JMI Entrance Exam 2025: Application Form (Out), Dates, Eligibility, Fees, Syllabus, Pattern

Chemistry: Unit 01

• Atomic mass, extraction of metals, gas laws, ideal gas equation, kinetic molecular theory of gases, constituents of the atom, nuclear model of atom, Bohr's atomic model (mathematical details excluded), quantum mechanical model of atom
• Aufbau principle, Hund's Rule
• Paul's exclusion principle, de Broglie equation, uncertainty principle, shapes of orbitals, modern periodic table, periodic trends in properties, ionization energy, electron affinity, atomic radii, and electronegativity, chemical bonds
• Quantum theory of covalent bonds, hydrogen bond, hybridization involving s.p. and d orbital, shapes of molecules, VSEPR concept, molecular orbital theory, solid state, X-ray studies of crystals, packing in crystals, crystal lattices
• Internal energy
• Enthalpy
• Hess's law
• Entropy, free energy, heat of reactions, concept of chemical equilibrium, law of equilibrium, Le Chatelier's principle, and its applications, ionisation of electrolytes, acid base equilibrium, solubility product, ionization of water, pH, redox reactions
• Galvanic cell and its EMF
• Electrode potential, effects of temperature, and concentration
• Electrolysis, oxidation number, solutions, lowering of vapour pressure, Raoult’s law
• Chemical kinetics, rates of reaction, its dependence on concentration, order of a reaction, factors affecting rate of a reaction, rate constant, half life period of first order reaction, absorption
• Colloidal state, preparation and properties of colloidal solutions, gold no, radioactivity
• Half life, carbon dating, chemical thermodynamics

Chemistry: Unit 02

• Preparation and properties of the following: Hydrogen, oxygen, halogens, noble gases, water, hydrogen peroxide, nitrogen, boron, silicon, phosphorous, sulphur, sodium, potassium, magnesium
• Preparation and properties of the following: Calcium
• Preparation and properties of the following: Aluminum, iron, copper, silver
• Preparation and properties of the following: Gold
• Preparation and properties of the following: Zinc, elements, cement, glass
• Preparation and properties of the following: Plastics, soaps, detergents, coordination compound

Chemistry: Unit 03

• Organic radicals, ions, inductive, electromeric and resonance effects, isomerism, homologous series
• General preparation and functional group properties of the following with emphasis on points noted against each of them-(a) Alkanes (free radical substitution) alkenes (electrophilic addition, Markownikoffs addition, peroxide effect) and alkynes
• (b) Alcohol, distinctions, holoform reaction (c) alkyl halides (nucleophlic substitution), (d) carbonyl compounds (nucleophilic, addition, polymerization, and condensation), (e) ethers and carboxylic acids
• (f) Amines (classification, distinction, basic nature), (g) benzene (resonance), toluene
• Phenol, glycerol
• Oils and fats, proteins, nucleic acids
• Carbohydrates and lipids

Mathematics: Unit 01

• Algebra of sets, relation, one
• Many one
• Onto and into mappings, inverse mapping, composite mapping
• Bounded and unbounded sets neighbourhood of a point, domain, codomain, range
• Square roots of polynomial quadratic surds
• Unity, A.P., H.P., G.P. and other related miscellaneous series, A.G.P., method of differences, sum of the squares and cubes of first n natural numbers, simple geometrical problems of permutations, and combinations
• General terms in the expansions of logarithmic, exponential series, binomial, and multinomial theorems, remainder theorem, factor theorem, rationalising factor of binomial surd of different orders
• Conversion of a fraction and a quadratic surds into a continued fraction, inequalities
• Periodic function
• Hyperbolic function, inverse hyperbolic functions, greatest integer functions, absolute function, signum function
• Even and odd functions, transcendental functions, rational, and irrational algebraic functions etc.

