## CERTIFICATE IN DISCRETE MATHEMATICS

Duration: 3 MONTHS

## Course Syllabus

Set Theory

• Definition of Sets, Venn Diagrams, complements, cartesian products, power sets, countingprinciple, cardinality and countability (Countable and Uncountable sets), proofs of some general identitites on sets, pigeonhole principle.
• Relation:Definition, types of relation, composition of relations, domain and range of a relation, pictorial representation of relation, properties of relation, partial ordering relation.
• Function: Definition and types of function, composition of functions, recursively defined functions.

Propositional logic:

• Proposition logic, basic logic, logical connectives, truth tables, tautologies, contradiction , normal forms(conjunctive and disjunctive), modus ponens and modus tollens, validity, predicate logic, universal and existential quantification. Notion of proof: proof by implication, converse, inverse, contrapositive, negation, and contradiction, direct proof, proof by using truth table, proof by counter example.
• Combinatories:Mathematical induction, recursive mathematical definitions, basics of counting, permutations, combinations, inclusion-exclusion, recurrence relations (nth order recurrence relation with constant coefficients, Homogeneous recurrence relations, Inhomogeneous recurrence relation),generating function (closed form expression, properties of G.F., solution of recurrence relation usingG.F, solution of combinatorial problem using G.F.)

Algebraic Structure:

• Binary composition and its properties definition of algebraic structure; Groyas Semi group, Monoid Groups, Abelian Group, properties of groups, Permutation Groups, Sub Group, Cyclic Group, Rings and Fields (definition and standard results).

Graphs:

• Graph terminology, types of graph connected graphs, components of graph, Euler graph, Hamiltonian path and circuits, Graph coloring, Chromatic number. Tree: Definition, types of tree(rooted, binary),properties of trees, binary search tree, tree traversing (preorder, inorder, postorder).
• Finite Automata:Basic concepts of Automation theory, Deterministic finite Automation(DFA), transition function, transition table, Non Deterministic Finite Automata (NDFA),Mealy and Moore Machine, Minimization of finite Automation.

