MCQ Bank

Subjects
All Subjects 56097 ACC311
Fundamentals of Auditing
F:210
210 ACC31Q
F:97
97 ACC501
Business Finance
F:248
248 ACC707
F:33
33 BIF101
Introduction to Bioinformatics
F:37
37 BIF401
Bioinformatics I
F:27
27 BIF401P
Bioinformatics I (Practical)
F:53
53 BIF501
Bioinformatics II
F:63
63 BIF501P
Bioinformatics II (Practical)
F:49
49 BIF601
Bioinformatics Computing I
F:25
25 BIF601P
Bioinformatics Computing I (Practical)
F:35
35 BIF602
Bioinformatics Computing II
F:3
3 BIF604
Special Topics in Bioinformatics
F:67
67 BIO101
Basic I-Biology
F:17
17 BIO102
Basic II-Chemistry
F:38
38 BIO201
M:30
30 BIO203
M:42
42 BIO303
M:29
29 BIO401
Biostatistics
F:24
24 BIO502
Genomics
F:20
20 BIO503
Biological Physics
M:30 F:48
78 BIO504P
Biochemistry I (Practical)
F:23
23 BIO504T
Biochemistry I (Theory)
F:12
12 BIO505P
Essentials of Genetics (Practical)
F:71
71 BIO505T
Essentials of Genetics (Theory)
F:11
11 BIO506P
Biochemistry II (Practical)
F:35
35 BIO506T
Biochemistry II (Theory)
F:16
16 BIO5101
Introduction to Biotechnology
F:25
25 BIO5105
Cell Biology
F:18
18 BIO601
Proteomics
F:20
20 BIO732
Gene Manipulation and Genetic Engineering
F:49
49 BNK601
Banking Laws & Practices
F:129
129 BNK603
Consumer Banking
F:115
115 BNK610
Islamic Banking Practices
F:69
69 BNK611
Economic Ideology in Islam
F:102
102 BNK612
Financial Jurisprudence in Islam
F:29
29 BNK613
Islamic Ethics in Business
F:23
23 BT101
Ecology, Biodiversity & Evolution-I
F:80
80 BT102
M:31 F:53
84 BT201
F:246
246 BT301
F:30
30 BT302
Immunology
M:55 F:35
90 BT401
Genetic Resources & Conservation
F:163
163 BT402
F:37
37 BT403
F:43
43 BT404
M:9
9 BT405
Nano Biotechnology
F:41
41 BT406
Research Methodology & Skill Enhancement
F:106
106 BT501
Health Biotechnology
F:141
141 BT503
Environment Biotechnology
F:74
74 BT504
Genomics and Proteomics
F:67
67 BT505
Biosensors
F:68
68 BT511P
Introduction to Biotechnology (Practical)
F:25
25 BT511T
F:27
27 BT512P
Microbial Biotechnology (Practical)
F:74
74 BT512T
Microbial Biotechnology (Theory)
F:170
170 BT513P
Principles of Biochemical Engineering (Practical)
F:71
71 BT513T
Principles of Biochemical Engineering (Theory)
F:37
37 BT601
Virology
F:69
69 BT603
F:21
21 BT604
F:19
19 BT605
Biosafety & Bioethics
F:58
58 BT611P
Food Biotechnology (Practical)
F:52
52 BT611T
Food Biotechnology (Theory)
F:55
55 BT612P
Fermentation Technology (Practical)
F:31
31 BT612T
Fermentation Technology (Theory)
F:12
12 BT613T
Agriculture Biotechnology (Theory)
F:28
28 BT614P
Industrial Biotechnology (Practical)
F:28
28 BT614T
Industrial Biotechnology (Theory)
F:37
37 CHE201
Physical Chemistry
F:77
77 CHE301
M:28
28 CS001
F:58
58 CS101
Introduction to Computing
F:751
751 CS201
Introduction to Programming
M:97 F:247
344 CS201P
Introduction to Programming (Practical)
F:200
200 CS202
F:192
192 CS204
F:77
77 CS205
Information Security
F:87
87 CS206
F:57
57 CS301
Data Structures
F:141
141 CS301P
Data Structures (Practical)
F:63
63 CS302
Digital Logic Design
F:192
192 CS302P
F:64
64 CS304
Object Oriented Programming
F:89
89 CS304P
Object Oriented Programming (Practical)
F:147
147 CS306
Introduction to Python
F:75
75 CS306P
Introduction to Python (Practical)
F:88
88 CS311
Introduction to Web Services Development
F:132
132 CS312
F:47
47 CS314
Introduction to Cellular Networks
F:84
84 CS315
