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**For MHT-CET Engineering, Pharmacy, Pharm D., B. Planning courses: **

- The syllabus and criteria of questions of question will be based on the Maharashtra State Board of Secondary, and Higher Secondary Education
- The Weightage Approximation will be – 20% of Std. XI curriculum, and 80% of Std. XII curriculum for MHT-CET examination.

Unlike JEE (Main), **there will be no Negative Marking, **but the difficulty level will be the same for Physics, Mathematics, Physics, Chemistry. The difficulty level of the Biology examination will also be at par with NEET.

The examination question will be based on:

(i) Std. XII – Physics, Chemistry, Biology, and Mathematics.

(i) Std. XI – Same as mentioned above.

**Physics:** Measurements, Scalars, and Vectors, Force, Friction in solids and liquids, Refraction of Light, Ray optics, Magnetic effect of electric current, Magnetism.

**Chemistry:** Some basic concepts of chemistry, States of Matter: Gases and liquids, Redox reaction, Surface chemistry, Nature of chemical bond, Hydrogen, s-Block elements(Alkali and alkaline earth metals), Basic principles and techniques in organic chemistry, Alkanes.

**Mathematics : **Trigonometric functions, Trigonometric functions of Compound Angles, Factorization Formulae, Straight Line, Circle and Conics, Sets, Relations and Functions, Probability, Sequences, and series.

**Biology :** **Section I - Botany**

Diversity in organisms, Biochemistry of cell, Plant Water Relations, and Mineral Nutrition, Plant Growth and Development.

**Section II – Zoology**

Organization of Cell, Animal tissues, Human Nutrition, Human Respiration

Learn & Find a brief on the syllabus of Physic, Chemistry, and Mathematics for HSc Board Examination (For exact details of syllabus, contact the relevant authorities). Learn about these selected topics, subjects, and keywords on easetolearn.com

**HSC Syllabus (Std. XII) of HSC Boards of Maharashtra**

**PHYSICS**

**1. Circular motion**

Angular displacement, Angular velocity and angular acceleration, Relation between linear velocity and angular velocity, Uniform circular motion, Radial acceleration, Centripetal and centrifugal forces, Banking of roads, Vertical circular motion due to earth’s gravitation, Equation for velocity and energy at different positions of vertical circular motion. Kinematical equations for circular motion in analogy with linear motion.

**2. Gravitation**

Newton’s law of gravitation, Projection of satellite, Periodic time, Statement of Kepler’s laws of motion, Binding energy and escape velocity of a satellite, Weightlessness condition in orbit, Variation of ‘g’ due to altitude, latitude, depth and motion, Communication satellite and its uses.

**3. Rotational motion**

Definition of M.I., K.E. of rotating body, Rolling motion, Physical significance of M.I., Radius of gyration, Torque, Principle of parallel and perpendicular axes, M.I. of some regular shaped bodies about specific axes, Angular momentum and its conservation.

**4. Oscillations**

Explanation of periodic motion, S.H.M., Differential equation of linear S.H.M. Projection of U.C.M. on any diameter, Phase of S.H.M., K.E. and P.E. in S.H.M., Composition of two S.H.M.’s having same period and along same line, Simple pendulum, Damped S.H.M.

**5. Elasticity**

General explanation of elastic property, Plasticity, Deformation, Definition of stress and strain, Hooke’s law, Poisson’s ratio, Elastic energy, Elastic constants and their relation, Determination of ‘Y’, Behaviour of metal wire under increasing load, Applications of elastic behaviour of materials.

**6. Surface tension**

Surface tension on the basis of molecular theory, Surface energy, Surface tension, Angle of contact, Capillarity and capillary action, Effect of impurity and temperature on surface tension.

**7. Wave motion**

Simple harmonic progressive waves, Reflection of transverse and longitudinal waves, Change of phase, Superposition of waves, Formation of beats, Doppler Effect in sound.

8. Stationary waves

Study of vibrations in a finite medium, Formation of stationary waves on string, Study of vibrations of air columns, Free and Forced vibrations, Resonance.

**9. Kinetic theory of gases and Radiation**

Concept of an ideal gas, Assumptions of kinetic theory, Mean free path, Derivation for pressure of a gas, Degrees of freedom, Derivation of Boyle’s law, Thermodynamics- Thermal equilibrium and definition of temperature, 1st law of thermodynamics, 2nd law of thermodynamics, Heat engines and refrigerators, Qualitative idea of black body radiation,Wein’s displacement law, Green house effect, Stefan’s law, Maxwell distribution, Law of equipartition of energy and application to Specific heat capacities of gases.

