# UTTARAKHAND TECHNICAL

Admission for Master of Computer Application (MCA) – 2015

Test Date: 19 June 2015 (Morning) Test Time: 8.00 am to 10.30 am

Eligibility: Recognized Bachelor’s Degree of minimum 3 year duration with Mathematics at 10+2 level or at Graduate Level. Obtained at least 50% (45% in case of candidates belonging to reserved category) at the qualifying examination. SYLLABUS: 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, arithmatic, geometric and harmonicprogression, 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, 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 example of maxima of minima, limits of functions, 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.