Detailed Syllabus of WBJEE 2025 | WBJEE Sample Papers, Section Wise & Full Mock Tests 2025 PDF Download

 Page 1


 
 
       
 
MATHEMATICS: 
Algebra 
A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ?n, ?n², ?n
3;
 
Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum. 
Logarithms: Definition; General properties; Change of base. 
Complex Numbers: Definition in terms of ordered pair of real numbers and properties of complex numbers; 
Complex conjugate; Triangle inequality; amplitude of complex numbers and its properties; Square root of 
complex numbers; Cube roots of unity; De Moivre's theorem (statement only) and its elementary applications. 
Solution of quadratic equation in complex number system. 
Polynomial equation: nth degree equation has exactly n roots (statement only); Quadratic Equations: 
Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; 
Formation of a quadratic equation, sign and magnitude of the quadratic expression ax
2
 +bx+c (where a, b, c are 
rational numbers and a ? 0). 
Permutation and combination: Permutation of n different things taken r at a time (r = n). Permutation of n 
things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n 
different things taken r at a time (r = n). Combination of n things not all different. Basic properties. Problems 
involving both permutations and combinations. 
Principle of mathematical induction: Statement of the principle, proof by induction for the sum of squares, 
sum of cubes of first n natural numbers, divisibility properties like 2
2n  
— 1 is divisible by 3 (n = 1), 7divides 
3
2n+1
+2
n+2 
(n = 1) 
Binomial theorem (positive integral index): Statement of the theorem, general term, middle term, equidistant 
terms, properties of binomial coefficients. 
Matrices: Concepts of m x n (m = 3, n = 3) real matrices, operations of addition, scalar multiplication and 
multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants 
(statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area 
of a triangle. Solutions of system of linear equations. (Not more than 3 variables). 
Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference 
of sets, Venn diagram, De Morgan's Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian 
product of sets. 
Relation and its properties. Equivalence relation — definition and elementary examples, mappings, range and 
domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping. 
Statistics and Probability: 
Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and 
multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, 
repeated independent trails and Binomial distribution. 
Trigonometry 
Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple 
angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions 
and their properties. 
 Coordinate geometry of two dimensions 
 Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar 
co-ordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of 
axes. 
Page 2


 
 
       
 
MATHEMATICS: 
Algebra 
A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ?n, ?n², ?n
3;
 
Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum. 
Logarithms: Definition; General properties; Change of base. 
Complex Numbers: Definition in terms of ordered pair of real numbers and properties of complex numbers; 
Complex conjugate; Triangle inequality; amplitude of complex numbers and its properties; Square root of 
complex numbers; Cube roots of unity; De Moivre's theorem (statement only) and its elementary applications. 
Solution of quadratic equation in complex number system. 
Polynomial equation: nth degree equation has exactly n roots (statement only); Quadratic Equations: 
Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; 
Formation of a quadratic equation, sign and magnitude of the quadratic expression ax
2
 +bx+c (where a, b, c are 
rational numbers and a ? 0). 
Permutation and combination: Permutation of n different things taken r at a time (r = n). Permutation of n 
things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n 
different things taken r at a time (r = n). Combination of n things not all different. Basic properties. Problems 
involving both permutations and combinations. 
Principle of mathematical induction: Statement of the principle, proof by induction for the sum of squares, 
sum of cubes of first n natural numbers, divisibility properties like 2
2n  
— 1 is divisible by 3 (n = 1), 7divides 
3
2n+1
+2
n+2 
(n = 1) 
Binomial theorem (positive integral index): Statement of the theorem, general term, middle term, equidistant 
terms, properties of binomial coefficients. 
Matrices: Concepts of m x n (m = 3, n = 3) real matrices, operations of addition, scalar multiplication and 
multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants 
(statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area 
of a triangle. Solutions of system of linear equations. (Not more than 3 variables). 
Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference 
of sets, Venn diagram, De Morgan's Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian 
product of sets. 
Relation and its properties. Equivalence relation — definition and elementary examples, mappings, range and 
domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping. 
Statistics and Probability: 
Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and 
multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, 
repeated independent trails and Binomial distribution. 
Trigonometry 
Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple 
angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions 
and their properties. 
 Coordinate geometry of two dimensions 
 Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar 
co-ordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of 
axes. 
 
 Concept of locus, locus problems involving all geometrical configurations,  
Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and 
parallelism of two lines. Distance of a point from a line. Distance between two parallel lines. Lines through the 
point of intersection of two lines. Angle bisector 
Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y 
may represent a circle. Equation of a circle in terms of endpoints of a diameter. Equation of tangent, normal 
and chord. Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of 
two intersecting circles. 
Definition of conic section, Directrix, Focus and Eccentricity, classification based on eccentricity. Equation of 
Parabola, Ellipse and Hyperbola in standard form, their foci, directrices, eccentricities and parametric 
equations. 
Co-ordinate geometry of three dimensions 
Direction cosines and direction ratios, distance between two points and section formula, equation of a straight 
line, equation of a plane, distance of a point from a plane. 
Calculus 
Differential calculus: Functions, domain and range set of functions, composition of two functions and inverse 
of a function, limit, continuity, derivative, chain rule and derivative of functions in various forms. Concept of 
differential. 
Rolle's Theorem and Lagrange's Mean Value theorem (statement only). Their geometric interpretation and 
elementary application. L'Hospital's rule (statement only) and applications. Second order derivative. 
Integral calculus: Integration as a reverse process of differentiation, indefinite integral of standard functions. 
Integration by parts. Integration by substitution and partial fraction. 
Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its 
applications. Properties of definite integrals. 
Differential Equations: Formation of ordinary differential equations, solution of homogeneous differential 
equations, separation of variables method, linear first order differential equations. 
Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, 
maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant 
acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary 
curves and Straight lines. Area of the region included between two elementary curves. 
Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple product.  
 