Mathematics: Unit 02

• Linear combination of vectors, linear dependence and independence of vectors, geometrical applications of dot (scalar) and cross (vector) product of two, three, and four vectors

Mathematics: Unit 03

• Classification of curves represented by general polynomial equations (homogeneous and non-homogeneous) of second degree in x and y, homogeneous equations of nth degree, detailed study of families of straight lines, and circles
• Parabola, ellipse, and hyperbola
• Condition of tangency of a line to a curve of any positive integral degree in x and, simple problems on plane, straight line in space, and sphere

Mathematics: Unit 04

• Trigonometrical conditional identities and equations, relations between sides, angles, and radii of incircle, circum circle, and excribed circle associated with triangle, inverse circular functions, polar form of complex number
• Euler's formula, values of (a+ib)p/q, applications of De-Moivre's theorem

Mathematics: Unit 05

• Multiplications of determinants and matrices, adjoint, and inverse of matrices, rank of matrix, Cramer's rule, applications of determinants, and matrices
• Geometrical transformations (i.e. reflection, rotation, translation, enlargement), their composition, and representation by matrices
• Limit, continuity, monotonicity
• Differentiability, differentiation of composite function, implicit relation, parametric forms, logarithmic differentiation, differentiation by transformations, increasing, and decreasing functions, tangent, normal
• Maxima and minima of a function of one variable, velocity, acceleration, Rolle's theorem, Lagrange's mean value theorem, standard results on successive (ordinary and partial) differentiation
• L' Hopital's rule, seven indeterminate forms, Euler's theorem on homogenous function for partial differentiation, simple problems on Leibnitz's theorem
• Equations of tangent plane and normal line at any point of 3D figures

Mathematics: Unit 06

• Integration by well known standard results, by substitutions, by parts, by partial fractions, some well known definite integrals, propelties of definite integrals, reduction formulae
• Applications of definite integral in finding the area of bounded region in x-y plane, volume, and lateral (curved) surface area of some well known 3-D solids obtained by revolution, mean value
• Mean square value
• Root mean square value of a function for a given interval, calculation of a interval in which the value of a given definite integral exists

Mathematics: Unit 07

• Formation of ordinary and partial differential equations
• General and particular solution of O.D.E. of I order and I degree (i.e. variable separable for, homogeneous form, linear form, exact form, and their reducible form obtained by some transformations, and integrating factors)
• O.D.E. of I order but not of I degree
• General solution of dny/dxn=G(x), d 2 y/dx 2 = H(y)

Mathematics: Unit 08

• Karl Pearson's simple correlation coefficient for a tabulated function between two variable, coefficients of covariance, and variation
• Lines of Regression
• Regression coefficients properties of binomial
• Normal and Poission distributions
• Measures of skewness and kurtosis
• Dynamics and statics: Standard formulas and elementary problems

General awareness/reasoning/general English: Unit 01

• Logical, symbolic, verbal, and mathematical reasoning, finding odd-one out, matching, differences, similarities, prediction, finding missing values in number series, alphabet series, test of direction sense, coding-decoding, number ranking
• Arithmetical reasoning, blood relations, analogy, decision making, nonverbal series, mirror images, grouping identical figures, and common reasoning fallacies

General awareness/reasoning/general English: Unit 02

• Vocabulary, punctuation, syntax, verb, forms, spelling, synonyms, antonyms, homonyms, tense, use of preposition, conjunctions, active and passive voice, simple, complex, and compound sentences, degree of comparison, and direct, and indirect speech

General awareness/reasoning/general English: Unit 03

• Current affairs, historical persons, events, places etc.

Chemistry: Unit 01

• Atomic mass, extraction of metals, gas laws, ideal gas equation, kinetic molecular theory of gases, constituents of the atom, nuclear model of atom, Bohr's atomic model (mathematical details excluded), quantum mechanical model of atom
• Aufbau principle, Hund's Rule
• Paul's exclusion principle, de Broglie equation, uncertainty principle, shapes of orbitals, modern periodic table, periodic trends in properties, ionization energy, electron affinity, atomic radii, and electronegativity, chemical bonds
• Quantum theory of covalent bonds, hydrogen bond, hybridization involving s.p. and d orbital, shapes of molecules, VSEPR concept, molecular orbital theory, solid state, X-ray studies of crystals, packing in crystals, crystal lattices
• Internal energy
• Enthalpy
• Hess's law
• Entropy, free energy, heat of reactions, concept of chemical equilibrium, law of equilibrium, Le Chatelier's principle, and its applications, ionisation of electrolytes, acid base equilibrium, solubility product, ionization of water, pH, redox reactions
• Galvanic cell and its EMF
• Electrode potential, effects of temperature, and concentration
• Electrolysis, oxidation number, solutions, lowering of vapour pressure, Raoult’s law
• Chemical kinetics, rates of reaction, its dependence on concentration, order of a reaction, factors affecting rate of a reaction, rate constant, half life period of first order reaction, absorption
• Colloidal state, preparation and properties of colloidal solutions, gold no, radioactivity
• Half life, carbon dating, chemical thermodynamics

