# GCET 2021 Syllabus for Chemistry, Physics, and Mathematics

GCET exam is conducted in three subjects viz. Physics, Chemistry, and Mathematics. Candidates who are interested in B.Pahrm. courses are not required to appear for the Mathematics paper. Each section comprises of 75 multiple choice questions from the syllabus prescribed by the Directorate of Technical Education, Goa. The syllabus is as per the topics of the class XII syllabus of the Goa Board of Secondary & Higher Secondary Education. Let’s check out the detailed GCET 2021 syllabus for all three sections.

## GCET Syllabus 2021 -

#### PHYSICS SYLLABUS

**UNIT I: ELECTROSTATICS**

Electric charges and their conservation. Coulomb’s law – superposition principle and continuous charge distribution, the force between two point charges, forces between multiple charges.

Electric field, electric field lines; electric field due to a point charge, electric dipole, electric field due to a dipole; torque on a dipole in a uniform electric field. Electric flux, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside), statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire.

Electric potential, electric potential due to a point charge, potential difference, 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 polarization, the combination of capacitors in series and in parallel, capacitors and capacitance, the capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor, Van de Graaff generator.

**UNIT II: CURRENT ELECTRICITY**

Electric current, the flow of electric charges in a metallic conductor, drift velocity and mobility, and their relation with electric current; electrical resistance, V-I characteristics (linear and non-linear), Ohm’s law, electrical energy and power, electrical resistivity and conductivity.

Carbon resistors, series and parallel combinations of resistors; colour code for carbon resistors; temperature dependence of resistance.

The internal resistance of a cell, potential difference, and emf of a cell, combination of cells in series and parallel. Kirchhoff ’s laws and simple applications. Wheatstone bridge, metre bridge.

Potentiometer – principle, and applications to measure potential difference, principles for comparing emf of two cells; measurement of internal resistance of a cell.

**UNIT III: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM**

Concept of the magnetic field, Oersted’s experiment. Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Biot - Savart law and its application to current carrying circular loop. Force on a moving charge in uniform magnetic and electric fields. Cyclotron.

Definition of ampere. Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current-carrying conductors. 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. The 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.

Bar magnet as an equivalent solenoid, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; magnetic field lines; Earth’s magnetic field and magnetic elements.

Para-, dia- and ferromagnetic substances, with examples.

Electromagnets and factors affecting their strengths. Permanent magnets.

**UNIT IV: ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS **

Electromagnetic induction; induced emf and current; Faraday’s law, Lenz’s Law, Eddy currents. Self and mutual inductance. 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, wattles current. AC generator and transformer.

**UNIT V: ELECTROMAGNETIC WAVES**

The idea of displacement current. Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic spectrum (microwaves, radio waves, visible, infrared, ultraviolet, x-rays, gamma rays) including elementary facts about their uses.

**UNIT VI: OPTICS**

Reflection of light, mirror formula, spherical mirrors. Refraction of light, total internal reflection, and its applications, optical fibres, thin lens formula, refraction at spherical surfaces, lenses, 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.

Scattering of light – the blue colour of the sky and reddish appearance of the sun at sunrise and sunset.

Optical instruments: Human eye, image formation, and accommodation, correction of eye defects (hypermetropia and myopia) using lenses.

Microscopes and astronomical telescopes (refracting and reflecting) and their magnifying powers.

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

Proof of laws of reflection and refraction using Huygens’ principle.

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

Diffraction due to a single slit, width of central maximum.

Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light; uses of plane polarised light and Polaroids, Brewster’s law.

**UNIT VII: DUAL NATURE OF MATTER AND RADIATION**

Photoelectric effect, Einstein’s photoelectric equation – particle nature of light, Hertz and Lenard’s observations.

Matter waves – wave nature of particles, de Broglie relation. Davisson-Germer experiment (only conclusion should be explained.)

**UNIT VIII: ATOMS AND NUCLEI**

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

Mass- mass defect; energy relation, the binding energy per nucleon and its variation with mass number; nuclear fission and fusion.

Composition and size of nucleus, atomic masses, isobars; isotopes, isotones. Radioactivity – alpha, beta and gamma particles/rays, their properties; radioactive decay law.

**UNIT IX: 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; I-V characteristics of LED, photodiode, solar cell, and Zener diode as a voltage regulator. Junction transistor, characteristics of a transistor; transistor action, transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (AND, OR, NOT, NAND and NOR). Transistor as a switch.

**UNIT X: COMMUNICATION SYSTEMS**

Elements of a communication system (block diagram only); bandwidth of transmission medium, the bandwidth of signals (speech, TV and digital data). Propagation of electromagnetic waves in the atmosphere, sky, and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave.