F:57
57 CS401
F:117
117 CS401P
F:94
94 CS402
M:67 F:140
207 CS403
Database Management Systems
F:162
162 CS403P
Database Management Systems (Practical)
F:120
120 CS405
Database Programming using Oracle 11g
F:70
70 CS406
F:28
28 CS407
Routing and Switching
F:70
70 CS408
Human Computer Interaction
M:94 F:76
170 CS409
Introduction to Database Administration
F:43
43 CS409P
F:59
59 CS411
Visual Programming
F:100
100 CS420
Web Development for Portable Devices
F:106
106 CS431
Wireless Communication
F:43
43 CS432
F:80
80 CS435
Cloud Computing
F:46
46 CS441
F:73
73 CS442
Introduction to Data Science
F:29
29 CS501
F:120
120 CS502
Fundamentals of Algorithms
F:156
156 CS504
Software Engineering - I
F:179
179 CS505
F:49
49 CS505P
F:96
96 CS506
Web Design and Development
F:196
196 CS507
Information Systems
M:87 F:165
252 CS508
F:227
227 CS510
F:63
63 CS513
Advanced Data Analytics and Business Intelligence
F:128
128 CS514
F:23
23 CS521
F:26
26 CS525
F:25
25 CS601
Data Communication
F:137
137 CS602
Computer Graphics
F:105
105 CS603
F:62
62 CS603P
F:54
54 CS604
F:177
177 CS604P
F:86
86 CS605
F:82
82 CS606
F:194
194 CS607
Artificial Intelligence
F:134
134 CS607P
Artificial Intelligence (Practical)
F:108
108 CS608
F:75
75 CS609
F:89
89 CS610
Computer Networks
F:126
126 CS610P
F:100
100 CS611
F:78
78 CS614
Data Warehousing
F:126
126 CS615
F:121
121 CS620
Modelling and Simulation
F:62
62 CS621
F:38
38 CS625
Professional Practices
M:30 F:27
57 CS626
F:30
30 CS627
F:39
39 CS628
F:30
30 CS636
F:40
40 ECE101
Introduction to Early Childhood Education
F:69
69 ECE201
Language Development of the Child
F:47
47 ECE202
Physical Development of the Child
F:29
29 ECE203
Children Literature and Educational Games
F:56
56 ECE204
Independence, Self-Management and Ethics in Early Years
F:24
24 ECE301
Psycho Social Development of the Child
F:19
19 ECE302
Education for Sustainable Development in Early Childhood Education
F:21
21 ECE402
Trends and Issues in Early Childhood Education
F:48
48 ECO302
Principles of Microeconomics
F:36
36 ECO303
Principles of Macroeconomics
F:20
20 ECO401
Economics
F:383
383 ECO402
Microeconomics
F:99
99 ECO403
Macroeconomics
F:137
137 ECO404
Managerial Economics
F:129
129 ECO501
Development Economics
F:32
32 ECO601
Business Econometrics
F:40
40 ECO603
International Economics
F:53
53 ECO604
F:64
64 ECO605
F:30
30 ECO606
Mathematical Economics I
F:108
108 ECO607
F:182
182 ECO608
F:57
57 ECO609
F:48
48 ECO610
F:74
74 ECO612
F:21
21 ECO613
F:50
50 ECO614
F:47
47 ECO615
F:55
55 ECO616
F:68
68 ECO622
F:29
29 EDU101
Foundations of Education
M:155 F:72
227 EDU201
Learning Theories
F:95
95 EDU301
General Methods of Teaching
F:20
20 EDU302
Human Development and Learning
F:57
57 EDU303
Child Development
F:113
113 EDU304
Introduction to Guidance and Counseling
F:33
33 EDU305
Classroom Management
M:120 F:88
208 EDU306
Teaching of Social Studies and Islamiat in Early Years of Education
F:48
48 EDU401
Contemporary Issues and Trends in Education
M:122 F:117
239 EDU402
Curriculum Development
F:46
46 EDU403
Art, Crafts and Calligraphy
F:37
37 EDU405
Classroom Assessment
F:87
87 EDU406
Critical Thinking and reflective Practice
M:45 F:75
120 EDU407
Research Methods in Education
F:24
24 EDU410
Teaching of Literacy Skills
M:37 F:65
102 EDU411
Teaching of Urdu
F:312
312 EDU430
