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NUCAT - Syllabus

Nitte University Common Admission Test

Exam Date: 06 May - 10 May 2023 (Tentative)

Computer Based Test

Updated On - February 03 2023 by Akriti Maurya

Unit I | Chapter 1: Physical World |

Unit II | Chapter 3: Motion in A Straight Line Chapter 4: Motion in A Plane |

Unit III | Chapter 5: Laws of Motion |

Unit IV | Chapter 6: Work, Energy and Power |

Unit V | Chapter 7: Systems of Particles and Rotational Motion |

Unit VI | Chapter 8: Gravitation |

Unit VII | Chapter 9: Mechanical Properties of Solids Chapter 10: Mechanical Properties of Fluids Chapter 11: Thermal Properties of Matter |

Unit VIII | Chapter 12: Thermodynamics |

Unit IX | Chapter 13: Kinetic Theory |

Unit X | Chapter 14: Oscillations Chapter 15: Waves |

Physics: Scope and excitement of physics, Physics-technology and society

Mention of fundamental forces in nature - Nature of physical laws.

Unit of measurement - System of units - SI units - Fundamental and derived units - Length, mass and time

measurements - Accuracy and precision of measuring instruments.

Errors in measurement; Significant figures.

Dimensions of physical quantities - Dimensional analysis and its applications: (a) Checking of dimensional consistencyof equations and (b) Deducing relation among physical quantities.

Position and frame of reference - Definitions of path length and displacement - Definitions of average speed and average velocity, instantaneous speed and instantaneous velocity and uniform and non-uniform motion.

Uniformly accelerated motion. Position-time graph,velocity-time graph: To show that area under the velocity time curve is equal to displacement. Kinematic equations for uniformly accelerated motion.

Derivation of v = vo + at , x = vo + 1⁄2 at2 and v2 = vo 2 + 2 a x using v-t graph - Relative velocity.

Elementary concepts of differentiation and integration for describing motion.

Scalars and vectors, Position and displacement vectors, Equality of vectors, Multiplication of a vector by real number. Addition and subtraction of two vectors: Triangle method and parallelogram method. Unit vector, Resolution of a vector, Rectangular components. Resultant of two concurrent vectors. Scalar and vector product of two vectors with examples. Motion in a plane with constant acceleration. Projectile motion: Derivations of equation of path, time of flight, maximum height and horizontal range, of a projectile. Uniform circular motion: Derivation of centripetal acceleration.

Aristotle’s fallacy, Newton’s first law of motion, Concept of inertia and force.

Concept of momentum - Newton’s second law of motion: Derivation of F⃗ = m a⃗ and definition of SI unit of force. Impulse, impulsive force and examples - Newton’s third law of motion, Identification of action and reaction pairs with examples in everyday life. Law of conservation of linear momentum: Statement and proof in the case of collision of two bodies. Condition for equilibrium of a particle under the action of concurrent forces. Friction: Static and kinetic friction - Laws of friction - Rolling friction - Methods of reducing of friction.

Dynamics of uniform circular motion: Derivation of maximum speed of a car moving on banked circular road and discuss in the case of level circular road by taking θ = 0.

Chapter 6: WORK, ENERGY AND POWER

WORK: Definition of Work: W = F⃗ . d⃗ and discussion of various cases - Work done by a constant force and by a

variable force. Kinetic energy - Work-energy theorem: Statement and proof in the case of rectilinear motion under constant acceleration. Concept of potential energy - Principle of conservation of mechanical energy: Statement and illustration in the case of freely falling body. Conservative and non-conservative forces with examples. Potential energy of a spring - Mention of expression V(x) = kx2/2.

POWER: Definition and derivation of power P = F⃗ . ⃗v . COLLISIONS: Elastic and inelastic collisions - Collisions in one dimension: Derivation of loss of kinetic energy in completely inelastic collisions - Derivation of final velocity of masses undergoing elastic collision. Collisions in two dimensions.

Chapter 7: SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

Definitions of a rigid body, translatory motion and rotatory motion - Centre of mass of a two-particle system.

Mention of expression for position coordinates of centre of mass of (a) n-particle system (b) a rigid body and (c) a uniform thin rod. Definition of angular velocity and mention of the relation v = r.Definitions of angular acceleration and moment of a force – torque - Angular momentum (l) of a particle: Derivation of dl= τ .

Equilibrium of rigid body: Mention of conditions for mechanical equilibrium of a rigid body.

Definitions of moment of inertia and radius of gyration.

Theorems of parallel and perpendicular axes: Statement and explanation.

Mention of expressions for moment of inertia of a simple geometrical objects.

Kinematics of rotational motion about a fixed axis: Mention of equation of rotational motion.

Comparison of linear and rotational motion.

Principle of conservation of angular momentum: Statement and illustrations.

Chapter 8: GRAVITATION

Kepler’s laws (three laws) of planetary motion: Statement and explanation.

Universal law of gravitation: Statement and explanation.

Acceleration due to gravity of earth: Derivation of relation between g and G.

Variation of acceleration due to gravity with altitude (height) and depth: Derivation of acceleration due

gravity at a point (a) above and (b) below the surface of earth.

Gravitational potential energy: Derivation of gravitational potential energy.

Escape speed: Definition and derivation of expression for escape speed from the principle of conservation of energy.

Earth satellites: Derivation of orbital speed of earth satellite - Geostationary and polar satellites.

Elasticity and plasticity - Elastic behavior of solids - Stress and strain - Hooke’s law: Stress – strain curve.