#### CHEMISTRY SYLLABUS

**UNIT I: SOLID STATE**

Classification of solids based on different binding forces: molecular, amorphous and crystalline solids(elementary idea), ionic covalent and metallic solids, unit cell in two dimensional and three-dimensional lattices, calculation of density of unit cell, packing efficiency, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, electrical and magnetic properties, point defects, Band theory of metals, conductors, semiconductors (n and p-type semiconductors), and insulators.

**UNIT II: SOLUTIONS **

Types of solutions, solubility of gases in liquids, solid solutions, expression of concentration of solutions of solids in liquids, colligative properties – relative lowering of vapour pressure, Raoult’s law, depression of freezing point, elevation of B.P., osmotic pressure, determination of molecular masses using colligative properties, Vant Hoff factor, abnormal molecular mass.

**UNIT III: ELECTROCHEMISTRY**

Redox reactions; specific and molar conductivity variations of conductivity with concentration, conductance in electrolytic solutions, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea), lead accumulator, dry cell – electrolytic cells and Galvanic cells; EMF of a cell, Nernst equation and its application to chemical cells, standard electrode potential. The relation between Gibbs energy change and EMF of a cell, fuel cells; corrosion.

**UNIT IV: CHEMICAL KINETICS**

Rate of a reaction (average and instantaneous), factors affecting rates of reaction: temperature, concentration, catalyst; rate law and specific rate constant, order and molecularity of a reaction; concept of collision theory (elementary idea - no mathematical treatment), integrated rate equations and half-life (only zero and first-order reactions). Arrhenius equation, Activation energy.

**UNIT V: SURFACE CHEMISTRY**

Adsorption – chemisorption and physisorption; factors affecting adsorption of gases on solids; activity and selectivity: enzyme catalysis; catalysis: homogenous and heterogeneous, colloidal state: distinction between true solutions, colloids and suspensions; lyophobic multimolecular and macromolecular colloids; lyophilic, properties of colloids; Brownian movement, Tyndall effect, electrophoresis, coagulation; emulsions – types of emulsions.

**UNIT VI: GENERAL PRINCIPLES AND PROCESSES OF ISOLATION OF ELEMENTS **

Principles and methods of extraction – oxidation, concentration, refining, reduction electrolytic method, occurrence and principles of extraction of copper, aluminium, zinc, and iron.

**UNIT VII: P-BLOCK ELEMENTS**

Group 15 elements: General introduction, occurrence, electronic configuration, oxidation states, nitrogen – preparation, properties and uses; trends in physical and chemical properties; compounds of nitrogen: preparation and properties of ammonia and nitric acid, Phosphorous-allotropic forms; compounds of phosphorous: preparation and properties of phosphine, oxoacids (elementary idea only), halides (PCl3, PCl5), oxides of nitrogen ( structure only).

Group 16 elements: General introduction, oxidation states, electronic configuration, occurrence, dioxygen: preparation, properties and uses; trends in physical and chemical properties; classification of oxides; ozone.

Sulphur – compounds of sulphur: preparation, properties and uses of sulphur dioxide; allotropic forms; sulphuric acid: properties, and uses, the industrial process of manufacture, oxoacids of sulphur (structures only).

Group 17 elements: General introduction, oxidation states, electronic configuration, occurrence, compounds of halogens: preparation, properties and uses of chlorine and hydrochloric acid, trends in physical and chemical properties; interhalogen compounds, oxoacids of halogens (structures only).

Group 18 elements: General introduction, occurrence, electronic configuration, trends in physical and chemical properties, uses.

**UNIT VIII: d AND f BLOCK ELEMENTS**

General introduction, occurrence and characteristics of transition metals, electronic configuration, general trends in properties of the first-row transition metals – ionization enthalpy, oxidation states, metallic character, ionic radii, catalytic property, colour, magnetic properties, alloy formation, interstitial compounds. Preparation and properties of K2 Cr2 O7 and KMnO4 Lanthanoids – oxidation states, electronic configuration, chemical reactivity, and lanthanoid contraction and its consequences.

Actinoids – oxidation states and comparison with lanthanoids, electronic configuration.

**UNIT IX: COORDINATION COMPOUNDS**

Coordination compounds: Introduction, coordination number, ligands, colour, bonding, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds, Werner’s theory VBT, CFT; isomerism (structural and stereo)importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems).

**UNIT X: HALOALKANES AND HALOARENES**

Haloalkanes: Nomenclature, physical and chemical properties, nature of C-X bond, 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 – trichloromethane, dichloromethane, tetrachloromethane, freons, iodoform, DDT.

**UNIT XI: ALCOHOLS, PHENOLS AND ETHERS**

Alcohols: methods of preparation, Nomenclature, physical and chemical properties (primary alcohols only); identification of primary, secondary and tertiary alcohols; uses with special reference to methanol and ethanol, mechanism of dehydration. Phenols: Nomenclature, physical and chemical properties, methods of preparation, electrophilic substitution reactions, acidic nature of phenol, uses of phenols. Ethers: methods of preparation, Nomenclature, physical and chemical properties, uses.