ICT in Education
M:276 F:147
423 EDU431
Test Development & Evaluation
M:33 F:62
95 EDU433
Professionalism in Teaching
M:84 F:66
150 EDU501
School, Community and Teacher
M:135 F:42
177 EDU505
M:29 F:41
70 EDU510
Teaching of Mathematics
F:15
15 EDU512
Teaching of Islamic Studies
F:86
86 EDU515
Teaching of Geography
F:12
12 EDU516
Teaching of English
M:31 F:54
85 EDU601
Philosophy of Education
F:129
129 EDU602
Educational Leadership and Management
F:52
52 EDU604
Comparative Education
F:103
103 EDU654
Addressing problems of learning through technology and pedagogy
M:98 F:25
123 EDU705
F:26
26 EDUA305
Classroom Management for Young Learners
F:52
52 EDUA402
Curriculum Development for Early Childhood Education
F:10
10 EDUA403
Teaching of Arts, Crafts & Calligraphy
F:49
49 EDUA405
Assessment and Evaluation in Early Years of Education
F:16
16 EDUA406
Reflective Practices and Critical Thinking in Early Years
F:47
47 EDUA411
Teaching of Urdu in Early Childhood
F:55
55 EDUA430
Use of Information and Communication Technology for Early Childhood Education
F:77
77 EDUA501
Role of School, Community & Teacher in Early Years of Education
F:32
32 EDUA510
Teaching of Mathematics in Early Childhood
F:11
11 EDUA516
Teaching of English in Early Childhood
F:51
51 EDUA601
Philosophical Foundations of Early Childhood Education
F:20
20 EDUA602
Leadership and Management of Early Childhood Education Programs
F:22
22 ENG001
F:417
417 ENG101
English Comprehension
F:344
344 ENG201
Business and Technical English Writing
M:47 F:289
336 ENG301
Business Communication
M:53 F:340
393 ENG401
F:63
63 ENG501
History of English Language
M:53 F:73
126 ENG502
Introduction to Linguistics
M:61 F:55
116 ENG503
Introduction to English Language Teaching
M:396 F:31
427 ENG504
Second Language Acquisition
F:44
44 ENG505
F:68
68 ENG506
World Englishes
F:60
60 ENG507
Phonetics and Phonology
F:64
64 ENG508
Semantics and Pragmatics
F:61
61 ENG509
Morphology and Syntax
M:17 F:50
67 ENG510
Sociolinguistics
F:41
41 ENG511
F:102
102 ENG512
F:44
44 ENG513
F:35
35 ENG514
F:57
57 ENG515
F:37
37 ENG516
F:50
50 ENG517
M:141 F:38
179 ENG518
M:17 F:65
82 ENG519
M:247 F:64
311 ENG520
M:116 F:112
228 ENG522
Applied Linguistics
M:38 F:92
130 ENG523
M:44 F:76
120 ENG524
M:20 F:48
68 ENG527
F:78
78 ENG529
M:15 F:34
49 ETH100
Effective Citizenship
F:145
145 ETH201
F:20
20 ETH202
Ethics (for Non-Muslims)
F:54
54 FIN611
Advanced Financial Accounting
F:113
113 FIN621
Financial Statement Analysis
F:168
168 FIN622
Corporate Finance
F:162
162 FIN623
Taxation Management
F:203
203 FIN624
Islamic Modes of Finance
F:99
99 FIN625
Credit & Risk Management
F:96
96 FIN630
F:217
217 FIN702
F:56
56 FIN703
F:104
104 FIN711
F:73
73 GSC101
General Science
F:423
423 GSC201
Teaching of General Science
F:47
47 GSCA201
Teaching of General Science in Early Years of Education
F:28
28 HRM613
Performance Management
F:59
59 HRM617
Training and Development
F:70
70 HRM624
Conflict Management
F:220
220 HRM626
Recruitment and selection
F:56
56 HRM627
Human Resource Development
F:300
300 HRM733
F:19
19 HRM737
F:20
20 ISL1151
F:126
126 ISL1252
F:87
87 ISL1253
F:73
73 ISL201
F:39
39 ISL202
Islamic Studies
F:903
903 ISL2351
F:24
24 ISL2352
F:84
84 ISL2453
F:26
26 ISL2454
F:52
52 IT430
E-Commerce
F:280
280 IT601
F:31
31 IT602
F:33
33 MB501P
Cell Biology (Practical)