**10. Wave theory of light**

Wave theory of light, Huygens’ Principle, Construction of plane and spherical wave front, Wave front and wave normal, Reflection at plane surface, Refraction at plane surface, Polarisation, Polaroids, Plane polarised light, Brewster’s law, Doppler effect in light.

**11. Interference and diffraction**

Interference of light, Conditions for producing steady interference pattern, Young’s experiment, Analytical treatment of interference bands, Measurement of

wavelength by biprism experiment, Diffraction due to single slit, Rayleigh’s criterion, Resolving power of a microscope and telescope, Difference between interference and diffraction.

**12. Electrostatics**

Gauss’ theorem proof and applications, Mechanical force on unit area of a charged conductor, Energy density of a medium, Dielectrics and electric polarisation, Concept of condenser, Capacity of parallel plate condenser, Effect of dielectric on capacity, Energy of charged condenser, Condensers in series and parallel, van-de- Graaff generator.

**13. Current electricity**

Kirchhoff’s law, Wheatstone’s bridge, Meter bridge, Potentiometer.

**14. Magnetic effects of electric current**

Ampere’s law and its applications, Moving coil galvanometer, Ammeter, Voltmeter, Sensitivity of moving coil galvanometer, Cyclotron.

**15. Magnetism**

Circular current loop as a magnetic dipole, Magnetic dipole moment of revolving electron, Magnetisation and magnetic intensity, Diamagnetism, Paramagnetism, Ferromagnetism on the basis of domain theory, Curie temperature.

**16. Electromagnetic inductions**

Laws of electromagnetic induction, proof of, e = – dØ dt Eddy currents, Self induction and mutual induction, Need for displacement current, Transformer, Coil rotating in uniform magnetic induction, Alternating currents, Reactance and impedance, LC oscillations (qualitative treatment only) Power in a.c circuit with resistance, inductance and capacitance, Resonant circuit, Wattless current, AC generator.

**17 Electrons and photons**

Photoelectric effect, Hertz and Lenard’s observations, Einstein’s equation, Particle nature of light.

**18 Atoms, Molecules and Nuclei**

Alpha particle scattering experiment, Rutherford’s model of atom. Bohr’s model, Hydrogen spectrum, Composition and size of nucleus, Radioactivity, Decay law, massenergy relation, mass defect, B.E. per nucleon and its variation with mass number, Nuclear fission and fusion, de Broglie hypothesis, Matter waves – wave

nature of particles, Wavelength of an electron, Davisson and Germer experiment, Continuous and characteristics X-rays.

**19 Semiconductors**

Energy bands in solids, Intrinsic and extrinsic semiconductors, P-type and Ntype semiconductor, P-N junction diode, I-V characteristics in forward and reverse bias, Rectifiers, Zener diode as a voltage regulator, Photodiode, Solar cell, I-V characteristics of LED, Transistor action and its characteristics, Transistor as an amplifier (CE mode), Transistor as a switch, Oscillators and Logic gates (OR, AND, NOT, NAND, NOR)

20 Communication systems

Elements of communication system, bandwidth of signals, bandwidth of transmission medium, Need for modulation, Production and detection of an amplitude modulated wave, space communication, Propagation of electromagnetic waves in atmosphere.

**CHEMISTRY**

**Unit 1: Solid State**

Classification of solids based on different forces; molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties, Band theory of metals, conductors and semiconductors and insulators and n and p type semiconductors.

**Unit 2 : Solutions and colligative properties**

Types of solutions, expression of concentration of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties –relative lowering of vapor pressure,Raoult’s law elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass.Van’t Hoff factor and calculations involving it.

**Unit 3 :Chemical thermodynamics and energetic Concepts of system**

Types of systems,surroundings. Work, heat, energy, extensive and intensive properties, state functions. First law of thermodynamics – internal energy and enthalpy,

Hess’ law of constant heat summation, enthalpy of bond dissociation, combustion, formation, atomization, sublimation. Phase transition,

ionization and solution and dilution Introduction of entropy as a state function, free energy change for spontaneous and non spontaneous processes, and equilibrium constant. Second and third law of thermodynamics

**Unit 4: Electrochemistry**

Redox reactions, conductance in electrolytic solutions, specific and molar conductivity, variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea), dry cell –electrolytic and galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion. Relation between Gibb’s energy change and emf of a cell.

