  # BCECE Syllabus

#### BCECE Syllabus 2023:

Just like the exam pattern, BCECE Syllabus 2023 also differs for various subjects. The syllabus covers the basic topics that will be very useful for the candidates. One can go through the important topics and their weightage before starting their preparation. Candidates can download the Syllabus 2023 in PDF format for all the subjects from the official website of the board. For your help, BCECE Syllabus 2023 is given below. BCECE Syllabus 2023 covers various topics from all the subjects. The BCECE Exam Syllabus 2023 covers the entire topic of the important subjects such that these topics will help the candidates in their further studies also. The BCECE Exam Syllabus 2023 covers topics from the subjects Physics, Chemistry, Mathematics, Biology, and Agriculture. These are the very basic subjects that are required for any further studies.

Given below is the BCECE Syllabus 2023 for the entire subject with its weightage. Have a look.

##### BCECE Syllabus – Mathematics
 Sets and Functions Sets and their representations, Empty set, Finite & Infinite sets, Equal sets, Subsets, Subsets of the set of real number especially intervals (with notations), Power set, Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, Complement of a set, Relation & Functions: Ordered pairs, Cartesian product of sets, Number of elements in the Cartesian product of two finite sets, Cartesian product of the reals with itself (upto R X R X R) Definition of relation, pictorial diagrams, domain, condomain and range of a relation, Function as a special kind of relation from one set to another, Pictorial representation of a function, domain, co-domain & range of a function, Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs, Sum, difference, product and quotients of functions Trigonometric Functions: Positive and negative angles, Measuring angles in radians & in degrees and conversion from one measure to another, Definition of trigonometric functions with the help of unit circle Truth of the identify sin2x + cos2 x = 1, for all x, Signs of trigonometric functions and a sketch of their graphs, Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x, & cos y., Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x, General solution of trigonometric equations of the type sin? = sin A, cos? = cos A and tan? = tan A, Proof and simple application of sine and cosine formula Algebra I Principle of Mathematical Induction: Processes of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers, The principle of mathematical induction and simple applications Complex Numbers and Quadratic Equations: Need for complex numbers, especially v-1, to be motivated by inability to solve every quadratic equation, Brief description of algebraic properties of complex numbers, Argand plane and polar representation of complex numbers, Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system Linear inequalities: Algebraic solutions of linear inequalities in one variable and their representation on the Number Line, Graphical solution of linear, inequalities in two variable, Solution of a system of linear inequalities in two variables - graphically Permutation & Combination: Fundamental principle of counting, Factorial n (n!) Permutation and combinations, derivation of formulae and their connections, simple applications Binomial Theorem: History, statement and proof of the binomial theorem for positive integral indices, Pascal's triangle, General and middle term in binomial expansion, simple applications Sequence and Series: Arithmetic progression (A.P.) arithmetic mean (A.M.) Geometric progression (G.P.), general term of a G.P., Sum of n terms of a G.P., geometric mean (G.M.), relation between A.M. and G. M., Sum to n terms of the special series, ?n and ?n2 and ?n3 Coordinate Geometry (I) Straight Lines: Brief recall of 2D from earlier classes, Slope of a line and angle between two lines Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form General equation of a line, Distance of a point from a line Conic Section: Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section, Standard equations and simple properties of parabola, ellipse and hyperbola, Standard equation of a circle Introduction to Three Dimensional Geometry: Coordinate axes and coordinate planes in three dimensions, Coordinates of a point, Distance between two points and section formula Calculus (I) Limits and Derivatives: Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit, Definition of derivative, relate it to the slope of the tangent of the curve, derivatives of the sum, difference, product and quotient of functions, Derivatives of polynomial and trigonometric functions Mathematical Reasoning Mathematically acceptable statements. Connecting words/phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through a variety of examples related to real life and Mathematics, Validating the statements involving the connecting words - the difference between contradiction, converse, and contrapositive Statistics The measure of dispersion; mean deviation, variance and standard deviation of ungrouped / grouped data, Analysis of frequency distributions with equal means but different variances Probability (I) Random experiments: outcomes, sample spaces (set representation), Events: occurrence of events, 'not', 'and' 'or' events, exhaustive events, mutually exclusive events Axiomatic (set theoretic) probability, connections with the theories of earlier classes, Probability of an event, probability of 'not' 'and' & 'or' events 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 Inverse Trigonometric Functions Definition, range, domain principal value branches, Graphs of inverse trigonometric functions, Elementary properties of inverse trigonometric functions Algebra (II) 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 matrices (restrict to square