UPPSC Aashram Paddhati Lecturer Syllabus 2021 उत्तर प्रदेश प्रवक्ता राजकीय आश्रम पद्धति इण्टर कालेज परीक्षा 2021 UPPSC Lecturer Aashram Paddhati Inter College Examination 2021 Uttar Pradesh PSC Lecturer Aashram Paddhati Written Exam Pattern 2021 UPPSC GAPIC Selection Process of Advertisement No. A-3/E-1/2021
UPPSC Aashram Paddhati Lecturer Syllabus 2021
Table of Contents
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Selection Process :
Preliminary Examination
Exam Pattern :
Exam Pattern for the Written Exam is as Follows:-
- प्रारम्भिक परीक्षा में सामान्य अध्ययन/वैकल्पिक विषय का एक प्रश्नपत्र होगा जो वस्तुनिष्ठ व बहुविकल्पी प्रकार का होगा।
- इसमें प्रश्नों की संख्या 120 (वैकल्पिक विषय के 80 प्रश्न तथा सामान्य अध्ययन के 40 प्रश्न) होगा जो कुल 300 अंकों का होगा।
- प्रारम्भिक परीक्षा का समय 2 घण्टे का होगा।
Exam Syllabus :
Exam Syllabus for Examination is given below :-
General Studies
- General Science (High School Standard)
- History of India
- Indian National Motion
- Indian Polity, Economy & Culture
- Indian Agriculture, Commerce & Trade
- World Geography & Indian Geography & Pure assets of India
- Current National and International Important events
- Logic & Reasoning based on General Intelligence.
- Particular information concerning Education, Culture, Agriculture, Industry Trade, Dwelling & Social Traditions of Uttar Pradesh.
- Elementary Mathematics as much as eighth level:- Arithmetic, Algebra and Geometry.
- Ecology and Environment.
वैकल्पिक विषय (Optionally available Subject)
वैकल्पिक विषयों का पाठ्यक्रम मुख्य परीक्षा की भाँति होगा।
Mains Examination
Exam Pattern :
Exam Pattern for the Written Exam is as Follows:-
प्रश्नपत्र | समय | पूर्णांक | |
प्रथम | सामान्य हिन्दी एवं निबन्ध (परम्परागत) | 02 घण्टा | 100 अंक |
द्वितीय | वैकल्पिक विषय (परम्परागत) | 03 घण्टा | 300 अंक |
Exam Syllabus :
Exam Syllabus for Examination is given below :-
प्रथम खण्ड – सामान्य हिन्दी – निर्धारित अंक-50
- अपठित गद्यांश का संक्षेपण, उससे सम्बन्धित प्रश्न, रेखांकित अंशों की व्याख्या एवं उसका उपयुक्त शीर्षक।
- 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:-
- साहित्य, संस्कृति
- राष्ट्रीय विकास योजनायें/क्रियान्वयन
- राष्ट्रीय-अन्तर्राष्ट्रीय, सामयिक सामाजिक समस्यायें/निदान
- विज्ञान तथा पर्यावरण
- प्राकृतिक आपदायें एवं उनके निवारण
- कृषि, उद्योग एवं व्यापार
(2) Optionally available Subjects
वैकल्पिक विषय
(द्वितीय प्रश्नपत्र)
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।
वैकल्पिक विषय का पाठ्यक्रम
Physics
(I) MECHANICS:- Vector algebra: scalar and vector merchandise, vector identities, background of vector calculus, idea of line, floor and quantity integrals, physical which means of gradient, divergence and curl, Gauss and Stoke’s theorems.
Centre of mass, rotating body of reference, co riolis force, movement of inflexible our bodies, second of inertia, theorem of parallel and perpendicular axes, motion of inertia of sphere, ring, cylinder and disc. Angular momentum, torque, central force, Kepler’s Law, movement of satellite tv for pc (together with geostationary satellite tv for pc), Galilieon transformation, special concept of relativity, Michelson – Morley experiment, Lorentz transformation equations, variation of mass and size with velocity, time dilation, addition of velocities and mass-energy equivalence relation.
Stream line and turbulent motions, Reynold’s number, Stoke’s law, Poiseulle’s components, stream of liquid by way of slender tube. Bernoulli’s components with applications, floor pressure, Stress- pressure relationship, Hooke’s Law, modulii of elasticity and interrelation between them Poisson’s ratio, elastic energy.
