SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is...
Transcript of SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is...
![Page 1: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/1.jpg)
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY B.E. Semester- (III) - MID SEMESTER EXAMINATION (winter’14 Session)
SUBJECT: Engineering Thermodynamics (2131905)
Date: 14-10-2014 TIME: 11:00 A.M. to 12:30 P.M Total Marks: 40
Instructions: 1. Question one is compulsory. 2. Attempt any three from rest of the questions
3. Figures to the right indicate full marks. 4. Assume suitable data if required.
Q.1 (i) Which of the following is closed system? 01
a. Water Pump b. I.C. Engine c. Car Battery d. jet engine in flight (ii) Steady Flow Energy Equation of Throttling Process for ideal gas 01 a. h1=h2 b. C1=C2 c. u1=u2 d. None of Above (iii) The Efficiency of Carnot Cycle Engine depend on 01 a. Tmax & Tmin b. Quality of fuel c. Material of Engine d. Surrounding Pressure (iv) Second Law of Thermodynamics defines 01 a. Internal Energy b. Entropy c. Heat d. Work (v) Efficiency of Otto Cycle at Compression ratio is 8 01 a. 60.32% b. 56.47% c. 52.86% d. 61.42% (vi) In a Carnot Vapor Cycle phase of working fluid after condenser is 01 a. Liquid b. Steam/ Vapour c. Mixture of Liquid & Vapour d. All of The Above (vii) Equal Volumes of all perfect gases at the same temperature &
pressure contain same number of molecules it is statement of 01
a. Boyle’s Law b. Combined Gas Law c. Gibbs Dalton’s Law d. Avogadro’s Law Q.2 (a) Prove that Energy “ A Property of System” 04
(b) In a steam power cycle, the dry and saturated steam is supplied at 15 bar. If the Condenser pressure is 0.4 bar, calculate the Carnot and Rankine cycle Efficiencies neglecting the pump work.
07
Q.3 (a) A Heat Engine is operated between 800 0C and 40 0C. It Drives a heat pump which works between 120 0C and 40 0C. Efficiency and COP of the Heat Engine and the Heat Pump are half of that of corresponding Carnot values. Calculate amount of heat rejected by heat pump at 120 0C when 100 kJ is absorb by Heat Engine at 800 0C and Net heat transfer to the reservoir at 40 0C
07
04 (b) Write comparison of Carnot and Rankine cycle.
![Page 2: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/2.jpg)
Q.4 (a) In a steam power station, steam flows steadily through a 0.2 m
diameter pipeline from the boiler to the turbine. At the boiler end, the
steam conditions are found to be: p= 4 MPa, t= 400 deg C, h= 3213.6
kJ/kg and v= 0.073 m3/kg. At the turbine end the condition are found
to be: p= 3.5 MPa, t=392 deg C, h= 3202.6 kJ/kg & v= 0.084 m3/kg.
There is a heat loss of 8.5 kJ/kg from the pipe line. Calculate the
steam flow rate.
05
06 (b) Explain P-V and T-s diagram for Diesel cycle. Derive the formula for the efficiency of the cycle.
Q.5 (a) Write down Vander wall’s equation of state. How does it differ from
ideal gas equation? 05
06 (b) An Air standard Otto cycle has a compression ratio of 8. At the start the compression process, the temperature is 260C and pressure is 1 bar. If the max temperature of the cycle is 10800 C. Calculate 1) The heat supplied per kg of air. 2) The thermal efficiency of the cycle.
************************
![Page 3: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/3.jpg)
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
B.E. Semester- (III) - MID SEMESTEREXAMINATION (Winter’14 Session)
SUBJECT: KINEMATIC OF MACHINES (2131906)
Date:15-10-2014 TIME: 11:00 A.M. to 12:30 P.M Total Marks: 40
Instructions: 1. Question one is compulsory.