## Eligibility

.

### All courses

# Course Name Duration View Enquiry
1 CERTIFICATE IN IT PROFICIENCY 2 MONTHS
2 CERTIFICATE IN DESKTOP PUBLISHING 3 MONTHS
3 CERTIFICATE IN COMPUTER BASED ENGLISH TYPING - 30 W.P.M. 4 MONTHS
4 CERTIFICATE IN ACCOUNT EXPERT WITH TALLY.ERP9 4 MONTHS
5 CERTIFICATE IN COMPUTER BASED ENGLISH TYPING - 40 W.P.M. 4 MONTHS
6 CERTIFICATE IN COMPUTER BASED MARATHI TYPING - 30 W.P.M. 4 MONTHS
7 CERTIFICATE IN COMPUTER BASED MARATHI TYPING - 40 W.P.M. 4 MONTHS
8 CERTIFICATE IN MS OFFICE AND INTERNET 3 MONTHS
9 CERTIFICATE IN TALLY.ERP9 ADVANCED 4 MONTHS
10 CERTIFICATE IN COMPUTERIZED ACCOUNTING 3 MONTHS
11 CERTIFICATE IN DATA ENTRY OPERATOR 6 MONTHS
12 CERTIFICATE IN INFORMATION TECHNOLOGY 3 MONTHS
13 CERTIFICATE IN OFFICE AUTOMATION 3 MONTHS
14 DIPLOMA IN SOFTWARE APPLICATION 6 MONTHS
15 CERTIFICATE IN PROGRAMMING IN C 3 MONTHS
16 CERTIFICATE IN TALLY.ERP9 BASIC 2 MONTHS
17 CERTIFICATE IN COMPUTER FUNDAMENTALS 3 MONTHS
18 ADVANCE CERTIFICATE IN COMPUTER FUNDAMENTALS 3 MONTHS
19 CERTIFICATE IN AUTOCAD 2 MONTHS
20 CERTIFICATE IN DIGITAL COMPUTER FUNDAMENTALS 3 MONTHS
21 MASTER CERTIFICATE IN COMPUTER APPLICATIONS AND ADVANCED ACCOUNTING 6 MONTHS
22 CERTIFICATE IN C++ PROGRAMMING 3 MONTHS
23 CERTIFICATE IN ADVANCED EXCEL 3 MONTHS
24 DIPLOMA IN OFFICE AUTOMATION 6 MONTHS
25 DIPLOMA IN DESKTOP PUBLISHING 6 MONTHS
26 CERTIFICATE IN COMPUTER APPLICATIONS 3 MONTHS
27 DIPLOMA IN INFORMATION TECHNOLOGY 6 MONTHS
28 CERTIFICATE IN ACCOUNTING AND TAXATION 3 MONTHS
29 CERTIFICATE IN FUNDAMENTALS OF COMPUTER AND INTERNET 3 MONTHS
30 CERTIFICATE IN HARDWARE AND NETWORKING 5 MONTHS
31 CERTIFICATE IN COMPUTER TEACHERS TRAINING 6 MONTHS
32 DIPLOMA IN FINANCIAL ACCOUNTING 9 MONTHS
33 CERTIFICATE IN SERVLET AND JSP 1 MONTH
34 CERTIFICATE IN COMPUTER HARDWARE 3 MONTHS
35 ADVANCE DIPLOMA IN INFORMATION TECHNOLOGY 6 MONTHS
36 CERTIFICATE IN WEB DESIGNING 2 MONTHS
37 CERTIFICATE IN INTERNET USAGE AND UTILITY 2 MONTHS
38 CERTIFICATE IN COMPUTER BASED HINDI TYPING - 30 W.P.M. 4 MONTHS
39 DIPLOMA IN COMPUTER SOFTWARE 6 MONTHS
40 CERTIFICATE IN BANKING AND MUTUAL FUND PRODUCTS 3 MONTHS
41 CERTIFICATE IN JAVA - CORE 3 MONTHS
42 ADVANCE DIPLOMA IN SOFTWARE ENGINEERING 1 YEAR
43 CERTIFICATE IN OFFICE PROFESSIONAL 3 MONTHS
