JKCET 2027 Exam: Date, Application Form, Eligibility, Syllabus, Counselling

Chemistry: Unit 01

• Laws of chemical combination, mole concept (numericals), percentage composition, chemical reactions, stoichiometry and calculations based on stoichiometry
• Atomic structure: Bohr's model of hydrogen atom, quantum numbers, Pauli's exclusion principle, Hund's rule and Aufbau principle
• Heisenberg's uncertainty principle, De-Broglie wave equation, and its significance, electronic configurations of atoms

Chemistry: Unit 02

• Law of mass action, Le-Chatelier's principle, and its application to physical and chemical equilibria
• Ionisation of weak electrolytes (Ostwald's dilution law), equilibrium constant, acids and bases: Acid base equilibria
• Bronsted-Lowry and Lewis concept, of acids and bases
• Ionic product of water
• pH and pOH scales, pKa and pKb values, solubility product, buffer solutions common ion effect, hydrolysis of salts

Chemistry: Unit 03

• Rate of chemical reaction, average and instantaneous rate, factors effecting rate of reaction, order and molecularity of reaction, integrated rate equation and half-life period (for zero and first order) reaction, activation energy and Arrhenius equation

Chemistry: Unit 04

• Vapour pressure, Raoult's law, ideal and non-ideal solutions, colligative properties
• Determination of molecular mass of non-volatile solutes through colligative properties
• Abnormal molecular masses and Van't Hoff factor, expression of concentration of solutions

Chemistry: Unit 05

• Energy changes taking place during chemical reactions, internal energy and enthalpy changes, enthalpy of combustion, solution and neutralization, and formation, and hydration
• Hess's law (numerical problems) laws of thermodynamics-first, second, and third, concepts of entropy and free energy, spontaneity of a chemical reaction

Chemistry: Unit 06

• Dependence of electrode and cell potential on concentration (Nernst equation), electrode potential as a criteria for product formation in electrolysis
• EMF of galvanic cell, relationship between free energy change and EMF of a cell
• Definition and units of equivalent, molar, and specific conductivity

Chemistry: Unit 07

• Boyle's Law, Charles's law, Dalton's law of partial pressure, Graham's law of diffusion of gases, Avogadro law
• Causes of deviation from ideal behaviour, ideal gas equation, and nature of 'R', Van der Waal's equation, surface tension and viscosity of liquids
• Crystalline and amorphous solids, crystal lattice, crystal types, packing efficiency, calculation of density of unit cell, number of atoms per unit cell in a cubic cell
• Coordination number, stoichiometric defects: Schottky, Frenkel, and interstitial
• Properties of solids: Electrical, magnetic, and dielectric

Chemistry: Unit 08

• Freundlich adsorption isotherm, preparation of colloidal solutions by physical and chemical method
• Electrical properties (cataphoresis, electroosmosis, coagulation, and protective colloids), homogeneous and heterogeneous catalysis

Chemistry: Unit 09

• Classification of elements as s, p, d, and f block elements
• Variation of Ionization energy, electron affinity, electronegativity, atomic and ionic radii along the period and down the group in the periodic table

Chemistry: Unit 10

• VSEPR: Shapes of simple molecules ( H₂O, NH₃, SO₂, CO₂, PCl₃, PCl₅, CIF₃, BF₃, SF₄, XeF₂, XeF₄)
• Molecular orbital theory: Energy levels and MO diagrams of H₂, H₂+,He₂, O₂+,O¹¯₂,O₂²¯and F₂
• Bond order and its significance

Chemistry: Unit 11

• S and P block elements: Electron configuration, oxidation states and trends in various properties like ionization energy, electron affinity, atomic radii, electronegativity and diagonal relationship
• Alkali metals: Hydration of ions, action with ammonia, flame colouration, solubility of hydroxides, carbonates and sulphates
• Alkaline earth metals: Solubility of carbonates, hydroxides, and sulphates
• Boron family: Structure of halides, relative, acid strength of trihalides of boron
• Carbon family: Hydrides and oxides
• Nitrogen family: Oxides of nitrogen and phosphorous, reducing nature, basic strength, and boiling points of their halides
• Oxygen family: Volatility, thermal stability, acid character, reducing character, and bond angles of their hydrides, oxyacids of sulphur
• Halogen family: Bond energy, colour, and oxidizing power, boiling point, acid strength and dipole moment, thermal stability, reducing power of hydracids, relative acidity and oxidizing power of oxyacids of halogens

Chemistry: Unit 12

• Electron configuration, oxidation states, colour, and magnetic properties of transition elements
• Oxides of vanadium, chromium, and manganese alloys of copper, silver, and iron
• Metallurgy of iron, copper, and zinc

