ICAR AIEEA (UG)
Official Syllabus:
Note: Taking reference from Notification of ICAR AIEEA(UG) 2024.
Indicative Syllabus for ICAR AIEEA(UG) 2024 :
1. PHYSICS:
Unit I: Electrostatics
Electric charges and their conservation.
- Coulomb’s law – force between two point charges, forces between multiple charges.
- Superposition principle and continuous charge distribution.
Electric field:
- Electric field due to a point charge, electric field lines.
- Electric dipole: Electric field due to a dipole, torque on a dipole in a uniform electric field.
Electric flux:
- Statement of Gauss’s theorem and its applications to find the field due to:
- Infinitely long straight wire.
- Uniformly charged infinite plane sheet.
- Uniformly charged thin spherical shell (field inside and outside).
Electric potential:
- Potential difference, electric potential due to a point charge, dipole, and system of charges.
- Equipotential surfaces, the electrical potential energy of a system of two point charges, and electric dipoles in an electrostatic field.
Conductors and insulators:
- Free charges and bound charges inside a conductor.
- Dielectrics and electric polarization.
Capacitors and capacitance:
- The combination of capacitors in series and parallel.
- Capacitance of a parallel plate capacitor with and without dielectric medium between the plates.
- Energy stored in a capacitor, Van de Graaff generator.
Unit II: Current Electricity
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, emf of a cell, combination of cells in series and parallel.
Kirchhoff’s laws:
- Simple applications.
- Wheatstone bridge, Meter Bridge.
Potentiometer:
- Principle and applications to measure potential difference and for comparing emf of two cells.
- Measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism
Magnetic field:
- Concept of the magnetic field, Oersted’s experiment.
- Biot-Savart law and its application to current-carrying circular loop.
Ampere’s law:
- 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 – its current sensitivity and conversion to ammeter and voltmeter.
Current loop as a magnetic dipole:
- 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.
Magnetic substances:
- Para-, dia-, and ferromagnetic substances, with examples.
- Electromagnets and factors affecting their strengths.
- Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents
Electromagnetic induction:
- Faraday’s law, induced emf, and current.
- Lenz’s Law, Eddy currents.
- Self and mutual inductance.
Alternating currents:
- Peak and RMS values of alternating current/voltage.
- Reactance and impedance.
- LC oscillations (qualitative treatment only), LCR series circuit, resonance.
- Power in AC circuits, wattless current.
- AC generator and transformer.
Unit V: Electromagnetic Waves
Need for displacement current.
- 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.
- Elementary facts about their uses.
Unit VI: Optics
Reflection of light:
- Spherical mirrors, mirror formula.
Refraction of light:
- Total internal reflection and its applications, optical fibers, refraction at spherical surfaces, lenses, thin lens formula, lens maker’s formula.
- Magnification, power of a lens, combination of thin lenses in contact and combination of a lens and a mirror.
- Refraction and dispersion of light through a prism.
Scattering of light:
- Blue color of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments:
- Human eye, image formation, and accommodation.
- Correction of eye defects (myopia and hypermetropia) using lenses.
- Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.
Wave optics:
- Wave front and Huygens’ Principle.
- Reflection and refraction of plane waves at a plane surface using wave fronts.
- Proof of laws of reflection and refraction using Huygens’ Principle.
Interference:
- Young’s double slit experiment and expression for fringe width.
- Coherent sources and sustained interference of light.
Diffraction:
- Diffraction due to a single slit, width of central maximum.
- Resolving power of microscopes and astronomical telescopes.
Polarization:
- Plane polarized light, Brewster’s law, uses of plane polarized light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation
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 (experimental details omitted; only the conclusion explained).
Unit VIII: Atoms and Nuclei
Alpha-particle scattering experiment:
- Rutherford’s model of the atom.
- Bohr model, energy levels, hydrogen spectrum.
Nucleus:
- Composition and size of nucleus, atomic masses, isotopes, isobars, isotones.
- Radioactivity: Alpha, beta, and gamma particles/rays, and their properties.
- Radioactive decay law.
- Mass-energy relation, mass defect.
- Binding energy per nucleon and its variation with mass number.
- Nuclear fission and fusion.
Unit IX: Electronic Devices
Energy bands in solids:
- Qualitative ideas only, conductors, insulators, and semiconductors.
