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V.S.B. ENGINEERING COLLEGE, KARUR DEPARTMENT OF CIVIL ENGINEERING ASSIGNMENT QUESTIONS GE 8292 ENGINEERING MECHANICS Year/Semester & Branch: I Year / II SEM B.E Civil Engineering Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and their reactions 2 922519103002 Ajithaa V What are the different components of building and explain each of them with neat sketches. 3 922519103003 Arunkumar A Explain about the three laws of mechanics with practical applications. 4 922519103004 Arun Raj E What are the everyday life applications of Kinematics? 5 922519103006 Girinath S List out the steps to be followed to draw the free body diagram of a rigid body. 6 922519103007 Hariharan B Write short notes on equilibrium of particle in 3D. 7 922519103008 Karthikeyan P Explain the different types of loads with neat sketch. 8 922519103009 Kungumaraj S Compare and Contrast Ladder friction and Wedge friction. 9 922519103010 Manoj A Classify the types of friction. 10 922519103011 Mohesh Anand S Discuss about the Polar moment of Inertia and state its significant 11 922519103012 Naresh Kumar R Two control rods are attached at A to lever AB. Using trigonometry and knowing that the force in the left-hand rod is F1 = 30 N, determine (a) the required force F2 in the right-hand rod if the resultant R of the forces exerted by the rods on the lever is to be vertical, (b) the corresponding magnitude of R. 12 922519103013 Naveen P A system of four forces acting on a body is shown in fig below. Determine the resultant force and its direction.

V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

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Page 1: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

V.S.B. ENGINEERING COLLEGE, KARUR

DEPARTMENT OF CIVIL ENGINEERING

ASSIGNMENT QUESTIONS

GE 8292 – ENGINEERING MECHANICS

Year/Semester & Branch: I Year / II SEM B.E Civil Engineering

Faculty Name: Mr.P.Suresh Kannan

Sl.No. Register No. Students name Question

1 922519103001 Abitha V Explain about the types of supports and their

reactions

2 922519103002 Ajithaa V What are the different components of building and

explain each of them with neat sketches.

3 922519103003 Arunkumar A Explain about the three laws of mechanics with

practical applications.

4 922519103004 Arun Raj E What are the everyday life applications of

Kinematics?

5 922519103006 Girinath S List out the steps to be followed to draw the free

body diagram of a rigid body.

6 922519103007 Hariharan B Write short notes on equilibrium of particle in 3D.

7 922519103008 Karthikeyan P Explain the different types of loads with neat

sketch.

8 922519103009 Kungumaraj S Compare and Contrast Ladder friction and Wedge

friction.

9 922519103010 Manoj A Classify the types of friction.

10 922519103011 Mohesh Anand S Discuss about the Polar moment of Inertia and state

its significant

11 922519103012 Naresh Kumar R

Two control rods are attached at A to lever AB.

Using trigonometry and knowing that the force in

the left-hand rod is F1 = 30 N, determine (a) the

required force F2 in the right-hand rod if the

resultant R of the forces exerted by the rods on the

lever is to be vertical, (b) the corresponding

magnitude of R.

12 922519103013 Naveen P

A system of four forces acting on a body is shown

in fig below. Determine the resultant force and its

direction.

Page 2: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

13 922519103014 Niranjan S

A horizontal line PQRS is 12m long where

PQ=QR=RS=4m.Forces of 1000,1500, 500 N act at

P,Q,R and S respectively and action of these forces

make angles of 90˚, 60˚, 45˚ and 30˚ respectively

with PS. Find the magnitude, direction and position

of the resultant force.

14 922519103015 Nithisrajan R

Determine the reactions of the beam shown in fig.

15 922519103016 Palanikumar C

Calculate the reaction at the supports of the truss

shown in fig.

Page 3: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

16 922519103017 Pradeesh S

Calculate the support reactions for the beam shown

below.

17 922519103018 Prasanth M

Two cables which have known tensions are

attached to the top of the tower AB. A third cable

AC is used as a wire as shown in fig. Determine the

tension in AC if the resultant of the forces exerted

at A by the three cables acts vertically downwards.

18 922519103019 Priyatharsan K

A beam AB is simply supported and carries loads

as shown in fig. Calculate the reaction at A and B.

19 922519103021 Rahul

Gandhi M E

Determine the magnitude and line of action of the

resultant of forces shown in fig.

