What is the syllabus for mca entrance exam of uptu?

Mathematics
  • Modern Algebra
  • Idempotent law
  • Identities
  • Complementary laws
  • Demorgan's theorem
  • Mapping
  • Inverse relation
  • Equivalence relation
  • Piano's Axiom
  • Definition of rational numbers and integers through equivalence relation

Algebra
  • Surds
  • Solution of simultaneous and quadratic equations
  • Arithmetic, Geometric and Harmonic progression
  • Binomial theorem for any index
  • Logarithms
  • Exponential and logarithmic series
  • Determinants
  • Probability
  • Dependent and independent events
  • Numerical problems on addition and multiplication of probability
  • Theorems of probability

Trigonometry
  • Simple identities
  • Trigonometric equations
  • Properties of triangles
  • Use of mathematical tables
  • Solution of triangles
  • Height and distance
  • Inverse functions
  • DeMoiver's theorem
  • Co-Ordinate Geometry
  • Co-ordinate geometry of the straight lines,
  • Pair of straight lines, circle, parabola, ellipse and hyperbola and their properties

Calculus
  • Differentiation of function of functions,
  • Tangents and normal
  • Simple examples of maxima of minima
  • Limits of function, integration of function ( by parts, by substitution and by partial fraction)
  • Definite integral ( application to volumes and surfaces of frustums of sphere, cone and cylinder )

Vectors
  • Position vector
  • Addition and subtraction of vectors
  • Scalar and vector products and their applications
  • Dynamics
  • Velocity
  • Composition of velocity
  • Relative velocity
  • Acceleration
  • Composition of acceleration
  • Motion under gravity
  • Projectiles
  • Laws of motions
  • Principles of conservation of momentum and energy
  • Direct impact of smooth bodies, pulleys

Statics
  • Composition of co-planar, concurrent and parallel forces
  • Moments and couples
  • Resultant of set of coplanar forces and conditions of equilibrium
  • Determination of Centroides in simple case
  • Problems involving friction

Statistics
  • Theory of probability, Mean, Median, Mode, Dispersion and Standard Deviation
  • Logical Ability
  • Analytical and logical questions will be asked in this section.