Table of Contents
UPPSC Lecturer Recruitment 2021
Uttar Pradesh Public Service Commission invites online applications for 124 various (Male and Female) UPPSC Lecturer vacancies. Aspirants can Download Official Advertisements and Apply Online through the link gave underneath. Candidates are advised to go through the UPPSC Lecturer official notification before applying online.
UTTAR PRADESH PUBLIC SERVICE COMMISSION
UPPSC LECTURER RECRUITMENT 2021
|VACANCY DETAILS. TOTAL POSTS = 124
UPPSC Lecturer PayScale. 9300-34800 Grade Pay 4800 level-8.
UPPSC Lecturer Exam Pattern
मुख्य (लिखित) परीक्षा हेतु परीक्षा योजना एवं पाठ्यक्रम
|प्रथम प्रश्नपत्र – सामान्य हिन्दी एवं निबन्ध (परम्परागत)||समय- 02 घण्टा||पूर्णांक – 100 अंक|
|द्वितीय प्रश्नपत्र – वैकल्पिक विषय (परम्परागत)||समय- 03 घण्टा||पूर्णांक – 300 अंक|
UPPSC Lecturer Syllabus
प्रथम खण्ड – सामान्य हिन्दी निर्धारित अंक-50
1- अपठित गद्यांश का संक्षेपण, उससे सम्बन्धित प्रश्न, रेखांकित अंशों की व्याख्या एवं उसका उपयुक्त शीर्षक।
2- अनेकार्थी शब्द, विलोम शब्द, पर्यायवाची शब्द, तत्सम एवं तद्भव, क्षेत्रीय, विदेशी (शब्द भण्डार), वर्तनी, अर्थबोध, शब्द-रूप, सन्धि, समास, क्रियायें, हिन्दी वर्णमाला, विराम चिन्ह, शब्द रचना, वाक्य रचना, अर्थ, मुहावरे एवं लोकोक्तियाँ, उत्तर प्रदेश की मुख्य बोलियाँ तथा हिन्दी भाषा के प्रयोग में होने वाली अशुद्धियाँ।
द्वितीय खण्ड – हिन्दी निबन्ध निर्धारित अंक-50
इसके अन्तर्गत एक खण्ड होगा। इस खण्ड में से एक निबन्ध लिखना होगा। इस निबन्ध की अधिकतम विस्तार सीमा 1000 शब्द होगी। निबन्ध हेतु निम्नवत् क्षेत्र होंगे:-
1- साहित्य, संस्कृति
2- राष्ट्रीय विकास योजनायें/क्रियान्वयन
3- राष्ट्रीय-अन्तर्राष्ट्रीय, सामयिक सामाजिक समस्यायें/निदान
4- विज्ञान तथा पर्यावरण
5- प्राकृतिक आपदायें एवं उनके निवारण
6- कृषि, उद्योग एवं व्यापार
UPPSC Lecturer Syllabus
(2) Optional Subjects
परीक्षा योजना– वैकल्पिक विषयों के (परम्परागत) प्रश्नपत्र की रचना हेतु प्रश्नपत्रों के स्वरूप एवं अंकों का विभाजन निम्नवत् है:-
1- प्रश्नों की कुल संख्या-20 होगी। सभी प्रश्न अनिवार्य होंगे। सभी प्रश्न खण्डों में विभाजित रहेंगे।
खण्ड-अ- के अन्तर्गत प्रश्नपत्र में 05 प्रश्न सामान्य उत्तरीय (उत्तरों की शब्द सीमा 250) एवं प्रत्येक प्रश्न 25 अंक का होगा।
खण्ड-ब- के अन्तर्गत 05 प्रश्न लघुउत्तरीय (उत्तरों की शब्द सीमा 150) एवं प्रत्येक प्रश्न 15 अंक का होगा।
खण्ड-स- के अन्तर्गत में 10 प्रश्न अतिलघु उत्तरीय (उत्तरों की शब्द सीमा 50) एवं प्रत्येक प्रश्न 10 अंक का होगा।
UPPSC Lecturer Syllabus
वैकल्पिक विषय का पाठ्यक्रम
(I) MECHANICS:- Vector algebra: scalar and vector products, vector identities, the background of vector calculus, the concept of line, surface and volume integrals, the physical meaning of gradient, divergence, and curl, Gauss and Stoke’s theorems.