Chemistry: Unit 02

• Preparation and properties of the following: Hydrogen, oxygen, halogens, noble gases, water, hydrogen peroxide, nitrogen, boron, silicon, phosphorous, sulphur, sodium, potassium, magnesium
• Preparation and properties of the following: Calcium
• Preparation and properties of the following: Aluminum, iron, copper, silver
• Preparation and properties of the following: Gold
• Preparation and properties of the following: Zinc, elements, cement, glass
• Preparation and properties of the following: Plastics, soaps, detergents, coordination compound

Chemistry: Unit 03

• Organic radicals, ions, inductive, electromeric and resonance effects, isomerism, homologous series
• General preparation and functional group properties of the following with emphasis on points noted against each of them-(a) Alkanes (free radical substitution) alkenes (electrophilic addition, Markownikoffs addition, peroxide effect) and alkynes
• (b) Alcohol, distinctions, holoform reaction (c) alkyl halides (nucleophlic substitution), (d) carbonyl compounds (nucleophilic, addition, polymerization, and condensation), (e) ethers and carboxylic acids
• (f) Amines (classification, distinction, basic nature), (g) benzene (resonance), toluene
• Phenol, glycerol
• Oils and fats, proteins, nucleic acids
• Carbohydrates and lipids

Mathematics: Unit 01

• Algebra of sets, relation, one
• Many one
• Onto and into mappings, inverse mapping, composite mapping
• Bounded and unbounded sets neighbourhood of a point, domain, codomain, range
• Square roots of polynomial quadratic surds
• Unity, A.P., H.P., G.P. and other related miscellaneous series, A.G.P., method of differences, sum of the squares and cubes of first n natural numbers, simple geometrical problems of permutations, and combinations
• General terms in the expansions of logarithmic, exponential series, binomial, and multinomial theorems, remainder theorem, factor theorem, rationalising factor of binomial surd of different orders
• Conversion of a fraction and a quadratic surds into a continued fraction, inequalities
• Periodic function
• Hyperbolic function, inverse hyperbolic functions, greatest integer functions, absolute function, signum function
• Even and odd functions, transcendental functions, rational, and irrational algebraic functions etc.

Mathematics: Unit 02

• Linear combination of vectors, linear dependence and independence of vectors, geometrical applications of dot (scalar) and cross (vector) product of two, three, and four vectors

Mathematics: Unit 03

• Classification of curves represented by general polynomial equations (homogeneous and non-homogeneous) of second degree in x and y, homogeneous equations of nth degree, detailed study of families of straight lines, and circles
• Parabola, ellipse, and hyperbola
• Condition of tangency of a line to a curve of any positive integral degree in x and, simple problems on plane, straight line in space, and sphere

Mathematics: Unit 04

• Trigonometrical conditional identities and equations, relations between sides, angles, and radii of incircle, circum circle, and excribed circle associated with triangle, inverse circular functions, polar form of complex number
• Euler's formula, values of (a+ib)p/q, applications of De-Moivre's theorem

Mathematics: Unit 05

• Multiplications of determinants and matrices, adjoint, and inverse of matrices, rank of matrix, Cramer's rule, applications of determinants, and matrices
• Geometrical transformations (i.e. reflection, rotation, translation, enlargement), their composition, and representation by matrices
• Limit, continuity, monotonicity
• Differentiability, differentiation of composite function, implicit relation, parametric forms, logarithmic differentiation, differentiation by transformations, increasing, and decreasing functions, tangent, normal
• Maxima and minima of a function of one variable, velocity, acceleration, Rolle's theorem, Lagrange's mean value theorem, standard results on successive (ordinary and partial) differentiation
• L' Hopital's rule, seven indeterminate forms, Euler's theorem on homogenous function for partial differentiation, simple problems on Leibnitz's theorem
• Equations of tangent plane and normal line at any point of 3D figures

