Bihar State Pcs conducts one of the most recognized Civil Services Exam in the country, where candidates compete for different PCS level posts like Sub Divisional Officer, District Sanapark Officer etc. To prepare for the exams, you must have a thorough understanding of the exam syllabus to crack it. The BPSC Syllabus for the Preliminary and Mains exam varies considerably, but the overall strategy for each is similar. First and foremost, you should have a crystal-clear conceptual understanding of the concepts involved in each subject to outperform your competition. To achieve this, you must allocate fixed time to revision and practice through previous year full-length papers and mock tests. Additionally, you should also be systematic in your answer-writing. This can be done by glancing through toppers answer scripts or getting yours evaluated from the mentors.
Moreover, you must constantly be asking questions about what you learn: how is it connected to that? How does this relate to the current affairs? The more you are curious about the subject, the easier it will be to link everything together and make sense of the topics. It is also important to read up on current affairs and keep a tab on the news to improve your general awareness. This can be done by reading newspapers like The Hindu or The Indian Express and also by watching weekly or monthly news channels.
In the BPSC Preliminary Exam, there will be a single paper that will test the candidates knowledge of Indian Politics, Economy, History of the nation and the State of Bihar. The questions in the exam will be objective in nature and will include both static as well as current affairs. It is important to score a minimum of 30% in this paper to be eligible for the Mains exam.
The BPSC Mains exam will consist of two General Studies papers and an Optional paper that you had chosen in your application form. The marks that you earn in this exam will be reflected in the final merit list. To make this process smooth and hassle-free, you must know the BPSC Maths Optional Syllabus to ensure that you prepare adequately for the exam.
There are 34 optional subjects that you can choose from to appear for the BPSC Mains. You must pick the subject that you are comfortable with and have an academic background in. If you are unsure of the best choice, you must refer to the BPSC Official Notice for more information. Moreover, you must make sure that you are familiar with the BPSC Mains Exam Pattern as it has undergone some changes in the 68th CCE. The marking system, course of study, and question format have all been altered.
BPSC Maths Optional Syllabus Paper-1
| Section-i |
Candidates shall answer not more than three questions from each section. Linear Algebra, Calculus, Analytic Geometry of two and three dimensions, Differential Equations. Vector, Tensor, Statics, Dynamics and Hydrostatics: (1) Linear Algebra. Vector space bases, dimension of finitely generated space. Linear transformations, Rank and nullity of a linear transformation, Cayley Hamilton theorem. Eigenvalues and Eigenvectors. Matrix of a linear transformation. Row and Column reduction. Echelon form. Equivalence. Congruence and similarity. Reduction to canonical forms. Orthogonal, symmetrical, skew-symmetrical, unitary, Hermitian and Skew-Hermitian matrices – their eigenvalues, orthogonal and unitary reduction of quadric and Hermitian forms, positive definite quadratic forms. Simultaneous reduction. |
(2) Calculus. Real numbers, limits, continuity, differentiability, Mean-Value theorem, Taylor’s theorem, indeterminate forms, Maxima and Minima, Curve Tracing, Asymptotes, Functions of several variables, partial derivatives. Maxima and Minima, Jacobian. Definite and indefinite integrals, double and triple integrals (techniques only). Application to Beta and Gamma functions. Areas, Volumes, Centre of gravity. |
(3) Analytic Geometry of two and three dimensions: First and second-degree equations in two dimensions in Cartesian and polar coordinates. Plane, Sphere, Paraboloid, Ellipsoid. Hyperboloid of one and two sheets and their elementary properties. Curves in space, curvature and torsion. Frenet’s formula. |
(4) Differential Equations. Order and Degree and a differential equation, differential equation of first order and degree, variables separable. Homogeneous, Linear and exact differential equations. Differential equations with constant coefficients. The complementary function and the particular integral of e power ax, cos(ax) , sin (ax), x power m into e power ax , e power ax into cos(bx), e power ax into sin(bx). |
