BCECE syllabus consists of important sections like Physics, Chemistry, Mathematics, Biology, and Agriculture. This exam is conducted on an offline basis. You will get around 90 minutes to complete each section. Some important topics that candidates should cover are as follows:

• The important topics in the Physics syllabus include the Physical World and Measurement, Kinematics, Laws of Motion, Gravitation, Optics, Atoms and Nuclei, etc.

• Chemistry includes topics like Structure of Atom, Hydrocarbons, Chemical Kinetics, Thermodynamics, Surface Chemistry, Equilibrium, etc.

• Biology has topics like Diversity In the Living World, Plant Physiology, Human Physiology, Sexual Reproduction, Biology And Human Welfare, etc.

• As a general candidate, you must secure at least 50% marks in the examination. Whereas, if you are from a reserved category, you must have at least 45% marks to qualify for the exam.

There have been no significant changes in the BCECE syllabus for 2024. However, we have given below some insights about the exam pattern:

• The total number of questions in the examination is 300.

• For every right answer, 4 marks will be awarded to candidates.

• A penalty of 1 mark will be deducted for every wrong answer.

BCECE Syllabus 2024 for Chemistry

The BCECE syllabus for chemistry and its topics are given below:

BCECE Syllabus 2024 for Biology

Biology is a comparatively easier section than the others. The table below shows the important topics covered in the syllabus:

BCECE Syllabus 2024 for Mathematics

• Sets: Sets and their representations, Empty sets, Finite & Infinite sets. Equal sets, Subsets, Subsets of the set of real numbers 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 (up to R X R X R). Definition of relation, pictorial diagrams, domain, codomain, and range of a relation. Function is a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain & range of a function. The 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 & degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. The 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. The general solution of trigonometric equations of the type sin? = sina, cos? = cosa and tan? = tana. 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 the 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: Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear, inequalities in two variables. 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 & Series: 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.), the relation between A.M. and G. M. Sum to n terms of the special series, ?n and ?n2 and ?n3.

Co-Ordinate Geometry (I):

• Straight Lines: Brief recall of 2D from earlier classes. The slope of a line and the 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, straight line, and a 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: Derivatives 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 tangent of the curve, derivative of sum, difference, product, and quotient of functions. Derivatives of polynomial and trigonometric functions.

Mathematical Reasoning:

• 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 & Probability (I):

• Statistics: Measure of dispersion; mean deviation, variance, and standard deviation of ungrouped / grouped data. Analysis of frequency distributions with equal means but different variances.

• Probability: 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:

• Relations and Functions: Types of relations: reflexive, symmetric, transitive, and equivalence relations, One to one and onto functions, composite functions inverse of a function, and 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 matrix (restricted to square matrices of order. 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: Determinants 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. Adjoint and inverse of a square matrix. Consistency, inconsistency, and number of solutions of a system of linear equations by examples, solving a system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

Calculus (II):

• Continuity and Differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of 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: 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 principles and understanding of the subject as well as real-life situations).

• Integrals: Integration is the 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-mentioned curves (the region should be 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 method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x.

Vectors And Three Dimensional Geometry (II):

• 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.

• 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. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Linear Programming:

• Linear Programming: Introduction, the definition of related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, 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 constaints).

Probability (II):

• Probability: Multiplication theory on probability. Conditional probability, independent events, total probability, Baye’s theorem, Random variable, and its probability distribution, mean, and variance of haphazard variable. Repeated independent (Bernoulli)trials and Binomial distribution.

BCECE Syllabus 2024 for Agriculture:

BCECE syllabus for 2024 agricultural subjects is given below:

• Introductory Agriculture and Agro meteorology
• Soil as a medium of plant growth
• Plant breeding and genetics
• Agricultural Engineering
• Crop protection
• Animal Husbandry, Dairy and Fish Production
• Cultivation of crops
• Cropping system
• Soil and water management
• Weed management
• Recent trends in agriculture
• Agricultural economics
• Basic Horticulture
• Fruit Production
• Vegetable production
• Flowers, medicinal and aromatic plants
• Preservation of fruits and vegetable
• Extension education

Guidelines by a BCECE Candidate

Ques. Is the level of examination tough in the BCECE examination?

Ques. Which books can I follow to cover the entire syllabus of mathematics?

Ques. What are the important chapters to study for the biology syllabus?

Ques. Does the syllabus contain questions from Class 11 as well?

Ques. Is it necessary to attempt both biology and mathematics questions?