PHYSICS: 
Physical World, Measurements, Units & dimensions: Physical World, Measurements, Units & dimensions 
Units & Dimensions of physical quantities, dimensional analysis & its applications, error in measurements, 
significant figures. 
Kinematics: Scalars & vectors, representation of vectors in 3D, dot & cross product & their applications, 
elementary differential & integral calculus, time-velocity & relevant graphs, equations of motion with uniform 
acceleration. 
Laws of motion: Newton’s laws of motion, using algebra & calculus, inertial & non inertial frames, conservation 
of linear momentum with applications, elastic & inelastic collisions, impulse centripetal force, banking of 
roads, relative velocity, projectile motion & uniform circular motion Work, power, energy: Work, power, 
energy Work, work-energy theorem, power, energy, work done by constant & variable forces, PE & KE, 
conservation of mechanical energy, conservative and nonconservative forces, PE of a spring, 
Motion of centre of mass, connected systems, Friction: Centre of mass of two-particle system, motion of 
connected system, torque, equilibrium of rigid bodies, moments of inertia of simple geometric bodies (2D) 
[without derivation] conservation of angular momentum, friction and laws of friction. 
Page 3


 
 
       
 
MATHEMATICS: 
Algebra 
A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ?n, ?n², ?n
3;
 
Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum. 
Logarithms: Definition; General properties; Change of base. 
Complex Numbers: Definition in terms of ordered pair of real numbers and properties of complex numbers; 
Complex conjugate; Triangle inequality; amplitude of complex numbers and its properties; Square root of 
complex numbers; Cube roots of unity; De Moivre's theorem (statement only) and its elementary applications. 
Solution of quadratic equation in complex number system. 
Polynomial equation: nth degree equation has exactly n roots (statement only); Quadratic Equations: 
Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; 
Formation of a quadratic equation, sign and magnitude of the quadratic expression ax
2
 +bx+c (where a, b, c are 
rational numbers and a ? 0). 
Permutation and combination: Permutation of n different things taken r at a time (r = n). Permutation of n 
things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n 
different things taken r at a time (r = n). Combination of n things not all different. Basic properties. Problems 
involving both permutations and combinations. 
Principle of mathematical induction: Statement of the principle, proof by induction for the sum of squares, 
sum of cubes of first n natural numbers, divisibility properties like 2
2n  
— 1 is divisible by 3 (n = 1), 7divides 
3
2n+1
+2
n+2 
(n = 1) 
Binomial theorem (positive integral index): Statement of the theorem, general term, middle term, equidistant 
terms, properties of binomial coefficients. 
Matrices: Concepts of m x n (m = 3, n = 3) real matrices, operations of addition, scalar multiplication and 
multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants 
(statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area 
of a triangle. Solutions of system of linear equations. (Not more than 3 variables). 
Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference 
of sets, Venn diagram, De Morgan's Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian 
product of sets. 
Relation and its properties. Equivalence relation — definition and elementary examples, mappings, range and 
domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping. 
Statistics and Probability: 
Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and 
multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, 
repeated independent trails and Binomial distribution. 
Trigonometry 
Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple 
angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions 
and their properties. 
 Coordinate geometry of two dimensions 
 Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar 
co-ordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of 
axes. 
 
 Concept of locus, locus problems involving all geometrical configurations,  
Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and 
parallelism of two lines. Distance of a point from a line. Distance between two parallel lines. Lines through the 
point of intersection of two lines. Angle bisector 
Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y 
may represent a circle. Equation of a circle in terms of endpoints of a diameter. Equation of tangent, normal 
and chord. Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of 
two intersecting circles. 
Definition of conic section, Directrix, Focus and Eccentricity, classification based on eccentricity. Equation of 
Parabola, Ellipse and Hyperbola in standard form, their foci, directrices, eccentricities and parametric 
equations. 
Co-ordinate geometry of three dimensions 
Direction cosines and direction ratios, distance between two points and section formula, equation of a straight 
line, equation of a plane, distance of a point from a plane. 
Calculus 
Differential calculus: Functions, domain and range set of functions, composition of two functions and inverse 
of a function, limit, continuity, derivative, chain rule and derivative of functions in various forms. Concept of 
differential. 
Rolle's Theorem and Lagrange's Mean Value theorem (statement only). Their geometric interpretation and 
elementary application. L'Hospital's rule (statement only) and applications. Second order derivative. 
Integral calculus: Integration as a reverse process of differentiation, indefinite integral of standard functions. 
Integration by parts. Integration by substitution and partial fraction. 
Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its 
applications. Properties of definite integrals. 
Differential Equations: Formation of ordinary differential equations, solution of homogeneous differential 
equations, separation of variables method, linear first order differential equations. 
Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, 
maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant 
acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary 
curves and Straight lines. Area of the region included between two elementary curves. 
Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple product.  
 
PHYSICS: 
Physical World, Measurements, Units & dimensions: Physical World, Measurements, Units & dimensions 
Units & Dimensions of physical quantities, dimensional analysis & its applications, error in measurements, 
significant figures. 
Kinematics: Scalars & vectors, representation of vectors in 3D, dot & cross product & their applications, 
elementary differential & integral calculus, time-velocity & relevant graphs, equations of motion with uniform 
acceleration. 
Laws of motion: Newton’s laws of motion, using algebra & calculus, inertial & non inertial frames, conservation 
of linear momentum with applications, elastic & inelastic collisions, impulse centripetal force, banking of 
roads, relative velocity, projectile motion & uniform circular motion Work, power, energy: Work, power, 
energy Work, work-energy theorem, power, energy, work done by constant & variable forces, PE & KE, 
conservation of mechanical energy, conservative and nonconservative forces, PE of a spring, 
Motion of centre of mass, connected systems, Friction: Centre of mass of two-particle system, motion of 
connected system, torque, equilibrium of rigid bodies, moments of inertia of simple geometric bodies (2D) 
[without derivation] conservation of angular momentum, friction and laws of friction. 
 
