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(CODE NO:086/90)
FIRST TERM  MARKS80 
UNITS  MARKS 
I Chemical Substances
Chemical reaction; Acids, bases and salts, Metals and Non Metal 
29
S 
II World of living
Life process; control and coordination in animals and plants 
19 
III Effects of current
Magnetic effects of currents 
26 
IV Natural Resources
Sources of Energy 
06 
TOTAL  80 
SECOND TERM  MARKS80 
UNITS  MARKS 
I Chemical Substances
Carbon compounds; Periodic classification of elements 
21 
II World of living
Reroduction; Heridity and evolution 
27 
III Natural Phenomena  26 
IV Natural Resources
Conservation of natural resources; the regional environment; our environment 
06 
TOTAL  80 
COURSE STRUCTURE
CLASS X (Theory)
One Paper Time : 2^{1/2} hours Marks : 60
Unit Marks
I. Chemical Substances 18
II. World of living 16
III. Effects of Current 10
IV. Light 8
V. Natural Resources 8
Total 60
Theme : Materials (55 Periods)
Unit 1 : Chemical Substances  Nature and Behaviour
Acids, bases and salts : General properties, examples and uses, concept of pH scale, importance of pH in everyday life; preparation and uses of sodium hydroxide, Bleaching powder, Baking soda, washing soda and Plaster of Paris.
Chemical reactions : Chemical Equation, Types of chemical reactions : combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation and reduction in terms of gain and loss of oxygen and hydrogen.
Metals and non metals : General properties of Metals and Nonmetals, reactivity series, Formation and properties of ionic compounds, Basic Metallurgical processes, corrosion and its prevention.
Carbon Compounds : Covalent bonding in carbon compounds. Versatile nature of carbon, Nomenclature of carbon compounds, Functional groups, difference between saturated hydrocarbons and unsaturated hydrocarbons, Ethanol and Ethanoic acid (only properties and uses), soaps and detergents.
Periodic classification of elements : Modern Periodic table, Gradation in Properties.
Theme : The world of the living (50 Periods)
Unit 2 : World of Living
Life Processes : "living" things; Basic concept of nutrition, respiration, transport and excretion in plants and animals.
Control and Coordination in animals and plants : Tropic movements in plants; Introduction to plant hormones; control and coordination in animals : voluntary, involuntary and reflex action, nervous system; chemical coordination : animal hormones.
Reproduction : Reproduction in animal and plants (asxual and sxual). Need for and methods of family planning. Safe sx vs HIV/AIDS. Child bearing and women's health.
Heridity and evolution : Heridity; Origin of life : brief introduction; Basic concepts of evolution.
Theme : How things work. (35 Periods)
Unit 3 : Effects of Current
Potential difference and electric current. Ohm's law; Resistance, Factors on which the resistance of a conductor depends. Series combination of resistors, parallel combination of resistors; Heating effect of Electric current; Electric Power, Inter relation between P, V, I and R.
Magnets : Magnetic field, field lines, field due to a current carrying wire, field due to current carrying coil or solenoid; Force on current carrying conductor, Fleming's left hand rule. Electro magnetic induction. Induced potential difference, Induced current. Fleming's Right Hand Rule, Direct current. Alternating current; frequency of AC. Advantage of AC over DC. Domestic electric circuits.
Theme : Natural Phenomena (20 Periods)
Unit 4 : Reflection of light at curved surfaces, Images formed by spherical mirrors, centre of curvature, principalaxis, principal focus, focal length. Mirror Formula (Derivation not required), Magnification. Refraction; laws of refraction, refractive index.Refraction of light by spherical lens, Image formed by spherical lenses, Lens formula (Derivation not required),Magnification. Power of a lens; Functioning of a lens in human eye, problems of vision and remedies, applications of
spherical mirrors and lenses.Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life.
Theme : Natural Resources (20 Periods)
Unit 5 : Conservation of natural resources : Management of natural resources. Conservation and judicious use of natural resources. Forest and wild life, coal and petroleum conservation. Examples of People's participationfor conservation of natural resources.
