Main sectors of Green Economy are as follows: 

•  E-waste management 
•  Green Transportation 
•  Renewable energy 
•  Green construction 
• Water management

Entrepreneurial values: 

(a) Innovativeness and Creativity 

(b) Independence or ownership 

(c) Quest for Outstanding Performance or Achievement 

(d) Respect for Work

a. Confidence 

b. Independence 

c. Perseverance 

d. Open mindedness

Three-color system used in India is PAL color system

(i) Self Help Groups pool their savings. 

(ii) A typical SHG has 15-20 members, usually belonging to one neighbourhood, who meet and save regularly. 

(iii) Saving per member varies from Rs. 25 to Rs. 100 or more, depending on the ability of the people to save. 

(iv) Members can take small loans from the group itself to meet their needs. 

(v) The group charges interest on these loans but this is still less than what the moneylender charges. 

(vi) After a year or two, if the group is regular in savings, it becomes eligible for availing loan from the bank.

Green jobs are found in many sectors of the economy. They help to cut the consumption of energy, raw materials and water through high-efficiency strategies, de-carbonize the economy and reduce greenhouse-gas emissions, minimize or avoid altogether all forms of waste and pollution, protect and restore ecosystems and biodiversity.

Pricing/selling/accounting/growing business/manufacturing

Government, Private agencies, People

a) Government 

b) NGO 

c) Business & industry 

d) Farmers 

e) Women

f) Workers & trade unions 

g) Native tribes 

h) Scientific & technological community 

i) Children & Youth

Farmers produce food and agricultural products for the whole country.

The most important stakeholder in a green economy is the people of the nation. Any economy exists because of its people. 

Government brings many policies but the success of the policy depends on how the people have adopted the change. If the policy affects the people negatively, it is bound to collapse. Hence, while laying down the policy, the interest of the people should be considered. The factors like education of the people of nation also play a pivotal role. 

If the masses are not educated and aware about the latest trends and needs, they will either reject the policies or would not be able to contribute to the extent to bring a desirable change.

Stakeholders in green economy: 

(a) Government 

(b) Non-Governmental Organisations (NGOs) 

(c) Business and Industry 

(d) Scientific and Technological Community 

(e) Workers and Trade Unions 

(f) Farmers 

(g) Women etc.

(i) Sustainable development aims at fulfilling the needs of today without compromising the needs of the future generation. 

(ii) Sustainability is the capability to use the resources judiciously and maintain the ecological balance. 

(iii) It lays emphasis on environmental protection and check environmental degradation.

(iv) Sustainability is important to stop over exploitation and over use of resources.

(i) D. Preservation of traditionalist beliefs in state and society

(ii) B. To restore conservative regime in Europe

(iii) A. To re-establish peace and stability in Europe.

(iv) C. Laying out a balance of power between all the great powers in Europe.

1.d
2.b
3.a
4.c

1. Electricity usage, 

2.Machine is on even when not in use.

Children and Youth: The youth are both the present and the future of our economy. They can participate actively in the protection of the environment and the promotion of economic and social development 

Governments: Governments and local authorities make and implement sustainable development laws, policies, strategies, standards, programs, agreements with other countries and actions.

C. Sustainable Development.

C. Sustainable Development

B. It allows different organs of government to be placed at the same level.

B. It allows different organs of government to be placed at the same level

C - Concurrent list

C. Concurrent list

b. Both A and R are true but R is not the correct explanation of A. 

Different people have different development goals because their notion or idea about development is different.