Semiconductor diode:
- I-V characteristics in forward and reverse bias, diode as a rectifier.
- I-V characteristics 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).
- Transistor as a switch.
Unit X: Communication Systems
Elements of a communication system:
- Block diagram only.
Bandwidth of signals:
- Speech, TV, and digital data.
- Bandwidth of transmission medium.
Propagation of electromagnetic waves:
- In the atmosphere, sky, and space wave propagation.
- Need for modulation.
- Production and detection of an amplitude-modulated wave.
2. CHEMISTRY:
Unit I: Solid State
Classification of solids based on different binding forces:
Molecular, ionic, covalent, and metallic solids.
- Amorphous and crystalline solids (elementary idea).
- Unit cell in two-dimensional and three-dimensional lattices.
- Calculation of density of unit cell.
- Packing in solids, packing efficiency, voids.
- Number of atoms per unit cell in a cubic unit cell.
- Point defects.
- Electrical and magnetic properties.
- Band theory of metals: Conductors, semiconductors, and insulators, n and p-type semiconductors.
Unit II: Solutions
Types of solutions.
Expression of concentration of solutions of solids in liquids.
- Solubility of gases in liquids.
- Solid solutions.
- Colligative properties:
- The relative lowering of vapor pressure, Raoult’s law.
- Elevation of boiling point, depression of freezing point, osmotic pressure.
- Determination of molecular masses using colligative properties.
- Abnormal molecular mass, Van’t Hoff factor.
Unit III: Electrochemistry
Redox reactions.
- Conductance in electrolytic solutions.
- Specific and molar conductivity - variations of conductivity with concentration.
- Kohlrausch’s Law.
- Electrolysis and laws of electrolysis (elementary idea).
- Dry cell, electrolytic cells, and Galvanic cells.
- Lead accumulator.
- EMF of a cell, standard electrode potential.
- Nernst equation and its application to chemical cells.
- Relation between Gibbs energy change and EMF of a cell.
- Fuel cells, corrosion.
Unit IV: Chemical Kinetics
Rate of a reaction (average and instantaneous).
- Factors affecting rates of reaction: concentration, temperature, catalyst.
- Order and molecularity of a reaction.
- Rate law and specific rate constant.
- Integrated rate equations.
- Half-life (only for zero and first-order reactions).
- Concept of collision theory (elementary idea, no mathematical treatment).
- Activation energy, Arrhenius equation.
Unit V: Surface Chemistry
Adsorption: Physisorption and chemisorption.
- Factors affecting adsorption of gases on solids.
- Catalysis: Homogeneous and heterogeneous, activity and selectivity.
- Enzyme catalysis.
- Colloidal state: Distinction between true solutions, colloids, and suspensions.
- Lyophilic, lyophobic multimolecular and macromolecular colloids.
- Properties of colloids: Tyndall effect, Brownian movement, electrophoresis, coagulation.
- Emulsions – types of emulsions.
Unit VI: General Principles and Processes of Isolation of Elements
Principles and methods of extraction:
- Concentration, oxidation, reduction, electrolytic method, and refining.
- Occurrence and principles of extraction of aluminum, copper, zinc, and iron.
Unit VII: p-Block Elements
Group 15 elements:
- General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties.
- Nitrogen: Preparation, properties, and uses; compounds of nitrogen.
- Preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only).
- Phosphorous: Allotropic forms, compounds of phosphorus.
- Preparation and properties of phosphine, halides (PCl₃, PCl₅), and oxoacids (elementary idea only).
Group 16 elements:
- General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties.
- Dioxygen: Preparation, properties, and uses.
- Classification of oxides, ozone.
- Sulphur: Allotropic forms, compounds of sulfur.
- Preparation, properties, and uses of sulfur dioxide.
- Sulfuric acid: Industrial process of manufacture, properties and uses, oxoacids of sulfur (structures only).
Group 17 elements:
- General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties.
- Compounds of halogens:
- Preparation, properties, and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens (structures only).
Group 18 elements:
- General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses.
Unit VIII: d and f Block Elements
General introduction, electronic configuration, occurrence and characteristics of transition metals.
- General trends in properties of the first-row transition metals: Metallic character, ionization enthalpy, oxidation states, ionic radii, color, catalytic property, magnetic properties, interstitial compounds, alloy formation.
- Preparation and properties of K₂Cr₂O₇ and KMnO₄.