Gravitation: Kepler’s laws, (only statement) universal law of gravitation, acceleration due to gravity (g), 
variation of g, gravitational potential & PE, escape velocity, orbital velocity of satellites, geostationary orbits. 
Bulk properties of matter: Elasticity, Hooke’s law, Young’s modulus, bulk modulus, shear, rigidity modulus, 
Poisson’s ratio elastic potential energy. Fluid pressure: Pressure due to a fluid column, buoyancy, Pascal’s law, 
effect of gravity on fluid pressure. Surface tension: Surface energy, phenomena involving surface tension, 
angle of contact, capillary rise, 
Viscosity: Coefficient of viscosity, streamline & turbulent motion, Reynold’s number, Stoke’s law, terminal 
velocity, Bernoulli’s theorem. Heat & Thermal Physics: Heat & temperature, thermal expansion of solids. 
liquids & gases, ideal gas laws, isothermal & adiabatic processes; anomalous expansion of water & its effects, 
sp. heat capacity,  Cp, Cv, calorimetry; change of state, specific latent heat capacity. Heat transfer; conduction, 
thermal and thermometric conductivity, convection & radiation, Newton's law of cooling, Stefan's law. 
Thermodynamics: Thermal equilibrium (Zeroth law of thermodynamics), heat, work & internal energy. 1st law 
of thermodynamics, isothermal & adiabatic processes, 2nd law of thermodynamics, reversible & irreversible 
processes. 
Kinetic theory of gases: Equation of state of a perfect gas, kinetic theory of gases, assumptions in Kinetic 
theory of gases, concept of pressure. & temperature; rms speed of gas molecules; degrees of freedom, law of 
equipartition of energy (introductory ideas) & application to specific heats of gases; mean free path, Avogadro 
number. 
Oscillations & Waves: Periodic motion – time period, frequency, time-displacement eqation, Simple harmonic 
motion (S.H.M) & its equation; phase; SHM in different sytems, restoring force & force const, energy in S.H.M.-
KE & PE, free, forced & damped oscillations (introductory ideas), resonance wave motion, equation for 
progressive wave, longitudinal & transverse waves, sound waves, Newton’s formula & Laplace’s correction, 
factors affecting the velocity of sound in air, principles of superposition of waves, reflection of waves, standing 
waves in strings & organ pipes, fundamental mode, harmonics &overtones, beats, Doppler effect. 
Electrostatics: Conservation of electric charges, Coulomb's law-force between two-point charges, forces 
between multiple charges; superposition principle & continuous charge distribution. Electric field, & potential 
due to a point charge & distribution of charges, electric field lines electric field due to a dipole; torque on a 
dipole in uniform electric field; electric flux, Gauss' theorem & its simple applications, conductors & insulators, 
free charges & bound charges inside a conductor; dielectrics & electric polarisation, capacitors & capacitance, 
combination of capacitors in series & in parallel, capacitance of a parallel plate capacitor with & without 
dielectric medium between the plates, energy stored in a capacitor. 
Current Electricity:  
Electric current, & conductor, drift velocity' mobility & their relation with electric current; Ohm's law, electrical 
resistance, Ohmic and non-Ohmic conductors, electrical energy & power, carbon resistors, colour codes, 
combination of resistances, temperature dependence of resistances, electric cell, emf and internal resistance 
of an electric cell, pd, combination of cells, secondary cells, (introductory) Kirchoff’s laws of electrical network, 
simple applications, principle of Wheatstone bridge, metre bridge and potentiometer and their uses, 
thermoelectricity; Seebeck effect; Peltier effect, thermo emf. 
Magnetic effect of current: Concept of magnetic field, Oersted's experiment, Biot - Savart law & its application 
to current carrying circular loop; Ampere's law & its applications to infinitely long straight  wire, straight and 
toroidal solenoids; force on a moving charge in uniform magnetic & electric fields, cyclotron frequency; 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 uniform magnetic field; moving 
coil galvanometer-its current sensitivity & conversion to ammeter & voltmeter, Inter-conversion of voltmeter 
& ammeter & change of their ranges. 
Magnetics: Current loop as a magnetic dipole & its magnetic dipole moment, magnetic dipole moment of a 
revolving electron, magnetic field intensity due to a magnetic dipole bar magnet along its axis & perpendicular 
to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; magnet as an equivalent 
solenoid, magnetic field lines; Earth's magnetic field & its magnetic elements. para-, dia- & ferro- magnetic 
substances, with examples. Electromagnets & the factors affecting their strengths, permanent magnets. 
Page 4


 
 
       
 
MATHEMATICS: 
Algebra 
A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ?n, ?n², ?n
3;
 
Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum. 
Logarithms: Definition; General properties; Change of base. 
Complex Numbers: Definition in terms of ordered pair of real numbers and properties of complex numbers; 
Complex conjugate; Triangle inequality; amplitude of complex numbers and its properties; Square root of 
complex numbers; Cube roots of unity; De Moivre's theorem (statement only) and its elementary applications. 
Solution of quadratic equation in complex number system. 
Polynomial equation: nth degree equation has exactly n roots (statement only); Quadratic Equations: 
Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; 
Formation of a quadratic equation, sign and magnitude of the quadratic expression ax
2
 +bx+c (where a, b, c are 
rational numbers and a ? 0). 
Permutation and combination: Permutation of n different things taken r at a time (r = n). Permutation of n 
things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n 
different things taken r at a time (r = n). Combination of n things not all different. Basic properties. Problems 
involving both permutations and combinations. 
Principle of mathematical induction: Statement of the principle, proof by induction for the sum of squares, 
sum of cubes of first n natural numbers, divisibility properties like 2
2n  
— 1 is divisible by 3 (n = 1), 7divides 
3
2n+1
+2
n+2 
(n = 1) 
Binomial theorem (positive integral index): Statement of the theorem, general term, middle term, equidistant 
terms, properties of binomial coefficients. 
Matrices: Concepts of m x n (m = 3, n = 3) real matrices, operations of addition, scalar multiplication and 
multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants 
(statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area 
of a triangle. Solutions of system of linear equations. (Not more than 3 variables). 
Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference 
of sets, Venn diagram, De Morgan's Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian 
product of sets. 
Relation and its properties. Equivalence relation — definition and elementary examples, mappings, range and 
domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping. 
Statistics and Probability: 
Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and 
multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, 
repeated independent trails and Binomial distribution. 
Trigonometry 
Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple 
angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions 
and their properties. 
 Coordinate geometry of two dimensions 
 Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar 
co-ordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of 
axes. 
 
