# JUST 2020 Syllabus

Exam Date : April 8, 2020 To April 15, 2020
Result Date : April 22, 2020

Syllabus for JUST Exam

• The Jain University Scholarship Test papers include questions based on the 10+2 syllabus in Physics, Chemistry, Mathematics and General English followed by major 10+2 Boards/Universities.

## Mathematics:

• Applications Of Matrices And Determinants: Adjoint, InverseProperties, Computation of inverses, the solution of a system of linear equations by matrix inversion method. Rank of a Matrix − Elementary transformation on a matrix, consistency of a system of linear equations, Cramer’s rule, Non-homogeneous equations, homogeneous linear system, rank method.

• Vector Algebra: Scalar Product – Angle between two vectors, properties of a scalar product, applications of dot products. Vector Product − Right handed and left handed systems, properties of vector product, applications of the cross product. The product of three vectors − Scalar triple product, properties of a scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors. Lines − Equation of a straight line passing through a given point and parallel to a given vector, passing through two given points (derivations are not required). The Angle between two lines. Skew lines − Shortest distance between two lines, condition for two lines to intersect, a point of intersection, collinearity of three points. Planes − Equation of a plane (derivations are not required), passing through a given point and perpendicular to a vector, given the distance from the origin and unit normal, passing through a given point and parallel to two given vectors, passing through two given points and parallel to a given vector, passing

through three given non-collinear points, passing through the line of intersection of two given planes, the distance between a point and a plane, the plane which contains two given lines, angle between two given planes, angle between a line and a plane. Sphere − Equation of the sphere (derivations are not required)whose center and radius are given, an equation of a sphere when the extremities of the given.

• Complex Numbers: Complex number system, Conjugate − properties, ordered pair representation. Modulus − properties, geometrical representation, meaning, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre’s theorem and its applications. Roots of a complex number − nth roots, cube roots, fourth roots.

• Analytical Geometry: Definition of a Conic − General equation of a conic, classification with respect to the general equation of a conic, classification

of conics with respect to eccentricity. Parabola − Standard equation of a parabola (derivation and tracing the parabola are not required), other standard parabolas, the process of shifting the origin, the general form of the standard equation, some practical problems. Ellipse − Standard equation of the ellipse (derivation and tracing the ellipse are not required), x2/a2 + y2/b2 = 1, (a > b), Other standard form of the ellipse, general forms, some practical problems, Hyperbola −standard equation (derivation and tracing the hyperbola are not required), x2/a2 −y2/b2=1, Other form of the hyperbola, parametric form of conics, chords. Tangents and Normals − Cartesian form and Parametric form, an equation of chord of contact of tangents from a point (x1, y1), Asymptotes, Rectangular

hyperbola – standard equation of a rectangular hyperbola.

• Differential Calculus– Applications 1: Derivative as a rate measure − rate of change − velocity − acceleration − related rates − Derivative as a measure of slope − tangent, normal and an angle between curves. Maxima and Minima. Mean value theorem − Rolle’s Theorem − Lagrange Mean Value Theorem − Taylor’s and Maclaurin’s series, l’ Hôpital’s Rule, stationary points − increasing, decreasing, maxima, minima, concavity convexity, points of inflection.

• Differential Calculus– Applications 2: Errors and approximations − absolute, relative, percentage errors, curve tracing, partial derivatives − Euler’s theorem.

• Integral Calculus And Its Applications: Properties of definite integrals, reduction formulae for sin x and cos n x (only results), Area, length,

• Differential Equations: Formation of differential equations, order, and degree, solving differential equations (1st order) − variable separable homogeneous, linear equations. Second order linear equations with constant coefficients f(x) = e me, sin mx, cos mx, x, x 2.

• Discrete Mathematics: Mathematical Logic − Logical statements, connectives, truth tables, Tautologies.

• Groups: Binary Operations − Semi groups − monoids, groups (Problems and simple properties only), an order of a group, order of an element.