- Lanthanoids: Electronic configuration, oxidation states, chemical reactivity, lanthanoid contraction, and its consequences.
- Actinoids: Electronic configuration, oxidation states, and comparison with lanthanoids.
Unit IX: Coordination Compounds
Coordination compounds: Introduction, ligands, coordination number, color, magnetic properties, and shapes.
- IUPAC nomenclature of mononuclear coordination compounds.
- Bonding: Werner’s theory, VBT, CFT.
- Isomerism: Structural and stereo.
- Importance of coordination compounds: In qualitative analysis, extraction of metals, and biological systems.
Unit X: Haloalkanes and Haloarenes
Haloalkanes:
- Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions.
- Optical rotation.
Haloarenes:
- Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only).
- Uses and environmental effects of: Dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT.
Unit XI: Alcohols, Phenols, and Ethers
Alcohols:
- Nomenclature, methods of preparation, physical and chemical properties (primary alcohols only), identification of primary, secondary, and tertiary alcohols, mechanism of dehydration, uses (with special reference to methanol and ethanol).
Phenols:
- Nomenclature, methods of preparation, physical and chemical properties, acidic nature, electrophilic substitution reactions, uses.
Ethers:
- Nomenclature, methods of preparation, physical and chemical properties, uses.
Unit XII: Aldehydes, Ketones, and Carboxylic Acids
Aldehydes and Ketones:
- Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties, mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes, uses.
Carboxylic Acids:
- Nomenclature, acidic nature, methods of preparation, physical and chemical properties, uses.
Unit XIII: Organic Compounds Containing Nitrogen
Amines:
- Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary, and tertiary amines.
Cyanides and Isocyanides: Mentioned at relevant places in context.
Diazonium salts:
- Preparation, chemical reactions, and importance in synthetic organic chemistry.
Unit XIV: Biomolecules
Carbohydrates:
- Classification (aldoses and ketoses), monosaccharides (glucose and fructose), D-L configuration, oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen): Importance.
Proteins:
- Elementary idea of α-amino acids, peptide bond, polypeptides, proteins, primary, secondary, tertiary, and quaternary structures (qualitative idea only), denaturation of proteins, enzymes.
Hormones:
- Elementary idea (excluding structure).
Vitamins:
- Classification and functions.
Nucleic Acids:
- DNA and RNA.
Unit XV: Polymers
Classification: Natural and synthetic, methods of polymerization (addition and condensation), copolymerization.
- Some important polymers: Natural and synthetic like polythene, nylon, polyesters, bakelite, rubber.
- Biodegradable and non-biodegradable polymers.
Unit XVI: Chemistry in Everyday Life
- Chemicals in medicines: Analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines.
- Chemicals in food: Preservatives, artificial sweetening agents, elementary idea of antioxidants.
- Cleansing agents: Soaps and detergents, cleansing action.
3. BIOLOGY:
Unit I: Reproduction
Reproduction in Organisms:
Reproduction, a characteristic feature of all organisms for continuation of species. Modes of reproduction – Asexual and sexual.
- Asexual reproduction: Modes - Binary fission, sporulation, budding, gemmule, fragmentation; vegetative propagation in plants.
Sexual reproduction in flowering plants:
- Flower structure.
- Development of male and female gametophytes.
- Pollination – types, agencies and examples.
- Outbreeding devices.
- Pollen-pistil interaction.
- Double fertilization.
- Post fertilization events: Development of endosperm and embryo, development of seed and formation of fruit.
- Special modes: Apomixis, parthenocarpy, polyembryony.
- Significance of seed and fruit formation.
Human Reproduction:
- Male and female reproductive systems.
- Microscopic anatomy of testis and ovary.
- Gametogenesis: Spermatogenesis and oogenesis.
- Menstrual cycle.
- Fertilization, embryo development up to blastocyst formation, implantation.
- Pregnancy and placenta formation (elementary idea).
- Parturition (elementary idea).
- Lactation (elementary idea).
Reproductive Health:
- Need for reproductive health and prevention of sexually transmitted diseases (STD).
- Birth control - Need and methods, contraception and medical termination of pregnancy (MTP).
- Amniocentesis.
- Infertility and assisted reproductive technologies - IVF, IUI, ZIFT, GIFT (elementary idea for general awareness).
Unit II: Genetics and Evolution
Heredity and Variation:
- Mendelian Inheritance.