 Concept of locus, locus problems involving all geometrical configurations,  
Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and 
parallelism of two lines. Distance of a point from a line. Distance between two parallel lines. Lines through the 
point of intersection of two lines. Angle bisector 
Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y 
may represent a circle. Equation of a circle in terms of endpoints of a diameter. Equation of tangent, normal 
and chord. Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of 
two intersecting circles. 
Definition of conic section, Directrix, Focus and Eccentricity, classification based on eccentricity. Equation of 
Parabola, Ellipse and Hyperbola in standard form, their foci, directrices, eccentricities and parametric 
equations. 
Co-ordinate geometry of three dimensions 
Direction cosines and direction ratios, distance between two points and section formula, equation of a straight 
line, equation of a plane, distance of a point from a plane. 
Calculus 
Differential calculus: Functions, domain and range set of functions, composition of two functions and inverse 
of a function, limit, continuity, derivative, chain rule and derivative of functions in various forms. Concept of 
differential. 
Rolle's Theorem and Lagrange's Mean Value theorem (statement only). Their geometric interpretation and 
elementary application. L'Hospital's rule (statement only) and applications. Second order derivative. 
Integral calculus: Integration as a reverse process of differentiation, indefinite integral of standard functions. 
Integration by parts. Integration by substitution and partial fraction. 
Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its 
applications. Properties of definite integrals. 
Differential Equations: Formation of ordinary differential equations, solution of homogeneous differential 
equations, separation of variables method, linear first order differential equations. 
Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, 
maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant 
acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary 
curves and Straight lines. Area of the region included between two elementary curves. 
Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple product.  
 
PHYSICS: 
Physical World, Measurements, Units & dimensions: Physical World, Measurements, Units & dimensions 
Units & Dimensions of physical quantities, dimensional analysis & its applications, error in measurements, 
significant figures. 
Kinematics: Scalars & vectors, representation of vectors in 3D, dot & cross product & their applications, 
elementary differential & integral calculus, time-velocity & relevant graphs, equations of motion with uniform 
acceleration. 
Laws of motion: Newton’s laws of motion, using algebra & calculus, inertial & non inertial frames, conservation 
of linear momentum with applications, elastic & inelastic collisions, impulse centripetal force, banking of 
roads, relative velocity, projectile motion & uniform circular motion Work, power, energy: Work, power, 
energy Work, work-energy theorem, power, energy, work done by constant & variable forces, PE & KE, 
conservation of mechanical energy, conservative and nonconservative forces, PE of a spring, 
Motion of centre of mass, connected systems, Friction: Centre of mass of two-particle system, motion of 
connected system, torque, equilibrium of rigid bodies, moments of inertia of simple geometric bodies (2D) 
[without derivation] conservation of angular momentum, friction and laws of friction. 
 
Gravitation: Kepler’s laws, (only statement) universal law of gravitation, acceleration due to gravity (g), 
variation of g, gravitational potential & PE, escape velocity, orbital velocity of satellites, geostationary orbits. 
Bulk properties of matter: Elasticity, Hooke’s law, Young’s modulus, bulk modulus, shear, rigidity modulus, 
Poisson’s ratio elastic potential energy. Fluid pressure: Pressure due to a fluid column, buoyancy, Pascal’s law, 
effect of gravity on fluid pressure. Surface tension: Surface energy, phenomena involving surface tension, 
angle of contact, capillary rise, 
Viscosity: Coefficient of viscosity, streamline & turbulent motion, Reynold’s number, Stoke’s law, terminal 
velocity, Bernoulli’s theorem. Heat & Thermal Physics: Heat & temperature, thermal expansion of solids. 
liquids & gases, ideal gas laws, isothermal & adiabatic processes; anomalous expansion of water & its effects, 
sp. heat capacity,  Cp, Cv, calorimetry; change of state, specific latent heat capacity. Heat transfer; conduction, 
thermal and thermometric conductivity, convection & radiation, Newton's law of cooling, Stefan's law. 
Thermodynamics: Thermal equilibrium (Zeroth law of thermodynamics), heat, work & internal energy. 1st law 
of thermodynamics, isothermal & adiabatic processes, 2nd law of thermodynamics, reversible & irreversible 
processes. 
Kinetic theory of gases: Equation of state of a perfect gas, kinetic theory of gases, assumptions in Kinetic 
theory of gases, concept of pressure. & temperature; rms speed of gas molecules; degrees of freedom, law of 
equipartition of energy (introductory ideas) & application to specific heats of gases; mean free path, Avogadro 
number. 
Oscillations & Waves: Periodic motion – time period, frequency, time-displacement eqation, Simple harmonic 
motion (S.H.M) & its equation; phase; SHM in different sytems, restoring force & force const, energy in S.H.M.-
KE & PE, free, forced & damped oscillations (introductory ideas), resonance wave motion, equation for 
progressive wave, longitudinal & transverse waves, sound waves, Newton’s formula & Laplace’s correction, 
factors affecting the velocity of sound in air, principles of superposition of waves, reflection of waves, standing 
waves in strings & organ pipes, fundamental mode, harmonics &overtones, beats, Doppler effect. 
Electrostatics: Conservation of electric charges, Coulomb's law-force between two-point charges, forces 
between multiple charges; superposition principle & continuous charge distribution. Electric field, & potential 
due to a point charge & distribution of charges, electric field lines electric field due to a dipole; torque on a 
dipole in uniform electric field; electric flux, Gauss' theorem & its simple applications, conductors & insulators, 
free charges & bound charges inside a conductor; dielectrics & electric polarisation, capacitors & capacitance, 
combination of capacitors in series & in parallel, capacitance of a parallel plate capacitor with & without 
dielectric medium between the plates, energy stored in a capacitor. 
Current Electricity:  
Electric current, & conductor, drift velocity' mobility & their relation with electric current; Ohm's law, electrical 
resistance, Ohmic and non-Ohmic conductors, electrical energy & power, carbon resistors, colour codes, 
combination of resistances, temperature dependence of resistances, electric cell, emf and internal resistance 
of an electric cell, pd, combination of cells, secondary cells, (introductory) Kirchoff’s laws of electrical network, 
simple applications, principle of Wheatstone bridge, metre bridge and potentiometer and their uses, 
thermoelectricity; Seebeck effect; Peltier effect, thermo emf. 
Magnetic effect of current: Concept of magnetic field, Oersted's experiment, Biot - Savart law & its application 
to current carrying circular loop; Ampere's law & its applications to infinitely long straight  wire, straight and 
toroidal solenoids; force on a moving charge in uniform magnetic & electric fields, cyclotron frequency; 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 uniform magnetic field; moving 
coil galvanometer-its current sensitivity & conversion to ammeter & voltmeter, Inter-conversion of voltmeter 
& ammeter & change of their ranges. 
Magnetics: Current loop as a magnetic dipole & its magnetic dipole moment, magnetic dipole moment of a 
revolving electron, magnetic field intensity due to a magnetic dipole bar magnet along its axis & perpendicular 
to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; magnet as an equivalent 
solenoid, magnetic field lines; Earth's magnetic field & its magnetic elements. para-, dia- & ferro- magnetic 
substances, with examples. Electromagnets & the factors affecting their strengths, permanent magnets. 
 
