MHT CET Exam 2027: Dates, Syllabus, Pattern & Preparation, Sample Papers

Class-XI-Chemistry: Unit 01

Class-XI-Chemistry: Unit 02

Class-XI-Chemistry: Unit 03

Class-XI-Chemistry: Unit 04

Class-XI-Chemistry: Unit 05

Class-XI-Chemistry: Unit 06

Class-XI-Chemistry: Unit 07

Class-XI-Chemistry: Unit 08

Class-XI-Chemistry: Unit 09

Class-XI-Chemistry: Unit 10

Class-XI-Mathematics: Unit 01

Class-XI-Mathematics: Unit 02

Class-XI-Mathematics: Unit 03

Class-XI-Mathematics: Unit 04

Class-XI-Mathematics: Unit 05

Class-XI-Mathematics: Unit 06

Class-XI-Mathematics: Unit 07

Class-XI-Mathematics: Unit 08

Class-XI-Mathematics: Unit 09

Class-XI-Mathematics: Unit 10

Class-XI-Biology: Unit 01

Class-XI-Biology: Unit 02

Class-XI-Biology: Unit 03

Class-XI-Biology: Unit 04

Class-XII-Physics: Unit 01

• 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

Class-XII-Physics: Unit 02

• 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

Class-XII-Physics: Unit 03

• 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

Class-XII-Physics: Unit 04

• 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

Class-XII-Physics: Unit 05

• 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

Class-XII-Physics: Unit 06

• 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

Class-XII-Physics: Unit 07

• Simple harmonic progressive waves, reflection of transverse and longitudinal waves, change of phase, superposition of waves, formation of beats, Doppler effect in sound

Class-XII-Physics: Unit 08

• Study of vibrations in a finite medium, formation of stationary waves on string, study of vibrations of air columns, free and forced vibrations, resonance

Class-XII-Physics: Unit 09

• 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, Wien's displacement law, greenhouse effect, Stefan's law, Maxwell distribution
• law of equipartition of energy and application to specific heat capacities of gases

Class-XII-Physics: Unit 10

• 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

Class-XII-Physics: Unit 11

• 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

Class-XII-Physics: Unit 12

• 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.

Class-XII-Physics: Unit 13

• Kirchhoff’s law, Wheatstone’s bridge, meter bridge, potentiometer

Class-XII-Physics: Unit 14

• Ampere’s law and its applications, moving coil galvanometer, ammeter, voltmeter, sensitivity of moving coil galvanometer, cyclotron

Class-XII-Physics: Unit 15

• 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

Class-XII-Physics: Unit 16

• 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, A.C. generator

Class-XII-Physics: Unit 17

• Photoelectric effect, Hertz and Lenard’s observations, Einstein’s equation, particle nature of light

Class-XII-Physics: Unit 18

• Alpha particle scattering experiment, Rutherford’s model of atom
• Bohr’s model, hydrogen spectrum, composition and size of nucleus, radioactivity, decay law, mass-energy 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

Class-XII-Physics: Unit 19

• Energy bands in solids, intrinsic and extrinsic semiconductors, P-type and N-type 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)

Class-XII-Physics: Unit 20

• 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

Class-XII-Chemistry: Unit 01

• 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

Class-XII-Chemistry: Unit 02

• 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

Class-XII-Chemistry: Unit 03

• 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’s 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

Class-XII-Chemistry: Unit 04

• 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 Gibbs energy change and EMF of a cell

Class-XII-Chemistry: Unit 05

• 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

Class-XII-Chemistry: Unit 06

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

Class-XII-Chemistry: Unit 07

• Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen – preparation, properties and uses; compounds of nitrogen
• Group 15 elements: Preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); phosphorus-allotropic forms; compounds of phosphorus
• Group 15 elements: 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
• Group 16 elements: Sulphur-allotropic forms; compounds of sulphur; preparation, properties and uses of sulphur dioxide; sulphuric 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
• Group 17 elements: Oxoacids of halogens (structure only)
• Group 18 elements: General introduction, electronic configuration. Occurrence, trends in physical and chemical properties, uses

Class-XII-Chemistry: Unit 08

• 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
• d-Block elements: General trends in properties of the first row transition metals-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

Class-XII-Chemistry: Unit 09

• 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)
• 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, trichloromethane
• Haloarenes: Tetrachloromethane, iodoform, freons, DDT

Class-XII-Chemistry: Unit 10

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

Class-XII-Chemistry: Unit 11

• 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, electrophilic substitution reactions, uses of phenols
• Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Class-XII-Chemistry: Unit 12