44 CERTIFICATE IN CATIA V5 1.5 MONTHS
45 ADVANCE DIPLOMA IN COMPUTER SOFTWARE 12 MONTHS
46 CERTIFICATE IN COMMUNICATION IN ENGLISH 3 MONTHS
47 CERTIFICATE IN PRINCIPLES AND PRACTICES OF LIFE AND GENERAL INSURANCE 3 MONTHS
48 CERTIFICATE IN FINANCIAL ACCOUNTING MANAGEMENT 3 MONTHS
49 CERTIFICATE IN INTRODUCTION TO C PROGRAMMING 3 MONTHS
50 CERTIFICATE IN COMPUTER BASED HINDI TYPING - 40 W.P.M. 4 MONTHS
51 DIPLOMA IN 2D AND 3D AUTOCAD 6 MONTHS
52 CERTIFICATE IN PHOTOSHOP 2 MONTHS
53 CERTIFICATE IN C# .NET PROGRAMMING 3 MONTHS
54 CERTIFICATE IN CAD 3 MONTHS
55 CERTIFICATE IN COMPUTER NETWORKING 3 MONTHS
56 CERTIFICATE IN VB.NET PROGRAMING 3 MONTHS
57 CERTIFICATE IN ASP.NET PROGRAMING 3 MONTHS
58 CERTIFICATE IN JAVA - ADVANCE 3 MONTHS
59 CERTIFICATE IN MOBILE PHONE REPAIRING 3 MONTHS
60 CERTIFICATE IN JAVA PROGRAMMING 3 MONTHS
61 CERTIFICATE IN C++ 2 MONTHS
62 CERTIFICATE IN ADVANCE NETWORKING 3 MONTHS
63 CERTIFICATE IN ADVANCE WIRELESS AND MOBILE COMMUNICATION 3 MONTHS
64 CERTIFICATE IN ADVANCE COMMUNICATION 3 MONTHS
65 CERTIFICATE IN BRAND MANAGEMENT 3 MONTHS
66 CERTIFICATE IN BUSINESS COMMUNICATION 3 MONTHS
67 CERTIFICATE IN BUSINESS COMPUTER APPLICATIONS 3 MONTHS
68 CERTIFICATE IN BUSINESS STRATEGY 3 MONTHS
69 CERTIFICATE IN CAPITAL MARKETS 3 MONTHS
70 CERTIFICATE IN CIRCUIT THEORY AND BASIC ELECTRONICS 3 MONTHS
71 CERTIFICATE IN COMPUTER APPLICATIONS IN INFRASTRUCTURE 3 MONTHS
72 CERTIFICATE IN COMPUTER GRAPHICS 3 MONTHS
73 CERTIFICATE IN COMPUTER ORGANIZATION AND SYSTEM ARCHITECTURE 3 MONTHS
74 CERTIFICATE IN COMPUTER ORGANIZATION 3 MONTHS
75 CERTIFICATE IN COMPUTER-BASED NUMERICAL METHODS 3 MONTHS
76 CERTIFICATE IN CONCEPTS OF SUPPLY CHAIN MANAGEMENT 3 MONTHS
77 CERTIFICATE IN CONSTRUCTING FINANCIAL PLAN AND WEALTH MANAGEMENT 3 MONTHS
78 CERTIFICATE IN CORPORATE COMMUNICATION 3 MONTHS
79 CERTIFICATE IN CORPORATE TAX PLANNING 3 MONTHS
80 CERTIFICATE IN DATA STRUCTURES 3 MONTHS
81 CERTIFICATE IN DATABASE MANAGEMENT SYSTEMS 3 MONTHS
82 CERTIFICATE IN DESIGN AND ANALYSIS OF ALGORITHMS 3 MONTHS
83 CERTIFICATE IN DIGITAL SYSTEMS DESIGN 3 MONTHS
84 CERTIFICATE IN DISCRETE MATHEMATICS 3 MONTHS
85 CERTIFICATE IN ELECTROMAGNETICS AND RADIATION 3 MONTHS
86 CERTIFICATE IN ENERGY AUDIT AND MANAGEMENT 3 MONTHS