2. Attempt any three from rest of the questions
3. Figures to the right indicate full marks.
4. Assume suitable data if required.
Q.1 1. A kinematic chain is known as a mechanism when 01
(a) none of the links is fixed (b) one of the links is fixed
(c) two of the links are fixed (d) all of the links are fixed
2 The mechanism forms a structure, when the number of degrees of freedom
(n) is equal to
01
(a) 0 (b) 1 (c) 2 (d) – 1
3. Which of the following is an inversion of double slider crank chain? 01
(a) Coupling rod of a locomotive (b) Pendulum pump
(c) Elliptical trammels (d) Oscillating cylinder engine
4 The angle between the direction of the follower motion and a normal to the
pitch curve is called
01
(a) pitch angle (b) prime angle (c) base angle (d) pressure angle
5 A circle drawn with centre as the cam centre and radius equal to the distance
between the cam centre and the point on the pitch curve at which the pressure
angle is maximum, is called
01
(a) base circle (b) pitch circle (c) prime circle (d) none of these
6. Involute profile is preferred to cycloidal because 01
(a) the profile is easy to cut (b) only one curve is required to cut
(c) the rack has straight line
profile and hence can be cut
accurately
(d) none of the above
7. The synthesis of mechanism deals with 01
(a) the determination of input and
output angles of a mechanism
(b) the determination of dimensions
of the links in a mechanism
(c) the determination of
displacement, velocity and
acceleration of the links in a
mechanism
(d) none of the above
Q.2 (a) Define the following terms:
1. Link 2. Locked Chain 3. Higher Pair 4. Ternary Joint 5. Degrees of
freedom 6. Constrained Motion 7. Quaternary Link
7
![Page 4: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/4.jpg)
(b)
Define the following terms as applied to cam with a neat sketch :-
(a)Base circle, (b) Pitch circle, (c) Pressure angle, and (d) Trace Point
4
Q.3 (a) A cam is to give the following motion to a knife-edged follower:
1. Outstroke during 60° of cam rotation; 2. Dwell for the next 30° of cam
rotation; 3. Return stroke during next 60° of cam rotation and 4. Dwell for the
remaining 210° of cam rotation.
The stroke of the follower is 40 mm and the minimum radius of the cam is 50
mm. The follower moves with uniform velocity during both the outstroke and
return strokes. Draw the profile of the cam when the axis of the follower
passes through the axis of the cam shaft,
7
(b) Sketch and describe the working of Beam Engine. 4
Q.4 (a) Derive an Expression for Length of Path of contact of Gears. 5
(b)
An epicyclic gear train as shown in fig. has a sun wheel S of 30 teeth and two
planet wheels P of 50 teeth. The planet wheel mesh with the internal teeth of
a fixed annular A. The driving shaft carrying the sun wheel transmits 4 KW
at 300 rpm. The driven shaft is connected to an arm which carries the planet
wheel. Determine the speed of the driven shaft.
6
Q.5 (a) Define:
i) Contact Ratio ii) Module iii) Circular Pitch
3
(b) Explain Function generation, Path generation and Motion generation. 3
(c) Determine the minimum number of teeth required on a pinion, in order to
avoid interference which is to gear with,
1. A wheel to give a gear ratio of 3 to 1 ; and 2. An equal wheel. The pressure
angle is 20° and a standard addendum of 1 module for the wheel may be
assumed.
5
************************
![Page 5: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/5.jpg)
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
B.E. Semester- (III) - MID SEMESTER EXAMINATION (winter’14 Session)
SUBJECT: Mechanics of Solids (2130003)
Date: 10-10-2014 TIME: 11:00 A.M. to 12:45 P.M Total Marks: 40
Instructions: 1. Question one is compulsory.
2. Attempt any three from rest of the questions
3. Figures to the right indicate full marks.
4. Assume suitable data if required.
Q.1 (1) The unit of couple is
(a) kN (b) kN/m
(c) kN.m (d) kN/m2
01
(2)
(3)
(4)
(5)
(6)
The magnitude of the force of friction between two bodies , one lying above
the other depends upon the roughness of the
(a) upper body (b) lower body
(c) the body having more roughness (d) both the bodies
The principle of moment is based on
(a) Lami's theorem (b) principle of superposition
(c) varignon's theorem (d) all of the above
If the ends of a body yield, the magnitude of thermal stress will
(a) increase (b) decrease
(c) remain same (d) none of these
The C.G of a right circular cone of diameter (d) and height (h) lies at a
distance of___________ from the base along the vertical axis.
