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Let the tens and the units digits of the required number be x and y, respectively. 

Required number = (10x + y) 

10x + y = 4(x + y) + 3 

⇒10x + y = 4x + 4y + 3 

⇒ 6x – 3y = 3 

⇒ 2x –y = 1 ……….(i) 

Again, we have: 

10x + y + 18 = 10y + x 

⇒9x – 9y = -18 

⇒x – y = -2 ……..(ii) 

On subtracting (ii) from (i), we get: 

x = 3 

On substituting x = 3 in (i) we get 

2 × 3 –y = 1 

⇒ y = 6 – 1 = 5 

Required number = (10x + y) = 10 × 3 + 5 = 30 + 5 = 35 

Hence, the required number is 35.

Let us consider,

One’s digit of a two digit number = x and

Ten’s digit = y

The number is x + 10y

By interchanging the digits,

One’s digit = y and ten’s digit = x

The number is y + 10x

As per the statement,

xy = 35 ………(1)

And, x + 10y + 18 = y + 10x

18 = y + 10x – x – 10y

x – y = 2 …(2)

using algebraic identity: (x + y)² = (x – y)² + 4xy

(x + y)² = (2)² + 4(35)

= 144

= (12)²

Or x + y = 12 …(3)

Subtracting (2) from (3), we get

2x =14

or x = 7

Form (1) : xy = 35

7(y) = 35

y = 5

Answer: The number is

x + 10y = 7 + 10(5) = 57

Let the tens and the units digits of the required number be x and y, respectively. 

Then, we have: 

xy = 35 …….(i) 

Required number = (10x + y) 

Number obtained on reversing its digits = (10y + x) 

∴(10x + y) + 18 = 10y + x 

⇒9x – 9y = -18 

⇒ 9(y – x) = 18 

⇒ y – x = 2 ……..(ii)

We know: 

(y + x)² – (y – x)² = 4xy 

⇒ (y + x) = ± √( x− y) ² + 4 

⇒ (y + x) = ± √4 + 4 ×35 = ± √144 = ±12 

⇒ y + x = 12 ……..(iii) (∵ x and y cannot be negative) 

On adding (ii) and (iii), we get: 

2y = 2 +12 = 14 

⇒y = 7 

On substituting y = 7 in (ii) we get 

7 – x = 2 

⇒ x = (7 – 2) = 5 

∴ The number = (10x + y) = 10 × 5 + 7 = 50 + 7 = 57 

Hence, the required number is 57.

Let us consider, one’s digit of the two digit number = x and

Ten’s digit = y

The number is x + 10y

By reversing the digits,

One’s digit = y and

ten’s digit = x

The number is y + 10x

Now, As per the statement,

4(x + y) + 3 = x + 10y

4x + 4y + 3 = x + 10y

3x – 6y = -3

x – 2y = -1 ……..(1)

And,

x + 10y + 18 = y + 10x

18 = y + 10x – x – 10y

9x – 9y = 18

x – y = 2 …(2)

On subtracting (1) form (2)

y = 3

Form (1): x = 2y – 1 = 2(3 ) – 1 = 5

Answer:

Number = x + 10y = 5 + 10 (3) = 35

Let’s assume the digit at unit’s place is x and at ten’s place is y. 

Thus from the question, the number we need to find is 10y + x. 

From the question since the number is 4 times the sum of the two digits. We can write, 

10y + x = 4(x + y)

⇒ 10y + x = 4x + 4y 

⇒ 4x + 4y – 10y - x = 0

⇒ 3x – 6y = 0

⇒ 3(x – 2y) = 0

⇒ x – 2y = 0 ……………… (i) 

Secondly, after reversing the digits, the new number formed is 10x + y. 

Again it’s given from the question that if 18 is added to the original number, the digits are reversed. Thus, we have 

(10y + x) + 18 = 10x + y 

⇒ 10x + y - 10y – x = 18

⇒ 9x – 9y = 18

⇒ 9(x -y) = 18

⇒ x – y = 18/9

⇒ x - y = 2 …………. (ii) 

Now by solving equation (i) and (ii) we can find the value of x and y and thus the number.

