1980 तक संयुक्त राज्य अमेरिका के 39 वें राष्ट्रपति रहे। राष्ट्रपति बनने से पहले वे संयुक्त राज्य अमेरिका की नौसेना में कार्यरत रहें, जॉर्जिया में सेनेटर रहे, और जॉर्जिया के गवर्नर भी रहे। राष्ट्रपति कार्यकाल के बाद वे मानव अधिकार संस्थाओं एवं परोपकारी संस्थाओं के साथ जुड़े रहे। उन्हें 2002 में नोबेल शान्ति पुरस्कार से सम्मानित किया गया।

प्रारंभिक जीवन :
जिम्मी कार्टर का जन्म जॉर्जिया के प्लेन्स नामक शहर में वाइस क्लीनिक अस्पताल में हुआ था जहाँ उनकी माँ लिलियन कार्टर नर्स थीं। उनके पिता अर्ल कार्टर का खेत था जिसमें वे कपास एवं मूंगफली उगाया करते थे। 1926 में जिम्मी की छोटी बहन ग्लोरिया, 1929 में रूथ, और 1937 में छोटे भाई बिली का जन्म हुआ। 1941 में जिम्मी ने प्लेन्स हाई स्कूल से दसवीं कक्षा पास की । 1941 में जिम्मी ने अमेरिकन्स शहर में स्थित जॉर्जिया साउथवेस्टर्न कॉलेज में पढ़ाई शुरू की। 1942 में उन्होंने यह कॉलेज छोड़ जॉर्जिया इंस्टिट्यूट ऑफ़ टॅकनॉलोजी में दाखिला लिया। 1943 में उन्हें एनापोलिस , मैरीलैंड स्थित यू. एस नेवल अकैडमी में दाखिला मिल गया और वे 1946 में वहाँ से उत्तीर्ण हुए। उत्तीर्ण होने के पश्चात वे संयुक्त राज्य अमेरिका की नौसेना की पहली परीक्षनात्मक पनडुब्बी में कार्यरत हुए।

जुलाई 7, 1947 को कार्टर ने बहन रूथ की सहेली एलानोर रोज़ालिन स्मिथ से विवाह कर लिया। 1947 में कार्टर के पुत्र जॉन विलियम का जन्म हुआ, 1950 में जेम्स अर्ल II का, 1952 में डॉनल जेफ़्फ़ी … का और 1967 में पुत्री एमी लिन का जन्म हुआ। 1953 में जिम्मी के पिता अर्ल की मृत्यु होने पर जिम्मी अपनी पत्नी के साथ जॉर्जिया वापिस लौट गए, पिता के खेती के कारोबार को संभालने के लिए।

कैरियर : 1962 में कार्टर को जॉर्जिया सेनेट में चुना गया। 1966 में उन्होंने जॉर्जिया को गवर्नर पद के लिए चुनाव लड़ा परन्तु जीत नहीं पाए। 1971 में वे फिर जार्जिया के गवर्नर पद के चुनाव में खड़े हुए और जीते। जिम्मी कार्टर, मेनाम बेगिन और अनवर अल-सदात 1978 में कैम्प डेविड में। 1977 में वे संयुक्त राज्य अमेरिका के 39 वे राष्ट्रपति बने। राष्ट्रपति के तौर पर इनके कार्यकाल में निम्न मुख्य घटनाएँ हुई।

1978 में कैम्प डेविड में कार्टर ने मिस्र के राष्ट्रपति अनवर अल – सदात और इजराइल के प्रधानमन्त्री मेनाखेम बेगिन के बीच समझौता करवाया जिसके नतीजे में 1979 में इज़राइल और मित्र के बीच में शान्ति कायम हुई।

1 जनवरी 1979 को संयुक्त राज्य अमेरिका ने चीनी जनवादी गणराज्य को राजनयिक मान्यता दी और दोनों के बीच में राजनयिक संबंध कायम हुए। इसी के साथ चीनी गणराज्य की राजनयिक मान्यता रद्द कर दी गयी और राजनयिक संबंध औपचारिक रूप से तोड़ दिए गए यद्यपि दोनों देशों ने अनौपचारिक रूप से राजनयिक संबंध जारी रखे।

1979 में हुई ईरान की इस्लामी क्रांति के दौरान नवंबर में तेहान में स्थित अमेरिकी दूतावास पर उग्रवादी छात्रों ने कब्जा कर लिया और 50 से अधिक अमेरिकी बंधी बना लिए गए। जब ईरान और संयुक्त राज्य अमेरिका कोई कूटनीतिक समाधान नहीं कर सके तो 1980 में सैन्य बल पर बंदियों को . छुड़ाने की नाकाम कोशिश की गई जिसमें अमेरिकी सैनिकों की जान गई। अंत में बंधी 1981 में 444 दिनों के पश्चात छोड़े गए।

सोवियत संघ के अफ़गानिस्तान पर हमला करने पर कार्टर ने आदेश दिया कि संयुक्त राज्य अमेरिका के खिलाड़ी मॉस्को में हो रहे 1980 ग्रीष्मकालीन ओलिम्पिक खेलों का बहिष्कार करेंगे। वे 1980 में राष्ट्रपति चुनाव में पुनः खड़े हुए परन्तु हार गए।

राष्ट्रपति कार्यकाल के पश्चात :
राष्ट्रपति कार्यकाल समाप्त होने के बाद कार्टर ने मानव अधिकार संबंधित अनेक संस्थाओं, एवं अनेक परोपकारी संस्थाओं के साथ काम किया है। 1982 में कार्टर ने अटलांटा, जॉर्जिया स्थित एमरी विश्वविद्यालय में कार्टर प्रेसिडेंशियल सेंटर की स्थापना की जो लोकतंत्र और मानव अधिकार संबंधित कार्य करता है।

कार्टर ने राष्ट्रपति कार्यकाल के पश्चात अनेक पुस्तकें भी लिखी हैं।
कार्टर को 2002 में नोबेल शान्ति पुरस्कार से सम्मानित किया गया।

हम भारतवासी Sunnary in English

We are Indians. We transform India into a holy heaven. We show the marvellous images of care and love in our hearts.