- Deviations from Mendelism: Incomplete dominance, co-dominance, multiple alleles and inheritance of blood groups, pleiotropy.
- Elementary idea of polygenic inheritance.
- Chromosome theory of inheritance.
- Chromosomes and genes.
- Sex determination: In humans, birds, honeybee.
- Linkage and crossing over.
- Sex-linked inheritance: Haemophilia, color blindness.
- Mendelian disorders in humans: Thalassemia.
- Chromosomal disorders in humans: Down’s syndrome, Turner’s and Klinefelter’s syndromes.
Molecular Basis of Inheritance:
- Search for genetic material and DNA as genetic material.
- Structure of DNA and RNA.
- DNA packaging.
- DNA replication.
- Central dogma.
- Transcription, genetic code, translation.
- Gene expression and regulation - Lac Operon.
- Genome and human genome project.
- DNA fingerprinting.
Evolution:
- Origin of life.
- Biological evolution and evidences for biological evolution (Paleontological, comparative anatomy, embryology, and molecular evidence).
- Darwin’s contribution.
- Modern Synthetic theory of Evolution.
- Mechanism of evolution - Variation (mutation and recombination) and natural selection with examples, types of natural selection.
- Gene flow and genetic drift.
- Hardy-Weinberg’s principle.
- Adaptive Radiation.
- Human evolution.
Unit III: Biology and Human Welfare
Health and Disease:
- Pathogens: Parasites causing human diseases (Malaria, Filariasis, Ascariasis, Typhoid, Pneumonia, common cold, amoebiasis, ringworm).
- Basic concepts of immunology - Vaccines.
- Cancer, HIV, and AIDS.
- Adolescence, drug, and alcohol abuse.
Improvement in Food Production:
- Plant breeding, tissue culture, single cell protein, biofortification.
- Apiculture and animal husbandry.
Microbes in Human Welfare:
- In household food processing, industrial production, sewage treatment, energy generation, and as bio-control agents and biofertilizers.
Unit IV: Biotechnology and Its Applications
Principles and Process of Biotechnology:
- Genetic engineering (Recombinant DNA technology).
Application of Biotechnology in Health and Agriculture:
- Human insulin and vaccine production.
- Gene therapy.
- Genetically modified organisms: Bt crops.
- Transgenic animals.
- Biosafety issues - Biopiracy and patents.
Unit V: Ecology and Environment
Organisms and Environment:
- Habitat and niche.
- Population and ecological adaptations.
- Population interactions: Mutualism, competition, predation, parasitism.
- Population attributes: Growth, birth rate and death rate, age distribution.
Ecosystems:
- Patterns, components.
- Productivity and decomposition.
- Energy flow.
- Pyramids of number, biomass, energy.
- Nutrient cycling (carbon and phosphorous).
- Ecological succession.
- Ecological services: Carbon fixation, pollination, oxygen release.
Biodiversity and Its Conservation:
- Concept of biodiversity.
- Patterns of biodiversity.
- Importance of biodiversity.
- Loss of biodiversity.
- Biodiversity conservation: Hotspots, endangered organisms, extinction, Red Data Book, biosphere reserves, national parks, sanctuaries, sacred groves, in-situ and ex-situ.
Environmental Issues:
- Air pollution and its control.
- Water pollution and its control.
- Agrochemicals and their effects.
- Solid waste management.
- Radioactive waste management.
- Greenhouse effect and global warming.
- Ozone depletion.
- Deforestation.
- Any three case studies as success stories addressing environmental issues.
4. MATHEMATICS:
Section B1: Applied Mathematics
UNIT I: RELATIONS AND FUNCTIONS
-
Relations and Functions
- Types of relations: Reflexive, symmetric, transitive, and equivalence relations.
- One-to-one and onto functions.
- Composite functions, inverse of a function.
- Binary operations.
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Inverse Trigonometric Functions
- Definition, range, domain, principal value branches.
- Graphs of inverse trigonometric functions.
- Elementary properties of inverse trigonometric functions.
UNIT II: ALGEBRA
-
Matrices
- Concept, notation, order, equality, types of matrices.
- Zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices.
- Addition, multiplication, and scalar multiplication of matrices.
- Simple properties of addition, multiplication, and scalar multiplication.
- Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).
- Elementary row and column operations.