Page 4: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

20 922519103023 Sanjeevi M

Two rollers each of weight 50n and of radious

10cm rest in a horizontal channal of width 35cm as

shown in fig. Find the reaction on the point of

contacts a, b, and c.

21 922519103024 Sasikumar P

A bend up beam ABC is shown in fig. It is hinged

at A and supported on rollers at C. If there is an

uniform wind pressure of 2kN/m on the vertical

side AB, and a central point load of 16KN at

middle of BC. Calculate the reactions offered by

the support.

22 922519103025 Sasi Rega M

A truss of 8m span is loaded as shown in fig. find

the support reaction the magnitude of P and the

tension in each cable.

Page 5: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

23 922519103026 Sathish T

Boom AB is held in the position shown by three

cables. Knowing that the tensions in cables AC and

AD are 900N and 1200 N, respectively, determine

(a) the tension in cable AE if the resultant of the

tensions exerted at point A of the boom must be

directed along AB, (b) the corresponding

magnitude of the resultant.

24 922519103027 Madurai Sivaneshan S

Two cables are tied together at C and are loaded as

shown. Determine the tension (a) in cable AC, (b)

in cable BC.

25 922519103028 Sri Mohan

Gandhi C Motion of a rigid body

26 922519103029 Tamizh Eniyan P Displacement in combined bodies

27 922519103030 Tamilmani T Location of points in mechanism

28 922519103031 Unnamalai K Changes of position: displacement curves

29 922519103032 Vanchi Kaviya S Explain about degrees of freedom

30 922519103033 Vasudevan R What is continuous motion and explain in detail?

Page 6: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

TECHNICAL ENGLISH

Year/Semester & Branch: I Year / II SEM B.E Civil Engineering

Faculty Name: Dr.T.Sadasivam

Sl.No. Register No. Students name Question

1 922519103001 Abitha V Write a set of eight Instructions to improve fluency in English.

2 922519103002 Ajithaa V Write a set of eight Instructions to keep your vehicle in good condition.

3 922519103003 Arunkumar A Write a set of eight Instructions for your friend who is planning to stay in his college hostel.

4 922519103004 Arun Raj E Write a set of eight Instructions that are to be followed by students in college library.

5 922519103006 Girinath S Write a set of eight Instructions to be followed to maintain laptops in good condition.

6 922519103007 Hariharan B Write a set of eight Instructions that could be followed by students to the examination hall.

7 922519103008 Karthikeyan P Write a set of eight Instructions for operating the ticket vending machine at a railway station.

8 922519103009 Kungumaraj S Write a set of eight Instructions for using your cell phone safely.

9 922519103010 Manoj A Write a set of eight Instructions for safety while using weldi g equipment.

10 922519103011 Mohesh Anand S Write a set of eight Instructions that could be followed to reduce pollution.

11 922519103012 Naresh Kumar R Write a set of eight Instructions that must be followed as safety measures in a chlorine plant.

12 922519103013 Naveen P Write a set of eight Instructions that must be followed in a chemical engineering lab.

13 922519103014 Niranjan S

As the Maintenance Engineer of Software

Company, give a set of eight instructions that

are to be followed by the lab assistants while

handling sophisticated equipment.

14 922519103015 Nithisrajan R

Write a job application letter to the following

advertisement published in the “The Hindu”

for the post of Deputy Manager, Design and

Development, with resume to the personnel

Manager, Lucas-TVS, Hosur,

India.

15 922519103016 Palanikumar C

Write a letter to the HRD Manager of Karur

Vysya Bank, Anna Salai, Chennai-600 017,

applying for the post of System Manager.

Add a separate resume to your covering

letter.

16 922519103017 Pradeesh S Write a set of eight Instructions advising your younger

sister on how to prepare for her Board exams.

Page 7: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

17 922519103018 Prasanth M Write a set of eight recommendations for safety measures in a chlorine plant.

18 922519103019 Priyatharsan K Write a set of eight Instructions to save petrol.

19 922519103021 Rahul

Gandhi M E

Write a set of eight recommendations to keep your country peaceful from war.

20 922519103023 Sanjeevi M Write a set of eight recommendations that should be followed to preserve our water resources.

21 922519103024 Sasikumar P Write a set of eight recommendations for

the proper maintenance of two-wheelers.