• Probability Distributions: Random Variable, Probability density function, distribution function, mathematical expectation, variance, Discrete Distributions − Binomial, Poisson, Continuous Distribution − Normal distribution

## Chemistry:

• Atomic Structure 2: Dual properties of electrons - de-Broglie relation - Heisenberg’s uncertainty principle - Wave nature of an electron - Schrodinger wave equation (only equation, no derivation) - Eigen values and Eigen function- significance only - molecular orbital method. Application to Homo diatomic and Hetero diatomic molecules - Metallic Bond - Hybridization of atomic orbitals Hybridization involving s, p, and d Orbitals - Types of forces between molecules.

• Periodic classification 2: Review of periodic properties - Calculation of atomic radii - Calculation of ionic radii - Method of determination of Ionisation potential - Factors affecting ionization potential - Method to determine the electron affinity - Factors affecting EA - Various scales on electronegativity values.

• p - Block Elements: Group -13 General trends - Potash alum- Preparation, Properties and uses - Group 14 General trends - Silicates - Types and structure - Silicones - Structure and uses - Extraction of lead - Group - 15. General trends - Phosphorous- Allotropes and extraction - Compounds of phosphorous - Group - 16. General trends - H2 SO4 - Manufacture and properties. - Group - 17 General characteristics. Physical and Chemical properties - Isolation of fluorine and its properties - Interhalogen compounds Group-18 Inert gases - Isolation, properties and uses.

• d - Block Elements: General characteristics of d-block elements - First transition series - Occurrence and principles of extraction - chromium, copper and zinc - Alloys -Second transition series - Occurrence and principles of extraction of silver -Third transition series - Compounds - K2 Cr2 O7 , CuSO4 5H2 O, AgNO3 , Hg2 Cl2 , ZnCO3 , Purple of Cassius. Unit 5 - f-block elements General characteristics of f - block elements and extraction - Comparison of Lanthanides and Actinides - Uses of lanthanides and actinides.

• Coordination Compounds and Bio-coordination Compounds: An introduction - Terminology in coordination chemistry - IUPAC nomenclature of mononuclear coordination compounds - Isomerism in coordination compounds - Structural isomerism - Geometrical isomerism in 4 - coordinate, 6 – coordinate complexes - Theories on coordination compounds - Werner’s theory (brief) - Valence Bond theory - Crystal field theory - Uses of coordination compounds - Biocoordination compounds. Haemoglobin and chlorophyll.

• Nuclear chemistry: Nuclear energy nuclear fission and fusion - Radiocarbon dating - Nuclear reaction in sun - Uses of radioactive isotopes.

• Solid state 2: Types of packing in crystals - X-Ray crystal structure - Types of ionic crystals - Imperfections in solids - Properties of crystalline solids - Amorphous solid.

• Thermodynamics 2: Review of I law - Need for the II law of thermodynamics - Spontaneous and nonspontaneous processes - Entropy - Gibb’s free energy - Free energy change and chemical equilibrium - Third law of thermodynamics.

• Chemical equilibrium 2: Applications of a law of mass action - Le Chatlier’s principle.

• Chemical Kinetics 2: First order reaction and pseudo first order reaction - Experimental determination of the first-order reaction - method of determining an order of reaction -temperature dependence of rate constant - Simple and complex reactions.

• Surface Chemistry: Adsorption - Catalysis - Theory of catalysis - Colloids - Preparation of colloids - Properties of colloids - Emulsions.

• Electrochemistry 1: Conductors, insulators and semiconductors - Theory of electrical conductance - Theory of strong electrolytes - Faraday’s laws of electrolysis - Specific resistance, specific conductance, equivalent and molar conductance - Variation of conductance with dilution - Kohlraush’s law - Ionic product of water, pH and pOH - Buffer solutions - Use of pH values.

• Electrochemistry 2: Cells - Electrodes and electrode potentials - Construction of cell and EMF - Corrosion and its preventions - commercial production of chemicals -Fuel cells.

