Delhi University conducts the Test for admission to a three-year full-time post graduate degree course in Master of Computer Applications (MCA).
ELIGIBILITY
Course Requirement | Marks Requirement | |
Any bachelor degree from the University of Delhi or any other University whose examination is recognized as equivalent to that of University of Delhi with at least one paper in Mathematical Sciences (Mathematics, Computer Science, Statistics, Operational Research) under annual mode/at least two papers in Mathematical Sciences (Mathematics, Computer Science, Statistics, Operational Research) in semester mode. | 60% marks in aggregate or equivalent of CGPA as per University norms wherever it is applicable. |
Note:
The candidates who are appearing in the final year examinations of the degree on the basis of which admission is sought are also eligible to apply (Relaxation will be given to the candidates belonging to SC, ST, and OBC category as per the University rules).
Admission Procedure:
Admission to the MCA programme is based on the Entrance Exam and Interview. For preparing the final merit list, 85% weightage will be given to the score in the entrance exam and 15% weightage will be given to the score in the interview. The entrance examination shall be of two hours duration. For other things, the rules of the University of Delhi shall be followed.
Entrance Examination:
MCA entrance examination shall consist of 50 objective type questions to be solved in 02 hours. The approximate distribution of questions will be as given below:
Sr. No. Subjects No. of Questions
1. Mathematics 30
2. Computer Science 04
3. English 10
4. Logical Ability 06
SYLLABUS
MATHEMATICS
• 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. 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. 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.
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 non-abelian 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 and examples of rings, examples of commutative and non-commutative rings, rings from number systems, Zn the ring of integers modulo n, the 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 properties Linear independence, basis, invariance of basis size, the dimension of a vector space. Linear Transformations on real and complex vector spaces: definition, examples, kernel, range, rank, nullity, isomorphism theorems.
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, the 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: Datatypes, 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 and correct usage of the English language.
IMPORTANT DATES
Sr. No. | Activity | Schedule |
1. | Availability of Application Form | First Week of June |
2. | Availability of Admit Card | Last Week of June |
3. | Date of the Exam | First Week of July |
4. | Declaration of the result | Third Week of July |