KEAM Mock Test

PHYSICS

UNITS & MEASUREMENT

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

KINEMATICS

Motion in a straight line: Position-time graph, speed and velocity

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)

Elementary concepts of differentiation and integration for describing motion

Scalar and vector quantities: Position and displacement vectors, general vectors and notation

Equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors

Unit vectors; Resolution of a vector in a plane - rectangular components

Scalar and Vector products of Vectors

Motion in a plane: Cases of uniform velocity and uniform acceleration-projectile motion

Uniform circular 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

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

Conservation of mechanical energy (kinetic and potential energies)

Non-conservative forces; motion in a vertical circle, elastic and inelastic collisions in one and two dimensions

MOTION OF SYSTEM OF PARTICLES AND RIGID BODY

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 uniform rod

Moment of a force, torque, angular momentum, conservation of angular momentum with some examples

Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion

Comparison of linear and rotational motions

Moment of inertia, radius of gyration

Values of M.I. for simple geometrical objects (no derivation)

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; gravitational potential

Escape velocity, orbital velocity of a satellite

PROPERTIES OF BULK MATTER

Elastic behaviour, Stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, shear, modulus of rigidity, poisson's ratio; elastic energy

Pressure due to a fluid column; Pascal's law and its applications

Effect of gravity on fluid pressure

Viscosity, Stokes' law, terminal velocity, Reynold's number, streamline and turbulent flow. Critical velocity

Bernoulli's theorem and its applications

Surface energy and surface tension, angle of contact, excess of pressure, application of surface tension ideas to drops, bubbles and capillary rise

Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases. Anomalous expansion

Specific heat capacity: Cp, Cv - calorimetry; change of state - latent heat

Heat transfer - conduction and thermal conductivity, convection and radiation

Qualitative ideas of Black Body Radiation, Wein's displacement law, and Green House effect

Newton's law of cooling and Stefan's law

THERMODYNAMICS

Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics)

Heat, work and internal energy. First law of thermodynamics

Isothermal and adiabatic processes

Second law of thermodynamics: Reversible and irreversible processes

Carnot engine

BEHAVIOUR OF PERFECT GAS AND KINETIC THEORY

Equation of state of a perfect gas, work done on compressing a gas

Kinetic theory of gases: Assumptions, concept of pressure

Avogadro's number

Kinetic energy and 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

OSCILLATIONS AND WAVES

Periodic motion - period, frequency, displacement as a function of time

Periodic functions

Simple harmonic motion (SHM) and its equation; phase; oscillations of a spring-restoring force and force constant; energy in SHM -kinetic and potential energies

Simple pendulum - derivation of expression for its time period

Wave motion. Longitudinal and transverse waves, speed of wave motion

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

ELECTROSTATICS

Electric charges and their conservation

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 a 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)

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 dipoles in an electrostatic 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

CURRENT ELECTRICITY

Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their relation with electric current

Ohm's law, electrical resistance, 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 and simple applications

Wheatstone bridge

MAGNETIC EFFECTS OF CURRENT 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 solenoids

Force on a moving charge in uniform magnetic and electric fields

Cyclotron

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 a magnetic field; moving coil galvanometer - its current sensitivity and conversion to ammeter and voltmeter

Current loop as a magnetic dipole and its magnetic dipole moment

Magnetic dipole moment of a revolving electron

Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis

Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid

Magnetic field lines

Para-, dia- and ferro - magnetic substances, with examples

ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS

Electromagnetic induction; Faraday's law, induced emf and current; Lenz's Law, Self and mutual inductance

Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance

LCR series circuit, resonance; power in AC circuits, wattless current

AC generator and transformer

ELECTROMAGNETIC WAVES

Need for displacement current

Electromagnetic waves and their characteristics (qualitative ideas only)

Transverse nature of electromagnetic waves

Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses

OPTICS

Reflection of light, spherical mirrors, mirror formula

Refraction of light, total internal reflection and its applications, 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 combination of a lens and a mirror

Refraction and dispersion of light through a prism

Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers

Wave optics: Wavefront and Huygens' principle, reflection and refraction of plane wave at a plane surface using wavefronts

Proof of laws of reflection and refraction using Huygens' principle

Interference, Young's double hole experiment and expression for fringe width, coherent sources and sustained interference of light

Diffraction due to a single slit, width of central maximum

Polarisation, plane polarised light; uses of plane polarised light and Polaroids

DUAL NATURE OF MATTER AND RADIATION

Photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equation - particle nature of light

Matter waves - wave nature of particles, De Broglie relation

ATOMS AND NUCLEI

Alpha - particle scattering experiment; Rutherford's model of atom; Bohr model, energy levels, hydrogen spectrum

