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Let a and r be the first term and common ratio of given G.P. 

∴ a₄= 16 

⇒ ar³ = 16 and a7 = 128 

⇒ a⁶ = 128 

Dividing (ii) and (i), we obtain

ar⁶/ar³ = 128/16

a3 = 3 

a³ = 2³ 

a = 2 

⇒ From (i), we have 

2(r³) = 16 

r³ = 8 

r³ = 23 

⇒ r = 2 

Hence, the first term and common ratio of the given series is 2 and 2.

Given polynomial is p(x) = x³ + x² – 4x – 4 

x – 2 is its factor, if p(2) = 0 

p(2) = (2)³ + (2)² – 4(2) – 4 = 8 + 4 – 8 – 4 = 0 

Thus, x – 2 is a factor of p(x). 

Now, x³ + x² – 4x + 4 = x²(x + 1) – 4(x + 1) 

= (x + 1) (x² – 4) 

= (x + 1) (x + 2) (x – 2) 

Hence, the required factors are (x + 1), (x + 2) and (x – 2). 

 (B)  E = \((\frac{1}{4\pi\in_0})\; \frac{2\lambda}{r}\)

(i) Light travels denser to rarer, speed of light increases. 

(ii) Red colour of light travels fastest in any medium except air.

(i) Electrical energy. 

(ii) Electrical bell.

(c) 34 × 10⁴Ω + 10%

(i) Flaw Save tomato is a plant having delayed fruit ripening. This was genetically modified by introducing the genes from a fish to reduce the freezer damage of the tomatoes. This gives a long life to tomatoes. 

(ii) Bt crops : Bt cotton and Bt brinjal, these are insect-resistant plants which are produced by introducing a cry gene of Bacillus thuringiensis that encode Cry protein. 

(iii) Virus free crops : Transgenic papaya, peeper, tobacco and tomatoes; these are virus free plants. By using tissue culture method we can produce disease-resistant plants. 

(iv) Biodegradable plastic : The biodegradable plastic is made from lactic acid which is produced at the time of bacterial fermentation of plant materials like discarded stalks of corn. In the process, molecules of lactic acid are chemically grouped to form the biodegradable plastic. In fact, the biodegradable plastic is a material which has most of the properties of plastic except the property of being non-biodegradable. The biodegradable plastic polyhydroxyalkanates eg., polyhydroxylbutyrate (PHB) are obtained commercially by fermentation with bacterium Alcaligenes eutrophus. The genetically engineered Arabidopsis plants produced polyhydroxylbutyrate (PHB) globules in their chloroplasts without effecting plant growth and development. The large scale of polyhydroxylbutyrate (PHB) can be extracted from leaves as well as from transgenic plants.

Objectives of HGP : 

(1) The goals of the original HGP were not only determine all 3 billion base pairs in the human genome with a minimal error rate, but also to identify’ all the genes in this vast amount of data. This part of the project is still ongoing although a preliminary count indicates about 30,000 genes in the human genome, which is far fewer than predicated by most scientists. 

(2) Another goal of the HGP was to develop faster and more efficient methods for DNA sequencing and sequence analysis and the transfer of these technologies to industry. 

(3) Another goal of the HGP is the study of its ethical, legal, and social implications. It is important to research these issues and find the most appropriate solutions before they become large dilemmas. Otherwise its effect will manifest in the form of major political concerns.

(i) Flavr Savor tomatoes are genetically modified tomatoes characterised by delayed ripening and longer shelf life.

(ii) One gene-oneenzyme hypothesis is the idea that genes act to the production of enzymes with each gene responsible for producing a single enzyme that intum affects a single step in a metabolic pathway. Concept was proposed by George Beadle and Edward Lawric Tatum in 1941. 

(iii) Glycine is optically inactive because it does not affect the plane of polarised light. 