Elastic moduli; Definitions and expressions of Young’s modulus, Bulk modulus and Shear modulus of rigidity.

Poisson’s ratio - Elastic energy.

Pressure: Definition - Derivation of pressure at a point inside a liquid - Gauge pressure.

Pascal’s law: Statement and its applications (hydraulic lift and hydraulic brakes).

Streamline flow: Equation of continuity - Turbulent flow - Critical speed.

Bernoulli’s principle; Statement - Explanation of Bernoulli’s equation - Illustration of Bernoulli’s principle in the case of (a) blood flow and heart attack (b) dynamic lift of a ball and aerofoil.

Viscosity: Definition and mention of expression for coefficient of viscosity. Stoke’s law.

Reynolds’s number: Mention of expression - Classification of nature of flow on the basis of Reynolds’s number.

Surface tension: Surface energy and surface tension - Angle of contact - Applications of surface tension ideas to drops, bubbles, capillary rise and action of detergents.

Temperature and heat, Thermal expansion of solids: linear, area and volume expansion of solids – Thermal expansion of liquids: Anomalous expansion of water, Thermal expansion of gases: Derivation of αV = 1/T for ideal gas. Specific heat capacity: Definition of heat capacity and specific heat capacity - Molar specific heat capacity at constant pressure and Molar specific heat capacity at constant volume.

Principle of calorimetry - Change of state ; melting, fusion, melting point, regelation, boiling point, sublimation point- Latent heat ; Latent heat of fusion and vapourisation. Heat transfer: Conduction and thermal conductivity, Convection: Sea breeze and land breeze, Radiation: Newton’s law of cooling. Stefan’s law - Qualitative ideas of black body radiation. Wien’s displacement law - Greenhouse effect.

Chapter 12: THERMODYNAMICS

Thermal equilibrium - Zeroth law of Thermodynamics: Statement and explanation.

Heat, internal energy and work - First law of thermodynamics: Statement and explanation, Isothermal process: Derivation of work-done in isothermal process.

Adiabatic process: Mention of the expression PVγ = constant, for adiabatic process.

Heat engines: Schematic representation and efficiency.

Refrigerators (Heat pumps): Schematic diagram and coefficient of performance.

Second law of thermodynamics: Kelvin-Planck statement and Clausius statement.

Reversible and irreversible processes. Carnot’s engine; Carnot cycle and efficiency.

Chapter 13: KINETIC THEORY

Equation of state of a perfect gas - Kinetic theory of an ideal gas: Derivation of P =13mnv̅2, Kinetic interpretation of temperature ; Mention of expression for average kinetic energy of a molecule in terms of absolute temperature - Definition of rms speed of gas molecules.

Degrees of freedom - Law of equipartition of energy: Statement and application to specific heat capacities of monatomic, diatomic and polyatomic gases - Concept of mean free path.

Periodic & oscillatory motion: Definitions of Period & Frequency, Displacement as a function of time. Periodic functions.

SIMPLE HARMONIC MOTION: Definition, equation, graphical representation of displacement with time, Phase.

Mention of expressions for velocity and acceleration - Force law for simple harmonic motion : F(t) = −kx(t).

Energy in simple harmonic motion: Derivations of kinetic energy, potential energy and total energy.

Oscillations due to a spring - Restoring force & force constant - Mention of expression for time period.

Simple pendulum: Derivation of expression for time period - Qualitative ideas of damped, forced and free

oscillations - Resonance.

Amplitude and phase - Wavelength and angular wave number - Period, frequency and angular frequency.

Speed of traveling wave: Mention of expression for velocity of wave: v = λ.

Mention of expression for speed of transverse wave on a stretched string v = √Tμ

Speed of a longitudinal wave(sound) ; Newton’s formula and Laplace’s correction.

Qualitative explanation of principle of superposition of waves. Reflection of waves at rigid and open boundary. Standing waves and normal modes: Theory, extension to stretched string and air columns - Fundamental mode and harmonics - Theory of beats. Doppler Effect: Explanation of the phenomenon.

Derivation of apparent frequency in the case of (a) moving source and stationary observer, (b) moving observer and stationary source and (c) both source and observer moving.

Unit I | Chapter 1: Electric Charges and Fields |

Unit II | Chapter 2: Electrostatic Potential and Capacitance |

Unit III | Chapter 3: Current Electricity |

Unit IV | Chapter 4: Moving Charges and Magnetism |

Unit V | Chapter 5: Magnetism and Matter Chapter 6: Electromagnetic Induction |

Unit VI | Chapter 7: Alternating Current Chapter 8: Electromagnetic Waves |

Unit VII | Chapter 9: Ray Optics and Optical Instruments |

Unit VIII | Chapter 10: Wave Optics |

Unit IX | Chapter 11: Dual Nature of Radiation and Matter Chapter 12: Atoms |

Unit X | Chapter 13: Nuclei Chapter 14: Semiconductor Electronics |

Electric charges and their properties: Additivity of charges, quantisation of charges and conservation of

charges, Coulomb’s law :Statement, explanation (only in free space) and expression in vector form -

Definition of SI unit of charge (coulomb) - Superposition principle - Statement, application to find the force

between multiple charges.

Electric field: Definition of electric field, Mention of expression for electric field due to a point charge,

Application of superposition principle to find electric field for a system of charges.

Continuous charge distribution: Definitions of surface, linear and volume charge densities,

Mention of expression for electric field due to a continuous charge distribution (for all three cases).