22 922519103025 Sasi Rega M Write a set of eight recommendations to keep the city free of air pollution.

23 922519103026 Sathish T Write a set of eight recommendations for safety measures in nuclear power plants.

24 922519103027 Madurai Sivaneshan S

Write a set of eight recommendations to a

group of students from Europe who have come

to spend their one month’s vacation in India.

25 922519103028 Sri Mohan

Gandhi C

Write a set of eight recommendations for water storage in your home.

26 922519103029 Tamizh Eniyan P Write a set of eight recommendations for traffic congestion in your area.

27 922519103030 Tamilmani T Write a set of eight recommendations for global warming.

28 922519103031 Unnamalai K Write a set of eight recommendations to control air pollution.

29 922519103032 Vanchi Kaviya S Write a set of eight recommendations to control noise pollution.

30 922519103033 Vasudevan R Write a set of eight recommendations to stop malpractice

in Examinations.

Page 8: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

V.S.B. ENGINEERING COLLEGE, KARUR

Department of Civil Engineering

Academic Year: 2019-2020 (Even Semester)

BE8251- BEEE : Assignment Questions

Name of the Faculty : T. Kamalam Class: I

Year / II Semester CIVIL

S.No. Register Number Name of the student Assignment Question

1.

922519103001

ABITHA V

Determine the equivalent resistance between terminals A and B of figure shown below. Find (i) Current in 15Ω resistor, (ii) Voltage across 18Ω resistor, (iii) Power dissipated in 7Ω resistor in the circuit shown below.

2.

922519103002

AJITHAA V

If Req=50Ω in the circuit shown in figure, find the value of R.

3.

922519103003 ARUNKUMAR A

Two resistors R1=40Ω and R2=25Ω are connected in parallel across 20V DC supply. Find the total power dissipated in the circuit.

4. 922519103004

ARUNRAJ E Derive expressions for star connected arms in terms of delta connected arms and delta connected arms in terms of star connected arms.

5. 922519103006 GIRINATH S

Explain the working principle of megger.

6. 922519103007

HARIHARAN B Explain the fundamental of electric potential and

potential difference.

7.

922519103008

KARTHIKEYAN

P

Calculate the total power supplied by the battery in the network shown in figure.

Page 9: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

8.

922519103009

KUNGUMARAJ

S

Determine the total current taken from the source.

9. 922519103010

MANOJ A Discuss how to reduce various losses in

transformer.

10. 922519103011

MOHESH ANAND

S

Make clear the working of non linear machines

with neat diagram.

11.

922519103012 NARESH KUMAR R

Explain the construction and principle of

working of a universal motor and mention its

applications.

12.

922519103013 NAVEEN P

Explain the principle of operation and

constructional details of linear synchronous

motor.

13. 922519103014

NIRANJAN S Differentiate Bipolar Junction Transistor and

Field Effect Transistor/

14. 922519103015

NITHISRAJAN R Compare the Transistor configurations in

Elaborate manner.

15. 922519103016 PALANIKUMAR C

Explain the working of transistor as switch.

16.

922519103017 PRADEESH S

Compare Avalanche breakdown and Zener

breakdown. State the difference of PN diode and

Zener diode.

17. 922519103018 PRASANTH M

Explain the function of JK-MS Flipflop.

18. 922519103019

PRIYATHARASAN

K

Explain the function of Clocked SR Flipflop.

19.

922519103021

RAGHU GANDHI M

E

In the circuit of figure find using “Kirchhoff’s Laws” the currents in the various elements. Find also the power delivered by the battery.

20. 922519103023 SANJEEVI M

Elaborate the function of Shift Register.

Page 10: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

21. 922519103024

SASIKUMAR P Differentiate the function of Binary up counter

and Binary down counter,

22. 922519103025 SASI REGA M

Explain the function of Mod-10 Counter.

23.

922519103026

SATHISH T

In the circuit of figure, it is given that the current in the branch OA is zero. Find the value of R and the current in it.

24.

922519103027

MADURAI

SIVANESAN S

In the wheatstone bridge circuit of figure, G is a galvanometer of resistance 10Ω. Find the current through it.

25.

922519103028

SRI MOHAN

GANDHI C

In the circuit of figure six resistors are connected to form and a Y. Find the effective resistance between (a) A and B (b) A and N.