87 CERTIFICATE IN ENERGY EFFICIENCY IN ELECTRICAL UTILITIES 3 MONTHS
88 CERTIFICATE IN ENRICHMENT - TRAINING AND DEVELOPMENT 3 MONTHS
89 CERTIFICATE IN ENTERPRISE RESOURCE AND PLANNING 3 MONTHS
90 CERTIFICATE IN ENTREPRENEURSHIP 3 MONTHS
91 CERTIFICATE IN FASHION RETAILING AND VISUAL MERCHANDISING 3 MONTHS
92 CERTIFICATE IN FINANCIAL MANAGEMENT 3 MONTHS
93 CERTIFICATE IN FINANCIAL MANAGEMENT FOR INFRASTRUCTURE PROJECTS 3 MONTHS
94 CERTIFICATE IN FINANCIAL PLANNING 3 MONTHS
95 CERTIFICATE IN FINANCIAL REPORTING AND CONTROL (ACCOUNTS) 3 MONTHS
96 CERTIFICATE IN FINANCIAL SERVICES MARKETING 3 MONTHS
97 CERTIFICATE IN FRANCHISE AND OPERATIONS MANAGEMENT 3 MONTHS
98 CERTIFICATE IN FRONT OFFICE OPERATIONS MANAGEMENT 3 MONTHS
99 CERTIFICATE IN FUTURE TRENDS AND COMPETENCY IN TELECOM BUSINESS 3 MONTHS
100 CERTIFICATE IN GENERAL ASPECTS OF ENERGY MANAGEMENT AND ENERGY AUDIT 3 MONTHS
101 CERTIFICATE IN HEALTH ECONOMICS AND INSURANCE 3 MONTHS
102 CERTIFICATE IN HORTICULTURE NURSERY MANAGEMENT 3 MONTHS
103 CERTIFICATE IN HUMAN RESOURCE MANAGEMENT 3 MONTHS
104 CERTIFICATE IN INDUSTRIAL MARKETING 3 MONTHS
105 CERTIFICATE IN INTERNATIONAL ECONOMY AND FINANCE 3 MONTHS
106 CERTIFICATE IN INTERNATIONAL MARKETING 3 MONTHS
107 CERTIFICATE IN INTRODUCTION TO DIGITAL ELECTRONICS 3 MONTHS
108 CERTIFICATE IN INVESTMENT PLANNING AND MANAGEMENT 3 MONTHS
109 CERTIFICATE IN LEADERSHIP AND ORGANISATIONAL BEHAVIOR 3 MONTHS
110 CERTIFICATE IN LEGAL ASPECTS OF SUPPLY CHAIN MANAGEMENT 3 MONTHS
111 CERTIFICATE IN LEGAL FRAMEWORK AND BUSINESS 3 MONTHS
112 CERTIFICATE IN LEGAL REGULATORY FRAMEWORK 3 MONTHS
113 CERTIFICATE IN LIFE INSURANCE 3 MONTHS
114 DIPLOMA IN WEB DESIGNING 9 MONTHS
115 CERTIFICATE IN MALL MANAGEMENT 3 MONTHS
116 CERTIFICATE IN MANAGEMENT INFORMATION SYSTEMS 3 MONTHS
117 CERTIFICATE IN MANAGERIAL ECONOMICS 3 MONTHS
118 CERTIFICATE IN MANAGERIAL FINANCE 3 MONTHS
119 CERTIFICATE IN MANAGERIAL PRACTICES AND ORGANIZATION BEHAVIOR 3 MONTHS
120 CERTIFICATE IN MANAGING E-BUSINESS 3 MONTHS
121 CERTIFICATE IN MANAGING FINANCIAL RESOURCES 3 MONTHS
122 CERTIFICATE IN MARINE INSURANCE 3 MONTHS
123 CERTIFICATE IN MARKETING AND PUBLIC RELATIONS MANAGEMENT 3 MONTHS
124 CERTIFICATE IN MARKETING MANAGEMENT 3 MONTHS
125 CERTIFICATE IN MATERIAL MANAGEMENT 3 MONTHS
