Uni-GAUGE Syllabus 2018 - ERA foundation, the exam conducting body has Uni-GAUGE 2018 syllabus for Physics, Chemistry and Mathematics. Candidates who are applying for the entrance exam must refer the syllabus of Uni-GAUGE 2018 to be able to prepare better. The questions in the entrance exam will be asked from the existing syllabus of class XI & XII or any equivalent exam. But, it is still important for candidates to refer to Uni-GAUGE syllabus 2018 as it is officially announced by the authorities and it also contains the topics and sub-topics of the subjects of the exam - Physics, Chemistry and Mathematics. The Uni-GAUGE 2018 syllabus can be divided by candidates according to their convenience while preparing for the exam, in which, they will be required to answer 180 questions. Candidates must know that for every correct answer in Uni-GAUGE, 1 mark will be awarded and there will be no negative marking for wrong answers in the exam. The complete syllabus of Uni-GAUGE 2018 can be checked by candidates from the full article given below.
Uni-GAUGE Syllabus for Physics (Class XI)
Physical World and Measurement
Physics - scope and excitement; nature of physical laws; Physics, technology and society, Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures, Dimensions of physical quantities, dimensional analysis and its applications.
Frame of reference, 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), Scalar and vector quantities; Position and displacement vectors, equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a plane - rectangular components. Scalar and 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, lubrication, Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on banked road).
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.
Motion of System of Particles and Rigid Body
Centre of mass of a two-particle system, momentum conservation and centre of mass, 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). Statement of parallel and perpendicular axes theorems and their applications.
Keplar'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. Geo-stationary satellites.
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, Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity. Bernoulli's theorem and its 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, 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, Green house effect.
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. Heat engine and refrigerator.
Behaviour of Perfect Gases and Kinetic Theory of Gases
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 mean free path, Avogadro's number.
Oscillations and Waves
Periodic motion - time period, frequency, displacement as a function of time. Periodic Functions, Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring-restoring force and force constant; energy in S.H.M. Kinetic and potential energies; simple pendulum derivation of expression for its time period, Free, forced and damped oscillations (qualitative ideas only), resonance, Wave motion. Transverse and longitudinal 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, Doppler.
Uni-GAUGE Syllabus for Physics (Class XII)
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). 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 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. Van de Graaff generator
Electric current, flow of electric charges in a metallic conductor, drift velocity, 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, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.
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 and toroidal solenoids, 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; moving coil galvanometer-its current sensitivity. 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; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets
Electromagnetic Induction and Alternating Currents
Electromagnetic induction; Faraday’s laws, induced emf and current; Lenz’s Law, Self and mutual induction. Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator and transformer
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.
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, lensmaker’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. Scattering of light - blue colour of sky and reddish apprearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying Powers. 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, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum, microscopes and astronomical telescopes. Polarisation, plane polarised light Brewster's law, uses of plane polarised light and Polaroids.
Dual Nature of Matter and Radiation
Dual nature of radiation. Photoelectric effect, Einstein’s photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained)
Atoms & Nuclei
Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen 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, nuclear fusion.
Energy bands in solids (Qualitative ideas only) conductors, insulator and semiconductors; semiconductor diode– I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of
a transistor, transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave.
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Uni-GAUGE 2018 Syllabus for Chemistry (Class XI & XII)
Introduction to Structure of Atom, Atomic models, Quantum Mechanical Model, Shapes of Atomic Orbitals, Rules for Filling Electrons in Orbitals, Stability of Completely Filled and half-filled Orbitals
Types of Chemical, Bonds, Valence Bond Theory, Molecular Orbital Theory, Hydrogen Bond
States of Matter: Gases and Liquids
Intermolecular Forces, Laws Governing Gaseous State, Ideal Behaviour, Deviation from Ideal Behaviour, Liquefaction of Gases, Liquid State
