** Eligibility**

For admission to first year of MCA in any institution affiliated to U. P. Technical University, a
candidate must have passed three years degree course from any recognized University; securing
minimum 45% (40% for SC/ST) marks in aggregate. Candidate must have minimum 40% (35% for
SC/ST) marks in mathematics at 10+2 level or at bachelor degree level.

** Exam Pattern**

There are 100 objective type questions which includes mathematics, statistics and logical ability.
The duration of exam is 2 hrs.

** Exam Syllabus**

** 1. MATHEMATICS **

**• Modern Algebra:** Idempotent law, identities, complementary laws, Demorgans 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:** Definition, 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, DeMoivers 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.

**2. STATISTICS**

Theory of probability, Mean, Median, Mode, Dispersion and Standard Deviation.

**3. LOGICAL ABILITY**