MODEL QUESTION PAPER CLASS XI BIOLOGY. Ans. Hint. Contraction of this with diaphragm increases the volume of thoracic cavity.

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1 MODEL QUESTION PAPER CLASS XI BIOLOGY 1. Mention role of intercostal muscle in respiration. Ans. Hint. Contraction of this with diaphragm increases the volume of thoracic cavity. 2. Name the pigment found on root nodules of legumes with function. Ans: Hint. Leghaemoglobin. Its protect nitrogenase from oxygenase and known as oxygen scavenger. 3. Explain the role of F 0 F 1 particle in energy production during aerobic respiration. Ans. Hint. F 1 head piece contains the site of ATP synthesis using proton gradient of ETC. 4. Why large no. of stomata on lower surface of dicot leaf. Ans: Hint: Helpful in regulation of transcription as lower surface in shade needs much stomata. 5. Draw and label structure of mitochondria. 6. Mention one characteristic of gm positive bacteria. Ans: Hint: Cell wall single layered and without pilli.

2 7. What is apoenzyme? Ans: Hint: The protein part of an enzyme. 8. Define protein. Ans: Hint: Amino acid made with specific three dimensional structure and C, H, O and N main component. 9. What are the functions of endoplasmic reticulum? Ans: Hint: Elaborate the following points: i. Manufacture of protein lipid ii. Membrane biogenesis iii. Mechanical strength to cell iv. Increases absorption surface of cell 10. Draw and label the diplotene phase and briefly narrate it. 11. Tomatoes, carrots and chillies are red in colour due to the presence of one pigment? Is it a photosynthetic pigment? Which property of the pigment is responsible for its ability to initiate the process of photosynthesis? Why is the rate of photosynthesis higher in the red and blue region of spectrum of light? Ans: Hint:

3 The pigments are chromoplasts; these are fat soluble carotinoid pigments like carotenes and xanthophylls. These are called accessory pigments; they absorb light and transfer energy to Chlorophyll a. The wave length of light: the visible light lies between the wave lengths of UV and IR. The most efficient is red light for photosynthesis. Green lights less effective. Maximum photosynthesis takes place in red and blue regions of spectrum of light. Chla and b absorb mostly blue and red light. 12. What are the advantages of giving scientific name to the organisms? Ans: Hint: i. universally accepted name ii. The technical terms gives the glimpses of its relation to the related one. 13. Differentiate between systematic and taxonomy. Ans: Hint: Systematic deals with evolutionary relationship and taxonomy deals with the classification and naming of organisms. Taxonomy can be considered as a branch of systematics. 14. Discuss the structure of virus and viroid. Ans: Hint: Virus: i. smaller than even bacteria ii. They can be filtered iii.dna or RNA could be the genetic material iv. Possess outer covering capsid v. Living only within host cell etc. Viroid: Smallest infectious pathogenic circular RNA without protein coat. 15. Which class of kingdom fungi has both uni and multicellular members? Ans: Hint: Ascomycetes 16. Sphagnum has a lot of economic importance justify. Ans: Hint: Provide peat used as fuel. 17. What features led to dominance of vascular plants- angiosperms? Ans: Hint: i. Deep roots, ii. Water proofing material like cutin, iii. Strong woody material for support above ground

4 18. What do you understand by diplontic cycle of plants? Ans: Hint: 19. How non chordate differ from chordate? 20. Enlist the main features of platylminthes with example. Ans: Hint: Eg.Turbellaria

5 21. Outline the role of coelom in animal. Ans: Hint: Fluid filled hollow structure acts as protective cushion. It has Immune system like role in invertebrates. Visceral organ lies in coelom. 22. Distinguish between prop and stlit root. Ans: Hint: 23. Draw and label the structure of dicot seed. Ans: Hint:

6 24. Mention the characters of basal placentation. Ans: Hint: Placenta at the base of ovary as following diagram 25. Mention the difference between tracheid and vessel. Ans: Hint: 26. Define trichome. Ans: Hint: Multicellular epidermal hair on stem for protection. 27. Why not photorespiration does take place in C4 plants? Ans: Hint: The reason is that they have a mechanism that increases the concentration of CO2 at the enzyme site. It occurs when C4 acid from mesophyll cell is broken down in bundle sheath

7 cells and releases CO2, hence increasing CO 2 concentration intra cellular. It also ensures that RUBISCO acts as carboxylase to minimize oxygenase activity of it. 28. Why less energy is produced during anaerobic respiration? Following are the reasons: Incomplete breakdown of respiratory substrate. Some of the products of anaerobic respiration can be oxidized further to release energy which shows that anaerobic respiration does not liberate the whole energy contained in the respiratory substrate. NADH 2 does not produce ATP as electron transport is absent. Oxygen is not utilized for securing electrons and protons. 29. What is chloride shift? What is its importance? Ans: Hint: Diffusion of Cl - electrochemical neutrality. from blood plasma into RBC. To maintain ionic balance & 30. Identify the secondary protein and quaternary proteins in following examples. Trypsin, Haemoglobin protein, Myosin protein, Actin protein, Albumin, globulin and explain what is tertiary protein. Ans: Hint: Secondary Protein: Myosin protein, Actin protein, Albumin, globulin, Trypsin Tertiary Protein: ( Hemoglobin protein ). [Note: Question marks will be variable from 1 to 4 depending upon content asked for.]

