COMEDK UGET 2024

PHYSICS SYLLABUS
Class-XI– (2022-23)

Unit I: Physical World and Measurement

Units and Measurements

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 II: Kinematics

Motion in a Straight Line

Frame of reference, Motion in a straight line: Elementary concepts of differentiation and integration for
describing motion Uniform and non-uniform motion, average speed and instantaneous velocity,
Uniformly accelerated motion, velocity time and position-time graphs. Relations for uniformly accelerated
motion (graphical treatment).

Motion in a Plane
Scalar and vector quantities; Position and displacement vectors, general vectors and their notations;
equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Unit
vector; Resolution of a vector in a plane - rectangular components. Scalar and Vector product of vectors.
Motion in a plane. Cases of uniform velocity and uniform acceleration-projectile motion. Uniform
circular motion.

Unit III: Laws of Motion

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 IV: Work, Energy and Power

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 avertical circle, elastic and inelastic collisions in one and two dimensions.

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 Unit V: Motion of System of Particles and Rigid Body
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, laws 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 VI: Gravitation

Gravitation
Kepler's laws of planetary motion. The universal law of gravitation.
Acceleration due to gravity and its variation with altitude and depth.
Gravitational potential energy and gravitational potential. Escape velocity. Orbital velocity of
a satellite.
Unit VII: Properties of Bulk Matter
Mechanical Properties of Solids
Elastic behavior, 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.
Surface energy and surface tension, angle of contact, excess of pressure across a curved
surface, application of surface tension ideas to drops, bubbles and capillary rise.
Thermal Properties of Matter
Heat, temperature, thermal expansion; thermal expansion of solids, liquids and gases,
Anomalous expansion of water; specific heat capacity; Cp, Cv - calorimetry; change of state -latent heat
capacity.
Heat transfer-conduction, convection and radiation, thermal conductivity, Qualitative ideas
of Blackbody radiation, Wein's displacement Law, Stefan's law.
Unit VIII: Thermodynamics
Thermodynamics
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

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 Unit IX: Behavior of Perfect Gases and Kinetic Theory of Gases

Kinetic Theory
Equation of state of a perfect gas, work done in compressing a gas.
Kinetic theory of gases - assumptions, concept of pressure . Kinetic interpretation of
temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement
only) and application to specific heat capacities of gases; concept of meanfree path, Avogadro's number.

Unit X: Oscillations and Waves

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

Waves
Wave motion. Transverse and longitudinal waves, speed of travelling wave. Displacement relation
for a progressive wave. Principle of superposition of waves, reflection of waves,standing waves in
strings and organ pipes, fundamental mode and harmonics, Beats.

CLASS XII - (2023-24)

Unit I: Electrostatics
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).
Electrostatic Potential and Capacitance
Electric potential, potential difference, electric potential due to a point charge, a dipole and system of
charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric
dipole in anelectrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric
polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a
parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.
(no derivation, formulae only).

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 Unit II: Current Electricity
Current Electricity
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, combination of cells in series and in parallel.
Kirchhoff’s laws, Wheatstone bridge.

Unit III: Magnetic Effects of Current and Magnetism

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. Torque experienced by a current loop in uniform magnetic field; Current
loop as a magnetic dipole and its magnetic dipole moment. Moving coil galvanometer-its current sensitivity.
and conversion to ammeter and voltmeter
Magnetism and Matter
Bar magnet, bar magnet as an equivalent solenoid, (qualitative treatment only)Magnetic field intensity due to
a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. (qualitative treatment only), Torque
on a magnetic dipole (bar magnet) in a uniform magnetic field; (qualitative treatment only), magnetic field
lines;
Magnetic properties of materials-Para-, dia- and ferro – magnetic substances, with examples
Magnetization of materials, effect of temperature on magnetic properties.

Unit IV: Electromagnetic Induction and Alternating Currents

Electromagnetic Induction
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, wattless current.
AC generator and Transformer.
Unit V: Electromagnetic waves
Electromagnetic Waves
Basic idea of displacement current. Electromagnetic waves and their characteristics Transverse nature of
electromagnetic waves. (Qualitative ideas only).
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays)
including elementary facts about their uses.

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 Unit VI: Optics
Ray Optics and Optical Instruments.
Ray Optics:
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and
optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens maker’s formula. Magnification,
power of a lens, combination of thin lenses in contact.. Refraction of light through a prism.
Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying
powers.
Wave Optics
Wave optics: Wave front and Huygen's principle, reflection and refraction of plane wave at a plane surface
using wave fronts. Proof of laws of reflection and refraction using Huygen's principle. Interference, Young's
double slit experiment and expression for fringe width, (No derivation final expression only) coherent sources
and sustained interference of light. Diffraction due to a single slit, width of central maximum, (qualitative
treatment only).
Unit VII: Dual Nature of Matter and Radiation
Dual Nature of Radiation and Matter

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 VIII: Atoms & Nuclei

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 this 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; nuclear
fission, nuclearfusion.
Unit IX: Electronic Devices
Semiconductor Electronics: Materials, Devices and Simple Circuits
Energy bands in solids conductors, insulator and semiconductors; (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.

