Enroll. No. _____________ SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018 SUBJECT: ADVANCED ENGINEERING MATHEMATICS (2130002) (ALL BRANCHES) DATE: 09-08-2018 TIME: 10:00 am to 11:45 am TOTAL MARKS: 40 Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required. Q.1* (a) Find the Laplace Transform of the function () = { 0, 0 < < , > . [03] (b) Find −1 ( −1 2 ). [03] (c) Find a Fourier Series for () = 2 , where − ≤ ≤ . [04] Q.2 (a) Find −1 [ 1 ( 2 +4) 2 ] using Convolution theorem. [06] (b) State the convolution theorem and verified it for () = and () = 2 . [05] (c) Find the Fourier integral representation of the function () = { 2 , || < 2 0 , || > 2 . [04] OR Q.2 (a) Solve using Laplace transform: " − 3′ + 2 = 4 + 3 , (0) = 1, ′(0) = −1. [06] (b) Find (i) −1 { 1 ( 2 +4)( 2 +9) } (ii) −1 { 1 ( 2 +4) }. [05] (c) Find the Fourier cosine series of () = , where 0≤≤ . [04] Q.3 (a) Expand () in Fourier series in the interval (0,2) if () = { − ; 0 < < − ; < < 2 . Hence show that 1 (2+1) 2 = 2 8 =0 . [06] (b) Find the Fourier Series for () = in (0,2π); a>0. [05] (c) Find the Laplace Transform of () () = t t 3 sin 2 () () = . [04] OR Q.3 (a) Express the function () = { 1 || ≤ 1 0 || ≥ 1 as a Fourier integral. Hence, evaluate (a) sin cos() 0 (b) sin 0 [06] (b) Find Fourier series of () = + 2 , − < < . Hence deduce that 2 6 = 1 1 2 + 1 2 2 + 1 3 2 +⋯ . [05] (c) Find ()( 3 + −3 + 3/2 ) () t t dt t t e L 0 sin [04]
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Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY

BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018

SUBJECT: ADVANCED ENGINEERING MATHEMATICS (2130002) (ALL BRANCHES)

DATE: 09-08-2018 TIME: 10:00 am to 11:45 am TOTAL MARKS: 40

Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.

Q.1*

(a) Find the Laplace Transform of the function 𝑓(𝑡) = {0, 0 < 𝑡 < 𝜋𝑠𝑖𝑛𝑡, 𝑡 > 𝜋

. [03]

(b) Find 𝐿−1(𝑡𝑎𝑛−1 2𝑠⁄ ). [03]

(c) Find a Fourier Series for 𝑓(𝑥) = 𝑥2, where −𝜋 ≤ 𝑥 ≤ 𝜋. [04]

Q.2

(a) Find 𝐿−1 [1

(𝑠2+4)2] using Convolution theorem. [06]

(b) State the convolution theorem and verified it for 𝑓(𝑡) = 𝑡 and 𝑔(𝑡) = 𝑒2𝑡. [05]

(c) Find the Fourier integral representation of the function 𝑓(𝑥) = {2 , |𝑥| < 20 , |𝑥| > 2

. [04]

OR

Q.2 (a) Solve using Laplace transform: 𝑦" − 3𝑦′ + 2𝑦 = 4𝑡 + 𝑒3𝑡, 𝑦(0) = 1, 𝑦′(0) = −1. [06]

(b) Find (i) 𝐿−1 {1

(𝑠2+4)(𝑠2+9)} (ii) 𝐿−1 {

1

𝑠 (𝑠2+4)}. [05]

(c) Find the Fourier cosine series of 𝑓(𝑥) = 𝑒−𝑥, where 0 ≤ 𝑥 ≤ 𝜋 . [04]

Q.3

(a) Expand 𝑓(𝑥) in Fourier series in the interval (0,2𝜋) if (𝑥) = {−𝜋 ; 0 < 𝑥 < 𝜋

𝑥 − 𝜋 ; 𝜋 < 𝑥 < 2𝜋 .

Hence show that ∑1

(2𝑟+1)2 =𝜋2

8∞𝑟=0 .