26. 922519103029

TAMIZH ENIYAN P Determine the current through 800Ω resistor in the network shown in figure using mesh analysis.

27. 922519103030

TAMILMANI T

Using nodal analysis, determine the current in the 20Ω resistor.

28. 922519103031 UNNAMALAI K Explain the function of Amplitude Shift Keying.

Page 11: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

V.S.B. ENGINEERING COLLEGE, KARUR

Department of Civil Engineering

Academic Year: 2019-2020 (EVEN Semester)

Assignment Questions

Class / Semester: I year / II Semester B.E. - Civil Engineering

Name of Subject: Physics for Civil Engineering

Name of Faculty member: Mr. P. Murali Krishna.

Sl. No. Regd Nums Name of the student Questions

1. 922519103001 ABITHA V Describe in detail about Air &

Structure Borne Sound Propagation.

2. 922519103002 AJITHAA V Describe in detail about Structure

Borne Sound Propagation

3. 922519103003 ARUNKUMAR A

Discuss about measurement of noise,

Reduction of noise by Town Planning

and Regional Planning consideration.

4. 922519103004 ARUN RAJ E Explain about daylight harnessing

systems.

5. 922519103006 GIRINATH S Explain about Environmental

Acoustics types.

6. 922519103007 HARIHARAN B Explain different types of earthquake

hazards.

7. 922519103008 KARTHIKEYAN P Explain different types of hazards.

8. 922519103009 KUNGUMARAJ S Explain in detail about seismology.

9. 922519103010 MANOJ A Explain the indices for measuring the

daylights.

10. 922519103011 MOHESH ANAND S Explain the indices for measuring the

thermal performance.

11. 922519103012 NARESH KUMAR R Explain the types of day lighting.

12. 922519103013 NAVEEN P Explain the uses of shape memory

alloys in the construction.

13. 922519103014 NIRANJAN S Explain the uses of steel in the

construction.

14. 922519103015 NITHISRAJAN R Give a brief discussion on seismology.

15. 922519103016 PALANIKUMAR C What are Acoustic absorbers and write

its types and functions?

16. 922519103017 PRADEESH S What are different engineering

materials and their uses ?

17. 922519103018 PRASANTH M What is noise pollution and state its

effects?

18. 922519103019 PRIYATHARSAN K Write about photometry and glares?

19. 922519103021 RAHUL GANDHI M E Write about sound transmission class?

20. 922519103023 SANJEEVI M Write about the uses of crystals in

29. 922519103032 VANCHI KAVIYA

S

Discuss about the function of D2H.

30. 922519103033 VASUDEVAN R Explain the different types of Fiber optic cable

in elaborate manner.

Page 12: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

construction?

21. 922519103024 SASIKUMAR P Write about the uses of polymers in

construction?

22. 922519103025 SASI REGA M Write note on different acoustic

materials?

23. 922519103026 SATHISH T Write the Design Principles of

Auditorium?

24. 922519103027 MADURAI SIVANESHAN S Write the Design Principles of Motion

picture hall?

25. 922519103028 SRI MOHAN GANDHI C Write about the uses of crystals in

construction?

26. 922519103029 TAMIZH ENIYAN P Explain about daylight harnessing

systems.

27. 922519103030 TAMILMANI T Describe in detail about Air &

Structure Borne Sound Propagation

28. 922519103031 UNNAMALAI K Explain the types of day lighting.

29. 922519103032 VANCHI KAVIYA S What is noise pollution and state its

effects?

30. 922519103033 VASUDEVAN R Explain the uses of shape memory

alloys in the construction.

V.S.B. ENGINEERING COLLEGE, KARUR

Department of Civil Engineering

Academic Year: 2019-2020 (EVEN Semester)

Assignment Questions

Class / Semester: I year / II Semester B.E. - Civil Engineering

Name of Subject: Environmental Science and Engineering

Name of Faculty member: Dr.S.Anand Kumar Varma

Sl. No. Regd Nums Name of the student Questions

1. 922519103001 ABITHA V Effects of Gaja cyclone inTamilnadu

2. 922519103002 AJITHAA V Compare tropical rain forest and

temperate rainforest

3. 922519103003 ARUNKUMAR A Compare any twoecosystems.

