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y – 3 = -4 (x + 2) 

i.e., 4x + y + 5 = 0.

Let ‘x’ be the marks obtained by student. 

Then (62 + 48 + x)/3 ≥ 60 ⇒ 110x + x ≥ 180, x ≥ 70

1. Given; 4x + 3 < 5x + 7

⇒ 4x – 5x < 7 – 3 

⇒ -x < 4 

⇒ x > -4. 

2. Given; 3(x – 1) < 2(x – 3) 

⇒ 3x – 3 ≤ 2x – 6 

⇒ 3x – 2x ≤ -6 + 3 

⇒ x ≤ -3.

Given;  \(\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}\)

⇒ 9(x – 2) ≤ 25(2 – x) 

⇒ 9x – 18 ≤ 50 – 25x 

⇒ 9x + 25x ≤ 50 + 18 

⇒ 34x ≤ 68 

⇒ x ≤ 2.

Let x denote the mark obtained by the student in Class XI examination, then;

 \(\frac{62+48+x}{3}\) ≥ 60 

⇒ 110 + x ≥ 1800 

⇒ x ≥ 70.

y = a^x + x²

\(\frac{\text{dy}}{\text{dx}} = \) \(\frac{\text{}d}{\text{dx}}\)a^x + \(\frac{\text{d}}{\text{dx}}\)x²

= a^x log a + 2x

(∵ \(\frac{\text{}d}{\text{dx}}\) a^x = a^x log a)

Concept: The LCM of two variables can be found using multiplying two variables.

Calculation:

Given: Subtract p/q and r/s

p/q - r/s

Taking LCM of q and s, that is, multiplying them, we get

(ps - qr)/qs

Hence, we conclude that by subtracting p/q and r/s, we get (ps - qr)/qs.

Synthetic division is a shortcut method for dividing a polynomial by a simple divisor of the form (x - n). The divisor must be of that form in order for synthetic division to work. If it's not, you'll have to use long division.

If you are given, say, the polynomial equation y = x²+ 5x + 6, you can factor the polynomial as y = (x + 3)(x + 2). Then you can find the zeroes of y by setting each factor equal to zero and solving. You will find that x = –2 and x = –3 are the two zeroes of y.

Synthetic division uses only the coefficients of a polynomial, or the constants in front of each x-term, so it saves a ton of writing compared to using long division of polynomials.

y = 9 log 3x

\(\cfrac{dy}{d\text x}=\cfrac{9}{3\text x}\times\cfrac{d}{d\text x}3\text x\) 

\(\Big(\)\(\therefore\cfrac{d}{d\text x}log \text x=\cfrac1{\text x}\) and chain rule\(\Big)\)

\(=\cfrac{9}{3\text x}\times3\) = \(\cfrac9{\text x}\)

The raw data is classified in various ways depending on the purpose. Generally data can be classified as follows:

• Chronological classification: When the data is grouped according to time, it is called as chronological classification, in such a classification, data are classified either in ascending or in descending order with reference to time such as years, quarters, months weeks days, etc. 
• Spatial classification: If the data are classified with reference to geographical locations such as countries, states, cities, districts, etc., it is called spatial classification. 
• Qualitative classification: When the data are classified on the basis of certain attributes or qualities like literacy, religion, gender, marital status etc., then it is called qualitative classification. These attributes can be classified on the basis of either the presence or the absence of a qualitative characteristic. 
• Quantitative classification: If the classification of data is done on the basis of certain characteristics like height, weight. age, income, marks of students etc., it is called as quantitative classification.

Sampling error refers to the differences between the sample estimate and the actual value of a characteristic of the population. It is the error that occurs when you make an observation from the samples taken from the population.

Thus, the difference between the actual value of a parameter of the population and its estimate is the sampling error. It is possible to reduce the magnitude of sampling error by taking a larger sample.

For example, suppose the height of 5 students (in inches) are 50, 55, 60, 65, 70. Now, the average height will be calculated by adding all these observations and dividing the sum by 5 . then we get 60 inches. If we select a sample of two students with height of 50 and 60 inches, then average height of sample will be 50 + 60 divided by 2, we get 55 inches. Here the sampling error of the estimate will be 60 (true value) minus 55 (estimate) = 5.