(II) THERMAL PHYSICS:- Idea of temperature and the zeroth law, first law of thermodynamics and inside energy, isothermal and adiabatic changes, second law of thermodynamics, Entropy, Carnot cycle and Carnot engine, absolute scale of temperature. Maxwell’s thermodynamical relations. The Clausius- Clapeyron equation, porus plug experiment and Joule Thomson effect.
Kinetic concept of gases, Maxwell distribution law of velocities, calculation of imply velocity, root imply sq. velocity and the Most possible velocity, degrees of freedom, Law of equipartition of energy, particular heats of gases, imply free path, transport phenomena.
Black body radiation, Stefan’s law, Newtons law of cooling Wien’s law, Rayleigh Denims law, Planck’s law, photo voltaic fixed.
Production of low temperatures by adiabatic demagnetization.
(III) WAVES AND OSCILLATIONS:- Oscillation, easy harmonic movement, stationary and progressive waves, damped harmonic-motion, forced oscillations and resonance, sharpness of resonance, wave equation, Aircraft and spherical waves superposition of waves. Fourier analysis of periodic waves- sq. and triangular waves, phase and group velocities, Beats.
(IV) OPTICS: Cardinal points of a coaxial system, easy problems on mixture of skinny lenses eyepiece- Ramsdon and Huygens eyepieces.
Huygen’s precept, circumstances for sustained interference Younger double slit experiment division of amplitude and wavefront, Fresnel biprism, Newtons rings, Michelson-interferometer, diffraction by straight edge, single, double and multiple slits. Rayleigh’s criterion, resolving power of optical devices.
Polarization, production and detection of polarized gentle (linear round and elliptical) Brewster’s law, Huygen’s concept of double refraction, optical rotation, ploearimeters.
LESERS:- Temporal and spatial coherence, stimulated emission, basic concepts about laser emission, Ruby and He-Ne lasers.
(V) ELECTRICITY AND MAGNETISM:- Gauss law and its applications, electrical potential, Kirchoff’s laws and their applications, Wheatstone’s bridge, Biot-Savart law, Ampere’s circuital law, and their applications. Magnetic induction and field power, magnetic field on the axis of round coil, Electro magnetic induction, Faraday’s and Lenz’s law, self and mutual inductances, alternating current, L.C.R. circuits, series and parallel resonance Circuits, high quality factor. Maxwell’s equations and electromagnetic waves transverse nature of electromagnetic waves, Poynting vector, dia-, para-, ferro-, antiferro- and feri-magnetism (qualitative method only), hysterisis.
(VI) MODEREN PHYSICS: Bohr’s concept of hydrogen atom, electron spin, Pauli’s exclusion precept, optical and X-ray spectra, spatial quantization and Stern-Gerlach experiment, vector model of the atom, spectral terms, fine construction of spectral traces J-J and L-S coupling, Zeeman effect, Raman effect, photoelectric effect, Compton effect, de Broglie waves, wave-particle duality, Uncertainty precept, postulates of quantum mechanics, Schrodinger wave equation and its applications to (i) particle in a field (ii) movement throughout a step potential (iii) one dimensional harmonic oscillator, and eigen values, Einstein’s and debye concept of particular warmth of solids. Band concept of solids energy band, Kronig-Penny model in a single dimension, energy hole, distinction between metals, semiconductors and insulators, variation of Fermi level with temperature and efficient mass.
Radio activity, alfa, beta and gamma radiations, elementary concept of alpha decay, nuclear binding energy, Semi emperical mass components, nuclear fission and fussion and nuclear reactors elementary particles, particle accelerator, cyclotron, linear accelerator, Elementary thought’s of tremendous conductivity. (VII) ELECTRONICS:- Intrinsic and extrinsic semiconductors, PN, junction, Zener diode, and their traits, unipolar and bipolar transisters photo voltaic cells, use of diode and transistor for rectification, amplification, oscillation, modulation and detection, waves. Logic gates and their reality tables, some applications.
Chemistry
(A) Physical chemistry Gaseous-state:- Molecular velocity of gases, imply free path and collision diameter, liquification of gases joule thomson effect in excellent and nonideal gases, Joule “Thomson coefficient, inversion temperature, Deviation from excellent gasoline habits vander waals equation of state, Law of corresponding state, crucial constants and their relations with-vander waals constants
Liquid state:- floor Stress, effect of temperature on floor pressure, viscosity, effect of temperature and strain on viscosity.
