KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307

INTERNAL TEST-I FEB 2014 INTERNAL TEST-I FEB 2014

(Answer All the

Questions)PART A - 2 Mark Qs (5x2=10)

1 Find the Particular integral of d2 yd x2 + 4y = sin 2x

2 Solve (D2 – 1) y = x3. Find the value of λ,if F⃗=(2 x−5 y ) i⃗ +( x+λy ) j⃗+(3 x−z ) k⃗ is solenoidal.4. State Gauss divergence theorem.5. Find the work done by the force in a moving particle in the force field given by F⃗ = 3x2 i⃗ +(2 xz− y ¿ j⃗ +z k⃗ along y=x from(0,0,0) to (2,1,3). PART B – 1x8=8 Mark6.(D2−3D+2 ) y=2cos (2x+3 )+2ex (8) PART C 2x16=32 Mark 7.a) Solve (D2 + 1)y = sin x sin 2x (8)

b)Solve (x2 D2 – xD +1) y =( log xx )

2

(8)

(or)8. a)Solve [ ( x+1 )2D2+( x+1 )D+1 ] y = 4 cos [log (x+1)]

(b) Solve the simultaneous equations dxdt

+2 y+3 y=2e2t ,

dydt

+3 x+2 y=0 (8)

9.a) Verify Green’s theorem in the XY plane for ∫c

❑

{¿¿) dx + x2 dy} where C is the

closed curve of the region bounded by y = x and y = x2 (16) (or) b) Verify Stoke’s theorem for A⃗ = (2x - y) i⃗ - y z2 j⃗ - y2z k⃗ Where S is upper half surface of the sphere x2 + y2 + z2 = 1 and C is its boundary (16)

(Answer All the Questions )PART A - 2 Mark Qs (5x2=10)

1 Find the Particular integral of d2 yd x2 + 4y = sin 2x

2 Solve (D2 – 1) y = x3. Find the value of λ,if F⃗=(2x−5 y )i⃗ +( x+λy ) j⃗+(3 x−z ) k⃗ is solenoidal.4. State Gauss divergence theorem.5. Find the work done by the force in a moving particle in the force field given by F⃗ = 3x2 i⃗ +(2 xz− y ¿ j⃗ +z k⃗ along y=x from(0,0,0) to (2,1,3). PART B – 1x8=8 Mark6.(D2−3D+2 ) y=2cos (2x+3 )+2ex (8) PART C 2x16=32 Mark 7.a) Solve (D2 + 1)y = sin x sin 2x (8)

b)Solve (x2 D2 – xD +1) y =( log xx )

2

(8)

(or)

NUMERICAL METHODSTime: 09:15 a.m. – 11:00 a.m.

50 Marks

NUMERICAL METHODSTime: 09:15 a.m. – 11:00 a.m.

50 Marks

KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307

INTERNAL TEST-I FEB 20148. a)Solve [ ( x+1 )2D2+( x+1 )D+1 ] y = 4 cos [log (x+1)]

(b) Solve the simultaneous equations dxdt

+2 y+3 y=2e2t ,

dydt

+3 x+2 y=0 (8)

9.a) Verify Green’s theorem in the XY plane for ∫c

❑

{¿¿) dx + x2 dy} where C is the

closed curve of the region bounded by y = x and y = x2 (16) (or) b) Verify Stoke’s theorem for A⃗ = (2x - y) i⃗ - y z2 j⃗ - y2z k⃗ Where S is upper half surface of the sphere x2 + y2 + z2 = 1 and C is its boundary (16)

1 Find the Particular integral of d2 yd x2 + 4y = sin 2x

2 Solve (D2 – 1) y = x

3. Prove that Curl (grad ϕ) = 0⃗

4. State Stoke’s theorem5. P.T 𝜵 (r n) = n r n-2 r⃗

PART B – 1x8=8 Mark6.Solve (D2 + 1) y = sec x by the method of variation of parameters

PART C 2x16=32 Mark 7.a) Solve (D2 + 1)y = sin x sin 2x (8)

b)Solve (x2 D2 – xD +1) y =( log xx )

2

(8)

(or)8. a)Solve [ ( x+1 )2D2+( x+1 )D+1 ] y = 4 cos [log (x+1)] by legender’s linear D.E (8)

(b) Solve the simultaneous equations dxdt

+2 y+3 y=2e2t ,

dydt

+3 x+2 y=0 (8)

