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, Inverse –Properties, 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, Nonhomogeneous 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 noncollinear 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  deBroglie 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 Group18 Inert gases  Isolation, properties and uses.

d  Block Elements: General characteristics of dblock 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  fblock elements General characteristics of f  block elements and extraction  Comparison of Lanthanides and Actinides  Uses of lanthanides and actinides.

Coordination Compounds and Biocoordination 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  XRay 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 firstorder 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  DL and RS 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. VI 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 – leadacid 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 – BiotSavart 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 fieldmoving 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. Selfinduction – Mutual induction – Selfinductance 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 – Xrays, 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. Xrays – production, properties, detection, absorption, diffraction of Xrays – Laue’s experiment – Bragg’s law, Bragg’s Xray spectrometer – Xray spectra – continuous and characteristic Xray 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 waveswave mechanical concept of the atom – wave nature of particles – De–Broglie relation – De–Broglie wave length of an electronelectron 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 nucleiBain bridge mass spectrometer. Nature of nuclear forces – Neutron – discovery – properties – artificial transmutation – particle accelerator Radioactivityalpha, beta and gamma radiations and their properties, αdecay, βdecay, and γdecay – Radioactive decay law – halflife – 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 PN Junction – Barrier potential and depletion layer. – PN 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 – pinout configuration – Basic applications. Inverting amplifier. Noninverting 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.