8 MODEL PAPER CLASS 11 ECONOMICS 1. Main purposes and functions of averages. (i) To represent a brief picture of data. (ii) Comparison (iii) Formulation of policies. (iv) Basis of statistical analysis. (v) One value for all the group or series. 2.Essentials of a good average. (i) Easy to understand. (ii) Easy to compute (iii) Rigidly defined. (iv) Based on all the items of series. (v) Certain in character (vi) Least effect of a change in the sample. (vii) Capable of algebric treatment 3. Merits of Arithmetic mean (i) Simplicity (ii) Certainty (iii) Based on all values. (iv) Algebric treatment possible. (v) Basis of comparasion. (vi) Accuracy test possible. 4.Demerits of Arithmetic mean. (i) Effect of extreme values. (ii) Mean value may not figure in the series (iii) unsuitability. (iv) Misleading conclusions. (v) Can not be used in case of qualitative phenomenon. 5. Merits of Median. (i) Simple measure of central tendency. (ii) It is not affected by extreme observations. (iii) Possible even when data is incomplete. K (iv) Median can be determined by graphic presentation of data. (v) It has a definite value.

9 6. Demerits of median. (i) Not based on all the items in the series. (ii) Not suitable for algebraic treatment. (iii) Arranging the data in ascending order takes much time. (iv) Affected by fluctuations of items. 7.Merits of mode (i) Simple and popular measure of central tendency. (ii) It can be located graphically with the help of histogram. (iii) Less effect of marginal values. (iv) No need of knowing all the items of series. (v) It is the most representative value in the given series. 8. Demerits of mode (i) It is an uncertain measure (ii) It is not capable of algebraic treatment. (iii) Procedure of grouping is complex. (iv) It is not based on all observations. 9.explain types of elasticity of demand: Perfectly Elastic Demand (E P = )... Perfectly Inelastic Demand (E P = 0)... Relatively Elastic Demand (E P > 1)... Relatively Inelastic Demand (E p < 1 )... Unitary Elastic Demand ( E p = 1) 10.What is market demand? (Delhi 2013) Ans. Market demand is sum of individual demand at different price level at a particular period of time by different people. 11.What does a rightward shift in demand curve indicate?

10 Ans. Increase in demand. 12.Give one reason for a shift in demand curve. (All India 2oi2) Ans. Shift in demand curve occurs due to changes in other determinants of demand like price of related goods, income of the consumers, etc other than own price of the commodity. 13.What causes an upward movement along a demand curveans. Increase in own price of the commodity causes an upward movement along a demand curve. 14.What is Law of Demand? Ans. Law of Demand states that other things remaining constant, quantity demanded of a commodity increases with a fall in its own price and diminishes with a rise in its own price. Geometrically, it is represented by a downward sloping demand curve. 15..What is meant by inferior goods in economicswhen is a good called an inferior good? Ans. Inferior goods are the goods for which the demand is inversely related to consumer s income, e.g. coarse cereals, tonned milk, etc. Note There is no list of good which are normal or inferior, it depends on the level of consumer s income. 16.What is meant by normal goods in economics

11 Ans. Normal goods are the goods for which the demand is directly related to consumer s income, i.e. with rise in income demand rises and vice-versa e.g. full cream milk, pulses, grains, etc. 17.What is demand schedule? (All India 2008) Ans. Demand schedule is a table showing the relationship between different quantities of a commodity to be purchased at different prices of that commodity. 18.Explain Different Periods in Production. Market period It is the period during which production factors can not be changed at all. Hence, the production function is written as Q x = F(L,K), where both labour and capital are taken as fixed. Short period It is a time period in which the producer can change only the variable factors of production while the fixed factors_of production remains constant. The production function is written as Q x = F (L, K), where labour is taken as a variable and capital as fixed factor. Long period It is a time period when the producer has enough time to change both fixed and variable factors of production, infact all factors are variable in the long-run. The production function is written as Q x = F (L, K) where both labour and capital are variable in nature. 19 Define.Total Product (TP) It is the sum total of output corresponding to each unit of the variable factor used in the process of production.

12 20.what is Marginal Product (MP) It is an additional output produced by the use of an additional unit of the variable factor, fixed factor remaining constant. Where, ATP = Change in Total Product AL = Change in labour (variable factor) 21.What is Average Product (AP) It is per unit output of the variable factor. 22.What is Returns to a Factor It refers to the behaviour of output when only one variable factor of production is increased fixed factors remaining constant. This is a short-run phenomenon. 23.What is Returns to Scale It refers to change in physical output of a good on account of increase in all inputs required to produce a good simultaneously in the same proportion. This is a long-term phenomenon. falls to become negative.

13 24.Mention assumptions of Law of Variable Proportion There are only two factors of production, i.e. labour and capital. Where labour is variable and capital is fixed. State of technology remains constant. 25 What are three Stages of Law of Variable Factor/Variable Proportions Stage of increasing returns to a factor Stage of diminishing returns to a factor Stage of negative returns to a factor CLASS XI GEOGRAPHY MODEL QUESTION PAPER 1. Name the latitude that passes through the centre of India? 2. What is the position of India in terms of area and population? 3. What is McMohan Line? What does it signify? It is a dividing line between India and China realism. To the East of Bhutan, the crest of the High Himalayas stands between India and China. It separates China from India. This crest of High Himalayas is known as the McMohan line. 4. Which states of India have common frontiers with China? These states are Jammu and Kashmir, Himachal Pradesh, Uttaranchal, Sikkim and Arunachal Pradesh. 5. Why is the sun inclined sometimes to the north and sometime to south at midday in Hyderabad but not in New Delhi? Hyderabad is situated between the Tropic of Cancer and the equator. When the sun is in aphelion, then it shines to the north of Hyderabad and when the sun is in the perihelion, it shines to the south of Hyderabad at midday. However, Delhi is in the north of Tropic of Cancer, so this phenomenon does not take place in Delhi. 6. What do you understand by 'Prime Meridian'? An imaginary line running from North Pole to South Pole through Greenwich, England, and used as reference point for longitude is known as Prime Meridian. In 1880, an international

