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GSEB Syllabus 2021

Gujarat Board will publish the Gujarat syllabus 2021 online for students. Students who are preparing for the Gujarat Board examination could refer to the syllabus to cover all the topics within the date of examination. Students of both classes 10th and 12th could download the Gujarat syllabus 2021 as PDF format.

Gujarat SSC syllabus 2021 consists of subjects like Sangeet, Yoga, Chitrakala, Social Science, Science, Hindi syllabus and in English Medium for Yoga, Health & Physical Education, English, and Social Science. Class 12th students can get Gujarat HSC Syllabus 2021 separately for all three streams, i.e. Science, Arts, and Commerce. Students can get the Gujarat syllabus 2021 for all class 12th subjects online on the official website of the board. 

The SSC exams will commence from 10th May 2021 to 20th May 2021 whereas HSC exams will commence from 5th May 2021 to 25th May 2021. As exams are around the corner, students are advised to go through the syllabus to plan their studies to score well. 

How to Download GSEB SSC/10th Syllabus 2021?

Students can follow the step by step procedure to download the GSEB SSC syllabus 2021 as mentioned below -

Step 1: Visit the official website of the Gujarat 10th Board - gseb.org

Step 2: Click on the "Syllabus" section on the home page.

Step 3: A new window pops up with the GSEB 10th/SSC syllabus 2021.

Step 4: Click on the respective subject syllabus. The syllabus will open in a new tab.

Step 5: Download and save the PDF for future reference.

How to Download GSEB HSC/12th Syllabus 2021?

The GSEB 12th syllabus 2021 is divided into streams like Science, Commerce and Arts. Students must download the syllabus of their respective streams by following the steps as mentioned below - 

Step 1: Visit the official website of the Gujarat 12th Board - gseb.org

Step 2: Click on the "Syllabus" section on the main Home page.

Step 3: A new window pops up with the "GSEB 12th/HSC Syllabus of Science/Commerce/Arts 2020".

Step 4: Click on the respective branch syllabus that is Science/Commerce/Arts. Syllabus file will open.

Step 5: Download and save the PDF for future reference.

Gujarat SSC Syllabus 2021 PDF Download

Students can download Gujarat 10th/SSC syllabus 2021 for individual subjects in both Gujarati and English languages using the links given in the table below. Click on the required topic to view the syllabus PDF.

Gujarat SSC Syllabus 2021 (in Gujarati and English)

New Syllabus - Gujarati Medium

New Syllabus - English Medium

Sangeet Kanthya Ane Swar Vadya Gujarati Medium

Yoga, Health and Physical Education- English Medium

Yoga Swasthya Shikshan Gujarati Medium

English First Language ENGLISH MEDIUM

Chitrakala Gujarati medium

Social Science - English Medium

Social Science Gujarati Medium

Hindi Second Language 

English Second Language Gujarati Medium

Gujarati Second Language

Gujarati First Language Gujarati Medium (Revised Edition)

 Gujarati First Language Gujarati Medium (Corrigenda)

Gujarat SSC Syllabus 2021 for Mathematics

UNIT I: NUMBER SYSTEM

Euclid's Division Lemma

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples,

Proofs of results and decimal expansions of rational numbers in terms of terminating and non-terminating recurring decimals.

UNIT II: ALGEBRA

1.POLYNOMIALS   

Zero of Polynomial

The relationship between zeros and their coefficients of quadratic polynomials.

 Statement and simple problems on the division algorithm for polynomials with real coefficients.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Pair of linear equations in two variables and their graphical solution. Also, the Geometric Representation of different possibilities of solutions/inconsistency.

Algebraic conditions for the number of solutions.

The solution of the 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          

The standard form of a quadratic equation ax2 + Bx + c = 0, (a ≠ 0).

The solution of the quadratic equations (only real roots) by factorization, by completing the square and by using the quadratic formula.

The relationship between discrimination and the nature of roots. Problems related to day to day activities to be practised.                

UNIT III: TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY               

a. Trigonometric ratios of an acute angle of a right-angled triangle.

b. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0o & 90o.

c. Values (with proofs) of the trigonometric ratios of 30o, 45o & 60o. Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES                   

Proof and applications of the identity sin2 A + cos2A = 1. Only simple identities will be given. Trigonometric ratios of complementary angles.