4. 922519103004 ARUN RAJ E Case study of keystonespecies

5. 922519103006 GIRINATH S Case studies on Human-

wildlifeconflicts

6. 922519103007 HARIHARAN B Write a case study on Taj

trapeziumcase

7. 922519103008 KARTHIKEYAN P Fukushima nuclear accident. A

casestudy

8. 922519103009 KUNGUMARAJ S Case study of groundwater pollution

inIndia

9. 922519103010 MANOJ A

Pollution problem in dyeing

industries in Karur District

–A casestudy.

10. 922519103011 MOHESH ANAND S Pollution on Indian Ocean. A review

11. 922519103012 NARESH KUMAR R Case study of Sterlite Industrial

Page 13: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

problem inTuticorin.

12. 922519103013 NAVEEN P Any two case study on soil pollution

13. 922519103014 NIRANJAN S Discuss oxygen cycle withdiagram

14. 922519103015 NITHISRAJAN R Any two case studies on

marinepollution

15. 922519103016 PALANIKUMAR C Discuss methods used for

sterilizingwater

16. 922519103017 PRADEESH S Explain application of

greenChemistry

17. 922519103018 PRASANTH M A study on Thermal pollution by

nuclear powerplant

18. 922519103019 PRIYATHARSAN K

Case study on renewable

energy resources-A

Worldscenario.

19. 922519103021 RAHUL GANDHI M E Explain nitrogen cycle withdiagram

20. 922519103023 SANJEEVI M Case17

study on globalwarming

21. 922519103024 SASIKUMAR P

War over water-

Conflicts of water in

India-A casestudy

22. 922519103025 SASI REGA M Land for Land-Tribal’sproblem

23. 922519103026 SATHISH T

Explain the impacts of

modern agriculture with

casestudy

24. 922519103027 MADURAI SIVANESHAN S Case study of energy

conversionprocess.

25. 922519103028 SRI MOHAN GANDHI C

A review on alternate energy

resources utilization in

TamilnaduState

26. 922519103029 TAMIZH ENIYAN P

Case study on renewable

energy resources-A

Worldscenario

27. 922519103030 TAMILMANI T Discuss phosphorous cycle with

diagram

28. 922519103031 UNNAMALAI K Case study on landdegradation

29. 922519103032 VANCHI KAVIYA S Case study on Methane gas in

deltaareas

30. 922519103033 VASUDEVAN R

Resettlement and

rehabilitation of Tribal

people- Astudy

Page 14: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

V.S.B. ENGINEERING COLLEGE, KARUR

Department of Civil Engineering

Academic Year: 2019-2020 (EVEN Semester)

Assignment Questions

Class: I Year / II Semester CIVIL

Subject Code/ Subject Name: MA8251 / Engineering Mathematics - II

Name of the faculty: Dr. M. Thangaraj

Sl.

No. Reg. No. Questions

1. 92251910

3001 Find the Eigenvalues and Eigenvectors of

𝟐 −𝟐 𝟑𝟏 𝟏 𝟏𝟏 𝟑 −𝟏

.

2. 92251910

3002 Find the Eigenvalues and Eigenvectors of

−𝟗 𝟐 𝟔𝟓 𝟎 −𝟑

−𝟏𝟔 𝟒 𝟏𝟏 .

3. 92251910

3003 Find the Eigenvalues and Eigenvectors of

𝟏𝟏 −𝟒 −𝟕𝟕 −𝟐 −𝟓𝟏𝟎 −𝟒 −𝟔

.

4. 92251910

3004 Find the Eigenvalues and Eigenvectors of

𝟐 𝟐 −𝟕𝟐 𝟏 𝟐𝟎 𝟏 −𝟑

.

5. 92251910

3006 Find the Eigenvalues and Eigenvectors of

𝟐 𝟐 𝟏𝟏 𝟑 𝟏𝟏 𝟐 𝟐

.

6. 92251910

3007 Find the Eigenvalues and Eigenvectors of

𝟐 −𝟐 𝟐𝟏 𝟏 𝟏𝟏 𝟑 −𝟏

.

7. 92251910

3008 Find the Eigenvalues and Eigenvectors of

𝟐 𝟎 𝟏𝟎 𝟐 𝟎𝟏 𝟎 𝟐

.