The Regional environment : Big dams : advantages and limitations; alternatives if any. Water harvesting. Sustainability of natural resources.
Sources of energy : Different forms of energy, conventional and nonconventional sources of energy: fossil fuels, solar energy; biogas; wind, water and tidal energy; nuclear. Renewable versus nonrenewable sources.
Our Environment : Ecosystem, Environmental problems, their solutions. Biodegradable and nonbiodegradable, substances ozone depletion.
PRACTICALS
LIST OF EXPERIMENTS
Marks : 40 (20 + 20 )
1. To find the pH of the following samples by using pH paper/universal indicator.
i) Dilute Hydrochloric acid
ii) Dilute NaOH solution
iii) Dilute Ethanoic acid solution
iv) Lemon juice
v) Water
vi) Dilute Sodium Bicarbonate Solution.
2. To study the properties of acids and bases HCl & NaOH by their reaction with
i) Litmus solution (Blue/Red)
ii) Zinc metal
iii) Solid Sodium Carbonate
3. To determine the focal length of 72
a) Concave mirror
b) Convex lens by obtaining the image of a distant object.
4. To trace the path of a ray of light passing through a rectangular glass slab for different angles of incidence. Measure the angle of incidence, angle of refraction, angle of emergence and interpret the result.
5. To study the dependence of current (I) on the potential difference (V) across a resistor and determine its resistance. Also plot a graph between V and I.
6. To determine the equivalent resistance of two resistors when connected in series.
7. To determine the equivalent resistance of two resistors when connected in parallel.
8. To prepare a temporary mount of a leaf peel to show stomata.
9. To show experimentally that light is necessary for photosynthesis.
10. To show experimentally that carbon dioxide is given out during respiration.
11. To study (a) binary fission in Amoeba and (b) budding in yeast with the help of prepared slides.
12. To determine the percentage of water absorbed by raisins.
13. To perform and observe the following reactions and classify them into:
i) Combination Reaction
ii) Decomposition Reaction
iii) Displacement Reaction
iv) Double Displacement Reaction
1. Action of water on quick lime.
2. Action of heat on Ferrous Sulphate crystals
3. Iron Nails kept in copper sulphate solution
4. Reaction between Sodium sulphate and Barium chloride solutions.
14. a) To observe the action of Zn, Fe, Cu and Al metals on the following salt solutions.
i) ZnSO4 (aq.)
ii) FeSO4 (aq.)
iii) CuSO4 (aq.)
iv) Al2 (SO4)3 (aq.)
b) Arrange Zn, Fe, Cu and Al metals in the decreasing order of reactivity based on the above result.
15. To study the following properties of acetic acid (ethanoic acid) :
73
i) odour
ii) solubility in wate
iii) effect on litmus
iv) reaction with sodium bicarbonate
SCHEME OF EVALUATION :
External Examination (to be conducted by the Board through multiple choice type written test) 20 Marks
Schoolbased handson practical examination. 20 Marks
RECOMMENDED BOOKS :
Science  Textbook for class IX  NCERT Publication
Science  Textbook for class X  NCERT Publication
Assessment of Practical Skills in Science  Class IX  CBSE Publication
Assessment of Practical Skills in Science  Class X  CBSE Publication
Chapter Summary
NCERT Book Solutions
Chapter Summary
NCERT Book Solutions
Chapter Summary
NCERT Book Solutions
Chapter Summary
NCERT Book Solutions
Class X
Theory Paper 1
3 Hours Marks 80 + 20
for internal assessment
Marks Periods
Unit 1 :India and the contemporary World  II 20 45
Unit 2 :India  Resources and their Development 18 40
Unit 3 :Democratic Politics II 18 40
Unit 4 :Understanding Economics  II 16 40
Unit 5 :Disaster Management 8 25
Internal Assessment
1. Tests (formative and summative) 10
2. Assignments (School & Home assignments) 05
3. Project work 05
Unit 1 : India and the Contemporary world  II
Themes  Objectives 
Students are required to choose any two themes each
from the first two sub units and one from the third subunit. In subunit 1.1, theme 3 is compulsory. For second theme in that subunit, students are required to choose any one from the first two themes. Thus all students are required to study five themes in all. Subunit 1.1 : Events and processes : 1. Nationalism in Europe : (a) The growth of nationalism in Europe after the 1830s. (b) The ideas of Giuseppe Mazzini etc. (c) General characteristics of the movements in Poland, Hungary, Italy, Germany and Greece. 