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Concept:

Geometric Progression (GP): The series of numbers where the ratio of any two consecutive terms is the same, is called a Geometric Progression.

​A Geometric Progression of n terms with first term a and common ratio r is represented as:

a, ar, ar², ar³, ..., ar^n-2, ar^n-1.

Calculation:

Given: Sum of the first two terms of GP is -2 and the fifth term of GP is 4 times the third term of GP

According to the question:

a + ar = -2           ...(1)

ar⁴ = 4 × ar²

r = ±2         ...(2)

Using equation (1), we get:

a = \(-\frac{2}{3}\)

Now, the sixth term of the GP = ar⁵ = \(-\frac{64}{3}\).

ANSWER IS :- { -4.18 }

log\(\frac{(0.01)^2}{1.5}\) = log(0.01)² - log 1.5 (log A/B = log A - log B)

= 2 log 0.01 - log 3/2

= 2 log 1/100 - (log 3 - log 2)

 = 2 log 10^-2 - log 3 + log 2

 = 2 x -2 log 10 - log 3 + log 2

 = -4 x 1 - 0.4771 + 0.3010 (\(\because\) log 10 = 2, log 3 = 0.4771, log 2 = 0.3010)

 = -4 .4774 + 0.3010

 = -4.1761

p ↔ q ≡ (p → q) ʌ (q → p)

≡ (∼p v q) ʌ (∼q v p)

\(\therefore\) ∼ (p ↔ q) ≡ ∼((∼p v q) ʌ (∼q v p))

≡ ∼ (∼ p v q) v ∼(∼ q v p)

(\(\because\) ∼(A ʌ B) ≡ ∼ A v ∼B)

≡ (∼(∼p) ʌ ∼ q) v (∼(∼q) ʌ ∼p)

≡ (p ʌ ∼q) v (q ʌ ∼p)

Hence, p ↔ q is logically equivalent to (p ʌ ∼q) v (q ʌ ∼p)

(a) Marginal revenue

Gandhian Economics is based on ethical foundations. Gandhi wrote “ Economics that hurts the moral well-being of an individual or a nation is immoral, and therefore , Sinful”. Gandhi repeated the same belief “ that economy is untrue which ignores or disregards moral values”.

Salient features of Gandhian Economic Thought:

(I) Village Republics: 

1. India lives in villages. 

2. He was interested in developing the villages as self – sufficient units.

3. He opposed extensive use of machinery, urbanization and industrialization.

(II) On Machinery:

1. Gandhi described machinery as ‘Great sin’. He said that “Books could be written to demonstrate its evils”. 

2. It is necessary to realize that machinery is bad. 

3. Instead of welcoming machinery as a boon, we should look upon it as an evil. 

4. It would ultimately cease..

(III) Industrialism:

1. Gandhi considered industrialism as a curse on mankind. 

2. He thought industrialism depended entirely on a country’s capacity to exploit.

(IV) Decentralization: Gandhi advocated a decentralized economy i.e., production at a large number of places on a small scale or production in the people’s homes. 

(V) Village Sarvodaya: 

1. According to Gandhi, “Real India was to be found in villages and not in towns or cities”. 

2. He suggested, self – dependent villages. 

(VI) Bread Labour: 

1. Gandhi realized the dignity of human labour. 

2. He believed that God created man to eat his bread by the sweat of his brow. 

3. Bread labour or body labour was the expression that Gandhi used to mean manual labour.

(VII) The Doctrine of Trusteeship: Trusteeship provides a means of transforming the present capitalist order of society into an egalitarian one.

(VIII) On the Food Problem:

1. Gandhi was against any sort of food controls. 

2. Once India was begging for food grain, but now India tops the world with very large production of food grains, fruits, vegetables, milk, egg, meat etc.

(IX) On Population:

1. Gandhi opposed the method of population control through contraceptives. 

2. He was, however, in favour of birth control through Brahmacharya or self – control.

3. He considered self – control as a sovereign remedy to the problem of over population,

(X) On Prohibition:

1. Gandhi regarded the use of liquor as a disease rather than a vice. 

2. He felt that it was better for India to be poor than to have thousands of drunkards. 

3. Many states depend on revenue from liquor sales.

(a) M.S. Swaminathan

(b) Must be less than average product

Transport: Tamil Nadu has a well established transportation system that connects all parts of the State. This is partly responsible for the investment in the State.