We fill our hearts with love discarding the feelings of high and low, rich and poor etc. We sprinkle the sap of ambrosia removing the mist patches like jealousy and hatred. We dispel the despair, fill hope and dispense confidence. We are Indians. We transform the world into a holy heaven.

We make the people who are extrapped in problems and difficulties realise the fact. We show the proper way to the people are led astray from the path of life. We enkindle the lights of life with the lamps of joy.

We are Indians. We transform India into a holy heaven.

We show the marvellous images of care and love in our hearts. We grow the groves of truth, non-violence, sacrifice, dedication and devotion. We remove all the adversities from the world and make it a heaven. We chant the spell of fraternity, universal rapport and make others chant.

We are Indians. We transform India into a holy heaven. We show the marvellous images of care and love in our hearts.

हम भारतवासी Summary in Telugu

మేము భారతీయులం. మేము ప్రపంచాన్ని పావనధామంగా తయారుచేస్తాం. మనస్సుల్లో శ్రద్ధ మరియు ప్రేమల అద్భుత దృశ్యాలను చూపుతాము.

ఉన్నవారు – లేనివారు (ఉన్నతమైన – నిమ్నమైన) అనే భేదభావాలు లేక హృదయాలలో ప్రేమను నింపుకుంటాము. ఈర్ష్యా – ద్వేషం అనే మంచు తెరలను తొలగించి అమృతరసాన్ని చిలికిస్తాం. నిరాశను దూరం చేసి ఆశను నింపి విశ్వాసాన్ని రేకెత్తిస్తాం, మేల్కొలుపుతాం. మేము భారతీయులం. ప్రపంచాన్ని పావనధామంగా తీర్చిదిద్దుతాం.

సమస్యలలో చిక్కుకుని ఊగిసలాడుతున్న ప్రజలకు యదార్థాన్ని తెలియజేస్తాం. జీవన పథం నుండి దారి మళ్ళి తిరుగుతున్నవారికి దారి చూపిస్తాం. సంతోష దీపాలతో జీవన జ్యోతులను వెలిగిస్తాం.

మేము భారతీయులం. ప్రపంచాన్ని పావనధామంగా తీర్చిదిద్దుతాం.

మనస్సుల్లో శ్రద్ధ, ప్రేమల అద్భుత దృశ్యాలను చూపుతాం. సత్యం, అహింస, త్యాగం, సమర్పణ మొదలైన తోటలను పెంచుతాం. ప్రపంచంలోని అన్ని కష్టాలను తొలగించి భూమిని స్వర్గంలా తీర్చిదిద్దుతాం. విశ్వబంధుత్వ మూలమంత్రాన్ని ప్రపంచంలో జపింపజేస్తాం, జపిస్తాం.

మేము భారతీయులం. ప్రపంచాన్ని పావనధామంగా తయారుచేస్తాం. మనస్సుల్లో శ్రద్ధ మరియు ప్రేమల అద్భుత దృశ్యాలను చూపుతాం.

अभिव्यक्ति-सृजनात्मकता

2 Marks Questions and Answers

निम्नलिखित प्रश्नों के उत्तर दो या तीन वाक्यों में लिखिए।

प्रश्न 1.
दुनिया को ‘पावन धाम’ बनाने के लिए हम क्या – क्या कर सकते हैं?
उत्तर:
मैं सच्चे भारतीय होने के कारण सारी दुनिया को पावन धाम बनाना चाहता हूँ। यह मेरा प्रमुख कर्तव्य है। इसके लिए मैं पहले अपने दिल में निर्मल और उत्तम भावनाएँ भर लूंगा। सबके दिलों में एकता और सौभ्रातृत्व भावना जगाने का प्रयत्न करूँगा। प्रेम भाव का महत्व समझाते लोगों को भेद – भावों से दूर रहने का आग्रह करूँगा। सारी मानव जाति एक है – यह नारा देते भक्ति और धर्मयुक्त जीवन बिताने बाध्य करूँगा। खुद सत्य, अहिंसा, त्याग, आत्म समर्पण जैसे उत्कृष्ट गुणों का प्रचार करते लोगों को रास्ता दिखाऊँगा।

प्रश्न 2.
आर.पी. निशंकजी के बारे में आप क्या जानते हैं? लिखिए।
उत्तर:

• आर.पी.निशंक आधुनिक हिंदी साहित्यकारों में विशिष्ट स्थान रखते हैं।
• इनकी रचनाओं का मुख्य प्रतिपाद्य देश भक्ति है। समर्पण, नंवकुर, मुझे विधाता बनना है, तुम भी मेरे साथ चलो, जीवन पथ में, कोई मुश्किल नहीं आदि उनकी चर्चित काव्य रचनाएँ हैं।

अभिव्यक्ति-सृजनात्मकता

4 Marks Questions and Answers

निम्नलिखित प्रश्नों के उत्तर छह पंक्तियों में लिखिए।

प्रश्न 1.
निराशा को दूर करने के क्या – क्या उपाय हैं?
उत्तर:
निराशा को दूर करने के लिए ये उपाय हैं –

• मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखाने से निराशा दूर हो जाती है ।
• दिल में प्यार बसाने से निराशा दूर कर सकेंगे |
• हम दूसरों में विश्वास जगायें तो निराशा दूर हो जायेगा ।
• ऊँच – नीच के भेद – भावों को मिटाने से भी निराशा दूर हो जायेगी।