14 agreement was reached to accept the longitude of Greenwich, England as the Prime Meridian from which all sea time will be measured. Prior to that England, Spain and France had their own Meridians through the Azores, Paris and London. Some early sea charts included all three Meridians on their surface. 7. Write a note on Unity in Diversity. 'Unity in Diversity is the term that was coined by the first prime minister of India, Jawahar Lal Nehru. He used this term in terms of cultural diversity and unity among the Indians. But, in geography, we use this term to discuss both cultural and geographical features. There are numerous diversities found in India. The factors that helped the emergence of this unique feature of the Indian policy are large geographical spreads of the subcontinent, which provide fertile ground for germination and blossoming of regional diversities in the social setup. Differentiation in the physical landscape has contributed to the emergence of different ways and patterns of human interaction with nature. The imagination of people led to the concentration of diverse elements in different regions. The factors that have contributed to the underlying unity of the social character in the country are: The monsoon rhythm of seasons that provide a strong element of uniformity. The horizontal spread of cultural and socio-economic attributes from different parts of the country. The ever going interaction through the inter-regional contact and exchanges thath generate the process of cultural fusion and strong bonds of unification and integration. The development of regional linkages and the emergence of a regional home market during the British rule in India. 8. What is the most important characteristic of the islands (Indian) located in the Arabian sea? 9. What is the most important geographical advantage of the Himalayas? 10. Which two forces are responsible for shaping the present geographical features of India? The two major forces responsible for landform development of the earth surface are: 1. Endogenitic Forces (Internal Forces) - like volcanoesand earthquake. 2. Exogenitic Forces (External Forces) - like Deposition and denudation. 11. Describe the characteristics of the Central Highlands. A wide hilly belt bordering the west by the Aravalli range and on east by the chota nagpur plateau is known as Central Highlands. Its southern limit is the rift valley of Narmada. It includes one half of M.P., one third of Rajasthan and a small part of U.P. Characteristics: 1. The whole region is forested and inhabited by Gonds, Santhals, Oraons and Bhils. 2. Its elevation ranges between 700 and 1,000 m above the mean sea level. 3. The Aravalli range and the east Rajasthan form the northern part of the highlands and the Vindhayan scrap land forms the southern highlands.

15 12. What do you understand by the term Doab? Give few examples from the Indian subcontinent. Doab is a flood plain formed in between two rivers. Doab separates two rivers but maintains a uniform character over the whole area. Four doabs in Punjab maintain a physical unit of the Punjab plain. 1. Bist Jalandhar Doab: Between the Satluj and Beas. 2. Bari Doab: Between Ravi and the Chenab. 3. Chaj Doab: Between the Chenab and the Jhelum. 4. Sind Sagar Doab: Between the Chenab and the Indus river. 13. Describe the features of Central Highlands. The major features of Central Highlands are as follows: It is a division of peninsular plateau. It consists of Malwa Plateau, Bundelkhand, Baghelkhand and Chhotanagpur plateau. Aravallis are in its north-west, Rajmahal hills in the north-east and Vindhyas in the south. It is made-up of hard igneous and metamorphic rocks. 14. Give an account of the distinct land features of the Great Plains. 15. Which states are located in western, central and eastern Himalayas? Western Himalayas: Jammu and Kashmir and Himachal Pradesh Central Himalayas: Uttaranchal Eastern Himalayas: West Bengal, Sikkim, and Arunachal pradesh 16. Who are decomposers? 17. Who are homo sapiens? 18. Define food web. Most animals are part of more than one food chain and eat more than one kind of food in order to meet their food and energy requirements. These interconnected food chains form a food web. 19. Distinguish between the tropical grasslands and the mid-latitude grasslands. 20. Distinguish between the Taiga biome and the Tundra biome. 21. Name the important cold currents of the Atlantic Ocean. Labrador current, canaries current, benguela current, falkland current and west wind drift are important currents of the Atlantic ocean. 22. What factors cause the waves to decay? The friction of water and sea floor. When the depth of the water is less than half the wavelength of the wave, the wave breaks. 23. What are the major characteristics of waves? The major characteristic of waves are as follows:. Wave crest and trough: The highest and the lowest points of the waves are known as the crest and the trough respectively.. Wave height: It is vertical distance between the bottom of the trough and the top of the crest. Wave amplitudes: It is one half of the wave height.

16 Wave period: It is merely the time interval between the two successive wave crests or troughs as they pass through a particular point. Wavelength: It is the horizontal distance between the two successive crests. Wave speed: It is the rate at which the wave moves through the water and is measured in knots. Wave frequency: It is the number of waves passing at a given point during one second time period. 24. What is conservation in respect to bio-diversity? 25. What are carnivorous plants? Carnivorous plants (sometimes called insectivorous plants) are those plants that derive some or most of their nutrients (but not energy) from trapping and consuming animals or protozoan, typically insects and other arthropods. 26. How is diversity among species measured? Diversity among species can be measured through their richness, abundance and types. 27. Discuss the importance of animals to humankind. 28. State the scientific importance of our bio-diversity. 29. Why is demarcation of ecosystem boundaries difficult and complex? 30. What do you mean by conservation of biodiversity?