Centre of mass, rotating frame of reference, Coriolis force, the motion of rigid bodies, the moment of inertia, theorem of parallel and perpendicular axes, movement of inertia of sphere, ring, cylinder, and disc. Angular momentum, torque, central force, Kepler’s Law, the motion of satellite (including geostationary satellite), Galilieon transformation, special theory of relativity, Michelson – Morley experiment, Lorentz transformation equations, variation of mass and length with velocity, time dilation, the addition of velocities and mass-energy equivalence relation.
Streamline and turbulent motions, Reynold’s number, Stoke’s law, Poiseulle’s formula, the flow of liquid through a narrow tube. Bernoulli’s formula with applications, surface tension, Stress-strain relationship, Hooke’s Law, moduli of elasticity and interrelation between them Poisson’s ratio, elastic energy.
(II) THERMAL PHYSICS:- Concept of temperature and the zeroth law, first law of thermodynamics and internal energy, isothermal and adiabatic changes, the second law of thermodynamics, Entropy, Carnot cycle and Carnot engine, the absolute scale of temperature. Maxwell’s thermodynamical relations. The Clausius- Clapeyron equation, porus plug experiment and Joule Thomson effect.
Kinetic theory of gases, Maxwell distribution law of velocities, calculation of mean velocity, root mean square velocity and the Most probable velocity, degrees of freedom, Law of equipartition of energy, specific heats of gases, mean free path, transport phenomena.
Black body radiation, Stefan’s law, Newton’s law of cooling Wien’s law, Rayleigh-Jeans law, Planck’s law, solar constant.
Production of low temperatures by adiabatic demagnetization.
(III) WAVES AND OSCILLATIONS:- Oscillation, simple harmonic motion, stationary and progressive waves, damped harmonic motion, forced oscillations and resonance, sharpness of resonance, wave equation, Plane and spherical waves superposition of waves. Fourier analysis of periodic waves- square and triangular waves, phase and group velocities, Beats.
(IV) OPTICS: Cardinal points of a coaxial system, simple problems on the combination of thin lenses eyepiece- Ramsden and Huygens eyepieces.
Huygen’s principle, conditions for sustained interference Young double-slit experiment division of amplitude and wavefront, Fresnel biprism, Newton’s rings, Michelson-interferometer, diffraction by a straight edge, single, double, and multiple slits. Rayleigh’s criterion, resolving power of optical instruments.
Polarization, production, and detection of polarized light (linear circular and elliptical) Brewster’s law, Huygen’s theory of double refraction, optical rotation, polarimeters.
LASERS:- Temporal and spatial coherence, stimulated emission, basic ideas about laser emission, Ruby and He-Ne lasers.
(V) ELECTRICITY AND MAGNETISM:- Gauss law and its applications, electric potential, Kirchoff’s laws and their applications, Wheatstone’s bridge, Biot-Savart law, Ampere’s circuital law, and their applications. Magnetic induction and field strength, magnetic field on the axis of the circular coil, Electromagnetic induction, Faraday’s and Lenz’s law, self and mutual inductances, alternating current, L.C.R. circuits, series, and parallel resonance Circuits, quality factor. Maxwell’s equations and electromagnetic waves transverse nature of electromagnetic waves, Poynting vector, dia-, para-, Ferro-, antiferro- and feri-magnetism (qualitative approach only), hysteresis.