(5) Vector, Tensor, Statics, Dynamics and Hydrostatics: (i) Vector Analysis – Vector Algebra, Differential of Vector function of a scalar variable, Gradient, Divergence and Curl in Cartesian Cylindrical and spherical co-ordinates and their physical interpretation. Higher order derivatives. Vector identities and Vector equations, Gauss and Stocks theorems. (ii) Tensor Analysis – Definition of Tensor, transformation of co-ordinates, contravariant and covariant tensor. Addition and multiplication of tensors, contraction of tensors, Inner product, fundamental tensor, Christoffel symbols, covariant differentiation. gradient, Curl and divergence in tensor notation. (iii) Statics – Equilibrium of a system of particles, work and potential energy. Friction, Common catenary. Principle of Virtual Work stability of equilibrium, Equilibrium of forces in three dimensions (iv) Dynamics – Degree of freedom and constraints. Rectilinear motion. Simple harmonic motion. Motion in a plane. Projectiles. Constrained motion. Work and energy motion under impulsive forces. Kepler’s laws. Orbits under central forces. Motion of varying mass. Motion under resistance. (v) Hydrostatics – Pressure of heavy fluids. Equilibrium of fluids under given system of forces Centre of pressure. Thrust on curved surfaces, Equilibrium and pressure of gases, problems relating to atmosphere. |
BPSC Maths Optional Syllabus Paper-2
| Section-i |
Candidates shall answer not more than three questions from each section. Linear Algebra, Calculus, Analytic Geometry of two and three dimensions, Differential Equations. Vector, Tensor, Statics, Dynamics and Hydrostatics: (1) Linear Algebra. Vector space bases, dimension of finitely generated space. Linear transformations, Rank and nullity of a linear transformation, Cayley Hamilton theorem. Eigenvalues and Eigenvectors. Matrix of a linear transformation. Row and Column reduction. Echelon form. Equivalence. Congruence and similarity. Reduction to canonical forms. Orthogonal, symmetrical, skew-symmetrical, unitary, Hermitian and Skew-Hermitian matrices – their eigenvalues, orthogonal and unitary reduction of quadric and Hermitian forms, positive definite quadratic forms. Simultaneous reduction. |
(2) Calculus. Real numbers, limits, continuity, differentiability, Mean-Value theorem, Taylor’s theorem, indeterminate forms, Maxima and Minima, Curve Tracing, Asymptotes, Functions of several variables, partial derivatives. Maxima and Minima, Jacobian. Definite and indefinite integrals, double and triple integrals (techniques only). Application to Beta and Gamma functions. Areas, Volumes, Centre of gravity. |
(3) Analytic Geometry of two and three dimensions: First and second-degree equations in two dimensions in Cartesian and polar coordinates. Plane, Sphere, Paraboloid, Ellipsoid. Hyperboloid of one and two sheets and their elementary properties. Curves in space, curvature and torsion. Frenet’s formula. |
(4) Differential Equations. Order and Degree and a differential equation, differential equation of first order and degree, variables separable. Homogeneous, Linear and exact differential equations. Differential equations with constant coefficients. The complementary function and the particular integral of e power ax, cos(ax) , sin (ax), x power m into e power ax , e power ax into cos(bx), e power ax into sin(bx). |
(5) Vector, Tensor, Statics, Dynamics and Hydrostatics: (i) Vector Analysis – Vector Algebra, Differential of Vector function of a scalar variable, Gradient, Divergence and Curl in Cartesian Cylindrical and spherical co-ordinates and their physical interpretation. Higher order derivatives. Vector identities and Vector equations, Gauss and Stocks theorems. (ii) Tensor Analysis – Definition of Tensor, transformation of co-ordinates, contravariant and covariant tensor. Addition and multiplication of tensors, contraction of tensors, Inner product, fundamental tensor, Christoffel symbols, covariant differentiation. gradient, Curl and divergence in tensor notation. (iii) Statics – Equilibrium of a system of particles, work and potential energy. Friction, Common catenary. Principle of Virtual Work stability of equilibrium, Equilibrium of forces in three dimensions (iv) Dynamics – Degree of freedom and constraints. Rectilinear motion. Simple harmonic motion. Motion in a plane. Projectiles. Constrained motion. Work and energy motion under impulsive forces. Kepler’s laws. Orbits under central forces. Motion of varying mass. Motion under resistance. (v) Hydrostatics – Pressure of heavy fluids. Equilibrium of fluids under given system of forces Centre of pressure. Thrust on curved surfaces, Equilibrium and pressure of gases, problems relating to atmosphere. |