प्रश्न 2.
विश्व बंधुत्व का अर्थ क्या है?
उत्तर:

• एक ही परिवार के सभी लोग जिस प्रकार बंधुत्व भाव से रहते हैं, उसी प्रकार विश्व भर के लोगों से बंधु भावना से रहना ही विश्व बंधुत्व है । केवल भारतीयों और भारत देश में ही विश्व बंधुत्व की भावना प्राचीन काल से आज तक चल रही है।
• हम हर हमेशा कहते भी हैं कि सर्वेजना सुखिनो भवंतु |
• जिस प्रकार हम प्रांतीय एवं जातीय भावना से रहते हैं उसी प्रकार विश्व बंधुत्व की भावना से भी रहना है।
• सारे विश्व की मंगल भावना ही विश्व बंधुत्व भावना है ।

प्रश्न 3.
ऊँच – नीच का भेद भाव मिटाने के लिए हमें क्या करना है?
उत्तर:

• ऊँच – नीच का भेद मिटाने के लिए हमें सबके प्रति श्रद्धा और प्रेम को दिखाना है ।
• सबके दिलों में प्यार बसाना है ।
• नफ़रत के कुहासे को तोडना है ।
• सामाजिक, आर्थिक , राजनीतिक एकता से हम ऊँच – नीच के भेद -भावों को मिटा सकते हैं ।
• दूसरों के निराशा को दूर करने से भी कुछ हद तक भेद भाव मिटा सकेंगे।
• हमारे पास जो कुछ आवश्यकता से अधिक है उसे ज़रूरतमंदों को दे देने से भी भेदभावों को हटा सकेंगे।

प्रश्न 4.
किसी काम को आत्मविश्वास के साथ क्यों करना है?
उत्तर:

• हम जो भी करें आत्मविश्वास के साथ करें तो वह काम ज़रूर पूरा होगा | सफल होगा |
• आत्मविश्वास में अद्भुत शक्ति निहित है ।
• आत्मविश्वास से हम जितने भी कष्ट से कष्ट एवं मुश्किल काम को भी बहुत आसानी के साथ कर सकते हैं।
• आत्मविश्वास हम में जीने की शक्ति को बढ़ाता है ।

प्रश्न 5.
जीवन पथ से भटकने वालों को हम कैसे राह दिखा सकते हैं?
उत्तर:

• मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखाकर हम जीवन पथ में भटकने वालों को राह दिखा सकते हैं।
• उलझन में उलझे लोगों को तथ्य दीप समझाकर राह दिखा सकेंगे |
• हम खुशियों के दीप जलाकर जीवन ज्योत जलाकर जीवन पथ से भटकने वालों को राह दिखा सकते हैं।

प्रश्न 6.
विश्व शांति से आपका अभिप्राय क्या है?
उत्तर:

• विश्व बंधुत्व भावना ही विश्वशांति है ।
• सारी दुनिया भर में शांति स्थापना ही विश्व शांति है ।
• देश भर के लोग मन में श्रद्धा तथा प्रेम के अद्भुत दृश्यों के साथ रहेंगे तो वही विश्व शांति है ।
• सत्य, अहिंसा, त्याग, समर्पण आदि भावों से हम रहेंगे तो विश्वशांति अवश्य होगी।
• युद्ध, दुख, लालच और सभी पीडाओं को मिटाने का एक मात्र साधन है – विश्वशांति ।
• जहाँ शांति है वहाँ सुख है, जहाँ सुख है वही स्वर्ग है । यह सब विश्व शांति के द्वारा ही साध्य है।

अभिव्यक्ति-सृजनात्मकता

8 Marks Questions and Answers

निम्नलिखित प्रश्नों के उत्तर आठ या दस पंक्तियों में लिखिए।

प्रश्न 1.
भारत की संस्कृति सारे विश्व को लुभाती है। इस कथन पर व्याख्या कीजिए|
उत्तर:
शीर्षक का नाम : “हम भारतवासी” है।
कवि का नाम : “आर.पी.निशंक’ है।

• भारतीय संस्कृति की मुख्य विशेषताएँ ये हैं कि
• भारतीय संस्कृति में ऊँच – नीच का भेद मिटाकर दिल में प्यार बसाने की शक्ति है।
• सत्य, अहिंसा, त्याग, समर्पण जैसे सद्गुणों का विकास करने की शक्ति है।
• जग के सारे क्लेशों को मिटाकर धरती को स्वर्ग बनाने की शक्ति है।
• विश्व के सारे लोगों में प्रेम और शांति की स्थापना कर सकती है।
• विश्व बंधुत्व रूपी मूलमंत्र दुनिया में सरसाने की शक्ति इस संस्कृति में है।
• इस प्रकार हम कह सकते हैं कि भारत की संस्कृति सारे विश्व को लुभाती है।

प्रश्न 2.
“भारतीय, विश्वशांति और विश्वबंधुत्व की पवित्र भावनाओं से दुनिया को पवित्र धाम बनायेंगे” हम भारतवासी कविता के आधार पर स्पष्ट कीजिए।
उत्तर:
शीर्षक का नाम : “हम भारतवासी” है।
कवि का नाम : “आर.पी.निशंक” है।

• हम भारतवासी दुनिया को पावन धाम बनायेंगे। मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखायेंगे।
• हम सब में ऊँच-नीच का भेद मिटाकर दिल में प्यार बसायेंगे।
• हम नफ़रत को दूर कर अमृत बरसायेंगे।
• हम सत्य, अहिंसा, त्याग और समर्पण की बगिया को महाकायेंगे।
• जग के सारे क्लेशों को मिटाकर धरती को स्वर्ग बनायेंगे।
• विश्व बंधुत्व रूपी मूल मंत्र हम दुनिया में सरसायेंगे।
• इस प्रकार भारतीय विश्वशांति, विश्व बंधुत्व की भावनाओं से दुनिया को पवित्र धाम बनायेंगे।