3. HEIGHTS AND DISTANCES                             

a. Simple and believable problems on heights and distances.

b. Problems should not involve more than two right triangles.

c. Angles of elevation and depression should be only 300, 450, 600.

UNIT IV: COORDINATE GEOMETRY

1. LINES (In two-dimensions)                              

a. Review the concepts of coordinate geometry done earlier including graphs of linear equations.

b. Awareness of the geometrical representation of quadratic polynomials.

c. The distance between two points and section formula.

d. Area of a triangle. Basic questions will be given.

UNIT V: GEOMETRY

1. TRIANGLES                                                           

Prove,

a) 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.

b) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

c) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

d) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

e) 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.

f) 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.

g) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.

h) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

I) In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.

2. CIRCLES

a) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

b) The lengths of tangents drawn from an external point to circle are equal.

3. CONSTRUCTIONS                                                          

a) Division of a line segment in a given ratio (internally)

b) Tangent to a circle from a point outside it.

c) Construction of a triangle similar to a given triangle.

UNIT VI: MENSURATION

1. AREAS RELATED TO CIRCLES                                   

a) Motivate the area of a circle; area of sectors and segments of a circle.

b) Problems based on areas and perimeter and circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60o, 90o & 120o only.

c) Plane figures involving triangles, simple quadrilaterals, and circle should be taken.

2. SURFACE AREAS AND VOLUMES                               

a) Problems with 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.

b) Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with the combination of not more than two different solids be taken.)

UNIT VII: STATISTICS AND PROBABILITY

1. STATISTICS

a) Mean, median, and mode of grouped data (a bimodal situation to be avoided). Cumulative frequency graph.

2. PROBABILITY

b) A classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.

Gujarat SSC Syllabus 2021 for Science

Unit 1: Chemical Substances - Nature and Behaviour 

a) Acids, bases and salts: Their definitions in terms of furnishing of H+ and OH— ions, General properties, examples and uses, the concept of pH scale (Definition relating to logarithm not required), the importance of pH in everyday life; preparation and uses of sodium hydroxide, Bleaching powder, Baking soda, washing soda and Plaster of Paris.

b) Chemical reactions: Chemical Equation, Balanced chemical equation, Implications of a balanced Chemical equation, Types of chemical reactions: combination, decomposition, displacement, double displacement, precipitation, neutralization, oxidation, and reduction.

c) Metals and non-metals: Properties of Metals and Non-metals, reactivity series, Formation, and properties of ionic compounds, Basic Metallurgical processes, corrosion, and its prevention.

d) Carbon Compounds: Covalent bonding in carbon compounds. Versatile nature of carbon, Homologous series Nomenclature of carbon compounds containing, Functional groups (halogens, alcohol, ketones, aldehydes, alkanes, and alkynes), the difference between saturated hydrocarbons and unsaturated hydrocarbons, Chemical properties of carbon compounds (combustion, oxidation, addition and substitution reaction).

e) Ethanol and Ethanoic acid (only properties and uses), soaps and detergents.
Periodic classification of elements: Need for classification, Modern Periodic table, Gradation in Properties.
Valency, Atomic number, metallic and non-metallic properties.

Unit 2: World of Living 

a) Life Processes: "living being"; the Basic concept of nutrition, respiration, transport, and excretion in plants and animals. Control and Co-ordination in animals and plants: Tropic movements in plants; Introduction to plant hormones; control and co-ordination in animals: the nervous system; voluntary, involuntary and reflex action, chemical co-ordination: animal hormones.

b) Reproduction: Reproduction in animals and plants (asexual and sexual). Reproductive health-need for and methods of family planning. Safe sex vs HIV/AIDS. Childbearing and women's health.


c) Heredity and evolution: Heredity; Model's contribution- Rules for the inheritance of traits; Sex determination: brief introduction; Basic concepts of evolution.

