TRIPURA-JEE - 2024

  Tripura Joint Entrance Examination (TJEE) is a state-level entrance exam. Tripura JEE is conducted offline; through this entrance exam, aspirants can pursue various Engineering, Agriculture, Veterinary, Fisheries, Paramedical, and other professional degree courses at the undergraduate level across the state of Tripura.

   Candidate must have passed the Class 10+ 2 exam or its equivalent exam from any recognized board. Domicile: The candidate must be a Tripura state resident or have a parent who is a Tripura state resident.

Syllabus for Physics

MODULE – 1

Physics: Scope and excitement; nature of physical laws; Physics, technology and society. Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; Accuracy and precision of measuring instruments; errors in measurement; significant figures Dimensions of physical quantities, dimensional analysis and its applications

Frame of reference (inertial and non-inertial frames), Motion in a straight line; Position-time graph, speed and velocity

Uniform and non-uniform motion, average speed and instantaneous velocity, uniformly accelerated motion, velocity-time and position-time graphs, for uniformly accelerated motion (graphical treatment), Elementary concepts of differentiation and integration for describing motion

Scalar and vector quantities: Position and displacement vectors, equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors, Unit vector, Zero Vector, Resolution of a vector in a plane, Scalar and Vector products of Vectors, Relative velocity

Motion in a plane, Cases of uniform velocity and uniform acceleration, projectile motion, Uniform circular motion

MODULE – 2

Force and inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion, Law of conservation of linear momentum and its applications, Problems using free body diagrams

Equilibrium of concurrent forces, Static and Kinetic friction, laws of friction, rolling friction

Dynamics of uniform circular motion, Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road)

Work done by a constant force and a variable force; kinetic and potential energies, work energy theorem, power

Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions, motion in a vertical circle

Centre of mass of a two-particle system, Centre of mass of a rigid body, momentum conservation and motion of centre of mass, centre of mass in some symmetric bodies.

Basic concepts of rotational motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration, Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications to some problems,Equilibrium of rigid bodies, rigid body rotation, equations of rotational motion

MODULE – 3

Kepler’s laws of planetary motion, the universal law of gravitation

Acceleration due to gravity and its variation with altitude, depth and rotation of earth Gravitational potential energy; gravitational potential, escape speed Orbital velocity, time period and mechanical energy of an artificial satellite, Geo-stationary satellites

Elastic behavior, Stress-strain relationship, Hooke’s law, Young modulus, bulkModulus, modulus of rigidity, poison’s ratio; elastic strain energy Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes), Effect of gravity on fluid pressure

Viscosity, Newton’s law of viscous force, coefficient of viscosity, Stoke’s law, terminal velocity, Reynold’s number, streamline and Turbulent flow, Critical velocity,Bernoulli’s theorem and its applications.

Idea of cohesive and adhesive forces, Surface energy and surface tension, angle of contact, excess Pressure for liquid drop, liquid bubble and air bubble, capillary rise

MODULE – 4

Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases, anomalous expansion of water and its effect, specific heat capacity at constant pressure and constant volume and their inter-relation, Calorimetry, change of state – idea of latent heat

Heat transfer- conduction and thermal conductivity, convection and radiation, Qualitative ideas of Black Body Radiation, absorptive and emissive powers, Kirchhoff’s law, Wien’s displacement law, Newton’s law of cooling and Stefan’s law, GreenHouse effect

Thermal equilibrium and definition of temperature (Zeroth law of Thermodynamics), Heat, work and internal energy

First law of thermodynamics, various thermodynamic processes viz. isothermal, adiabatic, isobaric, isochoric processes, work done in thermodynamic process (both isothermal and adiabatic)

Second law of the thermodynamics, Reversible and irreversible processes, Idea of heat engine, Carnot’s engine and its efficiency

Ideal gas laws, equation of state of a perfect gas,

Assumptions of kinetic theory of gases, concept of pressure, r. m. s. speed of gas molecules, Kinetic energy and temperature; degrees of freedom, law of equipartition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro’s number

MODULE – 5

Periodic motion - period, frequency, displacement as a function of time, Periodic functions, Simple harmonic motion (S.H.M.) and its equation; phase; mechanical energy in S.H.M.,Simple pendulum - expression for its time period; oscillations of a spring -restoring force and force constant; some other examples of SHM

Free, forced and damped oscillations (quantitative ideas only), simple examples, resonance

Wave motion, Longitudinal and transverse waves, speed of a wave,Expression for displacement of a plane progressive wave, relation between particle and wave velocity, Principle of superposition of waves, reflection of waves, Standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect in sound