प्रश्न 3.
विश्वशांति और विश्वबंधुत्व की भावना भारतवासी कैसे फैलायेंगे?
उत्तर:

• हम भारतवासी कविता के कवि श्री आर.पी. निशंक है।
• ये महान हिंदी साहित्यकार है, इनकी कविताओं का मुख्य विषय देश भक्ति है।
• प्रस्तुत कविता ‘मातृभूमि के लिए ‘संग्रह’ से लिया गया है।
• इस कविता में भारतीयों के लक्षणों के बारे में बताया गया है।
• भारतवासी दुनिया को पावन धाम बनायेंगे।
• श्रद्धा और प्रेम से दुनिया का मार्ग निर्देशन करेंगे।
• ऊँच – नीच का भेद मिटायेंगे, सब से प्यार करेंगे।
• नफ़रत मिटाकर अमृत रस सरसायेंगे, निराशा दूर भगाकर विश्वास जगायेंगे।
• उलझन में फंसे लोगों को राह दिखायेंगे, जीवन पथ से भटके लोगों को राह दिखायेंगे।
• सत्य, अहिंसा, त्याग, समर्पण आदि भावों से भरा समाज बनायेंगे।
• इस तरह विश्वशांति और विश्वबंधुत्व की भावना फैलायेंगे।

प्रश्न 4.
हम भारतवासी कविता का सारांश अपने शब्दों में लिखिए।
आर.पी. निशंक कृत “हम भारतवासी” पाठ का सारांश अपने शब्दों में लिखिए।
उत्तर:
हम भारतवासी
कविता का नाम : हम भारतवासी
कवि का नाम : श्री आर. पी. निशंक
रचनाएँ : समर्पण, नवंकुर,जीवन पथ में, मुझे विधाता बनना हैं, तुम भी मेरे साथ चलो, कोई मुश्किल नहीं आदि।
पुरस्कार : पद्म श्री

सारांश :
आधुनिक हिंदी साहित्यकारों में आर.पी. निशंक जी विशिष्ट स्थान रखते हैं। अपनी इस कविता में आप छात्रों में देश भक्ति भावना के साथ विश्व बंधुत्व विश्वशांति, अहिंसा, त्याग, समर्पण आदि उत्तम गुणों का विकास करना चाहते हैं।

कवि कहते हैं कि हम भारतवासी दुनिया को पावन धाम बनायेंगे। हम अपने मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखायेंगे। सब में ऊँच – नीच का भेद मिटाकर दिल में प्यार बसायेंगे। नफ़रत को दूर भगाकर अमृत बरसायेंगे। निराशा को दूर करके लोगों में विश्वास जगायेंगे। उलझनों में उलझे लोगों को तथ्य दीप समझायेंगे।

जीवन पथ से भटकनेवालों को सच्चा राह दिखायेंगे। खुशियाँ रूपी दीप जलाकर जीवन ज्योत जलायेंगे। सत्य, अहिंसा, त्याग, और समर्पण की बगिया महकायेंगे।

जग के समस्त क्लेशों को मिटाकर शक्तिभर धरती को स्वर्ण बनायेंगे। वसुदैक कुटुबंम भावना हम दुनिया से सरसायेंगे।

ऐसे सच्चे आशय मन में रखकर हम दुनिया को पावन धाम बनाने में अपना पूरा जीवन लगा देंगे।

विशेषताएं:
1. इस कविता में देश भक्ति, विश्व बंधुत्व, विश्व शांति, अहिंसा, त्याग अदि भाव व्यक्त किये गये हैं।
2. यह प्रेरणादायक कविता है।

प्रश्न 5.
“हम भारतवासी” कविता विश्व – बंधुत्व की ओर कदम बढाने की प्रेरणा देती है। – समझाइए।
उत्तर:
कवि : रमेश पोखरियाल निशांक’
जन्म : 15 अगस्त 1958
रचनाएँ : समर्पण, नवंकुर, मुझे विधाता बनाना है, तुम भी मेरे साथ चलो, जीवन पथ में, कोई मुश्किल नहीं आदि।
रचना का मुख्य विषय : देशभक्ति

एक ही परिवार के सभी लोग जिस प्रकार बंधुत्व भाव से रहते हैं उसी प्रकार विश्वभर के लोगों से बंधु भावना से रहना ही विश्व बंधुत्व है। सारे विश्व की मंगल कामना भारतीयों में आदिकाल से ही निहित है। इसी भावना के अन्तर्गत भारतवासी कहते हैं कि –

• हम भारतवासी दुनिया को पवित्र स्थल बनाएँगे।
• श्रद्धा और प्रेम से दुनिया का मार्गदर्शन करेंगे।
• लोगों में ऊँच – नीच भेद मिठाकर सब में प्यार भरेंगे।
• लोगों के बीच में हुई नफरत का भाव मिटाकर अमृत रस सरसाएँगे। उनके निराशा को दूर भगाकर उनमें विश्वास जगाएँगे।
• उलझन में फसे और जीवन पथ से भटके लोगों को सही राह दिखाएँगे।
• समाज को सत्य, अहिंसा, त्याग, समर्पण आदि भावों से भरेंगे।

इन भावनाओं से हमें पता चलता हैं कि यह कविता विश्व बंधुत्व की ओर कदम बढाने की प्रेरणा जरूर देती है।

प्रश्न 6.
धरती को स्वर्ग कैसे बना सकते हैं?
(या)
भारतवासी किन पवित्र भावनाओं से धरती को स्वर्ग बनाना चाहते हैं? विवरण दीजिए ।
उत्तर:

• विश्वशांति से धरती को स्वर्ग बना सकते हैं।
• आपस में प्रेम, श्रद्धा और प्यार आदि भावों को जगाकर धरती को स्वर्ग बना सकते हैं ।
• दिल में ऊँच – नीच के भेदभावों को दूर करके धरती को स्वर्ग बना सकेंगे।
• वैर भाव, ईर्ष्या, द्वेष आदि के बिना आपस में सहयोग के साथ रहकर धरती को स्वर्ग बना सकेंगे।
• विश्व बंधुत्व भावना से रहकर धरती को स्वर्ग बना सकेंगे।
• सत्य, अहिंसा, त्याग, समर्पण आदि सर्वोन्मत अंशों को प्रधानता देकर धरती को स्वर्ग बना सकेंगे ।
• मनुष्यों में निराशा को दूर भगाकर आशा दीप जलाकर धरती को स्वर्ग बना सकेंगे ।

प्रश्न 7.
निशंक जी किन भावनाओं से दुनिया को पावन धाम बनाना चाहते हैं?
उत्तर:
“हम भारतवासी” नामक कविता के कवि हैं श्री आर. पी. निशंक | “हम भारतवासी” नामक कविता में कवि देश भक्ति के साथ – साथ विश्वबंधुत्व, विश्वशांति, सत्य, अहिंसा, त्याग, समर्पण आदि सद्गुणों का विकास छात्रों में करते हैं।

कवि कहते हैं कि हम भारतवासी दुनिया को पावन धाम बनायेंगे | मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखायेंगे । हम सबमें ऊँच – नीच का भेद मिटाकर दिल में प्यार बसायेंगे | नफ़रत नामक कुहासे को तोड़कर हम अमृत सरसायेंगे | हम खुशी में निराशा को दूर भगाकर विश्वास जयायेंगे ।

कवि और कहते हैं कि उलझनों में उलझे लोगों को तथ्य दीप समझायेंगे | जीवन पथ से भटकते रहने वालों को राह दिखायेंगे | हम खुशियों के दीप जलाकर जीवन ज्योत जलायेंगे ।

कवि और कहते हैं हम सत्य, अहिंसा, त्याग और समर्पण की बगिये को महकायेंगे | जग के सारे क्लेशों को मिटाकर धरती को स्वर्ग बनायेंगे | विश्वबंधुत्व रूपी मूलमंत्र को हम दुनिया में सरसायेंगे |

प्रश्न 8.
‘वसुधैक कुटुंबम” की भावना को आर. पी. निशंक जी ने अपनी कविता में सुंदर ढंग से व्यक्त किया है – स्पष्ट कीजिए।
उत्तर:
“हम भारतवासी” नामक कविता के कवि हैं श्री आर. पी. निशंक | “हम भारतवासी” नामक कविता में कवि देश भक्ति के साथ – साथ विश्वबंधुत्व, विश्वशांति, सत्य, अहिंसा, त्याग, समर्पण आदि सद्गुणों का विकास छात्रों में करते हैं।

कवि कहते हैं कि हम भारतवासी दुनिया को पावन धाम बनायेंगे | मन में श्रद्धा और प्रेम का अद्भुत दृश्य दिखायेंगे | हम सबमें ऊँच – नीच का भेद मिटाकर दिल में प्यार बसायेंगे | नफ़रत नामक कुहासे को तोड़कर हम अमृत सरसायेंगे | हम खुशी में निराशा को दूर भगाकर विश्वास जयायेंगे ।

कवि और कहते हैं कि उलझनों में उलझे लोगों को तथ्य दीप समझायेंगे | जीवन पथ से भटकते रहने वालों को राह दिखायेंगे | हम खुशियों के दीप जलाकर जीवन ज्योत जलायेंगे ।

कवि और कहते हैं हम सत्य, अहिंसा, त्याग और समर्पण की बगिये को महकायेंगे । जग के सारे क्लेशों को मिटाकर धरती को स्वर्ग बनायेंगे । विश्वबंधुत्व रूपी मूलमंत्र को हम दुनिया में सरसायेंगे |

‘वसुधैक कुटुंबम’ का अर्थ है विश्व बंधुत्व की भावना । इस प्रकार आर. पी. निशंक अपनी कविता में “वसुधैक कुटुंबम’ की भावना को अपनी कविता “हम भारतवासी” में उभारा है |

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 1 Real Numbers Optional Exercise Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Optional Exercise

10th Class Maths 1st Lesson Real Numbers Optional Exercise Textbook Questions and Answers

Question 1.
Can the number 6ⁿ, n being a natural number, end with the digit 5? Give reason.
Answer:
Given number = 6ⁿ ; n ∈ N
6ⁿ to be end in 5; it should be divisible by 5
6ⁿ = (2 × 3)ⁿ
The prime factors of 6ⁿ are 2 and 3.
It can’t end with the digit 5.

Question 2.
Is 7 × 5 × 3 × 2 + 3 a composite number? Justify your answer.
Answer:
Given:
7 × 5 × 3 × 2 + 3
= 3 (7 × 5 × 2 + 1)
= 3 × (70 + 1)
= 3 × 71
∴ The given number has two factors namely 3 and 71.
Hence it is a composite number.

Question 3.
Prove that (2√3 + √5 ) is an irrational number. Also check whether (2√3 + √5) (2√3 – √5) is rational or irrational.
Answer:
To prove:
2√3 + √5 is an irrational number. On contrary, let us suppose that 2√3 + √5 be a rational number.
Then 2√3 + √5 = \(\frac{p}{q}\)
Squaring on both sides, we get


L.H.S = an irrational number.
R.H.S = p, q being integers, \(\frac{p^{2}-17 q^{2}}{4 q^{2}}\) is a rational number.
This is a contradiction to the fact that √l5 is an irrational. This is due to our assumption that 2√3 + √5 is a rational. Hence our assumption is wrong and 2√3 + √5 is an irrational number. Also,
(2√3 + √5) (2√3 – √5)
= (2√3)² – (√5)²
[∵ (a + b) (a – b) = a² – b²]
= 4 × 3 – 5
= 12 – 5 = 7, a rational number.