• Isomerism in Organic Chemistry: Geometrical isomerism - Conformations of cyclic compounds - Optical isomerism - Optical activity - Chirality - Compounds containing chiral centers - D-L and R-S notation - Isomerism in benzene.

• Hydroxy Derivatives: Nomenclature of alcohols - Classification of alcohols - General methods of preparation of primary alcohols - Properties Methods of a distinction between three classes of alcohols 1°, 2° and 3°) - Methods of preparation of dihydric alcohols. (glycol) - Properties - Uses - Methods of preparation of trihydric alcohols - Properties - Uses - Aromatic alcohols - Methods of preparation of benzyl alcohol - Properties - Uses - Phenols - Manufacture of phenols - Properties - Chemical properties - Uses of Phenols.

• Ethers: Ethers - General methods of preparation of aliphatic ethers - Properties - Uses - Aromatic ethers - Preparation of anisole - Reactions of anisole - Uses.

• Carbonyl Compounds: Nomenclature of carbonyl compounds - Comparison of aldehydes and ketones - General methods of preparation of aldehydes - Properties - Uses Aromatic aldehydes - Preparation of benzaldehyde - Properties - Uses - Ketones - general methods of preparation of aliphatic ketones (acetone) - Properties - Uses - Aromatic ketones - preparation of acetophenone- Properties - Uses - preparation of benzophenone - Properties.

• Carboxylic Acids: Nomenclature - Preparation of aliphatic monocarboxylic acids – formic acid - Properties - Uses - Tests for carboxylic acid - Monohydroxy mono carboxylic acids - Lactic acid – Sources - Synthesis of lactic acid - Aliphatic dicarboxylic acids - preparation of dicarboxylic acids – oxalic and succinic acids - Properties - Strengths of carboxylic acids - Aromatic acids - Preparation of benzoic acid - Properties - Uses - Preparation of salicylic acid - Properties - Uses - Derivatives of carboxylic acids - Preparation of acid chloride – acetyl chloride (CH3 COCl) - Preparation - Properties - Uses - Preparation of acetamide - Properties - Preparation of acetic anhydride - Properties - Preparation of esters methyl acetate - Properties.

• Organic Nitrogen Compounds: Aliphatic nitro compounds - Preparation of aliphatic nitroalkanes -Properties - Uses - Aromatic nitro compounds - Preparation - roperties - Uses - Distinction between aliphatic and aromatic nitro compounds - Amines -Aliphatic amines - General methods of preparation - Properties - Distinction between 1°, 2°, and 3° amines - Aromatic amines - Synthesis of benzylamine - Properties - Aniline–preparation - Properties - Uses - Distinction between aliphatic and aromatic amines - Aliphatic nitriles - Preparation - properties -Uses - Diazonium salts - Preparation of benzene diazoniumchloride - Properties.

• Biomolecules: Carbohydrates - structural elucidation - Disaccharides and polysaccharides - Proteins - Amino acids - a structure of proteins - Nucleic acids - Lipids.

• Chemistry in Action: Medicinal chemistry - Drug abuse - Dyes – classification and uses - Cosmetics – creams, perfumes, talcum powder and deodorants - chemicals in food - Preservatives artificial sweetening agents, antioxidants and edible colors - Insect repellant – pheromones and sex attractants - Rocket fuels - Types of polymers, preparation and uses.

## Physics:

• Electrostatics: Frictional electricity, charges, and their conservation; Coulomb’s law – forces between two point electric charges. Forces between multiple electric charges – superposition principle. Electric field – Electric field due to a point charge, electric field lines; Electric dipole, electric field intensity due to a dipole –behavior of dipole in a uniform electric field – application of electric dipole in a microwave oven. Electric potential – potential difference – electric potential due to a point charge and due to a dipole. Equipotential surfaces – Electrical potential energy of a system of two point charges. Electric flux – Gauss’s theorem and its applications to find field due to (1) infinitely long straight wire (2) uniformly charged infinite plane sheet (3) two parallel sheets and (4) uniformly charged thin spherical shell (inside and outside). Electrostatic induction – capacitor and capacitance – Dielectric and electric polarisation – parallel plate capacitor with and without dielectric medium – applications of capacitor – energy stored in a capacitor. Capacitors in series and in parallel – action of points – Lightning arrester – Van de Graaff generator.