matrices of order 2), Concept of elementary row and column operations, Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries) Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle, Adjoin and the inverse of a square matrix, Consistency, inconsistency, and number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix Calculus (II) Continuity and differentiability, the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, a derivative of an implicit function, Concept of exponential and logarithmic functions and their derivatives 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: Rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool), Simple problems (that illustrate basic principle and understanding of the subject as well as real-life situations) Integrals: Integration as inverse process of differentiation, Integration of a variety of functions by substitution by partial fractions and by parts, only simple integrals, 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 the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable) Differential Equations: Definition, order and degree, general and particular solutions of a differential equation, Formation of 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 the linear differential equation of the type: dy/ dx + py = q 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, the 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 Three - dimensional Geometry Direction cosines/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, Angle between (i) Two lines, (ii) Two planes, (iii) A-line and a plane, Distance of a point from a plane Linear Programming Introduction, the definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, the mathematical formulation of L.P. 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) Probability (II) Multiplication theorem on probability, Conditional probability, independent events, total probability, Bayes’ theorem, Random variable, and its probability distribution, mean and variance of haphazard variable, Repeated independent (Bernoulli) trials, and Binomial distribution
##### BCECE Syllabus – Biology
 Diversity in the Living world Diversity of living organism, Classification of the living organisms (five kingdom classification, major groups principles of classification within each kingdom), Systematics and binomial system of nomenclature, Salient features of animal (non-chordates up to phylum level, and chordates up to class level) and plant (major groups; Angiosperms up to subclass) classification, Botanical garden, herbaria, zoological parks museums Structural Organisation in Animals and Plants Tissues in animals and plants. Morphology, anatomy, and functions of different parts of flowering plants: Root, stem, leaf, inflorescence, flower, fruit and seed, Morphology, anatomy, and functions of different systems of an annelid (earthworm), an insect (cockroach) and an Amphibian (frog) Cell: Structure and Function Cell: Cell wall, cell membrane and cell organelles (plastids, mitochondria, endoplasmic reticulum, Golgi bodies/ dictyosomes, ribosomes, lysosomes, vacuoles, centrioles) and nuclear organization, Mitosis, meiosis, cell cycle, Basis chemical constituents of living bodies, Structure and functions of carbohydrates, proteins, lipids, and nucleic acids, Enzymes: Types, properties, and function Plant Physiology Movement of water, food, nutrients, and gases. Plants and Water: Mineral nutrition, Respiration, Photosynthesis, Plant growth and development Human Physiology Digestion and absorption, breathing and respiration, Body fluids and circulation, Excretory products and elimination, Locomotion, and Movement, Control and coordination Sexual Reproduction Pollination and fertilization in flowering plants, Development of seeds and fruits, Human reproduction: reproductive system in male and female, menstrual cycle. Production of gametes, fertilization, implantation, embryo development, pregnancy and parturition, Reproductive health-birth control, contraception, and sexually transmitted diseases Genetics and Evolution Mendelian inheritance, Chromosome theory of inheritance, deviations from Mendelian ratio (gene interaction-Incomplete dominance, codominance, Complementary genes, multiple alleles ), Sex determination in human beings: XX, XY, Linkage and crossing over, the Inheritance pattern of hemophilia and blood groups in human beings DNA: replication, transcription, translation, Gene expression and regulation, Genome and Human Genome Project, DNA fingerprinting Evolution: Theories and evidence Biology and Human Welfare Animal husbandry, Basic concepts of immunology, vaccines, Pathogens, Parasites, Plant breeding, tissue culture, food production, Microbes in household food processing, industrial production, sewage treatment, and energy generation, Cancer, and AIDS. Adolescence and drug/alcohol abuse Biotechnology and its applications Recombinant DNA technology, Applications in Health, Agriculture and Industry, Genetically modified (GM) organism; biosafety issues, Insulin, and Bt cotton Ecology and Environment Ecosystems: components, types, and energy flow, Species, population and community., Ecological adaptations, Centres of diversity and conservation of biodiversity, national parks, and sanctuaries, Environmental issues
##### BCECE Syllabus – Agricultural Science
 Introduction to Agriculture and Agrometeorology Plant breeding and genetics Soil as a medium of plant growth Agriculture Engineering Crop Protection Animal Husbandry, Dairy and Fish Production Cultivation of crops Crop Production Soil and water management Cropping system Recent trends in Agriculture Weed management Basic Horticulture Fruit production Flowers, medicinal and aromatic plants Agriculture economics Preservation of fruits and plants Vegetable production Extension education -
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