2. Nationalist Movement in Indo China : Factors leading to growth of rationalism in India (a) French colonialism in Indochina. (b) Phases of struggle against the French. (c) The ideas of Phan Dinh Phung, Phan Boi Chau, Nguyen Ac Quoc (d) The second world war and the liberation struggle. (e) America and the second Indochina war. 3. Nationalism in India : Civil Disobedience Movement (a) First world war, Khilafat and NonCooperation. (b) Salt Satyagraha. (c) Movements of peasants, workers, tribals. (d) Activities of different political groups. Subunit 1.2 : Economies and livelihoods : 4. Industrialization 1850s  1950s : (a) Contrast between the form of industrialization in Britain and India. (b) Relationship between handicrafts and industrial production, formal and informal sectors. (c) Livelihood of workers. Case studies : Britain and India. 5. Urbanization and urban lives : (a) Patterns of urbanization (b) Migration and the growth of towns. (c) Social change and urban life. (d) Merchants, middle classes, workers and urban poor. Case studies : London and Bombay in the nineteenth and twentieth century. 6. Trade and Globalization : (a) Expansion and integration of the world market in the nineteenth and early twentieth century. (b) Trade and economy between the two Wars. (c) Shifts after the 1950s. (d) Implications of globalization for livelihood patterns. Case study : The post War International Economic order, 1945 to 1960s. Subunit 1.3 : Culture, Identity and Society 7. Print culture and nationalism. (a) The history of print in Europe. (b) The growth of press in nineteenth century India. (c) Relationship between print culture, public debate and politics. 8. History of the novel: (a) Emergence of the novel as a genre in the west. (b) The relationship between the novel and changes in modern society. (c) Early novels in nineteenth century India. (d) A study of two or three major writers. Subunit 1.4 : Map Work (2 Marks) 

Themes  Objectives 
1. Resources : Types  natural and human;
Need for resource planning. 2. Natural Resources : land as a resource, soil types and distribution; changing land use pattern; land degradation and conservation measures. 3. Forest and Wild life resources : types and distribution ,depletion of flora and fauna; conservation and protection of forest and wild life. 4. Agriculture : types of farming, major crops, cropping pattern, technological and institutional reforms; their impact; contribution of Agriculture to national economy  employment and output. 5. Water resources : sources, distribution, utilisation, multipurpose projects, water scarcity, need for conservation and management, rainwater harvesting. (One case study to be introduced) 6. Mineral Resources : types of minerals, distribution, use and economic importance of minerals, conservation. 7. Power Resources : types of power resources : conventional and nonconventional, distribution and utilization, and conservation. 8. Manufacturing Industries : Types, spatial distribution, contribution of industries to the national economy, industrial pollution and degradation of environment, measures to control degradation. (One case study to be introduced) 9. Transport, communication and trade 10. Map Work (4 marks)

Understand the value of resources and the need for
their judicious utilisation and conservation; Identify various types of farming and discuss the various farming methods; To describe the spatial distribution of major crops as well as understand the relationship between rainfall regimes and cropping pattern; Explain various government policies for institutional as well as technological reforms since independence; Understand the importance of forest and wild life in our environment as well as develop concept towards depletion of resources. Understand the importance of agriculture in national economy; Understand the importance of water as a resource as well as develop awareness towards its judicious use and conservation; Discuss various types of minerals as well as their uneven nature of distribution and explain the need for their judicious utilisation; Discuss various types of conventional and nonconventional resources and their utilization Discuss the importance of industries in the national economy as well as understand the regional disparities which resulted due to concentration of industries in some areas; Discuss the need for a planned industrial development and debate over the role of government towards sustainable development; To explain the importance of transport and communication in the ever shrinking world; To understand the role of trade in the economic development of a country, 
Project / Activity
India and examine whether they reflect any relationship with climatic conditions and relief of the area.
pattern in the last decade.
