Diploma in Pharmacy (D.Pharm) Entrance

• UNIT 1: PHYSICAL WORLD AND MEASUREMENT

  5 टॉपिक

  • Need for measurement: Units of measurement
  • systems of units
  • SI units, fundamental and derived units
  • Significant figures
  • Dimensions of physical quantities, dimensional analysis and its applications

• UNIT 2: KINEMATICS

  14 में से 7 टॉपिक

  • Motion in a Straight Line
  • Frame of reference
  • Elementary concepts of differentiation and integration for describing motion
  • uniform and non-uniform motion, and instantaneous velocity
  • uniformly accelerated motion
  • velocity - time and position-time graphs
  • Relations for uniformly accelerated motion (graphical treatment)

• UNIT 3: LAWS OF MOTION

  7 टॉपिक

  • Laws of Motion Intuitive concept of force, Inertia, Newton's first law of motion
  • momentum and Newton's second law of motion
  • impulse
  • Newton's third law of motion
  • Law of conservation of linear momentum and its applications
  • Equilibrium of concurrent forces, Static and kinetic friction, laws of friction, rolling friction, lubrication
  • Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road)

• UNIT 4: WORK, ENERGY AND POWER

  5 टॉपिक

  • Work, Energy and Power
  • Work done by a constant force and a variable force
  • kinetic energy, work energy theorem, power
  • Notion of potential energy, potential energy of a spring, conservative forces: non-conservative forces, motion in a vertical circle
  • elastic and inelastic collisions in one and two dimensions

• UNIT 5: MOTION OF SYSTEM OF PARTICLES AND RIGID BODY

  7 टॉपिक

  • System of Particles and Rotational Motion
  • Centre of mass of a two-particle system, momentum conservation and Centre of mass motion
  • Centre of mass of a rigid body
  • centre of mass of a uniform rod
  • Moment of a force, torque, angular momentum, law of conservation of angular momentum and its applications
  • Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions
  • Moment of inertia, radius of gyration, values of moments of inertia for simple geometrical objects (no derivation)

• UNIT 6: GRAVITATION

  3 टॉपिक

  • Kepler's laws of planetary motion, universal law of gravitation
  • Acceleration due to gravity and its variation with altitude and depth
  • Gravitational potential energy and gravitational potential, escape speed, orbital velocity of a satellite

• UNIT 7: PROPERTIES OF BULK MATTER

  15 में से 7 टॉपिक

  • Mechanical Properties of Solids
  • Elasticity, Stress-strain relationship, Hooke's law, Young’s modulus, bulk modulus, shear modulus of rigidity (qualitative idea only), Poisson's ratio
  • elastic energy
  • Mechanical Properties of Fluids
  • Pressure due to a fluid column
  • Pascal's law and its applications (hydraulic lift and hydraulic brakes), effect of gravity on fluid pressure
  • Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's theorem and its simple applications

• UNIT 8: THERMODYNAMICS

  2 टॉपिक

  • Thermal equilibrium and definition of temperature, zeroth law of thermodynamics, heat, work and internal energy
  • First law of thermodynamics, Second law of thermodynamics: gaseous state of matter, change of condition of gaseous state -isothermal, adiabatic, reversible, irreversible, and cyclic processes

• UNIT 9: BEHAVIOUR OF PERFECT GAS AND KINETIC THEORY

  7 टॉपिक

  • Kinetic Theory
  • Equation of state of a perfect gas, work done in compressing a gas
  • Kinetic theory of gases - assumptions, concept of pressure, Expression for pressure exerted by a gas
  • Kinetic interpretation of temperature
  • rms speed of gas molecules
  • degrees of freedom, law of equipartition of energy (statement only) and application to specific heat capacities of gases
  • concept of mean free path, Avogadro's number

• UNIT 10: OSCILLATIONS AND WAVES

  16 में से 7 टॉपिक

  • Oscillations
  • Periodic motion - time period, frequency, displacement as a function of time, periodic functions and their applications
  • Simple harmonic motion (S.H.M) and its equations of motion
  • phase
  • oscillations of a loaded spring- restoring force and force constant
  • energy in S.H.M. Kinetic and potential energies
  • simple pendulum derivation of expression for its time period