- Invertible matrices and proof of the uniqueness of inverse, if it exists (all matrices will have real entries).
-
Determinants
- Determinant of a square matrix (up to 3 × 3 matrices).
- Properties of determinants, minors, cofactors, and applications in finding the area of a triangle.
- Adjoint and inverse of a square matrix.
- Consistency, inconsistency, and the number of solutions of a system of linear equations by examples.
- Solving a system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.
UNIT III: CALCULUS
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Continuity and Differentiability
- Continuity and differentiability.
- Derivative of composite functions, chain rule.
- Derivatives of inverse trigonometric functions, derivative of implicit functions.
- Concepts of exponential, logarithmic functions.
- Derivatives of log x and e^x.
- Logarithmic differentiation.
- Derivative of functions expressed in parametric forms.
- Second-order derivatives.
- Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.
-
Applications of Derivatives
- Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals.
- Approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool).
- Simple problems illustrating basic principles and real-life situations.
-
Integrals
-
Integration as inverse process of differentiation.
-
Integration of a variety a functions by substitution, partial fractions, and by parts only simple integrals of the type to be evaluated.
$ \int \frac{dx}{x^2 \pm a^2}, \quad \int \frac{dx}{\sqrt{x^2 \pm a^2}}, \quad \int \frac{dx}{\sqrt{a^2 - x^2}}, \quad \int \frac{dx}{\sqrt{ax^2 + bx + c}}, \quad \int \frac{dx}{\sqrt{ax^2 + bx + c}}, $
$ \int \frac{(px + q)}{ax^2 + bx + c} , dx, \quad \int \frac{(px + q)}{\sqrt {ax^2 + bx + c}} , dx, \quad \int \sqrt{a^2 \pm x^2} , dx \quad \text{and} \quad \int \sqrt{x^2 - a^2} , dx, $
$ \int \sqrt{ax^2 + bx + c} , dx \quad \text{and} \quad \int (px + q) \sqrt{ax^2 + bx + c} , dx $
-
Definite integrals as a limit of a sum.
-
Fundamental Theorem of Calculus (without proof).
-
Basic properties of definite integrals and evaluation of definite integrals.
-
-
Applications of Integrals
- Applications in finding the area under simple curves, especially lines, arcs of circles, parabolas, ellipses (in standard form).
- Area between two curves where the region is clearly identifiable.
-
Differential Equations
- Definition, order and degree, general and particular solutions of a differential equation.
- Formation of a differential equation whose general solution is given.
- Solution of differential equations by the method of separation of variables.
- Homogeneous differential equations of the first order and first degree.
- Solutions of linear differential equations of the type.
- dy/dx + Py = Q, where P and Q are functions of x or constant
- dx/dy + Px = Q, where P and Q are functions of y or constant
UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
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Vectors
- Vectors and scalars, magnitude and direction of a vector.
- Direction cosines/ratios of vectors.
- Types of vectors (equal, unit, zero, parallel, and collinear vectors).
- Position vector of a point, negative of a vector.
- Components of a vector, addition of vectors, multiplication of a vector by a scalar.
- Position vector of a point dividing a line segment in a given ratio.
- Scalar (dot) product of vectors, projection of a vector on a line.
- Vector (cross) product of vectors, scalar triple product.
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Three-Dimensional Geometry
- Direction cosines/ratios of a line joining two points.
- Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines.
- Cartesian and vector equation of a plane.
- Angle between:
- Two lines.
- Two planes.
- A line and a plane.
- Distance of a point from a plane.
UNIT V: LINEAR PROGRAMMING
- Introduction
- Related terminology: constraints, objective function, optimization.
- Different types of linear programming (LP) problems, mathematical formulation of LP problems.
- Graphical method of solution for problems in two variables.
- Feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
UNIT VI: PROBABILITY
-
Multiplication Theorem on Probability
- Conditional probability, independent events.
- Total probability, Baye’s theorem.
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Random Variables and Probability Distribution
- Mean and variance of a random variable.
- Repeated independent (Bernoulli) trials and Binomial distribution.
Section B2: Applied Mathematics
UNIT I: NUMBERS, QUANTIFICATION AND NUMERICAL APPLICATIONS
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Modulo Arithmetic
- Define modulus of an integer.
- Apply arithmetic operations using modular arithmetic rules.
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Congruence Modulo
- Define congruence modulo.