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 COMEDK UGET 2024

CHEMISTRY SYLLABUS
CLASS XI (2022-23)

1. 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.

2. Structure of Atom

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.

3. Classification of Elements and Periodicity in Properties

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.

4. Chemical Bonding and Molecular Structure

Valence electrons, ionic bond, covalent bond, bond parameters, Lewis’s 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.

5. 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).

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6. 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).

7. 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.

8. Organic Chemistry - Some Basic Principles and Techniques

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.

9. 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, the 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 electrophilic addition.
Alkynes - Nomenclature, the 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 the functional group in monosubstituted benzene. Carcinogenicity and toxicity.

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 CHEMISTRY SYLLABUS
CLASS XII (2023-24)

1. 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 Hoff factor.

2. 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.

3. 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.

4. 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.

5. 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).

6. 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.
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7. 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,
electrophilic substitution reactions, uses of phenols.
Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses.

8. 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.

9. 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.

10. Biomolecules

Carbohydrates - Classification (aldoses and ketoses), monosaccharides (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.

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 COMEDK UGET 2024

MATHEMATICS SYLLABUS
CLASS XI (2022-23)

Unit-I: Sets and Functions

1. Sets
Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of a
set of real numbers especially intervals (with notations). Universal set. Venn diagrams. Union and
Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.

2. Relations & Functions

Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite
sets. Cartesian product of the set of reals with itself (up to R x R x R). Definition of relation, pictorial
diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial
representation of a function, domain, co-domain and range of a function. Real valued functions,
domain and range of these functions, constant, identity, polynomial, rational, modulus, signum,
exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product
and quotients of functions.

3. Trigonometric 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. Domain and range of
trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny,
cosx & cosy and their simple applications. Deducing identities like the following:

Unit-II: Algebra

1. Complex Numbers and Quadratic Equations

Need for complex numbers, especially √−𝟏, to be motivated by inability to solve some of the
quadratic equations. Algebraic properties of complex numbers. Argand plane

2. Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation
on the number line.

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3. Permutations and Combinations
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of
Formulae for nPr and nCr and their connections, simple applications.

4. Binomial Theorem
Historical perspective, statement and proof of the binomial theorem for positive integral indices.
Pascal’s triangle, simple applications.

5. Sequence and Series

Sequence and Series. Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P.,
sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M.
and G.M.

Unit-III: Coordinate Geometry

1. Straight Lines
Brief recall of two dimensional geometry from earlier classes. Slope of a line and angle between two
lines. Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form,
two-point form, intercept form, Distance of a point from a line.

2. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a 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.

3. Introduction to Three-dimensional Geometry

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

Unit-IV: Calculus

1. Limits and Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive
idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic
functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum,
difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Unit-V: Statistics and Probability

1. Statistics
Measures of Dispersion: Range, Mean deviation, variance and standard deviation of
ungrouped/grouped data.

2. Probability
Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive
events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes.
Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

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 MATHEMATICS SYLLABUS
CLASS-XII (2023-24)

Unit-I: Relations and Functions

1. Relations and Functions

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

2. Inverse Trigonometric Functions

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

Unit-II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix,
symmetric and skew symmetric matrices. Operations on matrices: Addition and multiplication and
multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication.
Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is
the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the
uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors 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.

Unit-III: Calculus

1. Continuity and Differentiability

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions,
𝑙𝑖𝑘𝑒 sin−1 𝑥, cos−1 𝑥 and tan−1 𝑥, derivative of implicit functions. Concept of exponential and
logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of
functions expressed in parametric forms. Second order derivatives.

2. Applications of Derivatives
Applications of derivatives: rate of change of quantities, increasing/decreasing functions, 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).

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3. Integrals
Integration as inverse process of differentiation. Integration of a variety of functions by substitution,

by partial fractions and by parts, Evaluation of simple integrals of the following types and problems
based on them.

4. Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in
standard form only)

5. Differential Equations
Definition, order and degree, general and particular solutions of a differential equation. Solution of
differential equations by method of separation of variables, solutions of homogeneous differential

equations of first order and first degree. Solutions of linear differential equation of the type:

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a
vector. 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. Definition, Geometrical
Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of
vectors.

2. Three - dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector
equation of a line, skew lines, shortest distance between two lines. Angle between two lines

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 Unit-V: Linear Programming
1. Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, graphical
method of solution for problems in two variables, feasible and infeasible regions (bounded or
unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial
constraints).

Unit-VI: Probability
1. Probability
Conditional probability, multiplication theorem on probability, independent events, total probability,
Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

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