• UNIT 11: ELECTROSTATICS

  16 में से 7 टॉपिक

  • Electric Charges and Fields
  • Electric charges, Conservation of charge, Coulomb's law-force between two- point charges, forces between multiple charges
  • superposition principle and continuous charge distribution
  • Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field
  • Electric flux
  • statement of Gauss's theorem and its applications to find field due to infinitely long straight wire
  • uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside)

• UNIT 12: CURRENT ELECTRICITY

  9 में से 7 टॉपिक

  • Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current
  • Ohm's law, V-I characteristics (linear and non-linear)
  • electrical energy and power
  • electrical resistivity and conductivity
  • temperature dependence of resistance
  • Internal resistance of a cell
  • potential difference and emf of a cell

• UNIT 13: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM

  15 में से 7 टॉपिक

  • Moving Charges and Magnetism
  • Concept of magnetic field, Oersted's experiment
  • Biot - Savart law and its application to current carrying circular loop
  • Ampere's law and its applications to infinitely long straight wire
  • Straight solenoid (only qualitative treatment), force on a moving charge in uniform magnetic and electric fields
  • Force on a current-carrying conductor in a uniform magnetic field
  • force between two parallel current-carrying conductors-definition of ampere

• UNIT 14: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

  8 में से 7 टॉपिक

  • Electromagnetic Induction
  • Faraday's laws, induced EMF and current
  • Lenz's Law, Self and mutual induction
  • Alternating Current
  • Alternating currents, peak and RMS value of alternating current/voltage
  • reactance and impedance
  • LCR series circuit (phasors only), resonance, power in AC circuits, power factor, wattles current

• UNIT 15: ELECTROMAGNETIC WAVES

  2 टॉपिक

  • Basic idea of displacement current, Electromagnetic waves, their characteristics, their transverse nature (qualitative idea only)
  • Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses

• UNIT 16: OPTICS

  23 में से 7 टॉपिक

  • Ray Optics and Optical Instruments
  • Ray Optics: Reflection of light
  • spherical mirrors
  • mirror formula
  • refraction of light
  • total internal reflection and optical fibers
  • refraction at spherical surfaces

• UNIT 17: DUAL NATURE OF MATTER AND RADIATION

  3 टॉपिक

  • Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations
  • Einstein's photoelectric equation-particle nature of light
  • Experimental study of photoelectric effect Matter waves-wave nature of particles, de-Broglie relation

• UNIT 18: ATOMS AND NUCLEI

  8 में से 7 टॉपिक

  • Atoms
  • Alpha-particle scattering experiment
  • Rutherford's model of atom
  • Bohr model of hydrogen atom, Expression for radius of nth possible orbit, velocity and energy of electron in nth orbit, hydrogen line spectra (qualitative treatment only)
  • Nuclei
  • Composition and size of nucleus, nuclear force Mass-energy relation, mass defect
  • binding energy per nucleon and its variation with mass number

• UNIT 19: ELECTRONIC DEVICES

  5 टॉपिक

  • Semiconductor Electronics
  • Materials, Devices and Simple Circuits Energy bands in conductors
  • semiconductors and insulators (qualitative ideas only) Intrinsic and extrinsic semiconductors- p and n type
  • p-n junction Semiconductor diode - I-V characteristics in forward and reverse bias
  • application of junction diode - diode as a rectifier

इस विषय के 170 टॉपिक में से 109 दिखाए गए हैं।सभी 170 टॉपिक देखें →

• UNIT 1: SOME BASIC CONCEPTS OF CHEMISTRY & ATOMIC STRUCTURE

  10 टॉपिक

  • Laws of Chemical combination (numerical), Dalton's Atomic Theory, Concept of elements, atoms & molecules
  • Atomic and molecular masses, Mole concept and molar mass, percentage composition, empirical and molecular formula
  • chemical reactions, stoichiometry and calculation based on stoichiometry
  • Structure of Atom: Discovery of electron, proton and neutron, atomic number, isotopes and isobars
  • Thompson's model and its limitations, Rutherford's model and its limitations
  • Bohr's model & its limitations, concept of shells and sub-shells
  • Dual nature of matter and light, de-Broglie's relationship
  • Heisenberg's uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p and d- orbitals
  • Rules for filling electrons in orbitals- Aufbau's principle, Pauli's exclusion principle and Hund's rule
  • Electronic configuration of atoms, stability of half-filled and completely filled orbitals