(iv) (i) Chargaff’s rule states that purines and pyrimidines are equal in amount ;.e.,A+G = C + T 

(ii) Molar amount of purine adenine is always equal to molar amount of thymine. Similarly guanine is equal by cytosine 

(iii) Sugar deoxyribosome and phosphate occur in equimolar proportion 

(iv) The ratio of A + T/ G + Cis constant for a species. 

(v) Electroporation: It is the technique of introducing DNA into the cell by a brief exposure to a very high voltage electric pulse.

(i) HGP: Human Genome Project. 

(ii) STS: Sequence Tagged Sites. 

(iii) CSIR : Council of Scientific and Industrial Research.

(iv) LAF: Laminar Air Flow. 

(v) SCP: Single Cell Protein. .

NBRI: National Botanical Research Institute 

NBTB : National Biotechnology Board 

BLAST: Basic Local Alignment Search Tool

PIR : Protein Information Resource 

YAC : Yeast Artificial Chromosome

(i) PIR – Protein Information Resources 

(ii) SSB – Single Strand Breaks 

(iii) STS – Sequence Tagged Sites 

(iv) BAC – Bacterial Artificial Chromosome 

(v) GDB-Genomic Data Bank

(i) GDB (Genome Database): It is the official central repository for genome mapping data created by Human Genome Project. Its central node is located at the hospital for sick children. GDB holds a vast quantity of data submitted by hundreds of investigators. The GDB has many useful genome resource web-links on its resource page. 

MGD (Mouse Genome Database) is the primary public mouse genomic catalogue resource. The MGD includes information on mouse genetic markers and nomenclature, molecular segments, phenotypes, comparative mapping data, graphical display of linkage, cytogenetic and physical maps. 

(ii) PDB (Protein Data Bank) : This database has the sequence of those proteins, nucleic acid, whose 3-D structures are known by crystallography or NMR spectroscopy. 

Source : NCBI-USA; EBI, UK. 

PIR (Protein Information Resource): It is an integrated public bioinformatics resource to support genomic, proteomic and system biology, research and scientific studies.

(i) Protein Databases: The protein database is a collection of sequences from several sources, including translations from annotated coding regions in GenBank, RefSeq and TPA, as well as records from SwissProt, PIR, PRF, and PDB. Protein sequences are the fundamental determinants of biological structure and function. Protein databases are more specialized than primary sequence databases. They contain information derived from the primary sequence databases. 

Example : PIR, TIGR, PFam, PRINTS, ProDom, ProSite, ALIGN, SWISS-PROT & TREMBL, etc. 

(ii) Hardware and Software of computers 

Hardware: Hardware is the collection of physical components that constitutes a computer system including peripherals such as the monitor, mouse, keyboard, computer data storage, hard drive disk (HDD), system unit (graphic cards, sound cards, memory motherboard and chips), etc., all of which are physical objects that can be touched. In contrast, software is instructions that can be stored and ran by hardware.
Software: Written programs or procedures or rules and associated documentation pertaining to the operation of a computer system and that are stored in read/write memory. Bases on their goals, they could be Application software, System software, Malicious software or malware, etc.

Compound is PbSO₄

[CO(NH₃)₆]Cl₃

hexamine cobalt (III) chloride

This is to certify that Nikita Singh was a bonafide student of St Xavier School, Kolkata for eleven years. Her date of birth is June 19, 1995. Nikita joined the school in April 2000 in class I and left the school in March 2011, after completion of class XII.

Nikita has proved herself in all fields, from academic to co-curricular activities and sports. Her conduct through the years has been above reproach. She has maintained an impressive academic record. Her results in the school examinations have been commendable. In class X she passed the Indian Certificate of Secondary Education Examination with an aggregate of 90%, scoring 89% in science. In classes XI and XII she opted for science with computer. She has been a conscientious student.

Nikita has a flair for writing, which she uses to her advantage. As the Editor of the School Magazine she acquitted herself with credit. With her creative talents and innovative ideas, the magazine soared great heights.