**UNIT XII: ALDEHYDES, KETONES AND CARBOXYLIC ACIDS**

Aldehydes and Ketones: methods of preparation, nomenclature, physical and chemical properties, nature of carbonyl group, and mechanism of nucleophilic addition, the reactivity of alpha hydrogen in aldehydes; uses. Carboxylic Acids: Nomenclature, methods of preparation, acidic nature, physical and chemical properties; uses.

**UNIT XIII: ORGANIC COMPOUNDS CONTAINING NITROGEN **

Amines: Classification, Nomenclature, structure, physical and chemical properties, methods of preparation, uses, identification of primary secondary and tertiary amines. Cyanides and Isocyanides. Diazonium salts: chemical reactions, preparation, and importance in synthetic organic chemistry.

**UNIT XIV: BIOMOLECULES**

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

Proteins - Elementary idea of α - amino acids, polypeptides, peptide bond, proteins, primary structure, secondary structure, tertiary structure and quaternary structure (qualitative idea only), enzymes, denaturation of proteins. Hormones – Elementary idea (excluding structure). Vitamins – Classification and functions. Nucleic Acids: DNA and RNA

**UNIT XV: POLYMERS**

Classification – Natural and synthetic, copolymerization, methods of polymerization (addition and condensation). Some important polymers: natural and synthetic like polythene, polyesters, bakelite, nylon, rubber. Biodegradable and non-biodegradable polymers.

**UNIT XVI: CHEMISTRY IN EVERYDAY LIFE**

- Chemicals in medicines – analgesics, antiseptics, tranquillizers, disinfectants, antimicrobials, antibiotics, antifertility drugs, antacids, antihistamines.
- Chemicals in food – preservatives, elementary idea of antioxidants, artificial sweetening agents.
- Cleansing agents – cleansing action, soaps and detergents.

#### MATHEMATICS SYLLABUS

**UNIT I: RELATIONS AND FUNCTIONS**

- Relations and Functions Types of relations: Reflexive, transitive, symmetric, and equivalence relations. Composite functions, one to one and onto functions, the inverse of a function. Binary operations.
- Inverse Trigonometric Functions Definition, domain, range, principal value branches. Elementary properties of inverse trigonometric functions. Graphs of inverse trigonometric functions.

**UNIT II: ALGEBRA**

- Matrices Concept, order, notation, equality, transpose of a matrix, types of matrices, zero matrices, symmetric and skew-symmetric matrices. Simple properties of addition, multiplication and scalar multiplication, Addition, multiplication and scalar multiplication of matrices. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse. Concept of elementary row and column operations.
- Determinants Determinant of a square matrix (up to 3 × 3 matrices), minors, properties of determinants, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency, and the number of solutions of the system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

**UNIT III: CALCULUS**

- Continuity and Differentiability Continuity and differentiability, the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions. Derivatives of x e log and x e. Logarithmic differentiation. The derivative of functions expressed in parametric forms. Second-order derivatives. Lagrange’s and Rolle’s Mean Value Theorems (without proof) and their geometric interpretations
- Applications of Derivatives Applications of derivatives: Rate of change, increasing/decreasing functions, tangents, and normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (on basic principles, understanding of the subject, and real-life situations).
- Integrals Integration as an inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integral. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Evaluation of definite integrals, basic properties of definite integrals.
- Applications of the Integrals Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).
- Differential Equations- Definition, degree, and order, general and particular solutions of a differential equation. Formation of a differential equation from the general solution. The solution of differential equations by the method of separation of variables, homogeneous differential equations of the first order and first degree. Solutions of a linear differential equation.

**UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY**

- Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal, unit, zero, parallel and coplanar vectors), negative of a vector, position vector of a point, position vector of a point dividing a line segment in a given ratio, components of a vector, the addition of vectors, multiplication of a vector by a scalar. Scalar (dot) product of vectors, Vector (cross) product of vectors, projection of a vector on a line, scalar triple product.
- Three-dimensional Geometry- Direction cosines/ratios of a line joining two points. coplanar and skew lines, Cartesian and vector equation of a line, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two planes, (ii) two lines, (iii) a line and a plane. The distance of a point from a plane.

**UNIT V: LINEAR PROGRAMMING **

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, the mathematical formulation of L.P. problems, feasible and infeasible regions, graphical method of solution for problems in two variables, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

**UNIT VI: PROBABILITY**

Multiplication theorem on probability. Conditional probability, total probability, independent events, Baye’s theorem. Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Keep a check on the official 2020 notification for changes in the GCET 2020 syllabus, if any.

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