• UNIT 2: CHEMICAL EQUILIBRIUM

  10 टॉपिक

  • Equilibrium in physical and chemical processes
  • dynamic nature of equilibrium
  • law of mass action
  • equilibrium constant
  • factors affecting equilibrium: Le-Chatelier's principle equilibrium-ionization of acids and bases
  • strong and weak electrolytes
  • degree of ionization
  • Concept of pH
  • Hydrolysis of salts (elementary idea), buffer solutions
  • Solubility product, common ion effect (with suitable examples)

• UNIT 3: CHEMICAL KINETICS

  9 टॉपिक

  • Rate of reaction (average and instantaneous rate of a reaction)
  • factors affecting rate of reactions: (concentration, temperature, catalyst)
  • rate law
  • specific rate constant and order
  • molecularity of a reaction
  • integrated rate expression of zero and first order reactions and their derivations
  • half-life period
  • Concept of collision theory (elementary idea, no mathematical derivation)
  • Activation energy, Arrhenius equation

• UNIT 4: SOLUTIONS

  10 टॉपिक

  • Types of solutions
  • expression of concentration of solutions of solids in liquids
  • solubility of gases in liquids
  • solid solutions
  • colligative properties: relative lowering of vapor pressure of a solution
  • Raoult's law
  • elevation of boiling point
  • depression in freezing point temperature and osmotic pressure)
  • determination of molecular masses using colligative properties
  • Abnormal molecular mass, Van't Hoff factor and calculations involving it

• UNIT 5: CHEMICAL THERMODYNAMICS

  13 टॉपिक

  • Concepts of system, types of systems, surrounding, work, heat
  • energy intensive and extensive properties, state functions
  • First Law of Thermodynamics
  • internal energy
  • enthalpy
  • heat capacity
  • specific heat
  • molar heat capacity
  • measurement of E and H, Hess's law of constant heat summation
  • enthalpy of bond dissociation
  • combustion
  • formation, atomization, sublimation, phase transition ionization and dilution
  • Introduction of entropy as a state function, free energy change for spontaneous and non-spontaneous process and equilibrium

• UNIT 6: REDOX REACTIONS AND ELECTROCHEMISTRY

  12 टॉपिक

  • Concept of oxidation and reduction
  • redox reactions
  • oxidation number
  • balancing of chemical equations in redox reactions
  • applications of redox reactions
  • conductance in electrolytic solutions
  • specific conductivity
  • molar conductivity
  • variation of conductivity with concentration
  • Kohlrausch's law and its applications Electrolysis and laws of electrolysis (elementary idea)
  • dry cell-electrolytic cells and galvanic cells
  • Lead accumulator, emf of a cell, standard electrode potential, Nernst equation and its application to Chemical cells, relation between Gibb's energy change and emf of a cell, fuel cells, corrosion

• UNIT 7: PERIODIC PROPERTIES

  9 टॉपिक

  • Significance of classification, brief history of the development of periodic table
  • Modern periodic law and the present form of the periodic table
  • periodic trends in properties of elements: atomic radii
  • ionic radii
  • inert gas radii
  • ionization enthalpy
  • electron gain enthalpy
  • electronegativity
  • valency

• UNIT 8: CHEMICAL BONDING AND MOLECULAR STRUCTURE

  13 टॉपिक

  • Valence electrons
  • lonic bond
  • covalent bond
  • bond parameters
  • Lewis structure
  • polar character of covalent bond
  • valence bond theory
  • resonance
  • geometry of covalent molecules
  • VSEPR theory
  • concept of hybridization involving s, p and d-orbitals and shapes of some simple molecules
  • molecular orbital theory of homonuclear molecules (Qualitative idea only)
  • hydrogen bond

• UNIT 9: CO-ORDINATION CHEMISTRY

  2 टॉपिक

  • Co-ordination compounds: Introduction, ligands, co-ordination number, color, magnetic properties and shapes, IUPAC nomenclature of mononuclear co-ordination compounds
  • Bonding (Werner's theory, VBT and CFT), structural and stereoisomerisms, importance of coordination compounds in qualitative inclusion of analysis, extraction of metals and biological systems