(b) Both A and R are true but R is not the correct explanation of A

(i) C. Right to Vote

(ii) B. Right to information

(iii) C. Free and fair elections

(iv) D. Taken after following due processes

(i) D. Secondary, Primary Sector

(ii) B. a-3, b-4, c-2, d-1

(iii) B. Providing unskilled labour force

(iv) D. Infrastructure facilities

1.D
2.B
3.B
4.D 

C - Rio de Janeiro Earth Summit

i. Against Rowlatt Act 

ii. Jallianwala Bagh incidence 

iii. Khilafat Andolan

Gandhiji launched the Non-cooperation movement of 1921 because: 
According to Gandhiji , the British rule was established in India with the cooperation of Indians, and had survived only because of this cooperation. So time has arrived to withdraw cooperation to the British. 
First World War added to the misery of the Indian people. Heavy taxes, high prices, famines and epidemics made people's life miserable. 
Rowlatt Act invited large scale protests throughout the country. 
Jallianwala Bagh Massacre and the injustice done to Punjab made Indians angry which needed to be avenged.
To restore the status of the ruler of Turkey. 
To bring Swaraj or Self Rule to India. 
Mahatma Gandhi declared that the main objectives of the non cooperation movement were : 
To cripple the British administration and make them realize that they cannot function without the actual support of the Indians. 
To avenge the wrong done by the Government in Punjab (Jallianwala Bagh Massacre) in a non violent way. 
To bring about unity among the people. To inculcate a sense of nationalism. 
To promote khadi and to attain Swaraj. 

D. Asset as guarantee for loan

D. Leads to spread of technology, cultures and diseases from a region to another

Gandhiji launched the Non-cooperation movement of 1921 because: 
According to Gandhiji , the British rule was established in India with the cooperation of Indians, and had survived only because of this cooperation. So time has arrived to withdraw cooperation to the British. 
First World War added to the misery of the Indian people. Heavy taxes, high prices, famines and epidemics made people's life miserable. 
Rowlatt Act invited large scale protests throughout the country. 
Jallianwala Bagh Massacre and the injustice done to Punjab made Indians angry which needed to be avenged.
To restore the status of the ruler of Turkey. 
To bring Swaraj or Self Rule to India. 
Mahatma Gandhi declared that the main objectives of the non cooperation movement were : 
To cripple the British administration and make them realize that they cannot function without the actual support of the Indians. 
To avenge the wrong done by the Government in Punjab (Jallianwala Bagh Massacre) in a non violent way. 
To bring about unity among the people. 

To inculcate a sense of nationalism. 

To promote khadi and to attain Swaraj. 

Gandhiji launched the Non-cooperation movement of 1921 because: According to Gandhiji, the British rule was established in India with the cooperation of Indians, and had survived only because of this cooperation. So time has arrived to withdraw cooperation to the British. First World War added to the misery of the Indian people.

C. both P and Q

A. to help farmers across the country as the earlier policies concentrated development in a few states only

C. increasing export duties on agricultural products

A. diversifying their cropping pattern away from cereals

To increase the share of agriculture in the Gross Domestic Product, investment in agriculture should be increased in the areas like irrigation, bio manures, agricultural tools like tractors, harvesters, HYV seeds, etc. The subsidy on manures, fertilizers and other inputs should be increased so that the farmers can use them. Easy and flexible loan facilities should be made available to the farmers. Agro based industries should be set up in the rural areas. Value exhibited in the paragraph are: 

(a) Sustainability (b) Accepting challenges (c) Awareness 

(d) Decision making (e) Development of positive attitude

(c) less area under cultivation 

More than one-third of the crude steel production of the world comes from China.

(d) insufficient price incentives by the government

(d) Central Duck Breeding Farm – Chikmagalur

These are: 

REFUSE, REDUCE, REUSE, RECYCLE & UPCYCLE?

This problem has come a long way and the probable solution to this has been provided in 4Rs and 1U of sustainable development – REFUSE, REDUCE, REUSE, RECYCLE & UPCYCLE. Following these has definitely helped minimize the waste and pollution. But, the recyclers job at its best is trying to put a full stop to this problem. The concept of upcycling and the avenues it has created for a green market are luring and helps resolve this problem to a great extent.

a. Reproduce

Reproduce is a part of 4Rs of sustainable development.

A relation from a set A to set B  is nothing but a subset of the cartesian product of A and B which is denoted by AXB. The types of relations are nothing but their properties. There are different types of relations namely reflexive, symmetric, transitive and anti symmetric which are defined and explained as follows through real life examples.

Reflexive relation:

A relation R is said to be reflexive over a set A if (a,a) € R for every a € R.

Example-1:

If A is the set of all males in a family, then the relation “is brother of” is not reflexive over A. Because any person from the set A cannot be brother of himself.

Example-2:

The relation R = {(1,1)(2,2)(3,3)} is reflexive over the set A = {1,2,3}.

Symmetric relation:

A relation R is said to be symmetric if (a,b) € R => (b,a) € R

Example-1:

If A is the set of all males in a family, then the relation “is brother of” is symmetric over A.

Because if a is brother of b then b is brother of a.

