# What is the syllabus for mca entrance exam of uptu?

Mathematics

Algebra

Trigonometry

Vectors

Statics

Statistics

- 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.