• UNIT 10: ORGANIC CHEMISTRY-SOME BASIC PRINCIPLES AND TECHNIQUES

  4 टॉपिक

  • General introduction to organic chemistry, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds
  • Electronic displacement in a covalent bond: inductive effect, electromeric effect, resonance and hyper-conjugation
  • Homolytic and heterolytic fission of a covalent bond, free radicals, electrophiles, nucleophiles, carbocations and carbanions
  • Types of organic reactions

• UNIT 11: d and f-BLOCK ELEMENTS

  6 टॉपिक

  • General introduction
  • electronic configuration
  • occurrence and characteristics of the transition meals
  • general trends in properties of first row transition metals (metallic character, IE, electrode potential, oxidation state, ionic radii, catalytic properties, colored ions, complex formation, magnetic properties, interstitial compounds, alloy formation)
  • Preparation and properties of K2Cr2O7 and KMnO4 Lanthanides: electronic configuration, oxidation state, chemical reactivity and lanthanide contraction and its consequences
  • Actinides- electronic configuration, oxidation states and comparison with lanthanoids

• UNIT 12: HYDROCARBONS

  28 टॉपिक

  • Classification of hydrocarbons
  • Alkanes: Nomenclature, isomerism, conformations (ethane only), physical properties
  • Chemical reactions including free radical mechanism of halogenation, combustion and Pyrolysis
  • Alkenes: Nomenclature
  • structure of double bond (ethene)
  • geometrical isomerism
  • methods of preparation
  • physical properties
  • chemical reactions- addition of hydrogen. halogen
  • water
  • hydrogen halides (Markownikov's addition and peroxide effect). ozonolysis
  • oxidation
  • mechanism of electrophilic addition
  • Alkynes: Nomenclature
  • structure of triple bond (ethyne)
  • chemical reactions: acidic character of alkynes
  • addition reaction of hydrogen
  • halogens
  • hydrogen halides and water
  • Aromatic hydrocarbons introduction
  • IUPAC nomenclature
  • Benzene resonance
  • aromaticity
  • chemical properties
  • mechanism of electrophilic substitution-nitration
  • sulphonation
  • halogenations Friedel Craft's alkylation and acylation
  • directive influence of functional group in mono substituted benzene

• UNIT 13: HALOALKANES AND HALOARENES

  10 टॉपिक

  • Haloalkanes: Nomenclature, nature of C-X bond, physical & chemical properties, mechanism of substitution reactions
  • Stability of carbocations, R-S and d-1 configurations
  • Haloarenes: Nature of C-X bond
  • substitution reactions (directive influence of halogens for mono substituted compounds only)
  • Stability of carbocations
  • R-S and D-L configurations Uses and environmental effects of-dichloromethane
  • trichloromethane
  • tetrachloromethane
  • iodoform
  • freon, and DDT

• UNIT 14: ALCOHOLS, PHENOLS AND ETHERS

  5 टॉपिक

  • Alcohols: Nomenclature, methods of preparation, physical & chemical properties (of primary alcohols only), identification of primary, secondary & tertiary alcohols
  • mechanism of dehydration of alcohols
  • Uses, some important compounds - methanol and ethanol
  • Phenols: Nomenclature, methods of preparation, physical & chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols
  • Ethers: Nomenclature, methods of preparation, physical & chemical properties and uses

• UNIT 15: ALDEHYDES, KETONES AND CARBOXYLIC ACIDS

  7 टॉपिक

  • Aldehydes and Ketones: Nomenclature
  • nature of carbonyl group
  • methods of preparation
  • physical & chemical properties & mechanism of nucleophilic addition reaction to C=O group
  • reactivity of alpha hydrogen in aldehydes
  • uses
  • Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical & chemical properties and uses

• UNIT 16: ORGANIC COMPOUNDS CONTAINING NITROGEN

  3 टॉपिक

  • Amines: Nomenclature, classification, structure, methods of preparation, physical & chemical properties, uses, identification of primary, secondary & tertiary amines
  • Cyanides and Isocyanides: Structures of cyanide and isocyanide groups, nomenclature, preparation, physical properties and chemical reactions
  • Diazonium Salts: Preparation and chemical reactions (mechanism of diazotization), and importance aesthetic organic chemistry