• 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

Class-XII-Chemistry: Unit 13

• 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

Class-XII-Chemistry: Unit 14

• Carbohydrates: Classification (aldoses and ketoses), monosaccharides d-l configuration (glucose and fructose), oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen), importance
• Proteins: Elementary idea of α -amino acids, peptides, linkage, polypeptides, proteins; structure of amines-primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes
• Proteins: Lipids and hormones (elementary idea) excluding structure, their classification and functions
• Vitamins: Classification and functions
• Nucleic acids: DNA and RNA

Class-XII-Chemistry: Unit 15

• 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

Class-XII-Chemistry: Unit 16

• Chemicals in medicines: Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines elementary idea of antioxidants
• Chemicals in food: Preservatives, artificial sweetening agents
• Cleansing agents: Soaps and detergents, cleansing action

Class-XII-Botany: Unit 01

• Genetic basis of inheritance: Mendelian inheritance. deviations from Mendelian ratio (gene interaction-incomplete dominance, codominance, multiple alleles and inheritance of blood groups), pleiotropy, elementary idea of polygenic inheritance
• 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 Crick's model, DNA Packaging, semi-conservative replication of eukaryotic DNA
• Gene-its nature, expression and regulation: 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)

Class-XII-Botany: Unit 02

• Biotechnology-process and application: Genetic engineering (recombinant DNA technology)-transposons, plasmids, bacteriophages; producing restriction fragments, preparing and cloning a DNA library, gene amplification (PCR)
• Biotechnology-process and application: Application of biotechnology in agriculture- bt crops. Biosafety issues (biopiracy and patents)
• 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
• 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

Class-XII-Botany: Unit 03

• 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
• Photosynthesis: Photorespiration, factors affecting photosynthesis. Law of limiting factors
• 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

Class-XII-Botany: Unit 04

• Reproduction in plants: Modes of reproduction (asexual and sexual). Asexual reproduction; uniparental modes-vegetative propagation, micropropagation sexual reproduction: Structure of flower development of male gametophyte, structure of anatropous ovule
• Reproduction in plants: Development of female gametophyte. Pollination: Types and agencies. outbreeding devices; pollen-pistil interaction. Double fertilization: Process and significance
• Reproduction in plants: 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

Class-XII-Botany: Unit 05

• 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
• Organisms and environment-I -habitat and niche: Ecological services-carbon fixation, pollination, oxygen release. Environmental issues: Agrochemicals and their effects, solid waste management, greenhouse effect and global warming, ozone depletion
• Organisms and environment-I -habitat and niche: Environmental issues-deforestation, case studies (any two)

Class-XII-Zoology: Unit 01

• 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
• Origin and the evolution of life: Hardy Weinberg principle; adaptive radiation. origin and evolution of human beings
• 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 basis of inheritance: Chromosomal disorders in human-Down’s syndrome, Turner’s syndrome and Klinefelter’s syndrome.

Class-XII-Zoology: Unit 02

• Genetic engineering and genomics: DNA fingerprinting. Genomics and human genome project. Biotechnological applications in health: Human insulin and vaccine production, gene therapy. Transgenic animals

Class-XII-Zoology: Unit 03

• Human health and diseases: Concepts of immunology-immunity types, vaccines, structure of antibody, antigen-antibody complex, antigens on blood cells
• Human health and diseases: Pathogens and parasites (amoebiasis, malaria, filariasis, ascariasis, typhoid, pneumonia, common cold and ringworm). Adolescence, drug and alcohol abuse. Cancer and aids
• Animal husbandry: Management of farms and farm animals. Dairy. Poultry. Animal breeding. Bee-keeping. Fisheries. Sericulture. LAC culture

Class-XII-Zoology: Unit 04

• 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
• Circulation: Blood related disorders-hypertension, coronary artery disease, angina pectoris, and heart failure. ECG, lymphatic system (brief idea): Composition of lymph and its functions
• 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: Renin-angiotensin, atrial natriuretic factor
• Excretion and osmoregulation: ADH and diabetes insipidus, role of other organs in excretion. Disorders; kidney failure, dialysis, kidney stone (renal (renal calculi). Transplantation. Uraemia, nephritis
• Control and coordination: 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
• Control and coordination: Endocrine system, endocrine glands, hormones and their functions. Mechanism of hormone action. Hormones as messengers and regulators
• Control and coordination: Hormonal imbalance and diseases-common disorders (Dwarfism, Acromegaly, cretinism, goitre, exophthalmic goitre, diabetes mellitus, Addison’s disease)