(a) h/6 (b) h/2
(c) h/3 (d) h/4
Moment of a triangle of base (b) and height (h) about axis passing through
C.G and parallel to the base is
(a) bh3/36 (b) bh
3/4
(c) bh3/12 (d) hb
3/12
Modulus of elasticity is the ratio of
01
01
01
01
01
![Page 6: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/6.jpg)
(7) (a) stress to strain (b) force to cross-sectional area
(c) strain to stress (d) stress to original length
01
Q.2 (a) (1)What should be the value of θ in fig-1 which will make the motion of
1000N block down the plane to impend? The coefficient of friction for all
contact surfaces is 1/3.
(2) state laws of dry friction.
05
02
04 (b) A system of four forces shown in Fig. 2, has resultant 50 kN along + X –
axis.Determine magnitude and inclination of unknown force P.
Q.3 (a) (1) Determine magnitude, direction and perpendicular distance
from ‘O’ of the resultant for the force system shown in Fig. 3
(2) what must be the length of 5mm diameter aluminium wire so that
it can be twisted through one complete revolution without
exceeding a hearing stress of 42 MN/m2
. Modulus of rigidity(G) =
27 GN/m2
03
03
05
(b) Determine co-ordinates of centroid with respect to ‘O’ of the section shown
in fig- 4
Q.4 (a) (1) Write down the statement of parallel axis theorem and perpendicular axis
theorem.
(2) Write down the statement of pappus guildinus theorem of surface of
revolution and volume of solid.
(3) Enlist various types of loads and types of supports.
02
02
02
05 (b) A cord supported at A and B carries a load of 20kN at C and a load of W at
D as shown in fig-5. Find the value of W so that CD remains horizontal.
Q.5 (a) Determine the location of centroid and moment of inertia of the given lamina
in Fig-6 about centroidal X axis.
05
06
(b) A steel member ABCD with three different circular cross-section and
lengths as follows, is subjected to an axial pull of 150kN. Compute
the net change in the length of the member if the modulus of
elasticity (E)=200GPa.
AB: diameter=40mm and length=750mm
BC: diameter=25mm and length=1000mm
CD: diameter=30mm and length=1200mm
![Page 7: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/7.jpg)
Fig-1 Fig-2 Fig-3
Fig-4 fig-5
Fig-6
![Page 8: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/8.jpg)
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
B.E. Semester- (III) - MID SEMESTER EXAMINATION (Winter’14 Session)
SUBJECT: Manufacturing Process-I (2131903)
Date: 11-10-2014 TIME: 11:00 A.M. to 12:30 P.M Total Marks: 40
Instructions: 1. Question one is compulsory. 2. Attempt any three from rest of the questions
3. Figures to the right indicate full marks. 4. Assume suitable data if required.
Q.1 Answer the following Multiple Choice Questions.
07
1 Which of the following is not a type of tool material (a) Diamond (b) Tantalum (c) Ceramics (d) Cast Iron
2 Which of the following term is associated with Drilling (a) Arbor (b) Shank (c) Lead Screw (d) Feed Rod
3 The size of shaper is defined by (a) Floor Size (b) Maximum Stroke Length (c) Weight of Machine (d) Size of the work piece
4 The Size of planner is defined by (a) Floor Size (b) Maximum Stroke Length (c) Weight of the machine (d) Size of the work piece that can be machined
5 In milling machine, Cutter is mounted on (a) Indexing Plate (b) Table (c) Arbor (d) All of Above
6 Which of the following is single point cutting tool (a) Grinding Wheel
![Page 9: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/9.jpg)
(b) Milling Cutter (c) Turning Tool (d) Drilling Tool
7 Which of the following is suitable for mass production of large size
cylindrical parts (a) Turret Lathe (b) Engine Lathe (c) Tool Room Lathe (d) Bench Lathe
Q.2 (a) Sketch and explain Basic parts of lathe machine. 06 (b)
Classification of basic machine tools.
05
Q.3 (a) Explain Operations performed on lathe machine.(Any Four) 06
(b)
Compare Centre lathe, Turret Lathe, Capstan Lathe.
05
Q.4 (a) Explain Nomenclature of Twist Drill 05
(b)
Why Flutes are provided in Twist Drill? Explain the application of Coolant.
03
(c) What is Indexing? Name Different Indexing methods. 03
Q.5 (a) Explain Up-milling and down-milling. List Merits and demerits of Up-
milling and down-milling.