Pursuing Bharatanatyam as an activity since the age of twelve, Nikita has evolved into a graceful dancer. She has represented the school at various Inter-school Dance competitions and won laurels, both for the school and for herself.

Nikita has been blessed with an innate artistic talent. Consequently, she studied Art as a subject. She stood first in the cartooning and Poster-Making competition held by the Indian Public Schools Conference (IPSC). She also represented the school at a competition organised by the UNICEF on child labour, where phe emerged a winner. She has also been a part of the school Badminton team. The team stood second in the West Bengal State Competition, 2008.

Nikita has always been popular with her teachers and classmates. She is a friendly and outgoing girl with excellent leadership qualities. She has been a source of inspiration and a role model for other students. She has strong moral values and principles.

Nikita intends to pursue Engineering as a career. In am sure her literary and practicality skills along with her determined attitude will help her achieve this aim. Nikita has been an examplary student and an asset for St. Xavier. I hope to see her go from strength to strength in all her endeavours.

Signature 

(S.K. Saxena) 

Principal

Objectives of the Khalistan Movement: 

1. The transfer of the federally administered city of Chandigarh to Punjab. 

2. The transfer of Punjabi-speaking and contiguous areas of Haryana to Punjab. 

3. Decentralization of States under the existing constitution, limiting the Central Government’s role. 

4. The call for land reforms and industrialization of Punjab, along with safeguarding the rights of the weaker sections of the population. 

5. The enactment of an all India Gurudwara (Sikh house of worship) Act. 

6. Protection of minorities residing outside Punjab, but within India. 

7. Reservation of government’s recruitment quota restricting the number of Sikhs in armed forces.

1. Ammonia 

2. Hydrogen Chloride 

3. Ethyne 

4. Ethane 

5. Hydrogen Sulphide

Among the elements given below, the element with the least electronegativity is Lithium.

1. Ferric ion/Fe³⁺ .

2. Lead ion/Pb²⁺ . 

3. Calcium ions/Ca²⁺ .

(i) Fe³⁺ 

(ii) Pb²⁺ 

(iii) Ca²⁺ 

(i) Ammonia 

(ii) Hydrogen chloride 

(iii) Ethyne 

(iv) Ethane 

(v) Hydrogen sulphide.

Iron atom contains four unpaired electrons. In the presence of external magnetic field, their spins (domains) are oriented in the direction of field and the substance thus has very large magnetic moment. The alignment persists even in the absence of external field and it remains magnetised. Thus, it is ferromagnetic in nature.

(i) Fluorine is passed through a cold, dilute NaOH solution.

2NaOH + 2F₂ → OF₂ + 2NaF + H₂O

(ii) Hydrogen peroxide is treated with acidified KMnO₄ solution.

2KMnO₄ + 3H₂SO₄ + 5H₂O₂ → k₂SO₂ + 2MnSO₂ + 8H₂O + 5O₂

(iii) Sulphuric acid is treated with hydrogen sulphide.

2KMnO₄ + 3H₂SO₄ + 5H₂S → k₂SO₄ + 2MnSO₄ + 8H₂O + 5S

(i) Cl₂ + 2NaOH → NaOCl + NaCl + H₂O

(ii) SO₂ + 2NaOH → Na₂SO₃ + H₂O

Given P = 100 W, V = 220 V = 220 V, R = ?, I = ?

R = \(\frac{V^2}{P}\) = \(\frac{(200)^2}{100}\) = 400 Ω

When five are connected in series then R_net = 5 x 400 = 2000 Ω

Hence current in the circuit

I = \(\frac{V}{R_{net}}\) \(\frac{200}{2000}\) = 0.1 A

In loop AFEBA

17 I₁ + 5I₂ = 34

In loop BEDCB

18 I₁ + 5I₂ = 10

Solving the Above two equations

I₁ = 2A, I₂ = 0

In current electricity, Ohm’s law is obeyed by all metals

Electric flux emerging out of the cube is Zero

(i) Resonarce. 