F:48
48 MB502P
Molecular Biology (Practical)
F:111
111 MB502T
Molecular Biology (Theory)
M:119 F:67
186 MB503T
F:35
35 MB504P
Methods in Molecular Biology (Practical)
F:46
46 MB504T
Methods in Molecular Biology (Theory)
F:53
53 MCD401
F:10
10 MCD403
F:20
20 MCD504
Acting and Performance
F:80
80 MCM101
Introduction to Mass Communication
F:98
98 MCM301
Communication skills
F:66
66 MCM304
Mass Media in Pakistan
F:52
52 MCM310
Journalistic Writing
F:114
114 MCM311
Reporting and Sub-Editing
F:96
96 MCM401
Fundamentals of Public Relations
F:108
108 MCM411
Introduction to Broadcasting
F:76
76 MCM431
F:118
118 MCM501
Advertising for Print and Electronic Media
F:105
105 MCM511
Theories of Communication
F:44
44 MCM514
F:21
21 MCM515
F:21
21 MCM516
F:55
55 MCM517
F:68
68 MCM520
F:67
67 MCM532
F:42
42 MCM601
Media Management
F:99
99 MCM604
F:115
115 MCM610
Mass Communication Law & Ethics
F:85
85 MGMT611
Human Relations (alt. code=HRM611)
F:205
205 MGMT614
Supply Chain Management
F:43
43 MGMT615
Transportation & Logistics Management
F:42
42 MGMT617
Production Planning and Inventory Control
F:44
44 MGMT622
Management Skills
F:149
149 MGMT623
Leadership & Team Management - MGMT623 (alt. code=HRM623)
M:87 F:160
247 MGMT625
F:126
126 MGMT627
Project Management
F:130
130 MGMT628
F:234
234 MGMT629
F:99
99 MGMT630
F:112
112 MGMT631
Enterprise Resource Planning
F:43
43 MGT101
Financial Accounting
F:330
330 MGT111
Introduction to Public Administration
F:197
197 MGT201
Financial Management
F:110
110 MGT211
Introduction To Business
F:175
175 MGT301
Principles of Marketing
F:215
215 MGT302
Digital Marketing
F:39
39 MGT401
Financial Accounting II
F:30
30 MGT402
Cost & Management Accounting
F:107
107 MGT404
F:135
135 MGT411
Money & Banking
F:194
194 MGT415
Introduction to Business Analytics
F:86
86 MGT501
Human Resource Management
F:396
396 MGT502
Organizational Behaviour
M:167 F:555
722 MGT503
Principles of Management
F:325
325 MGT504
F:214
214 MGT510
Total Quality Management (alt. code=MGMT510)
M:100 F:561
661 MGT513
Public Administration in Pakistan
F:80
80 MGT520
International Business
F:231
231 MGT522
Introduction to Public Policy
F:116
116 MGT601
F:121
121 MGT602
Entrepreneurship
F:270
270 MGT603
Strategic Management
F:330
330 MGT604
Management of Financial Institutions (alt. code=BNK604)
F:123
123 MGT605
F:66
66 MGT610
M:20 F:231
251 MGT611
Business & Labor Law
F:122
122 MGT612
F:77
77 MGT613
Production / Operations Management
F:220
220 MGT621
F:114
114 MGT701
F:52
52 MGT703
F:46
46 MGT713
F:44
44 MGT714
F:71
71 MGT717
F:42
42 MGT723
F:20
20 MGT725
F:67
67 MGTE630
Knowledge Management
M:34 F:19
53 MIC501P
Microbiology (Practical)
F:71
71 MIC501T
Microbiology (Theory)
F:40
40 MKT501
Marketing Management
F:250
250 MKT529
Export Marketing
F:53
53 MKT530
Consumer Behaviour
F:71
71 MKT610
Customer Relationship Management
F:83
83 MKT621
Advertising & Promotion
F:94
94 MKT624
Brand Management
F:114
114 MKT627
Sales Management
F:61
61 MKT630
International Marketing
F:127
127 MKT703
F:37
37 MKT726
F:20
20 MTH001
F:276
276 MTH100
General Mathematics
F:216
216 MTH101
Calculus And Analytical Geometry
F:1292
1292 MTH102
F:32
32 MTH104
Sets and Logic
F:64
64 MTH201
F:68
68 MTH202
Discrete Mathematics
F:238
238 MTH301
F:406
406 MTH302
Business Mathematics & Statistics
F:778
778 MTH303