Thermodynamic Terms, Thermodynamic Quantities, First Law of Thermodynamics, Thermochemistry, Spontaneity, Third Law of Thermodynamics
Introduction to Equilibrium, Equilibrium in Physical Processes, Equilibrium in Chemical Processes, Types of Chemical Equilibria, Applications of Equilibrium Constant, Factors Affecting Equilibria, Ionic Equilibrium in Solution, Ionization of Acids and Bases, Buffer Solutions, Solubility Equilibria of Sparingly Soluble Salts
Introduction to Solid State Chemistry, Classification of Solids on the Basis of Order in the Arrangement, Crystal Lattices and Unit Cells, Close Packing in solids, Imperfections in Solids, Electrical Properties, Magnetic Properties
Introduction to solutions, Types of Solutions, Expressing the Concentration of Solutions of Solids in Liquids, Solubility, Vapour Pressure of Liquid Solutions, Classification of Liquid-Liquid Solutions on the basis of Raoult’s Law, Colligative Properties, Abnormal Molecular Mass
Redox reactions and Electrochemistry
Oxidation and Reduction Reactions, Redox Reactions in Terms of Electron Transfer Reactions, Oxidation Number, Types of Redox Reactions, Balancing of Redox Reactions, Types of Electrochemical Cells, Electrolysis, Conductance in Electrolytic Solutions, Galvanic Cells, Corrosion
s- Block & p-Block Elements and metallurgy
S-Block Elements Group 1 Elements & Group 2 Elements, P-Block Elements Group 13, 14, 15,16, 17 and 18 Elements
d and f - Block Elements and Coordination Compounds
d-Block elements, F-Block Elements, Coordination Compounds, IUPAC Nomenclature of Coordination Compounds, Valence Bond Theory as Applied to
Coordination Compounds, Importance of Coordination Compounds
Adsorption on a Surface, Catalysis, Colloids
Rate of Chemical Reaction, Factors Affecting Rate of a Reaction, Integrated Rate Equations and Half Life, Temperature Dependence of Rate of Reaction, Collision Theory
Hydrocarbons, Haloalkanes and Haloarenes
Types of Hybridization of Carbon, Classification of Organic Compounds, IUPAC Nomenclature of Organic Compounds, Stereochemistry and Isomerism, Homolytic and Heterolytic Fission of a Covalent Bond, Basics of Organic Reaction, Electronic Displacements in a Covalent Bond, Aromaticity, Alkanes (Upto 5 Carbon Atoms), Alkenes (Upto 5 Carbon Atoms), Alkynes (Upto 5 Carbon Atoms), Arenes, Haloalkanes and haloarenes
Oxygen containing Organic compounds
Structure, Preparation of Alcohols and Phenols, Properties of Alcohols, Phenols and Ethers, Preparation of Ethers & chemical
Properties, Structure of Aldehydes, Ketones and Carboxylic Acids, Preparation of Aldehydes and Ketones, Physical, Chemical Properties and Uses of Aldehydes and Ketones, Carboxylic acids
Nitrogen containing Organic compounds
Structure, Preparation of Amines, Physical and Chemical Properties of Amines, Diazonium Salts
Bio-Molecules and Polymers
Chemistry in everyday life
Chemicals in Medicines, Food and Hygiene (Soaps and Detergents)
Environmental, Pollution, Water Pollution, Industrial Pollution
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Uni-GAUGE Syllabus 2018 for Mathematics (Class XI)
Sets and their representations, Empty Set, Singleton Set, Finite and infinite Sets, Equivalent and Equal Sets, Subsets, Power Set, Universal Set, Complement of a Set, Intervals as Subsets of R, Venn diagrams, Union and Intersection of Sets, Difference of sets, Laws of Operations on Sets, Properties of Complement Sets, Practical Problems on union and Intersection of Sets
Relations and Functions
Ordered Pairs, Cartesian Product of Sets, Definition of Relation, Arrow Diagram, Domain, Codomain and Range of a Relation, Function as a Special Kind of Relation from one Set to another, Pictorial representation of a Function, Domain, Codomain and Range of a Function, Real valued functions and their graphs
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, Sign of trigonometric functions, Domain and range of trigonometric functions, Trigonometric functions as periodic functions, their amplitude, argument, period and graph, Trigonometric functions of sum and difference of two angles, Express sum and difference of T-Functions as the product of T-ratios, Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x, General solution of trigonometric equations of the type sin = sin , cos = cos and tan = tan . finding general solutions of sin , cos = cos and tan = tan, Proof and simple applications of sine and cosine rules
Principle of Mathematical Induction
Process of proof by induction, Principle of mathematical induction and its applications
Complex Numbers and Quadratic Equations
Need for complex number, especially iota to be motivated by inability to solve some of quadratic equation, Standard form of complex number, Modulus and conjugate of complex number, Multiplication and division of complex numbers, Polar representation of complex number, Argand Plane, Statement of Fundamental theorem of algebra, Square root of a complex number, Solution of quadratic equations in the complex number system
Linear and Quadratic Inequalities
Linear inequations, Algebraic solutions of linear inequations in one variable, Algebraic solutions of linear inequations in two variables, Graphical solution of linear inequations in two variables, Inequations solving modulus functions
Permutation and Combination
Fundamental principles of counting, Factorial n (n!), Permutation, Combinations, Derivation of properties of combination, Types of permutations, Simple applications
Pascal’s Triangle, History, statement and proof of the binomial theorems for positive integral indices, General and middle term in binomial expansion, Application of binomial theorem
Sequences and Series