(ii) The frequency of the tuning fork and the natural frequency of the vibrating air column become equal. The air column vibrates with large amplitude thus producing a loud sound.

(i) The person is trying to change the values of the electronic components to produce vibrations of frequency equal to that of the incoming radio waves which he wants to receive. 

(ii) The phenomenon involved in tuning the radio set is resonance

(iii) Resonance : When the frequency of the externally  applied periodic force is equal to the natural frequency of the body, the body starts vibrating large amplitude, producing a loud sound.

(i) Principle of SONAR is based on echo. 

(ii) Given : v = 340 m/s, t = 1.8s

Distance travelled by sound = 2d

Distance = speed x Time

2d = v x t

d = (v x t)/2

  = (340 x 1.8)/2

  = 170 x 1.8

 = 306 m.

The person is trying to change the values of the electronic components to produce vibrations of frequency equal to that of the incoming radio waves which he wants to receive.

Quality of the sound enables a person to differentiate between two sounds of same loudness and frequency but produced by different instruments.

Pitch enables a person tn differentiate between two sounds with equal loudness but having different frequencies.

(i) (1) Glucagon—Produced in alpha cells of pancreas. 

(2) Insulin—Produced in beta cells of pancreas. 

(ii) 

(1) Glucagon—It helps to convert glycogen to glucose when blood glucose level falls. 

(2) Insulin—It helps to convert excess glucose to glycogen when there is higher level of glucose in blood. 

(iii) It is both exocrine as well as endocrine gland. As exocrine, it secretes pancreatic juice containing digestive enzymes and pour them into duodenum part of intestine through pancreatic duet. As endocrine, it secretes hormones like insulin, glucagon and somatostatin and pour them directly into blood. 

(iv) Insulin is a protein by composition so if it is given orally it will get digested in the stomach and will not be able to perform its function. 

(v) Islets of Langerhans. 

(vi) In the abdomen in the loop of small intestine close to duodenum part of small intestine.

(1) Destroys the soil as well as the crop. 

(2) Acid rain corrodes the buildings, statues, etc.

(i) Photosynthesis process leads to release of oxygen which is essential for all life on earth. It also produces food for all heterotrophs. 

(ii) Lack of nucleus helps in having more surface area for absorption and transport of oxygen. Lack of mitochondria helps in the way that RBC would not consume any oxygen that it is transporting. 

(iii) Water is a hypotonic medium, so endosmosis occurs due to which water enters into potato cells making them firm and larger in size i.e., making them turgid. 

(iv) In summer, body loses large amount of water by perspiration or direct evaporation. So blood is order to maintain its osmotic concentration reabsorbs large amount of water from the tubules of Nephron due to which there is less water left to be released as urine. So urine becomes thicker whereas in winter, there is less reabsorption. So thin urine is passed. 

(v) In hilly areas there is scarcity of iodine in the soil and in their diet. Deficiency of iodine leads to simple goitre.

(i) Genes: Genes are units of heredity that determine particular traits (e.g., colour of hair, blood group, colour of eye etc.) 

(ii) Cytokinesis in plant cells: Cells in multicellular plants do not have centrioles. The division of cytoplasm occurs by the formation of a new cell wall in the equatorial regien at the end of anaphase. In telophase, new cellulose particles are gradually deposited in the equatorial zone. The particles extend on either side, from the centre towards the periphery (centrifugal) until it completely divides the cell. These particles fuse together to form a delicate plate membrane. 

(iii) Guttation: The loss of water in the form of water droplets along the margins of leaves through hydathodes. It takes place due to increased hydrostatic pressure that builds up within the cells. The wall pressure that develops in fully turgid parenchymatous cells force the water out. 