Class-XII-Zoology: Unit 05

• 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
• Human reproduction: Pregnancy, placenta, parturition and lactation (elementary idea). Reproductive health-birth control, contraception and sexually transmitted diseases. MTP, amniocentesis
• Human reproduction: Infertility and assisted reproductive technologies-IVF, ZIFT, GIFT (elementary idea for general awareness)

Class-XII-Zoology: Unit 06

• 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
• Organisms and environment-II: 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
• Organisms and environment-II: Environmental issues-air pollution and its control, water pollution and its control and radioactive waste management (case studies any two)

Class-XII-Mathematics: Unit 01

• Statements-introduction, sentences and statement, truth value of statement, open sentences, compound statement, quantifier and quantified statements, logical connectives: Conjunction, disjunction, negation, implication/ conditional, biconditional
• Truth tables of compound statements, examples related to real life and mathematics, statement patterns and logical equivalence-tautology, contradiction, contingency, duality, negation of compound statement, contrapositive, converse, inverse
• Algebra of statements-idempotent law, associative law, commutative law, distributive law, identity law, complement law, involution law, De Morgan's laws, difference between converse, contrapositive, contradiction
• Application-introduction to switching circuits (simple examples)

Class-XII-Mathematics: Unit 02

• Elementary transformation of a matrix-revision of cofactor and minor, elementary row transformation, elementary column transformation, inverse of a matrix-existence and uniqueness of inverse of a matrix, inverse by elementary transformation
• Adjoint method, application-solution of system of linear equations by-reduction method, inversion method

Class-XII-Mathematics: Unit 03

• Trigonometric equations-general solution of trigonometric equation of the type: sinθ, = 0, cosθ = 0, tanθ = 0, sinθ = sinα, cosθ = cosα, tanθ = tanα, sin2 θ = sin2 α, cos2 θ = cos2 α, tan2 θ = tan2 α, acosθ + bsinθ = C
• Solution of a triangle: Polar coordinates, sine rule, cosine rule, projection rule, area of a triangle, application, Heron’s formula, Napier Analogues, inverse trigonometric functions-definitions, domain, range, principle values, graphs of inverse
• Solution of a triangle: Trigonometric function, properties of inverse functions

Class-XII-Mathematics: Unit 04

• Pair of lines passing through origin-combined equation, homogeneous equation, theorem-the joint equation of a pair of lines passing through origin and its converse
• Acute angle between the lines represented by ax2 + 2hxy + by2 =0, condition for parallel lines, condition for perpendicular lines, pair of lines not passing through origin-combined equation of any two lines
• Condition that the equation ax2 + 2hxy + by2 + 2gx + 2fy + c=0 should represent a pair of lines (without proof), acute angle between the lines (without proof), condition of parallel and perpendicular lines, point of intersection of two lines

Class-XII-Mathematics: Unit 05

• Tangent of a circle-equation of a tangent at a point to (1) standard circle, (2) general circle, condition of tangency only for line y = mx + c to the circle x2 + y2 = a2 , tangents to a circle from a point outside the circle, director circle
• Length of tangent segments, normal to a circle-equation of normal at a point

Class-XII-Mathematics: Unit 06

• Tangents and normals-equations of tangent and normal at a point for parabola, ellipse, hyperbola; condition of tangency for parabola; ellipse, hyperbola; tangents in terms of slope for parabola, ellipse, hyperbola, tangents from a point outside conics
• Locus of points from which two tangents are mutually perpendicular, properties of tangents and normals to conics (without proof)

Class-XII-Mathematics: Unit 07

• Revision, collinearity and coplanarity of vectors: Linear combination of vectors, condition of collinearity of two vectors, conditions of coplanarity of three vectors, section formula: Section formula for internal and external division, midpoint formula
• Section formula: Centroid formula, scalar triple product: Definition, formula, properties, geometrical interpretation of scalar triple product, application of vectors to geometry-medians of a triangle are concurrent, altitudes of a triangle are concurrent
• Angle bisectors of a triangle are concurrent, diagonals of a parallelogram bisect each other and converse, median of trapezium is parallel to the parallel sides and its length is half the sum of parallel sides
• Angle subtended on a semicircle is right angle

Class-XII-Mathematics: Unit 08

• Direction cosines and direction ratios: Direction angles, direction cosines, direction ratios, relation between direction ratio and direction cosines, angle between two lines, condition of perpendicular lines