Stable State:- symmetry in crystal systems, Miller inclices shut packing, coordination number, construction of Nacl and CaF2, crystal-defects.
Thermodynamics:- first law of thermodynamics and its limitations, enthalpies of a system, warmth of response formation, combustion and neutralization, Hess’s law and its application bond energy and resonance energy, warmth capacities at fixed quantity and fixed strain, relationship between. Cp and Cv intensive and intensive properties, statement of second law of thermodynamics Carnot cycle, idea of entropy, variation of entropy with temperature and quantity/strain, idea of free energy: Helmholtz and Gibbs free energies, Gibbs – Helmholtz equation, thermodynamic standards of equilibrium, Clapeyron- clausius equation and its application, van;t hoff equation and Gibbs- Duhem equation.
Dilute solution:- Supreme and non excellent solutions, Raoult’s Law colligative properties (thermodynamic therapy) Lowring of vapour strain, osmotic strain, elevation of boiling point and melancholy of freezing point in solution, irregular colligative properties molecular weight willpower by colligative properties.
Surfacephenomenon- physical and chemical adsorption Fraundlich adsorption isotherm Langmuir adsorption isotherm.
Colloidal State – Coagulation, Coagulation Worth Gold-number, Hardy-Schulze rule, stability of colloids, zeta potential
Chemical Kinetics-Molecularity and order of response, rate of response Zero first second and third order reactions and their willpower effect of temperature on response velocity, energy of activation, catalysis, standards of catalysis, enzymes catalysis, major salt effect in ionic reactions.
Chemical equilibrium- Law of mass action and its application to homogeneous and heterogeneous equilibria, relationship between Kp and Kc. Le chatelier precept and its application to chemical equilibrium, degree of dissociation and irregular; 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,particular and molecular conductances, variation of conductances with dilution of solutions, Kohlausch’s law of independent migration of ions, components affecting the conductances, types of single electrode and their potentials, EMF of the cell, Nernest equation. EMF and equilibrium fixed, idea of focus cell With and with out transference, liquid junction potential chemical cells with out transference, gas cells
B- Inorganic:
Atomic structure- dual nature of particle, Heisenberd’s uncertainity precept, Schrodinger’s wave equation atomic orbitatals, quantum numbers, shapes of s,p,d. orbitals, Aufbau precept and pauli’s exclusion precept, Hunds law, electronic configuration of components, trendy periodic table, periodic properties of the weather and their variation in 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 concept and its application, stability of nucleus, mass defect and nuclear binding energy, radioactivity, nuclear reactions-fusion and fission, carbon courting.
- S-block elements-chemistry of lithium and berilium, irregular habits and diagonal relationship.
- P-block elements- chemical reactivity of components in group, inert pair effect, construction of their hydrides and halides, oxyacids of N, P, S and halogens, interhalogens
- d-block components: General characteristics- variable oxidation state, advanced formation, magnetic properties, color and catalytic properties,
coordination compounds-nomenclature, stereo chemistry of steel, advanced and isomerisation, efficient atomic number and valence bond concept, crystal field concept, crystal field splitting in tetrahedral and Octahedral complexes, crystal field stabilization energy substitution response in sq. planar complexes, electronic spectrum, molecular orbital energy level diagram in tetrahedral and octahedrdal 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- Construction and performance of myoglobin Hemoglobin, chlorophyll and cyano cobalamine- - f-block components: Electronic construction, lanthanide contraction and its penalties, magnetic and spectral properties and their variations from transition metalsion exchange and solvent extraction strategies of separation of lanthanides chemistry of actinides.