(iv) Diapedes insipidus: The condition occurs due to lesser secretion of vasopressin (Anti-diuretic hormone) from the posterior lobe of pituitary gland. The disease is characterized by excretion of large amounts of urine and subsequent dehydration and thirst. No sugar or albumin is present in the urine. A person with severe diabetes insipidus may die due to dehydration if deprived of water for few days. 

(v) Disinfectants: These are powerful chemical substances used for destroy¬ing microbes in spots, places for sterilizing operation theatres and surgical instruments. They are not applied on the body due to their strong corrosive nature eg. Cresol, Phenol, Lysol, DDT etc.

Diabetes insipidus : It is a disease due to the deficiency of ADH (antidiuretic hormone) in which large amount of urine is secreted, resulting loss of water from the body.

(i) Green plants are the only organisms present nature can trap solar energy with the help of green chlorophyll to make their own food through photosynthesis. The other organisms directly or indirectly depend on plants. Herbivores directly depend on plants while carnivores get their food through herbivores which in turn get their food from plants.

(ii) The erythrocyte lacks nucleus and mitochondria to accommodate more hemoglobin pigment in it. Lack of mitochondria in erythrocyte cell will help to save the oxygen to be transported to the cells and tissues of the body.

(iii) The cells of potato cube have hyper-tonic solution when compared to outer hypo tonic water. Due to end osmosis water enter into potato cells and become turgid. Due to this potato cubes become firm and rigid.

(iv)  In summer through perspiration our body loose more water. Less water is involved in the formation of urine and hence it is thicker. During winter, water loss through sweating is very minimum and hence more water is available for the formation of urine and hence it is thinner as well as more in quantity.

(v) Simple goiter is caused due to the nutritional deficiency of iodine. The crops grown in hilly region do not contain any iodine due to leaching away of the iodine during rains. Such food taken from these crops leads to deficiency of iodine and causes this defect to the people.

(a) The President is elected by the members of an Electoral College consisting of the elected members of both Houses of Parliament and of the Legislative Assemblies of the states and the Union Territories of Delhi and Puducherry. 

(b) (i) National Emergency: It is declared when president of India is satisfied that the security of India or any part there of is threatened or is likely to be threatened by war or external aggression. 

(ii) Financial Emergency: It is declared when financial stability or credit of India is threatened. 

(iii) Constitutional Emergency: It is declared when the government of a state Cannot run according to the provisions of the constitution or when a state government is unable to carry out the directions of the Union government due to a political deadlock or failure. 

(c) Executives powers of the President: 

1. Power to appoint and remove the High Dignitaries of the state like Attorney— General of India, Auditor-General of India, chief justice and judges of the Supreme Courts and the High Courts, etc. 

2. Administration of Union Territories and Border Areas. 

3. President is the head of all Union officials. All executive orders are issued in the name of the President. 

4. Control over the State Governments during President’s rule.

(a) The speaker of the Lok Sabha is elected from among its own members soon after the newly elected house meets for the first time. Functions: 

1. The speaker preside over the meetings of the house. All speeches and remarks are addressed to the speaker. 

2. He allots time for the discussion and decides who shall have the floor. 

3. The speaker maintains order in the house when members become unruly, he may order them to withdraw or can adjourn the house. 

(b) 1. Members belonging to any political party shall be disqualified for being a member of House, if he has voluntarily given up his membership of such political party. 

2. Nominated members of a house shall be disqualified for being a member of the house, if he joins any political party after the expiry of six months from the date on which he takes his seat. 

(c) Lok Sabha is considered to be more powerful than the Rajya Sabha because: 

1. Motions of No confidence against the government can only be introduced and passed in the Loksabha if passed the prime minister and his council will resign hence Rajya Sabha has no real power. 

2. The money bills are introduced only in the Lok Sabha. Referring money bills to the Rajya Sabha is a mere constitutional formality. 

3. The council of Ministers is responsible only to Lok Sabha.

(a) The Mughal Empire which had lost its prestige after the life imprisonment of Bahadur Shah, was completely wiped out as an impact of the uprising of 1857. 