Mathematics: Unit 06

• Integration by well known standard results, by substitutions, by parts, by partial fractions, some well known definite integrals, propelties of definite integrals, reduction formulae
• Applications of definite integral in finding the area of bounded region in x-y plane, volume, and lateral (curved) surface area of some well known 3-D solids obtained by revolution, mean value
• Mean square value
• Root mean square value of a function for a given interval, calculation of a interval in which the value of a given definite integral exists

Mathematics: Unit 07

• Formation of ordinary and partial differential equations
• General and particular solution of O.D.E. of I order and I degree (i.e. variable separable for, homogeneous form, linear form, exact form, and their reducible form obtained by some transformations, and integrating factors)
• O.D.E. of I order but not of I degree
• General solution of dny/dxn=G(x), d 2 y/dx 2 = H(y)

Mathematics: Unit 08

• Karl Pearson's simple correlation coefficient for a tabulated function between two variable, coefficients of covariance, and variation
• Lines of Regression
• Regression coefficients properties of binomial
• Normal and Poission distributions
• Measures of skewness and kurtosis
• Dynamics and statics: Standard formulas and elementary problems

General awareness/reasoning/general English: Unit 01

• Logical, symbolic, verbal, and mathematical reasoning, finding odd-one out, matching, differences, similarities, prediction, finding missing values in number series, alphabet series, test of direction sense, coding-decoding, number ranking
• Arithmetical reasoning, blood relations, analogy, decision making, nonverbal series, mirror images, grouping identical figures, and common reasoning fallacies

General awareness/reasoning/general English: Unit 02

• Vocabulary, punctuation, syntax, verb, forms, spelling, synonyms, antonyms, homonyms, tense, use of preposition, conjunctions, active and passive voice, simple, complex, and compound sentences, degree of comparison, and direct, and indirect speech

General awareness/reasoning/general English: Unit 03

• Current affairs, historical persons, events, places etc.

Chemistry: Unit 01

• Atomic mass, extraction of metals, gas laws, ideal gas equation, kinetic molecular theory of gases, constituents of the atom, nuclear model of atom, Bohr's atomic model (mathematical details excluded), quantum mechanical model of atom
• Aufbau principle, Hund's Rule
• Paul's exclusion principle, de Broglie equation, uncertainty principle, shapes of orbitals, modern periodic table, periodic trends in properties, ionization energy, electron affinity, atomic radii, and electronegativity, chemical bonds
• Quantum theory of covalent bonds, hydrogen bond, hybridization involving s.p. and d orbital, shapes of molecules, VSEPR concept, molecular orbital theory, solid state, X-ray studies of crystals, packing in crystals, crystal lattices
• Internal energy
• Enthalpy
• Hess's law
• Entropy, free energy, heat of reactions, concept of chemical equilibrium, law of equilibrium, Le Chatelier's principle, and its applications, ionisation of electrolytes, acid base equilibrium, solubility product, ionization of water, pH, redox reactions
• Galvanic cell and its EMF
• Electrode potential, effects of temperature, and concentration
• Electrolysis, oxidation number, solutions, lowering of vapour pressure, Raoult’s law
• Chemical kinetics, rates of reaction, its dependence on concentration, order of a reaction, factors affecting rate of a reaction, rate constant, half life period of first order reaction, absorption
• Colloidal state, preparation and properties of colloidal solutions, gold no, radioactivity
• Half life, carbon dating, chemical thermodynamics

Chemistry: Unit 02

• Preparation and properties of the following: Hydrogen, oxygen, halogens, noble gases, water, hydrogen peroxide, nitrogen, boron, silicon, phosphorous, sulphur, sodium, potassium, magnesium
• Preparation and properties of the following: Calcium
• Preparation and properties of the following: Aluminum, iron, copper, silver
• Preparation and properties of the following: Gold
• Preparation and properties of the following: Zinc, elements, cement, glass
• Preparation and properties of the following: Plastics, soaps, detergents, coordination compound

