# 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.