(VI) MODERN PHYSICS: Bohr’s theory of hydrogen atom, electron spin, Pauli’s exclusion principle, optical and X-ray spectra, spatial quantization and Stern-Gerlach experiment, vector model of the atom, spectral terms, the fine structure of spectral lines J-J and L-S coupling, Zeeman effect, Raman effect, photoelectric effect, Compton effect, de Broglie waves, wave-particle duality, Uncertainty principle, postulates of quantum mechanics, Schrodinger wave equation and its applications to (i) particle in a box (ii) motion across a step potential (iii) one-dimensional harmonic oscillator, and eigenvalues, Einstein’s and debye theory of specific heat of solids. Band theory of solids energy band, Kronig-Penny model in one dimension, energy gap, the distinction between metals, semiconductors, and insulators, variation of Fermi level with temperature and effective mass.
Radioactivity, alfa, beta and gamma radiations, elementary theory of alpha decay, nuclear binding energy, Semi-empirical mass formula, nuclear fission, and fusion and nuclear reactors elementary particles, particle accelerator, cyclotron, linear accelerator, Elementary idea of superconductivity.
(VII) ELECTRONICS:- Intrinsic and extrinsic semiconductors, PN, junction, Zener diode, and their characteristics, unipolar and bipolar transistors solar cells, use of diode and transistor for rectification, amplification, oscillation, modulation and detection, waves. Logic gates and their truth tables, some applications.
UPPSC Lecturer Syllabus
(A) Physical chemistry Gaseous-state:- Molecular velocity of gases, mean free path and collision diameter, liquefaction of gases Joule Thomson effect in ideal and nonideal gases, Joule “Thomson coefficient, inversion temperature, Deviation from ideal gas behavior Vander Waals equation of state, Law of corresponding state, critical constants and their relations with-Vander Waals constants
Liquid state:- surface Tension, the effect of temperature on surface tension, viscosity, the effect of temperature, and pressure on viscosity.
Solid State:- symmetry in crystal systems, Miller inclines close packing, coordination number, the structure of NaCl and CaF2, crystal-defects.
Thermodynamics:- first law of thermodynamics and its limitations, enthalpies of a system, heat of reaction formation, combustion and neutralization, Hess’s law and its application bond energy and resonance energy, heat capacities at constant volume and constant pressure, the relationship between. Cp and Cv extensive and intensive properties, statement of the second law of thermodynamics Carnot cycle, the concept of entropy, variation of entropy with temperature and volume/pressure, the concept of free energy: Helmholtz and Gibbs free energies, Gibbs – Helmholtz equation, thermodynamic criteria of equilibrium, Clapeyron- Clausius equation and its application, VAn;t Hoff equation and Gibbs- Duhem equation.
Dilute solution:- Ideal and non-ideal solutions, Raoult’s Law colligative properties (thermodynamic treatment) Lowering of vapor pressure, osmotic pressure, the elevation of boiling point, and depression of freezing point in solution, abnormal colligative properties molecular weight determination by colligative properties.
Surfacephenomenon- physical and chemical adsorption Freundlich adsorption isotherm Langmuir adsorption isotherm.
Colloidal State – Coagulation, Coagulation Value Gold-number, Hardy-Schulze rule, stability of colloids, zeta potential
Chemical Kinetics-Molecularity and order of reaction, rate of reaction Zero first second, and third-order reactions and their determination effect of temperature on reaction velocity, the energy of activation, catalysis, criteria of catalysis, enzymes catalysis, primary salt effect in ionic reactions.
Chemical equilibrium- Law of mass action and its application to homogeneous and heterogeneous equilibria, the relationship between Kp and Kc. Le chatelier principle and its application to chemical equilibrium, degree of dissociation and abnormal; molecular Weight hydrolysis of salts, Bronsted & lewis acid, and base. pH, buffer solution, solubility, and solubility product of sparingly soluble salts:-
Electrochemistry- Electrolytic conductance-equivalent, specific and molecular conductances, variation of conductances with the dilution of solutions, Kohlausch’s law of independent migration of ions, factors affecting the conductances, types of a single electrode and their potentials, EMF of the cell, Nernst equation. EMF and equilibrium constant, the concept of concentration cell With and without transference, liquid junction potential chemical cells without transference, fuel cells
Atomic structure- dual nature of particle, Heisenberg’s uncertainty principle, Schrodinger’s wave equation atomic orbitals, quantum numbers, shapes of s,p,d. orbitals, Aufbau principle and Pauli’s exclusion principle, Hund’s law, electronic configuration of elements, the modern periodic table, periodic properties of the elements and their variation in the periodic table, chemical bond- Ionic bond, lattice energy, Born- Haber cycle, salvation energy, Covalent bond (Fajan’s rule) Bond order, energy level diagram, of homonuclear and heteronuclear molecules, Hybridisation and shapes of inorganic molecules and ions, valence shell electron pair repulsion theory and its application, stability of the nucleus, mass defect and nuclear binding energy, radioactivity, nuclear reactions-fusion and fission, carbon dating.