Electric dipole: Definition of electric dipole and dipole moment.

Derivation of electric field due to a dipole (a) at any point on its axis (b) at any point on its equatorial plane.

Derivation of the torque on an electric dipole in a uniform electric field and expression in vector form.

Electric field lines: Properties and representation

Electric flux: Concept of electric flux - Area element vector, electric flux through an area element.

Gauss’s Law: Statement and its applications to find electric field due to (a) infinitely long straight charged

wire,

(b) Uniformly charged infinite plane sheet and

(c) uniformly charged thin spherical shell (field inside and outside).

Chapter 2: ELECTROSTATIC POTENTIAL AND CAPACITANCE

Electric Potential: Definition of electric potential at a point - Definition of potential difference,

Derivation of electric potential due to a point charge, Mention of expression for electric potential due a short electric dipole at any point, Comparison of the variation of electric potential with distance between a point charge and an electric dipole, Application of superposition principle to find electric potential due to a

system of charges. Equipotential surfaces: Properties, Derivation of the relation between electric field and potential. Electric potential energy: Definition of electric potential energy of a system of charges.

Derivation of electric potential energy of a system of two point charges in the absence of external electric

field, Mention of expression for electric potential energy of a system of two point charges in an external electric field. Mention of expression for the electric potential energy of an electric dipole placed in a uniform electric field. Electrostatics of conductors: Dielectrics and electric polarization. Polar and non-polar dielectrics and their behavior in the absence and presence of external electric field. Capacitors and capacitance: Parallel plate capacitor - Derivation of the capacitance of a capacitor without dielectric medium,

Mention of expression for capacitance of a capacitor with dielectric medium - Definition of dielectric

constant. Combination of capacitors: Derivation of effective capacitance of two capacitors (a) in series combination and (b) in parallel combination. Derivation of energy stored in a capacitor.

|UNIT-III

Chapter 3: CURRENT ELECTRICITY

Definition of electric current, Electric currents in a conductor - Definition of current density.

Ohm’s law: Statement and explanation, Limitations of Ohm’s law.

Dependence of electrical resistance on the dimensions of conductor and mention of R= l/A,

Electrical resistivity and conductivity - Derivation of the relation

j E = (equivalent form of Ohm’s law).Drift of electrons and origin of resistivity; Definitions of drift velocity, relaxation time and mobility. Expression for conductivity of a material : = ne2/m. Colour code of carbon resistors - Temperature dependence of resistivity of metals and semiconductors. Electrical energy and power:Mention of expression for power loss. COMBINATION OF RESISTORS: Derivation of effective resistance of two resistors (a) in series combination and (b) in parallel combination.

CELLS: Definitions of internal resistance of a cell, terminal potential difference and emf of a cell.

Derivation of current drawn by external resistance [I=/(R+r)].

Combination of cells: Derivation of expressions for equivalent emf and equivalent internal resistance

(a) in series and (b) in parallel combination.

Kirchhoff’s rules: Statements and explanation.

Wheatstone bridge: Derivation of balancing condition - Metre Bridge.

Potentiometer: Principle - Mention of applications of Potentiometer:

(a) to compare emf’s of two cells and (b) to measure internal resistance of a cell.

Concept of magnetic field, Oersted’s experiment, Force on a moving charge in uniform magnetic and

electric fields, Lorentz force, Derivation of magnetic force on a current carrying conductorF⃗ = I(l

× B⃗ ). Motion of a charge in a uniform magnetic field: Nature of trajectories, Derivation of radius and angular

frequency of circular motion of a charge in uniform magnetic field, Velocity selector: Crossed electric and magnetic fields serve as velocity selector. Cyclotron: Principle, construction, working and uses.

Biot–Savart law: Statement, explanation and expression in vector form. Derivation of magnetic field on the axis of a circular current loop - Right hand thumb rule to find it.

Ampere’s circuital law: Statement and explanation - Application of Ampere’s circuital law to derive the

magnetic field due to an infinitely long straight current carrying wire.

Solenoid and toroid: Mentionof expression for the magnetic field at a point inside a solenoid and a toroid.

Derivation of force between two parallel current carrying conductors -definition of ‘ampere’.

Current loop as a magnetic dipole - Qualitative explanation and definition of magnetic dipole moment.

Mention of expression for torque experienced by a current loop in a magnetic field.

Derivation of magnetic dipole moment of a revolving electron in an atom and obtain the value of Bohr

magneton.

Moving Coil Galvanometer(MCG): Mention of the expression for the angular deflection.

Definitions of current sensitivity and voltage sensitivity - Conversion of galvanometer to ammeter and

voltmeter.

UNIT-V

Bar magnet: Properties of magnetic field lines,Bar magnet as an equivalent solenoidwith derivation.

Dipole in a uniform magnetic field: Mention of expression for time period of oscillation of small compass

needle in a uniform magnetic field.

Gauss law in magnetism: Statement and explanation.

Earth’s magnetic field and its elements:

Declination, Dip and horizontal component of Earth’s field– HE and their variation

Definitions of magnetisation (M), magnetic intensity (H), susceptibility () and permeability (o and r).

Magnetic properties of materials: Paramagnetic,diamagnetic and ferromagnetic substances - Examples and

properties, Curie’s law and Curie temperature.

Hysteresis: Hysteresis loop, definitions of retentivity and coercivity - Permanent magnets and

electromagnets.