Posters
Note : Any similar activities may be taken up.
Unit 3 : Democratic Politics II
Themes  Themes Objectives 
1. Power sharing mechanisms in democracy
Why and how is power shared in democracies? How has federal division of power in India helped national unity? To what extent has decentralisation achieved this objective? How does democracy accommodate different social groups? 2. Working of Democracy Are divisions inherent to the working of democracy? What has been the effect of caste on politics and of politics on caste? How has the gender division shaped politics? How do communal divisions affect democracy? 3. Competition and contestations in democracy How do struggles shape democracy in favour of ordinary people? What role do political parties play in competition and contestation? Which are the major national and regional parties in India? Why have social movements come to occupy large role in politics?
4. Outcomes of democracy Can or should democracy be judged by its outcomes? What outcomes can one reasonably expect of democracies? Does democracy in India meet these expectations? Has democracy led to development, security and dignity for the people? What sustains democracy in India? 5. Challenges to democracy Is the idea of democracy shrinking? What are the major challenges to democracy in India? How can democracy be reformed and deepened? What role can an ordinary citizen play in deepening democracy? 

Unit 4 : Understanding Economics II
Themes  Learning Objectives 
1. The Story of Development : The
traditional notion of development; National Income and Percapita Income. Growth of NI  critical appraisal of existing development indicators (PCI, IMR, SR and other income and health indicators) The need for health and educational development; Human Development Indicators (in simple and brief as a holistic measure of development. The approach to this theme : Use case study of three states (Kerala, Punjab and Bihar) or take a few countries (India, China, Sri Lanka and one developed country) 2. The Role of Service Sector in Indian Economy : What is service sector (through examples) : Importance of Service Sector in generating employment and income to the nation (with the help of a few case studies); Growth of Service Sector in India; India as a major service provider to the world; The need for public investment ; The role of important infrastructure, education and health 3. Money and Financial System : Role of money in an economy : Historical origin; Formal and Informal financial institutions for Savings and Credit  General Introduction; Select one formal institution such as a nationalized commercial bank and a few informal institutions; Local money lenders, landlords, self help groups, chit funds and private finance companies. 4. Globalisation : What is Globalisation (through some simple examples); How India is being globalised and why ; Development Strategy prior to 1991. State Control of Industries : Textile goods as an example for elaboration; Economic Reforms 1991; Strategies adoped in Reform measures (easing of capital flows; migration, investment flows); Different perspectives on globalisation and its impact on different sectors; Political Impact of globalisation. 5. Consumer Awareness : How consumer is exploited (one or two simple case studies) factors causing exploitation of consumers; Rise of consumer awareness; how a consumer should be in a market; role of government in consumer protection 

Suggested Activities
Theme 2 :
Visit to banks and money lenders / pawnbrokers and discuss various activities that you have observed in banks in the
classroom;
Participate in the meetings of self help groups, which engaged in micro credit schemes in the locality of learners and
observe issues discussed.
Theme 4 :
Provide many examples of service sector activities. Use numerical examples, charts and photographs.
Theme 5 : Collect logos of standards available for various goods and services. Visit a consumer court nearby and
discuss in the class the proceedings; Collect stories of consumer exploitation and grievances from news papers and
consumer courts.