Tamil Nadu is served by an extensive road network in terms of its spread and quality, providing links between urban centres, agricultural market-places and rural habitations in the countryside. However, there is scope for improvement.

Road Transport:

1. There are 28 national highways in the State covering a total distance of 5,036 km. 

2. The State has a total road length of 167,000 km, of which 60,628 km are maintained by Highways Department.

Rail Transport:

1. Tamil Nadu has a well-developed rail network as part of Southern Railway, Head quartered at Chennai. 

2. Tamil Nadu has a total railway track length of 6,693 km and there are 690 railway stations in the State. 

3. Main rail junctions in the State include Chennai, Coimbatore, Erode, Madurai, Salem, Tiruchirapalli and Tirunelveli. 

4. Chennai has a well – established suburban Railway network, a Mass Rapid Transport system and is currently developing a Metro System, with its first underground stretch operational since May 2017.

Air Transport:

1. Tamil Nadu has four major international airports.

2. Chennai International Airport is currently the third largest airport in India. 

3. Other international Airports in Tamil Nadu include Coimbatore International Airports, Madurai International Airport and Tiruchirapalli International Airport. 

4. It also has domestic airports at Tuticorin, Salem, and Madurai. 

5. Increased industrial activity has given rise to an increase in passenger traffic as well as freight movement which has been growing at over 18% per year.

Ports:

1. Tamil Nadu has three major ports; one each at Chennai, Ennore and Tuticorin, as well as one intermediate port in Nagapattinam, and 23 minor ports.

2. The ports are currently capable of handling over 73 million metric tonnes of cargo annually (24 % share of India). 

3. All the minor ports are managed by the Tamil Nadu Maritime Board, Chennai Port. 

4. This is an artificial harbour and the second principal port in the country for handling containers. 

5. It is currently being upgraded to have a dedicated terminal for cars capable of handling 4,00,000 vehicles. 

6. Ennore port was recently converted from an intermediate port to a major port and handles all the coal and ore traffic in Tamil Nadu.

(c) Equations

Identify the formuld of estimating average cost TC/Q.

(a) Marginal product

The Headquarters of Southern Railway is at Chennai.

1. Tamil Nadu is the largest textile hub of India.

2. Tamil Nadu is known as the “Yam Bowl” of the country accounting for 41% of India’s cotton yam production. 

3. The textile industry plays a significant role in the Indian economy by providing direct employment to an estimated 35 million people, and thereby contributing 4% of GDP and 35% of gross export earnings. 

4. The textile sector contributes to 14% of the manufacturing sector. 

5. From spinning to garment manufacturing, entire textile production chain facilities are in Tamil Nadu. 

6. About half of India’s total spinning mill capacity is in Tamil Nadu. 

7. The western part of Tamil Nadu comprising Coimbatore, Tirupur, Erode, Dindigul and Karur has the majority of spinning mills manufacturing cotton, polyester, blended yam and silk yam used by garment units in Tamil Nadu, Maharastra etc.,

8. Yam is also exported to China, Bangladesh, etc., 

9. Tirupur known as “knitting city” is the exporter of garments worth USD (United States Dollar) 3 billion. 

10. Karur is the major home for textile manufacturing (curtain cloth, bed linens, kitchen linens, toilet linens, table linens, wall hangings etc.,) and export hub in India. 

11. Erode is the main cloth market in South India for both retail and wholesale ready – mades.

The cost per unit of output is denoted by Average cost.

Revenue received from the sale of additional unit is turned as Marginal revenue.

Rent is the reward for the use of Land.

(d) All the above

(c)  Margina

Correct option is: (B) 0

Genetic variation affects the production of the drug principle reserpine
in the medicinal plant Rauwolfia

(B) Two adjacent pyrimidine residues to form covalently bonded dimer 

(B) 60 S ribosomal subunit

(C) Ribosomal protein

(B) Cyclohexamide blocks elongation during translation