Organic farming is free from chemicals.

A measure that divides the series into hundred equal parts is called Percentiles.

Price index numbers measure the general changes in prices between the current year and the base year. The general price index is used to measure the value of money. 

The following are the different types of price index numbers:

• Consumer Price Index 
• Wholesale Price Index 
• Retail Price Index 
• Producer Price Index.

Statistics plays a very important role in the field of economics. It helps in study of economics in many ways:

1. It helps to understand economic problems: By using various statistical tools, effort is being made to find the causes behind the economic problems with the help of qualitative and the quantitative facts. Once the causes of a problem are identified. it is easier to formulate certain policies to tackle them.

2. It enables an economist to present economic facts in a precise and definite form: Statistics help the economists to present economic facts with accuracy. It also helps in proper comprehension of that is stated in the subject matter. When economic facts are expressed in statistical terms. they become exact. Exact facts are more convincing than vague statements. For instance, saying 350 people have died in Kashmir unrest since 2000. is more accurate than saying that a lot of people have died in the unrest.

3. Helps in condensing mass data into a few numerical measures: Statistics condenses the mass data into a few numerical measures like mean, variance, correlation, etc. These numerical measures help to summarise data. For example, it would be impossible to remember the income of all the people of a country. But we can remember average income i.e., per capital income. 

4. It is used to find relationships between different economic factors: An economist may be interested in finding out what happens to the demand for a commodity when its price changes or what will be impact on inflation, when the government has more budget deficits. Such situations can be dealt, if any relationship exists between the various economic factors. Here, the nature of relationship can be studied with the help of statistical tools.

5. It helps in formulation of plans and policies: Sometimes, formulating plans and policies require the knowledge of future trends. For instance, an economic planner has to decide in 2010 how much the economy should produce in 2016-17. In other words, one must know what could be the expected level of consumption in 2016-17. So. the statistical tools to predict consumption in 2016-17 could be based on the data of consumption of past years obtained by surveys.

Infrastructure facilities can be classified into Two types.

Environment refers to the totality of the physical conditions on the earth or a part of it. In other words, it refers to physical surroundings. conditions, circumstances. etc., in which a person lives.

Environment is defined as the total planetary inheritance and the totality of all resources and includes biotic (birds, animals and plants, forests, fishes) and a biotic (air, water, land, rocks and sunlight) factors.

Thy major functions of environment are as follows:

• The environment supplies both renewable and nonrenewable resources. Renewable resources are those resources that can he used again and again. There will be a continuous supply of resources. Example, water, forest, land etc.
• Non-renewable resources are those which get exhausted with extraction and use. Example. mineral resources like petrol. coal, iron ore etc. 
• The environment assimilates waste. That means that environment absorbs the solid and liquid wastes created by humans and other living beings. 
• The environment sustains the life on earth by providing both genetic and bio-diversities. 
• Environment also provides aesthetic sceneries like beautiful scenery of forest lands, water falls, mountains like the Himalaya ranges. lagoons, glaciers, valleys. etc.

Non-renewable resources are those which get exhausted with extraction and use. Example: mineral resources like petrol, coal, iron ore, etc.

It is true that the scarcity is the root of all economic problems. If there had been no scarcity there would have been no economic problem. This would have not necessitated the study of economics.

In our daily life, we face various forms of scarcity. The queues at the railway booking counters, over crowded buses, heavy traffic on roads, the rush to get a ticket to watch a movie of a popular film actor or actress, are all the manifestations of scarcity. We face scarcity because the things that satisfy our wants are limited in availability.

Further, the resources which the producers have are limited and also have alternative uses. For instance, take the case of food that we eat everyday. It satisfies our want of nourishment. 

Farmers employed in agriculture grow crops that produce our food. At any point of time, the resources in agriculture like land, labour, water, chemical fertilizers, etc, all these resources have alternative uses.

The same resources can be used in the production of non-food crops. Thus, alternative uses of resources give rise to the problem of choice between different commodities that can be produced by those resources.