[06]

(b) Find the Fourier Series for 𝑓(𝑥) = 𝑒𝑎𝑥 in (0,2π); a>0. [05]

(c) Find the Laplace Transform of (𝑖) 𝑓(𝑡) = tt 3sin 2

(𝑖𝑖) 𝑓(𝑡) =𝑠𝑖𝑛𝑤𝑡

𝑡. [04]

OR

Q.3

(a) Express the function 𝑓(𝑥) = {1 𝑓𝑜𝑟 |𝑥| ≤ 1

0 𝑓𝑜𝑟 |𝑥| ≥ 1 as a Fourier integral.

Hence, evaluate (a) ∫sin 𝜔 cos(𝜔𝑥)

𝜔𝑑𝜔

0 (b) ∫

sin 𝜔

𝜔

0𝑑𝜔

[06]

(b) Find Fourier series of 𝑓(𝑥) = 𝑥 + 𝑥2, − 𝜋 < 𝑥 < 𝜋. Hence deduce that 𝜋2

6=

1

12+

1

22+

1

32+ ⋯ .

[05]

(c) Find (𝑖)𝐿(𝑡3 + 𝑒−3𝑡 + 𝑡3/2) (𝑖𝑖)

t t

dtt

teL

0

sin

[04]

Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

BE - SEMESTER–III • MID SEMESTER-I EXAMINATION– WINTER 2018

SUBJECT: MECHANICS OF SOLIDS (2130003) (CL/ME/AERO)

DATE: 10-08-2018 TIME: 10:00 am to 11:30 am TOTAL MARKS: 40

Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.

Q.1 (a) State the fundamental principles of mechanics and explain any one. [03]

(b) Explain parallelogram law of forces in brief with a neat figure. [03]

(c) What does notations E, G, K & μ mean? Explain the significance with

relationship between any three.

[04]

Q.2 (a) An electric lamp in street as shown in Fig 1 is having 50 N weight suspended by

two wires of 4 m and 3 m length. The horizontal distance between two fixed

points is 5 m from which two wires were suspended. Find out tension in both

wires.

[06]

(b) Determine the support reactions at A & B for the beam loaded as shown in Fig 2 [05]

(c) State ‘Hooks Law’. Derive formula to determine change in length (δL) for the

uniform, homogeneous axially loaded member of length (L), c/s area (A) and

modulus of elasticity (E), subjected to axial tensile force (P).

[04]

OR

Q.2 (a) A system of four forces shown in Fig 3 has resultant 50 kN along + X - axis.

Determine magnitude and inclination of unknown force P.

[06]

(b) Discuss types of loads & supports based on the reactions that occur in beams

with neat sketch for each.

[05]

(c) A stepped circular bar ABC is axially loaded as shown in Fig 4 is in equilibrium.

The diameter of part AB is 50 mm throughout its length, whereas diameter part

BC is uniform decreasing from 40 mm at B to 30 mm at C. Determine (i)

magnitude of unknown force ‘P’ (ii) stress in part AB and (iii) change in length

of part BC. Take modulus of elasticity = 2 x 105 N/mm2.

[04]

Q.3 (a) Determine deformation in each part of the bar ABCD shown in Fig 5

Take E = 2 x 105 N/mm2.

[06]

(b) State Lami’s theorem and derive the equation with neat diagram. [05]

(c) A cylindrical roller weighing 1000 N is resting between two smooth surfaces

inclined at 60º and 30º with horizontal as shown in Fig 6. Draw free body diagram

and determine reactions at contact points A and B.

[04]

OR

Page 1 of 2

Q.3 (a) Derive formula for the elongation (δL) of a uniformly tapering circular bar of

length (L) subjected to axial tensile force (P), c/s area (A) and modulus of

elasticity (E).

[06]

(b) State and prove Varignon’s theorem with a neat diagram. [05]

(c) Explain drawing a neat graph the salient features of a stress-strain curve for mild

steel in tension test.

[04]

Page 2 of 2

Figure 1 Figure 2

Figure 3 Figure 4

Figure 5 Figure 6

Enroll. No. _____________SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY

BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018

SUBJECT: Manufacturing Process-I (2131903) (ME)

DATE: 08-08-2018 TIME: 10:00 am to 11:30 am TOTAL MARKS: 40Instructions: 1. All the questions are compulsory.

2. Figures to the right indicate full marks.3. Assume suitable data if required.

Q.1 (a) Define machining process. Give detail classification of machiningprocess.

[03]

(b) Explain with neat sketch different types of chips.[Any three] [03](c) Draw a front view, top view and side view of single point cutting

tool with labeling. [04]

Q.2 (a) Draw a neat sketch of lathe machine. Explain a working of variouslathe machine parts.