17 MODEL QUESTION PAPER CLASS 11 Sub histor M ) 1) )What was popularised by Anabaptists? 2) What do you mean by indulgences? 3) Who organised Society of Jesus and what was the purpose of the society? 4) What was the contribution of Kepler in astronomy? 5) List out the important events of 16 th and 17 th century during the Renaissance period in Europe? 6) Who was Filippo Brunelleschi? 7) What was the contribution of Michelangelo Buonarroti in St Peter s Church? 8) Give a list of some important events of the 15 th century which occurred during the period of Renaissance. 9) Mention important events of the 14 th century during the period of Renaissance? 10) Who was Jacob Burckhardt? 11) How did the new concept of human beings free the people from clutches of feudal system? 12) What were the factors that led to the advancement of architecture? 13) What changes did the humanists' view of history bring about? 14) Which factors led to the revival of Italian cities? 15) What was the role of Universities in propagating Humanities? 16) What do you mean by town air makes free? 17) Marks:2 18) What do you mean by manor? 19) What were the rights given to the Lords? 20) What were the contradictions found in the common European life even when the Christianity was the main religion? 21) Who were monks? 22) What was the historical background of the name "France"? 23) What were the main features of feudalism in Europe? 24) How was Genghis Khan s political system different from Attila s? 25) What does the Great Wall of China symbolize? 26) Why was Genghis Khan successful in defeating the Chinese? 27) Why did India escape the attention of Genghis Khan? 28) What were the problems encountered by the army of Genghis Khan?

18 29) What was the effect of Genghis Khan conferring titles? 30) Briefly mention about the administrative features of Genghis Khan's rule. 31) How was the Mongol rule a unifying factor? 32) Where was Genghis Khan from and what was his contribution? 33) How was the military success of Genghis Khan achieved? 34) How was Mongol authority established after various conquests? POLITICAL SCIENCE CLASS 11 a. Mention the tool which is used by the people to exercise their power. b. Who has the ultimate power in a democracy? c. '' Elections play an important role in the democracy ''. Comment. d. Name the Election Commissioner who introduced electoral reforms in India. e. M f. What is the basis of democracy? g. Write a short note on the '' Plurality System ''? h. What is Proportional Representation System? i. Compare the First Past The Post and Proportional Representation System. j. What is Reserved Constituency? k. Write a short note on the '' Delimitation Commission ''. l. Why open and competitive nature of the Indian one-party dominance was affected in the Fourth General Elections of India? m. '' Political parties play vital role in all democratic states ''. In the light of this statement explain the different types of party states that prevails in the world. n. Explain the reasons behind the adoption of the '' First Past The Post '' system in India. o. Why did the framers of the Costituent Assembly emphasised on the independence of the Election Commission? p. Describe the duties of the commission who conducts elections in India. q. What is '' Zero Hour ''? r. Mention two states that have more representation in the Parliament. s. How Parliament becomes the people's institution? t. What is a bill? u. Mention the qualifications for the membership of the upper house of the Indian Parliament. v. '' The composition of Senate is based on the federal principle ''. Comment. w. Who is an integral part of the Indian Legislature? x. Which is the most powerful Upper House of the world? y. Write a short note on the Question Hour. z. Under the Indian Constitution which is a supreme institution of the people? aa. What does the term budget imply?

19 bb. Name the authority which coordinates with the Legislature and Executive in India. cc. Mention the functions of the Speaker of the Lok Sabha. dd. '' Lok Sabha is vested with the special powers ''. Comment. ee. '' Some of the special powers are assigned to the Rajya Sabha as well ''. Comment. ff. How does the Indian parliament exercises its control over the executive? gg. the functions of the law making body of India. a. What are entrenched inequalities? Give two examples from India. b. Discuss the Liberal view on equality. c. Is it possible to attain economic equality? d. What is 'Affirmative action'? e. rite a note on the Karl Marx's contribution to political theory. f. Briefly discuss the nature of global inequality with examples. g. Is it possible to create a competitive economy and at the same time bring all inequality to an end? h. In 63 years since independence, how far do our India has progressed on the road to equality? i. Examine the difference between equality of opportunity and equality of outcome. j. Positive discrimination led to the strengthening of identity politics. Analyse. k. Find out the difference between the social and natural Inequalities. l. What are the different dimensions of equality.

20 New Delhi Support Material in Mathematics (Important Formula & questions) For Class XI (2012) Chapter 7- (PERMUTATION & COMBINATION) Chapter 8- (BINOMIAL THEOREM) Chapter 9- (SEQUENCE AND SERIES) Chapter 10- STRAIGHT LINES Chapter 11- CONIC SECTIONS Chapter 12- THREE DIMENSIONAL CO- ORDINATE GEOMETRY Prepared under guidance of Ms. Usha Aswath Iyer Director, ZIET Bhubaneswar Content Verified by- Sh. Sulapani Sarangi Principal. KV Puri Prepared by- Sh. Nabaghan Nayak PGT (Mathematics), ZIET Bhubaneswar

21 CHAPTER-7 (PERMUTATION & COMBINATION) Points to be remembered 1. Fundamental principle of counting:- If one operation can be performed in 'm' different ways and if corresponding to each way of performing this operation,there are 'n' different ways of performing second operation,the two operations together can be performed in (mxn) ways. 2. Factorial:- The continued product of first 'n' natural numbers is called factorial 'n' or 'n' factorial and is denoted as 'n!'. 3. 0! has no meaning. Conventionally, we define 0! =1. 4. The number of permutation (arrangements of 'n' different things taken 'r' at a time given by n P r (0<=r<=n) n P r = n!/(n-r)! 5. The number of ways in which 'r' vacant places can be filled up with 'n' different things is given by n r. 6. The number of permutations of 'n' things taken altogether,when 'p' of the things are alike of one kind, 'q' of them alike of another kind, 'r' of them alike of a third kind and the remaining all different is given by:- n!/(p!q!r!). 7. The number of ways of arranging 'n' distinct objects along a round table= (n-1)! Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 1

