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(i) sin (cos^-1(\(\frac{5}{13}\))) = \(\sqrt{1-cos^2(cos^{-1}(\frac5{13}))}\)

 = \(\sqrt{1-(\frac5{13})^2}\) = \(\sqrt{\frac{13^2-5^2}{13^2}}\) = \(\frac{\sqrt{169-25}}{13}\)

 = \(\frac{\sqrt{144}}{13}\) = \(\frac{12}{13}\)

(ii) cos(sin^-1(-7/25)) = \(\sqrt{1-sin^2(sin^-1(-7/25))}\)

 = \(\sqrt{1-(-7/25)^2}\)

 = \(\frac {\sqrt{25^2-7^2}}{25}\) = \(\frac{\sqrt{625-49}}{25}\) = \(\frac{\sqrt{576}}{25}\) = \(\frac{24}{25}\)

(iii) tan(sin^-1(\(\frac{15}{17}\))) = \(\cfrac{sin(sin^{-1}(\frac{15}{17}))}{cos(sin^{-1}(\frac{15}{17}))}\) = \(\cfrac{\frac{15}{17}}{\sqrt{1-sin^2(sin^{-1}(\frac{15}{17}))}}\)

 = \(\cfrac{\frac{15}{17}}{\sqrt{1-\frac{15^2}{17^2}}}\) = \(\cfrac{\frac{15}{17}}{\frac{\sqrt{289-225}}{17}}\) = \(\frac{15}{\sqrt{64}}\) = \(\frac{15}8\)

(iv) cot[cosec^-1(25/7)] = \(\sqrt{cosec^2(cosec^{-1}(25/7))-1}\)

 = \(\sqrt{(\frac{25}7)^2-1}\) = \(\sqrt{\frac{625-49}{7^2}}=\frac{\sqrt{576}}7=\frac{24}7\)

(v) sin (tan^-13/4) = \(\frac{tan(tan^{-1}3/4)}{\sqrt{1+tan^2(tan^{-1}3/4)}}\)

 = \(\frac{3/4}{\sqrt{1+(3/4)^2}}\)

 = \(\cfrac{\frac34}{\frac{\sqrt{16+9}}4}\) = 3/5

(vi) sec (cot^-1(-5/12)) = \(\sqrt{1+\frac{1}{cot^2(cot(-5/12))}}\)

 = \(\sqrt{1+\frac{1}{(-5/12)^2}}\)

 = \(\sqrt{1+\frac{12^2}{5^2}}\) = \(\frac{\sqrt{25+144}}{5}\) = \(\frac{13}5\)

(a) N ( N − 1 ) / 2

(a) British method

(a) Ladder method

The correct answer is Maluti.

• Maluti:
  • It is a tiny village in Jharkhand with more than 70 exquisite terracotta temples dating back to the 17th century.
  • It is known as the village of temples.
  • It originally had an auspicious number of 108 temples, of which only 72 survives today.
  • Maluti’s temples are decked with detailed and intricate terracotta carvings based on Hindu mythologies, especially the epics – Ramayana and the Mahabharata.
  • The main temple of the Maluti site is Ma Mauliksha Temple, which is the main deity of the royal family of Baj Basanta Ray and the Guardian Goddess of Maluti.
  • Global Heritage Fund has declared this site as one of the world’s 12 most endangered cultural heritage sites.

Phenols require harsher conditions, e.g., high temperature. The phenol becomes a complex with AlCl₃ and consequently its activity is decreased.

• It is caused by from factories, demolition works.
• Noise from sirens land speakers used in various festivals etc. 
• The biggest Noise Pollution is produced by traffic and 
• The sea traffic. The Noise Pollution is confined to the harbour due to loading and unloading activities being carried.

The population of the world is unevenly distributed. The distribution of population is expressed in terms of density. The density is the ratio between the numbers of people in to the size of land.

Distribution of population of the world has been divided into three regions.

1. Area of high density: The three principal high density zones are:

(a) Eastern, Southern and South – Eastern part of Asia. 

(b) North – Western part of Europe. 

(c) North – Eastern part of USA and South Eastern part of Canada.

2. Area of high density: The population moderately dense in tropical regions of the world and moist temperature regions of the Argentina South-East Africa and Eastern Australia.

3. Area of low density: The areas which are nearest to the North and South poles hot and cold desertes and high rain fall zones near the equator have very low density of population.

• Asia is the most populous continent. It accounts about ‘61 percent’ of the world population. 
• Africa is second most populated continent with 13 percent. 
• Europe has 12 percent. 
• South America 8.5 percent. 
• Northern America 5 percent. 
• Oceania is the least – populated region which has 0.5 percent. 
• Antarctica is uninhabited permanently

The term sustainable development is defind as development to acheive the needs of present generation without compromising future generation. 

