**CUSAT CAT Syllabus 2020** – Cochin University of Science and Technology is responsible for releasing the syllabus of CUSAT CAT 2020. The syllabus will be based on selected topics of science and mathematics. The CUSAT CAT 2020 syllabus is divided into three sections: Physics, Chemistry and Mathematics. These three sections are further divided into sub-topics. To land a seat in the desired B.Tech program, a candidate needs to know the exact syllabus for better preparation and better performance. Read the complete article to know the detailed syllabus of CUSAT CAT 2020. Also, read about the exam pattern which candidates should follow to practise the best of his/her capabilities.

## CUSAT CAT 2020 Syllabus

CUSAT CAT 2020 will be held on April 18 and 19. The syllabus of Common Admission Test (CAT) conducted by Cochin University of Science and Technology is divided into 3 sections: Physics, Chemistry, and Mathematics. To know the detailed syllabus of CAT CUSAT 2020 read the table below.

CUSAT CAT Syllabus For Maths

Units |
Chapters & Concepts |

Relations and Functions | Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, the inverse of a function. Binary operations.
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. |

Algebra | Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, the transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).The concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries). The determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, 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. |

Calculus | Continuity and Differentiability
Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. The concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation. Applications of derivatives: the rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations). Integration as the inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable). Definition, order, and degree, general and particular solutions of a differential equation. Formation of the differential equation whose general solution is given. A solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of the linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants. dx/dy + px = q, where p and q are functions of y or constants. |

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

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### CUSAT CAT Syllabus For Physics

Unit |
Chapters & Concepts |

Electrostatics | Chapter-1: Electric Charges and Fields
Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field. Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).
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, the combination of capacitors in series and in parallel, the capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. |

Current Electricity | Chapter-3: Current Electricity
Electric current, the flow of electric charges in a metallic conductor, drift velocity, mobility and them relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, the color code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. The internal resistance of a cell, potential difference, and emf of a cell, a combination of cells in series and in parallel. Kirchhoff’s laws and simple applications. Wheatstone bridge, meter 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 | Chapter-4: Moving Charges and Magnetism
The 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 the infinitely long straight wire. Straight and toroidal solenoids, Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current-carrying conductors-definition of the ampere. Torque experienced by a current loop in the uniform 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. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic fieldand magnetic elements. Para-, dia- and ferromagnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets. |

Electromagnetic Induction and Alternating Currents | Chapter-6: Electromagnetic Induction
Electromagnetic induction; Faraday’s laws, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual induction.
Alternating currents, peak and the 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 | Chapter-8: Electromagnetic Waves
The basic idea of displacement current, Electromagnetic waves, their characteristics, them transverse nature (qualitative ideas only). Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses. |

Optics | Chapter-9: Ray Optics and Optical Instruments
Ray Optics: Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection, and its applications, optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s formula. Magnification, the power of a lens, the combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of the light – blue color of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics: Wavefront 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. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light Brewster’s law, uses of plane polarised light and Polaroids. |

Dual Nature of Matter and Radiation | Chapter-11: Dual Nature of Radiation and Matter
Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; the only conclusion should be explained). |

Atoms & Nuclei | Chapter-12: Atoms
Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum.
Composition and size of the nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity-alpha, beta and gamma particles/rays, and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion. |

Electronic Devices | Chapter-14: Semiconductor Electronics: Materials, Devices, and Simple Circuits
Energy bands in conductors, semiconductors, and insulators (qualitative ideas only) Semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; Special purpose p-n junction diodes: LED, photodiode, solar cell, and Zener diode and their characteristics, zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor and transistor as an amplifier (common emitter configuration), the basic idea of analog and digital signals, Logic gates (OR, AND, NOT, NAND and NOR). |

Communication Systems | Chapter-15: Communication Systems
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, satellite communication. Need for modulation, amplitude modulation. |

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### CUSAT CAT Syllabus For Chemistry