Unit 3: Effects of Current

a) Electric current, potential difference, and electric current. Ohm's law; Resistance, Resistivity, Factors on which the resistance of a conductor depends. Series combination of resistors, a parallel combination of resistors and its applications in daily life; Heating effect of Electric current and its applications in daily life.

b) Electric Power, Interrelation between P, V, I, and R.
Magnetic effects of current: Magnetic field, field lines, field due to a current-carrying conductor, field due to current carrying coil or solenoid; Force on a current-carrying conductor, Fleming's left-hand rule.

c) Electromagnetic induction. The induced potential difference, Induced current, Fleming's Right-Hand Rule, Direct current. Alternating current; frequency of AC. An advantage of AC over DC. Domestic electric circuits.

Unit 4:

a) Reflection of light at curved surfaces, Images formed by spherical mirrors, centre of curvature, principal axis, principal
focus, focal length. Mirror Formula (Derivation not required), Magnification.

b) Refraction; laws of refraction, refractive index.Refraction of light by a spherical lens, Image formed by spherical lenses, Lens formula (Derivation not required), Magnification. Power of a lens;

c) The functioning of a lens in the human eye, defects of vision and their corrections, applications of spherical mirrors and lenses. Refraction of light through a prism, dispersion of light, scattering of light, applications in daily life.

Unit 5: Management of natural resources

a) Management of natural resources. Conservation and judicious use of natural resources. Forest and wildlife, coal and petroleum conservation. Examples of People's participation in the conservation of natural resources.The Regional environment: Big dams: advantages and limitations; alternatives if any. Water harvesting. Sustainability of natural resources.

b) Sources of energy: Different forms of energy, conventional and non-conventional sources of energy: fossil fuels, solar energy; biogas; wind, water, and tidal energy; nuclear. Renewable versus non-renewable sources.

c) Our Environment: Eco-system, Environmental problems, Ozone depletion, waste production, and their solutions. Biodegradable and non-biodegradable, substances.

Gujarat SSC Syllabus 2021 for English

READING                        
Questions 1 and 2 two unseen passages of total 500 words with a variety of questions including 4 marks for vocabulary. Only prose passages will be used. One will be factual and the other will be literary.

Passage 1 - 200 words  - Four or five comprehension questions 8 marks
Passage 2 - 300 words -Four or five comprehension questions and two questions on vocabulary.
Marks for vocabulary will not exceed 4 marks. 12 marks

WRITING                    
1. Letter Writing - One letter based on provided verbal stimulus and context.                 
Type of letter : Informal: Personal such as to family and friends.
Formal: Letter of complaints, inquiries, requests, applications
2. Writing a short paragraph on a given outline/topic in about 60 words
3. Composition: A short writing task based on a verbal and/or visual stimulus. (diagram, picture, graph, map, chart, table, flowchart, etc.) Maximum words 80                       

GRAMMAR                   
A variety of short questions involving the use of particular structures within a context. Test types used will include cloze, gap-filling, sentence-completion, sentence-reordering, dialogue-completion, and sentence-transformation (including combining sentences). The Grammar syllabus will include the following areas for teaching:
1. Use of non-finite.
2. Sentence connectors: as, since, while, then, just because, just, until.
3. Clauses with what, where and how.
4. Past Tense.
5. Modals: can, could, may, must, might.
Note: All other areas covered in Class IX will also be tested in Class X as this is an integrated course for this area of learning.

TEXTBOOKS               
First Flight - NCERT Textbook for Class X
Prose 20 Marks

1. Two extracts from different prose lessons included in Textbook (Approximately 100 words each)         
These extracts chosen from different lessons will be literary and discursive in nature Each extract will be of 5 marks. One mark in each extract will be for vocabulary. 4 marks in each passage will be used for testing local and global comprehension besides a question on interpretation.

2. One out of two questions extrapolative in nature based on any one of the prose lessons from Textbook to be answered in about 80 words. 

3. One out of two questions on Drama Text (local and global comprehension question) (30-40 words)                

Poetry       
1. One extract from a poem from the prescribed reader followed by two or three questions to test the local and global comprehension of the set text.      

2. Two out of three short answer type questions on the interpretation of themes and ideas contained in the poems to be answered in 30-40 words each.         

Footprints without Feet - NCERT Supplementary Reader for Class X            

3. One out of two questions from Supplementary Reader to interpret, evaluate and analyse character, plot or situations occurring in the lessons to be answered in about 100 words.     