On subtracting the equation (i) from equation (ii), we get; 

(x - y) – (x – 2y) = 2 - 0 

⇒ x – y – x + 2y = 2

⇒ y = 2 

Putting the value of y in the equation (i) to find x, we get 

x – 2 x 2 = 0 

⇒ x – 4 = 0 

⇒ x = 4 

Hence, the required number is 10 x 2 + 4 = 24

Human wants are unlimited and productive resources such as land and other natural resources, raw material, capital equipments etc. with which goods and services are produced to satisfy those wants, are scarce. The problem of scarcity of resources is felt not only by individuals but also by the society as a whole. This gives rise to the problem of how to use scarce resources to attain maximum satisfaction. This is generally called ‘the Economic Problem’. Every economic system, be it capitalist, socialist or mixed, has to deal with this central problem of scarcity of resources relative to wants for them. The central economic problem is further divided into four basic economic problems. 

These are:

(i) What to produce : Every society has to decide which goods are to be produced and in what quantities. Whether more guns should be produced or more butter should be produced; or whether more capital goods like machines, equipments, dams etc., will be produced or more consumer goods such as bread will be produced. Not only the society has to decide about what goods are to be produced, but it has also to decide in what quantities these goods would be produced. In a nutshell, a society must decide how much wheat, how many hospitals, how many schools, how many machines, how many metres of cloth, etc. have to be produced.

(ii) How to produce : There are various alternative techniques of producing a commodity. For example, cotton cloth can be produced with either handlooms or power looms or automatic looms. Production with fyandlooms involves use of more labour and production while automatic loom involves use of more machines and capital. A society has to decide whether it will produce cotton cloth using labour-intensive techniques or capital-intensive techniques. Likewise, for all goods and services, it has to decide whether to use labour intensive techniques or capital-intensive techniques. Obviously, the choice would depend on the availability of different factors of production (i.e., labour and capital) and their relative prices. It is in the society’s interest to use those techniques of production that make best use of the available resources.

(iii) For whom to produce : Another important decision which a society has to take is for whom to produce. The society cannot satisfy all the wants of all the people. Therefore, it has to decide who should get how much of the total output of goods and services. In other words, it has to decide about the share of different people in the national cake of goods and services.

(iv) What provision should be made for economic growth : A society would not like to use all its scarce resources for current consumption only. This is because if it uses all the resources for current consumption and no provision is made for future production, the society of the people would remain stagnant, and in the future, the level of living may decline. Therefore, a society has to decide how much savings and investment (i.e. how much sacrifice of current consumption) should be made for future progress.

Different economies solve the central problems differently:

Following are the details:

Market Economy : The market economy is an independent economy; it means that the producers are free to make decisions, on what basis do they make their decisions on ‘how and for whom?’ Yes, it is based on the value system. Producers choose to produce goods in which the prices are relatively high because they are interested in maximizing their revenue, they would like to adopt the production technology or would like to use those inputs, whose the price is relatively low. Because they are interested in reducing their costs. They will produce goods, and services for those buyers who are ready to provide them the maximum possible value, because they are interested in maximizing their profits.

Centrally Planned Economy : Decision relating to a centrally planned economy, is made by some central authority appointed by the government of the country, on ‘what, how and for whom’? and not on the basis of price mechanism.

All decisions are taken into account to maximize social welfare, and contrary to the market economy, maximization of profit is not considered. Those goods and services will be produced which the central authority (or government) finds most useful for the society. That technology of production will be adopted which is socially most useful. For example, in case of collective unemployment, labour-intensive technology will be given preference (rather than capital intensive technology) so that unemployment is low. Goods will be produced preferably for those residents who suffer from hunger or starvation, even when it involves incurring loss in production it.

Mixed Economy : Mixed economy combines the good qualities and avoids the flaws of market economy and centrally organized economies. Decision on the basis of price mechanism as well as on ‘what, how and for whom’ ? the goods are to be produced is based on social considerations. Such a situation can be described as the condition of ‘regulated price system’. In some areas of production, the producers are free to make their own decisions, while in other areas, decisions are taken entirely on the basis of social considerations. For example, In India, growers are free to produce cloth or steel to maximize their profits. But post and telegraph services are the monopoly of the government. The government provides these services at a nominal rate so that the poorest can afford them.