Chapter 6: ELECTROMAGNETIC INDUCTION

Experiments of Faraday and Henry, Magnetic flux: = B⃗ . A⃗ ; Statement and explanation of Faraday’s law of

electromagnetic induction, Lenz’s law: Statement, explanation and its significance as conservation of

energy.

Motional emf: Derivation of expression for motional emf: = Blv,

Eddy currents - Advantages of eddy currents with common practical applications.

Inductance: Mutual inductance: Mention of expression for mutual inductance of two coaxial solenoids,

Mention of expression for induced emf: = −MdIdt .

Self-inductance: Mention of expression for self-inductance of solenoid,

Mention of expression for induced emf: = −LdIdt.

Derivation of energy stored in the coil.

AC generator: Labelled diagram

Derivation of instantaneous emf in an ac generatorε = NBAω(sinωt) = ε0(sinωt).

UNIT-VI

Chapter 7: ALTERNATING CURRENT

Mention of expression for instantaneous, peak and rms values of alternating current and voltage.

AC voltage applied to a resistor: Derivation of expression for current, mention of phase relation between

voltage and current and phasor representation.

AC voltage applied to an inductor: Derivation of expression for current, mention of phase relation between

voltage and current, phasor representation and mention of expression for inductive reactance.

AC voltage applied to a capacitor: Derivation of expression for current, mention of phase relation between

voltage and current, phasor representation and mention of expression for capacitive reactance.

AC voltage applied to series LCR circuit: Derivation of expression for impendence, current and phase angle

using phasor diagram only- Electrical resonance - Derivation of expression for resonant frequency(0)

Mention of expressions for bandwidth and sharpness (quality factor).

Mention of expression for power in an ac circuit - Power factor and qualitative discussion in the case of

resistive, inductive and capacitive circuit - Meaning of wattless current.

LC oscillations: Qualitative explanation, Mention of expressionfor frequency of LC oscillations and

Mention of expression for total energy of LC circuit.

Transformer: Principle, construction and working - Mention of expression for turns ratio - Sources of energy

losses.

Displacement current - Mention the need for displacement current (inconsistency of Ampere’s circuital law)

Mention of expression for displacement current - Mention of expression for Ampere-Maxwell law.

Electromagnetic waves: Sources and nature of electromagnetic waves and their characteristics.

Mention of expression of speed of light (in vacuum and in medium in terms of permeability and

permittivity).

Electromagnetic spectrum: Wavelength range of various regions (parts or components) and their uses.

UNIT-VII

Reflection of light by spherical mirrors: Sign convention (Cartesian rule) - Focal length of spherical

mirrors. Derivation of the relation: f = R/2in the case of a concave mirror, Mirror equation: Derivation of

mirror equation in the case of concave mirror producing a real image - Definition and expression for linear

magnification(m).

Refraction of light: Explanation of phenomenon and consequences - Laws of refraction.

Total internal reflection (TIR): Explanation of phenomenon - Mention of conditions for TIR.

Definition of critical angle(iC) - Mention the relation between refractive index (n) and iC: (siniC= 1/n).

Mention of applications total internal reflection (mirage, total reflecting prisms and optical fibers).

Refraction at spherical surfaces: Derivation of the relation between u, v, n and R.

Refraction by a lens: Derivation of lens-maker’s formula – Mention of thin lens formula.

Definition and expression for linear magnification.

Power of a lens and mention of expression for it (P = 1/f).

Combination of thin lenses in contact: Derivation of equivalent focal length of two thin lenses in contact.

Refraction of light through a prism: Derivation of refractive index of the material of the prism.

Scattering of light: Rayleigh’s scattering law (I1/λ4): Blue colour of the sky and reddish appearance of the sun at sunrise and sunset.

OPTICAL INSTRUMENTS:MICROSCOPE: Simple microscope, Ray diagram for image formation, Mention of expression for the magnifying power. Compound microscope: Ray diagram for image formation - Mention of expressions for the magnifying power when the final image is at (a) least distance of distinct vision and (b) infinity. TELESCOPE: Ray diagram for image formation, Mentionof expression for the magnifying power and

length of the telescope (tube length)L = fo + fe, Schematic ray diagram of reflecting telescope.

UNIT-VIII

Chapter 10: WAVE OPTICS

Wave front (plane, spherical and cylindrical) - Huygens’ principle.

Refraction of plane wave at a plane surface (rarer to denser): Derivation of Snell’s law.

Reflection of a plane wave by a plane surface: Derivation of the law of reflection.

Explanation of refraction of plane wave through a thin prism and convex lens through diagrams,

Reflection of plane wave by a concave mirror through diagram.

INTERFERENCE OF LIGHT:

Coherent sources - Theory of interference (with equal amplitude – arriving at the conditions for constructive

and destructive interference)- Young’s experiment: Brief description –Derivation of expression for fringe

width.

DIFFRACTION OF LIGHT: Explanation of the phenomenon - Diffraction due to a single slit - Mention of

the conditions for diffraction minima and maxima - Intensity distribution curve - Resolving power of an

optical instruments, Mention of expressions for limit of resolution of (a) microscope and (b) telescope.

Methods of increasing the resolving power of microscope and telescope.

POLARISATION: Explanation of the phenomenon - Plane polarised light - Polaroids and its uses - Pass

axis.

Malu’s law, Polarisation by reflection,

Brewster’s angle - Arriving at Brewster’s law - Statement of Brewster’s law.