4. One out of two short answer type questions of interpretative and evaluative nature based on lessons to be answered in 30-40 words.

5. One out of two short answer type questions based on factual aspects of the lessons to be answered in 20-30 words.

Gujarat HSC Syllabus PDF Download

Gujarat HSC Syllabus PDF 2021

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Mathematics

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Political Science

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Psychology

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Accountancy

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Biotechnology

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Biology 

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Computer Science

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Economics

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English Elective

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Entrepreneurship

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Geography

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History

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Fashion Studies

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Home Science

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GSEB HSC/12th Syllabus of Biology

  • Chapter 1: Physiology of Plants

  • Chapter 2: Physiology of Animals

  • Chapter 3: Reproduction, Growth, and Development

  • Chapter 4: Ecology and Environment

  • Chapter 5: Biology and Human Welfare

Gujarat HSC Syllabus 2021 Biology

Name of the Subject

Topics

Physiology of Plants

The cell as a functional unit, Composition of protoplasm; water relations; Absorption and conduction (Diffusion, osmosis, plasmolysis, permeability, water potential, absorption) -Theories of the ascent of sap - root pressure, suction force transpiration - importance. Factors affecting rate o transpiration; mechanism of stomatal opening and closing; (Potassium ion theory); factors affecting the movement of guard cells.

-Mineral absorption - functions of mineral elements; essential major elements and trace elements; deficiency symptoms of elements; theories

of translocation; translocation of solutes; Nitrogen metabolism, Nitrogen metabolism with emphasis on biological nitrogen fixation.

-Photosynthesis - significance; site of photosynthesis (functional importance of chlorophyll structure) Photochemical and biosynthetic phases.

Electron transport system;

-Photophosphorylation (cyclic and noncyclic)

C3 and C4 metabolic pathway; photorespiration, factors affecting - photosynthesis; mode of nutrition (Autotrophic, heterotrophic, saprophytic,

parasitic and insectivorous plants) chemosynthetic nutrition.

Physiology of Animals

-Nutrition and its types; nutrients food and vitamins; the digestive system of invertebrate (Cockroach)

-Digestive system and digestion process in humans (ingestion, digestion, absorption, assimilation, the formation of fecal matter, defecation)

(Intracellular and extracellular); the role of enzymes and hormones indigestion.

-Malnutrition and undernutrition; disorder related to nutrition. Gaseous exchange in animals (Earthworm, Cockroach)

- Respiration in humans; respiratory organs; mechanism of respiration.

- Breathing and it's regulation; transport of gases through blood; common respiratory disorders, prevention, and cure.

Circulation of Body Fluids - Open circulatory system in cockroach; closed circulatory system in humans; Blood and its composition and beating

process; pulmonary and systemic circulation; Heartbeat and pulse; rhythmicity of heart, beat.

Blood-related disorders - Hypertension, atheroma, and arteriosclerosis; ECG - Pacemaker; lymphatic system; immunity, immune system.

-Elimination of nitrogenous excretory substances - Ammonotelism, Ureotelism, Urecotelism Excretory system of cockroach and humans

Composition and formation of urine.

- Role of the kidney in osmoregulation, Kidney failure; dialysis, Kidney-transplantation, Role of ADH, the role of skin and lungs.

Locomotion and movements -

Reproduction, Growth, and Development

-Modes of reproduction in flowering plants; vegetative propagation (natural and artificial); the significance of vegetative propagation; sexual

reproduction; development of. male and female gametophyte, Pollination (types and factors); Double fertilization, incompatibility, embryo

development, parthenogenesis and parthenocarpy.

-Characters of plant growth, growth regulators (phytohormones) Auxins, Gibberellins, Cytokinins, ethylene, ABA, Seed germination -

mechanism and factors; the role of growth regulators in dormancy of seeds; senescence, abscission. Plant movement, geotropism, phototropism,

turgor growth movements, (tropics, nastic, and nutation) Flowering, Photoperiodism, -Vernalization

-Sexual and asexual reproduction in animals in general. The male and female reproductive system of humans; reproductive cycle in human,

oogenesis, fertilization - physical and chemical events.