Example-2:

If A is the set of mothers and B is the set of children in a family then a relation R on AxB is not symmetric because if a is mother of b then b cannot be mother of a.

Transitive relation:

A relation R is said to be symmetric if (a,b) € R, (b,c) € R => (a,c)  € R.

Example-1:

If A is the set of all males in a family, then the relation “is brother of” is transitive over A.

Because if a is brother of b and b is brother of c then a is brother of c.

Example-2:

The relation R = {(1,1)(2,2)(3,3)(1,2)(2,3)} is not transitive over the set A = {1,2,3} because thought (1,2), (2,3) € R , (1,3) is not in R.

Properties of Union of  Sets

i)   Commutative Law: The union of two or more sets follows the commutative law i.e., if we have two sets A and B then,

A∪B=B∪A

Example: A = {a, b} and B = {b, c, d}

So, A∪B = {a, b, c, d}

B∪A = {b, c, d, a}

Since, in both the union, the group of elements is same. Therefore, it satisfies commutative law.

A ∪ B = B ∪ A

ii) Associative Law: The union operation follows the associative law i.e., if we have three sets A, B and C then

(A ∪ B) ∪ C = A ∪ (B ∪ C)

Example: A = {a, b} and B = {b, c, d} and C = {a, c, e}

(A ∪ B) ∪ C = {a, b, c, d} ∪ {a, c, e} = {a, b, c, d, e}

A ∪ (B ∪ C) = {a, b} ∪ {b, c, d, e} = {a, b, c, d, e}

Hence, associative law proved.

iii)  Identity Law: The union of an empty set with any set A gives the set itself i.e.,

A ∪ ∅ = A

Suppose, A = {a, b, c} and ∅ = {}

then, A ∪ ∅ = {a, b, c} ∪ {} = {a, b, c}

iv)  Idempotent Law: The union of any set A with itself gives the set A i.e.,

A ∪ A = A

Suppose, A = {1, 2, 3, 4, 5}

then A ∪ A = {1, 2, 3, 4, 5} ∪ {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5} = A

v)  Domination Law: The union of a universal set U with its subset A gives the universal set itself.

A ∪ U = U

Suppose, A = {1, 2, 4, 7} and U = {1, 2, 3, 4, 5, 6, 7}

then A ∪ U = {1, 2, 4, 7} ∪ {1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7} = U

Hence, proved.

Intersection of Sets Properties:

Some Properties of the Operation of Intersection are listed below:

(i) Commutative law: A ∩ B = B ∩ A

Consider two sets A = {1, 2, 3, 4, 5, 6} and B = {2, 3, 5, 7}.

Now, A ∩ B = {1, 2, 3, 4, 5, 6} ∩ {2, 3, 5, 7} = {2, 3, 5}

B ∩ A = {2, 3, 5, 7} ∩ {1, 2, 3, 4, 5, 6} = {2, 3, 5}

Therefore, A ∩ B = B ∩ A.

(ii) Associative law: (A ∩ B) ∩ C = A ∩ (B ∩ C)

Let A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, and C = {5, 6, 7, 8 }.

Now, 

A ∩ B = {1, 2, 3, 4} ∩ {3, 4, 5, 6} = {3, 4}

(A ∩ B) ∩ C = {3, 4} ∩ {5, 6, 7, 8} = { } = φ

And

B ∩ C = {3, 4, 5, 6} ∩ {5, 6, 7, 8} = {5, 6}

A ∩ (B ∩ C) = {1, 2, 3, 4} ∩ {5, 6} = { } = φ

Therefore, (A ∩ B) ∩ C = A ∩ (B ∩ C)

(iii) Law of φ and U: φ ∩ A = φ, U ∩ A = A

Consider φ = { } and A = {10, 11, 12}.

φ ∩ A = { } ∩ {10, 11, 12} = { } = φ

Let U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} and A = {4, 8, 12, 16, 20}.

U ∩ A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} ∩ {4, 8, 12, 16, 20} = {4, 8, 12, 16, 20} = A

(iv) Idempotent law: A ∩ A = A

Suppose A = {a, b, c, d, e} such that A ∩ A = {a, b, c, d, e} ∩ {a, b, c, d, e} = {a, b, c, d, e} = A

(v) Distributive law: A ∩ (B U C) = (A ∩ B) U (A ∩ C), i. e., ∩ distributes over U

Let us take three sets A = = {2, 4, 6, 8}, B = {2, 3, 5, 7} and C = {3, 4, 5, 6}.