**Unit 5: Chemical kinetics Rate of reaction (average and instantaneous)**

factors affecting rate of reaction; concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant, integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment). Activation energy, Arrhenius equation.

Unit 6 :General principles and processes of isolation of elements

Principles and methods of extraction – concentration, oxidation, reduction electrolytic method and refining; occurrence and principle of extraction of aluminium, copper, zinc and iron

**Unit 7: p-Block elements Group 15 elements**

General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen – preparation, properties and uses; compounds of nitrogen; preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); Phoshorous-allotropic forms; compounds of phosphorous; preparation and properties of phosphine, halides (PCl3,PCl5) and oxoacids (elementary idea only).

**Group 16 elements**

General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen; preparation, properties and uses;

Classification of oxides, simple oxides; Ozone. Sulphur – allotropic forms; compounds of sulphur; preparation, properties and uses of sulphur dioxide; sulphurc acid; industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only).

**Group 17 elements:**

General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens; preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens (structure only).

**Group 18 elements:**

General introduction, electronic configuration. Occurrence, trends in physical and chemical properties, uses.

**Unit 8 : d and f Block Elements**

d-Block Elements - General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation preparation and properties of K2Cr2O7 and KMnO4.

f-Block elements- Lanthanoids – Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences. Actinoids – Electronic configuration, oxidation states. Comparison with lanthanoids.

**Unit 9: Coordination compounds**

Coordination compounds – Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, bonding; Werner’s theory, VBT, CFT. isomerism, (structural and stereo) importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems).

**Unit 10 : Halogen derivatives of alkanes (and arenes)**

Haloalkanes : Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions. Stability of carbocations,R-S and d-l configuration

Haloarenes : Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only) stability of carbocations, R-S and d-l configurations. Uses and environmental effects of – dichloromethane, thrichloromethane, tetrachloromethane, iodoform, freons, DDT.

**Unit 11 : Alcohols, phenols and ethers**

Alcohols : Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol.

Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols.

Ethers : Nomenclature, methods of preparation, physical and chemical properties, uses.

**Unit 12 : Aldehydes, ketones and carboxylic acids**

Aldehydes and ketones : Nomenclature, nature of carbonyl group, methods of preparation. Physical and chemical properties, mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses.

Carboxylic acids : Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses.

**Unit 13: Organic compounds containing nitrogen**

Nitro compounds-General methods of preparation and chemical reactions

Amines : Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines. Cyanides and isocyanides: Will be mentioned at relevant places in context.

Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry.

**Unit 14: Biomolecules**

Carbohydrates: Classification (aldoses and ketoses), monosaccahrides d-l configuration (glucose and fructose), oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen), importance.

Proteins: Elementary idea of α -amino acids, peptide, linkage, polypeptides, proteins; structure of amines-primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes.

Lipids and hormones (elementary idea) excluding structure, their classification and functions.

Vitamins: Classification and functions.

Nucleic acids: DNA and RNA

**Unit 15: Polymers**

Classification - natural and synthetic, methods of polymerization (addition and condensation), copolymerization. Some important polymers; natural and synthetic like polythene, nylon, polyesters, bakelite, and rubber. Biodegradable and non biodegradable polymers.

**Unit 16: Chemistry in everyday life **

1. Chemicals in medicines : analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines elementary idea of antioxidants

2. Chemicals in food : Preservatives, artificial sweetening agents.

3. Cleansing agents : Soaps and detergents, cleansing action.

**Biology**

**Section I – BOTANY**

**Unit 1: Genetics and Evolution**

Chapter 1 - Genetic Basis of Inheritance:

Mendelian inheritance. Deviations from Mendelian ratio (gene interactionincomplete dominance, co-dominance, multiple alleles and Inheritance of blood

groups), Pleiotropy, Elementary idea of polygenic inheritance.

Chapter 2 - Gene: its nature, expression and regulation: Modern concept of gene in brief-cistron, muton and recon. DNA as genetic material, structure of DNA as given by

Watson and Cricks model, DNA Packaging, semi conservative replication

of eukaryotic DNA.

RNA: General structure, types and functions. Protein Synthesis; central dogma,

Transcription; Translation-Genetic Code,

Gene Expression and Gene Regulation (The Lac operon as a typical model of

gene regulation).