A- ORGANIC CHEMISTRY:-
1- ORGANIC CHEMISTRY- Some Basic Rules Methods:-
- (a) Classification of natural compounds
- (b) I UPAC Nomenclature of natural compounds
- (c) Types of natural recation
- (d) Mechanism of natural reaction- Homolytic & Hetrolytic fission of coralent Bond, carbocations, cambanians carbenes, free Radicals, Electrophile & Nueleophile Sn 1 & sn 2 response
- (e) Electronic Displacements in covalent Bond- Inductive effect, electromeric effect Resonance, Hyperconjugation
- (f) purification of natural Compounds:- fractional Distillation, chromatography
- (g) estiation of components in natural compounds
2- Isomerism:-
structural & stereo Isomerism, (Geometrical & optical Isomerism) Tautormerism conformation
3- Hydrocarbon:-
a- General strategies of preparation, physical & chemical properties of Alkane, Alkene & Alkynes, Location of double bonds by ozonolysis of Alkene.
b- Fragrant Hydrocarbon:-
Benzene- It’s construction, resonance Aromaticity preperation & physical and chemical properties of Benzene
Mechanism of electrophlic substitution- nitration, sulphonation, Halogenation, freidal craft’s Alkylation & Acylation. Directive Affect of teams in mono substituted benzene. Carcinogenacity & (Toxicity chemistry of toluene)
c- Derivatives of Benzene:-
Preperation, Physical & chemical properties of Phenol, Aniline, Anisole Benzaldehyde & Benzoic Acid
4- Haloalkanes:-
General Strategies of preperation, physical and chemical properties preparation and properties of chloroform and lodoform, Freon
5- Alcohols:- classification, General strategies of preparation, Physical & chemical properties, mechanism, of dehydration of Alcohol, Denatured spirit, power alcohol, Absolute Alcohol fermentation of Alcohol Properties of Glyecerol.
6. Aldehyde & Ketones:-
General Strategies of preparation, Physical & chemical properties, mechanism of Nucleophilic addition. 7- Ether:- General strategies of preparation of ether, physical & chemical Properties of Ether &makes use of
8- Carborxylic acid and their Derivatives:-
General Strategies of preparation physical and properties, lnfluence of substituents group on acidic nature of carboxylic acid, General strategies of preparation & properties of acid, Halide, ester, Amide,& Anhydride
9- Natural compounds containing nitrogen:-
- Amines:- classification, general strategies of preparation & properties, basic character of Amines, Distinction between major secondry and tertiary amines
- Nitro Compounds:- General strategies of preparation & properties of nitoro compounds
- Cyanides & Isocyanides:- General strategies of preparation & properties of cyanides & isocyanides
10. Bio-molecules:-
- a- Carbohydrates:- classification, Molisch’s test of carbohydrate, Glucose & fructose: Preparation & properties, open & Ring construction of glucose mutarotation, Annomers.
- b- Proteins: Alpha Amino acids, peptide bond, polypeptide, protein, construction of protein- Main, secondry & tertiary construction, denaturation of proteins, Zwitter ion, Iso electrical points;
- c- Lipids & harmones;
oil & fat introducation, distinction between oil & fat properties.
steroids- Pure & Manmade steroid Harmones- classification & physiological perform - d- Nutritional vitamins- classification & features deficiencey ailments of nutritional vitamins
- e- Nucleic acids- Nucleotides & nucleosides, Distinction between DNA and RNA primay construction of DNA DNA finger printing
11- Polymers:- classification pure & artificial polymers, strategies of polymerisation (addition & condensation) addition polymers-polythene, Teflon, PVC buna-s, Buna-N condensation polymer-Nylon 6, NyIon 6,6, backelite, methyl melamine, Biodegradable & non biodegradable polymers
12- Chemistry in on a regular basis life:-
- a- chemical compounds in medicine:- Analgesic, tranquilizers, Antiseptics, Disinfectant, antimicrobials, antibiotics, antacids, antihistamins. antioxidants
- b- chemical compounds in meals: food preservative, artificxal sweetening agent,
- c- cleaning agents-distinction between soaps & detergents cleaning action of Soaps.
Biology
Section:- (A)- BOTANY
(1) Plant Variety-
- Classification (Taxonomy) of plants.
- Study of habits and habitats, Construction and copy of the followings-
- Algae
- Bryophyta
- Pteridophyta
- Gymnosperms
- Angiosperm with the next families- Cruciferae, Compositae, Malvaceae, Liliacae and Solanaceae.
(2) Angiosperms- Morphology and Morphological Modifications in roots, stem, leaves and so on. Histology, growth, copy and development.
(3) Plant Physiology-
- Water Relations-Transpiration, Translocation.
- Photocynthesis.
- Respiration and metabolism.
- Plant Vitamin (Vitamins, Nitrogen fixation).