B U C = {2, 3, 5, 7} U {3, 4, 5, 6} = {2, 3, 4, 5, 6, 7}

A ∩ (B U C) = {2, 4, 6, 8} ∩ {2, 3, 4, 5, 6, 7} = {2, 4, 6}

A ∩ B = {2, 4, 6, 8} ∩ {2, 3, 5, 7} = {2}

A ∩ C = {2, 4, 6, 8} ∩ {3, 4, 5, 6} = {4, 6}

(A ∩ B) U (A ∩ C) = {2} U {4, 6} = {2, 4, 6}

Therefore, A ∩ (B U C) = (A ∩ B) U (A ∩ C)

M/s Jaggimal Kirorimal
M. G. Road
Dholpur
March 14, 20–
M/s Amar Trading Company
47 Station Road
Ajmer

Subject: Outstanding Payment

Dear Sir,

We are sorry to note that a customer of your goodwill has not noticed our previous letter dated February 5, 20– for the settlement of our account.
Maybe, it might escape from your knowledge.
We request you to remit us a sum of 20,000/- (Twenty thousand only) standing against you at your earliest.

Yours faithfully
For Jaggimal Kirorimal
B. P. Sharma
(Proprietor)

37 Adarsh Nagar
Jaipur
25 November 2020
The Editor
The Times of India
New Delhi

Subject: Views regarding child labour in India

Dear Sir,

Even after 70 years of India’s independence, it is bone-chilling and blood – curdling to have a look at the children being enslaved by the eerie shadow of manual labour and being forbidden to avail school education. Child labour is banned in India by the government but still, we can see a number of children working at many places. They are compelled to do even hazardous jobs. There should be public awakening in this matter, and strict action should be taken.

Yours faithfully
Aditya

7 Adarsh Nagar
Churu
13 October 2020
M/s Tulip Appliances
M.G. Road, Jaipur

Subject: Complaint regarding the defective washing machine

Dear Sir,

I bought a washing machine from your showroom with a warranty of 2 years. But only 8 months have passed by and it has started troubling me. For a month its dryer has not been functioning properly while the system creates a loud noise during the washing of clothes. It gave me an electric shock when I switched it on yesterday. I hope you will understand the urgency of the situation and send a technician to rectify these defects or replace it soon.

Yours faithfully
Anoop

137 Jawahar Nagar
Jaipur
12 October 2020
M/s L.K. Agency
Station Road

Jaipur Sub: Replacement of defective washing machine.

Dear Sirs,

I regret to inform you that on 8 October, 2020 . I purchased a Tiger washing machine from your shop vide cash memo No. 372 of that date. On 9th October the machine worked alright. But today the machine does not work. It has jammed. The other defect is that water leaks out from its water tank. You are requested to replace this machine at an early date.

Thanking you

Yours faithfully

Raj Kumar Seth

4, Avas Vikas Colony
Churu
20 October 2020
Chief Medical Officer District Hospital Churu

Subject: The dissatisfactory situation of the City Hospital

Sir,

The City Hospital has always been a blessing to the citizens of the city. It has played an excellent role in the health services for the welfare of the people. But for some time, doctors are not available on time. Patients return hopelessly, emergencies go unattended, the X-ray machine is lying dead. The rich can go to the private hospitals but what to say about the poor who cannot afford these facilities.
The situation seeks your personal attention and appropriate action.

Yours faithfully
Shailabh/Surbhi

18, Katra Mahesh Das
Deeg
September 10, 2020
The Niren Watch Company
149 Banerjee Road
Kolkata

Subject: A complaint regarding a defective watch

Dear Sir,

I am sorry to state that the watch sent by you last month by V.P.P. is not working properly. It stops very often. The parcel was received intact. Hence, I think there is some mechanical defect in the watch. I am sending the watch, invoice and guarantee-card back to you and I request you to replace it by another thoroughly checked watch.

Yours faithfully
Prakash Gupta

y = \(\sqrt{px}, p>0\)

For domain of function y, we required

px \(\geq\) 0

⇒ x \(\geq\) \(\frac0p\) (\(\because\) p > 0, so on dividing sign remains same)

⇒ x \(\geq0\)

Hence, domain of function y = \(\sqrt{px},p>0 \,is \,x \in [0,\infty )\)