Mathematical Methods
F:160
160 MTH304
F:35
35 MTH401
F:226
226 MTH403
F:147
147 MTH404
F:41
41 MTH405
F:132
132 MTH501
Linear Algebra
F:366
366 MTH5101
Calculus I
F:27
27 MTH5102
Calculus II
F:12
12 MTH601
F:266
266 MTH603
F:160
160 MTH621
F:105
105 MTH622
F:62
62 MTH631
F:167
167 MTH632
F:97
97 MTH633
F:54
54 MTH634
F:67
67 MTH641
F:179
179 MTH642
F:76
76 MTH643
F:22
22 MTH644
F:101
101 MTH645
F:63
63 MTH646
F:91
91 MTH647
F:53
53 PAD603
F:60
60 PAK301
Pakistan Studies
M:10 F:155
165 PAK302
Pakistan Studies
F:131
131 PAK522
Ideology and Constitution of Pakistan
F:51
51 PHY101
Physics
F:626
626 PHY301
F:95
95 PSC201
International Relations
F:85
85 PSC401
F:48
48 PSY101
Introduction to Psychology
F:409
409 PSY401
F:166
166 PSY402
F:43
43 PSY403
Social Psychology
F:262
262 PSY404
Abnormal Psychology
F:137
137 PSY405
Personality Psychology
F:174
174 PSY406
Educational Psychology
M:182 F:244
426 PSY407
F:175
175 PSY408
F:207
207 PSY409
F:143
143 PSY502
History & Systems of Psychology
F:264
264 PSY504
Cognitive Psychology
F:126
126 PSY505
Developmental Psychology
F:108
108 PSY510
F:179
179 PSY511
Environmental Psychology
F:69
69 PSY512
Gender Issues in Psychology
F:192
192 PSY513
F:175
175 PSY514
F:104
104 PSY515
Cross Cultural Psychology
F:140
140 PSY516
F:88
88 PSY610
F:81
81 PSY611
Ethical Issues in Psychology
F:132
132 PSY631
F:116
116 PSY632
F:180
180 PSYP402
F:90
90 PSYP610
F:171
171 PSYP631
F:185
185 SE601
F:21
21 SE601P
F:61
61 SE602
F:36
36 SOC101
Introduction to Sociology
M:121 F:1279
1400 SOC201
Social Statistics
F:191
191 SOC301
Introduction to Social Work
F:63
63 SOC302
Sociological Theories
F:94
94 SOC401
Cultural Anthropology
M:137 F:143
280 SOC402
F:59
59 SOC403
Gender Studies
F:80
80 SOC404
Pakistani Society and Culture
F:109
109 SOC509
F:89
89 SOC601
F:45
45 SOC602
Sociology of Education
F:50
50 SOC603
Sociology of Development
F:50
50 SOC604
Community Development
F:61
61 SOC605
Population Dynamics
F:51
51 SOC606
F:45
45 SOC607
F:90
90 SOC608
F:57
57 SOC609
F:82
82 SOC610
Electronic Media & Virtual Community
F:86
86 SOC611
F:58
58 SOC612
F:60
60 SOC613
F:70
70 SOC614
F:46
46 SOC615
F:65
65 SOC616
F:40
40 SOC617
F:59
59 STA301
Statistics and Probability
F:402
402 STA302
Data Analytics and Business Intelligence
F:34
34 STA621
F:64
64 STA630
Research Methods
M:76 F:298
374 STA631
Inferential Statistics
F:29
29 STA641
Statistical Packages and its Applications
F:87
87 STA642
Probability Distributions
F:59
59 STAT404
F:29
29 URD100
Urdu Language
F:42
42 URD101
Urdu
F:158
158 ZOO102
F:9
9 ZOO103
F:10
10 ZOO403
F:50
50 ZOO501
F:23
23 ZOO501P
F:44
44 ZOO501T
Developmental Biology (Theory)
F:115
115 ZOO502
F:9
9 ZOO503
F:153
153 ZOO504
F:139
139 ZOO505
F:27
27 ZOO507
F:21
21 ZOO510
Economic Zoology
F:136
136 ZOO511P
F:56
56 ZOO511T
F:27
27 ZOO512P
Animal Diversity: Invertebrates
F:25
25 ZOO512T
Animal Diversity: Invertebrates (Theory)
F:248
248 ZOO513P
Animal Diversity: Chordates (Practical)
F:34
34 ZOO513T
Animal Diversity: Chordates (Theory)
F:10
10 ZOO516P
F:36
36 ZOO516T
Animal Form & Function-I (Theory)
F:42
42 ZOO517P
F:29
29 ZOO517T
F:74
74 ZOO518P
F:71
71 ZOO518T
F:20
20 ZOO519P
F:55
55 ZOO519T
Physiology (Theory)
F:17
17 ZOO603T
Fish Biology (Theory)
F:13
13
Koi subject nahi mila
Clear
56097 result(s)
MTH642 Final Term Unsolved
Q63