- Plant growth regulators (Phytohormones).
- Flowering and Stress Physiology
- Plant growth and actions.
(4) Microbiology-
- Viruses, Phytoplasma, Archaebacteria, Eubacteria.
- Fungi (general traits, classification growth and copy, life cycle).
- Economic significance of Micro-organisms.
(5) Economic Botany-
- Medicinal and Fragrant Plants.
- Food Plants.
- Forage and Fodder Plants.
- Fibre Crops.
- Fruit and Vegetable Plants.
- Ethnobotany.
- Decorative Plants.
- Oil Yielding Plants.
- Timber Plants.
- Miscellaneous makes use of of Plants.
(6) Plant Pathology
- Causes, effects, control and treatment of varied Plant ailments.
- Organic Control of Numerous Plant weeds, ailments and parasites.
(7) Ecology and Environment-
- Idea of Ecology and Environment
- Numerous Habitats & Ecological Niches.
- Ecosystem- Construction and performance, Ecosystems stability, carrying capability, Food- chain, Food -web, Energy stream, Ecological Pyramids, Biomes.
- Population, biotic community.
- Bio-geo-Chemical Cycles.
- Ecological Succession.
- Pure Sources and their conservation.
- Biodiversity and its conservation (In-situ and Ex-situ).
- Environmental Pollution- Causes and its sick effects. Air, Water and Soil Pollution. Radioactive pollution, Noise Pollution, Ozone depletion , Acid rain, Eutrophication, Organic magnification, Ocean pollution, Ocean acidification, Control and prevention of varied environmental Pollutions. Local weather change, global warming and green- house effect, Environmental management. Renewable energy sources, food Security. for rising human population.
Section – B Zoology
(1) Animal Variety-
(i) Animal Taxonomy with attribute features.
(2) Non-Chordates-
- Classification of Non-chordate phyla.
- Morphology, Anatomy, Vitamin, Respiration and copy of the next Non-chordates- Amoeba, Sycon Hydra, Ascaris, Cockroach, Pila and Star-fish.
- Parasitic protozoa
- Parasitic adaptation in Helminths.
- Economic significance of bugs.
(3) Chordates-
- Classification of chordates and various-classes of chordates with attribute features and examples.
- Aquatic adaptation in fishes.
- Origin and evolution of terrestrial chordates.
- Flying diversifications in birds.
- Phylogeny of prototheria, Metatheria and eutheria.
(4) Anatomy of – Frog, Pigeon and Rabbit.
(5) Animal Histology- Study of varied tissues.
(6) Animal Physiology and Biochemistry-
- Vitamin and Digestion.
- Respiration and metabolism.
- Circulation-blood Coronary heart. & Circulatory system.
- Osmo regulation and Excretion.
- Motion and locomotion.
- Nervous co-ordination and integration. Sense Organs.
- Chemical co-ordination (Hormones and pheromones).
- Immune system.
(7) Animal Embryology-
- Gametogenesis
- Fertilization in lower and higher animals.
- Types of Eggs and cIeavage.
- Organogenesis.
- Development of Frog and Metamorphosis.
- Foetal membranes in Birds.
- Placenta in mammals. Regeneration.
- Human copy and reproductive physiology.
(8) Cell Biology (Cytology and Molecular Biology)
- Prokaryotic and eukaryotic cells- their construction and properties.
- Cell division (mitosis and meiosis).
- Construction and features of varied cell organelles.
- Chromosome construction and their habits throughout cell division.
- Nucleic acids-Molecular construction of DNA and RNA.
DNA ‘as genetic material
DNA replication and restore. - Genetic: code central dogma, protein synthesis and Gene expression.
(9) Genetics-
- Mendel’s laws of inheritance.
- Co-dominance- and incomplete dominance and interplay of Genes.
- Chrosomal concept of inheritance.
- Linkage and crossing over.
- Sex-determination.
- Multiple gene inheritance and polypody.
- Human genetic problems.
- Mutation.
(10) Biotechnology-
- Ideas, rules and scope of Biotechnology.
- Instruments and strategies in Biotechnology.
- Recombinant DNA technology and its applications in human welfare.
- Tissue culture, somatic hybridization.
- Genetically modified Organisms, GM. crops (Threat and considerations), Gene Bank and moral considerations.