Chemistry: Unit 03

• Organic radicals, ions, inductive, electromeric and resonance effects, isomerism, homologous series
• General preparation and functional group properties of the following with emphasis on points noted against each of them-(a) Alkanes (free radical substitution) alkenes (electrophilic addition, Markownikoffs addition, peroxide effect) and alkynes
• (b) Alcohol, distinctions, holoform reaction (c) alkyl halides (nucleophlic substitution), (d) carbonyl compounds (nucleophilic, addition, polymerization, and condensation), (e) ethers and carboxylic acids
• (f) Amines (classification, distinction, basic nature), (g) benzene (resonance), toluene
• Phenol, glycerol
• Oils and fats, proteins, nucleic acids
• Carbohydrates and lipids

Mathematics: Unit 01

• Algebra of sets, relation, one
• Many one
• Onto and into mappings, inverse mapping, composite mapping
• Bounded and unbounded sets neighbourhood of a point, domain, codomain, range
• Square roots of polynomial quadratic surds
• Unity, A.P., H.P., G.P. and other related miscellaneous series, A.G.P., method of differences, sum of the squares and cubes of first n natural numbers, simple geometrical problems of permutations, and combinations
• General terms in the expansions of logarithmic, exponential series, binomial, and multinomial theorems, remainder theorem, factor theorem, rationalising factor of binomial surd of different orders
• Conversion of a fraction and a quadratic surds into a continued fraction, inequalities
• Periodic function
• Hyperbolic function, inverse hyperbolic functions, greatest integer functions, absolute function, signum function
• Even and odd functions, transcendental functions, rational, and irrational algebraic functions etc.

Mathematics: Unit 02

• Linear combination of vectors, linear dependence and independence of vectors, geometrical applications of dot (scalar) and cross (vector) product of two, three, and four vectors

Mathematics: Unit 03

• Classification of curves represented by general polynomial equations (homogeneous and non-homogeneous) of second degree in x and y, homogeneous equations of nth degree, detailed study of families of straight lines, and circles
• Parabola, ellipse, and hyperbola
• Condition of tangency of a line to a curve of any positive integral degree in x and, simple problems on plane, straight line in space, and sphere

Mathematics: Unit 04

• Trigonometrical conditional identities and equations, relations between sides, angles, and radii of incircle, circum circle, and excribed circle associated with triangle, inverse circular functions, polar form of complex number
• Euler's formula, values of (a+ib)p/q, applications of De-Moivre's theorem

Mathematics: Unit 05

• Multiplications of determinants and matrices, adjoint, and inverse of matrices, rank of matrix, Cramer's rule, applications of determinants, and matrices
• Geometrical transformations (i.e. reflection, rotation, translation, enlargement), their composition, and representation by matrices
• Limit, continuity, monotonicity
• Differentiability, differentiation of composite function, implicit relation, parametric forms, logarithmic differentiation, differentiation by transformations, increasing, and decreasing functions, tangent, normal
• Maxima and minima of a function of one variable, velocity, acceleration, Rolle's theorem, Lagrange's mean value theorem, standard results on successive (ordinary and partial) differentiation
• L' Hopital's rule, seven indeterminate forms, Euler's theorem on homogenous function for partial differentiation, simple problems on Leibnitz's theorem
• Equations of tangent plane and normal line at any point of 3D figures

Mathematics: Unit 06

• Integration by well known standard results, by substitutions, by parts, by partial fractions, some well known definite integrals, propelties of definite integrals, reduction formulae
• Applications of definite integral in finding the area of bounded region in x-y plane, volume, and lateral (curved) surface area of some well known 3-D solids obtained by revolution, mean value
• Mean square value
• Root mean square value of a function for a given interval, calculation of a interval in which the value of a given definite integral exists

Mathematics: Unit 07

• Formation of ordinary and partial differential equations
• General and particular solution of O.D.E. of I order and I degree (i.e. variable separable for, homogeneous form, linear form, exact form, and their reducible form obtained by some transformations, and integrating factors)
• O.D.E. of I order but not of I degree
• General solution of dny/dxn=G(x), d 2 y/dx 2 = H(y)