• UNIT 17: MOLECULES OF LIFE

  10 टॉपिक

  • Carbohydrates: Classification (aldoses and ketoses)
  • mono saccharides: Glucose
  • fructose: structure
  • preparation and chemical reactions
  • oligosaccharidees (sucrose, lactose & maltose) Polysaccharides: (starch cellulose and glycogen)
  • importance
  • Proteins: Elementary idea of amino acids: peptide bond, polypeptides and primary, secondary, etary and qualemary structure of proteins (Qualitative idea only), denaturation of proteins
  • enzymes, lips & harmones, their classification & functions
  • Nucleic Acids: DNA and RNA (purines and pyrimidines, nucleosides, nucleotides and fragments up to four nucleotides)
  • Vitamins: Classification and functions, sources and deficiency diseases

इस विषय के सभी 161 टॉपिक दिखाए गए हैं।कम टॉपिक दिखाएँ

• Unit I: Diversity of Life

  11 में से 7 टॉपिक

  • Biodiversity
  • Variety of living organisms
  • Need and History of classification – Artificial, Natural and Phylogenetic classifications
  • Biosystematics: Taxonomy and Systematics
  • Concept of species and Taxonomical hierarchy
  • Binomial nomenclature
  • Herbarium

• Unit II: Kingdom Plantae

  5 टॉपिक

  • Classification of plants into major groups
  • General characters of Algae, Bryophyta, Pteridophyta and Gymnosperms and their classes
  • Morphology of Flowering plants and their function: Morphology of root, stem and leaf (without their modifications)
  • Morphology of Inflorescence, flower, fruit and seed
  • Description of family Solanaceae

• Unit III: Plant Anatomy

  2 टॉपिक

  • Tissue systems in plants – Epidermal, ground and vascular tissue systems
  • Anatomy and functions of dicot and monocot root, stem and leaves

• Unit IV: Plant Physiology

  21 में से 7 टॉपिक

  • Respiration: Cellular respiration
  • Glycolysis, Kreb’s cycle and Electron transport system (along with ATP energetics)
  • Chemiosmotic hypothesis
  • Aerobic and Anaerobic respirations
  • Amphibolic pathways
  • Respiratory quotient
  • Photosynthesis: Historical background

• UNIT V: Diversity in Living World

  4 टॉपिक

  • Animal Kingdom
  • General characters and classification of animals (non-chordates up to phyla level and chordates up to the level of class)
  • National Parks with special reference to Dachigam, Kishtwar, Salim Ali, Kazinag and Hemis
  • Concept of Sanctuaries and Biosphere reserves

• Unit VI: Structural Organisation and Animal Biomolecules

  5 टॉपिक

  • Morphology, Anatomy and functions of digestive, circulatory, respiratory, nervous and reproductive systems of Frog
  • Basic chemical constituents of living bodies
  • Bio-molecules: Structure and function of Carbohydrates, proteins, lipids and Nucleic acids
  • Primary and secondary metabolites
  • Enzymes: Types, Properties and functions

• Unit VII: Cell Structure and Function

  6 टॉपिक

  • Cell: Brief description of cell
  • Cell theory
  • Prokaryotic and Eukaryotic cell, Cell wall, Membrane and Cell organelles (Plastids, Mitochondria, E.R., Golgi, Ribosomes, Lysosomes, Nucleus, Vacuoles, centrioles and Cytoskeleton)
  • Cilia and Flagella
  • Nuclear organisation
  • Cell Division: Cell Cycle, Mitosis and Meiosis

• Unit VIII: Human Physiology

  31 में से 7 टॉपिक

  • Breathing and Respiration: Respiratory system in humans
  • mechanism of breathing and its regulation in humans
  • respiratory volume
  • Exchange of gases and their transport
  • Respiratory disorders
  • Body fluids and Circulation: Composition of blood
  • Blood groups and Rh factor

• Unit IX: Reproduction in Flowering Plants

  10 में से 7 टॉपिक

  • Sexual Reproduction: Flower structure
  • Development of male and female gametophytes
  • Pollination - types, agencies and examples
  • Out breeding devices
  • Pollen-Pistil interactions
  • Double fertilization
  • Post fertilization events - Development of Endosperm, embryo

