Let x be any positive integer. Then, it is of the form 3q or, 3q + 1 or, 3q + 2.

So, we have the following cases :

Case I : When x = 3q.

then, x³ = (3q)³ = 27q³ = 9 (3q³) = 9m, where m = 3q³.

Case II : When x = 3q + 1

then, x³ = (3q + 1)³

= 27q³ + 27q² + 9q + 1

= 9 q (3q² + 3q + 1) + 1

= 9m + 1, where m = q (3q² + 3q + 1)

Case III. When x = 3q + 2

then, x³ = (3q + 2)³

= 27 q³ + 54q² + 36q + 8

= 9q (3q² + 6q + 4) + 8

= 9 m + 8, where m = q (3q² + 6q + 4)

Hence, x³ is either of the form 9 m or 9 m + 1 or, 9 m + 8.

Major steps that were taken towards decentralisation in 1992 were:

• It was made obligatory to hold elections for choosing members of local governmental institutions
• Seats were reserved for people belonging to scheduled castes and scheduled tribes and other backward classes in local bodies.
• One-third of the seats are reserved for women.
• State Election Commission was constituted in the states for holding elections in government bodies.
• It was made mandatory for the State Governments to share powers and revenues with local bodies.

To show experimentally that carbon dioxide is released during respiration.

Procedure:
1. Take the conical flask and place some germinating gram or pea seeds in it.

2. Insert the shorter end of the glass tube through the hole in the cork and fix it on the conical flask.

3. Before fixing the cork, hang a test tube containing KOH solution inside the conical flask with the help of a thread.

4. Take coloured water in the beaker and keep the longer end of the glass tube dipped inside it.

5. Make the conical flask airtight by applying Vaseline on its rim.

6. Note the initial level of water in the tube.

7. Observe and note the rise in the water level after an hour, without disturbing the apparatus.

Observations:

Water level rises up in the bent tube. The rise in the level of water indicates that CO2 is produced by germinating seeds during respiration. Actually, the germinating seeds respire and produce CO2, which is absorbed by KOH solution. This creates a vacuum in the conical flask. The air present in the bent glass tube moves into the conical flask. This pulls the water in the bent tube further up.

Let height of air craft = h = 1500√3 and ground distance= d
Then we have tan 60 = h/d
                             √3 = 1500√3/d
                         ⇒  d =1500
The ground distance is  1500m
Let the  ground distance after 15 second is d1
  We have tan 30 =1500 √3/d1
              ⇒  1/√3 = 1500√3/d1
             ⇒     d1 = 4500
The ground distance is 4500m
The plane has traveled d1-d = 4500-1500=3000 m
Plane has traveled  3000 m  in 15 sec.
Hence the speed = distance/time
                           = 3000/15
                           = 200 m/s   or  200*3600/1000 =720 km/h
Speed of Jet plane is 720 km/h

Gomasthas were the officials of the East India Company. They were mainly recruited to supervise, collect supplies and check the quality of cloth woven by the Indian weavers.

But, there were frequent clashes between the Indian weavers and gomasthas because of the following reasons:

1. Gomasthas were very arrogant. They even beat the Indian weavers and whipped them. They came with sepoys.

2. The weavers were paid meager prices for their goods. They could not bargain for their costs. They were not able to sell it to other different buyers instead.

3. Moreover, the Gomasthas were outsiders. Earlier, the brokers were the people who lived in the same villages as the weavers, took care of them and helped them when they were in need. But these Gomasthas punished the weavers if there is any delay in supply.

4. The East India company gave loans to the weavers to purchase the raw materials while placing the order. The loans that were taken by the Indian weavers from the East India Company put them in a pitiable situation that they had to give their finished goods to Gomasthas who punished them for the delay in supply.

Thus, the appointment of Gomasthas led to clashes.