Mathematics: Unit 08

• Karl Pearson's simple correlation coefficient for a tabulated function between two variable, coefficients of covariance, and variation
• Lines of Regression
• Regression coefficients properties of binomial
• Normal and Poission distributions
• Measures of skewness and kurtosis
• Dynamics and statics: Standard formulas and elementary problems

General awareness/reasoning/general English: Unit 01

• Logical, symbolic, verbal, and mathematical reasoning, finding odd-one out, matching, differences, similarities, prediction, finding missing values in number series, alphabet series, test of direction sense, coding-decoding, number ranking
• Arithmetical reasoning, blood relations, analogy, decision making, nonverbal series, mirror images, grouping identical figures, and common reasoning fallacies

General awareness/reasoning/general English: Unit 02

• Vocabulary, punctuation, syntax, verb, forms, spelling, synonyms, antonyms, homonyms, tense, use of preposition, conjunctions, active and passive voice, simple, complex, and compound sentences, degree of comparison, and direct, and indirect speech

General awareness/reasoning/general English: Unit 03

• Current affairs, historical persons, events, places etc.

Chemistry: Unit 01

• Atomic mass, extraction of metals, gas laws, ideal gas equation, kinetic molecular theory of gases, constituents of the atom, nuclear model of atom, Bohr's atomic model (mathematical details excluded), quantum mechanical model of atom
• Aufbau principle, Hund's Rule
• Paul's exclusion principle, de Broglie equation, uncertainty principle, shapes of orbitals, modern periodic table, periodic trends in properties, ionization energy, electron affinity, atomic radii, and electronegativity, chemical bonds
• Quantum theory of covalent bonds, hydrogen bond, hybridization involving s.p. and d orbital, shapes of molecules, VSEPR concept, molecular orbital theory, solid state, X-ray studies of crystals, packing in crystals, crystal lattices
• Internal energy
• Enthalpy
• Hess's law
• Entropy, free energy, heat of reactions, concept of chemical equilibrium, law of equilibrium, Le Chatelier's principle, and its applications, ionisation of electrolytes, acid base equilibrium, solubility product, ionization of water, pH, redox reactions
• Galvanic cell and its EMF
• Electrode potential, effects of temperature, and concentration
• Electrolysis, oxidation number, solutions, lowering of vapour pressure, Raoult’s law
• Chemical kinetics, rates of reaction, its dependence on concentration, order of a reaction, factors affecting rate of a reaction, rate constant, half life period of first order reaction, absorption
• Colloidal state, preparation and properties of colloidal solutions, gold no, radioactivity
• Half life, carbon dating, chemical thermodynamics

Chemistry: Unit 02

• Preparation and properties of the following: Hydrogen, oxygen, halogens, noble gases, water, hydrogen peroxide, nitrogen, boron, silicon, phosphorous, sulphur, sodium, potassium, magnesium
• Preparation and properties of the following: Calcium
• Preparation and properties of the following: Aluminum, iron, copper, silver
• Preparation and properties of the following: Gold
• Preparation and properties of the following: Zinc, elements, cement, glass
• Preparation and properties of the following: Plastics, soaps, detergents, coordination compound

Chemistry: Unit 03

• Organic radicals, ions, inductive, electromeric and resonance effects, isomerism, homologous series
• General preparation and functional group properties of the following with emphasis on points noted against each of them-(a) Alkanes (free radical substitution) alkenes (electrophilic addition, Markownikoffs addition, peroxide effect) and alkynes
• (b) Alcohol, distinctions, holoform reaction (c) alkyl halides (nucleophlic substitution), (d) carbonyl compounds (nucleophilic, addition, polymerization, and condensation), (e) ethers and carboxylic acids
• (f) Amines (classification, distinction, basic nature), (g) benzene (resonance), toluene
• Phenol, glycerol
• Oils and fats, proteins, nucleic acids
• Carbohydrates and lipids

Mathematics: Unit 01

• Algebra of sets, relation, one
• Many one
• Onto and into mappings, inverse mapping, composite mapping
• Bounded and unbounded sets neighbourhood of a point, domain, codomain, range
• Square roots of polynomial quadratic surds
• Unity, A.P., H.P., G.P. and other related miscellaneous series, A.G.P., method of differences, sum of the squares and cubes of first n natural numbers, simple geometrical problems of permutations, and combinations
• General terms in the expansions of logarithmic, exponential series, binomial, and multinomial theorems, remainder theorem, factor theorem, rationalising factor of binomial surd of different orders
• Conversion of a fraction and a quadratic surds into a continued fraction, inequalities
• Periodic function
• Hyperbolic function, inverse hyperbolic functions, greatest integer functions, absolute function, signum function
• Even and odd functions, transcendental functions, rational, and irrational algebraic functions etc.