• Unit X: Genetics

  15 में से 7 टॉपिक

  • Heredity and variation Mendelian inheritance
  • deviations from Mendelism: Incomplete Dominance
  • Co-dominance
  • Multiple alleles and inheritance of blood groups
  • Pleiotropy
  • Elementary idea of polygenic inheritance
  • Chromosomal theory of Inheritance

• Unit XI: Biology and Human Welfare

  6 टॉपिक

  • Tissue Culture: Cellular totipotency, technique and application of tissue culture
  • Microbes in Human welfare: Microbes in food processing, industrial production, sewage treatment, energy generation (Biogas) and microbes as bio-control agents, Biopesticides and Bio-fertilizers
  • Antibiotics
  • production and judicious use
  • Application of Biotechnology in Agriculture: Genetically Modified organisms - BT crops
  • Biopiracy and patents

• Unit XII: Ecology and Environment

  12 में से 7 टॉपिक

  • Populations: Population attributes and Population growth
  • Population interactions -mutualism, competition, predation, parasitism
  • population attributes - growth, birth rate and death rate, age distribution
  • Ecosystems: Patterns, components
  • productivity and decomposition
  • energy flow
  • Ecological pyramids: Pyramids of number, biomass and energy

• Unit XIII: Reproduction in Animals

  10 में से 7 टॉपिक

  • Human Reproduction: Male and Female reproductive systems
  • Microscopic anatomy of testis and ovary
  • Gametogenesis (spermatogenesis and oogenesis; menstrual cycle)
  • Fertilisation, embryo development upto blastocyst formation, implantation
  • Pregnancy and placenta formation
  • Elementary idea of Parturition and Lactation
  • Reproductive Health: Need for reproductive health and prevention of Sexually Transmitted Diseases (STDs)

• Unit XIV: Genetics and Evolution

  14 में से 6 टॉपिक

  • Sex determination – in humans, birds and honey bee
  • Linkage and Crossing over
  • Sex linked inheritance: Haemophilia and colour blindness
  • Mendelian disorders in humans – Thalassemia
  • Chromosomal disorders in humans: Down's syndrome, Turner's syndrome and Klinefelter's syndrome Genome and Human genome project
  • DNA fingerprinting

• UNIT XV: Biology in Human Welfare

  5 टॉपिक

  • Health and Disease: Basic concepts of immunology - vaccines
  • Pathogens
  • parasites causing human diseases (Hepatitis, Malaria, Dengue, Filariasis, Ascariasis, Typhoid, Pneumonia, Common cold, Amoebiasis, Ring worm) and their control
  • Cancer, HIV and AIDS
  • Adolescence: drug and alcohol abuse

• UNIT XVI: Biotechnology and its Applications

  5 टॉपिक

  • Biotechnology: Principles and processes
  • Genetic Engineering (Recombinant DNA Technology)
  • Application of biotechnology in health: Human insulin and vaccine production stem cell technology, gene therapy
  • Transgenic Animals
  • Bio-safety issues

इस विषय के 162 टॉपिक में से 93 दिखाए गए हैं।सभी 162 टॉपिक देखें →

• UNIT 1: SETS, RELATIONS AND FUNCTIONS

  9 में से 6 टॉपिक

  • Sets and their representation, finite and infinite sets, empty set subsets, subset of real numbers especially intervals, universal set
  • Venn diagram, union and intersection of sets
  • Difference of sets, Compliment of a set
  • Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets
  • Relations, Domain, co- domain and range of relation, types of relation, reflexive, symmetric, transitive and equivalence relation
  • Functions as special kind of relations from one set to another, domain, co-domain and range of a function

• UNIT 2: COMPLEX NUMBER; LINEAR INEQUATION; LINEAR PROGRAMMING

  12 में से 6 टॉपिक

  • Complex number: Argand’s plane, algebraic properties of complex numbers
  • Solution of Quadratic equation in the complex number system
  • Square root of a complex number
  • Linear inequation: Linear Inequalities, Algebraic solution of linear inequalities in one variable and their representations on number line
  • Linear programming: Introduction
  • definition of related terminology such as constraints