Unit 5 : Disaster Management
25 Periods
Tsunami
Prescribed Textbooks :
1. India and the Contemporary WorldII (History)  Published by NCERT
2. Contemporary India II (Geography)  Published by NCERT
3. Democratic Politics II (Political Science)  Published by NCERT
4. Understanding Economic Development II  Published by NCERT
5. Together Towards a Safer India  Part III, a textbook an Disaster Management  Published by CBSE.
This area should give the introduction of Course
NCERT Book Solutions  Thinking of the Text
Maths Course Structure
CLASS X
One Paper Time : 3 Hours Marks : 80
UNITS MARKS
I. NUMBER SYSTEMS 04
II. ALGEBRA 20
III. TRIGONOMETRY 12
IV. COORDINATE GEOMETRY 08
V. GEOMETRY 16
VI. MENSURATION 10
VII. STATISTICS AND PROBABILITY 10
TOTAL 80
UNIT I : NUMBER SYSTEMS
1. REAL NUMBERS (15) Periods
Euclid's division lemma, Fundamental Theorem of Arithmetic  statements after reviewing work done earlier
and after illustrating and motivating through examples, Proofs of results  irrationality of decimal
expansions of rational numbers in terms of terminating/nonterminating recurring decimals.
UNIT II : ALGEBRA
1. POLYNOMIALS (6) Periods
Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference
to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real
coefficients.
2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions/
inconsistency.
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically
 by substitution, by elimination and by cross multiplication. Simple situational problems must be included.
Simple problems on equations reducible to linear equations may be included.
3. QUADRATIC EQUATIONS (15) Periods
Standard form of a quadratic equation ax^{2} + bx + c = 0, (a ≠ 0). Solution of the quadratic equations
(only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship
between discriminant and nature of roots.
Problems related to day to day activities to be incorporated.
4. ARITHMETIC PROGRESSIONS (8) Periods
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.
UNIT III : TRIGONOMETRY
1. INTRODUCTION TO TRIGONOMETRY (12) Periods
Trigonometric ratios of an acute angle of a rightangled triangle. Proof of their existence (well defined);
motivate the ratios, whichever are defined at 0^{o} & 90^{o}. Values (with proofs) of the trigonometric ratios of
30^{o}, 45^{o} & 60^{o}. Relationships between the ratios.
2. TRIGONOMETRIC IDENTITIES (16) Periods
Proof and applications of the identity sin^{2} A + cos^{2} A = 1. Only simple identities to be given. Trigonometric
ratios of complementary angles.
3. HEIGHTS AND DISTANCES (8) Periods
Simple and believable problems on heights and distances. Problems should not involve more than two right
triangles. Angles of elevation / depression should be only 30^{o}, 45^{o}, 60^{o}.
UNIT IV : COORDINATE GEOMETRY
1. LINES (In twodimensions) (15) Periods
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of
geometrical representation of quadratic polynomials. Distance between two points and section formula
(internal). Area of a triangle.
UNIT V : GEOMETRY
1. TRIANGLES (15) Periods
Definitions, examples, counter examples of similar triangles.
1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
63
3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are
proportional and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are
equal and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including
these angles are proportional, the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the
hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each
other.
7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their
corresponding sides.
8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other
two sides.
9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the
angles opposite to the first side is a right traingle.
2. CIRCLES (8) Periods
Tangents to a circle motivated by chords drawn from points coming closer and closer to the point.
1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to circle are equal.
3. CONSTRUCTIONS (8) Periods
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.
UNIT VI : MENSURATION
1. AREAS RELATED TO CIRCLES (12) Periods
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and
perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems
should be restricted to central angle of 60^{o}, 90^{o} & 120^{o} only. Plane figures involving triangles, simple
quadrilaterals and circle should be taken.)
2. SURFACE AREAS AND VOLUMES (12) Periods
(i) Problems on finding surface areas and volumes of combinations of any two of the following: cubes,
cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems
with combination of not more than two different solids be taken.)
UNIT VII : STATISTICS AND PROBABILITY
1. STATISTICS (15) Periods
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
2. PROBABILITY (10) Periods
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on
single events, not using set notation.