Chemistry: Unit 13

• Introduction, ligands, coordination number, IUPAC nomenclature
• Bonding theories: Werner's, VBT, and CFT
• Isomerism in coordination compounds (ionization, linkage, hydrate, geometrical, and optical)
• Applications of coordination complexes in biology, medicine, and analytical chemistry

Chemistry: Unit 14

• Nomenclature of organic compounds (monofunctional and polyfunctional groups), inductive, eletromeric resonance and hyper conjugation effects, reaction intermediates, carbocations, carbanions and free radicals with their general stability order
• Types of organic reactions (addition, substitution, elimination, and redox reactions), aromaticity on the basis of Huckel rule
• Ortho, meta, and para directing groups., electro and nucleophiles

Chemistry: Unit 15

• Structural isomerism in alkanes, alkenes, alkynes, and arenes, stereoisomerism: Geometrical and optical isomerism, chirality, origin of chirality, specific rotation, racemisation and resolution, conformations in ethane and cyclohexane
• Relative configuration (D, L-nomenclature), absolute (R and S system of nomenclature)

Chemistry: Unit 16

• Haloalkanes, haloarenes, alcohols, and phenols: General methods of preparation and properties
• Chloroform and iodoform

Chemistry: Unit 17

• Ethers, aldehydes, ketones, monocarboxylic acids: General methods of preparation and properties
• Derivatives of monocarboxylic acids like acid halides, acid anhydrides acid amides, and esters
• Acidic motive of carboxylic acids

Chemistry: Unit 18

• Cyanides, Isocyanides, nitro compounds, and amines: General methods of preparation and properties
• Relative basic character of amines

Chemistry: Unit 19

• Carbohydrates: Definition, classification, mutarotation, structure of amino-acids, peptides and proteins (Molisch's and ninhydrin tests)
• Classification and uses of vitamins
• Chemicals in medicine and health care, dyes, and drugs
• Chemical reactions in atmosphere, ozone depletion, and its effects
• Acid rain, green house effect, and global warming

Chemistry: Unit 20

• Introduction, classification, methods of polymerisation (addition, condensation, free radical, cationic, and anionic)
• Natural and synthetic polymers: Polythene, nylon, polyester, Bakelite, and rubber
• Biodegradable and non-Biodegradable polymers

Mathematics: Unit 01

• Sets: Sets and their representation, finite and infinite sets, empty set subsets, subset of real numbers especially intervals, power set, universal set. Venn diagram, union and intersection of sets. Difference of sets, compliment of a set. Ordered pairs
• Sets: Cartesian product of sets, number of elements in the Cartesian product of two finite sets
• Relations: Domain, co domain, and range of relation, types of relations, reflexive, symmetric, transitive, and equivalence relations
• Functions: Functions as special kind of relations from one set to another, domain, co domain, and range of a function. One to one, onto functions. Real valued functions of the real variable; constant, identity, polynomial, rational, modulus
• Functions: Signum and the greatest integer functions with their graphs. Sum, difference, product, and quotients of functions. Composition of functions, inverse of a function, binary operations

Mathematics: Unit 02

• Complex number: Conjugate of a complex number, modulus and amplitude (argument) of a complex number, Argand's plane and polar representation of complex numbers, algebraic properties of complex numbers. Fundamental theorem of algebra
• Complex number: Solution of quadratic equation in the complex number system. Square root of a complex number
• Linear inequation: Algebraic solution of linear inequalities in one variable and two variables
• Linear programming: Introduction, definition of related terminology such as constraints, objective function, optimization, different type of linear programming problem (LP), mathematical formulation of LP problem
• Linear programming: Graphical method of solution for problems in two variables, feasible, and infeasible regions, feasible and infeasible solutions, optimal feasible solutions

Mathematics: Unit 03

• Sequence and series: Arithmetic progression (AP), arithmetic mean (AM), nth term, sum to n-terms of an AP, geometric progression (GP), geometric mean (GM), nth term
• Sequence and series: Sum to n-terms and sum to infinity of a GP relation between AM, and GM sum to n terms of Σn, Σn², and Σn³
• Permutation and combination: Fundamental principle of counting, factorial n, permutations P (n, r) and combinations C (n, r), simple applications
• Binomial Theorem: Binomial theorem for positive integral power general and middle terms in the binomial expansion. Pascal’s triangle and simple applications