UNIT-IX

Electron emission: Definition of electron volt (eV) and work function - Types of electron emission.

Photoelectric effect: Mention of Hertz’s observations - Mention of Hallwachs’ and Lenard’s observations.

Definition of threshold frequency - Explanation of the phenomenon of Photoelectric effect,

Experimental setup to study Photoelectric effect - observations.

Mention of effect of (a) intensity of light on photocurrent, (b) potential on photocurrent and (c) frequency of

incident radiation on stopping potential - Definition of stopping potential.

Einstein’s photoelectric equation: Explanation of experimental results.

Particle nature of light: Characteristics of photon.

Wave nature of matter: de-Broglie hypothesis - Mention of de-Broglie relation.

Mention of expression for de-Broglie wavelength in terms of (a) kinetic energy and (b) acceleration

potential.

Davisson and Germer experiment: (No experimental details) Brief explanation of conclusion - wave nature

of electrons on the basis of electron diffraction.

|Chapter 12: ATOMS

Alpha particle scattering: Schematic diagram of Geiger-Marsden experiment, observations and conclusion.

Rutherford’s model of an atom- Derivation of total energy of electron in hydrogen atom in terms of orbit radius.

Atomic spectra: Spectral series of hydrogen, Mention of empirical formulae for wave number (1/λ) of

different series. Bohr model of hydrogen atom: Bohr’s postulates - Derivation of Bohr radius - Derivation

of energy of electron in stationary states of hydrogen atom - Line spectra of hydrogen atom, Derivation of

frequency of emitted radiation - Mention of expression for Rydberg constant - Energy level diagram - de-

Broglie’s explanation of Bohr’s second postulate - Limitations of Bohr model.

UNIT-X

Chapter 13: NUCLEI

Definition of atomic mass unit(u)- Isotopes, isobars and isotones – Composition, size, mass and density of the nucleus,

Einstein’s mass energy relation - Nuclear binding energy; Brief explanation of mass defect and binding

energy - Binding energy per nucleon - Binding energy curve - Nuclear force and its characteristics.

Nuclear fission and nuclear fusion with examples.

Radioactivity: Law of radioactive decay - Derivation of N = Noe−λt,Activity (decay rate) and its units: becquerel and curie.

Definition and derivation of half-life of radioactive element - Definition of mean life and mention its

expression.

Alpha decay, beta decay (negative and positive) and gamma decay with examples - Q value of nuclear

reaction.

Energy bands in solids: Valance band, conduction band and energy gap.

Classification of solids on the basis of energy bands.

Semiconductors: Intrinsic and Extrinsic semiconductors (p type and n type), p-n junction, p-n junction

formation.

Semiconductor diode: Forward and reverse bias: I-V characteristics,

Definitions of cut-in-voltage, breakdown voltage and reverse saturation current.

Diode as a rectifier: Circuit diagram, working, input and output waveforms for (a) half-wave and (b) full-wave rectifiers.

Zener diode: I-V characteristics - Zener diode as a voltage regulator.

Optoelectronic junction devices:

Working principles and mention of applications of photodiode, LED and solar cell.

Logic gates: Logic symbol and truth table of NOT, OR, AND, NAND and NOR gates.

Unit I Some Basic Concepts of Chemistry

Unit II Structure of Atom

Unit III Classification of Elements and Periodicity in Properties

Unit IV Chemical Bonding and Molecular Structure

Unit V States of Matter: Gases and Liquids

Unit VI Chemical Thermodynamics

Unit VII Equilibrium

Unit VIII Redox Reactions

Unit IX Hydrogen

Unit X s -Block Elements

Unit XI Some p -Block Elements

Unit XII Organic Chemistry: Some basic Principles and Techniques

Unit XIII Hydrocarbons

Unit XIV Environmental Chemistry

Some Basic Concepts of Chemistry

General Introduction: Importance and scope of Chemistry.

Nature of matter, laws of chemical combination, Dalton's atomic theory: concept of elements, atoms and

molecules.

Atomic and molecular masses, mole concept and molar mass, percentage composition, empirical and

molecular formula, chemical reactions, stoichiometry and calculations based on stoichiometry.

Discovery of Electron, Proton and Neutron, atomic number, isotopes and isobars. Thomson's model and its

limitations. Rutherford's model and its limitations, Bohr's model and its limitations, concept of shells and

subshells, dual nature of matter and light, de Broglie's relationship, Heisenberg uncertainty principle,

concept of orbitals, quantum numbers, shapes of s, p and d orbitals, rules for filling electrons in orbitals -

Aufbau principle, Pauli's exclusion principle and Hund's rule, electronic configuration of atoms, stability of

half-filled and completely filled orbitals.

Significance of classification, brief history of the development of periodic table, modern periodic law and

the present form of periodic table, periodic trends in properties of elements -atomic radii, ionic radii, inert

gas radii, Ionization enthalpy, electron gain enthalpy, electronegativity, valency. Nomenclature of elements

with atomic number greater than 100.

Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of

covalent bond, covalent character of ionic 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 diatomic molecules(qualitative idea only),

Hydrogen bond.

States of Matter: Gases and Liquids

Three states of matter, intermolecular interactions, types of bonding, melting and boiling points, role of gas

laws in elucidating the concept of the molecule, Boyle's law, Charles law, Gay Lussac's law, Avogadro's

law, ideal behaviour, empirical derivation of gas equation, Avogadro's number, ideal gas equation.