The Euler number (Eu) is equal to _____.

  • A) Eu = \frac{\rho V^2}{P_0-P_{\infty}}
  • B) Eu = \frac{\rho (P_0-P_{\infty})}{V^2}
  • C) Eu = \frac{P_0-P_{\infty}}{ V^2}
  • D) Eu = \frac{P_0-P_{\infty}}{\rho V^2}
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH642 Final Term Unsolved
Q64

The Reynolds number (Re) is equal to _____.

  • A) Re=\frac{\mu} {\rho VL}
  • B) Re=\frac { VL}{\mu}
  • C) Re=\frac { VL}{\rho\mu}
  • D) Re=\frac {\rho VL}{\mu}
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH642 Final Term Unsolved
Q65

Let \(n\) be total parameters and\(j\) equal to number of primary dimensions, then expected number of \(\Pi\)’s (\(k\)) equal to_____.

  • A) \(k=n-j\)
  • B) \(k=2n-j\)
  • C) \(k=j-n\)
  • D) \(k=n+j\)
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH642 Final Term Unsolved
Q66

If \(g=1.63 m/s^2, w_0 = 1.83m/s\ and\ z_0 =2m\) , then Froude number is equal to ____.

  • A) \(Fr=1.01\)
  • B) \(Fr=1.05\)
  • C) \(Fr=1\)
  • D) \(Fr=1.03\)
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MTH642 Final Term Unsolved
Q67

\(m L^2 t^{-2}\) is dimension of ____.

  • A) force
  • B) energy
  • C) linear momentum
  • D) moment
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MTH642 Final Term Unsolved
Q68

The Euler number (\(Eu\)) is equal to _____.

  • A) \(Eu = \frac{\rho V^2}{P_0-P_{\infty}}\)
  • B) \(Eu = \frac{P_0-P_{\infty}}{ V^2}\)
  • C) \(Eu = \frac{\rho (P_0-P_{\infty})}{V^2}\)
  • D) \(Eu = \frac{P_0-P_{\infty}}{\rho V^2}\)
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MTH642 Final Term Unsolved
Q69

\(m L^{-1} t^{-2}\) is dimension of ____.

  • A) force
  • B) momentum
  • C) pressure
  • D) energy
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MTH642 Final Term Unsolved
Q70

The Strouhal number (\(St \)) is equal to _____.

  • A) \(St=\frac{fL}{V}\)
  • B) \(St=\frac{V}{fL}\)
  • C) \(St=\frac{fL}{Vg}\)
  • D) \(St=\frac{Vg}{fL}\)
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MTH642 Final Term Unsolved
Q71

The Froude number (\(Fr\)) is equal to _____.