Mathematics: Unit 04

• Positive and negative angles, measuring angles in radians and in degrees, conversion from one measure to another
• Definition of trigonometric functions with the help of unit circle
• Periodicity of trigonometric functions
• Basic trigonometric identities sin²x+cos²x=1 for all sign of x etc
• Trigonometric functions and their graphs
• Expressions for sin (x ± y),cos (x ± y), tan (x ± y),cot (x ± y), sum and product formulae
• Identities related to Sin2x, Cos2x, tan2x, Sin3x, Cos3x, and tan3x
• General and principal solutions of trigonometric equations of the type sin x= sin a, cos x= cos a , tan x= tan a
• Inverse trigonometric functions: Range, domain, principal value branches. Graphs of inverse trigonometric functions, elementary properties of inverse trigonometric functions

Mathematics: Unit 05

• Matrices: Concepts, notation, order, equality, types of matrices, zero matrix, transpose of matrix, symmetric, and skew symmetric matrices. Addition, multiplication, scalar multiplication of matrices
• Matrices: Simple properties of addition, multiplication, and scalar multiplication of matrices. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (order 2x2)
• Matrices: Concept of elementary row and column operation, invertible matrices and uniqueness of inverse, if it exists. (matrices with real entries)
• Determinants: Determinants of square matrix (up to 3x3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding area of a triangle. Adjoint and inverse of a square matrix
• Determinants: Consistency, inconsistency, and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables using inverse of a matrix, Cramer rule, and its applications

Mathematics: Unit 06

• Concept of limit of a function;Theorems on Limits; evaluation of limits using standard results
• Continuity: Continuity of a function at a point. Continuity of sum, product, and quotient of functions
• Derivative: Definition of a derivative of a function, geometrical interpretation of the derivative. Derivative of sum, difference, product and quotient of two or more functions. Derivative of algebraic and composite functions
• Derivative: Derivative of trigonometric and inverse trigonometric functions. Chain rule, derivative of implicit functions. Derivative of logarithmic and exponential functions. Logarithmic differentiation
• Derivative: Derivative of functions expressed in parametric forms
• Second order derivatives: Rolle's and Lagrange's mean value theorem and their geometrical interpretation and their simple applications
• Application of derivative: Rate of change, increasing and decreasing functions, tangents and normals, approximation, maxima and minima (first derivative and second derivative test). Simple problems

Mathematics: Unit 07

• Integration as inverse process of differentiation
• Integration of variety of functions by substitution, by parts, by partial fractions
• Simple integrals; definite integrals as a limit of a sum
• Fundamental theorem of calculus
• Basic properties of definite integrals evaluation of definite integrals
• Application of integrals: Application in finding the area under simple curves, especially lines. Areas of circles, parabolas and ellipses (in standard form), area under the curve y= sinx, y= cosx, area between the above two curves
• Differential Equations: Definition, order and degree of a differential equation. General and particular solutions of a differential equation. Formation of a differential equation whose general solution is given
• Differential Equations: Solution of differentiation equation by method of separation of variables. Solution of homogeneous differential equation of first order and first degree
• Differential Equations: Solution of linear differential equation of the type dy/dx+py = q, where p and q are functions of x alone and dx/dy+px = q, where p and q are functions of y alone

Mathematics: Unit 08

• Distance between two points, section, slope of a line, angle between two lines, various forms of equations of lines, point-slope form, intercept form, two point form, and normal form
• General equation of a line, distance of a point from a line
• Conic Section: Sections of a cone, circles, parabola, ellipse, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of conic section
• Standard equation of a circle, parabola, ellipse and hyperbola, and their simple properties

Mathematics: Unit 09

• Statistics: Measure of dispersion, mean, deviation, variance, and standard deviation of ungrouped/ grouped data. Analysis of frequency distribution with equal means but different variances
• Probability: Random experiment-outcome, sample spaces. Events: Mutually exclusive and exhaustive events. Axiomatic (set theoretic) probability, probability of an event, probability of 'not' and 'or' events. Multiplication theorem on probability
• Probability: Conditional probability, independent events, total probability, Baye's theorem, random variable and its probability, distribution, mean, and variance of a random variable. Repeated independent (Bernouli) trials and binomial distribution

Mathematics: Unit 10

• Vectors and scalars, magnitude, and direction of a vector direction cosines and ratios of a vector
• Types of vector, equal, zero, unit, parallel and collinear vectors
• Position vector of a point, negative of a vector, components of a vector, addition of vectors, scalar multiplication, position vector of a point dividing a line segment in a given ratio
• Scalar (dot) product of vectors, projection of a vector on a line
• Vector (cross) product of vectors, scalar triple product
• Coordinate axes and coordinate planes in three dimensions of a point, distance between two points and sectional formula
• Straight lines and space: Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a line (in various forms), coplanar and skew-lines, shortest distance between two lines
• Planes: Cartesian and vector equation of a plane (in various forms). Distance of a point from a plane. Angle between: i) Two lines, (ii) two planes, (iii) a line and a plane