As you are looking for syllabus of Pre Ph.D Entrance Exam for Computer Science discipline conducted by Jai Narain Vyas University (JNVU), so here is syllabus:

Jai Narain Vyas University (JNVU) Pre Ph.D Entrance Exam Syllabus

DISCRETE MATHEMATICAL STRUCTURES AND ITS APPLICATIONS IN COMPUTER SCIENCE
Formal Methods: Induction and Analogy, Abstraction, deduction.
Sets, sequences, empty set, power set, operations on sets, Venn diagram, ordered pair,
principle of inclusion and exclusion.
Introduction to mathematical logic, statements and notations, well-formed formulas,
tautologies, tautological implications, normal forms, the theory of Inference for statement
calculus, predicate logic.
Graph Terminology, Degrees of Nodes, Isomorphic Graphs, Dijkstra’s Shortest Path
Algorithm, Planar Graphs, Eulerian Graphs, Hamiltonian Graphs, Traveling Salesman
Problem.
Trees, Introduction, Rooted and Other Trees, Representation of Prefix Codes,
representation of Arithmetic Expression, Representation of Prefix Codes, Spanning
Trees, Traversing Binary Trees, Binary Search Trees.
Relations, matrix and graph representation of relation, properties of relations, partitions.
Equivalence Relations, Compatibility Relations, Composition of Binary Relations,
Transitive and symmetric closures, partially ordered set, lattices.
Functions, Matrix representation of functions, composition of function, inverse function.
Algebraic Structures, General properties of algebraic systems, groupoids, semigroup,
monoids, group, rings. Applications of algebra to control structure of a program.
Homomorphism, congruences, admissible partitions. Groups and their graphs.

DATA STRUCTURES AND ALGORITHMS
Introduction to data structure, String storage representation and manipulation. Marcov
algorithm and primitive data structures.
Concepts of non primitive data structures. Linear data structure. Array, stack, queue,
their applications and implementations using sequential storage representation and
linked representation.
Linear linked list, double linked list, circular linear linked list and generalised lists and
applications.
Concept of non-linear data structures, Tree, graph, set and their representation, Binary
Tree, Threaded tree, different techniques of tree traversal, breadth first search, depth first
search, application of tree and graph such that Polish notation, concepts of heap.
Sorting, searching algorithms and comparative study of different sorting and
searching techniques such that selection sort, heap sort, bubble sort, quick sort, merge
sort and radix sort. Linear search and binary search, hashing. External sorting.

DATA BASE SYSTEM
Introduction to database systems. A historical prespective, file systems v/s DBMS,
advantages of a DBMS, Data abstraction , models, instances and schemes. Data
independency. Data definition and manipulation languages. Database manager,
administration and users. Overall system structure.
Entities and entity sets. Relationships and relationship sets. Attributes, mapping, keys,
E-R diagram and its conversion to tables. Design of an E-R database scheme.
Structure of relational database. The relational algebra. The tuple and domain relational
calculus. Modification of databases and views.
Query languages, SQL and query by examples. Security of databases against
misuse. Domain constraints, referential integrity, functional dependencies,
assertions and triggers. Pitfall in relational database design. Normalization using
functional, multi valued and join dependencies. Domain key normal form. Alternative
approaches to database design.
Data storage, Physical storage media, files organization, organisation of records into
blocks, sequential files , mapping relational data to files, data dictionary storage, buffer
management,
Basic concept of indexing and hashing, properties of indexes, index specification in
SQL,. B+ - Tree and B-Tree index files. Hash base indexing, static hash functions,
dynamic hash function.

OPERATING SYSTEM AND SYSTEM PROGRAMMING
Introduction to operating system, operating system functions, batch processing systems,
multiprogramming systems, time sharing systems, real time operating systems.
Process management, process concept, process scheduling, operation on processes,
cooperating processes, interprocess communication.
CPU scheduling, scheduling algorithms – first come first served, shortest job first,
priority based, round robin, multilevel queue, multilevel feedback queue.
Process synchronization, critical section problem, semaphores, monitors. Deadlocks,
deadlock prevention, deadlock avoidance, deadlock detection.
Memory management, contiguous allocation, paging, segmentation, virtual memory,
demand paging, page replacement, page replacement algorithms – first in first out
algorithm, optimal algorithm, least recently used algorithm.
File concepts, directory structure, file protection, allocation of disk space.
I/O systems, I/O hardware – polling, interrupts, direct memory access. Disk scheduling,
disk scheduling algorithms – first come first served algorithm, shortest seek time first
algorithm, SCAN algorithm, C-SCAN algorithm, C-LOOK algorithm.
Protection and security in an operating system, access matrix, capabilities.
Assemblers, loaders, Linkers, Maacro-Assemblers, Compiler’s phases and passes.