S-block elements-chemistry of lithium and beryllium, abnormal behavior, and diagonal relationship.
P-block elements- chemical reactivity of elements in the group, inert pair effect, the structure of their hydrides and halides, oxyacids of N, P, S and halogens, interhalogens
d-block elements: General characteristics- variable oxidation state, complex formation, magnetic properties, color, and catalytic properties,
coordination compounds-nomenclature, stereochemistry of metal, complex and isomerization, effective atomic number and valence bond theory, crystal field theory, crystal field splitting into tetrahedral and Octahedral complexes, crystal field stabilization energy substitution reaction in square planar complexes, electronic spectrum, molecular orbital energy level diagram in tetrahedral and octahedral complexes (bond only) orgel energy level diagram for d-1 and d_9 states
Organometallic chemistry- Definition, nomenclature, and classification of organometallic compounds
Bioinorganic chemistry- Structure and function of myoglobin Hemoglobin, chlorophyll, and cyano cobalamine-
f-block elements: Electronic structure, lanthanide contraction and its consequences, magnetic and spectral properties, and their differences from transition metalsion exchange and solvent extraction methods of separation of lanthanides chemistry of actinides.
A- ORGANIC CHEMISTRY:-
1- ORGANIC CHEMISTRY- Some Basic Principles Techniques:-
(a) Classification of organic compounds
(b) I UPAC Nomenclature of organic compounds
(c) Types of organic reaction
(d) Mechanism of organic reaction- Homolytic & Hetrolytic fission of covalent Bond, carbocations, cambanians carbenes, free Radicals, Electrophile & Nueleophile Sn 1 & sn 2 reaction
(e) Electronic Displacements in covalent Bond- Inductive effect, electromeric effect Resonance, Hyperconjugation
(f) purification of organic Compounds:- fractional Distillation, chromatography
(g) estimation of elements in organic compounds
structural & stereo Isomerism, (Geometrical & optical Isomerism) Tautormerism conformation
a- General methods of preparation, physical & chemical properties of Alkane, Alkene & Alkynes, Location of double bonds by ozonolysis of Alkene.
b- Aromatic Hydrocarbon:-
Benzene- Its structure, resonance Aromaticity preparation & physical and chemical properties of Benzene
Mechanism of electrophilic substitution- nitration, sulphonation, Halogenation, Friedel craft’s Alkylation & Acylation. Directive Influence of groups in monosubstituted benzene. Carcinogenicity & (Toxicity chemistry of toluene)
c- Derivatives of Benzene:-
Preparation, Physical & chemical properties of Phenol, Aniline, Anisole Benzaldehyde & Benzoic Acid
General Methods of preparation, physical and chemical properties preparation and properties of chloroform and iodoform, Freon
5- Alcohols:- classification, General methods of preparation, Physical & chemical properties, mechanism, of dehydration of Alcohol, Denatured spirit, power alcohol, Absolute Alcohol fermentation of Alcohol Properties of Glycerol.