9.a) Verify Green’s theorem in the XY plane for ∫c

❑

{¿¿) dx + x2 dy} where C is

the closed curve of the region bounded by y = x and y = x2 (16) (or) b) Verify Stoke’s theorem for A⃗ = (2x - y) i⃗ - y z2 j⃗ - y2z k⃗ Where S is upper half surface of the sphere x2 + y2 + z2 = 1 and C is its boundary (16)

9)(a)Using Newton’s forward interpolation formula , find the polynomial f(x) satisfying the following data. Hence evaluate y at x = 5

X 4 6 8 10y 1 3 8 10

b)From the data given below find the number of students whose weight is between 60 to 70

Weight 0-40 40-60 60-80 80-100 100-120No of

students250 120 100 70 50

(OR)

KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307

INTERNAL TEST-I FEB 2014

10 (a)Find f(3) by using Newton’s divided difference formula for the following table

x 0 1 2 4 5F(x) 1 14 15 5 6

(b) Obtain the cubic spline approximation for the function y = f(x) from the following data, given that yo

// = y3 // = 0X: -1 0 1 2Y: -1 1 3 35

KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307

INTERNAL TEST-I FEB 2014

(OR) (OR)10. analyze the portal frame as shown in fig.4 by using stiffness matrix method

INTERNAL TEST-I FEB 2014ME 2353-FINITE ELEMENT ANALYSIS

Time: 09:15 a.m. – 11:00 a.m.50

Marks

(Answer All the Questions)PART A - 2 Mark Qs (5x2=10)

1.What is meant by primary structure?2. define flexibility co efficient3.What is meant by stiffness cofficient?4. define degree of kinematic indeterminacy5.define degree redundancy?

PART B – 1x8=8 Mark2x16=32 Mark

INTERNAL TEST-I FEB 2014ME2026 – UNCONVENTIONAL MACHINING PROCESS

Time: 09:15 a.m. – 11:00 a.m.50

Marks

(Answer All the Questions)PART A - 2 Mark Qs (5x2=10)

1.What are the industrial needs for UCM?2.List down the various mechanical energy based Unconventional Machining Processes.3.What are the different machining characteristics will respect to which the non-traditional machining processes can be analyzed?4.Distinguish traditional & non-traditional machining processes?5.How will you compare various non-traditional processes?

PART B – 1x8=8 Mark2x16=32 Mark

6. What is the need for the development of UCM process? Explain with examples. (8)7. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations. (16)

(OR)8.With a neat sketch explain the process of AJM? Write its advantages and applications.(16)

9. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations.(16)

(OR)10.Discuss the effects of the following parameters on the material removal and surface finish in ultrasonic machining:

a. Amplitude and frequencyb. Abrasive size

KARAIKUDI INSTITUTE OF TECHNOLOGY KARAIKUDI INSTITUTE OF TECHNOLOGY KIT & KIM TECHNICAL CAMPUS KIT & KIM TECHNICAL CAMPUS Keeranipatti, Thalakkavur, Karaikudi – 630 307 Keeranipatti, Thalakkavur, Karaikudi – 630 307

INTERNAL TEST-I FEB 2014c. Concentration of abrasivesd. Material hardness

INTERNAL TEST-I FEB 2014ME2026 – UNCONVENTIONAL MACHINING PROCESS

Time: 09:15 a.m. – 11:00 a.m.50

Marks

(Answer All the Questions)PART A - 2 Mark Qs (5x2=10)

1.What are the industrial needs for UCM?2.List down the various mechanical energy based Unconventional Machining Processes.3.What are the different machining characteristics will respect to which the non-traditional machining processes can be analyzed?4.Distinguish traditional & non-traditional machining processes?5.How will you compare various non-traditional processes?

PART B – 1x8=8 Mark2x16=32 Mark

6. What is the need for the development of UCM process? Explain with examples. (8)7. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations. (16)

(OR)8.With a neat sketch explain the process of AJM? Write its advantages and applications.(16)

9. Make a comparison between traditional and unconventional machining processes in terms of cost, application, scope, machining time, advantages & limitations.(16)

(OR)10.Discuss the effects of the following parameters on the material removal and surface finish in ultrasonic machining:a. Amplitude and frequency

b. Abrasive sizec. Concentration of abrasivesd. Material hardness