• Current Electricity: Electric current – flow of charges in a metallic conductor – Drift velocity and mobility and their relation to electric current. Ohm’s law, electrical resistance. V-I characteristics – Electrical resistivity and conductivity. Classification of materials in terms of conductivity – Superconductivity (elementary ideas) – Carbon resistors – color code for carbon resistors – Combination of resistors – series and parallel – Temperature dependence of resistance – Internal resistance of a cell – Potential difference and emf of a cell. Kirchoff’s law – illustration by simple circuits – Wheatstone’s Bridge and its application for the temperature coefficient of resistance measurement – Metre bridge – Special case of Wheatstone bridge – Potentiometer – principle – comparing the emf of two cells. Electric power – Chemical effect of current – Electro chemical cells Primary (Voltaic, Lechlanche, Daniel) – Secondary – rechargeable cell – lead-acid accumulator.

• Effects Of Electric Current: Heating effect. Joule’s law – Experimental verification. Thermoelectric effects – Seebeck effect – Peltier effect – Thomson effect – Thermocouple, Thermo emf, neutral and inversion temperature. Thermopile. Magnetic effect of electric current – Concept of magnetic field, Oersted’s experiment – Biot-Savart law – Magnetic field due to an infinitely long current carrying straight wire and circular coil – Tangent galvanometer – Construction and working – Bar magnet as an equivalent solenoid – magnetic field lines. Ampere’s circuital law and its application. Force on a moving charge in a uniform magnetic field and electric field – cyclotron – Force on current carrying conductor in a uniform magnetic field, forces between two parallel current carrying conductors – definition of ampere. Torque experienced by a current loop in a uniform magnetic field-moving coil galvanometer – Conversion to ammeter and voltmeter – Current loop as a magnetic dipole and its magnetic dipole moment – Magnetic dipole moment of a revolving electron.

• Electromagnetic Induction And Alternating Current: Electromagnetic induction – Faraday’s law – induced emf and current – Lenz’s law. Self-induction – Mutual induction – Self-inductance of a long solenoid – mutual inductance of two long solenoids. Methods of inducing emf – (1) by changing magnetic induction (2) by changing area enclosed by the coil and (3) by changing the orientation of the coil (quantitative treatment) analytical treatment can also be included. AC generator – commercial generator. (Single phase, three phase). Eddy current – Applications – Transformer – Long distance transmission. Alternating current – measurement of AC – AC circuit resistance – AC circuit inductor – AC circuit with a capacitor - LCR series circuit – Resonance and Q – factor: power in AC circuits.

• Electronics Waves And Wave Optics: Electromagnetic waves and their characteristics – Electromagnetic spectrum, Radio, microwaves, Infrared, visible, ultraviolet – X-rays, gamma rays. Emission and Absorption spectrum – Line, Band, and continuous spectra – Fluorescence and phosphorescence. Theories of light – Corpuscular – Wave – Electromagnetic and Quantum theories. Scattering of light – Rayleigh’s scattering – Tyndal scattering – Raman effect – Raman spectrum – Blue color of the sky and reddish appearance of the sun at sunrise and sunset. Wavefront and Huygen’s principle – Reflection, Total internal reflection, and refraction of plane wave at a plane surface using wavefronts. Interference – Young’s double slit experiment and expression for fringe width – coherent source - interference of light. Formation of colors in thin films – analytical treatment – Newton’s rings. Diffraction – differences between interference and diffraction of light – diffraction grating. Polarisation of light waves – polarisation by reflection –Brewster’s law - double refraction - Nicol prism – uses of plane polarised light and polaroids – rotatory polarisation – polarimeter.