Composition and size of nucleus, atomic masses, isotopes, isobars; isotones

Radioactivity - alpha, beta and gamma particles/rays and their properties; radioactive decay law

Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number

Nuclear fission and fusion

ELECTRONIC DEVICES

Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors

Semiconductor diode - I-V characteristics in forward and reverse bias, diode as a rectifier

CHEMISTRY

SOME BASIC CONCEPTS OF CHEMISTRY

General Introduction: Importance and scope of chemistry

Historical approach to particulate 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 and empirical and molecular formula

Chemical reactions, stoichiometry and calculations 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 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 exclusion principle and Hund's rule

Electronic configuration of atoms, stability of half filled and completely filled orbitals

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, valence

Nomenclature of elements with atomic number greater than 100

CHEMICAL BONDING AND MOLECULAR STRUCTURE

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

THERMODYNAMICS

Concepts of system, 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

Introduction of entropy as a state function, Second law of thermodynamics, Gibbs energy change for spontaneous and non-spontaneous process

Criteria for equilibrium

Third law of thermodynamics – Brief introduction

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 polybasic acids, acid strength, concept of pH

Hydrolysis of salts (elementary idea), buffer solutions, Henderson equation, solubility product, common ion effect (with illustrative examples)

REDOX REACTIONS AND ELECTROCHEMISTRY

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions in terms of loss and gain of electron and change in oxidation numbers

Applications of redox reactions

Conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch's Law, electrolysis and laws of electrolysis (elementary idea)

Dry cell – electrolytic cells and Galvanic cells; lead accumulator

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

Fuel cells; corrosion

SOLUTIONS

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

Solubility of gases in liquids, solid solutions

Colligative properties – relative lowering of vapour pressure, Raoult's law

Elevation of B.P., depression of freezing point, osmotic pressure

Determination of molecular masses using colligative properties

Abnormal molecular mass, Vant Hoff factor

CHEMICAL KINETICS

Rate of a reaction (average and instantaneous), factors affecting rates 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, Arrhenious equation

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 lanthenoids

COORDINATION COMPOUNDS

Coordination compounds: Introduction, ligands, coordination number, colour, magnetic properties and shapes

IUPAC nomenclature of mononuclear coordination compounds

Bonding, Werner's theory VBT,CFT

Isomerism (structural and stereo)

Importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems)

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, electromeric 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, Alkenes, Alkynes – Nomenclature, isomerism, conformations, physical properties, chemical reactions

Aromatic hydrocarbons – Introduction, IUPAC nomenclature

Benzene: resonance, aromaticity; chemical properties: mechanism of electrophilic substitution

Directive influence of functional group in mono-substituted benzene

Carcinogenicity and toxicity

HALOALKANES AND HALOARENES

Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions, optical rotation

Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for 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, and mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses

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

ORGANIC COMPOUNDS CONTAINING NITROGEN

Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary secondary and tertiary amines

Cyanides and Isocyanides – will be mentioned at relevant places in context

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

BIOMOLECULES

Carbohydrates – Classification (aldoses and ketoses), monosaccharide (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen): importance

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

Hormones – Elementary idea (excluding structure)

Vitamins – Classification and functions

Nucleic Acids: DNA and RNA

MATHEMATICS

ALGEBRA

Sets and their representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Universal set; Venn Diagrams; Complement of a set; Operations on Sets (Union, Intersection and Difference of Set); Applications of sets: Ordered Pairs, Cartesian Product of Two sets

Relations, reflexive, symmetric, transitive and equivalence relations

Domain, Co-domain and Range: Functions: into, onto, one - one into, one-one onto Functions; Constant Function; Identity Function; composition of Functions; Invertible Functions

Complex Numbers in the form a+bi ; Real and Imaginary Parts of a complex Number; Complex Conjugate, Argand Diagram, Representation of Complex Number as a point in the plane; Modulus of a Complex Number; Algebra of Complex Numbers

Geometric Progression (G.P): first Term, Common Ratio and nth term, Sum to n Terms. Geometric Mean (G.M); Insertion of Geometric Means, Relation between AM and GM

Fundamental Principle of Counting; The Factorial Notation; Permutation as an Arrangement; Meaning of P(n, r); Combination: Meaning of C(n,r); Applications of Permutations and Combinations

Statement of Binomial Theorem; Proof of Binomial Theorem for positive integral Exponent using Principle of Mathematical Induction and also by combinatorial Method; General and Middle Terms in Binomial Expansions; Properties of Binomial Coefficients

Concept of a Matrix; Types of Matrices; Equality of Matrices; Operations of Addition, Scalar Multiplication and Multiplication of Matrices; Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only

Determinant of a Square Matrix; Minors and Cofactors; singular and non-singular Matrices; Applications of Determinants in finding the Area of a Triangle