(b) First session of Indian National Congress was presided by W.C. Banneijee in Mumbai in 1885. Second session of India National Congress was presided by Dadabhai Naoroji in Kolkata in 1886. 

(c) Lord Curzons Argument: The area of Bengal was too large and it was difficult for the British to administer efficiently. Secondly, to divide bengalis on religious and territorial ground to weaken the growing nationalism in Bengal. Hence according to Lord Curzon, Partition of Bengal was a administrative necessity. 

(d) Lucknow pact demonstrated the unity between the congress and the Muslim League. It was signed in 1916. 

(e) The Lahore session was considered historic because under the guidance of congress president Jawaharlal Nehru a resolution for Pooma Swaraj (complete independance), was passed in this session. It was in this session, the Indian National Flag was hoisted and the pledge for independence was taken by the Leaders of the congress. 

(f) Contributions of INA: 

1. The INA along with Japanese army overran many territories in south east asia. They captured the strong military post klang Klang. 

2. They gave tough fight to the british forces in assam hills and captured Ukhral and Kohima. The heroic acts of INA inspired Indians. 

(g) The Congress accepted the 

Mountbatten plan due to following reasons: 

1. The Muslim League had obstructed the smooth functioning of the Interim Government earlier so it was difficult for Congress to accept it as an ally in Government. 

2. A smaller united and strong India was better than a big but weak country. 

3. Large scale communal riots and loss of lives and property had clearly shown that much more bloodshed will occur if partition was done.

4. Any further delay in the transfer of power could bring civil war in India as British were instigating the rulers of the native states for freedom. 

5. The Congress felt that partition would do away with communal electorates and other undemocratic procedures.

(h) Bombing of Hiroshima and Nagasaki by United State caused significant damage to these cities of Japan. Huge number of casualties caused by the bombs dropped on these cities which made Japan to surrender to the Allies in August 1945. 

(i) UNICEF—United Nations International Children’s Emergency Fund. 

UNESCO—United Nations Educational, Scientific and Cultural Organisation. 

(j) Human right violated in Afghanistan. For example : 

1. The women were under almost permanent “House Arrest”. They could not move out of the houses. If at all they moved out, they had to wear burqa. 

2. The film or T.V. set was taboo in Afghanistan, as education in subject other than what is written in Islamic scriptures is prohibited.

(a) The Parliament can make laws with respect to all those matter which are not mentioned in any of the three lists-the union list, the state list and the concurrent list. 

(b) 5 years. 

(c) The Union Parliament has co-equal powers with the State Legislatures over the 47 subjects mentioned in the concurrent list. 

1. If there is a conflict between the laws passed by the Union Parliament and a State Legislature on the subject mentioned in the concurrent list, the law passed by the Union Government prevails. 

2. In all the matters of the legislation including the constitutional amendment, the extent of the Rajya Sabha’s power is same as that of the Lok Sabha. 

3. All bills other than the money bills may be introduced in either house and follow the same procedure. (any one) 

(d) Deputy Chairman of Rajya Sabha who is elected from amongst its members, presides over the meeting of the Rajya Sabha in the absence of the Vice-President of India. 

(e) President of India appoints Council of Ministers on the advice of Prime Minister of India. 

(f) Impeachment. 

(g) If there is deadlock between the two houses while passing an Ordinary bill in the parliament, the President calls for joint session of both the houses. 

(h) Court of the District Judge. 

(i) The High Court has the power to exercise Judicial Review and judge the validity of law. If any law, executive order of any ordinance passed by the state legislature or any authority infringes the fundamental rights or contravenes any provision of the constitution the High court can declares it null and void. 

(j) Lok Adalat means The People Court. These courts were set up to provide legal aid and quick justice to those who are not in a position to engage lawyers or bear the expenses of the legal proceeding. This eliminated high costs and delay in imparting Justice.