Embryonic development up to three germinal layers and their derivatives. Embryonic membranes, General aspect of the placenta.

-Cellular growth Growth rate, growth map, growth - regulation and hormones; Mechanism and types of- regeneration. Ageing - cellular and

extracellular changes; principles of ageing.

Ecology and Environment

-Organism and their environment; factors - Air, Water, Soil, temperature, light, biota; a range of tolerance; ecological adaptations

page 1 / 2

Gujarat Board Biology Syllabus for Class 12 001
Education Boards

-Levels of an organisation - Structure and functions, productivity, energy flow, ecological efficiencies; decomposition and nutrient cycling; major
biomes - forests, grasslands and deserts.
ecological succession - types and mechanism; Natural resources types and resources. Environment pollution - kinds, sources and abatement of
air, water soil and noise pollution.
-Global environmental changes, green-house effects; global warming; sea-level rise and ozone layer depletion. Living resources
- Terrestrial, marine and other aquatic resources; biodiversity - benefits and evaluation, threats.
Endangered species, extinctions, conservation of biodiversity (biosphere reserves and other protected areas) National and international efforts
both governmental and non-governmental; environmental ethics and legislation.

 

-Population, environment and development; Population growth and factors (Vitality, mortality, immigration, emigration, age and sex ratio)
-Impact of population growth; Reproductive health; common problems of adolescence; social and moral implications; mental and addictive
disorders; population as a resource.
-Food production, Hybridization, improved varieties, biofertilizers plant tissue culture and its applications; crop and animal diseases;
biopesticides; genetically modified food; BioWar; biopiracy, biopatent, biotechnology and sustainable agriculture.
-Recent research in vaccines, organ transplantation, immune disorders; modern techniques in diseases diagnosis; AIDS, STD, Cancer (types,
causes, diagnosis, remedy) Biotechnology in therapeutics - hormones, interferon and immuno modulations.

Gujarat HSC Syllabus 2021 of Accountancy

  • Chapter 1: Partnership Accounts

  • Chapter 2: Reconstruction of Partnership

  • Chapter 3: Dissolution of Partnership Firm

  • Chapter 4: Share Capital Transaction

  • Chapter 5: Accounting for Debentures

  • Chapter 6: Analysis of Financial Statements

  • Chapter 7: Deshi Nama System

Gujarat HSC Syllabus Accountancy 2021

Name of the Unit

Topics

Partnership Accounts

Form of a partnership firm - partnership Deed - Meaning and Impact.

Special features of partnership final accounts: Fixed v/s fluctuating capital accounts, distribution of profit amongst partners.

Adjustments of 11th Std. and relating to Guarantee of profits, Joint life Policy (only explanation relating to accounting entries of Joint life Policy.

Reconstruction of Partnership

-Charges in P. & L. ratio of existing partners - sacrifice ratio & Gain or benefit ratio.

-Revaluation of Assets & Liabilities, Distribution of accumulated profit & Reserves - Goodwill - Factors affecting the valuation of goodwill and

methods of valuation of goodwill :

-Average Profit (Simple and weighted), Super Profit (only Explanation of the concept of super profit), method of capitalizing it (only Explanation),

Accounting Treatment of Goodwill)

-Admission of a partner: Problems Arising on Admission of a partner, New Profit sharing ratio after Admission of a Partner -Sacrifice ratio,

Entries for goodwill on Admission, accounting entries for revaluation of Assets and Liabilities, accounting entries for distribution of

accumulated profits, Adjustment of Capital Accounts.

-Retirement or Death of Partner: New profit-sharing ratio after retirement, Gain ratio, Treatment of Goodwill on retirement, Accounting entries

for revaluation of Assets & Liabilities, Distribution of Accumulated Profit or Reserve, Adjustments for Joint life Policy and Capital Accounts.

(Note: Examples of Retirement and Admission together is not included.)

Dissolution of Partnership Firm

-Meaning, mode of settlement of Accounts: Entries on Dissolution Realisation Account and Preparation of necessary accounts and also Profit &

Loss in Realisation A/c.

(Piecemeal Distribution, sale to company & Insolvency of Partnership is not Included.)