**Unit 2: Biotechnology and its application**

Chapter 3 - Biotechnology: Process and Application :

Genetic engineering (Recombinant DNA technology):

Transposons, Plasmids, Bacteriophages; Producing Restriction Fragments, Preparing and cloning a DNA Library, Gene Amplification (PCR).

Application of Biotechnology in Agriculture – BT crops

Biosafety Issues (Biopiracy and patents)

**Unit 3: Biology and Human Welfare **

Chapter 4 - Enhancement in Food Production

Plant Breeding Tissue Culture: Concept of Cellular Totipotency, Requirements of Tissue Culture (in brief), Callus Culture, Suspension Culture. Single Cell Protein. Biofortification.

Chapter 5 - Microbes in Human Welfare:

Microbes in Household food processing. Microbes in Industrial Production. Microbes in Sewage Treatment. Microbes in Biogas (energy) Production. Microbes as Biocontrol Agents.

Microbes as Biofertilizers.

**Unit 4: Plant Physiology :**

Chapter 6 - Photosynthesis

Autotrophic nutrition Site of Photosynthesis Photosynthetic Pigments and their role. Light-Dependent Reactions (Cyclic and non-cyclic photophosphorylation)

Light-Independent Reactions (C3 and C4 Pathways)

Chemiosmotic hypothesis, Photorespiration, Factors affecting Photosynthesis. Law of limiting factors.

Chapter 7 - Respiration ATP as currency of Energy Mechanism of Aerobic (Glycolysis, TCA Cycle and Electron Transport System) and Anaerobic Respiration. Fermentation

Exchange of gases Amphibolic pathway. Respiratory quotient of Nutrients. Significance of Respiration.

**Unit 5: Reproduction in Organisms**

Chapter 8 - Reproduction in Plants Modes of Reproduction (Asexual and Sexual).

Asexual reproduction; uniparental modesvegetative propagation, micropropagation Sexual Reproduction: structure of flower Development of male gametophyte,

Structure of anatropous ovule. Development of female Gametophyte.

Pollination: Types and Agencies. Outbreeding devices; pollen-pistil interaction. Double Fertilization: Process and Significance.

Post-fertilization changes (development of endosperm and embryo, development of seed and formation of fruit)

Special modes-apomixis, parthenocarpy, polyembryony. Significance of seed and fruit formation.

**Unit 6: Ecology and Environment**

Chapter 9: Organisms and Environment -I : Habitat and Niche Ecosystems: Patterns, components, productivity and decomposition, energy flow; pyramids of number, biomass,

energy; nutrient cycling (carbon and phosphorous). Ecological succession, Ecological servicescarbon fixation, pollination, oxygen release. Environmental issues:

agrochemicals and their effects, solid waste management, Green house effect and global warming, ozone depletion, deforestation, case studies (any two).

**Section II - ZOOLOGY**

**Unit 1: Genetics and Evolution :**

Chapter 10 - Origin and the Evolution of Life :

Origin of Life: Early Earth, Spontaneous, assembly of organic compounds, Evolution: Darwin’s contribution, Modern Synthetic Theory of evolution, Biological Evidences, Mechanism of evolution; Gene flow and genetic drift;Hardy- Weinberg principle; Adaptive radiation. Origin and Evolution of Human being.

Chapter 11 - Chromosomal Basis of Inheritance

The Chromosomal Theory. Chromosomes. Linkage and Crossing Over.

Sex-linked Inheritance (Haemophilia and colour blindness).

Sex Determination in Human being, birds, honey bee.Mendelian disorders in humans-Thalassemia. Chromosomal disorders in human: Down’s syndrome,

Turner’s syndrome and Klinfelter’s syndrome.

**Unit 2: Biotechnology and its application**

Chapter 12- Genetic Engineering and Genomics DNA Finger Printing. Genomics and Human Genome Project. Biotechnological Applications in Health:Human insulin and vaccine production, Gene Therapy. Transgenic animals.

**Unit 3: Biology and Human Welfare**

Chapter 13- Human Health and Diseases Concepts of Immunology: Immunity Types, Vaccines, Structure of Antibody, Antigen-Antibody Complex, Antigens on blood cells. Pathogens and Parasites (Amoebiasis, Malaria, Filariasis, Ascariasis, Typhoid, Pneumonia, Common cold and ring worm). Adolescence, drug and alcohol abuse. Cancer and AIDS.