 
Electromagnetic induction & alternating current: Electromagnetic induction; Faraday's laws, induced emf & 
current; Lenz's Law, eddy currents, self & mutual induction, alternating currents, peak and rms value of 
alternating current and voltage; reactance and impedance; LR & CR circuits, phase lag & lead, LCR series 
circuit, resonance; power in AC circuits, wattless current. 
Electromagnetic waves: Electromagnetic waves and their characteristics (qualitative ideas only), transverse 
nature of electromagnetic waves, electromagnetic spectrum, applications of the waves from the different 
parts of the spectrum  
Optics I (Ray optics): Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal 
reflection & its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, 
lensmaker's formula. Newton's relation: Displacement method to find position of images (conjugate points) 
Magnification, power of a lens, combination of thin lenses in contact, combination of a lens & a mirror 
refraction and dispersion of light through a prism; optical instruments, human eye, image formation & 
accommodation, correction of eye defects (myopia, hypermetropia) using lenses, microscopes & astronomical 
telescopes (reflecting & refracting) & their magnifying powers. 
Optics II (Wave Optics): Scattering of light - blue colour of the sky, elementary idea of Raman effect; wave 
optics: wave front & Huygens' principle, reflection & refraction of plane wave at a plane surface using wave 
fronts. Proof of laws of reflection & refraction using Huygens' principle Interference, Young's double slit 
experiment & expression for fringe width, coherent sources, Fraunhoffer diffraction due to a single slit, 
Particle nature of light & wave particle dualism: Photoelectric effect, Hertz and Lenard’s observations; 
Einstein’s photoelectric equation - particle nature of light, matter waves; wave nature of particles, de Broglie 
relation.  
Atomic Physics: Alpha-particle scattering expt Rutherford's nuclear atom model of atom; Bohr model of 
hydrogen atom, energy levels in a hydrogen atom, hydrogen spectrum, continuous & characteristic xrays. 
Nuclear Physics: Composition & size of nucleus, atomic masses, isotopes, isobars; isotones, radioactivity - 
alpha, beta & gamma particles/ rays & their properties; radioactive decay law; massenergy relation, mass 
defect; binding energy per nucleon & its variation with mass number; nuclear fission & fusion. 
Solid state Electronics: Energy bands in solids (qualitative ideas only), conductors, insulators & semiconductors; 
semiconductor diode – I-V characteristics in forward & reverse bias, diode as a rectifier; 
I-V characteristics of LED, photodiode, solar cell & Zener diode; Zener diode as a voltage regulator, junction 
transistor (BJT), transistor action, characteristics of a BJT, BJT as an amplifier (CE configuration) & oscillator; 
logic gates (OR, AND, NOT, NAND & NOR). 
 
CHEMISTRY: 
Atoms, Molecules and Chemical Arithmetic: 
Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s Hypothesis and its applications. 
Atomic mass; Molecular mass; Equivalent weight; Valency; Gram atomic weight; Gram molecular weight; Gram 
equivalent weight and mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on 
mole concept) involving common oxidation – reduction, neutralization, and displacement reactions; 
Concentration in terms of mole fraction, molarity, molality and normality. Percentage composition, empirical 
formula and molecular formula; Numerical problems. 
Atomic Structure: 
Concept of Nuclear Atom – electron, proton and neutron (charge and mass), atomic number.  utherford’s 
model and its limitations; Extra nuclear structure; Line spectra of hydrogen atom. Quantization of energy 
(Planck’s equation E = h?); Bohr’s model of hydrogen atom and its limitations, Sommerfeld’s modifications 
(elementary idea); The four quantum numbers, ground state electronic configurations of many electron atoms 
and mono – atomic ions; The Aufbau Principle; Pauli’s Exclusion Principle and Hund’s Rule. Dual nature of 
matter and light, de Broglie's relationship, Uncertainty principle; The concept of atomic orbitals, shapes of s, p 
and d orbitals (pictorial approach). 
Radioactivity and Nuclear Chemistry: 
Page 5


