DU MCA Syllabus 2023 - Check Section & Topic wise Syllabus PDFs here

Section

No. of Questions

Marks

Mathematics

30

120

English

10

40

Logical Ability

6

24

Computer Science

4

16

Total

50

200

Particulars

Details

Mode of Exam

Computer Based Test (CBT)

Medium of Exam

English

Duration of Exam

2 hours

Number of Questions

50

Type of Questions

Multiple choice questions

Marking Scheme

+4 for every correct response

-1 for every incorrect response

0 for no response

Subject

Topic

Sub-Topic

Mathematics (Calculus)

Calculus

Limit and continuity of a function: (ε-δ and sequential approach).

Properties of continuous functions including intermediate value theorem

Differentiability

Rolle’s theorem

Lagrange’s mean value theorem

Cauchy mean value theorem with geometrical interpretations

Uniform continuity

Definitions and techniques for finding asymptotes singular points

Tracing of standard curves

Integration of irrational functions.

Reduction formulae

Rectification

Quadrature

Volumes Sequences to be introduced through the examples arising in Science beginning with finite sequences, followed by concepts of recursion and difference equations. For instance, the sequence arising from Tower of Hanoi game, the Fibonacci sequence arising from branching habit of trees and breeding habit of rabbits

Convergence of a sequence and algebra of convergent sequences.

Illustration of proof of convergence of some simple sequences such as (–1)n /n, I/n2 , (1+1/n)n , sin n/n, xn with 0 < x < 1

Graphs of simple concrete functions such as polynomial, trigonometric, inverse trigonometric, exponential, logarithmic and hyperbolic functions arising in problems or chemical reaction, simple pendulum, radioactive decay, temperature cooling/heating problem and biological rhythms

Successive differentiation

Leibnitz theorem

Recursion formulae for higher derivative

Functions of two variables

Graphs and Level Curves of functions of two variables

Partial differentiation upto second order

Computation of Taylor’s Maclaurin’s series of functions such as ex , log(1 + x), sin (2x), cos x

Their use in polynomial approximation and error estimation

Formation and solution of Differential equations arising in population growth, radioactive decay, administration of medicine and cell division

Geometry and Vector Calculus

Techniques for sketching parabola, ellipse and hyperbola

Reflection properties of parabola, ellipse and hyperbola

Classification of quadratic equations representing lines, parabola, ellipse and hyperbola

Differentiation of vector valued functions, gradient, divergence, curl and their geometrical interpretation

Spheres, Cylindrical surfaces. Illustrations of graphing standard quadric surfaces like cone, ellipsoid

Mathematics (Algebra)

Complex Numbers

Geometrical representation of addition, subtraction, multiplication and division of complex numbers

Lines half planes, circles, discs in terms of complex variables

Statement of the Fundamental Theorem of Algebra and its consequences, De Moivre’s theorem for rational indices and its simple applications

Matrices

R, R2 , R3 as vector spaces over R

Standard basis for each of them

Concept of Linear Independence and examples of different bases

Subspaces of R2 , R3

Translation, Dilation, Rotation, Reflection in a point, line and plane

Matrix form of basic geometric transformations

Interpretation of eigenvalues and eigenvectors for such transformations and eigenspaces as invariant subspaces

Matrices in diagonal form

Reduction to diagonal form upto matrices of order 3

Computation of matrix inverses using elementary row operations

Rank of matrix

Solutions of a system of linear equations using matrices

Illustrative examples of above concepts from Geometry, Physics, Chemistry, Combinatorics and Statistics

Groups

Definition and examples of groups, examples of abelian and nonabelian groups: the group Zn of integers under addition modulo n and the group U (n) of units under multiplication modulo n

Cyclic groups from number systems, complex roots of unity, circle group, the general linear group GL (n,R), groups of symmetries of (i) an isosceles triangle, (ii) an equilateral triangle, (iii) a rectangle, and (iv) a square, the permutation group Sym (n), Group of quaternions, Subgroups, cyclic subgroups, the concept of a subgroup generated by a subset and the commutator subgroup of group, examples of subgroups including the center of a group

Cosets, Index of subgroup, Lagrange’s theorem, order of an element

Normal subgroups: their definition, examples, and characterizations

Quotient groups

Rings

Definition an examples of rings, examples of commutative and noncommutative rings, rings from number systems, Zn the ring of integers modulo n, ring of real quaternions, rings of matrices, polynomial rings, and rings of continuous functions

Subrings and ideals, Integral domains and fields, examples of fields: Zp , Q, R, and C

Field of rational functions

Vector spaces

Definition and examples of vector spaces

Subspaces and its propertie

Linear independence, basis, invariance of basis size, dimension of a vector space

Linear Transformations on real and complex vector spaces: definition, examples, kernel, range, rank, nullity, isomorphism theorems

Mathematics (Real Analysis)

Real Sequences

Finite and infinite sets, examples of countable and uncountable sets

Real line, bounded sets, suprema and infima, statement of order completeness property of R, Archimedean property of R, intervals

Concept of cluster points and statement of Bolzano Weierstrass’ theorem

Cauchy convergence criterion for sequences

Cauchy’s theorem on limits, order preservation and squeeze theorem, monotone sequences and their convergence

Infinite Series

Infinite series

Cauchy convergence criterion for series, positive term series, geometric series, comparison test, convergence of p-series, Root test, Ratio test, alternating series, Leibnitz’s test

Definition and examples of absolute and conditional convergence

Sequences and series of functions, Pointwise and uniform convergence

M-test, change or order of limits

Power Series: radius of convergence, Definition in terms of Power series and their properties of exp (x), sin (x), cos (x)

Riemann Integration

Riemann integral, integrability of continuous and monotonic functions

Computer Science

Data representation

Boolean circuits and their simplification

C-programming: Data types, constants and variables, operators and expressions

Control structures

Use of functions, scope

Arrays

Logical ability & English Comprehension

Problem-solving using basic concepts of arithmetic, algebra, geometry and data analysis

Reading comprehension

Correct usage of English language