22 8. The number of ways of arranging 'n' persons along a round table so that no person has the same two neighbours=(n-1)!/2 9. In forming a necklace, there is no distinction between a clockwise and anticlock wise direction. Hence, the no. of necklace formed with 'n' beads of different colours =(n-1)!/2 10. The number of combination of 'n' different things taken 'r' at a time is given by n C r, (0<=r<=n) n C r = n!/r!(n-r)! 11. n C r + n C (r-1) = (n+1) C r where 1<=r<=n, and n,r belongs to N. 12. n C r / n C (r-1) = (n-r+1)/r where n,r belongs to N, 1<=r<=n. 13. The number of ways in which (m+n) things can be divided into two groups containing 'm' and 'n' things respectively is given by= (m+n)!/m! n! SHORT ANSWER TYPE QUESTIONS 1. Find HCF & LCM of 4!,5!,6!? 2. If 1/8! + 3/7! = x/9!, find x? 3. Find 'n' if 5 P(4,n)=6 P(5,n-1)? 4. In how many ways can the letters of the word "EQUATION" be arranged? 5. Ten students are participating in a race. In how many ways can the first three prizes be won? 6. In how many ways can 4 books on mathematics and 3 books on english be placed on a shelf so that books on the same subject always remain together? Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 2

23 7. How many words can be formed out of letters of the word "TRIANGLE". How many of those will begin with 'T' and end with 'E'? 8. In how many ways can 3 prizes be given to 10 students when a student can receive any number of prizes? 9. How many different arrangements can be made from the letters of the word "ENGINEERING"? 10. In how many ways can 6 beads of different colours form a necklace? 11. Evaluate 10 C C 6? 12. If C(2n,3):C(n,3):: 11:1,find 'n'? 13. Find the no. of straight lines and no. of triangles that can be formed from 15 non collinear points? 14. Find the no. of all 4-digit nos. with no digit being repeated? 15. Find the no. of all 3-digit even natural nos? LONG ANSWER TYPE QUESTIONS(4 MARKS) 1. How many nos. greater than can be formed by using the digits 4,5,6,7,8 if no digit is repeated in any no.? 2. Find the no. of ways in which the letters of "ARRANGEMENT" can be arranged so that the 2 R's and 2 A's don't occur together? 3. A committee of 6 is to be formed from 6 boys and 4 girls. In how many ways can this be done if the committee contains : (a) 2 girls? (b) atleast 2 girls? Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 3

24 4. A man has 7 relatives, 4 of them are ladies and 3 gentlemen, his wife also has 7 relatives, 3 of them are ladies and 4 gentlement. In how many ways can they invite a dinner party of 3 ladies and 3 gentleman so that there are 3 of man's relatives and 3 of wife's relatives? 5. Find the no. of all possible arrangement of the letters of the word "MATHEMATICS" taken 4 at a time? 6. From a class of 25 students, 10 are to be chosen for an excursion party. there are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen? 7. Find the no. of ways in which 5 boys and 5 girls can be seated in 10 seats in a row if the boys and girls are to be seated alternately? 8. In how many ways can the letters of the word "ASSASSINATION" be arranged so that all the S's are together? 9. In an experiment, a question paper consists of 12 questions divided into 2 parts i.e part1 & part2 containing 5 & 7 questions. A student is required to attempt 8 questions in all, selecting atleast 3 from each part. In how many ways can a student select the questions? 10. How many 6-digit nos. can be formed from the digits 0,1,3,5,7,9 which are divisible by 10 and no digit is repeated? 11. Prove that 2n C n = ( (2n-1)X2 n )/n! 12. How many even nos. are there with 3-digits such that if 5 is one of the digits, then '7' is the next digit? 13.A teacher wants to arrange 5 students on the plat form such that the buy YUSUF occupies the first position and the girls GEETA & SEETA are always together. How many such arrangements are possible? 14. How many different nos. with distinct digits can be formed from the digits 2,3,5,7,9. How many of them are odd? Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 4

25 CHAPTER-8 (BINOMIAL THEOREM) Points to be remembered:- 1. If 'n' is a natural no., 'x' & 'a' are any two nos. then (x+a) n = n C 0 x n + n C 1 x (n-1) a+ n C 2 x (n-2) a n C r x (n-r) a r n C n a n. 2. General term: T (r+1) = n C r x (n-r) a r 3. Middile terms: (a) If 'n' is even,there is only one middle term. Required middle term=t( (n/2)+1) (b) If 'n' is odd, there are two middle terms. Required middle terms are= T ((n+1)/2) and T ((n+3)/2) 4. (r+1)th term from end in the expansion of (x+a)(r+1beginning in the expansion of (x+a)^n. SHORT ANSWER TYPE QUESTIONS(1 MARK EACH) 1. Find the 3rd term in the expansion of (2x+3/x 2 ) 7 2. Write the general term in the expansion of (3x 2-1/5x) 8 3. Write the values of 6 C C C C 6 4. Find the term void of 'x' in the expansion of (x/a +a/x) Find the no. of terms in the expansion of (1+x) 12 + (1-x) Find 'n' if the coefficient of 3rd term from the end in the expansion of (1+x) n is 45 Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 5

26 7. Find teh no. of non-zero terms in gthe expansion of ( Find the coefficients of x m and x n in the expansion of (1+x) (m+n) 9. If p+q=1, then find the value value of 10. If the coefficient of (r+4) th & (2r+1) th terms in the expansion of (1+x) 18 are equal, find 'r' 11. Find the middle term in the expansion of (x+ 1/x) Write the 1st two terms in the expansion of (1+0.01) Using binomial theorem, evaluate (11) Find the term containing x 3 in the expansion of (x-2y) Find the integral parts of LONG ANSWER TYPE QUESTIONS (4 MARKS EACH) 1. Simplify (x+y) 6 + (x-y) 6 and hence evaluate ( 2 +Ѵ 3) 6 + (2 Ѵ3) 6 2. Using binomial theorem prove that 3 (2n+2) -8n-9 is divisible by 64 for all n belongs to N. 3. Find 'a','b' & 'n' if the 1st three terms in the expansion of (a+b) n are 729,7290 & If 6 th, 7 th, 8 th & 9 th terms in the expansion of (x+y) n are a,b,c & d then prove that (b 2 -ac)/(c 2 -bd) =4a/3c 5. Find the coefficient of 'x' in the expansion of (1-2x^3+3x^5)(1+1/x)^8? 6. If the term free from 'x' in the expansion of ( 1 2x) 10 is 405, find 'k'? Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 6