INTERNAL ASSESSMENT 20 Marks
Evaluation of activities 10 Marks
Project Work 05 Marks
Continuous Evaluation 05 Marks
RECOMMENDED BOOKS
1. Mathematics  Textbook for class IX  NCERT Publication
2. Mathematics  Textbook for class X  NCERT Publication
3. Guidelines for Mathematics Laboratory in Schools, class IX CBSE Publication
4. Guidelines for Mathematics Laboratory in Schools, class X  CBSE Publication
Chapter Summary
1. Euclid’s division lemma :
Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 ≤ r < b.
2. Euclid’s division algorithm : This is based on Euclid’s division lemma. According to this, the HCF of any two positive integers a and b, with a > b, is obtained as follows:
Step 1 : Apply the division lemma to find q and r where a = bq + r, 0 ≤ r < b.
Step 2 : If r = 0, the HCF is b. If r ≠ 0, apply Euclid’s lemma to b and r.
Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be
HCF (a, b). Also, HCF(a, b) = HCF(b, r).
3. The Fundamental Theorem of Arithmetic :
Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
4. If p is a prime and p divides a2, then p divides q, where a is a positive integer.
5. To prove that 2, 3 are irrationals.
6. Let x be a rational number whose decimal expansion terminates. Then we can express x in the form p
q , where p and q are coprime, and the prime factorisation of q is of the form 2n5m, where n, m are nonnegative integers.
7. Let x = p/q be a rational number, such that the prime factorisation of q is of the form 2n5m,where n, m are nonnegative integers. Then x has a decimal expansion which terminates.
8. Let x = p/q be a rational number, such that the prime factorisation of q is not of the form 2n 5m, where n, m are nonnegative integers. Then x has a decimal expansion which isnonterminating repeating (recurring).
NCERT Book Solutions
Chapter Summary
1. Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
2. A quadratic polynomial in x with real coefficients is of the form ax^{2} + bx + c, where a, b, c are real numbers with a ≠ 0.
3. The zeroes of a polynomial p(x) are precisely the xcoordinates of the points, where the graph of y = p(x) intersects the x axis.
4. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
5. The division algorithm states that given any polynomial p(x) and any nonzero polynomial g(x), there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
NCERT Book Solutions
Chapter Summary
1. Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is
a_{1}x + b_{1}y + c_{1} = 0
a_{2}x + b_{2}y + c_{2} = 0
where a_{1}, a_{2}, b_{1}, b_{2}, c_{1}, c_{2} are real numbers, such that a_{1}^{2}+b_{1}^{2} ≠ 0, a_{2}^{2}+b_{2}^{2} ≠ 0.
2. A pair of linear equations in two variables can be represented, and solved, by the:
(i) graphical method
(ii) algebraic method
3. Graphical Method :
The graph of a pair of linear equations in two variables is represented by two lines.
(i) If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent.
(ii) If the lines coincide, then there are infinitely many solutions — each point on the line being a solution. In this case, the pair of equations is dependent (consistent).
(iii) If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent.
4. Algebraic Methods : We have discussed the following methods for finding the solution(s) of a pair of linear equations :
(i) Substitution Method
(ii) Elimination Method
(iii) Crossmultiplication Method
5. There are several situations which can be mathematically represented by two equations that are not linear to start with. But we alter them so that they are reduced to a pair of linear equations.
NCERT Book Solutions
Given that,
S_{n} = 4n − n^{2}
First term, a = S_{1} = 4(1) − (1)2 = 4 − 1 = 3
Sum of first two terms = S_{2}
= 4(2) − (2)2 = 8 − 4 = 4
Second term, a_{2} = S_{2} − S_{1} = 4 − 3 = 1
d = a_{2} − a = 1 − 3 = −2
a_{n} = a + (n − 1)d
= 3 + (n − 1) (−2)
= 3 − 2n + 2
= 5 − 2n
Therefore, a_{3} = 5 − 2(3) = 5 − 6 = −1
a_{10} = 5 − 2(10) = 5 − 20 = −15
Hence, the sum of first two terms is 4. The second term is 1. 3rd, 10^{th}, and nth terms are −1, −15, and 5 − 2n respectively.
