let 'a' be any positive integer and b=2
By euclid's division algorithm
a=bq+r       0≤r<b
a=2q+r       0≤r<2
(i.e) r =0,1
r=0 , a=2q+0=> a=2q
r=1, a=2q+1
if a is the form of 2q then 'a' is an even integer and positive odd integer is of the form 2q+1

The process of unification of Germany:

1. The middle-class Germans had tried to fight for a united nation governed by an elected parliament in 1848 but were repressed by the monarchy and military.

2. Otto von Bismarck, chief minister of Prussian led the movement for unification of Germany. He was supported by the bureaucracy and the Prussian army.

3. After three wars with Austria, Denmark, and France, Prussia won and unified Germany. The Prussian king, William I, was proclaimed the German emperor in January 1871.

The 1848 revolution of the liberals refers to the various national movements pioneered by educated middle classes alongside the revolts of the poor, unemployed and starving peasants and workers in Europe. While in countries like France, food shortages and widespread unemployment during 1848 led to popular uprisings, in other parts of Europe (such as Germany, Italy, Poland, and the Austro-Hungarian Empire), men and women of the liberal middle classes came together to voice their demands for the creation of nation-states based on parliamentary principles. The political, social and economic ideas supported by the liberals were:

•  Politically, they demanded constitutionalism with national unification, nation-state with a written constitution and parliamentary administration.
•  Socially, they wanted to rid society of its class-based partialities and birthrights. Serfdom and bonded labor had to be abolished.
•  Economically they demanded freedom of markets and right to property. The abolition of state-imposed restrictions on the movements of goods and capital.

The female figures as an allegory of the nation:Artists found a way out to represent a country in the form of a person. Then nations were portrayed as female figures.The female figure was chosen to personify the nation did not stand for any particular woman in real life. It gave the abstract idea of the nation a concrete form. Thus the female figure became an allegory of the nation.During the French Revolution artists used the formal allegory to portray idea such as Liberty Justice and the Republic.

The nationalism groups became more increasingly intolerant of each other & were ever ready to go to war by the last quarter of 19th century.The major European powers,in turn,manipulated the nationalist aspirations of the subject peoples in Europe to further their own imperialist aims.There was intense rivalry among the European powers over trade & colonies as well as naval & military might during this period.The rivalries were very evident in the way the Balkan problem unfolded.Each power-Russia,Germany,England,Austro-Hungary-was keen on countering the hold of other powers over the Balkans,& extending its own control over the area.

Giuseppe Mazzini was an Italian revolutionary in 19th century Europe. His contributions were:

• Mazzini was an Italian revolutionary who later became a member of the secret society of the Carbonari.
• At a young age of 24 in 1831, he was exiled for attempting a revolution in Liguria.
• To further spread the revolutionary ideas, he founded two more underground societies- ‘Young Italy’ in Marseilles and ‘Young Europe’ in Berne, whose members were like-minded young men from Poland, France, Italy and the German states.
• Mazzini believed that God had created nations to be the natural units of mankind. Thus, Italy cannot remain divided into various kingdoms. It has to be a single unified republic.
• Following his example, secret societies were set up in Germany, France, Switzerland and Poland. Mazzini’s opposition to monarchy and his vision of democratic republics scared the conservatives. Metternich described him as ‘the most dangerous enemy of our social order’.

Italy, before its unification, was divided into seven states. While northern states were under the Hapsburg dynasty of Austria, central states were under the control of the Pope. Southern states were ruled by the Bourbon dynasty of Spain. Giuseppe Garibaldi has been one of the most celebrated of all Italian freedom fighters. Sailor by profession, he joined the secret society, ‘Young Italy’. He supported King Victor Emmanuel II in his efforts to unify the Italian states. He organised an army to achieve the unification of Italy. People joined his army in large numbers and came to be known as ‘Red Shirts’.

By the end of 1860, he along with his army had conquered the states of Sicily and Naples which further paved the way for the unification of Italy

The history of nationalism in Britain unlike the rest of Europe because:

• In Britain the formation of the nation-state was not the result of a sudden upheaval or revolution.
• The primary identities of the people who inhabited the British Isles were ethnic ones - such as English, Welsh, Scot or Irish.
• The Act of Union (1707) between England and Scotland resulted in the formation of the 'United Kingdom of Great Britain' meant that England was able to impose its influence on Scotland. Scotland's distinctive culture and political institutions were systematically suppressed.
• The Scottish Highlanders were forbidden to speak their Gaelic language or wear their national dress and large numbers were forcibly driven out of their homeland.
• The English helped the Protestants of Ireland to establish their dominance over a largely Catholic country. Catholic revolts against British dominance were suppressed. Ireland was forcibly incorporated into the United Kingdom in 1801.
• The symbols of the new Britain - the British flag, the national anthem, the English language were actively promoted and the older nations survived only as subordinate partners in this union.

The Revolutions of 1830 were a revolutionary wave in Europe which took place in 1830. It included two "romantic nationalist" revolutions, the Belgian Revolution in the United Kingdom of the Netherlands and the July Revolution in France along with revolutions in Congress Poland and Switzerland. It was followed eighteen years later, by another and possibly even stronger wave of revolutions known as the Revolutions of 1848.

Language played an important role in Poland in developing nationalist sentiments. After Russian occupation, the Polish language was forced out of schools and the Rusian language was imposed everywhere. In 1831, an armed rebellion against Russian rule took place which was ultimately crushed. Following this, many members of the clergy in poland began to use language as a weapon of national resistance.