The activities related to the production, distribution and consumption of goods and services in a specific region is called economy. On the basis of economies, countries are divided into three groups.

Capitalist Economy, Socialist Economy and Mixed Economy.

1. Capitalistic Economy is a kind of economy in which the means of production is in the hands of the private sector, e.g. Germany, Japan, the U.S.A. 

2. Socialist Economy is a kind of economy in which the means of production belongs to the society i.e. the government’s control, e.g. China, Russia. 

3. Mixed Economy is a kind of economy in which there is a co-existence of both private and public sectors, e.g. India, Sweden, the U.K.

Helpful in analysis of the individual unit problem.

Economics is an important Social Science Subject.

• We use Economics on a large scale in agriculture, trade, finance, administration, law and in our daily life. 
• Economics holds a paramount importance in the overall social development of humans.

1. Economics is a study of people in ordinary business of life – Alfred Marshall (1890). 

2. “Economics is study of wealth” Adam Smith 1776 (Father of economics)

(c) because of both (a) and (b)

Adam smith is the father of economics. Economics is the study of wealth.

No, I cannot imagine a situation of scarcity without the problem of choice because scarcity and choice are inseparable at all levels of decision-making.

Correct option is (4) a, b, c, and d

Correct option is (d) Adam Smith

• According to Lionel Robbins, “Economics is a science which studies human behaviour as a relationship between ends and scarce means which have alternative uses”. 
• Since human wants are unlimited their priority is determined. 
• The satisfaction of the basic needs are given priority. 
• A scarce resource like land can be used either for agriculture or industries or development of infrastructure. 
• In this way, Economics studies human behaviour related to unlimited wants with limited resources that have alternative uses

Every year February 10 and August 10 are observed as the National Deworming Day (NDD). The day aims at eradicating intestinal worms among children in the age group of 1-19 years. On this day, Albendazole tablet (deworming drug) is administered to children.

The correct answer is C) Both A & B.

Epicalyx: 

1. Epicalyx is an additional whorl of sepal like structures formed by bracteole which occurs on the outside of calyx. 

2. These are 5-8 in number. 

3. It is a characteristic feature of family Malvaceae. 

4. They are protective in function, e.g. Ladies finger

GEAC (Genetic Engineering approval committee)

GM crops have the ability to resist diseases So the use of chemical pesticide can be decreased. This helps to keep the nitrogen fixing and other useful microbes in the soil as live.

GEAC (Genetic Engineering Approval Committee) They take decisions regarding the validity of GM research and the safety of introducing GM- organisms for public services.

1. Agro – chemical based agriculture

2. Organic agriculture

3. Genetically engineered crop-based agriculture.

DNA probe is a small DNA segment that recognize complementary sequence in DNA molecule and allow identification and isolation of specific DNA sequence from an organism.

The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. The disorder is caused due to the deletion of the gene for adenosine deaminase. In some children ADA deficiency can be cured by bone marrow transplantation; in others it can be treated by – enzyme replacement therapy, in which functional ADA is given to the patient by injection. But the problem- with both of these approaches that they are not completely curative. As a first step towards gene therapy, lymphocytes from the blood of the patient are grown in a culture outside the body. A functional ADA cDNA (using a retroviral vector) is then introduced into these lymphocytes, which are subsequently returned to the patient. However, as these cells are not immortal, the patient requires “periodic infusion of such genetically engineered lymphocytes. However, if the gene isolate from marrow cells producing ADA is introduced into cells at early embryonic stages, it could be a permanent cure.

Presence of a pathogen (bacteria, viruses, etc.) is normally suspected only when the pathogen has produced a disease symptom. By this time the concentration of pathogen is already very high in the body. However, very low concentration of a bacteria or virus (at a time when the symptoms of the disease are not yet visible) can be detected by amplification of their nucleic acid by PCR.

GEAC – Genetic Engineering approval committee. 

Objectives of GEAC are 

(i) To make decisions regarding validity of GM research. 

(ii) Safety of introducing GMO for public use.

A single stranded DNA or RNA, tagged with a radioactive molecule (probe) is allowed to hybridise to its complementary DNA in a clone of cells followed by detection using autoradiography. The clone having the mutated gene will hence not appear on the photographic film, because the probe will not have complementarity with the mutated gene.

