JMI ENTRANCE Mathematics (BTech / BSc / Commerce Programmes) Syllabus

JMI ENTRANCE Mathematics (BTech / BSc / Commerce Programmes): topic-wise syllabus

1. 1

   Algebra

   ~14 marks

   • Sets, Relations & Functions — Types, Domain, Range, Inverse, Composite Functions, Binary Operations
   • Complex Numbers — Argand Plane, Modulus, Argument, De Moivre's Theorem, Roots of Unity
   • Quadratic Equations — Nature of Roots, Relations between Roots, Formation of Equations
   • Sequences & Series — AP, GP, HP, Arithmetic/Geometric Mean, Summation, Infinite Series
   • Matrices & Determinants — Operations, Inverse, Rank, System of Linear Equations, Properties of Determinants
   • Binomial Theorem — Expansion, General Term, Middle Term, Binomial Coefficients Properties
   • Permutations & Combinations — Factorial, Selections, Arrangements, Circular Permutations
   • Probability — Events, Conditional, Bayes Theorem, Random Variables, Binomial/Poisson Distribution
   • Mathematical Reasoning — Statements, Connectives, Truth Tables, Tautology, Contradiction
2. 2

   Calculus

   ~16 marks

   • Limits & Continuity — Standard Limits, L'Hopital Rule, Continuity, Differentiability, Cauchy/Rolle/Lagrange Theorems
   • Differentiation — Derivatives of Standard Functions, Chain Rule, Implicit, Logarithmic/Parametric Differentiation
   • Applications of Derivatives — Tangents, Normals, Maxima/Minima, Rate of Change, Monotonicity, Approximation
   • Integration — Standard Integrals, Substitution, Parts, Partial Fractions, Definite Integrals, Properties, Area Under Curve
   • Differential Equations — Order, Degree, Variable Separable, Homogeneous, Linear, Bernoulli, Exact DE
   • Vector Algebra & 3D Geometry — Dot/Cross Product, Lines, Planes, Distances, Angles
   • Partial Differentiation & Multiple Integrals — Partial Derivatives, Maxima/Minima of Two Variables, Double/Triple Integrals
3. 3

   Trigonometry

   ~6 marks

   • Trigonometric Ratios, Identities, Compound/Multiple/Submultiple Angles
   • Trigonometric Equations — General Solutions, Principal Values
   • Inverse Trigonometric Functions — Domain, Range, Properties
   • Heights & Distances — Angle of Elevation/Depression, Applications
   • Hyperbolic Functions & Properties
4. 4

   Coordinate Geometry

   ~8 marks

   • Straight Lines — Slope, Equation Forms, Distance, Angle, Pair of Lines
   • Circles — Equation, Centre, Radius, Tangent, Normal, Chord of Contact, Orthogonal Circles
   • Conic Sections — Parabola, Ellipse, Hyperbola, Standard Equations, Tangents, Normals, Properties
   • Locus & Transformation of Axes
5. 5

   Statistics & Linear Programming

   ~6 marks

   • Statistics — Mean, Median, Mode, Standard Deviation, Variance, Correlation, Regression
   • Linear Programming — Graphical Method, Feasible Region, Optimal Solution, Dual
   • Numerical Methods — Interpolation, Newton's Forward/Backward, Lagrange, Numerical Integration