• Atomic Physics: Atomic structure – discovery of the electron – specific charge (Thomson’s method) and charge of the electron (Millikan’s oil drop method) – alpha scattering – Rutherford’s atom model. Bohr’s model – energy quantization – energy and wave number expression – Hydrogen spectrum – energy level diagrams – sodium and mercury spectra - excitation and ionization potentials. Sommerfeld’s atom model. X-rays – production, properties, detection, absorption, diffraction of X-rays – Laue’s experiment – Bragg’s law, Bragg’s X-ray spectrometer – X-ray spectra – continuous and characteristic X-ray spectrum – Mosley’s law and atomic number. Masers and Lasers – spontaneous and stimulated emission – normal population and population inversion – Ruby laser, He–Ne laser – properties and applications of laser light – holography

• Dual Nature Of Radiation And Matter Relativity: Photoelectric effect – Light waves and photons – Einstein’s photoelectric equation – laws of photoelectric emission – particle nature of energy – photoelectric equation – work function – photocells and their application. Matter waves-wave mechanical concept of the atom – wave nature of particles – De–Broglie relation – De–Broglie wave length of an electron-electron microscope. The concept of space, mass, time – Frame of references. Special theory of relativity – Relativity of length, time and mass with velocity – (E = mc 2).

• Nuclear Physics: Nuclear properties – nuclear Radii, masses, binding energy, density, charge – isotopes, isobars, and isotones – Nuclear mass defect – binding energy. Stability of nuclei-Bain bridge mass spectrometer. Nature of nuclear forces – Neutron – discovery – properties – artificial transmutation – particle accelerator Radioactivity-alpha, beta and gamma radiations and their properties, α-decay, β-decay, and γ-decay – Radioactive decay law – half-life – means life. Artificial radioactivity – radio isotopes – effects and uses Geiger – Muller counter. Radiocarbon dating – biological radiation hazards Nuclear fission – chain reaction – atom bomb – nuclear reactor – nuclear fusion – Hydrogen bomb – cosmic rays – elementary particles

• Semiconductor Devices And Their Applications: Semiconductor theory – energy band in solids – difference between metals, insulators, and semiconductors based on band theory – semiconductor doping – Intrinsic and Extrinsic semiconductors. Formation of P-N Junction – Barrier potential and depletion layer. – P-N Junction diode – Forward and reverse bias characteristics – diode as a rectifier – more zen diode. Zener diode as a voltage regulator – LED. Junction transistors – characteristics – transistor as a switch – transistor as an amplifier – transistor biasing – RC, LC coupled and direct coupling in amplifier – feedback amplifier – positive and negative feedback – advantages of negative feedback amplifier – oscillator – condition for oscillations – LC circuit – Colpitts oscillator.

Logic gates – NOT, OR, AND, EXOR using discrete components – NAND and NOR gates as universal gates – integrated circuits.

Laws and theorems of Boolean’s algebra – operational amplifier – parameters – pin-out configuration – Basic applications. Inverting amplifier. Non-inverting amplifier – summing and difference amplifiers. Measuring Instruments – Cathode Ray oscilloscope – Principle – Functional units – uses. Multimeter – construction and uses.

• Communication Systems: Modes of propagation, ground wave – skywave propagation. Amplitude modulation, merits, and demerits – applications – frequency modulation – advantages and applications – phase modulation. Antennas and directivity. Radio transmission and reception – AM, and FM – superheterodyne receiver. T.V.transmission and reception – scanning and synchronizing. Vidicon (camera tube) and picture tube – block diagram of a monochrome TV transmitter and receiver circuits. Radar – principle – applications. Digital communication – data transmission and reception – principles of fax, modem, satellite communication – wire, cable, and Fibre - optical communication.

## General English:

• This paper includes questions on general English like spotting the errors, sentence improvement, vocabulary, etc.

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### Discussion Forum

Q
chemistry topics

What are the topics for Chemistry we need to refer to?

A

Hi Hansika, chemistry has various topics in it and which is going to be asked in question some of them are p-block elements, nuclear chemistry, solid state and some others which you can get at the JUST Syllabus section.

Q
Mathematics syllabus

What is the mathematics syllabus for JUST?