27 7. If 'n' is an even positive integer,show that the middle term in the expansion of (x+1/x) n is equal to n C n /2 8. Prove that the coefficient of x n in the expansion of (1+x) 2n is twice the coefficient of x n in the expansion of (1+x) (2n-1) 9. If the coefficient of (r-1)th, rth and (r+1)th terms in the expansion of (1+x) n are in the ration 1:3:5,find both 'n' & 'r'? 10. If a 1,a 2,a 3 & a 4 are the coefficients of any 4 consecutive terms in the expansion of (1+x) n, prove that (a 1 /(a 1 +a 2 )) +(a 3 /(a 3 +a 4 )) = 2a 2 /(a 2 +a 3 ) Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 7

28 Points to remember :- CHAPTER-9 (SEQUENCE AND SERIES) 1: A function f: N-->R is called a real sequence where 'N' is the set of natural nos. & R be the set of real numbers. 2. A sequence following some definite rule( or rules) is called a progression. 3. If the terms of aq sequence are connected by plus or minus signs, a series is formed. 4. A sequence is called an arithmetic progression iff the difference of any term from its preceding term is constant. 5. General term of an A.P Tn=a+(n-1)d 6. Sum to n-terms of an A.P : Sn=(n/2)[2a+(n-1)d] 7. Arithmetic mean between two nos. 'a' & 'b' is A.M=(a+b)/2 8. To insert 'n' arithmetic means between two given numbers, we have : A n = a +n[(b-a)/(n+1)] 9. General term of G.P = T n = ar (n-1) 10. Sum to n-terms of a G.P= { a(r n -1 )/(r-1), if r>1 & a(1-r n )/(1-r), if r<1 } 11. G.M between two positive nos. 'a' & 'b' is G.M=(ab) 1/2 12. Arithmetic mean between two distinct positive nos. is always greater than their G.M. 13. If the sum is given, then in an A.P Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 8

29 (i) 3 nos. are taken as a-d, a, a+d. (ii) 4 nos. are taken as a-3d, a-d, a+d, a+3d. 14. If the product is given, then in a G.p (i) Three nos. are taken as: a/r, a, ar (ii) four nos. are taken as: a/r 3, a/r, ar, ar n = n(n+1)/ n 2 = n(n+1)(2n+1)/ n 3 =[n(n+1)/2] a + ar + ar 2 + ar = a/(1-r) if r<1) SHORT ANSWER TYPE QUESTIONS (1 MARK EACH) 1. If 1/5, x & 1/4 are in A.P, find 'x'? 2. Find the sum of first 30 terms of the series ? 3. If A n = (n 2 +1)/2n, find A 5? 4. Find the sum of all 2-digit nos.? 5. Find the fourth term of the sequence 1,4,9...? 6. Find 'n' if n = 210? 7. Find the no. of terms in the series if the last term is 95? 8. If S n = 5n 2 + 2n, find T n? 9. Find 'x' if x+9, x-6 & 4 are three consecutive terms of a G.P? 10. Find the G.M between 64/27 & 3/16? Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 9

30 11. Find the 5 th term of the sequence 1/2, 3/4, 7/8, 15/16,...? 12. Find which term of the sequence 12,8,16/3... is 512/729? 13. Sum the series ? 14. Find the 5 th term of the sequence 1,3,7,15...? 15. Write the n th term of the sequence 1, 1+2, 1+2+3, Find the sum : ? LONG ANSWER TYPE QUESTION (4/6MARKS) 1. The 4 th term of an A.P is equal to 3 times the first term and the seventh term exceeds twice the 3 rd term by 1. Find the 1st term & the common difference? 2. In an A.P p th, q th and r th terms are 'a','b' & 'c', prove that p(b-c) + q(c-a)+ r(a-b)= If a 2,b 2,c 2 are in A.P, prove that a/(b+c), b/(c+a), c/(a+b) are in A.P 4. If the roots of the equation a(b-c)x 2 + b(c-a)x + c(a-b)=0 are equal, prove that 1/a, 1/b,1/c are in A.P. 5. The sum of n-terms of two arithmetic series are in the ratio (7n+1):(4n+27), find the ratio of their 11th terms? 6. The sum of first p,q,r terms of an A.P are a,b &c, prove that a(q-r)/p + b(r-p)/q + c(p-q)/r =0 7. The sum of three consecutive nos. in an A.P is 18 and their product is 192. Find the numbers? 8. The ratio of the 2nd to 7th of 'n' A.M's between -7 & 65 is 1:7, find 'n'? 9. Three numbers whose sum is 15 are in A.P. If 8, 6 & 4 be added to them Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 10

