# UPSEE 2020 Exam - Detailed Syllabus for Paper-5 Aptitude Test

The Uttar Pradesh State Entrance Examination (UPSEE) comprises of eight papers. Out of the eight papers, UPSEE Paper-5 is conducted for the lateral entry in the B.Tech. and MCA courses. Lateral entry means direct admission to the 2nd year of the course. Here are the details on who can take admission through the lateral entry:

- Engineering diploma holders/B.Sc. graduates with Mathematics are eligible for admission to the 2nd year of B.Tech.
- BCA graduates/B.Sc. Information Technology/Computer Science candidates are eligible for admission to the 2nd year of MCA.

Make sure you meet the eligibility criteria before filling the application form. The article here focuses on the syllabus of the Paper-5. Candidates can check out the pattern and topics of the Paper-5 for preparation of the entrance exam.

## UPSEE 2020 Paper-5 Syllabus -

[Aptitude Test for B.Sc. Graduates in Engineering (Lateral Entry)/ 2nd Year MCA (Lateral Entry)]

### Part 1: Mathematics

**Algebra:** Sets relations & functions, Mapping Inverse relations, De-Morgan's Law, Equivalence relations, Definition of rationals and integers through equivalence relation, Peano's axioms, Indices and surds, A.P., G.P. and H.P., Solutions of simultaneous and quadratic equations, Special sums i.e. ∑n2 and ∑n3 (n∑N ), Partial fraction, exponential series, Binomial theorem for any index, Logarithm and Logarithmic series. Determinants and their use in solving simultaneous linear equations, Matrices, Inverse of a matrix, Use of the matrix for solving equations, and Algebra of matrices.

**Probability:** Definition, Numerical problem on addition and multiplication, Dependent and independent events, the theorem of probability.

**Trigonometry:** Identities, Trigonometric equations, solution of triangles, properties of triangles, heights and distances, Complex numbers and their properties, Inverse function, Cube roots of unity, De-Moivre's theorem.

**Coordinate Geometry:** Pair of straight lines, General equation of second degree, circles, parabola, ellipse and hyperbola, tracing of conics.

**Calculus:** Limits & continuity of functions, tangents & normal, Differentiation of function of function, Simple examples of Maxima & Minima, Integration of function by parts, by substitution and by partial fraction, Indeterminate forms, definite integral, application to volumes and surfaces of frustums of the sphere, cone and cylinder. Differential equations of the first order and of the first degree.

**Vectors:** Algebra of vectors, scalar and vector products of two and three vectors and their applications.

**Dynamics:** Velocity, relative velocity, the composition of velocity, acceleration, the composition of accelerations, Laws of motion, Motion under gravity, Projectiles, Principles of conservation of momentum and energy, the direct impact of smooth bodies.

**Statics:** Composition of coplanar, determination of centroid in simple cases, concurrent and parallel forces moments and couples resultant of the set of coplanar forces and condition of equilibrium, Problems involving friction.

### Part 2: Computer Concepts

**Computer Basics:** Organization of computer, Input/ Output devices, Central Processing unit (CPU), Structure of instructions in CPU, Memory organization, Computer memory.

**Data Representation:** Representation of characters, Binary and hexadecimal representation, Integers, Binary arithmetic – addition, subtraction, division, multiplication, signed arithmetic and two’s complement arithmetic. Floating point representation of numbers, Boolean algebra, normalized floating point representation, truth tables, Venn diagrams.

**Data Structures-** Arrays, lists, stacks, queues

**Computer Architecture:** Block structure of computers, Communication between the processor and I/O devices, Interrupts

**Computer Language-** Assembly language and high-level language, Computer programming in C

**Operating System Basics**

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