126 CERTIFICATE IN MISCELLANEOUS INSURANCE 3 MONTHS
127 CERTIFICATE IN NETWORK MANAGEMENT 3 MONTHS
128 CERTIFICATE IN OBJECT ORIENTED ANALYSIS AND DESIGN 3 MONTHS
129 CERTIFICATE IN OBJECT ORIENTED PROGRAMMING USING C++ 3 MONTHS
130 CERTIFICATE IN OPERATING SYSTEMS 3 MONTHS
131 CERTIFICATE IN OPERATIONS MANAGEMENT 3 MONTHS
132 CERTIFICATE IN ORGANIZATIONAL BEHAVIOUR 3 MONTHS
133 CERTIFICATE IN OVERVIEW OF INDIAN INFRASTRUCTURE MANAGEMENT 3 MONTHS
134 CERTIFICATE IN PATTERN RECOGNITION 3 MONTHS
135 CERTIFICATE IN PORTFOLIO MANAGEMENT 3 MONTHS
136 CERTIFICATE IN PRINCIPLES OF MANAGEMENT 3 MONTHS
137 CERTIFICATE IN PRODUCT AND BRAND MANAGEMENT 3 MONTHS
138 CERTIFICATE IN PRODUCTION PLANNING AND CONTROL 3 MONTHS
139 CERTIFICATE IN PROFESSIONAL SKILL DEVELOPMENT 3 MONTHS
140 CERTIFICATE IN PROJECT ADMINISTRATION 3 MONTHS
141 CERTIFICATE IN PROJECT EXECUTION 3 MONTHS
142 CERTIFICATE IN PROJECT MANAGEMENT 3 MONTHS
143 CERTIFICATE IN PROJECT PLANNING CONCEPTS 3 MONTHS
144 CERTIFICATE IN QUANTITATIVE TECHNIQUES IN BUSINESS 3 MONTHS
145 CERTIFICATE IN REAL ESTATE AND RETAIL SPACE MANAGEMENT 3 MONTHS
146 CERTIFICATE IN RECRUITMENT, SELECTION AND RETENTION 3 MONTHS
147 CERTIFICATE IN RETAIL MARKETING 3 MONTHS
148 CERTIFICATE IN RETAIL PERSONNEL MANAGEMENT 3 MONTHS
149 CERTIFICATE IN RETAIL SALES AND CUSTOMER SERVICE 3 MONTHS
150 CERTIFICATE IN 3D S MAX 3 MONTHS
151 CERTIFICATE IN RISK MANAGEMENT 3 MONTHS
152 CERTIFICATE IN JAVA 7 PROGRAMMING 2 MONTHS
153 CERTIFICATE IN JAVA 8 PROGRAMMING 2 MONTHS
154 CERTIFICATE IN ROBOTICS 3 MONTHS
155 CERTIFICATE IN SECURITY ANALYSIS 3 MONTHS
156 CERTIFICATE IN PHP AND MYSQL 2 MONTHS
157 CERTIFICATE IN STATISTICS 3 MONTHS
158 CERTIFICATE IN STRATEGIC HUMAN RESOURCE MANAGEMENT 3 MONTHS
159 CERTIFICATE IN STRATEGIC MANAGEMENT FOR HOSPITAL 3 MONTHS
160 CERTIFICATE IN STRATEGIC RETAIL MANAGEMENT 3 MONTHS
161 CERTIFICATE IN STRESS ANALYSIS 3 MONTHS
162 CERTIFICATE IN SUPPLY CHAIN MANAGEMENT 3 MONTHS
163 CERTIFICATE IN TECHNOLOGY AND OPERATIONS MANAGEMENT 3 MONTHS
164 CERTIFICATE IN WEB TECHNOLOGIES AND MULTIMEDIA 3 MONTHS
165 CERTIFICATE IN WEB TECHNOLOGY 2 MONTHS
166 CERTIFICATE IN WIRELESS NETWORKS: FUNDAMENTAL AND FUTURE REVOLUTIONS 3 MONTHS
167 CERTIFICATE IN FINANCIAL ACCOUNTING WITH TALLY.ERP9 3 MONTHS