- Apply the definition in various problems.
-
Allegation and Mixture
- Understand the rule of allegation to produce a mixture at a given price.
- Determine the mean price of a mixture.
- Apply the rule of allegation.
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Numerical Problems
- Solve real-life problems mathematically.
-
Boats and Streams
- Distinguish between upstream and downstream.
- Express the problem in the form of an equation.
-
Pipes and Cisterns
- Determine the time taken by two or more pipes to fill or empty.
-
Races and Games
- Compare the performance of two players with respect to time, distance covered, or work done.
-
Partnership
- Differentiate between active and sleeping partners.
- Determine the gain or loss to be divided among the partners in proportion to their investments and time.
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Numerical Inequalities
- Describe basic concepts of numerical inequalities.
- Write and solve numerical inequalities.
UNIT II: ALGEBRA
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Matrices and Types of Matrices
- Define matrix.
- Identify different types of matrices.
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Equality of Matrices, Transpose of a Matrix, Symmetric and Skew-Symmetric Matrices
- Determine equality of two matrices.
- Write the transpose of a matrix.
- Define symmetric and skew-symmetric matrices.
UNIT III: CALCULUS
-
Higher Order Derivatives
- Determine second and higher-order derivatives.
- Understand differentiation of parametric and implicit functions.
-
Marginal Cost and Marginal Revenue Using Derivatives
- Define marginal cost and marginal revenue.
- Find marginal cost and marginal revenue.
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Maxima and Minima
- Determine critical points of a function.
- Find local maxima and minima, as well as absolute maxima and minima values.
UNIT IV: PROBABILITY DISTRIBUTIONS
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Probability Distribution
- Understand random variables and their probability distributions.
- Find probability distributions for discrete random variables.
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Mathematical Expectation
- Apply arithmetic mean to find the expected value of a random variable.
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Variance
- Calculate the variance and standard deviation of a random variable.
UNIT V: INDEX NUMBERS AND TIME BASED DATA
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Index Numbers
- Define index numbers as a special type of average.
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Construction of Index Numbers
- Construct different types of index numbers.
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Test of Adequacy of Index Numbers
- Apply the time reversal test.
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Time Series
- Identify time series as chronological data.
- Distinguish between different components of time series.
- Solve practical problems based on time series analysis.
UNIT VI: INFERENTIAL STATISTICS
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Population and Sample
- Define population and sample.
- Differentiate between population and sample.
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Parameter and Statistics
- Define parameter with reference to population.
- Define statistics with reference to sample.
- Explain the relation between parameter and statistic.
- Interpret statistical significance and inferences.
- State and explain the Central Limit Theorem.
UNIT VII: FINANCIAL MATHEMATICS
- Perpetuity and Sinking Funds
- Explain the concept of perpetuity and sinking fund.
- Calculate perpetuity and differentiate between sinking fund and saving account.
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Valuation of Bonds
- Define the concept of bond valuation.
- Calculate bond value using present value approach.
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Calculation of EMI
- Explain the concept of EMI.
- Calculate EMI using various methods.
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Linear Method of Depreciation
- Define the concept of linear method of depreciation.
- Interpret cost, residual value, and useful life of an asset.
- Calculate depreciation.
UNIT VIII: LINEAR PROGRAMMING
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Introduction and Related Terminology
- Familiarize with terms related to Linear Programming Problem (LPP).
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Mathematical Formulation of LPP
- Formulate Linear Programming Problems.
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Different Types of LPP
- Identify and formulate different types of LP problems.
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Graphical Method of Solution for Problems in Two Variables
- Draw the graph for a system of linear inequalities involving two variables.
- Find the solution graphically.
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Feasible and Infeasible Regions
- Identify feasible, infeasible, and bounded regions.
- Understand optimal feasible solutions.
5. AGRICULTURE:
Unit-1: Agrometeorology, Genetics and Plant Breeding, Biochemistry and Microbiology
Agrometeorology: Elements of Weather - rainfall, temperature, humidity, wind velocity, sunshine, weather forecasting, climate change in relation to crop production.
Genetics & Plant Breeding:
- (a) Cell and its structure, cell division - mitosis and meiosis and their significance.
- (b) Organization of the genetic materials in chromosomes, DNA, and RNA.
- (c) Mendel’s laws of inheritance. Reasons for the success of Mendel in his experiments, absence of linkage in Mendel’s experiments.