Deviation from ideal behaviour, liquefaction of gases, critical temperature, kinetic energy and molecular

speeds (elementary idea), Liquid State- vapour pressure, viscosity and surface tension (qualitative idea

only, no mathematical derivations)

Chemical Thermodynamics

Concepts of System and types of systems, surroundings, work, heat, energy, extensive and intensive

properties, state functions.

First law of thermodynamics -internal energy and enthalpy, heat capacity and specific heat, measurement

of ΔU and ΔH, Hess's law of constant heat summation, enthalpy of bond dissociation, combustion,

formation, atomization, sublimation, phase transition, ionization, solution and dilution. Second law of

Thermodynamics (brief introduction)

Introduction of entropy as a state function, Gibb's energy change for spontaneous and non- spontaneous

processes, criteria for equilibrium.

Third law of thermodynamics (brief introduction).

UNIT-VII

Equilibrium

Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action,

equilibrium constant, factors affecting equilibrium - Le Chatelier's principle, ionic equilibrium- ionization

of acids and bases, strong and weak electrolytes, degree of ionization, ionization of poly basic acids, acid

strength, concept of pH, hydrolysis of salts (elementary idea), buffer solution, Henderson Equation,

solubility product, common ion effect (with illustrative examples).

Redox Reactions

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, in terms

of loss and gain of electrons and change in oxidation number, applications of redox reactions.

UNIT-IX

Hydrogen

Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen,

hydrides-ionic covalent and interstitial; physical and chemical properties of water, heavy water, hydrogen

peroxide -preparation, reactions and structure and use; hydrogen as a fuel

UNIT-X

Group 1 and Group 2 Elements

General introduction, electronic configuration, occurrence, anomalous properties of the first element of

each group, diagonal relationship, trends in the variation of properties (such as ionization enthalpy, atomic

and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens, uses.

Preparation and Properties of Some Important Compounds:

Sodium Carbonate, Sodium Chloride, Sodium Hydroxide and Sodium Hydrogen carbonate, Biological

importance of Sodium and Potassium.

Calcium Oxide and Calcium Carbonate and their industrial uses, biological importance of Magnesium and

Calcium.

UNIT-XI

Some p-Block Elements

General Introduction to p -Block Elements

Group 13 Elements: General introduction, electronic configuration, occurrence, variation of properties,

oxidation states, trends in chemical reactivity, anomalous properties of first element of the group, Boron -

physical and chemical properties, some important compounds: Borax, Boric acid, Boron Hydrides,

Aluminium: Reactions with acids and alkalies, uses.

Group 14 Elements: General introduction, electronic configuration, occurrence, variation of properties,

oxidation states, trends in chemical reactivity, anomalous behaviour of first elements. Carbon-catenation,

allotropic forms, physical and chemical properties; uses of some important compounds: oxides. Important

compounds of Silicon and a few uses: Silicon Tetrachloride, Silicones, Silicates and Zeolites, their uses

UNIT-XII

General introduction, methods of purification, qualitative and quantitative analysis, classification and

IUPAC nomenclature of organic compounds. Electronic displacements in a covalent bond: inductive

effect, electrometric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a

covalent bond: free radicals, carbocations, carbanions, electrophiles and nucleophiles, types of organic

reactions.

Hydrocarbons

Classification of Hydrocarbons

Aliphatic Hydrocarbons:

Alkanes - Nomenclature, isomerism, conformation (ethane only), physical properties, chemical reactions

including free radical mechanism of halogenation, combustion and pyrolysis.

Alkenes - Nomenclature, structure of double bond (ethene), geometrical isomerism, physical properties,

methods of preparation, chemical reactions: addition of hydrogen, halogen, water, hydrogen halides

(Markovnikov's addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilicaddition.

Alkynes - Nomenclature, structure of triple bond (ethyne), physical properties, methods of preparation,

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, halogenation, Friedel Craft's alkylation and acylation,

directive influence of functional group in monosubstituted benzene. Carcinogenicity and toxicity.

Environmental Chemistry

Environmental pollution - air, water and soil pollution, chemical reactions in atmosphere, smog, major

atmospheric pollutants, acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse

effect and global warming- pollution due to industrial wastes, green chemistry as an alternative tool for

reducing pollution, strategies for control of environmental pollution.

Unit II Solutions

Unit III Electrochemistry

Unit IV Chemical Kinetics

Unit V Surface Chemistry

Unit VI General Principles and Processes of Isolation of Elements

Unit VII p -Block Elements

Unit VIII d -and f -Block Elements

Unit IX Coordination Compounds

Unit X Haloalkanes and Haloarenes

Unit XI Alcohols, Phenols and Ethers

Unit XII Aldehydes, Ketones and Carboxylic Acids

Unit XIII Amines

Unit XIV Biomolecules

Unit XV Polymers

Unit XVI Chemistry in Everyday Life

Classification of solids based on different binding 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, packing efficiency, voids, number of atoms

per unit cell in a cubic unit cell, point defects, electrical and magnetic properties.

Band theory of metals, conductors, semiconductors and insulators and n and p type semiconductors.

Solutions

Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in

liquids, solid solutions, Raoult's law, colligative properties - relative lowering of vapour pressure, elevation

of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using

colligative properties, abnormal molecular mass, Van't Hofffactor.

Electrochemistry

Redox reactions, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical

cells, Relation between Gibbs energy change and EMF of a cell, conductance in electrolytic solutions,

specific and molar conductivity, variations of conductivity with concentration, Kohlrausch's Law,

electrolysis and law of electrolysis (elementary idea), dry cell-electrolytic cells and Galvanic cells, lead

accumulator, fuel cells,corrosion.