 
 
       
 
MATHEMATICS: 
Algebra 
A.P., G.P., H.P.: Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ?n, ?n², ?n
3;
 
Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum. 
Logarithms: Definition; General properties; Change of base. 
Complex Numbers: Definition in terms of ordered pair of real numbers and properties of complex numbers; 
Complex conjugate; Triangle inequality; amplitude of complex numbers and its properties; Square root of 
complex numbers; Cube roots of unity; De Moivre's theorem (statement only) and its elementary applications. 
Solution of quadratic equation in complex number system. 
Polynomial equation: nth degree equation has exactly n roots (statement only); Quadratic Equations: 
Quadratic equations with real coefficients; Relations between roots and coefficients; Nature of roots; 
Formation of a quadratic equation, sign and magnitude of the quadratic expression ax
2
 +bx+c (where a, b, c are 
rational numbers and a ? 0). 
Permutation and combination: Permutation of n different things taken r at a time (r = n). Permutation of n 
things not all different. Permutation with repetitions (circular permutation excluded). Combinations of n 
different things taken r at a time (r = n). Combination of n things not all different. Basic properties. Problems 
involving both permutations and combinations. 
Principle of mathematical induction: Statement of the principle, proof by induction for the sum of squares, 
sum of cubes of first n natural numbers, divisibility properties like 2
2n  
— 1 is divisible by 3 (n = 1), 7divides 
3
2n+1
+2
n+2 
(n = 1) 
Binomial theorem (positive integral index): Statement of the theorem, general term, middle term, equidistant 
terms, properties of binomial coefficients. 
Matrices: Concepts of m x n (m = 3, n = 3) real matrices, operations of addition, scalar multiplication and 
multiplication of matrices. Transpose of a matrix. Determinant of a square matrix. Properties of determinants 
(statement only). Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. Finding area 
of a triangle. Solutions of system of linear equations. (Not more than 3 variables). 
Sets, Relations and Mappings: Idea of sets, subsets, power set, complement, union, intersection and difference 
of sets, Venn diagram, De Morgan's Laws, Inclusion / Exclusion formula for two or three finite sets, Cartesian 
product of sets. 
Relation and its properties. Equivalence relation — definition and elementary examples, mappings, range and 
domain, injective, surjective and bijective mappings, composition of mappings, inverse of a mapping. 
Statistics and Probability: 
Measure of dispersion, mean, variance and standard deviation, frequency distribution. Addition and 
multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, 
repeated independent trails and Binomial distribution. 
Trigonometry 
Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple 
angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions 
and their properties. 
 Coordinate geometry of two dimensions 
 Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. Polar 
co-ordinates, transformation from Cartesian to polar coordinates and vice versa. Parallel transformation of 
axes. 
 
 Concept of locus, locus problems involving all geometrical configurations,  
Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and 
parallelism of two lines. Distance of a point from a line. Distance between two parallel lines. Lines through the 
point of intersection of two lines. Angle bisector 
Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y 
may represent a circle. Equation of a circle in terms of endpoints of a diameter. Equation of tangent, normal 
and chord. Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of 
two intersecting circles. 
Definition of conic section, Directrix, Focus and Eccentricity, classification based on eccentricity. Equation of 
Parabola, Ellipse and Hyperbola in standard form, their foci, directrices, eccentricities and parametric 
equations. 
Co-ordinate geometry of three dimensions 
Direction cosines and direction ratios, distance between two points and section formula, equation of a straight 
line, equation of a plane, distance of a point from a plane. 
Calculus 
Differential calculus: Functions, domain and range set of functions, composition of two functions and inverse 
of a function, limit, continuity, derivative, chain rule and derivative of functions in various forms. Concept of 
differential. 
Rolle's Theorem and Lagrange's Mean Value theorem (statement only). Their geometric interpretation and 
elementary application. L'Hospital's rule (statement only) and applications. Second order derivative. 
Integral calculus: Integration as a reverse process of differentiation, indefinite integral of standard functions. 
Integration by parts. Integration by substitution and partial fraction. 
Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its 
applications. Properties of definite integrals. 
Differential Equations: Formation of ordinary differential equations, solution of homogeneous differential 
equations, separation of variables method, linear first order differential equations. 
Application of Calculus: Tangents and normals, conditions of tangency. Determination of monotonicity, 
maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant 
acceleration. Geometric interpretation of definite integral as area, calculation of area bounded by elementary 
curves and Straight lines. Area of the region included between two elementary curves. 
Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple product.  
 
PHYSICS: 
Physical World, Measurements, Units & dimensions: Physical World, Measurements, Units & dimensions 
Units & Dimensions of physical quantities, dimensional analysis & its applications, error in measurements, 
significant figures. 
Kinematics: Scalars & vectors, representation of vectors in 3D, dot & cross product & their applications, 
elementary differential & integral calculus, time-velocity & relevant graphs, equations of motion with uniform 
acceleration. 
Laws of motion: Newton’s laws of motion, using algebra & calculus, inertial & non inertial frames, conservation 
of linear momentum with applications, elastic & inelastic collisions, impulse centripetal force, banking of 
roads, relative velocity, projectile motion & uniform circular motion Work, power, energy: Work, power, 
energy Work, work-energy theorem, power, energy, work done by constant & variable forces, PE & KE, 
conservation of mechanical energy, conservative and nonconservative forces, PE of a spring, 
Motion of centre of mass, connected systems, Friction: Centre of mass of two-particle system, motion of 
connected system, torque, equilibrium of rigid bodies, moments of inertia of simple geometric bodies (2D) 
[without derivation] conservation of angular momentum, friction and laws of friction. 
 