Chapter 14- Animal Husbandry

Management of Farms and Farm Animals. Dairy. Poultry. Animal Breeding. Bee-Keeping. Fisheries. Sericulture Lac culture

**Unit 4: Human Physiology **

Chapter 15- Circulation Blood composition and coagulation, Blood groups. Structure and pumping action of Heart. Blood Vessels.

Pulmonary and Systemic Circulation. Heart beat and Pulse. Rhythmicity of Heart beat. Cardiac output, Regulation of cardiac activity.

Blood related disorders: Hypertension, coronary artery disease, angina pectoris, and heart failure. ECG, Lymphatic System (Brief idea): Composition of lymph and its functions.

Chapter 16- Excretion and osmoregulation

Modes of excretion-Ammonotelism, ureotelism, uricotelism. Excretory System.

Composition and formation of urine. Role of Kidney in Osmoregulation.

Regulation of kidney function: reninangiotensin, atrial natriuretic factor, ADH and Diabetes inspidus, role of other organs in excretion. Disorders; Kidney failure, Dialysis, Kidney stone (renal calculi). Transplantation. Uraemia, nephritis.

Chapter 17- Control and Co-ordination

Nervous System Structure and functions of brain and Spinal cord, brief idea about PNS and ANS. Transmission of nerve impulse. Reflex action. Sensory receptors (eye and ear), Sensory perception, general idea of other sense organs. Endocrine System Endocrine glands Hormones and their functions Mechanism of hormone action. Hormones as messengers and regulators.

Hormonal imbalance and diseases: Common disorders (Dwarfism, Acromegaly, cretinism, goiter, exopthalmic goiter, Diabetes mellitus, Addison’s disease)

**Unit 5: Reproduction in Organisms **

Chapter 18- Human Reproduction

Reproductive system in male and female. Histology of testis and ovary. Reproductive cycle. Production of gametes, fertilization, implantation. Embryo development up to three germinal layers. Pregnancy, placenta, parturition and lactation (Elementary idea). Reproductive health-birth control, Contraception and sexually transmitted diseases.MTP, Amniocentesis; Infertility

and assisted reproductive technologies- IVF, ZIFT, GIFT (elementary idea for general awareness).

**Unit 6: Ecology and Environment **

Chapter 19-Organisms and Environment-II :

Population and ecological adaptations: population interactions-mutualism, competition, predation, parasitism, population attributes- growth, birth rate

and death rate, age distribution. Biodiversity and its conservation- Biodiversity- concept, patterns, importance, loss. Threats to and need for biodiversity conservation, Hotspots, endangered organisms,extinction,red data book, biosphere reserves, national parks and sanctuaries. Environmental issues: air pollution and its control, water pollution and its control and radioactive waste management. (Case studies any two)

**MATHEMATICS**

**Unit 1: Sets, Relations And Functions**

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.

**Unit 2: Complex Numbers And Quadratic Equations**

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.

**Unit 3: Matrices And Determinants**

Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

**Unit 4: Permutations And Combinations**

Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.

**UNIT 5: MATHEMATICAL INDUCTION**

Principle of Mathematical Induction and its simple applications

**Unit 6: Binomial Theorem and Its Simple Applications:**

Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.

**Unit 7: Sequences And Series**

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: Sn, Sn2, Sn3. Arithmetic - Geometric progression.

**Unit 8: Limit, Continuity and Differentiability**

Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolles and Lagranges Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

**Unit 9: Integral Calculus**

Integral as an anti - derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities.

Evaluation of simple integrals of the type

Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

**Unit 10: Differential Equations**

Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type:

dy

-- + p (x) y = q (x)

dx

**Unit 11: Co-Ordinate Geometry**

Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

Straight lines

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines.

Circles, conic sections

Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

**UNIT 12: Three Dimensional Geometry**

Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.

**UNIT 13: Vector Algebra**

Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.

**Unit 14: Statistics And Probability**

Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

Probability: Probability of an event, addition and multiplication theorems of probability, Bayes theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.

**Unit 15: Trigonometry**

Trigonometrical identities and equations. Trigonometrical functions. Inverse trigonometrical functions and their properties. Heights and Distances.

**Unit 16: Mathematical Reasoning **

Statements, logical operations and, or, implies, implied by, if and only if. Understanding of tautology, contradiction, converse and contrapositive.