Working

• The axle is rotated such that it moves in the clockwise directions that is AB moves up and CD moves down.
• According to Fleming's Right Hand rule, the induced current is setup in the coil along B1-> AB -> BC -> CD -> B2. This means that the external current flows from B2 to B1.
• After half a rotation, arm CD starts moves up and AB moves down.
• According to Fleming's Right Hand rule, the induced current is setup in the coil along B2-> AB -> BC -> CD -> B1. This means that the external current flows from B1 to B2.
• Thus after every half rotation of the coil, the current changes direction. This is called an AC current.
• AC current(Alternating current) : Changes its direction after equal intervals of time. It is easier to transmit this current over long distances due to lesser loses and hence this is the current that is supplied to our houses from the electricity department.

Scientific name of coconut is Cocos nucifera.The genus is Cocos and the species is nucifera.

The genus name is written first in binomial nomenclature starting with a capital letter, whereas the species name comes second and it starts with a small letter.

Copper metal when exposed to air turns green in colour due to corrosion. When copper vessel is exposed to air in rainy season, the metal reacts with gases and moisture and atmospheric gases to form a mixture of copper carbonate and copper hydroxide. This gives a green colour to the surface of copper metal.  

The reaction is as follows:

2Cu + H₂O + CO₂ + O₂ →  Cu(OH)₂  +  CuCO₃

The consumer movement arose due to the following factors
(i) Dissatisfaction of consumers, as many unfair practices were being indulged by the sellers like short weighing, black marketing, adulteration, etc.
(ii) There was no legal system available for consumers to protect them from exploitation in the marketplace.
If consumers were not happy with a particular brand, product or shop, they generally avoid buying that brand or product or would stop purchasing from that particular shop.
(iii) It was presumed that it was the responsibility of consumers to be careful while buying a commodity or availing of a service.
Evolution of Consumer Movement The Consumer Movement in India started as a social force with the need to protect consumers against unfair and unethical trade practices being followed by many retailers and manufacturers.
These included creating artificial shortages, hoarding cereals and other agricultural products, black marketing of goods and adulteration of cooking oils and food items.
Till 1986, consumer organisations were highlighting issues by writing articles in newspapers and magazines about these bad practices of merchants. But nowadays, as the consumers have become more aware, the number of consumer groups have grown who have highlighted these malpractices. In 1986, the Government of India enacted the Consumer Protection Act, also known as COPRA. This was a major step in the Consumer Movement in India.

Ferrous Minerals:  Ferrous minerals contain iron content and are helpful in the development of metallurgical industries. Iron ore, chromite, cobalt, etc are the examples of ferrous minerals.

Non-ferrous Minerals:  These minerals do not contain iron content and play an important role in a number of industries like, engineering and electrical industries. Copper, zinc, lead and aluminum are the examples of non-ferrous minerals.

 (i) Construction cost of roads is much lower than that of railway lines.
(ii) Roads can traverse comparatively more dissected and undulating topography.

(iii) Roads can negotiate higher gradients of slopes and as such can traverse mountains such as the Himalayas.
(iv) Road transport is economical in transportation of few persons and relatively smaller amount of goods over short distances.
(v) It also provides door-to-door service, thus the cost of loading and unloading is much lower and used as a feeder to other modes of transport such as they provide a link between railway stations, air and sea ports.                           

Resistivity or specific resistance is resistance of a conducting material of unit length and having unit area of cross section. It is a property of material and depends on nature of material.
SI unit is Ohm-m (Ω.m)

Roman Catholic church began to keep an index of prohibited books from mid 16th century because :

(i) printed religious literature stimulated a variety of interpretations of faith, even among the little educated working class in the early 16th century.

(ii) menocchio, an italian miller, reinterpreted the bible in a away that enraged the roman catholic church.

(iii) such instances worried the church about people reading the various interpretations of the religion and questioning the church.

(iv) Hence, it imposed severe controls over publishers and booksellers and began maintaining an index of prohibited books.