Share Capital Transaction

-Share & Share Capital: Meaning and types.

-Accounting of Share Capital

-Issue of Equity & Preference shares, its Allotment, Private placement, and public subscription, oversubscription and under subscription, to

issue share, at par, at a premium and at discount, calls received in advance, calls-in-arrears, issue of shares for consideration other than cash.

-Share forfeiture: Accounting entries, reissue of forfeited shares.

-Disclosure of share capital in the company's Balance sheet.

Accounting for Debentures

-Issue of Debentures: Meaning of Debenture, Issue of debentures at par and at premium, issue of debentures for consideration other than

cash, Debentures issued as collateral security.

-Redemption of Debenture: Meaning, consideration for Redemption of debentures,

(A) Repayment on a specified date

(i) Sinking Fund

(ii) Accumulated Profits. and

(iii) From Capital obtained through issue of new shares and debentures.

Analysis of Financial Statements

-Financial statement of the company
- Structure of Balance Sheet: With only Main Headings.
-Analysis and interpretation of financial statement: Meaning, importance, objectives & Limitations.
Methods used in the analysis of financial statements
(a) Comparative Financial and Operating Statements,
(b) Common size statements
-Accounting Ratio: Meaning and objectives, types of ratios.
-Liquidity ratios Current ratio,
Liquid ratio.
Solvency ratios Debt - Equity ratio total assets to debt, Proprietary ratio.
(Debt - equity-ratio) Activity Ratios: Turnover ratio, Debtors Turnover, Creditors Turnover, working capital turnover ratio.
Profitability Ratios: Gross Profit ratio, Net profit ratio, operating ratio.
(Note: only the calculation of the above ratios from given information is included.)

Deshi Nama System

-Different books: Rojmel, Bethomel, Peta Nondh - (Jama Nondh & Udhar Nondh), Preparation of Khatavahi.
-Utaro (Trial Balance)
-Havala mel or Achad mel
-Preparation of final accounts 2 methods
(i) Kharid - Vakra Khata Method
(ii) Vatav Khata Method

Gujarat HSC Syllabus 2021 of Mathematics

  • Chapter 1: Relations And Functions

  • Chapter 2: Algebra

  • Chapter 3: Calculus

  • Chapter 4: Vectors And Three-Dimensional Geometry

  • Chapter 5: Linear Programming

  • Chapter 6: Probability

Gujarat HSC Syllabus Mathematics 2021

Name of the Unit

Topics

Relations And Functions

  • Relations and Functions: Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, the inverse of a function. Binary operations.

  • Inverse Trigonometric Functions:

    Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Algebra

  • Matrices:

    Concept, notation, order, equality, types of matrices, zero matrices, transpose of a matrix, symmetric and skew-symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices.

  • Determinants: Determinants of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Calculus

  • Continuity and Differentiability: 

    Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function.Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretations.

  • Applications of Derivatives: Applications of derivatives: rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

  • Integrals: Integration as an inverse process of differentiation. Integration of a variaty of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated.Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

  • Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).

  • Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx+ py = q, where p and q are functions of x.

Vectors And Three-Dimensional Geometry

  • Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors.

  • Three - dimensional Geometry: Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between(i) two lines,(ii) two planes,(iii) a line and a plane. Distance of a point from a plane.

Linear Programming

  • Linear Programming: Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Probability

Probability: Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Gujarat SSC Syllabus 2021 Highlights

Gujarat SSC Syllabus Highlights 2021

Conducting Authority

Gujarat Secondary and Higher Secondary Board of Secondary Education

Acronym

GSHSBSE

Exam Name

Gujarat SSC Board Examination 2021

Category

Gujarat SSC Syllabus 2021

Mode of Syllabus

PDF

Official Website

gseb.org

Gujarat HSC Syllabus 2021 Highlights

Gujarat HSC Syllabus Highlights 2021

Conducting Authority

Gujarat Secondary and Higher Secondary Board of Secondary Education

Acronym

GSHSBSE

Exam Name

Gujarat HSC Board Examination 2021

Category

Gujarat HSC Syllabus 2021

Mode of Syllabus

PDF

Official Website

gseb.org

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