31 respectively, then these are in G.P. Find the numbers? 10. Prove that the product of first n-terms of a G.P,whose first term is 'a' & last term is 'l' is (al) (n/2) 11. If a,b,c,d are in G.P, prove that (a 2 + b 2 + c 2 ) (b 2 + c 2 + d 2 )=(ab + bc + cd) Find the sum of n terms of the sequence 7, 77, 777,7777,...? Problems for bright students Q1.The sum of two numbers is six times their geometric mean. Show that the numbers are in the ratio ( 3+2 2)/(3 2 2) Q2.Show that the ratio of the sum of first n- terms of a G.P to the sum of terms from (n +1)th to (2n)th term is 1/ r n Q3.Show that 1 x x n(n+1) 2 3n x x n 2 x(n+1) 3n +1 Q4.Sum the series : upto n-terms Q5. If S 1,S 2 & S 3 denote respectively the sum of first n- natural numbers, their squares & their Cubes then show that 9S 2 2 = S 3 ( 1+ 8 S 1 ) Q6. If a,b, c are in G.P & the equations a x b x + c = 0 & dx 2 + 2ex + f = 0 have a common root then show that d/a, e/b, f/c are in A.P. Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 11

32 Points to be remembered : CHAPTER 10 STRAIGHT LINES 1) Distance between two points ( x 1, y 1 ) &(x 2,y 2 ) is (x 2 x 1 ) 2 + (y 2 y 1 ) 2 2) Centroid of a triangle having vertices (x 1, y 1 ),( x 2,y 2 ) &( x 3,y 3 ) is ( ( x 1 +x 2 +x 3 )/3,(y 1 +y 2 +y 3 )/3) 3) Incentre of a triangle is given by ( (ax 1 + bx 2 + cx 3 )/(a + b+ c), (ay 1 + by 2 + cy 3 )/(a + b+ c)) 4) Equation of a line having slope m & Y- intercept c is given by y= mx + c 5) Equation of a line passing through a given point (x 1, y 1 ) & having slope m is given by y y 1 = m( x x 1 ) 6) Equation of a line passing through two given points (x 1, y 1 ) &( x 2,y 2 ) is given by y y 1 = ( x x 1 ) y2 y1 x2 x1 7) Equation of a line making intercepts a & b from the co-ordinate axis is given by x/a + y/b = 1 8) Equation of a line in normal form is given by x cosα + y sinα = p 9) Angle between two lines having slopes m 1 & m 2 is given by Tanθ = (m 1 m 2 )/ (1 + m 1.m 2 ) a) Two lines will be parallel if m 1 = m 2 & perpendicular if m 1.m 2 = -- 1 Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 12

33 10) Distance of a point (x 1, y 1 ) from the line ax+ by + c = 0 is given by / (ax 1 + by 1 + c)/ a 2 +b 2 / SHORT ANSWER TYPE QUESTIONS 1) Find the incentre of the triangle whose vertices are (1,2),(3,4) &(-- 5,4) 2) Find the equation of the line having slope 2 & passing through the point (3,--5) 3) Find the equation of the line passing through two given points (-- 4, 3) & (4,6) 4) Find the distance of the point(x,y) from the origin. 5) Write the slope of the line which is parallel to x- axis. 6) Find x if the points (-2,3),(3,5)&(x,4) are collinear. 7) Find the angle between the lines 2x 3y + 2 = 0 & x 2y = 5 8) Find the point on the line 2x + 5y +4 = 0 whose ordinate is 5 9) Find x if the point ( x,5) is equidistance from the points (6,7) & (3,8) 10) Find the equation of the line passing through the point (2, --1) & making an angle of 30 0 with x- axis. Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 13

34 LONG ANSWER TYPE QUESTIONS (4/6) MARKS 1) Find the co-ordinates of the foot of the perpendicular from the point (-- 1,3) to the line 3x 5y = 4 2) Find the distance of the point (2,5) from the line x/2 + y/3 = 1 measured parallel to the line y = 2x + 3 3) If p & q be the lengths of perpendiculars from the origin to the lines x cosθ y sinθ = k cos2θ & x secθ + y cosecθ = k, respectively, prove that p q 2 = k 2 4) In triangle ABC with vertices A(2,3),B(4,-1) & C(1,2) find the equation & length of altitude from the vertex A. 5) Find the image of the point (2,5) with respect to the line 3x 5y = 2, considering the line as a plane mirror. 6) Find the equation of a line drawn perpendicular to the line x/4 + y/6 = 1, through the point where it meets the y- axis. 7) If the lines y = 3x + 1 & 2y = x+3 are equally inclined to the line y= mx + 4, find the value of m 8) Find the equation of the line through the intersectionof the lines 4x+ 7y =3 & 5x y = 0 & perpendicular to the line 3x 2y = 0 9) Find the equation of the line mid way between the parallel lines 9x 6y 7 = 0 & 3x + 2y + 6 = 0 10) Find the co-ordinates of the incentre of the triangle formed by the lines y = 15, 5x 12y = 0 & 3x+ 4y = 0 Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 14

35 Points to be remembered: CHAPTER 11 CONIC SECTIONS A conic section (or a conic) is a curve of intersection of a right circular cone of two nappes & a plane. The curves so obtained are called parabola, ellipse & hyperbola. 1) The equation of a circle having centre at (h,k) & radius r is given by (x - h) 2 + (y - k) 2 = r 2 It is called central form of the circle. 2) If the centre is at the origin then the equation becomes x 2 + y 2 = r 2 It is called simplest or standard form of circle. 3) x 2 + y 2 +2gx +2fy + c = 0 is called general form of circle 4) If the two end points of the diameter of a circle are (x 1,y 1 ) &(x 2,y 2 )then the equation of the circle is ( x x 1 ) (x x 2 ) + (y y 1 )(y y 2 ) = 0 It is called the diametric form of the circle. 5) x = r cosθ, y = r sinθ, 0< θ< 2π is the parametric representation of the circle x 2 + y 2 = r 2, θ is called the parameter 6) x = h + r cosθ & Y = k + r sinθ 0< θ< 2π is the the parametric equation of the circle (x - h) 2 + (y - k) 2 Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 15

