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Homology is based on divergent evolution. These have similar anatomical structure but perform different function. 

Example - Thorn of Bougainvillea and tendril of cucurbita/Forelimbs of human and horse. (any other appropriate example).

Detailed Answer:

Homology is based on divergent evolution. It indicates the common ancestry. The homologous organs, though perform different functions but have the same fundamental structure. During development these organs follow the same basic plan of organization but however in adult condition they get modified to perform different function in response to adaptation according to different environmental conditions. e.g. the forelimbs of man, whole and bat. They have same structural plan but have different functions.

Different between homology and analogy are:

Adaptive radiation is defined as the process of evolution of different species in a given geographical area starting from single species and radiated to other habitats.

Example:

• Australian marsupials, each different from the other, have evolved from an ancestral stock.
• Darwin’s finches – from the original seed eating stock insectivores and vegetarian birds have evolved.

Convergent evolution.

Convergent evolution.

Adaptive Radiation 

▪ It is the evolutionary process in which different species starting from a common point in a geographical area radiate to other geographical areas. Examples: 

i. Darwin’s finches 

• Darwin observed many varieties of finches in the same island. 

• All varieties had evolved from original seed-eating finches. 

• With alteration in beaks some became insectivorous and some vegetarian.

Oparin and Haldane proposed that the first life form could have come from the „ nonliving organic molecules like RNA, protein etc.

The orgaine molecules must have been produced by chemical evolution, i.e. formation of divers organic molecules from inorganic constituents.

The condition, of the earth that favoured chemical origin were

(i) very high temperature 

(ii) volcanic storms

(iii) Reducing atmosphere that contained methane, ammonia and water vapour. 

• Energy must have been produced by U-V radiation and lightning.
• Analysis of the products of their experiment showed the presence of amino acids which help to form proteins.

The first formed cells were anaerobic heterotrophs. But slowly some of these cells developed coloured proteins, that could release oxygen, in a process that could have been similar to the light reactions of photosynthesis. As oxygen started coming into the atmospheres is as the atmosphere started becoming an oxidising one, new formes of life could not arise from nonliving organic molecules.

The organisms started becoming aerobic and autotrophic. The single celled organism slowly became multicellular form, where some became autotrophic while many remained heterotrophic. Plants like bryophytes were the first to invade land, followed by reptiles among animals.

Different birds Archaeopteryx.

Darwin’s finches of Qalapago island exhibiting a variety of beaks.

Yes, Darwin has been aware of Mendel’s work. Even though Mendel had talked of inheritable ‘factors’ influencing phenotype, Darwin either ignored these observations or kept silence. Darwin would have been able to explain the origin of variations. He asserted that variations, which are heritable and which make resource utilisation better for few (adapted to habitat better) will enable only those to reproduce and leave more progeny. Hence for a period of time, over many generations, survivors will leave more progeny and there would be a change in population characteristic and hence new forms appear to arise.

In his book, Darwin states that the origin of all life forms is due to random Chance.

(d) CH₄ ,NH₃ ,H₂ ,H₂O

(b) the golden age of the reptiles

(c) H M S Beagle

(c) Greater variation in Asia than in Africa

The term evolution describes heritable changes in one or more characteristics of a population of species from one generation to the other.

• Theory of Special creation : God or super natural powers created the life. 
• Theory of Panspermia/Cosmozoic : Greek thinkers thought units of life called spores were transferred to different planets including earth. 'Panspermia' is still a favourite idea for some astronomers.  
• Theory of Spontaneous Generation : life has come from decaying matter like straw. 
• Louis Pasture discarded the spontaneous generation of life by using swan necked flask experiment.

(b) origin of universe

Big bang theory explains the origin of universe as a singular huge explosion in physical terms. The primitive Earth had no proper atmosphere, but consisted of ammonia, methane, hydrogen and water vapour. The climate of the Earth was extremely high. UV rays from the Sun split up water molecules into hydrogen and oxygen. Gradually the temperature cooled and the water vapour condensed to form rain. Rain water filled all the depressions to form water bodies. Ammonia and methane in the atmosphere combined with oxygen to form carbon dioxide and other gases.

• Single huge explosion expanded universe. The gases condensed under gravitation and formed the galaxies of the present day universe.
• There was no atmosphere on early earth. Water vapour, methane, carbondioxide and ammonia released from molten mass covered the surface. 
• The UV rays from the sun brokeup water into Hydrogen and Oxygen and the lighter H₂ escaped.
• Oxygen combined with ammonia and methane to form water, CO₂ and others. The ozone layer was formed.

(a) 

▪ There has been gradual evolution of life forms with new forms arising at different periods of history. 

▪ Any population has built-in variations in characteristics which adapt it better to environment. 

▪ The characteristics which enable some populations or individuals to survive better in natural conditions (climate, food, physical factors) would out-breed others (Survival of the fittest). 

▪ Those populations which are better fit (reproductively fit) in an environment will be selected by nature and will survive more (Natural selection). 

▪ Adaptability is inherited and fitness is the end result of ability to adapt and get selected by nature. 

(b) Natural selection is based on following factual observations: 

• Limited natural resources.

• Stable population size except seasonal fluctuation.

• Varying characteristics of members of a population. 

• Most of the variations are inherited.