- (d) Quantitative inheritance, continuous and discontinuous variation in plants.
- (e) Monogenic and polygenic inheritance.
- (f) Role of Genetics in Plant breeding, self and cross-pollinated crops, methods of breeding in field crops - introduction, selection, hybridization, mutation and polyploidy, tissue and cell culture.
- (g) Plant Biotechnology - definition and scope in crop production.
Biochemistry: pH and buffers, classification and nomenclature of carbohydrates, proteins, lipids, vitamins, and enzymes.
Microbiology: Microbial cell structure. Micro-organisms - Algae, Bacteria, Fungi, Actinomycetes, Protozoa, and Viruses. Role of micro-organisms in respiration, fermentation, and organic matter decomposition.
Unit-2: Livestock Production
Scope and Importance:
- (a) Importance of livestock in agriculture and industry, White revolution in India.
- (b) Important breeds - Indian and exotic, distribution of cows, buffaloes, and poultry in India.
Care and Management:
- (a) Systems of cattle and poultry housing.
- (b) Principles of feeding, feeding practices.
- (c) Balanced ration - definition and ingredients.
- (d) Management of calves, bullocks, pregnant and milch animals, as well as chicks, cockerels, and layers, poultry.
- (e) Signs of sick animals, symptoms of common diseases in cattle and poultry: Rinderpest, black quarter, foot and mouth, mastitis, haemorrhagic septicaemia, coccidiosis, Fowl pox, and Ranikhet disease, their prevention, and control.
Artificial Insemination: Reproductive organs, collection, dilution, and preservation of semen, and artificial insemination. Role of artificial insemination in cattle improvement.
Livestock Products: Processing and marketing of milk and milk products.
Unit-3: Crop Production
Introduction:
- (a) Targets and achievements in food grain production in India since independence and its future projections, sustainable crop production, commercialization of agriculture, and its scope in India.
- (b) Classification of field crops based on their utility - cereals, pulses, oil seeds, fibre, sugar, and forage crops.
Soil, Soil Fertility, Fertilizers, and Manures:
- (a) Soil, soil pH, soil texture, soil structure, soil organisms, soil tilth, soil fertility, and soil health.
- (b) Essential plant nutrients, their functions, and deficiency symptoms.
- (c) Soil types of India and their characteristics.
- (d) Organic manure, common fertilizers, including straight, complex, fertilizer mixtures, and biofertilizers; integrated nutrient management system.
Irrigation and Drainage:
- (a) Sources of irrigation - rain, canals, tanks, rivers, wells, tube wells.
- (b) Scheduling of irrigation based on critical stages of growth, time interval, soil moisture content, and weather parameters.
- (c) Water requirement of crops.
- (d) Methods of irrigation and drainage.
- (e) Watershed management.
Weed Control: Principles of weed control, methods of weed control (cultural, mechanical, chemical, biological, and integrated weed management).
Crops: Seed bed preparation, seed treatment, time and method of sowing/planting, seed rate, dose, method, and time of fertilizer application, irrigation, intercultural and weed control. Common pests and diseases caused by bacteria, fungi, viruses, and nematodes and their control. Integrated pest management, harvesting, threshing, post-harvest technology: storage, processing, and marketing of major field crops - rice, wheat, maize, sorghum, pearl millet, groundnut, mustard, pigeon-pea, gram, sugarcane, cotton, and berseem.
Unit-4: Horticulture
(a) Importance of fruits and vegetables in the human diet, crop diversification, and processing industry.
(b) Orchard location and layout, ornamental gardening, and kitchen garden.
(c) Planting system, training, pruning, intercropping, protection from frost and sunburn.
(d) Trees, shrubs, climbers, annuals, perennials - definition and examples. Propagation by seed, cutting, budding, layering, and grafting.
(e) Cultivation practices, processing, and marketing of:
- (i) Fruits - mango, papaya, banana, guava, citrus, grapes.
- (ii) Vegetables - radish, carrot, potato, onion, cauliflower, brinjal, tomato, spinach, and cabbage.
- (iii) Flowers - gladiolus, canna, chrysanthemums, roses, and marigold.
(f) Principles and methods of fruit and vegetable preservation.
(g) Preparation of jellies, jams, ketchup, chips, and their packing.
Note: Besides above syllabus, any other question of scientific and educational importance may be asked.
BETA