Ex: Sustainable development takes care of ecological, social and economic aspects of development.

Life is a concept in biology. It is about the characteristics, state, or mode that separates a living thing from dead matter. The word itself may refer to a living being or to the processes of which living things are a part.

Answer: 150 million km

1. Megakaryocytes 

2. Sino – atrial node (SAN) 

3. Corpus callosum

1. hepatic portal vein

2. hepatic portal vein carries nutrients from intestine to liver.

There are two restrictions operating this question.
1.  For a number to be odd, the unit digit should be either 1,3,5,7 or 9.
2. Thousand can not be filled with 8 or 9. For unit digit when it is filled with 9,  the thousands place can be filled in 7 ways.
Namely any digit from 1 to 7 the remaining two places can be filled in 8×7=56 ways.
∴Total no. formed in this way=56×7=392
Now if units place is filled with any of the four digits 1,3,5 or 7, the thousand′s place can be filled in 6 ways and the remaining two places can be filled in 8×7=56 Ways.
∴The total no. formed in the way=56×6×4=1344.
∴Total=392+1344=1736

(A) Chief cells of parathyroid glands

False fruit:

In most plants, the development of fruit takes place from the ovary, while other floral parts degenerate and fall off. How ever in a few species such as apple, Straberry etc. The thalamus also contributes to fruit formation. Such fruit are called false fruit. Example: Apple and strawbery.

True fruit:

Most fruit how ever develop only from the ovary and are called true fruits. Example: Berry

Parathenocarpic fruit:

Although in most of the species, fruits are the results of fertilization, there are a few species in which fruits develop without fertilization such fruits are called parthenocarpic fruit, e.g Banana.

Polyembryony:

It is the phnomenon of two or more embroyos devloping from a single fertilizer egg. Due to the embryos resulting from the same egg, the embryos are identical to one another, but are genetically diverse from the parents.

Mutation is the inheritable change occuring in the organisms due to change in chromosome number, structure gene. The term mutation was given by Hugo de Vries. It was first observed in his experimental plant evening primerose. Oenothera lamarckiana. Mutation is following types.

(a) Genomic mutation: It is caused by change in number of chromosomes. It is two types:

(i) Euploidy

(ii) Aneuploidy

(b) Chromosomal aberration: It is due to change in chromosome structure. It is of 2 types.

(i) Intra chromosomal Modification: It is caused by breaking of chromosomal segments and their loss or gain within a single chromosome, e.g. deletion, inversion, etc.

(ii) Interchromosomal modification: Which involve two chromosomes causing loss of one and gain of other e.q duplication, translocation.

Mutation are the raw materials of evolution. Evolution absolutely depends on mutation because this the only way that new alleles and new regulatory regions are created but this seems paradoxical because most mutation that we observe are harmful, neutral or beneficial.

Polymerase-I:

It is the enzyme that carries in the daughter nucleotides and DNA helicase is the one that unwinds the double helix to the replication.

Polymerase-II:

It is specialized repair enzyme. Like Pol I, a large number of Pol II, molecules reside in the cell (about 100). The enzyme is more processive than Pol I.

Genetically modified organism:

It is the result of a laboratory process where genes from the DNA of one species are extracted and artificially forced into the genes of an unrelated plant or animal. The foreign genes may come from bacteria, viruses, insects, animal even human.

Benefits of genetically modified plants are following:

The plants produced through genetic engineering contain genes usually from an unrelated organism. Such genes are called transgenes and the plants having transgenes are called transgenic plants. There is a soil bacterium Bacillus thuringiensis which produces proteins to kill certain insects. These toxic proteins crystals are called insecticidal proteins also named as Bt toxin proteins. Bt toxin proteins exist as inactive protoxins but once an insect ingest the inactive toxin, it is converted into an active form of toxin. The activated toxin binds to the surface of midgut epithelia cells and create pores, which eventually leads to death of the insect.

Such specific Bt toxin genes are isolated from Bacillus thuringiensis and incorporated into several crops such as cotton. The choice of gene depends upon the crop and the targeted pest. Toxin is coded by a gene named Cry.

Micro injection:

It is the use of a glass micropipetle to inject a liquid substance at a microscopic or borderline macroscopic level. The target is of ten a living cell but may also include intercellular space.

Microinjection is a technique of delivering foreign DNA into a living cell (a cell, egg, oocyle of animals) through a glass micro pittle. One end of gass micropipette is heated until the glass becomes some what lialvified. It is quickly stretched which forms a very finde tip at the heated end. The tip of the pipette attains to about 0.5 mm diametre which resembles an injection needle. The process of delivering foreigh DNA is done under a powerful microscope. Cells to be micro injected are place in container.