1 d) Sticking to methods to promote inequalities. 

2 True 

3 Directly 

4 a) Both Assertion (A) and Reason (R) are true.

Urban poor are those who live in cities and towns without basic needs. Example: push cart, vendors, street cobblers, women who string flowers, rag pickers, vendors and beggars.

The economic infrastructural facilities are those which directly contribute towards economic development. The ma in economic infrastructures are energy, transportations communication, banking. insurance, warehouse, etc.

1 b) Economic 

2 active role of public and private sectors.

3 True 

4 Higher investment requirements/longer gestation period of the project.

The major threats of environment in India are as follows: 

1. Threat of poverty induced environmental degradation. 

2. Threat of pollution from the rapidly growing industrial sector. air pollution, water contamination, soil erosion, deforestation and wildlife extinction.

The economic infrastructural facilities are those which directly contribute towards economic development. The main economic infrastructures are energy, transportation, communication, banking, insurance, warehouse, etc.

Human capital refers to that part of population which possesses skills, knowledge, education and experience. It also includes the ability of human beings to give their best and their ability to create economic value for things.

The self-employed are those workers who own and operate an enterprise themselves to earn their livelihood. 

The best examples for self-employed are as follows:

• People running petty shops. 
• People having their own transport enterprises. 
• Farmers working in their own farm land. 
• Engineers running their own construction companies. 
• Teachers running their own tutorial or coaching centres. 
• People having their own autos and cabs.

Human memory works with less than its usual capacity in matters like taking medicine. The author explains that human memory represents the willingness to remember certain things. It forgets what it does not wish to remember. Humans are blessed with “selective amnesia”.

The main health indicators are as follows: 

• Infant mortality rate. 
• Maternal mortality rate.
• Life expectancy level. 
• Nutrition level. 
• Incidence of communicable and non-communicable diseases.

1. The English exploited the Indian farmers. 

2. Camel has a big hump on its back. 

3. Elephant is the largest land animal of the present day.

The women who carry out household works like cooking, fetching water and fuel wood and participating in farm labour are generally not included in labour force. This is mainly because, they are not paid wages in cash or in the form of grains mostly there is no payment for them.

• It is the support system for the efficient working of the industrial sector. 
• It encourages speedy development of agricultural sector.

The agriculture and industry largely depend on infrastructure. Transportation of seeds, pesticides, fertilizers and the produce using modem roadways, railways and shipping facilities help in development of agriculture which leads to the development of the economy.

Moneylenders and traders exploited small and marginal farmers and landless labourers by:

• Charging very high rates of interest. 
• Manipulating the accounts to keep them permanently in a debt trap. 
• Trespassing the agricultural lands by misusing their illiteracy. 
• Making debtors into bonded labourers. 

• Commercial Banks 
• Regional Rural Banks (RRBs) 
• Cooperative Societies 
• Land Development Banks.

All those who are engaged in economic activities, in whatever capacity-high or low are called workers. Even if some of them temporarily abstain from work due to illness, injury or other physical disability, bad weather, festivals, social or religious functions are also workers. Apart from these, the labour force also consists of those who help the main workers and other self employed workers.

Rural development means improvement of the socioeconomic lives of rural people by providing basic infrastructures which make them to engage in productive activities. In simple words, the term rural development refers to the overall development of the rural economy.

Education and health are two main sources of human capital. Education raises the standard and quality of living of people. It increases the productive capacity and productivity of the workforce by enhancing their skills. Health indirectly helps in the economic development by supplying active energetic and healthy work force for better production.

The various forms of health expenditures are as follows: 

• Preventive medicine (vaccination). 
• Curative medicine (medical intervention during illness). 
• Social medicine (spread of health awareness). 
• Provision of clean drinking water and good sanitation.

Starvation and hunger are the main features of the poorest households. They do not possess any assets. They live in slums and some sleep in public places. In rural areas, they are landless labourers. Many do not get even two meals a day. They lack basic literacy and skills and have limited economic opportunities.

Sustainable development is the development that satisfies the needs of the present without compromising the capacity of future generations, guaranteeing the balance between economic growth, care for the environment and social well-being.