• UNIT 3: SEQUENCE AND SERIES, PERMUTATION AND COMBINATION & BINOMIAL THEOREM

  9 में से 6 टॉपिक

  • Sequence and series: Arithmetic mean (A.M)
  • nth term
  • Geometric progression (G.P)
  • Geometric Mean (G.M)
  • sum to n-terms and sum to infinity of a G.P. Relation between A.M and G.M. Permutation and combination: Fundamental principle of counting
  • factorial n, permutations P(n,r) and combinations C(n,r)

• UNIT 4: TRIGONOMETRIC AND INVERSE TRIGONOMETRY FUNCTIONS

  6 टॉपिक

  • Positive and negative angles, measuring angles in radians and in degrees, Conversion from one measure to another
  • Definition of trigonometric functions with the help of unit circle
  • Basic Trigonometric identities sin2x+cos2x=1 for all Sign of x etc
  • Trigonometric functions and their graphs
  • sum and product formulae
  • Identities related to Sin2x, Cos2x, tan2x, Sin3x, Cos3x, and tan3x

• UNIT 5: MATRICES AND DETERMINANTS

  7 में से 6 टॉपिक

  • Matrices, concepts, notation, order, equality, types of matrices, Zero matrix, transpose of matrix, Symmetric and skew symmetric matrices
  • Addition, multiplication, scaler multiplication of matrices, simple properties of addition, multiplication and scaler multiplication of matrices
  • Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (order 2x2)
  • Concept of elementary row and column operation, Invertible matrices and uniqueness of inverse, if it exists.(Matrices with real entries)
  • Determinants of square matrix (upto 3x3 matrices) properties of determinants, minors, cofactors and applications of determinants in finding area of a triangle
  • Adjoint and inverse of a square matrix

• UNIT 6: LIMIT, CONTINUITY AND DIFFERENTIATION

  15 में से 6 टॉपिक

  • Concept of limit of a function
  • Theorems on Limits, Evaluation of limits using standard results
  • Continuity of a function at a point
  • Continuity of Sum, product and quotient of functions
  • Derivative: definition of a derivative of a function, geometrical interpretation of the derivative
  • Derivative of sum, difference, product and quotient of two or more functions

• UNIT 7: INTEGRATION AND DIFFERENTIAL EQUATIONS

  12 में से 6 टॉपिक

  • Integration as inverse process of differentiation
  • Integration of variety of functions by Substitution, by parts, by partial fractions
  • Simple integrals of the type
  • Definite integrals as a Limit of a sum
  • Fundamental Theorem of calculus
  • Basic properties of definite integrals Evaluation of definite integrals

• UNIT 8: STRAIGHT LINES AND CONIC SECTIONS

  4 टॉपिक

  • Distance between two points, section, slope of a line, angle between two lines, various forms of equations of lines, point-slope form, intercept form, two point form
  • Distance of a point from a line
  • Conic Section: Sections of a cone, circles, parabola, ellipse, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of conic section
  • Standard equation of a circle, parabola, ellipse, and hyperbola and their simple properties

• UNIT 9: STATISTICS AND PROBABILITY

  5 टॉपिक

  • STATISTICS Measure of dispersion, Range, mean, deviation, variance and standard deviation of ungrouped/ grouped data
  • PROBABILITY :Random Experiment: outcome, sample spaces
  • Events: Mutually exclusive and exhaustive events
  • Axiomatic (set theoretic) probability, probability of an event, probability of “Not” and “Or” events
  • Multiplication theorem on probability, conditional probability, independent events, total probability, Baye’s theorem, random variable and its probability, distribution, mean of a random variable

• UNIT 10: VECTORS AND THREE DIMENSIONAL GEOMETRY

  8 में से 6 टॉपिक

  • Vectors and scalars, magnitude and direction of a vector Direction Cosines and ratios of a vector
  • Types of vector, equal, zero, unit, parallel and collinear vectors
  • Position vector of a point , negative of a vector, components of a vector, addition of vectors, Scalar multiplication, position vector of a point dividing a line segment in a given ratio
  • Scalar (dot) product of vectors, Vector (cross) product of vectors
  • STRAIGHT LINES AND SPACE Coordinate Axis and Coordinate Planes in three dimension, coordinate of point, distance between two points
  • Direction cosines and direction ratios of a line joining two points

इस विषय के 87 टॉपिक में से 57 दिखाए गए हैं।सभी 87 टॉपिक देखें →