Enzyme Linked Immuno-sorbent Assay (ELISA) is used for the detection of AIDS. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.

Gene expression can be controlled by using RNA molecule. The technology is called RNA interference or RNAi. It is used to block the expression of certain genes and also referred to as gene silencing. During this process a complementary RNA to the mRN A being produced by the gene is introduced into the cell. This RNA binds to the mRNA making it double stranded and therefore stops translation. Resistance to nematode Meloidegyne incognita in tomato has been achieved by this method.

GEAC (Genetic Energy Approval Committee) is an Indian government organisation. 

Its objective are to

 (a) examine the validity of GM (Genetic modification of organism) research.

(b) inspect the safety of introducing GM for public services.

A diagnostic technique helps us to identify a disease.

Example: ELISA is a test for HIV. 

A therapeutic agent on the other hand helps in the treatment of a disease.

Example: Antibiotics for bacterial infections.

Limitations of green revolution:

1. The Green Revolution succeeded in tripling the food supply but yet it was not enough to feed the growing human population. Increased yields have partly been due to the use of improved crop varieties, but mainly due to the use of better management practices and use of agrochemicals (fertilisers and pesticides). However, for farmers in the developing world, agrochemicals are often too expensive, and further increases in yield with existing varieties are not possible using conventional breeding.

2. Use of agrochemicals causes eutrophication in aquatic ecosystems and biomagnification in terrestrial ecosystems.

3. Water logging and soil salinity are some of the problems that have come in the wake of green revolution.

Water of crystallisation

Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: 

1. Made crops more tolerant to abiotic stresses (cold, drought, salt, heat).

2. Reduced reliance on chemical pesticides (pest-resistant crops).

3. Helped to reduce post-harvest losses.

4. Increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil).

5. Enhanced nutritional value of food, e.g., Vitamin ‘A’ enriched rice.

1. Sodium sulphate

Na₂CO₃ + H₂SO₄ → Na₂SO₄ + H₂O + CO₂

2. Zinc carbonate

Zn(NO₃)₂ + Na₂CO₃ → ZnCO₃ + 2NaNO₃

3. Copper (II) sulphate

CuCO₃ + H₂SO₄ → CuSO₄ + H₂O + CO₂

4. Iron (II) sulphate.

Fe + H₂SO₄ → FeSO₄ + H₂

GMO stands for Genetically Modified Organism. It differs from a hybrid because in a hybrid,cross is done between total genomes of two species or strains, where as in a GMO, foreign gene(s) is introduced in the organism and is usually maintained as extra-chromosomal entity or is integrated into the genome of the organism. .

Guru Nanak Dev Ji spent his last years at Kartarpur (now in Pakistan).

Guru Nanak Dev Ji had started showing disinterest in education and worldly affairs at a very young age. His father engaged him in cattle grazing to divert his interest to worldly affairs. While on cattle-grazing rounds, he remained engrossed in deep meditation and his cattle strayed into fields of the other people. Troubled by the complaints of neighbouring farmers, his father decided to put him in business. He gave him twenty rupees to start some business but Guru Nanak Dev Ji spent all the money in feeding the saints and wanderers. This incident of his life is popular as ‘Sacha Sauda’ or the Pious Deal.

Guru Arjan Dev Ji brought about the following social reforms:

1. Guru Sahib tried to encourage widow remarriage.
2. Guru Sahib prohibited the use of liquor and intoxicants by his Sikh followers.

The natural solid fuel is Coal

Akbar had very friendly relations with Guru Arjan Dev Ji. The opponents of Guru Arjan Dev Ji tried to poison the ears of Akbar against Guru Sahib, but Akbar rebuffed them. Due to Guru Sahib’s advice, Akbar remitted the land tax of the farmers of Punjab during the year of bad harvests.

The history of Sikh religion entered a new phase with the coming of Guru Arjan Dev Ji to Guru Gaddi. It was the result of his efforts that Sikhs were blessed with Harmandir Sahib Ji and numerous other places of pilgrimage. Not only that, the Sikhs got their first sacred and divine book when Guru Arjan Dev Ji compiled the Adi Granth Sahib. The Hindus had their Ramayana, the Muslims their Quran Sharif, the Christians their Bible, and the Sikhs their Guru Granth Sahib Ji.