05
(b) What is Quick Return Mechanism and also Explain hydraulic type of quick return mechanism.
06
***********************
![Page 10: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/10.jpg)
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
B.E. Semester- (III) - MID SEMESTER EXAMINATION (Winter’14 Session)
SUBJECT: Material Science & Metallurgy (2131904)
Date:16-10-2014 TIME: 11:00 A.M. to 12:30 P.M Total Marks: 40
Instructions: 1. Questionone is compulsory. 2. Attempt any three from rest of the questions
3. Figures to the right indicate full marks. 4. Assume suitable data if required. 5. Draw suitable sketch if required.
Q.1 (i) Pearlite is made up of alternate layers of
a) Ferrite and Austenite b) Ferrite and Cementite c) Austenite and Cementite d) Ferrite and Bainite
01
(ii) Coordination number in simple cubic crystal structure is a) 14 b) 8 c) 2 d) 6
01
(iii) Rate of solidification depends upon a) Rate of nucleation b) Rate of growth c) Both (a & b) d) Rate of Cooling
01
(iv) Twinning deformation occurs due to a) Gradual loading b) Sudden loading c) Both (a & b) d) none of these
01
(v) A solid + liquid result in a solid upon cooling during …………reaction. a) Eutectic b) Peritectic c) Eutectoid d) none of these
01
(vi) Atomization process is used for a) Low melting point material b) High melting point Material c) Hard Material d) All of these
01
(vii) Repeatable entity of a crystal structure is known as a) Crystal b) lattice c) Unit cell d) Miller indices
01
Q.2 (a) Explain selection criteria for engineering materials. 04
05 (b) Define Dislocation. Explain the mechanism of Edge dislocation &
Screw dislocation
(c) Draw miller indices of following Planes:- (1 0 0 ) , (1 1 1) 02
Q.3 (a) What is the significance of Recovery and Recrystallization process 06
![Page 11: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/11.jpg)
and also mention the mechanism of grain growth.
05 (b) Explain the Solidification process of pure metal and Differentiate
planar and dendritic mode of solidification.
Q.4 (a) Draw Iron – Carbon equilibrium diagram and write the suitable
reaction.
06
03 (b) Write compositions, properties and application of white cast iron.
(c) Define Shrinkage and Pipe Defects. 02 Q.5 (a) Explain in detail Basic process of powder metallurgy. 04
04
(b) What is plastic deformation and differentiate slip deformation and
twinning deformation
(c) Describe and illustrate the following imperfections that can occurs in
crystal lattice.
(i) Frenkel defect
(ii)Schottky defect
03
************************
![Page 12: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/12.jpg)
ROLL NO. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
B.E. Semester-III (ME) - MID SEMESTER EXAMINATION
SUBJECT: (131901) Electrical Machines & Electronics
DATE: 10/10/2014 TIME: 02:00 to 03:30 pm TOTAL MARK: 40 Instructions: 1. Question – 1 is compulsory.
2. Attempt any 3 out of remaining 4. 3. Figure to the right indicates full marks. 4. Assume Suitable data if required.
Q.1 Answer the following questions. (07)
1) DC motor yoke is generally made of
(a) wood (b) copper
(c) Cast Iron (d) aluminum
2) A transformer is a constant
(a) Current device (b) Voltage device
(c) Main flux device (d) Power device
3) During parallel operation of transformers incorrect polarity will result in
(a) Open circuit (b) Regeneration of power
(c) Dead short circuit (d) Power factor will be different from that of the connected load
4) In performing the short circuit test of a transformer
(a) High-voltage side is short-circuited (b) Any side is short-circuited with preference
(c) Low-voltage side is short-circuited (d) None of these
5) The function of a Commutator in a DC machine is
(a) to provide easy speed control (b) to improve commutation
(c) to convert AC Emf to DC Emf (d) to convert ac current to DC current
6) Isolators are used to disconnect a circuit when
(a) line is on full load (b) line is energized
(c) Circuit breaker is not open (d) There is no current in the line.
7) Which one of the following is not a type of tariff?