  • A) \(Fr=\frac {\sqrt{gL}}{ V}\)
  • B) \(Fr=\frac {{gL}}{ V}\)
  • C) \(Fr=\frac { V}{gL}\)
  • D) \(Fr=\frac { V}{\sqrt{gL}}\)
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MTH642 Final Term Unsolved
Q72

\(m L^2 t^{-1}\) is dimension of ____.

  • A) moment
  • B) force
  • C) angular momentum
  • D) linear momentum
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MTH642 Final Term Unsolved
Q73

If \(t=3.01s, w_0=1.83m/s\ and\ z_0=2m\), then dimensionless time (\(t^*\)) is equal to________.

  • A) \(t^*=2.79\)
  • B) \(t^*=2.75\)
  • C) \(t^*=2.7\)
  • D) \(t^*=2.71\)
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MTH642 Final Term Unsolved
Q74

The Reynolds number (\(Re\)) is equal to _____.

  • A) \(Re=\frac{\mu} {\rho VL}\)
  • B) \(Re=\frac { VL}{\rho\mu}\)
  • C) \(Re=\frac { VL}{\mu}\)
  • D) \(Re=\frac {\rho VL}{\mu}\)
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MTH642 Final Term Unsolved
Q75

The Froude number (Fr) is equal to _____.

  • A) Fr=\frac { V}{gL}
  • B) Fr=\frac {\sqrt{gL}}{ V}
  • C) Fr=\frac { V}{\sqrt{gL}}
  • D) Fr=\frac {{gL}}{ V}
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q0

Which of the following discretized factor is utilized to check the stability of finite difference scheme in Fourier transform,

  • A) data:image/png;base64,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.
  • B) data:image/png;base64,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.
  • C) data:image/png;base64,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.
  • D) data:image/png;base64,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.
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q1

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  • A) data:image/png;base64,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 .
  • B) data:image/png;base64,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 .
  • C) data:image/png;base64,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 .
  • D) data:image/png;base64,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 .
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q2

The Fourier method for stability analysis of PDEs is mainly used to:

  • A) Solve the PDE analytically
  • B) Optimize the grid spacing
  • C) Approximate boundary conditions
  • D) Determine whether numerical errors grow, decay, or remain bounded over time
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q3

In Jacobi’s method for a 2D Laplace equation on a uniform grid, the value at an interior point (i, j) is updated using:

  • A) The average of its four nearest neighbors
  • B) The average of its eight surrounding neighbors
  • C) Its value from the previous step minus the residual
  • D) Only the left and right neighbors
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q4

Which of the following mathematical expression represents the standard five-point formula for 2D Laplace partial differential equation for the uniform step size in both x and y direction?