Question 4.
If x² + y² = 6xy, prove that 2 log (x + y) = log x + log y + 3 log 2.
Answer:
Given: x² + y² = 6xy
x² + y² + 2xy = 6xy + 2xy
(x + y)² = 8xy
Taking logarithms on both sides log (x + y)² = log8xy
⇒ 2log(x + y)= log8 + logx + logy [∵ logx^m = mlogx]
[∵ logxy = logx + logy]
= log2³ + logx + logy
⇒ 2log(x + y) = logx + logy + 3log2

Question 5.
Find the number of digits in 42013, if log₁₀2 = 0.3010.
Answer:
Given:
log₁₀2 = 0.3010
4²⁰¹³ = (2²)²⁰¹³ = 2⁴⁰²⁶
∴ log₁₀ 2⁴⁰²⁶ = 4026 log₁₀2
[∵ log x^m = m log x]
= 4026 × 0.3010 = 1211.826.
So 1211 + 1 = 1212
∴ 4²⁰¹³ has 1212 digits in its expansion.
(∵ characteristic 1211)

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 1 Real Numbers Ex 1.5 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.5

10th Class Maths 1st Lesson Real Numbers Ex 1.5 Textbook Questions and Answers

Question 1.
Determine the values of the following,
i) log₂₅5
Answer:

ii) log₈₁3
Answer:

iii) log₂(\(\frac{1}{16}\))
Answer:

iv) log₇1
Answer:
log₇1 = log₇7⁰ = 0 log₇7 = 0

v) log_x√x
Answer:

vi) log₂512
Answer:
log₂512 = log₂2⁹    [∵ 512 = 2⁹]
= 9log₂2   [∵ log x^m = m log x]
= 9 × 1    [∵ log_aa = 1]
= 9

vii) log₁₀0.01
Answer:

viii) \(\log _{\frac{2}{3}}\left(\frac{8}{27}\right)\)
Answer:

ix) \(2^{2+\log _{2} 3}\)
Answer:
\(2^{2+\log _{2} 3}\) = 2² . \(2^{\log _{2} 3}\)   [∵ a^m . aⁿ = a^m+n]
= 4 × 3 [∵ \(\log _{\mathrm{a}} \mathrm{N}\) = N]
= 12

Question 2.
Write the following expressions as log N and find their values.
i) log 2 + log 5
Answer:
log 2 + log 5
= log 2 × 5   [∵ log m + log n = log mn]
= log 10
= 1

ii) log₂ 16 – log₂ 2
Answer:

iii) 3 log₆₄4
Answer:

iv) 2 log 3 – 3 log 2
Answer:
2 log 3 – 3 log 2
= log 3² – log 2³
= log 9 – log 8
= log \(\frac{9}{8}\)

v) log 10 + 2 log 3 – log 2
Answer:
log 10 + 2 log 3 – log 2
= log 10 + log 3² – log 2
= log 10 + log 9 – log 2    [∵ m log a = log a^m]
= log \(\frac{10 \times 9}{2}\)    [∵ log a + log b = log ab; log a – log b = log \(\frac{a}{b}\)]
= log 45

Question 3.
Evaluate each of the following in terms of x and y, if it is given x = log₂3 and y = log₂ 5.
i) log₂15
Answer:
log₂15 = log₂ 3 × 5
= log₂3 + log₂5   [∵ log mn = log m + log n]
= x + y

ii) log₂7.5
Answer:

iii) log₂60
Answer:
log₂60 = log₂2² × 3 × 5
= log₂2² + log₂3 + log₂5
= 2 log₂2 + x + y
= 2 + x + y

iv) log₂6750
Answer:

log₂6750
= log₂2 × 3³ × 5³
= log₂2 + log₂33 + log₂5³
= 1 + 3 log₂3 + 3 log₂5
= 1 + 3x + 3y

Question 4.
Expand the following,
i) log 1000
Answer:
log 1000 = log 10³
= 3 log 10
= 3 × 1
= 3

ii) \(\log \left[\frac{128}{625}\right]\)
Answer:

iii) log x²y³z⁴
Answer:
log x²y³z⁴ = logx² + logy³ + logz⁴ [∵ log ab = log a + log b]
= 2 log x + 3 log y + 4 log z
[∵ log a^m = m log a]

iv) \(\log \frac{\mathbf{p}^{2} \mathbf{q}^{3}}{\mathbf{r}}\)
Answer:

iv) \(\log \sqrt{\frac{x^{3}}{y^{2}}}\)
Answer:

Question 5.
If x² + y² = 25xy, then prove that 2 log (x + y) = 3log3 + logx + logy.
Answer:
Given: x² + y² = 25xy
We know that (x + y)² = x² + y² + 2xy
= 25xy + 2xy    [∵ x² + y² = 25xy given]
(x + y)² = 27xy
Taking ‘log’ on both sides
log (x + y)² = log 27xy
2 log (x + y) = log 27 + log x + log y
= log 3³ + log x + log y
⇒ 2 log (x + y) = 3log3 + log x + log y

Question 6.
If \(\log \left(\frac{\mathbf{x}+\mathbf{y}}{3}\right)\) = \(\frac{1}{2}\) (log x + log y), then find the value of \(\frac{x}{y}+\frac{y}{x}\).
Answer:

(squaring on both sides)
⇒ (x + y)² = (3√xy)²
⇒ x² + y² + 2xy = 9xy
⇒ x² + y² = 9xy – 2xy = 7xy

Question 7.
If (2.3)^x = (0.23)^y = 1000 then find the value of \(\frac{1}{x}-\frac{1}{y}\).
Answer:
Given (2.3)^x = (0.23)^y = 1000 = 10³

Question 8.
If 2^x+1 = 3^1-x then find the value of x.
Answer:
Given: 2^x+1 = 3^1-x
log 2^x+1 = log 3^1-x
(x + 1) log 2 = (1 – x) log 3
x log 2 + log 2 = log 3 – x log 3
x log 2 + x log 3 = log 3 – log 2
x (log 3 + log 2) = log 3 – log 2

Question 9.
Is
i) log 2 is rational or irrational? Justify your answer.
Answer:
Let log₁₀2 = x
Then 10^x = 2
But 2 can’t be written as 10^x for any value of x
∴ log 2 is irrational.

ii) log 100 is rational or irrational? Justify your answer.
Answer:
Let log₁₀100 = x
⇒ log₁₀10² = x
⇒ 2 log₁₀10 = x = 2
∴ log 100 is rational.
∴ log 100 = 2
Hence rational.

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 1 Real Numbers Ex 1.3 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.3

10th Class Maths 1st Lesson Real Numbers Ex 1.3 Textbook Questions

Question 1.
Write the following rational numbers in their decimal form and also state which are terminating and which have non-terminating repeating decimals.
i) \(\frac{3}{8}\)
ii) \(\frac{229}{400}\)
iii) 4\(\frac{1}{5}\)
iv) \(\frac{2}{11}\)
v) \(\frac{8}{125}\)
Answer:
i) \(\frac{3}{8}\)

[!! Denominator 8 = 2³, consists of only 2’s. Hence a terminating decimal.]
∴ \(\frac{3}{8}\) = 0.375 is a terminating decimal.

ii) \(\frac{229}{400}\)

[!! Denominator 400 = 2⁴ × 5² = 2ⁿ × 5^m. Hence a terminating decimal.]
∴ \(\frac{229}{400}\) = 0.5725 is a terminating decimal.

iii) 4\(\frac{1}{5}\)
4\(\frac{1}{5}\) = 4 + \(\frac{1}{5}\)

[!! Denominator is 5. Hence a terminating decimal.]
∴ 4\(\frac{1}{5}\) = 4.2 is a terminating decimal.

iv) \(\frac{2}{11}\)

[!! Denominator is not of the form 2^m × 5ⁿ. Hence a non-terminating repeating decimal.]
∴ \(\frac{2}{11}\) = \(0 . \overline{18}\) is a non terminating, repeating decimal.

v) \(\frac{8}{125}\)

[!! Denominator 125 = 5³. Hence a terminating decimal.]
∴ \(\frac{8}{125}\) = 0.064 is a terminating decimal.

Question 2.
Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form.
i) \(\frac{13}{3125}\)
ii) \(\frac{11}{12}\)
iii) \(\frac{64}{455}\)
iv) \(\frac{15}{1600}\)
v) \(\frac{29}{343}\)
vi) \(\frac{23}{2^{3} \cdot 5^{2}}\)
vii) \(\frac{129}{2^{2} \cdot 5^{7} \cdot 7^{5}}\)
viii) \(\frac{9}{15}\)
iX) \(\frac{36}{100}\)
X) \(\frac{77}{210}\)
Answer:
i) \(\frac{13}{3125}\)
Note: We check whether the denominator is of the form 2ⁿ . 5^m or not? If yes, the rational number can be expressed as a terminating decimal. If not, it can’t be expressed as a terminating decimal.

[!! Denominator is of the form 2^m × 5ⁿ. Hence a terminating decimal.]
3125 = 5⁵
∴ \(\frac{13}{3125}\) is a terminating decimal.

ii) \(\frac{11}{12}\)
The denominator 12 is not a factor of 11. Moreover 12 = 2² × 3.
[!! Denominator is not of the form 2^m × 5ⁿ.]
∴ \(\frac{11}{12}\) is a non terminating, repeating decimal.

iii) \(\frac{64}{455}\)

[!! Denominator is not of the form 2^m × 5ⁿ. Hence a non terminating decimal.]
∴ 455 = 5 × 7 × 13
Hence\(\frac{64}{455}\) is a non terminating, repeating decimal.

iv) \(\frac{15}{1600}\)

∴ 1600 = 2⁶ × 5² [∵ The denominator is of the form 2ⁿ . 5^m]
Hence \(\frac{15}{1600}\) is a terminating decimal.

v) \(\frac{29}{343}\)

343 = 7³ [Not of the form 2ⁿ . 5^m]
∴ \(\frac{29}{343}\) is a non terminating, repeating decimal.

vi) \(\frac{23}{2^{3} \cdot 5^{2}}\)
\(\frac{23}{2^{3} \cdot 5^{2}}\) is a terminating decimal.
[∵ The denominator is of the form 2ⁿ . 5^m]

vii) \(\frac{129}{2^{2} \cdot 5^{7} \cdot 7^{5}}\)
\(\frac{129}{2^{2} \cdot 5^{7} \cdot 7^{5}}\) is a non terminating, repeating decimal.

viii) \(\frac{9}{15}\)
\(\frac{9}{15}\) = \(\frac{3}{5}\)
Denominator is of the form 2ⁿ . 5^m.
∴ \(\frac{9}{15}\) = \(\frac{3}{5}\) is a terminating decimal.

ix) \(\frac{36}{100}\)
100 = 2² × 5² is of the form 2ⁿ . 5^m
Hence \(\frac{36}{100}\) is a terminating decimal.

x) \(\frac{77}{210}\)

210 = 2 × 3 × 5 × 7 is not of the form 2ⁿ . 5^m
Given fraction has a non-terminating, repeating decimal expansion.