168 CERTIFICATE IN ANDROID APPLICATION DEVELOPMENT 3 MONTHS
169 CERTIFICATE IN HTML5 1 MONTH
170 CERTIFICATE IN CASCADING STYLE SHEETS 1 MONTH
171 CERTIFICATE IN JAVA SCRIPT 1 MONTH
172 CERTIFICATE IN JQUERY AND JQUERY-UI 1 MONTH
173 CERTIFICATE IN BOOTSTRAP 1 MONTH
174 CERTIFICATE IN ANGULAR JS 1 MONTH
175 CERTIFICATE IN WEB DESIGNING - FOUNDATION 3 MONTHS
176 CERTIFICATE IN PROFESSIONAL WEB DESIGNING 3 MONTHS
177 CERTIFICATE IN PROFESSIONAL WEB DEVELOPER 3 MONTHS
178 DIPLOMA IN HARDWARE ENGINEERING 6 MONTHS
179 CERTIFICATE IN ADVANCED INTERIOR DESIGN 12 MONTHS
180 CERTIFICATE IN BASIC INTERIOR DESIGN 9 MONTHS
181 ADVANCE DIPLOMA IN MULTIMEDIA APPLICATIONS 1 YEAR
182 ADVANCE DIPLOMA IN INFORMATION TECHNOLOGY 1 YEAR
183 CERTIFICATE IN CREATIVE DIGITAL ARTS 3 MONTHS
184 CERTIFICATE IN FINANCIAL ACCOUNTING 3 MONTHS
185 CERTIFICATE IN C PROGRAMMING 2 MONTHS
186 CERTIFICATE IN COMPUTER PROFICIENCY (LITTLE BYTE) 4 MONTHS
187 CERTIFICATE IN BASIC BEAUTY PARLOUR 3 MONTHS
188 CERTIFICATE IN BASIC TAILORING 3 MONTHS
189 CERTIFICATE IN BASIC FASHION DESIGNING 6 MONTHS
190 CERTIFICATE IN ADVANCED FASHION DESIGNING 1 YEAR
191 DIPLOMA IN PROFESSIONAL COMPUTER TEACHERS TRAINING 1 YEAR
192 CERTIFICATE IN SCRATCH PROGRAMMING 2 MONTHS
193 ALL INDIA CERTIFICATE IN INFORMATION TECHNOLOGY 2 MONTHS
194 DIPLOMA IN OFFICE MANAGEMENT 6 MONTHS
195 CERTIFICATE IN PAYROLL MANAGEMENT 2 MONTHS
196 CERTIFICATE IN WIREMAN 6 MONTHS
197 ADVANCE DIPLOMA IN COMPUTER APPLICATION 1 YEAR
198 DIPLOMA IN DATA ENTRY OPERATOR 1 YEAR
199 DIPLOMA IN COMPUTER APPLICATION 1 YEAR
200 ADVANCE DIPLOMA IN COMPUTER APPLICATION 6 MONTHS
201 MASTER DIPLOMA IN COMPUTERIZED ACCOUNTING 6 MONTHS
202 DIPLOMA IN COMPUTERIZED ACCOUNTING 6 MONTHS
203 CERTIFICATE IN ADVERTISING AND SALES PROMOTION 3 MONTHS
204 MASTER DIPLOMA IN COMPUTER APPLICATIONS AND ADVANCED ACCOUNTING 1 YEAR
205 DIPLOMA IN YOGA 1 YEAR
206 DIPLOMA IN ENVIRONMENTAL SANITATION 1 YEAR
207 CERTIFICATE IN COMPUTER CONCEPT 3 MONTHS
208 DIPLOMA IN COMPUTER CONCEPT 6 MONTHS
209 CERTIFICATE IN HOTEL MANAGEMENT 3 MONTHS
210 DIPLOMA IN HOTEL MANAGEMENT 1 YEAR
211 ADVANCE DIPLOMA IN COMPUTER APPLICATIONS AND PROGRAMMING 1 YEAR
212 DIPLOMA IN HTML 6 MONTHS
213 DIPLOMA IN NETWORK ADMINISTRATION 6 MONTHS
214 CERTIFICATE IN HTML 3 MONTHS