Chemical Kinetics

Rate of a 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.

Surface Chemistry

Adsorption - physisorption and chemisorption, factors affecting adsorption of gases on solids, catalysis:

homogenous and heterogenous, activity and selectivity of solid catalysts; enzyme catalysis, colloidal state:

distinction between true solutions, colloids and suspension; lyophilic, lyophobic, multi-molecular and

macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis,

coagulation, emulsion - types of emulsions.

Principles and methods of extraction - concentration, oxidation, reduction - electrolytic method and

refining; occurrence and principles of extraction of aluminium, copper, zinc and iron.

UNIT-VII

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); Phosphorus -

allotropic forms, compounds of Phosphorus: Preparation and properties of Phosphine, Halides 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,

Ozone, 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, Oxoacids of halogens (structures only).

Group 18 Elements: General introduction, electronic configuration, occurrence, trends in physical and

chemical properties, uses.

**UNIT-VIII**

d and f 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.

Lanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction

and its consequences.

Actinoids - Electronic configuration, oxidation states and comparison with lanthanoids.

**UNIT-IX**

Coordination Compounds

Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and

shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT,

and CFT; structure and stereoisomerism, importance of coordination compounds (in qualitative analysis,

extraction of metals and biological system).

**UNIT-X**

Haloalkanes and Haloarenes

Haloalkanes: Nomenclature, nature of C–X bond, physical and chemical properties, optical rotation

mechanism of substitution reactions.

Haloarenes: Nature of C–X bond, substitution reactions (Directive influence of halogen in

monosubstituted compounds only).

Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform,

freons, DDT.

**UNIT-XI**

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 with

special reference to 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-XII**

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-XIII**

Amines

Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties,

uses, identification of primary, secondary and tertiary amines.

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

**UNIT-XIV**

Biomolecules

Carbohydrates - Classification (aldoses and ketoses), monosaccahrides (glucose and fructose), D-L

configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen);

Importance of carbohydrates.

Proteins -Elementary idea of - amino acids, peptide bond, polypeptides, proteins, structure of proteins -

primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of

proteins; enzymes. Hormones - Elementary idea excluding structure.

Vitamins - Classification and functions.

Nucleic Acids: DNA and RNA.

**UNIT-XV**

Polymers

Classification - natural and synthetic, methods of polymerization (addition and condensation),

copolymerization, and some important polymers: natural and synthetic like polythene, nylon polyesters,

bakelite, rubber. Biodegradable and non-biodegradable polymers.

**UNIT-XVI**

Chemistry in Everyday life

Chemicals in medicines - analgesics, tranquilizers antiseptics, disinfectants, antimicrobials, antifertility

drugs, antibiotics, antacids, antihistamines.

Chemicals in food - preservatives, artificial sweetening agents, elementary idea of antioxidants.

Cleansing agents- soaps and detergents, cleansing action.

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 (structures only).

Group 18 Elements: General introduction, electronic configuration, occurrence, trends in physical and

chemical properties, uses.

d and f 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.

Lanthanoids - Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction

and its consequences.

Actinoids - Electronic configuration, oxidation states and comparison with lanthanoids.

Coordination Compounds

Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and

shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT,

and CFT; structure and stereoisomerism, importance of coordination compounds (in qualitative analysis,

extraction of metals and biological system).

Haloalkanes and Haloarenes

Haloalkanes: Nomenclature, nature of C–X bond, physical and chemical properties, optical rotation

mechanism of substitution reactions.

Haloarenes: Nature of C–X bond, substitution reactions (Directive influence of halogen in

monosubstituted compounds only).

Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform,

freons, DDT.

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 with

special reference to 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.

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.

Amines

Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties,

uses, identification of primary, secondary and tertiary amines.

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

Biomolecules

Carbohydrates - Classification (aldoses and ketoses), monosaccahrides (glucose and fructose), D-L

configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen);

Importance of carbohydrates.

Proteins -Elementary idea of - amino acids, peptide bond, polypeptides, proteins, structure of proteins -

primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of

proteins; enzymes. Hormones - Elementary idea excluding structure.

Vitamins - Classification and functions.

Nucleic Acids: DNA and RNA.

Polymers

Classification - natural and synthetic, methods of polymerization (addition and condensation),

copolymerization, and some important polymers: natural and synthetic like polythene, nylon polyesters,

bakelite, rubber. Biodegradable and non-biodegradable polymers.

Chemistry in Everyday life

Chemicals in medicines - analgesics, tranquilizers antiseptics, disinfectants, antimicrobials, antifertility

drugs, antibiotics, antacids, antihistamines.

Chemicals in food - preservatives, artificial sweetening agents, elementary idea of antioxidants.

Cleansing agents- soaps and detergents, cleansing action.

Unit I SETS AND FUNCTIONS

Unit II ALGEBRA

Unit III COORDINATE GEOMETRY

Unit IV CALCULUS

Unit V MATHEMATICAL REASONING

Unit VI STATISTICS AND PROBABILITY

1 Sets

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of

the set of real numbers especially intervals (with notations). Power set. Universal set. Venn

diagrams. Union and intersection of sets. Difference of sets. Complement of a set, Properties of

Complement sets.

Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two

finite sets. Cartesian product of the reals with itself (upto R × R × R).

Definition of relation, pictorial diagrams, domain, co-domain and range of a relation.

Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions

Positive and negative angles. Measuring angles in radians and in degrees and conversion from

one measure to another. Definition of trigonometric functions with the help of unit circle. Truth

of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions and sketch of their

graphs. Expressing sin(x + y) and cos(x + y) in terms of sinx, siny, cosx and cosy.

Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of

trigonometric equations of the type sinθ = sinα, cosθ = cosα and tanθ = tanα. Proofs and

simple applications of sine and cosine formulae.

1.Principle of Mathematical Induction

Process of the proof by induction, motivating the application of the method by looking at natural

numbers as the least inductive subset of real numbers. The principle of mathematical induction

and simple applications.

Need for complex numbers, especially √−1 , to be motivated by inability to solve every

quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane

and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra,

solution of quadratic equations in the complex number system, Square-root of a Complex

number.

Linear inequalities, Algebraic solutions of linear inequalities in one variable and their

representation on the number line. Graphical solution of linear inequalities in two variables.

Solution of system of linear inequalities in two variables - graphically.

Fundamental principle of counting. Factorial n. Permutations and combinations derivation of

formulae and their connections, simple applications.

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s

triangle, general and middle term in binomial expansion, simple applications.

Sequence and Series. Arithmetic Progression (A.P.), Arithmetic Mean (A.M.), Geometric

Progression (G.P.), general term of a G.P., sum of n terms of a G.P. Arithmetic and geometric

series, infinite G.P. and its sum, geometric mean (G.M.). Relation between A.M. and G.M. Sum

to n terms of the special series : ∑n , ∑ n2and ∑ n3.

COORDINATE GEOMETRY

1.Straight Lines

Brief recall of 2-D from earlier classes, shifting of origin. Slope of a line and angle between two

lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept

form, two-point form, intercepts form and normal form. General equation of a line. Equation of

family of lines passing through the point of intersection of two lines. Distance of a point from a

line.

Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line and pair of

intersecting lines as a degenerated case of a conic section. Standard equations and simple

properties of parabola, ellipse and hyperbola. Standard equation of a circle.

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance

between two points and section formula.

1.Limits and Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically,

Intuitive idea of limit. limx→0

loge(1+x)x, limx→0ex−1x. Definition of derivative, relate it to slope of tangent of

the curve, derivative of sum, difference, product and quotient of functions. Derivatives of

polynomial and trigonometric functions.

MATHEMATICAL REASONING

the understanding of “if and only if (necessary and sufficient) condition”, “implies”,

“and/or”, “implied by”, “and”, “or”, “there exists” and their use through variety of

examples related to real life and Mathematics. Validating the statements involving

the connecting words - difference between contradiction, converse and

contrapositive.

STATISTICS AND PROBABILITY

1.Statistics

Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped

data. Analysis of frequency distributions with equal means but different variances.

Random experiments: outcomes, sample spaces (set representation). Events: Occurrence of

events, ‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events. Axiomatic (set

theoretic) probability, connections with the theories of earlier classes. Probability of an event,

probability of ‘not’, ‘and’, & ‘or’ events.

Unit I RELATIONS AND FUNCTIONS

Unit II ALGEBRA

Unit III CALCULUS

Unit IV VECTORS AND THREE-DIMENSIONAL GEOMETRY

Unit V LINEAR PROGRAMMING

Unit VI PROBABILITY

RELATIONS AND FUNCTIONS

1. Relations and Functions

Types of relations: Reflexive, symmetric, transitive and equivalence relations. One to one and onto

functions, composite functions, inverse of a function. Binary operations.

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

Elementary properties of inverse trigonometric functions.

1. Matrices

Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix,

symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of

matrices, simple properties of addition, multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors,

cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of

a square matrix. Consistency, inconsistency and number of solutions of system of linear

equations by examples, solving system of linear equations in two or three variables (having

unique solution) using inverse of a matrix.

1. Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of

inverse trigonometric functions, derivative of implicit function. Concepts of exponential,

logarithmic functions. Derivatives of logex and ex. Logarithmic differentiation. Derivative of

functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean

Value Theorems (without proof) and their geometric interpretations.

Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and

normals, approximation, maxima and minima (first derivative test motivated geometrically and

second derivative test given as a provable tool). Simple problems (that illustrate basic principles

and understanding of the subject as well as real-life situations).

Integration as inverse process of differentiation. Integration of a variety of functions by

substitution, by partial fractions and by parts. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Applications in finding the area under simple curves, especially lines, arcs of

circles/parabolas/ellipses (in standard form only), area between the two above said curves (the

region should be clearly identifiable).

Definition, order and degree, general and particular solutions of a differential equation.

Formation of differential equation whose general solution is given. Solution of differential

equations by method of separation of variables, homogeneous differential equations of first order

and first degree. Solutions of linear differential equation of the type –dydx+ Py = Q , where P and Q are functions of x or constants dxdy+ Px = Q , where P and Q are functions of y or constants.

Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors.

Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point,

negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a

scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of

vectors, projection of a vector on a line. Vector (cross) product of vectors, scalar triple product.

Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar

and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle

between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

types of linear programming (L.P.) problems, mathematical formulation of L.P. problems,

graphical method of solution for problems in two variables, feasible and infeasible regions,

feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constrains).

probability, Baye’s theorem. Random variable and its probability distribution, mean and variance

of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

03 Jan 2023

10 Jan 2023

06 May - 10 May 2023

₹ 1,000

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