Mathematics: Unit 02

• Linear combination of vectors, linear dependence and independence of vectors, geometrical applications of dot (scalar) and cross (vector) product of two, three, and four vectors

Mathematics: Unit 03

• Classification of curves represented by general polynomial equations (homogeneous and non-homogeneous) of second degree in x and y, homogeneous equations of nth degree, detailed study of families of straight lines, and circles
• Parabola, ellipse, and hyperbola
• Condition of tangency of a line to a curve of any positive integral degree in x and, simple problems on plane, straight line in space, and sphere

Mathematics: Unit 04

• Trigonometrical conditional identities and equations, relations between sides, angles, and radii of incircle, circum circle, and excribed circle associated with triangle, inverse circular functions, polar form of complex number
• Euler's formula, values of (a+ib)p/q, applications of De-Moivre's theorem

Mathematics: Unit 05

• Multiplications of determinants and matrices, adjoint, and inverse of matrices, rank of matrix, Cramer's rule, applications of determinants, and matrices
• Geometrical transformations (i.e. reflection, rotation, translation, enlargement), their composition, and representation by matrices
• Limit, continuity, monotonicity
• Differentiability, differentiation of composite function, implicit relation, parametric forms, logarithmic differentiation, differentiation by transformations, increasing, and decreasing functions, tangent, normal
• Maxima and minima of a function of one variable, velocity, acceleration, Rolle's theorem, Lagrange's mean value theorem, standard results on successive (ordinary and partial) differentiation
• L' Hopital's rule, seven indeterminate forms, Euler's theorem on homogenous function for partial differentiation, simple problems on Leibnitz's theorem
• Equations of tangent plane and normal line at any point of 3D figures

Mathematics: Unit 06

• Integration by well known standard results, by substitutions, by parts, by partial fractions, some well known definite integrals, propelties of definite integrals, reduction formulae
• Applications of definite integral in finding the area of bounded region in x-y plane, volume, and lateral (curved) surface area of some well known 3-D solids obtained by revolution, mean value
• Mean square value
• Root mean square value of a function for a given interval, calculation of a interval in which the value of a given definite integral exists

Mathematics: Unit 07

• Formation of ordinary and partial differential equations
• General and particular solution of O.D.E. of I order and I degree (i.e. variable separable for, homogeneous form, linear form, exact form, and their reducible form obtained by some transformations, and integrating factors)
• O.D.E. of I order but not of I degree
• General solution of dny/dxn=G(x), d 2 y/dx 2 = H(y)

Mathematics: Unit 08

• Karl Pearson's simple correlation coefficient for a tabulated function between two variable, coefficients of covariance, and variation
• Lines of Regression
• Regression coefficients properties of binomial
• Normal and Poission distributions
• Measures of skewness and kurtosis
• Dynamics and statics: Standard formulas and elementary problems

General awareness/reasoning/general English: Unit 01

• Logical, symbolic, verbal, and mathematical reasoning, finding odd-one out, matching, differences, similarities, prediction, finding missing values in number series, alphabet series, test of direction sense, coding-decoding, number ranking
• Arithmetical reasoning, blood relations, analogy, decision making, nonverbal series, mirror images, grouping identical figures, and common reasoning fallacies

General awareness/reasoning/general English: Unit 02

• Vocabulary, punctuation, syntax, verb, forms, spelling, synonyms, antonyms, homonyms, tense, use of preposition, conjunctions, active and passive voice, simple, complex, and compound sentences, degree of comparison, and direct, and indirect speech

General awareness/reasoning/general English: Unit 03

• Current affairs, historical persons, events, places etc.