215 DIPLOMA IN WINDOWS SERVER ADMINISTRATION 6 MONTHS
216 DIPLOMA IN NURSERY TEACHER TRAINING 1 YEAR
217 CERTIFICATE IN NURSERY TEACHER TRAINING 4 MONTHS
218 CERTIFICATE IN INDIAN GOODS AND SERVICE TAX 2 MONTHS
219 DIPLOMA IN DIESEL MECHANICS 1 YEAR
220 DIPLOMA IN WELDING TECHNOLOGY 1 YEAR
221 DIPLOMA IN ELECTRICIAN 1 YEAR
222 DIPLOMA IN COMPUTER OPERATOR AND PROGRAMMING ASSISTANT 1 YEAR
223 CERTIFICATE IN TALLY.ERP 9 WITH GST 3 MONTHS
224 CERTIFICATE IN COMPUTERIZED ACCOUNTING WITH GST 3 MONTHS
225 CERTIFICATE IN COREL DRAW 2 MONTHS
226 CERTIFICATE IN REVIT ARCHITECTURE 2 MONTHS
227 MASTER DIPLOMA IN COMPUTER ENGINEERING 1 YEAR
228 DIPLOMA IN TALLY.ERP9 WITH GST 1 YEAR
229 CERTIFICATE IN STAAD.PRO 1 MONTH
230 DIPLOMA IN PLUMBING 1 YEAR
231 CERTIFICATE IN SECURITY MANAGEMENT 3 MONTHS
232 CERTIFICATE IN ELECTRONIC SECURITY SERVICES 3 MONTHS
233 DIPLOMA IN SECURITY MANAGEMENT 6 MONTHS
234 DIPLOMA IN COMPUTER APPLICATION 6 MONTHS
235 CERTIFICATE IN COMPUTER APPLICATION 6 MONTHS
236 CERTIFICATE IN VIDEO EDITING 2 MONTHS
237 DIPLOMA IN CYBER LAW 6 MONTHS
238 CERTIFICATE IN FINANCIAL ACCOUNTING WITH TALLY.ERP9 6 MONTHS
239 CERTIFICATE IN SPOKEN ENGLISH 3 MONTHS
240 CERTIFICATE IN ENGLISH GRAMMAR 3 MONTHS
241 CERTIFICATE IN ENGLISH COMMUNICATION 6 MONTHS
242 DIPLOMA IN BEAUTY PARLOUR 1 YEAR
243 DIPLOMA IN COMPUTER AND DIGITAL APPLICATION 6 MONTHS
244 DIPLOMA IN TAILORING 6 MONTHS
245 CERTIFICATE IN SOLIDWORKS 2 MONTHS
246 DIPLOMA IN COMPUTER BASED ENGLISH TYPING - 30 W.P.M. 6 MONTHS
247 DIPLOMA IN COMPUTER BASED ENGLISH TYPING - 40 W.P.M. 6 MONTHS
248 CERTIFICATE IN DIGITAL PHOTOGRAPHY 3 MONTHS
249 DIPLOMA IN HARDWARE AND NETWORKING 1 YEAR
250 CERTIFICATE IN ANGULAR 2 MONTHS
251 CERTIFICATE IN PROFESSIONAL AUTOCAD 3 MONTHS
252 CERTIFICATE IN CARPENTER 2 MONTHS
253 CERTIFICATE IN CREO 3 MONTHS
254 CERTIFICATE IN PRO-E 3 MONTHS
255 ADVANCE CERTIFICATE IN LIBRARIAN 6 MONTHS
256 DIPLOMA IN BUILDING CONSTRUCTION 1 YEAR
257 CERTIFICATE IN ABC (DUMMY COURSE FOR SOFTWARE TESTING) 1 YEAR
258 DIPLOMA IN CARPENTER 1 YEAR
259 CERTIFICATE IN WINDOWS APP AND ADO.NET 1 MONTH
260 CERTIFICATE IN ASP.NET WITH MVC 1 MONTH
261 ADVANCE CERTIFICATE IN FINANCIAL ACCOUNTING 3 MONTHS
262 DIPLOMA IN BANKING AND FINANCE SERVICE 6 MONTHS
263 DIPLOMA IN COMPUTER TEACHERS EDUCATION 1 YEAR