Question 3.
Write the following rationals in decimal form using Theorem 1.4.
i) \(\frac{13}{25}\)
ii) \(\frac{15}{16}\)
iii) \(\frac{23}{2^{3} \cdot 5^{2}}\)
iv) \(\frac{7218}{3^{2} \cdot 5^{2}}\)
v) \(\frac{143}{110}\)
Answer:
i) \(\frac{13}{25}\)

ii) \(\frac{15}{16}\)
\(\frac{15}{16}\) = \(\frac{15}{2 \times 2 \times 2 \times 2}\)

iii) \(\frac{23}{2^{3} \cdot 5^{2}}\)

iv) \(\frac{7218}{3^{2} \cdot 5^{2}}\)

v) \(\frac{143}{110}\)

Question 4.
The decimal form of some real numbers are given below. In each case, decide whether the number is rational or not. If it is rational, and expressed in form p/q, what can you say about the prime factors of q?
i) 43.12345678?
ii) 0.120120012000120000 ……….
iii) \(43 . \overline{123456789}\)
Answer:
i) 43.123456789
The given decimal expansion is terminating. Hence it is a rational number and the denominator q is of the form 2ⁿ . 5^m.

ii) 0.120120012000120000 …………
The given decimal expansion is neither terminating nor repeating.
Hence it is not a rational number. It represents an irrational number.

iii) \(43 . \overline{123456789}\)
The given real number is a repeating decimal with period 123456789. Hence it is a rational number.

AP State Board Syllabus AP SSC 10th Class Maths Textbook Solutions Chapter 1 Real Numbers Ex 1.4 Textbook Questions and Answers.

AP State Syllabus SSC 10th Class Maths Solutions 1st Lesson Real Numbers Exercise 1.4

10th Class Maths 1st Lesson Real Numbers Ex 1.4 Textbook Questions and Answers

Question 1.
Prove that the following are irrational,
i) \(\frac{1}{\sqrt{2}}\)
ii) √3 + √5
iii) 6 + √2
iv) √5
v) 3 + 2√5
Answer:
i) \(\frac{1}{\sqrt{2}}\)
On the contrary, suppose that is a \(\frac{1}{\sqrt{2}}\) rational number;
then \(\frac{1}{\sqrt{2}}\) is of the form where \(\frac{p}{q}\) and q are integers.
∴ \(\frac{1}{\sqrt{2}}\) = \(\frac{p}{q}\)
⇒ \(\frac{\sqrt{2}}{1}\) = \(\frac{q}{p}\)
(i.e.,) √2 is a rational number and it is a contradiction. This contradiction arised due to our supposition that \(\frac{1}{\sqrt{2}}\) is a rational number.
Hence \(\frac{1}{\sqrt{2}}\) is an irrational number.

ii) Suppose √3 + √5 is not an irrational number.
Then √3 + √5 must be a rational number.
√3 + √5 = \(\frac{p}{q}\), q ≠ 0 and p, q ∈ Z
Squaring on both sides

but √15 is an irrational number.
\(\frac{p^{2}-8 q^{2}}{2 q^{2}}\) is a rational number
(p² – 8q², 2q² ∈ Z, 2q² ≠ 0)
but an irrational number can’t be equal to a rational number, so our supposition that √3 + √5 is not an irrational number is false.
∴ √3 + √5 is an irrational number.

iii) 6 + √2
To prove: 6 + √2 is an irrational number.
Let us suppose that 6 + √2 is a rational number.
∴ 6 + √2 = \(\frac{p}{q}\), q ≠ 0
⇒ √2 = \(\frac{p}{q}\) – 6
⇒ √2 = Difference of two rational numbers
⇒ √2 = rational number But this contradicts the fact that √2 is an irrational number.
∴ Our supposition is wrong.
Hence the given statement is true.
6 + √2 is an irrational number.

iv) √5
To prove: √5 is an irrational number.
On the contrary, let us assume that √5 is a rational number.
∴ √5 = \(\frac{p}{q}\), q ≠ 0
If p, q have a common factor, on cancelling the common factor let it be
reduces to \(\frac{a}{b}\) where a, b are co-primes.
Now √5 = \(\frac{a}{b}\), where HCF (a, b) = 1
Squaring on both sides we get
⇒ (√5)² = \(\left(\frac{a}{b}\right)^{2}\)
⇒ 5 = \(\frac{\mathrm{a}^{2}}{\mathrm{~b}^{2}}\)
⇒ 5b² = a²
⇒ 5 divides a² and thereby 5 divides 5
Now, take a = 5c
then, a² = 25c²
i.e., 5b² = 25c²
⇒ b² = 5c²
⇒ 5 divides b² and thereby b.
⇒ 5 divides both b and a.
This contradicts that a and b are co-primes.
This contradiction arised due to our assumption that √5 is a rational number.
Hence our assumption is wrong and the given statement is true, i.e., √5 is an irrational number,

v) 3 + 2√5
To Prove: 3 + 2√5 is an irrational.
On the contrary, let us assume that 3 + 2√5 is a rational number.

Here p, q being integers we can say that \(\frac{p-3q}{2q}\) is a rational number.
This contradicts the fact that √5 is an irrational number. This is due to our assumption “3 + 2√5 is a rational number”.
Hence our assumption is wrong.
∴ 3 + 2√5 is an irrational number.

Question 2.
Prove that √p + √q is an irrational, where p, q are primes.
Answer:
Given that p, q are primes.
Hence fp and fq are irrationals.
[∵ p, q have no factors other than 1 ∵ they are primes.]
Now √p + √q = sum of two irrational numbers = an irrational number
Hence proved.