MODULE – 6

Frictional electricity, Electric charge and its conservation, Coulomb’s law-forces between two point charges, forces between multiple charges; dielectric constant, superposition principle and continuous charge distribution

Electric field, Electric field due to a point charge, Electric field lines, Electric dipole, Electric field intensity at various positions due to an electric dipole, Torque on an electric dipole in a uniform electric field, Potential energy of an electric dipole

Electric flux, Gauss’s law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside)

Electric potential, potential difference, Electric potential for a point charge, electric dipole and system of charges; Equipotential surfaces, Electrical potential energy of a system of two point charges in an electrostatic field

Conductors and insulators, free charges and bound charges inside a conductor, Dielectrics and electric polarization, capacitor and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor, Van de Graff generator

MODULE – 7

Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their 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, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance, Internal resistance of a cell, potential difference and e. m. f. of a cell, combination of cells in series and in parallel, elementary idea of secondary cell.

Kirchhoff’s laws and their applications, Wheatstone bridge, Metre Bridge, Potentiometer Principle and applications to measure potential difference, and for comparing e. m. f. of two cells; measurement of internal resistance of a cell.

Concept of magnetic field, Oersted’s experiment, Biot-Savart’s law and its application to current carrying circular loop.

Ampere’s circuital law and its applications to 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. Force between two parallel current-carrying conductors-definition of ampere, Torque experienced by a current loop in a magnetic field; moving coil galvanometer, current sensitivity and voltage sensitivity, conversion of galvanometer to ammeter and voltmeter.

MODULE – 8

Current loop as a magnetic dipole and its magnetic dipole moment, 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 field and magnetic elements

Para-, dia-and ferro-magnetic substances, with examples Electromagnets and factors affecting their strengths, Permanent magnets

Electromagnetic induction; induced e. m. f. and current, Faraday’s law, Lenz’s Law, Eddy currents, self and mutual inductance

Alternating currents, peak and r. m. s. value of alternating current/ voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits and power factor, wattles current, AC generator and transformer

Displacement current and its need, electromagnetic waves and their characteristics (qualitative ideas only), transverse nature of electromagnetic waves, electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses.

MODULE – 9

Reflection of light, spherical mirrors, mirror formula Refraction of light, total internal reflection and its applications, optical fibers, Refraction at spherical surface, lenses, thin lens formula, lens-maker’s formula.

Newton’s relation: Displacement method to find position of images (conjugate points) 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 - blue colour of the sky and reddish appearance of the sum at sunrise and sunset, Elementary idea of Raman Effect

Optical instruments: Human eye, image formation and accommodation, correction of eye defects (myopia, hypermetropia, presbyopia and astigmatism) using lenses, Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.

Wave optics: Wavefront and Huygen’s principle, reflection and refraction of plane waves 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; Malus law, Brewster’s law, uses of plane polarised light and Polaroids.

MODULE – 10

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

Alpha- particle scattering experiments; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum Composition and size of nucleus, atomic masses, isotopes, isobars; isotones.

Radioactivity- alpha, beta and gamma rays and their properties decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors (intrinsic and extrinsic); semiconductor diode, I-Vcharacteristics in forward and reverse bias, diode as a rectifier; I-Vcharacteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator

Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator, Logic gates (OR, AND, NOT, NAND and NOR gates) and their applications

Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation, Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System

Syllabus for Mathematics

MODULE-1

Sets: Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set.Venndiagrams. Operations on set, Union and intersection, Difference of sets, Complement of a set. Properties of complement sets.Simple problems on union and intersection on not more than three sets.

Relations & Mapping: Ordered pairs.Cartesian product of sets.Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x Rx R).Different types of relations, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain & range of a function.Real valued functions of real variables, domain and range of these functions. Different types of functions.Graphs of function.Sum, difference, product and quotients of functions.

MODULE-2

Sequence and Series: Arithmetic progression (A.P), arithmetic mean (A.M) Geometric progression (G.P), Geometric mean(G.M).Sum of n terms of A.P and G.P., Relation between A.M. and G.M of two real numbers. Arithmetic, Geometric and Arithmetricogeometric series. Sum to n terms of the special series Σn ,Σn 2 and Σn 3 .Infinite G.P and its sum.

Complex Numbers: Complex numbers as ordered pair of reals, representation of a complex number in form of a+ ib. Polar form and conjugate of a complex number, Argand diagram, algebra of complex numbers, modulus and argument of a complex number. Square and cube root of complex numbers and their properties, triangle inequality, simple problems.