A brief description of the activities and contributions of Guru Arjan Dev Ji is given as follows:

1. Construction of Sri Harmandir Sahib: Guru Arjan Dev Ji completed the work of construction of Amritsar and Santokhsar Sarovars after the expiry of Guru Ram Das Ji. Guru Sahib constructed Sri Harmandir Sahib in the midst of Amritsar Sarovar. Guru Sahib constructed a door each in all the four directions of Sri Harmandir Sahib. These four doors convey the message that Sri Harmandir Sahib is open to all the religions, castes and tribes without any discrimination. Guru Sahib told his followers that a pilgrimage to Sri Harmandir Sahib would bestow the benefit of 68 places of pilgrimage of the Hindus. In this manner, Sri Harmandir Sahib became one of the most sacred and important rebgious places.

2. Foundation of Tarn Taran: Guru Arjan Dev Ji founded the city of Tarn Taran as well. The city was founded in the heart of Majha region. It is also an important place of pilgrimage like Amritsar for the Sikhs. Guru Ji also constructed many other buildings and Sarovars.

3. Construction of Baoli at Lahore: On his tour to Lahore, Guru Arjan Dev Ji got constructed a Baoli in the Dubbi Bazaar. The Baoli soon became an important place of pilgrimage for the Sikhs of the surrounding region.

4. Foundation of Hargobindpur and Chheratta: Guru Arjan Dev Ji founded the city of Hargobindpur on the banks of river Beas to celebrate the birth of his son Hargobind Ji. Apart from this he also got a well dug at Chheratta near Amritsar in order to provide water to the local people. Guru Sahib also arranged for six pulleys to draw Water from the well and the area is known after those pulleys as Chheratta.

5. Foundation of Kartarpur: In 1593, Guru Arjan Dev Ji founded the city of Kartarpur and also built a Sarovar in Kartarpur which is called Gangsar.

6. Improvement in the Masand System: Guru Arjan Dev Ji felt the need to improve Masand system. Guru Sahib instructed the Sikh followers to deposit one-tenth (Daswandh) of their annual income with the Masands. The Masands deposited the collections in the main treasury (Guru Ki Golak) at Amritsar on every Baisakhi day. The Masands appointed their representatives to collect donations. Those representatives were called Sangatias. The one-tenth donation was called Daswandh. Apart from the work of collection of Daswandh, the Masands also spread the message of Sikh religion.

7. Compilation of the Adi Granth Sahib: Gum Arjan Dev Ji bestowed upon the Sikhs a sacred and religious book by compiling the Adi Granth Sahib. Guru Ar^an Dev Ji compiled Adi Granth Sahib at Ramsar. Bhai Gurdas Ji assisted Guru Sahib in its compilation. The work of compilation was cofnpleted in 1604. Guru Sahib included the hymns of first four Gurus, followed by the hymns of Bhakti saints and finally the sayings of Bhatt Bahiyan. Guru Arjan Dev Ji also included his own Bani in the holy book.

8. Encouraged Horse Trade: Guru Arjan Dev Ji encouraged the Sikhs to start trading in horses. The Sikhs were benefited from the trading in horses in the following ways:

• Trading in horses was the most profitable business in those days. As a result, the Sikhs became very rich by trading in the horses. They contributed Daswand regularly out of their income from this trade.
• The Sikhs became fully trained in making a selection of good horses. It helped them in the long run in organising a Sikh cavalry.

9. Spread of Religious Teachings: Guru Arjan Dev Ji made many people his followers by his religious teachings. Guru Sahib impressed the people with his ideals, teachings, amiable personality, sweet temper, and toleration. Many Muslims also joined the Sikh religion under the influence of Guru Arjan Dev Ji.
Thus the Sikh religion progressed tremendously under the spiritual leadership of Guru Arjan Dev Ji. The Adi Granth Sahib, the most sacred book of the Sikhs, was compiled, the cities like Tara Taran, Kartarpur, Hargobindpur, were founded and the Sikh religion was blessed with Sri Harmandir Sahib.

The crystalline allotrope of carbon is Graphite

1. LPG

2. three, four 

3. Oxygen

Petrol, diesel, kerosene, wood and coal