Subject 
Set I  Set II  Set III 
English (Communicative)  Set I  Set II  Set III 
English (Language and Literature)  Set I  Set II  Set III 
English (Language and Literature) (NE)  Set II  
Hindi (Course A)  Set I  Set II  Set III 
Hindi (Course A) (NE)  Set II  
Hindi (Course B)  Set I  Set II  Set III 
Hindi (Course B) (NE)  Set II  
Matchematics (For Blind Candidates only) (Urdu Version)  Set II  
Mathematics  Set I  Set II  Set III 
Mathematics (Blind candidates)  Set II  
Mathematics (For Blind Candidates Only) (Punjabi Version)  Set II  
Mathematics (NE)  Set II  
Mathematics (Panjabi Version)  Set I  
Mathematics (Urdu Version)  Set I  
Science and Technology  Set I  Set II  Set III 
Science and Technology (For Blind Candidates only)  Set II  
Science and Technology (NE)  Set II  
Science and Technology (Urdu Version)  Set I  
Social Science  Set I  Set II  Set III 
Social Science (NE)  Set II 
Courtesy: CBSE India
Other Subjects
Subject  Set I  Set II  Set III 
Arabic  Set I  Set II  
Assamese  Set II  
Bengali  Set I  Set II  
Bhutia  Set II  
Commerce  Set I  Set II  
Communicative Sanskrit  Set I  Set II  
English (Communicative)  Set II  
French  Set I  Set II  
German  Set I  Set II  
Gujarati  Set II  
Home Science  Set I  Set II  
Introductory Information Technology  Set I  Set II  
Kannada  Set II  
Lepcha  Set II  
Limboo  Set II  
Malayalam  Set II  
Manipuri  Set II  
Marathi  Set II  
Mizo  Set II  
Music Hindustani (Instrumental Melodic)  Set II  
Music Hindustani (Instrumental Percussion)  Set II  
Music Hindustani (Vocal)  Set I  Set II  
Music Karnataka (Vocal)  Set II  
Nepali  Set II  
Oriya  Set II  
Painting  Set I  Set II  
Persian  Set II  
Practical Skills in Science and Technology  Set I  Set II  Set III 
Practical Skills in Science and Technology (For Blind Candidates only) (Punjabi  
Practical Skills in Science and Technology (For Blind Candidates)  
Practical Skills in Science and Technology (For Blind Candidates) (Urdu Version)  
Practical Skills in Science and Technology (Punjabi Version)  
Practical Skills in Science and Technology (Urdu Version)  
Punjabi  Set I  Set II  
Russian  Set II  
Science and Technology (For Blind Candidates only) (Urdu Version)  Set II  
Science and Technology (Punjabi Version)  Set I  
Sindhi  Set II  
Social Science (Punjabi Version)  Set I  
Social Science (Urdu Version)  Set I  
Spanish  Set II  
Tamil  Set I  Set II  
Telugu  Set II  
Tibetan  Set II  
Urdu (Course A)  Set I  Set II  
Urdu (Course B)  Set I  Set II 
, Class 10
CBSE Class X 2009 Papers  
Set I  Set II  Set III 
CBSE Maths  CBSE Maths  CBSE Maths 
CBSE Science  CBSE Science  CBSE Science 
CBSE Class X 2008 Papers  
All India  Delhi  Foreign 
CBSE Maths  CBSE Maths  CBSE Maths 
CBSE Science  CBSE Science  CBSE Science 
CBSE Class X 2007 Papers  
All India  Delhi  Foreign 
CBSE Maths  CBSE Maths  CBSE Maths 
CBSE Science  CBSE Science  CBSE Science 
CBSE Class X 2006 Papers  
All India  
CBSE Maths  
CBSE Science 
CBSE Class X 2005 Papers  
All India  
CBSE Maths  
CBSE Science 
CBSE Class X 2004 Papers  
All India  
CBSE Maths  
CBSE Science 