36 7) Main points about Parabola Equation Y 2 = 4ax(a > 0) Y 2 = --4ax(a > 0) x 2 = 4ay(a > 0) x 2 = --4ay(a > 0) Axis Y= 0 Y= 0 X = 0 X = 0 Directrix X = --a X = a Y = --a Y = a Focus (a,0) (--a,0) (0,a) (0, - a) Vertex (0,0) (0,0) (0,0) (0,0) Length of latus rectum Equation of latus rectum Focal distance of the point (x,y) 4a 4a 4a 4a X = a X = --a Y = a Y = --a a + x a -- x a + y a y Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 16

37 8) Main points about ellipse Equation x 2 /a 2 + y 2 /b 2 =1, (a>b>0) x 2 /b 2 + y 2 /a 2 =1, (a>b>0) Equation of major axis y = 0 x = 0 Length of major axis 2a 2a Equation of minor axis x = 0 Y = 0 Length of minor axis 2b 2b Vertices (a,0) (0,a) Foci (ae,0) (0,ae) Directrices x = a/e Y = a/e Equation of latus rectum x = ae Y = ae Length of latus rectum 2b 2 /a 2b 2 /a Centre (0,0) (0,0) Focal distance of any point(x,y) a ex,a + ex a ey,a + ey Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 17

38 9) Main points about hyperbola Equation x 2 /a 2 -- y 2 /b 2 =1, (a>0,b>0) x 2 /a 2 --y 2 /b 2 =1, (a>0,b>0) Equation of transverse axis y = 0 x = 0 Length of transverse axis 2a 2a Equation of conjugate axis x = 0 Y = 0 Length of conjugate axis 2b 2b Vertices (a,0) (0,a) Foci (ae,0) (0,ae) Directrices x = a/e Y = a/e Equation of latus rectum x = ae Y = ae Length of latus rectum 2b 2 /a 2b 2 /a Centre (0,0) (0,0) Focal distance of any point(x,y) /ex a/, /ex + a/ /ey a/, /ey + a/ Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 18

39 SHORT ANSWER TYPE QUESTIONS 1. Find the equation of the circle whose centre is (0,0) & radius 5 cm. 2. Find the vertex & focus of the parabola x 2 =-- 4ay 3. Find the point on the parabola y 2 = 4ax whose focal distance is 4 4. Find the centre & radius of the circle x 2 + y 2 2x + 3y = 4 5. Find k if the line y = 3x + k touches the circle x2 + y2 = If two ends of the diameter of a circle are (2,3) & (5,--1) find the equation of the circle. 7. Write down the foci of the hyperbola x 2 y 2 = 1 8. Find the centre of the ellipse 9x 2 + 4y 2 = If the line y = mx + 1 is a tangent to the parabola y 2 = 4x find m 10. Find the length of semi- major & semi minor axis of the ellipse 16 x y 2 = 400 LONG ANSWER TYPE QUESTION (4/6MARKS) 1. Find the equation of the circle circumscribing the triangle whose vertices are (2,0),(3,-2) &(6,4) 2. Find the equation of the circle which touches both the axes & the line 3x + 4y = 6 3. Show that the area of the triangle inscribed in the parabola y 2 =4ax is 1/8a (y 1 y 2 )(y 2 y 3 )(y 3 y 1 ) where y 1,y 2 & y 3 are the coordinates of the angular points. Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 19

40 4. Find the co-ordinates of the foci, vertices, the length of latus rectum & eccentricity of the ellipse 100 x y 2 = An arch is in the form of a parabola with its axis vertical. The arch is 10 m high & 5 m wide at the base. How wide is it 2m from the vertex of the parabola. 6. A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3cm from the end in contact with the x- axis. 7. An equilateral triangle is inscribed in the parabola y 2 = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle. 8. Find the area of the triangle formed by the lines joining the vertex of the parabola x 2 = 12y to the ends of its latus rectum. 9. An arch in the form of a semi ellipse. It is 8m wide & 2m high at the centre. Find the height of the arch at a point 1.5 m from one end. 10. Find the equation of the ellipse which passes through (-3,1) & has eccentricity 2/5, with x-axis as its major axis & centre at the origin. Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 20

41 CHAPTER 12 THREE DIMENSIONAL CO- ORDINATE GEOMETRY Points to be remembered: 1) A locus is the set of all those points & only those points in space which satisfy certain given geometrical condition or conditions. 2) An equation in x, y & z is called the equation of the given locus if and only if it is satisfied by the co-ordinates of every point in the locus & by the co-ordinates of no other point in space. 3) Distance formula : The distance between the points (x 1,y 1,z 1 ) & (x 2,y 2,z 2 ) is given by ѵ(x 2 x 1 ) 2 + (y 2 y 1 ) 2 4) Section formula : The co-ordinates of a point which divides the join of two points(x 1,y 1,z 1 ) & (x 2,y 2,z 2 ) in the ratio m:n internally is given by (mx 2 + nx 1 / m+n, my 2 + ny 1 / m+n) Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 21

42 SHORT ANSWER TYPE QUESTIONS 1) Find the distance of the point (1,-2.3) from the origin. 2) Find the mid point of the line joining (3,4,5) & (0,3,4) 3) Write the equation of the Y-Z plane. 4) Find x if the point (2,4,0) is at a distance of 10 units from the pont (3,5,x) 5) Find the points on Y- axis which are at a distance of 2Ѵ 6 units from the point ( -2,6,4) LONG ANSWER TYPE QUESTION (4 MARKS) 1) Show that the points (5,-1,1), (7,-4,7),(1,-6,10) & (-1,-3,4)are the vertices of a rhombus. 2) Find the ratio in which the line segment joinig (3,5,7) &(--1,4,2) is divided by Y-Z plane. ************************************************************ Study Material- Mathematics-Class-XI [ ZIET Bhubaneswar] Page 22