(a) Simple Tariff (a) Simple Tariff
(c) Current Factor Tariff (c) Current Factor Tariff
![Page 13: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/13.jpg)
Q.2 (A) Explain the use of CT & PT for current and voltage measurements. (04)
Q.2 (B) Discuss the comparison between core type and shell type transformer. (04)
Q.2 (C) Define the following terms. (03)
1) Feeders 2) Distributors 3) Supply mains
Q.3 (A) Define power factor. And explain power factor improving methods. (06)
Q.3 (B) Draw Schematic diagram of a DC machine with labels. Also state functions of (05)
(i) Pole and Pole shoe
(ii) Commutator and brush Q.4 (A) Define the term Tariff. Also explain the types of Tariff. (07)
Q.4 (B) Explain the working principle of single phase transformer. (04)
Q.5 (A) Derive an EMF equation for single phase transformer. (04)
Q.5 (B) Give the comparison between AC & DC transmission system. (03)
Q.5 (C) Calculate no of turns on both primary and secondary for following given data. A 10 KVA,
500/250 v, 50 Hz, 1-phase transformer has a net area of cross section 30 cm2 and max flux
density is 1.2 Tesla. (04)
& BEST OF LUCK &
![Page 14: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/14.jpg)
Enroll. No. _____________
SILVER OAK COLLEGE OF ENGINEERING & TECHNOLOGY
B.E. Semester- (III) - MID SEMESTER EXAMINATION (Winter’14 Session)
SUBJECT: Advanced Engineering Mathematics (2130002)
Date:09-10-2014 TIME: 11:00 A.M. to 12:45 P.M Total Marks: 40
Instructions: 1. Questionone is compulsory.
2. Attempt any three from rest of the questions
3. Figures to the right indicatefull marks.
4. Assume suitable data if required
Q-1 Select the correct answer from the option given for each question.
(1) .________1 n 07
(a) )(nn (b) )1( nn
(c) )1()1( nn (d) ) )1()1( nn
(2)
Find the Order and Degree of xydx
dysin
2
1
(a) Order 1,Degree 1 (b) Order 1,Degree 2
(c) Order 2,Degree 1 (d) Order 2,Degree 2
(3) Solve .0' yxy
(a) cyx (b) cxy
(c) cyx / (d) cyx
(4) Two solutions )(1 xy and )(2 xy are said to be linearly dependent if ?
(a) 0),( 21 yyw (b) 0),( 21 yyw
(c) 1),( 21 yyw (d)None of these
(5) Laplace of sinkt=________
(a)
22 ks
k
(b)
22 ks
s
(c)
22 ks
k
(d)
22 ks
s
(6) Laplace of __________3 t
(a)
3
1
s (b) 3ln
1
s
(c) se (d) None of these
(7) The Particular Integral of (D+1)2y=e
- x is?
(a) xe
x
2
2
(b) xe
x
2
2
(c) xex 2 (d) xxe
Q.2 (a)
Using method of undetermined coefficients, find the general solution
of 325102 2 xyyy
6
![Page 15: SILVER OAK COLLEGE OF ENGINEERING & … 2014.pdfa. Water Pump b. I.C ... Which of the following is an inversion of double slider crank chain? 01 (a) ... Pendulum pump (c) ...](https://reader031.fdocuments.us/reader031/viewer/2022022003/5aa2b5857f8b9a80378d5365/html5/thumbnails/15.jpg)
(b) Obtain the Fourier series to represent the function
20,)(4
1)( 2 xxxf
5
Q.3 (a) Solve using Laplace Transform
𝑦 ′′ + 2𝑦 ′ + 𝑦 = 𝑒−𝑡 ,𝑦 0 = −1 𝑎𝑛𝑑𝑦 ′ 0 = 1
6
(b)
Solve xydx
yd2tan4
2
2
by method of variation parameter.
5
Q.4 (a)
(i)Solve: 23 11 xey
dx
dyx x
6
(ii)Solve the D.E. by the exact differential.
0)1(,01 ydyxedxeex yyx
(b) Find Fourier Series for 22)( xxxf in the interval (0,3)
5
Q.5 (a)
(i)Using convolution theorem ,determine 𝐿−1
𝑎
𝑠2 (𝑠2+𝑎2)
6
(ii)Find𝐿−1 𝑙𝑛 1 +𝑤2
𝑠2
(b)
Solve )sin()23( 2 xeyDD 5
*******