Gravitation: Kepler’s laws, (only statement) universal law of gravitation, acceleration due to gravity (g), 
variation of g, gravitational potential & PE, escape velocity, orbital velocity of satellites, geostationary orbits. 
Bulk properties of matter: Elasticity, Hooke’s law, Young’s modulus, bulk modulus, shear, rigidity modulus, 
Poisson’s ratio elastic potential energy. Fluid pressure: Pressure due to a fluid column, buoyancy, Pascal’s law, 
effect of gravity on fluid pressure. Surface tension: Surface energy, phenomena involving surface tension, 
angle of contact, capillary rise, 
Viscosity: Coefficient of viscosity, streamline & turbulent motion, Reynold’s number, Stoke’s law, terminal 
velocity, Bernoulli’s theorem. Heat & Thermal Physics: Heat & temperature, thermal expansion of solids. 
liquids & gases, ideal gas laws, isothermal & adiabatic processes; anomalous expansion of water & its effects, 
sp. heat capacity,  Cp, Cv, calorimetry; change of state, specific latent heat capacity. Heat transfer; conduction, 
thermal and thermometric conductivity, convection & radiation, Newton's law of cooling, Stefan's law. 
Thermodynamics: Thermal equilibrium (Zeroth law of thermodynamics), heat, work & internal energy. 1st law 
of thermodynamics, isothermal & adiabatic processes, 2nd law of thermodynamics, reversible & irreversible 
processes. 
Kinetic theory of gases: Equation of state of a perfect gas, kinetic theory of gases, assumptions in Kinetic 
theory of gases, concept of pressure. & temperature; rms speed of gas molecules; degrees of freedom, law of 
equipartition of energy (introductory ideas) & application to specific heats of gases; mean free path, Avogadro 
number. 
Oscillations & Waves: Periodic motion – time period, frequency, time-displacement eqation, Simple harmonic 
motion (S.H.M) & its equation; phase; SHM in different sytems, restoring force & force const, energy in S.H.M.-
KE & PE, free, forced & damped oscillations (introductory ideas), resonance wave motion, equation for 
progressive wave, longitudinal & transverse waves, sound waves, Newton’s formula & Laplace’s correction, 
factors affecting the velocity of sound in air, principles of superposition of waves, reflection of waves, standing 
waves in strings & organ pipes, fundamental mode, harmonics &overtones, beats, Doppler effect. 
Electrostatics: Conservation of electric charges, Coulomb's law-force between two-point charges, forces 
between multiple charges; superposition principle & continuous charge distribution. Electric field, & potential 
due to a point charge & distribution of charges, electric field lines electric field due to a dipole; torque on a 
dipole in uniform electric field; electric flux, Gauss' theorem & its simple applications, conductors & insulators, 
free charges & bound charges inside a conductor; dielectrics & electric polarisation, capacitors & capacitance, 
combination of capacitors in series & in parallel, capacitance of a parallel plate capacitor with & without 
dielectric medium between the plates, energy stored in a capacitor. 
Current Electricity:  
Electric current, & conductor, drift velocity' mobility & their relation with electric current; Ohm's law, electrical 
resistance, Ohmic and non-Ohmic conductors, electrical energy & power, carbon resistors, colour codes, 
combination of resistances, temperature dependence of resistances, electric cell, emf and internal resistance 
of an electric cell, pd, combination of cells, secondary cells, (introductory) Kirchoff’s laws of electrical network, 
simple applications, principle of Wheatstone bridge, metre bridge and potentiometer and their uses, 
thermoelectricity; Seebeck effect; Peltier effect, thermo emf. 
Magnetic effect of current: Concept of magnetic field, Oersted's experiment, Biot - Savart law & its application 
to current carrying circular loop; Ampere's law & its applications to infinitely long straight  wire, straight and 
toroidal solenoids; force on a moving charge in uniform magnetic & electric fields, cyclotron frequency; 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 uniform magnetic field; moving 
coil galvanometer-its current sensitivity & conversion to ammeter & voltmeter, Inter-conversion of voltmeter 
& ammeter & change of their ranges. 
Magnetics: Current loop as a magnetic dipole & its magnetic dipole moment, magnetic dipole moment of a 
revolving electron, magnetic field intensity due to a magnetic dipole bar magnet along its axis & perpendicular 
to its axis, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; magnet as an equivalent 
solenoid, magnetic field lines; Earth's magnetic field & its magnetic elements. para-, dia- & ferro- magnetic 
substances, with examples. Electromagnets & the factors affecting their strengths, permanent magnets. 
 
 
Electromagnetic induction & alternating current: Electromagnetic induction; Faraday's laws, induced emf & 
current; Lenz's Law, eddy currents, self & mutual induction, alternating currents, peak and rms value of 
alternating current and voltage; reactance and impedance; LR & CR circuits, phase lag & lead, LCR series 
circuit, resonance; power in AC circuits, wattless current. 
Electromagnetic waves: Electromagnetic waves and their characteristics (qualitative ideas only), transverse 
nature of electromagnetic waves, electromagnetic spectrum, applications of the waves from the different 
parts of the spectrum  
Optics I (Ray optics): Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal 
reflection & its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, 
lensmaker's formula. Newton's relation: Displacement method to find position of images (conjugate points) 
Magnification, power of a lens, combination of thin lenses in contact, combination of a lens & a mirror 
refraction and dispersion of light through a prism; optical instruments, human eye, image formation & 
accommodation, correction of eye defects (myopia, hypermetropia) using lenses, microscopes & astronomical 
telescopes (reflecting & refracting) & their magnifying powers. 
Optics II (Wave Optics): Scattering of light - blue colour of the sky, elementary idea of Raman effect; wave 
optics: wave front & Huygens' principle, reflection & refraction of plane wave at a plane surface using wave 
fronts. Proof of laws of reflection & refraction using Huygens' principle Interference, Young's double slit 
experiment & expression for fringe width, coherent sources, Fraunhoffer diffraction due to a single slit, 
Particle nature of light & wave particle dualism: Photoelectric effect, Hertz and Lenard’s observations; 
Einstein’s photoelectric equation - particle nature of light, matter waves; wave nature of particles, de Broglie 
relation.  
Atomic Physics: Alpha-particle scattering expt Rutherford's nuclear atom model of atom; Bohr model of 
hydrogen atom, energy levels in a hydrogen atom, hydrogen spectrum, continuous & characteristic xrays. 
Nuclear Physics: Composition & size of nucleus, atomic masses, isotopes, isobars; isotones, radioactivity - 
alpha, beta & gamma particles/ rays & their properties; radioactive decay law; massenergy relation, mass 
defect; binding energy per nucleon & its variation with mass number; nuclear fission & fusion. 
Solid state Electronics: Energy bands in solids (qualitative ideas only), conductors, insulators & semiconductors; 
semiconductor diode – I-V characteristics in forward & reverse bias, diode as a rectifier; 
I-V characteristics of LED, photodiode, solar cell & Zener diode; Zener diode as a voltage regulator, junction 
transistor (BJT), transistor action, characteristics of a BJT, BJT as an amplifier (CE configuration) & oscillator; 
logic gates (OR, AND, NOT, NAND & NOR). 
 