- Aldehyde & Ketones:-
General Methods of preparation, Physical & chemical properties, mechanism of Nucleophilic addition. 7- Ether:- General methods of preparation of ether, physical & chemical Properties of Ether &uses
8- Carboxylic acid and its Derivatives:-
General Methods of preparation physical and properties, the influence of substituents group on acidic nature of carboxylic acid, General methods of preparation & properties of acid, Halide, ester, Amide,& Anhydride
9- Organic compounds containing nitrogen:-
a- Amines:- classification, general methods of preparation & properties, the basic character of amines, Distinction between primary secondary and tertiary amines
b- Nitro Compounds:-
General methods of preparation & properties of nitro compounds
c- Cyanides & Isocyanides:-
General methods of preparation & properties of cyanides & isocyanides
a- Carbohydrates:- classification, Molisch’s test of carbohydrate, Glucose & fructose: Preparation & properties, open & Ring structure of glucose mutarotation, Annomers.
b- Proteins: Alpha Amino acids, peptide bond, polypeptide, protein, the structure of protein- Primary, secondary & tertiary structure, denaturation of proteins, Zwitter ion, Isoelectric points;
c- Lipids & hormones; oil & fats introduction, the difference between oil & fats properties.
steroids- Natural & Artificial steroid Hormones- classification & physiological function
d- Vitamins- classification & functions deficiency diseases of vitamins
e- Nucleic acids-
Nucleotides & nucleosides, Difference between DNA and RNA primary structure of DNA DNA fingerprinting
11- Polymers:- classification natural & synthetic polymers, methods of polymerization (addition & condensation) addition polymers-polythene, Teflon, PVC buna-s, Buna-N condensation polymer-Nylon 6, NyIon 6,6, bakelite, methyl melamine, Biodegradable & non-biodegradable polymers
12- Chemistry in everyday life:-
a- chemicals in medicine:- Analgesic, tranquilizers, Antiseptics, Disinfectant, antimicrobials, antibiotics, antacids, antihistamines. antioxidants
b- chemicals in foods: food preservative, artificial sweetening agent,
c- cleansing agents-difference between soaps & detergents cleansing action of Soaps.
UPPSC Lecturer Syllabus
Section:- (A)- BOTANY
(1) Plant Diversity-
(a) Classification (Taxonomy) of plants.
(b) Study of habits and habitats, Structure and reproduction of the followings-
(v) Angiosperm with the following families- Cruciferae, Compositae, Malvaceae, Liliaceae, and Solanaceae.
(2) Angiosperms- Morphology and Morphological Modifications in roots, stem, leaves, etc. Histology, growth, reproduction, and development.
(3) Plant Physiology-
(i) Water Relations-Transpiration, Translocation.
(iii) Respiration and metabolism.
(iv) Plant Nutrition (Nutrients, Nitrogen fixation).
(v) Plant growth regulators (Phytohormones).
(vi) Flowering and Stress Physiology
(vii) Plant growth and movements.
(4) Microbiology- (i) Viruses, Phytoplasma, Archaebacteria, Eubacteria.
(ii) Fungi (general characteristics, classification growth, and reproduction, life cycle).
(iii) Economic importance of Micro-organisms.
(5) Economic Botany-
(i) Medicinal and Aromatic Plants.
(ii) Food Plants.
(iii) Forage and Fodder Plants.
(iv) Fibre Crops.
(v) Fruit and Vegetable Plants.
(vii) Ornamental Plants.
(viii) Oil Yielding Plants.
(x) Miscellaneous uses of Plants.
(6) Plant Pathology
(i) Causes, effects, control, and cure of various Plant diseases.
(ii) Biological Control of Various Plant weeds, diseases, and parasites.
(7) Ecology and Environment-
(i) Concept of Ecology and Environment
(ii) Various Habitats & Ecological Niches.
(iii) Ecosystem- Structure and function, Ecosystem Stability, carrying capacity, Food- chain, Food -web, Energy flow, Ecological Pyramids, Biomes.
(iv) Population, biotic community.
(v) Bio-geo-Chemical Cycles.
(vi) Ecological Succession.
(vii) Natural Resources and their conservation.
(viii) Biodiversity and its conservation (In-situ and Ex-situ).