Arithmetic Progression, Geometric Progression, Arithmetic mean, Geometric mean, Sum to n terms of an A.P., Sum to n terms of a G.P., Infinite G.P. and its sum, Relation between A.M. and G.M, Sum to n terms of special series, Arithmeticogeometric series, Harmonic Progression
Brief recall of two dimensional geometry from earlier classes, Shifting of origin, Slope of a line, Angle between two lines, Various forms of equation of a line: parallel to axis, point slop form, slop intercept form, two point form, intercept form, and normal form, General equation of a line, Equation of family of lines passing through the point of intersection of two lines, Distance of a point from a line, Distance between parallel lines
Introduction to section of a cone, Circle (Standard form), Circle (general form), Parabola (standard form), Parabola (general form), Ellipse (standard form) horizontal & vertical ellipse, Ellipse (general form), Hyperbole (standard form), Hyperbole (general form), Application of conic section
Introduction to Three dimensional Geometry
Co-ordinate axes and co-ordinate planes in three dimensions, Distance between two points and section formula, Some results on line in space
Limits and Continuity
Limit of function, Fundamental theorem on limits, Standard results on limits and their application, Trigonometric limits, Infinite limits, One sided limit, Continuity
Random experiment: outcomes, sample spaces (set representation), Events: occurrence of events, 'or', 'and', & 'not' events, Exhaustive events, mutually exclusive events Axiomatic (set theoretic) probability, Probability of an event, Odds of an event, Probability of occurrence of a complementary events, Results on probability, Addition theorem
Uni-GAUGE Syllabus for Mathematics (Class XII)
Relations and Functions
Types of relations : reflexive, symmetric, transitive and equivalence relations, One to one and on to functions, Composite functions, Inverse of a function and binary operations, Concept of exponential and logarithmic function to the base, logarithmic function as inverse of exponential function and their graphs
Inverse trigonometric functions
Definition of inverse trigonometric function in a unit circle, Range, domain, principal value branches, Graphs of inverse trigonometric functions, Elementary properties of inverse trigonometric functions, Problems based on properties
Matrices, Equality of matrices, Operation on matrices, Multiplication of matrices, Transpose of matrix, Symmetric and skew- symmetric matrices, Concept of elementary row and column transformations
Determinant of a square matrix (up to 3 × 3 matrices), Application of determinant, Properties of determinants, Cramer’s Rule
Adjoint and Inverse of a matrix
Adjoint of a matrix, Singular and Non singular matrix, Invertible matrices, Solving a system of linear equations by Matrix method
Differentiability, Product Rule, Quotient Rule, Derivatives of implicit functions, Derivative of logarithmic and exponential functions, Derivative of Infinite Series, Logarithmic differentiation, Differentiation of one function with respect to another), Derivatives of functions expressed in parametric form, Second order derivative
Applications of Derivatives
Rate of change, Increasing/ decreasing functions, Rolle's theorem, Lagrange's mean value theorem (without proof) and their geometrical interpretation and simple application, Tangents and normals, Approximations, Maxima and minima (local maxima/ local minima and absolute maxima/ absolute minima), first derivative test, second derivative test, simple problems (that illustrate basic principles and understanding of the subject as well as real life situations)
Integration as an inverse process of differentiation, Integration of a variety of functions by substitution, Integration by parts, Some special integrals, Integration by partial fraction
Fundamental theorem of calculus (without proof), Definite integral by substitution, Basic properties of definite integrals and evaluation of definite integrals, Definite integrals as a limit of sum
Application of the integrals
Finding the areas of circles/ parabolas/ ellipses (in standard form only), Area bounded by a curve and a line, Area bounded between two curves
Definition, order and degree, General and particular solutions of a differential Equation, Formation of Differential equation, Homogenous differential equation of first order and first degree, Linear equation of first order, Applications of differential equation
Vectors and Scalars, Magnitude and direction of a vector, Position vector of a point, Components of a vector, Addition of vectors, Properties of addition of vectors, Multiplication of a vector by a scalar, Position vector of a point dividing a line segment in a given ratio, Direction cosines and direction ratios of vector, Scalar (dot product) of Vectors, Projection of a vector on a number line, Vector Product, Scalar triple product
Brief recall of direction cosines and direction ratios of a line, Cartesian and vector equation of a straight line, Angle between two lines, Shortest distance between two lines, Distance between Parallel lines, Equation of a plane in normal form, Equation of a plane passing through a given point, Equation of plane in intercept Form, Equation of plane in General form, Equation of Plane through the intersection of two planes, Angle between two planes, Distance of a point from a plane, Image of a point in plane, Coplanar lines
Conditional Probability, Multiplication theorem on Probability, Independent Events, Total Probability, theorem, Random variable and its probability Distribution, Mean and variance of random variable, Repeated independent (Bernoulli) trials and Binomial Distribution
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By following the syllabus of Uni-GUAGE, candidates will be able to prepare better and perform well in the entrance exam.