[06]

(b) Different between capstan and turret lathe machine. [05](c) Enlist various accessories of lathe machine. Explain any one with

neat sketch.[04]

ORQ.2 (a) Enlist a different method of taper turning. Explain taper turning

method by the using of taper attachment with neat sketch. [06]

(b) Classify a various operations of lathe machine. Explain any fouroperations with neat sketch.

[05]

(c) What is mandrel? Classify different types of mandrel. [04]

Q.3 (a) Explain with neat sketch of Jig boring machine. Write anadvantage, disadvantage and application of Jig boring machine.

[06]

(b) Draw and explain working of horizontal boring machine. [05](c) Figure out a various operation i) Reaming ii) Boring iii) Counter

boring iv) Counter sinking. [04]

ORQ.3 (a) Classify a various sawing machine. Explain with neat sketch of

vertical band saw machine.[06]

(b) Explain geometry of broaching tool. [05](c) Define the term “broaching”. Write an advantage, disadvantage

and application of broaching. [04]

Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY

BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018

SUBJECT: MATERIAL SCIENCE & METALLURGY (2131904) (ME)

DATE: 07-08-2018 TIME:10:00 am to 11:30 am TOTAL MARKS:40

Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.

Q.1 (a) Explain the requirement of engineering materials. [03]

(b) What is Powder Metallurgy? Explain the process of Powder Metallurgy. [03]

(c) Explain Criteria for Selection of Engineering Material. [04]

Q.2 (a) Explain with neat sketches the arrangement of atoms, in S.C, B.C.C, F.C.C. and

H.C.P. lattice. And Also write Effective Number of atom, Atomic Packing Factor,

Co-ordination Number for all Lattices. Define unit cell.

[06]

(b) Explain edge dislocation and screw dislocation. [05]

(c) Draw a unit cell and show the following planes (a) (113) (b) (102) (c) (111) and (d)

(001).

[04]

OR

Q.2 (a) Explain the strain hardening process. Also mention the effect of strain hardening

on properties of metals.

[06]

(b) Draw sketch of Recovery, Recrystallization and Grain growth graph. [05]

(c) Explain the difference between slip and twinning mechanisms [04]

Q.3 (a) Differentiate between Homogeneous and Heterogeneous nucleation processes. Also

discuss the conditions under which growth may be of planar and dendritic type.

[06]

(b) Define Powder Metallurgy. State advantages, limitations and applications of

Powder Metallurgy.

[05]

(c) With neat sketches, explain Solidification of Metal. [04]

OR

Q.3 (a) Explain the “Hune-Rothery Rules” for solid solution, with suitable case study. [06]

(b) What is phase diagram? Explain Lever rule. [05]

(c) What is Gibb’s phase rule? Calculate the degree of freedom, for eutectic

composition in binary phase diagram.

[04]

Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018

SUBJECT: ENGINEERING THERMODYNAMICS (2131905) (ME)

DATE: 11-08-2018TIME: 10:00 am to 11:30 am TOTAL MARKS: 40

Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.

Q.1 (a) Derive steady flow energy equation for a given control volume. Apply SFEE to following

engineering applications: a) Nozzle b) Boiler [05]

(b) Explain the effect of regeneration on Brayton cycle. [05]

Q.2 (a) Gases produced during the combustion of a fuel-air mixture, enter a nozzle at 300 kPa,

1500C and 20 m/s and leave the nozzle at 100 kPa and 1000C. The exit area of the nozzle

is 0.03 m2. Assume that these gases behave like an ideal gas with Cp = 1.15 kJ/kg-K and

γ = 1.3, and that the flow of gases through the nozzle is steady and adiabatic. Determine

(i) the exit velocity and (ii) the mass flow rate of the gases.

[06]

(b) Derive the air standard efficiency of constant volume cycle. [05]

(c) Define a thermodynamic system. Differentiate between open system, closed system and

an isolated system. [04]

OR

Q.2 (a) The air compressor takes in air steadily at the rate of 0.6 kg/sec from the surroundings

with pressure of 100.0kPa and density of 1.05 kg/m3. The air entry velocity is 7 m/sec.

