Exam Scheme:

Note :-

1. Objective type paper
2. All questions carry equal marks.
3. There will be Negative Marking.
4. Medium of Competitive Exam: Bilingual in English & Hindi.

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Syllabus : Mathematics-I

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1. Algebra
   1. Different kinds of sets and their basic properties
   2. Relations
   3. Type of relations
   4. Functions
   5. Kind of functions
   6. Composite functions
   7. Groups and their properties
   8. Order of an element
   9. Order of a group
   10. Permutation groups
   11. Cyclic groups and their properties
   12. Subgroups and their properties
   13. Co-sets and their properties
   14. Homomorphism and Isomorphism
   15. Normal sub group and their properties

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2. Matrix and Determinants
   1. Various types of matrices
   2. Their basic operations and properties
   3. Invertible matrices and their inverse
   4. Determinant and their properties
   5. Solution of system of linear equations in two or three variables

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3. Differential Calculus
   1. Limit
   2. Continuity and Differentiability
   3. Increasing and decreasing function
   4. Tangents and normals
   5. Maxima and Minima of functions of one and two variables
   6. Mean Value Theorems
   7. Curvature
   8. Asymptotes
   9. Partial Differentiation
   10. Euler's theorem
   11. Envelopes and Evolutes

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4. Integral Calculus
   1. Beta-Gamma functions
   2. Double and triples integrals
   3. Quadrature
   4. Rectification
   5. Surfaces and volumes

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5. Two dimensional Geometry
   1. Circle
   2. Parabola
   3. Ellipse and Hyperbola and their properties (rectangular co-ordinate system only)
   4. System of Circle's and their properties

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6. Vector Calculus
   1. Differentiation of Vectors
   2. Del operator
   3. Gradient
   4. Divergent
   5. Curl and directional derivative
   6. Their identities and related theorems
   7. Integration of Vectors
   8. Line
   9. Surface and Volume integration of vectors
   10. Gauss-Divergence
   11. Stoke's and Green's theorem

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7. Ordinary Differential Equations
   1. First order Linear and non-linear differential equation
   2. Singular solutions and extraneous Loci
   3. Second order linear differential equation with constant and variable coefficients
   4. Simultaneous and Total Differential equations

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8. Statics
   1. Forces
   2. Resultant of Forces
   3. Law of Parallelogram
   4. Equilibrium of co-planner forces
   5. Moments
   6. Friction
   7. Virtual work and catenaries

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9. Dynamics
   1. Velocity and acceleration along radial and transverse directions and along tangential and normal direction
   2. Simple Harmonic motion
   3. Rectilinear motion under various laws
   4. Projectiles

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10. Complex Analysis
    1. Complex numbers and their algebraic properties D'Movier's theorem and its applications
    2. Polar representation
    3. Square root of a complex number
    4. Application in finding the roots of the equation
    5. Separation of Real and Imaginary Part
    6. Continuity and differentiability of complex functions
    7. Analytic function
    8. Cauchy Riemann equations
    9. Cauchy's theorem
    10. Cauchy's integral formulae