Quadratic Equations: Its rational, irrational and complex roots, relation between roots and coefficients of a quadratic equation, nature of roots, formation of quadratic equation, symmetric functions of the roots, quadratic expressions, its maximum and minimum values. Simple applications.

Permutations & Combinations: Fundamental theorem of counting, permutation as arrangement and combination as selection. Permutation and combination of like and unlike things. Circular permutation is to be excluded. Simple applications.

MODULE-3

Binomial Theorem: Binomial theorem for positive integral indices, general and middle term, term independent of x and greatest term in binomial expansion, simple applications.

Matrices and Determinant: Matrices of order ≤ 3, algebra of matrices, types of matrices, determinant up to 3rd order. Properties of determinants, evaluation of determinants, area of triangle by using determinant, Adjoint and evaluation of inverse of a square matrix using determinant and by elementary transformations test of consistency and solution of simultaneous linear equations using inverse of a matrix and determinants(Cramer’s rule).

MODULE-4

Trigonometric ratios of associated angles, compound angles, multiple and submultiple angles, conditional identities, general solution of trigonometric equations, inverse circular functions, simple applications.

Properties of triangles: Sine, Cosine, Tangent rules, formula for semi angels, expression for area of a triangle, circum radius.

MODULE-5

Straight Line: Cartesian coordinate system, translation of coordinate axes, Locus of a point, Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line, concurrence of three straight lines. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line. Equation of internal and external bisectors of angles between two intersecting lines, Centroid, orthocenter, circumcentre of a triangle.

Conic Sections: Standard form of equation of circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given. Point of intersection of a line and a circle with the centre at origin and condition for a line to be tangent to a circle, Equation of the tangent and simple properties.

Conics: Parabola,ellipse, hyperbola in standard form, condition for y = mx+c to be a tangent and their simple properties.

MODULE-6

Vectors: Idea of vectors and scalars, types of vector, components of a vector in two and three dimensional space, Triangle and parallelogram laws of vectors, scalars and vector products, scalar triple product. Geometrical representation of product of vectors. Simple applications.

Three dimensional Geometry: Direction angles,direction cosines / ratios of a line joining two points. Orthogonal projection of a line segment on a straight line. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines Cartesian and vector equation of a plane in Cartesian and vector forms. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a line and plane from a point. Condition of co-planarity of two straight lines, condition for a straight line to lie on a plain and simple application.

MODULE-7

Continuity and Differentiability: Limit, Continuity and differentiability of function, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivate of implicit functions, concept of exponential and logarithmic functions. Logarithmic functions as inverse of exponential functions. Derivatives of different types of functions. Second order derivatives. Rolle’s Theorem and Lagrange’s Mean value theorems (without proof) and their geometric interpretations and simple applications. Indeterminate forms using L’Hospital rule.

MODULE-8

INTEGRAL CALCULUS: Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts. Only simple integrals of the following type to be evaluated. ∓ , ∓ , ∓ , √ , √ , √ ∓ , √ + + , ( + ) √ + + , ( !") !" , , !" , # $%& , # '$ , # [)() + )′ ()]. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Differential Equations: Definitions, order and degree, general and particular solutions of a differential equation.Formation of different equations whose general solution is given. Solution of differential equations by method of specification of variables, homogeneous differential equations of first order and first degree solutions of linear differential equations of the type: + + , = , where nd are functions of only .

MODULE-9

Applications of derivatives: Rate of change, approximation of functions increasing, decreasing functions,Tangent and normal,maxima and minima. Simple applications. Application of the Integrals: Area of finite region bounded by curves.

MODULE-10

Probability: Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events. Multiplication theorem on probability, Conditional probability, dependent and independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of random variable. Repeatedindependent (Bernoulli) trials and Binomial distribution its mean and variance.

Statistics: Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

Mathematical Reasoning: Mathematically acceptable statements. Connecting words/phrases- consolidating the understanding of ‘if and only if (necessary and sufficient) condition”, “implies”, “and/or”,“implied by”, ”and”, “or”, “there exists” and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words difference between contradiction. Converse and contrapositive, truth table.

Linear Inequalities:

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their

representation on the number line.Graphical solution of linear inequalities in two variables.

Solution of a system of linear inequalities in two variables-graphically. Inequalities involving

modulus function.

Linear Programming: Mathematical formulation of L.P Problems in two variables - diet problem, manufacturing problem, transportation problem, investment problem, graphical method of solution for problems in two variables. feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions  (upto three non-trivial constraints).

Official site - https://tbjee.nic.in/