264 CERTIFICATE IN COMPUTER AWARENESS PROGRAM 2 MONTHS
265 CERTIFICATE IN PYTHON 2 MONTHS
266 DIPLOMA IN GRAPHIC DESIGN 6 MONTHS
267 DIPLOMA IN COMPUTER OPERATOR 6 MONTHS
268 CERTIFICATE IN ETABS 45 DAYS
269 DIPLOMA IN DIGITAL CITIZEN 6 MONTHS
270 DIPLOMA IN STENOGRAPHY 1 YEAR
271 DIPLOMA IN COMPUTER BASED MARATHI TYPING - 30 W.P.M. 6 MONTHS
272 DIPLOMA IN COMPUTER BASED MARATHI TYPING - 40 W.P.M. 6 MONTHS
273 DIPLOMA IN COMPUTER BASED HINDI TYPING - 30 W.P.M. 6 MONTHS
274 DIPLOMA IN COMPUTER BASED HINDI TYPING - 40 W.P.M. 6 MONTHS
275 DIPLOMA IN COMPUTER APPLICATION AND DTP 1 YEAR
276 CERTIFICATE IN ADVANCE COMPUTER COURSE IN FANDAMENTAL WITH HTML 3 MONTHS
277 DIPLOMA IN COMPUTER BASED ENGLISH TYPING - 30 W.P.M. 1 YEAR
278 DIPLOMA IN COMPUTER BASED ENGLISH TYPING - 40 W.P.M 1 YEAR
279 DIPLOMA IN OFFICE MANAGEMENT WITH TALLY 6 MONTHS
280 CERTIFICATE IN MS OFFICE 2 MONTH
281 CERTIFICATE IN INDUSTRIAL FIRE AND SAFETY 6 MONTHS
282 DIPLOMA IN FIRE AND SAFETY ENGINEERING 1 YEAR
283 DIPLOMA IN TALLY.ERP9 WITH GST 6 MONTHS
284 DIPLOMA IN GST WITH TALLY ERP.9 6 MONTHS
285 DIPLOMA IN FASHION DESIGNING 8 MONTHS
286 CERTIFICATE IN ADOBE ILLUSTRATOR 2 MONTHS
287 CERTIFICATE IN BIM ENGINEERING 6 MONTHS
288 CERTIFICATE IN CNC OPERATING 3 MONTH
289 CERTIFICATE IN CNC OPERATING AND PROGRAMMING 6 MONTHS
290 CERTIFICATE IN PRIMAVERA 2 MONTHS
291 DIPLOMA IN CNC OPERATING AND PROGRAMMING 1 YEAR
292 CERTIFICATE IN COMPUTER BASED ENGLISH TYPING - 30 W.P.M. 2 MONTHS
293 CERTIFICATE IN COMPUTER BASED ENGLISH TYPING - 40 W.P.M. 2 MONTHS
294 CERTIFICATE IN COMPUTER BASED MARATHI TYPING - 30 W.P.M. 2 MONTHS
295 CERTIFICATE IN COMPUTER BASED MARATHI TYPING - 40 W.P.M. 2 MONTHS
296 CERTIFICATE IN COMPUTER BASED HINDI TYPING - 30 W.P.M. 2 MONTHS
297 CERTIFICATE IN COMPUTER BASED HINDI TYPING - 40 W.P.M. 2 MONTHS
298 CERTIFICATE IN TESTING 1 MONTH
299 CERTIFICATE IN C++ 20 DAYS
300 DIPLOMA IN DIGITAL MARKETING 6 MONTHS
301 CERTIFICATE IN UNIGRAPHICS NX 2 MONTHS
302 CERTIFICATE IN AUTOCAD 20 DAYS
303 DIPLOMA IN COMPUTER EDUCATION 1 YEAR
304 CERTIFICATE IN VISUAL BASIC 3 MONTHS
305 DIPLOMA IN COMPUTERIZED INDUSTRIAL ACCOUNTING 1 YEAR
306 DIPLOMA IN WEB DESIGNING AND WEB DEVELOPMENT 1 YEAR
307 DIPLOMA IN FINANCIAL ACCOUNTING 1 YEAR
308 CERTIFICATE IN TESTKING 2 MONTH