Transpose, Adjoint and Inverse of a Matrix; Consistency and Inconsistency of a system of Linear Equations; Solving System of Linear Equations in Two or Three variables using Inverse of a Matrix

Solutions of Linear Inequalities in one variable and its Graphical Representation; solution of system of Linear Inequalities in one variable

TRIGONOMETRY

Degree measures and Radian measure of positive and negative angles; relation between degree measure and radian measure, definition of trigonometric functions with the help of a unit circle, periodic functions, concept of periodicity of trigonometric functions

Value of trigonometric functions of x for x = 0, π/6, π/4, π/3, π/2, π, 2π/3, 3π/2, 2π; trigonometric functions of sum and difference of numbers

Trigonometric functions of multiple and submultiples of numbers

Inverse Trigonometric functions. Range, domain, principal value branch and graphs of inverse trigonometric functions

Trigonometric equations and identities

Graph of the trigonometric functions; y = Sin x ; y = Cos x ; y = Tan x

GEOMETRY

Cartesian system of coordinates in a plane. Distance formula, Slope of line, parallel and perpendicular lines. Various forms of equations of a line parallel to axes, slope-intercept form, The Slope point form, Intercept form, Normal form, General form, Intersection of lines. Angles between two lines, condition for concurrency of three lines, Distance of a point from a line

Sections of a cone. Circles, standard form of the equation of a circle, its radius and centre. Equations of conic sections [Parabola, Ellipse and Hyperbola] in standard form and simple properties

Vectors and scalars, Magnitude and Direction of a vector, Types of vectors (Equal vectors, unit vector, Zero vector). Position vector of a point, Localized and free vectors, parallel and collinear vectors, Negative of a vector, components of a vector, Addition of vectors, multiplication of a vector by a scalar, position vector of point dividing a line segment in a given ratio, Application of vectors in geometry. Scalar product of two vectors, projection of a vector on a line, vector product of two vectors

Coordinate axes and coordinate planes in three dimensional space, coordinate of a point in space, distance between two points, section formula, direction cosines, and direction ratios of a line joining two points, projection of the join of two points on a given line, Angle between two lines whose direction ratios are given, Cartesian and vector equation of a line through (i) a point and parallel to a given vector (ii) through two points, coplanar and skew lines, Shortest distance between two lines, Condition for the intersection of two lines

STATISTICS

Mean deviation, variance, standard deviation for grouped an ungrouped data. Random experiments and sample space, Events as subset of a sample space, occurrence of an event, sure and impossible events, Exhaustive events, Algebra of events, Meaning of equality likely outcomes, mutually exclusive events

Probability of an event; Theorems on probability; Addition rule, Multiplication rule, Independent experiments and events. Finding P (A or B), P (A and B), Bayes' theorem

CALCULUS

Concept of a real function; its domain and range; Modulus Function, Greatest integer function: Signum functions; Trigonometric functions and inverse trigonometric functions and their graphs; composite functions, Inverse of a function

Limit of a function; meaning and related notations; Left and right hand limits; Fundamental theorems on limits without proof; Continuity of a function at a point, Sum, Product and quotient of continuous functions; Continuity of special functions- Polynomial, Trigonometric, exponential, Logarithmic and Inverse trigonometric functions

Derivative of a function; its geometrical and physical significance; Relationship between continuity and differentiability; Derivatives of polynomial, basic trigonometric, exponential, logarithmic and inverse trigonometric functions from first principles; derivatives of sum, difference, product and quotient of functions; derivatives of polynomial, trigonometric, exponential, logarithmic, inverse trigonometric and implicit functions; Logarithmic differentiation; derivatives of functions expressed in parametric form; chain rule and differentiation by substitution; Derivatives of Second order

Rate of change of quantities; increasing and decreasing functions and sign of the derivatives; maxima and minima; Greatest and least values

Integration as inverse of differentiation; properties of integrals; Integrals involving algebraic, trigonometric, exponential and logarithmic functions; Integration by substitution; Integration by parts; Integrals of the type; Integration of rational functions; Partial fractions and their use in integration; Integrals of the type

Fundamental theorems of integral calculus without proof; Evaluation of definite integrals by substitution and by using properties

Application of definite integrals in finding areas bounded by a curve, circle, parabola and ellipse in standard form between two ordinates and x-axis; Area between two curves, line and circle; line and parabola: line and ellipse

Definition; order and degree; general and particular solutions of a differential equation; solution of differential equations by method of Separation of variables; Homogeneous differential equations of first order and their solutions; Solution of linear differential equations of the type dy/dx + P(x)y = Q(x) where P(x), Q(x) are functions of x or constants

LINEAR PROGRAMMING

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming 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 constraints)

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