Polish was used for church gathering and all religious instruction. As a result, a large number of priest and bishops were put in jail or sent to Siberia by the Russian authorities as punishment for their refusal to preach in Russian. The use of Polish came to be seen as a symbol of the struggle against Russian Dominance.

 Italy  had a long history of political fragmentation are
(a) Italians were scattered over several dynastic states  as well  as  the multi-national Habsburg empire.
(b) During the middle of the 19th century, Italy was divided into seven states   of   which   only   one, Sardinia-Piedmont was ruled by an Italian Princely House.
(c) The   North    under   Austrian Habsburgs, the center was ruled by the pope and the southern regions were under the domination of the Bourbon kings of Spain.
(d) Even the Italian language had not any standard common form. It had many regional and local variations.  

The act of union of 1707 had a major impact on the Scottish people :
1.rhe Catholic clans that inhabited Scotland faced terrible repression when they tried to assert their freedom.
2.the Scottish Highlanders were forbidden to speak their Gaelic language.
3.they were not allowed to wear their national dresses.
4.a large number of people were driven out of their homeland.

• Political Fragmentation: Like Germany, Italy was also politically fragmented. During the middle of the 19th century, Italy was divided into seven states, of which only one, Sardinia- Piedmont was ruled by an Italian Prince.
• Role ofMazzini: Giuseppe Mazzini made efforts to unite Italian Republic. He had formed a secret society called ‘Young Italy’ for achieving his goal.
• Role of Count Cavour: He was the chief minister who led the movement to unify Italy. He formed a tactful diplomatic alliance with France and defeated the Austrian forces.
• Role of Giuseppe Garibaldi: Garibaldi also formed armed volunteers. In 1860, they marched into South Italy and the Kingdoms of Two Sicilies and succeeded in driving out the Spanish rulers.
• In 1861, Victor Emmanuel II was proclaimed King of United Italy.

When a ray of light is incident normally on a plane mirror it means that the angle of incidence is 0^ₒ. From the law of reflection, we find that angle of reflection is also 0. Thus, for normal incidence on a plane mirror, angle of incidence and angle of reflection are 0^ₒ​.

The principle focus of concave mirror is a point on its principle axis to which all the light rays which are parallel and close to the axis, converge after reflection from the mirror.

Principal Focus of a Concave Mirror:
Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

Answer: A. Banks

1. Formal sources of credit do not include employers as there is no role of these employers all these works are related to banks and the cooperatives.
2. Employers are there merely to serve the bank staff and do the work as it is asked to do by their owner.

3. Moneylenders are informal source of credit

Accessory reproductive organs are those structures which help in the transfer and meeting of the two kinds of *** cells.

Accessory glands in male reproductive system are:

1. Seminal vesicles

2. Prostate gland

3. Cowper's gland

Seminal vesicles secrete an alkaline medium for the transportation of sperms. The mixture of the fluid and sperms is known as semen. Prostate glands pour its alkaline secretion into the semen to neutralize acid in female ******. Secretion of Cowper’s gland acts as a lubricant.

SELF Help Group are small groups of 15-20 members of rural people in particular women belonging to one neighbouhood who meet and saves regularly. The members of the group can take small loan to meet their needs on low interest rate.
Functioning:

• Most of the decisions regarding the savings and loan activities are taken by the group members.
• The group decides as regards the loans to be granted- the purpose, amount, interest to be
  charged, repayment schedule etc.
• Group is responsible for the repayment of the loan.
• Any case of non-repayment of loan, by any one member is followed up seriously by other members in the group.
• The SHG help borrowers overcome the problem of collateral.
• They provide timely loans for a variety of purposes and at a reasonable interest rate.
• The group provrdes a platform to discuss and act on a variety of social issues such as health, nutrition, domestic violence, etc.

Flow of energy in an ecosystem is as follows. 

• The green plants in a terrestrial ecosystem capture about 1% of the energy of sunlight that falls on their leaves and convert it into food energy. 
• When green plants are eaten by primary consumers, a great deal of energy is lost as heat to the environment, some amount goes into digestion and in doing work and the rest goes towards growth and reproduction. 
• An average of 10% of the food eaten is turned into its own body and made available for the next level of consumers.
• Therefore, 10% can be taken as the average value for the amount of organic matter that is present at each step and reaches the next level of consumers. 
• Since so little energy is available for the next level of consumers, food chains generally consist of only three or four steps. 
• The loss of energy at each step is so great that very little usable energy remains after four trophic levels. 
• There are generally a greater number of individuals at the lower trophic levels of an ecosystem, the greatest number is of the producers.
• The length and complexity of food chains vary greatly. 
• Each organism is generally eaten by two or more other kinds of organisms which in turn are eaten by several other organisms. 
• So instead of a straight line food chain, the relationship can be shown as a series of branching lines called a food web.

Flow of energy is unidirectional because the energy that is captured by the autotrophs does not revert back to the solar input and the energy which passes to the herbivores does not come back to autotrophs. 

As it moves progressively through the various trophic levels it is no longer available to the previous level.

Secondly, the energy available at each trophic level gets diminished progressively due to loss of energy at each level.

a ns w e r 

In human beings,  male produce two types of sperm cells, one is having X- chromosome, while other type is having a Y -chromosome. Females produce ova, all of them having X chromosome. 

The value of B is 0°

Step-by-step explanation:

given sin 2B = 2 sin B

we have to find the value of B

then

hence , The value of B is 0°