Units |
Chapters & Concepts |

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. |

Solutions | Types of solutions, expression of concentration of solutions of solids in liquids, the solubility of gases in liquids, solid solutions, colligative properties – relative lowering of vapor pressure, Raoult’s law, elevation of boiling point, depression of freezing point, osmotic pressure,determination of molecular masses using colligative properties, abnormal molecular mass, can’t Hoff factor. |

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

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

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

General Principles and Processes of Isolation of Elements | Principles and methods of extraction – concentration, oxidation, reduction – electrolytic method and refining; occurrence and principles of extraction of aluminum, copper, zinc, and iron. |

p – Block Elements | Group 15 Elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen preparation properties & uses; compounds of nitrogen, preparation, and properties of ammonia and nitric acid, oxides of nitrogen (Structure only) ; Phosphorus – allotropic forms, compounds of phosphorus: preparation and properties of phosphine, halides PCl3 , PCl5 and oxoacids (elementary idea only).
Group 16 Elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties, dioxygen: Preparation, Properties and uses, classification of oxides, Ozone, Sulfur -allotropic forms; compounds of sulfur: Preparation properties and uses of sulfur-dioxide, sulphuric acid: industrial process of manufacture, properties and uses; oxoacids of sulphur (Structures only). Group 17 Elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens, Preparation properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens (structures only). Group 18 Elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses. |

d and f-Block Elements | General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first-row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, color, catalytic property, magnetic properties, interstitial compounds, alloy formation, preparation and properties of K2Cr2O7 and KMnO4.
Lanthanoids – Electronic configuration, oxidation states, chemical reactivity, and lanthanoid contraction and its consequences. Actinoids – Electronic configuration, oxidation states, and comparison with lanthanoids. |

Coordination Compounds | Coordination compounds – Introduction, ligands, coordination number, color, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds.
Bonding, Werner’s theory, VBT, and CFT; structure and stereoisomerism, the importance of coordination compounds (in qualitative inclusion, extraction of metals and biological system). |

Haloalkanes and Haloarenes | Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions, optical rotation.
Haloarenes: Nature of C -X bond, substitution reactions (Directive influence of halogen in monosubstituted compounds only. Uses and environmental effects of – dichloromethane, trichloromethane, tetrachloromethane, iodoform freons, DDT. |

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

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

Organic Compounds Containing Nitrogen | Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines.
Cyanides and Isocyanides – will be mentioned at relevant places in context. Diazonium salts: Preparation, chemical reactions, and importance in synthetic organic chemistry. |

Biomolecules | Carbohydrates – Classification (aldoses and ketoses), monosaccahrides (glucose and fructose), D-L configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen) importance.
Proteins – Elementary idea of α – amino acids, peptide bond, polypeptides, proteins, the structure of proteins – primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Hormones – Elementary idea excluding structure. Vitamins – Classification and functions. Nucleic Acids: DNA and RNA. |

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

Chemistry in Everyday life | Chemicals in medicines – analgesics, tranquilizers antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines.
Chemicals in food – preservations, artificial sweetening agents, elementary idea of antioxidants. Cleansing agents – soaps and detergents, cleansing action. |

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### Exam Pattern for CUSAT CAT 2020

Aspirants can check the paper pattern of CUSAT CAT 2020 before applying for the exam. The test pattern covers the number of questions, types of questions and the total marks of the test. Read the table below to know more about the CUSAT CAT exam pattern.

Particulars |
Details |

Mode of Examination | Online |

Duration | 3 Hours |

Sections | 3 sections
Paper I – Mathematics Paper II – Physics & Chemistry |

Number of Questions | Paper I (Mathematics) – 125 questions,Paper II (Physics & Chemistry) – 75 questions & 50 questions, respectively |

Total Questions | 250 |

Maximum Marks | Paper I: 375 marks,Paper II: Physics- 225 marks, Chemistry- 150 marks |

Marking Scheme | 3 marks for every correct answer |

Negative Marking | 1 mark |

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