(ix) Environmental Pollution- Causes and its ill effects. Air, Water, and Soil Pollution. Radioactive pollution, Noise Pollution, Ozone depletion, Acid rain, Eutrophication, Biological magnification, Ocean pollution, Ocean acidification, Control and prevention of various environmental Pollutions. Climate change, global warming and green-house effect, Environmental management. Renewable energy sources, food security. for the rising human population.
Section – B
(1) Animal Diversity-
(i) Animal Taxonomy with characteristic features.
(i) Classification of Non-chordate phyla.
(ii) Morphology, Anatomy, Nutrition, Respiration, and reproduction of the following Non-chordates- Amoeba, Sycon Hydra, Ascaris, Cockroach, Pila, and Star-fish.
(iii) Parasitic protozoa
(iv) Parasitic adaptation in Helminths.
(v) Economic importance of insects.
(i) Classification of chordates and various classes of chordates with characteristic features and examples.
(ii) Aquatic adaptation in fishes.
(iii) Origin and evolution of terrestrial chordates.
(iv) Flying adaptations in birds.
(v)Phylogeny of Prototheria, Metatheria, and Eutheria.
(4) Anatomy of – Frog, Pigeon, and Rabbit.
(5) Animal Histology- Study of various tissues.
(6) Animal Physiology and Biochemistry-
(i) Nutrition and Digestion.
(ii) Respiration and metabolism.
(iii) Circulation-blood Heart. & Circulatory system.
(iv) Osmoregulation and Excretion.
(v) Movement and locomotion.
(vi) Nervous coordination and integration. Sense Organs.
(vii) Chemical coordination (Hormones and pheromones).
(viii) Immune system.
(7) Animal Embryology-
(ii) Fertilization in lower and higher animals.
(iii) Types of Eggs and cleavage.
(v) Development of Frog and Metamorphosis.
(vi) Foetal membranes in Birds.
(vii) Placenta in mammals. Regeneration.
(viii) Human reproduction and reproductive physiology.
(8) Cell Biology (Cytology and Molecular Biology)
(i) Prokaryotic and eukaryotic cells- their structure and properties.
(ii) Cell division (mitosis and meiosis).
(iii) Structure and functions of various cell organelles.
(iv) Chromosome structure and their behavior during cell division.
(v) Nucleic acids-Molecular structure of DNA and RNA.
DNA ‘as genetic material
DNA replication and repair.
(vi) Genetic: code central dogma, protein synthesis, and Gene expression.
(i) Mendel’s laws of inheritance.
(ii) Co-dominance- and incomplete dominance and interaction of Genes.
(iii) Chrosomal theory of inheritance.
(iv) Linkage and crossing over.
(vi) Multiple gene inheritance and polypody.
(vii) Human genetic disorders.
(i) Concepts, principles, and scope of Biotechnology.
(ii) Tools and techniques in Biotechnology.
(iii) Recombinant DNA technology and its applications in human welfare.
(iv) Tissue culture, somatic hybridization.
(v) Genetically modified Organisms, GM. crops (Risk and concerns), Gene Bank, and ethical concerns.
(11) Organic Evolution-
(i) concept and principles of evolution.
(ii) Origin of life.
(iii) Theories of evolution (Lamark, Darwin).
(iv) Evidence for evolution.
(v) Neo-Darwinism and synthetic theory of evolution.
(vii) Human evolution.
UPPSC Lecturer Syllabus
- Relation and functions: Types of relations: reflexive, symmetric, transitive, and equivalence relations. Equivalence class. One-one and onto functions, composite of functions, the inverse of a function, Binary operation.
(i) Matrices: Types of matrices, zero matrix, transpose of a matrix, symmetric and skew-symmetric Matrices. Addition, multiplication & scalar multiplication of matrices. Singular and non-singular matrices. Invariable matrices.
(ii) Determinants: Determinants of a square matrix (up to 3×3 matrix) Properties of determinants, Adjoin, and inverse of a square matrix. Consistency and number of solutions of the system of linear equations by examples. Solving system of linear equations in two or three variables (having unique solutions).
(iii) Theory of equations of degree greater than or equal to two. Arithmetical, Geometrical, and Harmonic progressions. Permutations and combinations, Bionomical theorem. Sum of exponential and logarithmic series.