Class-XII-Mathematics: Unit 09

• Equation of line passing through given point and parallel to given vector, equation of line passing through two given points, distance of a point from a line, distance between two skew lines, distance between two parallel lines (vector approach)

Class-XII-Mathematics: Unit 10

• Equation of plane in normal form, equation of plane passing through the given point and perpendicular to given vector, equation of plane passing through the given point and parallel to two given vectors
• Equation of plane passing through three noncollinear points, equation of plane passing through the intersection of two given planes, angle between two planes, angle between line and plane, condition for the coplanarity of two lines
• Distance of a point from a plane (vector approach)

Class-XII-Mathematics: Unit 11

• Introduction of L.P.P., definition of constraints, objective function, optimization, constraint equations, nonnegativity restrictions, feasible and infeasible region, feasible solutions, mathematical formulation-mathematical formulation of L.P.P.
• Different types of L.P.P. problems, graphical solutions for problem in two variables, optimum feasible solution

Class-XII-Mathematics: Unit 12

• Continuity of a function at a point: Left hand limit, right hand limit, definition of continuity of a function at a point, discontinuity of a function, types of discontinuity, algebra of continuous functions, continuity in interval-definition
• Continuity of some standard functions-polynomial, rational, trigonometric, exponential and logarithmic function.

Class-XII-Mathematics: Unit 13

• Revision-revision of derivative, relationship between continuity and differentiability-left hand derivative and right hand derivative (need and concept), every differentiable function is continuous but converse is not true
• Derivative of composite function-chain rule, derivative of inverse function, derivative of inverse trigonometric function: Derivative of implicit function definition and examples, derivative of parametric function-definition of parametric function
• Exponential and logarithmic function-derivative of functions which are expressed in one of the following form-(a) product of functions, (b) quotient of functions, (c) higher order derivative, second order derivative, (d) [f(x) ] [g(x)]

Class-XII-Mathematics: Unit 14

• Geometrical application-tangent and normal at a point, Rolle's theorem, and mean value theorem and their geometrical interpretation (without proof), derivative as a rate measure-introduction, increasing and decreasing function
• Derivative as a rate measure-approximation (without proof), maxima and minima-introduction of extrema and extreme values, maxima and minima in a closed interval, first derivative test, second derivative test

Class-XII-Mathematics: Unit 15

• Indefinite integrals-methods of integration, substitution method, integrals of the various types, integration by parts (reduction formulae are not expected), integration by partial fraction-factors involving repeated and non-repeated linear factors
• Non-repeated quadratic factors, definite integral-definite integral as a limit of sum, fundamental theorem of integral calculus (without proof), evaluation of definite integral-(1) by substitution
• Evaluation of definite integral-(2) integration by parts, properties of definite integrals

Class-XII-Mathematics: Unit 16

• Area under the curve: Area bounded by curve and axis (simple problems), area bounded by two curves, volume of solid of revolution-volume of solid obtained by revolving the area under the curve about the axis (simple problems)

Class-XII-Mathematics: Unit 17

• Definition-differential equation, order, degree, general solution, particular solution of differential equation, formation of differential equation-formation of differential equation by eliminating arbitrary constants (at most two constants)
• Solution of first order and first degree differential equation-variable separable method, homogeneous differential equation (equation reducible to homogeneous form are not expected), linear differential equation, applications: Population growth
• Applications: Bacterial colony growth, surface area, Newton's laws of cooling, radioactive decay

Class-XII-Mathematics: Unit 18

• Bivariate frequency distribution-bivariate data, tabulation of bivariate data, scatter diagram, covariance of ungrouped data, covariance for bivariate frequency distribution, Karl Pearson’s coefficient of correlation

Class-XII-Mathematics: Unit 19

• Probability distribution of a random variable-definition of a random variable, discrete and continuous random variable, probability mass function (p.m.f.), probability distribution of a discrete random variable
• Cumulative probability distribution of a discrete random variable, expected value, variance and standard deviation of a discrete random variable, probability density function (p.d.f.), distribution function of a continuous random variable

Class-XII-Mathematics: Unit 20

• Definition of Bernoulli trial, conditions for binomial distribution, binomial distribution (P.M.F.), mean, variance and standard deviation, calculation of probabilities (without proof), Normal distribution: P.D.F, mean, variance and standard deviation
• Normal distribution: Standard normal variable, simple problems (without proof)