(11) Natural Evolution-
- Idea and rules of evolution.
- Origin of life.
- Theories of evolution (Lamark, Darwin).
- Evidences for evolution.
- Neo-Darwinism and artificial concept of evolution.
- Variations.
- Human evolution.
Mathmatics
1. Relation and features: Types of relations: reflexive, Symmetric, transitive and equivalence relations. Equivalence class. One-one and onto features, composite of features, inverse of perform, Binary operation.
2. Algebra:
- 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. Invartable matrices.
- Determinants: Determinants of a sq. matrix (as much as 3×3 matrix) Properties of determinants, Adjoin and inverse of a sq. matrix. Consistency and number of solutions of system of linear equations by examples. Fixing system of linear equations in two or three variables (having unique solutions).
- Idea of equations of degree greater than or equal to 2. Arthmatical, Geometrical and Hormonical progressions. Permutations and combos, Bionomical theorem. Sum of exponential and logerthimic series.
- Probability: Multiplication theorem on probability, Conditional probability, Independent events. Total probability. Bayes’s theorem distribution.
3. Calculus .
- Limit of a perform: Continuity & differentiability, spinoff of composite features, and differentiation of various types of features. Chain rule, Roles theorem and lagrange imply worth theorem, Maclaurins & Taylor’s series. L. Hospitals rule, partial differentiation, successive differentiation, Leibnitz theorem, equation of tangent & regular to a given curve, Maxima, minima, growing and lowering features.
- Integration: Numerous strategies of intergration particular integration as a limit of sum, Basic properties of particular integrals & evalution of particular integrals. Application to find the area under easy curves of spheres, cones & cylinders.
- Differential equations: Order and degree of a differential equations. Formation of differential equations whose general solution is given. Solution of differential equations of Ist order & Ist degree. Linear differential equations with fixed coefficients Homogeneous differential equations.
4. Co-oridnate geometry of two dimensions:
Equation of the pair of straight traces in homogeneous and non homogeneous form. Situations when a non homogeneous equation of 2nd degree symbolize circle, parabola ellipse and hyperbola. equation of tangents & normals to the above conics. Frequent tangents to the 2 conics, Pair of tangents. Chord of contacts, polarlines to the above conics.
5. Vectors and three dimensional geometry:
- Vectors: Vector & scalars. Unit vectors, Direction cosines/ratios of a vector. Multiplication of a Vector by scalar, dot product, cross product of vector and their in physics (work done and moments, anguler velocity, projection of a vector on a line. Angle between two vector.)
- Three dimension Geometry: Direction cosine/ratios of line becoming a member of two points, Cartesian and vector equation of a line. Coplanar and skew traces, shortest distance between to traces, cartesian and vector equation of a airplane. Angle between (a) two traces (b) two planes (c) A line and a airplane Distance of a point from a airplane. Intersection of two line, Intersection of a line of airplane & intersection of two airplane. Equation of a airplane passing by way of the intersection of two planes.
- Equation of a sphere, cones cylinders.
6. Group: Examples- particularly the group of nth rots of unity, group of residue class modulo n and modulo p where p is a chief. Subgroups, Homomorphism and isomorphisms properties of Homomorphism. Subgroups generated by a subset. Order of aspect in a group, Cyclic group, Symmetric group – Sn. Lagrange theorem, Fermat’s theorem with application point of view. Regular subgroups,Elementary theorem of Homomorphism, Endomorphisim, automorphism, First isomorphism theorem and second isomorphism theorem.
Ring and field with easy 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 areas. Linear transformation, Karnel and picture, of a-linear transformation, Rank and nullity of linear transformations, Rank nullity theorem. Composite of linear transformations and its rank & nullity. Singular and non singular linear transformation, Transpose, of a 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; floor integral, quantity integral, Green’s theorem, Gauss-divergence theorem, stokes’s theorem, (From application point of view).
Rieman integration: Integration of discontinuous features, Lower and upper integals of a bounded features, Integration of a step perform and signum perform.
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: Movement of a projectile in vertical airplane under gravity, Work power and energy Direct influence of easy our bodies, Radial and transverse Velocity and acceleration. Tangential and regular acceleration.
Trignometry: Trignometric equations , Properties of triangles Inverse round features, Height and distance, Advanced numbers, D-mioivers theorem & its application, nth roots of unity.
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