The pressure ratio of air compressor is 7. The leaving air has density of 5.26 kg/m3 and

leaves with velocity of 5.0 m/sec. The internal energy of the leaving air is 100kJ/kg more

than that at entering. Cooling water in the compressor jackets absorbs heat from air at the

rate of 65 KW.

i) Compute the rate of shaft work to air ii) Find the ratio of inlet pipe diameter to outlet pipe diameter.

[06]

(b) Explain Joule Experiment in details. [05]

(c) Justify that heat & work transfer is a path function and not a point function. [04]

Q.3 (a) A closed cycle ideal gas turbine plant operates between temperature limits of 800°C and

30°C and produces a power of 100 kW. The plant is designed such that there is no need

for a regenerator. A fuel of calorific 45000kJ/kg is used. Calculate the mass flow rate of

air through the plant and rate of fuel consumption.

Assume Cp = 1 kJ/kg-K and γ = 1.4.

[06]

(b) Compare Otto, Diesel and Dual cycle for

i) Same compression ratio and heat supplied

ii) Same Max. Pressure and temperature

[05]

(c) Prove that “Energy is a property of a system”. [04]

OR

Q.3 (a) In an air standard Diesel cycle the compression ratio is 14 and the beginning of Isentropic

compression is at 110kPa and 30˚C. If the fuel cut off takes place at 5% of stroke, find the

air standard efficiency and mean effective pressure.

[06]

(b) Draw schematic and T-S diagram of intercooling and reheating on Brayton cycle. [05]

(c) Differentiate between microscopic and macroscopic point of view. [04]

Enroll. No. _____________

SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY

ADITYA SILVER OAK INSTITUTE OF TECHNOLOGY

BE - SEMESTER–III • MID SEMESTER-I EXAMINATION – WINTER 2018

SUBJECT: KINEMATICS OF MACHINES (2131906) (ME)

DATE: 06-08-2018 TIME: 10:00 am to 11:30 am TOTAL MARKS:40

Instructions: 1. All the questions are compulsory. 2. Figures to the right indicate full marks. 3. Assume suitable data if required.

Q.1 (a) Explain the terms in relation to gears:

(1) Module

(2) Circular Pitch

(3) Pressure Angle

[03]

(b) What is inversion of mechanism? Explain all inversion of four bar chain

mechanism.

[03]

(c) Explain degree of freedom with neat sketch. Also explain Grubler’s criterion and

State Grashof’s law.

[04]

Q.2 (a) PQRS is a four bar chain with link PS fixed. The lengths of the links are

PQ= 62.5 mm; QR = 175 mm; RS = 112.5 mm; and PS = 200 mm.

The crank PQ rotates at 10 rad/s clockwise.

Draw the velocity diagram when angle QPS = 60° and Q and R lie on the same side

of PS. Find the angular velocity of links QR and RS.

[06]

(b) Explain whitworth quick return motion mechanism with neat sketch. [05]

(c) Classify and explain different types of kinematic pair. [04]

OR

Q.2 (a) The crank of a slider crank mechanism rotates clockwise at a constant speed of

300 r.p.m. The crank is 150 mm and crank angle of 45° from inner dead centre

position. The length of connecting rod is 600 mm long.

Determine :

1. linear velocity of the midpoint of the connecting rod, and

2. Angular velocity of the connecting rod,

[06]

(b) Sketch and explain any two inversions of a double slider crank chain. [05]

(c) Explain different types of constrained motions with neat sketch. [04]

Q.3 (a) A pinion having 30 teeth drives a gear having 80 teeth. The profile of the gears is

involute with 20° pressure angle, 12 mm module and 10 mm addendum. Find the

length of path of contact, arc of contact and the contact ratio.

[06]

(b) State and prove the law of gearing. [05]

(c) What do you understand by the term ‘interference’ as applied to gears? What are the

various ways to avoid interference? [04]

OR

Q.3 (a) Two 20° involute spur gears have a module of 15mm. The addendum is one module.

The larger gear has 50 teeth and the pinion has 13 teeth will be interference occur? If

it occurs,

(i.) To what value the pressure angle be changed to eliminate interference.

(ii.) If the pressure angle is to be kept 20° only, by what value the addendum of

gear tooth be decreased to avoid interference.

(iii.) Calculate the length of path of contact and contact ratio for the case (i) above.

[06]

(b) Derive an expression for the length of the path of contact in a pair of meshed spur

gears.

[05]

(c) Derive an expression for the minimum number of teeth required on the pinion in

order to avoid interference in involute gear teeth when it meshes with wheel.

[04]