  • A) data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAa0AAAA5CAIAAAAKtOOBAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAZDSURBVHhe7ZxRdeMwEEVDIRhCwRwKoRiWQhiEQRgUQRGUQAmUgTl07+moPqptyZIcO7b17kdPZqLIoyf5WUq7e/oWQoi6kQ8KIWpHPiiEqB35oBCiduSDQojakQ8KIWrnUD7Ytu3tdnt5eXGxEEIkcBwfvN/v5/P5dDrJB4UQWRzEB6/XKz7Ii6Zp5INCiCyO9v0gJigfFEJkIR8UQtSOfFAIUTvyQSFE7cgHhRC1Ix8UQtSOfFAIUTvyQSFE7RzKB9u2vVwup9OJFy4lhBBTHMQH397e2AbigB2EJN3bQggR5mjnYiGEyKU6H/S3jbfbzWWFEPuEu9jdzzPu6Ep90AVCiKMgH8ygKh9kpB8fHy6oksoVYOxVrXb5YCrywaqQD8oHU0jVqG3b19dXrsRPl/pVeV+/lh364PV6PZ/Pl8vF/2sb2vz7988Fu4VRpLiAFDiqAuk+eAAFqHZxH2ya5vPzE7F8We/3O+HX15eL90DPB5lmfPz9/Z1kd8MwUsID/NmNP6gQUuDACjAcRuGCMMdQgGpXOhejFw8NF3x/szfkAeKC2ZhDRaCBazqD0XMxk02Sibdwj/4+CqOYdAFDChxSgUQfNPauANWu5IO4nn8u7oXPgvHHce1+GPXBnr/3wr1giz5OyBSkwDEUwAjcOMO4pgP2rgBDW8MHeTJwJZ4So6HBwTmyQ8Q0EdcFT2LUByf93Y4M6c9GWjLS+KzYuSO9T25gig/dxqPQf2L7MgXMd1zwl5RqRxWY2WePByowurZnVrv0GoiUN6RMgQjFCkTKjvTJR9bwwd622Z488UFmwfDoMAINXNMZ2FVc8ANzQKYzdJuDYkHbtmW5cBWepcWd9KBCVqRVniV4YvtiBaylC34prtZ4bJ+J7TelwChlfY6WN0qxAqPMVGC07Mk+5xScpJHh/5IEN+TJ0KuVEEZLtIGB/9uop2A6uuAH/+thyhsKbZl0ie2zfCryEesTSV0chRUAvOgVNkli+2IFaEPeBb8kVhtSYE6fQxLbTypA2MsYZMi74JfEaldYA6PljVKswCiJ1T52DZBfwwc56HElNMIEGYDZIiF5q8+ktMZDKDFrU70QJr0LfrB9LsXb9PNIJERoXvAWDchbxtonQlfxWaFP6z+d3DIS2xcrQIa8CwZMXp0GQwVm9tkjsf2kAqG1PbNaGgwViDPZp0+8PJ9iBeJMVkuDoQLxskN9kl/DB7s9IMaHWOjC0Y8ML6wB42maxl4PwTfZ1rrgeTDHPYlt4knykzHi6QzKP9WS4V2aWUiecEhvbugtMiv0xkd6XzIM6fU5zMRJbL+QAsOMz74U6K3tvShAS9q7IMoBFCDfVZtLtsFHwB8jm3xELK4yC9wWRVwwwCbbBWnE/T0EF4qMd6Gn60KEFKCYyCji1YYUmNPncoTW9hIKxNmaAnHKFChTlfwmfJAHCDeMC/5ixr/C/Jmy4OIBBT7ICgAXJBP3QZYUDVyQDJU/6x4YVaBsvRohBeb0uRyhtb2EAnG2pkCcMgXKVCW/CR+0+hgbrmdht+OND+xRcF128tyxkWuhe24lfAR9WQSRGe3BsYJK/O8B6MEPrU8XpGEWf//7h0rrEFIgMq3DahMVyOpzNbguhXVruyOrWobcC3e0BkIKRChWoGwNkM/VsyPPEeJwdOLmt4eGWVInGfUVHC1z4TbjQhASEZCedw1aumwU5p7G/HTxFNZ5h12Fj/uXI8+MumAKWxY+ZNx7qxBSYHS9hqpNVCCrz9Xw17ZPVrV04pdNfkdrIKTAKDMVsI+74JdQn3a/G4l39JCgX8wEw/YHzPhHD1YPBEHZuvPCdLHkRuB5gAt0TwVKpUL2jBbWgBTgdvB3MVJgUwqs4Rdm5L4tPhxuMB5WdgnbvFh+g1Aq+1a2pS6uDykgBbamwOJ+gSWVfcOaBd7X7Tft5Guvt4btVVkBrAOXqgwpIAU2qMB2903psA30v4vsfBBnXHQTKoQ4BkfwQTO+UeSDQohJjuCDPbZ8LhZCbBD5oBCidg7oF03T4IPVfgkthMjlaD5o/5gEzjv8z4SFEE9B50chRO3IB4UQtSMfFELUjnxQCFE78kEhRO3IB4UQtSMfFELUjnxQCFE78kEhRO3IB4UQtSMfFELUzff3f0WzJOJA9+v2AAAAAElFTkSuQmCC.
  • B) data:image/png;base64,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.
  • C) data:image/png;base64,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.
  • D) data:image/png;base64,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.
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q5

Compared to Jacobi’s method, Gauss–Seidel’s method generally:

  • A) Does not require initial guesses
  • B) Converges more slowly
  • C) Cannot be used for PDEs
  • D) Converges faster because updated values are used immediately
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
MTH646 Final Term Unsolved
Q6

Which type of PDE is typically used to model steady-state heat conduction in a solid?

  • A) Elliptic PDE
  • B) Hyperbolic PDE
  • C) Parabolic PDE
  • D) Ordinary differential equation
Answer abhi available nahi — is question ka AI/admin se answer milne ka intezar hai.
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