Restriction endonuclease:

A restriction enzyme is an enzyme that cleaves DNA into fragments at or hear specific recognition sites with in the molcule known as restriction siles.

In genetic engineering restriction enzymes are used to cut DNA into smaller fragments. The cuts are always made at specific nucteotide sequences. Dfferent restriction enzymes recogise and cut different DNA sequences.

(i) One codon codes for only one amino acid. 

(ii) Some amino acids are coded by more than one codon.

Sewage is composed of a total of 90% water and 1% solid wastes. In addition, it also includes various microbes like Colliforms, Streptococci, Clostridia, Lactobacilli, Mincrofungi, Protozoans and micro algae. Such microbes do the natural treatment of sewage.

Hazards of Sewage: The proper placement of sewage has the primary importance. It sewage is treated in river, it has many fateful consequences, as such.

(a) Many water born diseases occur due to infection of such microbes.

(b) Due to this there is deficiency of dissolved oxygen. Due to such oxygen deficiency, many aerial aquatic microbes die.

A. I-4, II-3, III-1, IV-2

C. Decentralised system.

Lencho had complete faith in God. The sentences which tell us about this faith are as follows: 

i. But in the hearts of all who lived in that solitary house in the middle of the valley, there was a single hope: help from God. 

ii. All through the night, Lencho thought only of his one hope: the help of God, whose eyes, as he had been instructed, see everything, even what is deep in one’s conscience. 

iii. “God,” he wrote, “If you don’t help me, my family and I will go hungry this year. 

iv. Lencho showed not the slightest surprise on seeing the money; such was his confidence. 

v. “God: Of the money that I asked for, only seventy pesos reached me. Send me the rest, since I need it very much. But don’t send it to me through the mail because the post office employees are a bunch of crooks. Lencho.”

(A) T_C/(T_H – T_C) 

Order and safety are necessary for any civilization because no civilization can develop in indisciplined society. Society cannot survive without order and safety. If there is no order or discipline our society will destroy itself. If order and safety exist in any society people can make a use of their talent freely. 

While conversing with others we should be very careful about our talk. In general conversation if there is a group we should take a fair share of it and allow others to speak. If we are only two we should share equally. It is not good to go on speaking and speaking. We should give chance to other to speak. This is a good way of conversation.

We should be careful about our speech while conversing with others. We should try to follow some principles in this regard. In our general conversation if the company is large, we should take only fair share of it and allow others to speak. If we are only two, each one of us should share it equally. It is quite tiring to go on listening so when one has already spoken a little, one should keep quite and allow the others to speak. If he does not respond, it means he does not like the conversation to continue.

While conversing with others we should be very careful about our talk. In general conversation if there is a group we should take a fair share of it and allow others to speak. If we are only two we should share equally. It is not good to go on speaking and speaking. We should give chance to other to speak. This is a good way of conversation. 

It was so cold that Halku felt as if all his blood had frozen and that ice rather than blood had filled his veins. When he tried to sleep, the cold tortured him and made his heart beat faster. Halku shivered and was unable to sleep because of the extreme cold. 

Countryside life is better than town life. It is because countryside is full of natural beauty. Countryside life is simple and peaceful. 

The banker came to know that the lawyer had escaped from the cell before the fixed time. He at once went to the cell to verify it. He read the notes of the lawyer and realised how great the lawyer was. He started weeping. He started hating himself as he had gone to kill a noble soul.

Soil is commonly stratified into horizons at different depth. These layers differ in their physical, chemical and biological properties. This succession of super-imposed horizons is called soil profile.

(d) Self and group have a harmonious co-existence

Correct option is (1) 5.11 

\(\underset{Inorganic \\\,\,sample} {AB_r} + AgNO_3 \longrightarrow AgBr(s) + ANO_3\)

∵ 1 mole of Br^- ion precipitated by 1 mole of AgNO₃ to form 1 mol AgBr.

∵ 6 - 4 ml at 0.2 M AgNO₃ is required to complete precipitate the impurity (Br^-).

∴ Number of moles of AgNO₃ required = 0.0064 x 0.2 = 0.00128 mol.

∴ Number of moles of AgBr formed = 0.00128 mol.

∴ Number of moles of Br^- in sample = 0.00128 mol.

∴ Mass of Br^- in sample = 0.00128 x 80 = 0.1024 g

∴ Mass percentage of impurity (Br^-) = \(\frac{0.1024}{2.00} \times 100 \) = 5.12 %

Correct option is  A) had had

Correct option is B) as if