CHEMISTRY: 
Atoms, Molecules and Chemical Arithmetic: 
Dalton’s atomic theory; Gay Lussac’s law of gaseous volume; Avogadro’s Hypothesis and its applications. 
Atomic mass; Molecular mass; Equivalent weight; Valency; Gram atomic weight; Gram molecular weight; Gram 
equivalent weight and mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on 
mole concept) involving common oxidation – reduction, neutralization, and displacement reactions; 
Concentration in terms of mole fraction, molarity, molality and normality. Percentage composition, empirical 
formula and molecular formula; Numerical problems. 
Atomic Structure: 
Concept of Nuclear Atom – electron, proton and neutron (charge and mass), atomic number.  utherford’s 
model and its limitations; Extra nuclear structure; Line spectra of hydrogen atom. Quantization of energy 
(Planck’s equation E = h?); Bohr’s model of hydrogen atom and its limitations, Sommerfeld’s modifications 
(elementary idea); The four quantum numbers, ground state electronic configurations of many electron atoms 
and mono – atomic ions; The Aufbau Principle; Pauli’s Exclusion Principle and Hund’s Rule. Dual nature of 
matter and light, de Broglie's relationship, Uncertainty principle; The concept of atomic orbitals, shapes of s, p 
and d orbitals (pictorial approach). 
Radioactivity and Nuclear Chemistry: 
 
 
Radioactivity a-, ß-, ? rays and their properties; Artificial transmutation; Rate of radioactive decay, decay 
constant, half-life and average age life period of radio-elements; Units of radioactivity; Numerical problems. 
Stability of the atomic nucleus – effect of neutron-proton (n/p) ratio on the modes of decay, group 
displacement law, radioisotopes and their uses (C, P, Co and I as examples) isobars and isotones (definition and 
examples), elementary idea of nuclear fission and fusion reactions. 
The Periodic Table and Chemical Families: 
Modern periodic law (based on atomic number); Modern periodic table based on electronic configurations, 
groups (Gr. 1-18) and periods. Types of elements – representative (s-block and p- block), transition (d-block) 
elements and inner transition (f-block/lanthanides and actinides) and their general characteristics. Periodic 
trends in physical and chemical properties – atomic radii, valency, ionization energy, electron affinity, 
electronegativity, metallic character, acidic and basic characters of oxides and hydrides of the representative 
elements (up to Z = 36). Position of hydrogen and the noble gases in the periodic table; Diagonal relationships. 
Chemical Bonding and Molecular Structure: 
Valence electrons, the Octet rule, electrovalent, covalent and coordinate covalent bonds with examples; 
Properties of electrovalent and covalent compounds. Limitations of Octet rule (examples); Fajans Rule. 
Directionality of covalent bonds, shapes of poly – atomic molecules (examples); Concept of hybridization of 
atomic orbitals (qualitative pictorial approach): sp, sp2  , sp3 and dsp2 . Molecular orbital energy diagrams for 
homonuclear diatomic species – bond order and magnetic properties. Valence Shell Electron Pair Repulsion 
(VSEPR) concept (elementary idea) – shapes of molecules. Concept of resonance (elementary idea), resonance 
structures (examples). Elementary idea about electronegativity, bond polarity and dipole moment, inter- and 
intra-molecular hydrogen bonding and its effects on physical properties (mp, bp and solubility); Hydrogen 
bridge bonds in diborane. 
Coordination Compounds: 
Introduction, Double salts and complex salts, coordination compounds (examples only), Werner's theory, 
coordination number (examples of coordination number 4 and 6 only), colour, magnetic properties and 
shapes, IUPAC nomenclature of mononuclear coordination compounds. 
Solid State: 
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 & p type semiconductors. 
Liquid State: 
Vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations). 
Gaseous State: 
Measurable properties of gases. Boyle’s Law and Charles Law, absolute scale of temperature, kinetic theory of 
gases, ideal gas equation – average, root mean square and most probable velocities and their relationship with 
temperature. Daltons Law of partial pressure, Grahams Law of gaseous diffusion. Deviations from ideal 
behavior. Liquefaction of gases, real gases, van der Waals equation; Numerical problems. 
 
Chemical Energetics and Chemical Dynamics: 
Chemical Energetics – Conservation of energy principle, energy changes in physical and chemical 
transformations. First law of thermodynamics; Internal energy, work and heat, pressure – volume work; 
Enthalpy. Internal energy change (?E) and Enthalpy change (?H) in a chemical reaction. Hesss Law and its 
applications (Numerical problems). Heat of reaction, fusion and apourization; Second law of thermodynamics; 
Entropy; Free energy; Criterion of spontaneity. Third law of thermodynamics (brief introduction). 
Chemical Equilibria – The Law of mass action, dynamic nature of chemical equilibria. Equilibrium constants, Le 
Chateliers Principle. Equilibrium constants of gaseous reactions (Kp and Kc) and relation between them 
(examples). Significance of ?G and ?Gº.