8. 92251910

3009 Find the Eigenvalues and Eigenvectors of

𝟏 𝟏 𝟑𝟏 𝟓 𝟏𝟑 𝟏 𝟏

.

9. 92251910

3010 Find the Eigenvalues and Eigenvectors of

𝟐 𝟎 𝟏𝟎 𝟑 𝟎𝟏 𝟎 𝟐

.

10. 92251910

3011 Find the Eigenvalues and Eigenvectors of

𝟔 −𝟐 𝟐−𝟐 𝟑 −𝟏𝟐 −𝟏 𝟑

.

11. 92251910

3012 Find the Eigenvalues and Eigenvectors of

𝟑 −𝟏 𝟏−𝟏 𝟓 −𝟏𝟏 −𝟏 𝟑

.

12. 92251910

3013

Verify Cayley – Hamilton Theorem and find its inverse of the following

matrix 𝟒 𝟑 𝟏𝟐 𝟏 −𝟐𝟏 𝟐 𝟏

.

13. 92251910

3014

Verify Cayley – Hamilton Theorem and find its inverse of the following

matrix 𝟏 𝟑 𝟕𝟒 𝟐 𝟑𝟏 𝟐 𝟏

.

Page 15: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

14. 92251910

3015

Verify Cayley – Hamilton Theorem and find its inverse of the following

matrix 𝟑 𝟏 𝟏−𝟏 𝟓 −𝟏𝟏 −𝟏 𝟑

.

15. 92251910

3016

Verify Cayley – Hamilton Theorem and find its inverse of the following

matrix 𝟕 𝟐 −𝟐−𝟔 −𝟏 𝟐𝟔 𝟐 −𝟏

.

16. 92251910

3017 When 3 3 3 3x y z xyz , find , . and at

1,2,3.

17. 92251910

3018

Find .F

and F

of the vector point function

3 2 42 2F xz i x yz j yz k

at 1, 1,1

.

18. 92251910

3019 Show that the vector

2 2 22 2 2F xy z i x yz j y zx k

is

irrotational and find its scalar potential.

19. 92251910

3021 Show that the vector

2 2 2 33 2 1 4 3 3 2F x y i xy y z j y k

is

irrotational and find its scalar potential.

20. 92251910

3023 Show that the vector

2 2 22 2 2 2F y xy i xy z j x z y z k

is

irrotational and find its scalar potential.

21. 92251910

3024 Show that

2 2 3 2 3 2 3 2 2F y z yz x i xz xy j xy xz z k

is

both solenoidal and irrotational.

22. 92251910

3025 Evaluate

.S

f n dS

, where

2 2 2f x y i x j yz k

and S is the surface

of the plane 2 2 6x y z in the first octant.

23. 92251910

3026

Evaluate

.V

F dV

, where

22 3 2 4F x z i y j xz k

and V is

bounded by the planes 0, 0, 0x y z and

2 2 4x y z .

24. 92251910

3027

Verify Green’s theorem in the plane for

2 3 2 2C

x xy dx y xy dy

,

where C is the square with vertices

(0,0),(2,0),(2,2) and (0,2).

25. 92251910

3028

Evaluate by Green’s theorem in the plane

2 cosh sinC

x y dx y x dy

, where C is the rectangle with

Vertices 0,0 , ,0 , ,1

and (0,1).

26. 92251910

3029 Verify the divergence theorem for the function

2A x i z j yz k

over

the cube 1, 1, 1x y z .

Page 16: V.S.B. ENGINEERING COLLEGE, KARUR …...Faculty Name: Mr.P.Suresh Kannan Sl.No. Register No. Students name Question 1 922519103001 Abitha V Explain about the types of supports and

27. 92251910

3030

Verify the divergence theorem for the function 24F xz i y j yz k

over the cube

0,x 1, y 0, 1, 0, 1x y z z .

28. 92251910

3031

Verify the divergence theorem for the function

2 22F x z i x y j xz k

over the cube

0,x 1, y 0, 1, 0, 1x y z z .

29. 92251910

3032

Verify the divergence theorem for the function 2 2 2F xy i yz j zx k

over the cube

0,x 1, y 0, 2, 0, 3x y z z .

30. 92251910

3033

Verify Stoke’s theorem 2 22 ,A x y i yz j y z k

where S is the upper

half of the sphere 2 2 2 1x y z and

C is its boundary in the xy plane