(iv) Probability: Multiplication theorem on probability, Conditional probability, independent events. Total probability. Bayes’s theorem distribution.
(i) Limit of a function: Continuity & differentiability, derivative of composite functions, and differentiation of different types of functions. Chain rule, Roles theorem, and Lagrange mean value theorem, Maclaurins & Taylor’s series. L. Hospitals rule, partial differentiation, successive differentiation, Leibnitz theorem, equation of tangent & normal to a given curve, Maxima, minima, increasing and decreasing functions.
(ii) Integration: Various methods of integration definite integration as a limit of sum, Basic properties of definite integrals & evaluation of definite integrals. Application in finding the area under simple curves of spheres, cones & cylinders.
(iii) Differential equations: Order and degree of differential equations. Formation of differential equations whose general solution is given. Solution of differential equations of Ist order & Ist degree. Linear differential equations with constant coefficients Homogeneous differential equations.
- Coordinate geometry of two dimensions:
Equation of the pair of straight lines inhomogeneous and non-homogeneous form. Conditions when a non-homogeneous equation of 2nd degree represent circle, parabola ellipse, and hyperbola. equation of tangents & normals to the above conics. Common tangents to the two conics, Pair of tangents. Chord of contacts, polar lines to the above conics.
- Vectors and three-dimensional geometry:
(i) Vectors: Vector & scalars. Unit vectors, Direction cosines/ratios of a vector. Multiplication of a Vector by scalar, dot product, the cross product of vector and their in physics (work done and moments, angular velocity, projection of a vector on a line. Angle between two vectors.)
(ii) Three dimension Geometry: Direction cosine/ratios of a line joining two points, Cartesian and vector equation of a line. Coplanar and skew lines, the shortest distance between two lines, cartesian and vector equation of a plane. The angle between (a) two lines (b) two planes (c) A-line and a plane Distance of a point from a plane. The intersection of two-line, Intersection of a line of plane & intersection of two planes. Equation of a plane passing through the intersection of two planes.
(iii) Equation of a sphere, cones cylinders.
- Group: Examples- especially the group of nth roots of unity, group of residue class modulo n and modulo p where p is a prime. Subgroups, Homomorphism and isomorphisms properties of Homomorphism. Subgroups generated by a subset. Order of element in a group, Cyclic group, Symmetric group – Sn. Lagrange theorem, Fermat’s theorem with application point of view. Normal subgroups, Fundamental theorem of Homomorphism, Endomorphism, automorphism, First isomorphism theorem, and second isomorphism theorem.
Ring and field with simple examples as -(Zn,.+,) & (zp,.+)
Linear Algebra: vector space with examples, subspace, linear dependence and independence, Basis and dimension of a vector space, Quotient space, Sum, and direct slim of spaces. Linear transformation, Kernel, and image, of a-linear transformation, Rank, and nullity of linear transformations, Rank nullity theorem. Composite of linear transformations and their rank & nullity. Singular and non-singular linear transformation, Transpose, of linear transformations, matrix of a linear transformation. Vector differentiation: Gradient, divergence, curl, first-order vector identities. Directional derivatives (with application point of view).
Vector integration: Line integral; surface integral, volume integral, Green’s theorem, Gauss-divergence theorem, stokes’ theorem, (From application point of view).
Rieman integration: Integration of discontinuous functions, Lower and upper integrals of bounded functions, Integration of a step function, and signum function.
Statics: Equilibrium of a body under the action Of-three forces, coplanar forces, Equilibrium of a Body Under the Action of a system of coplanar forces, Centre of gravity catenary Friction.
Dynamics: Motion of a projectile in a vertical plane under gravity, Work power, and energy Direct impact of smooth bodies, Radial, and transverse Velocity and acceleration. Tangential and normal acceleration.
Trigonometry: Trigonometric equations, Properties of triangles Inverse circular functions, Height and distance, Complex numbers, D-movers theorem & its application, nth roots of unity.