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Code No: X0121/R07

II B.Tech I Semester Supplementary Examinations, May- 2011

MATHEMATICS - II

(Com. to CE, CHEM,MMT, AE,BT)

Time: 3 hours Max Marks: 80

Answer any FIVE Questions

All Questions carry equal marks

1. a) Define the rank of a matrix and find the rank of the following matrix by reducing it to

Echolon from

��

�

�

��

�

�

−− 1348

13748

3124

5312

b) Show that the only real number λ for which the system x+2y+3z = λ x;

3x+y+2z = λ y; 2x+3y+z = λ z has non zero solution is 6 and solve the system

completely.

2. Find the eigen values and eigen vectors of the following matrix

��

�

�

��

�

�

−

−

720

262

025

3. a) Show that the eigen value of a Skew-Hermitian matrix are purely imaginary or

zero.

b) Prove that the matrix ��

��

�

−+

+−+=

ii

iiA

11

11

2

1 is a unitary matrix.

4. a) Find the fourier series for the function

f(x) = ��

<<

<<−−

π

ππ

xx

x

0,

0,

and hence deduce the series 85

1

3

1

1

1 2

222

π=−−−−−+++

b) Find the half range sine series for the function f(t) = t – t2, 0<t<1

5. a) Solve xp –yq = y2-x

2

b) Solve x2p

2+y

2q

2 = z

2

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Code No: X0121/R07

6. A tightly stretched string with fixed end points x=0 and x=l is initially in a position given by

y = y 0 Sin3

l

xπ. If it is released from rest from this position, find the displacement y(x, t).

7. a) Using parseval’s identities, prove that )(2))(( 2222

0 baabtbta

dt

+=

++∞ π

b) Find f(x) if its fourier sine transform is 21 s

s

+

8. a) Find Z [ ]θ)1( +nSin

b) Solve the difference equation yk+1 + yk = 1, y0 = 0 by z-transform.

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Code No: X0121/R07


MATHEMATICS - II

(Com. to CE, CHEM, MMT, AE,BT)




1. 1. (a) Find the rank of the matrix A =

��

�

�

��

�

�

−

−

−

2121

3011

2024

6022

by reducing it to normal form.

b) If a+b+c � 0, show that the system of equations -2x+y+z = a; x-2y+z = b;

x+y-2z = c has no solution. If a+b+c = 0, show that it has infinitely many solutions.

2. Show that the matrix

��

�

�

��

�

�

−

−

−

=

210

321

221

A satisfies its characteristic equation. Hence find A-1

.

3. By Legranges reduction transform the quadratic form X1 AX to sum of squares form

for

��

�

�

��

�

�

−

−=

1824

262

421

A . Also find nature, index, rank and signature of the quadratic form.

4. a) Find the Fourier series for f(x) = e-x

in π20 << x

b) Find the Fourier series for expansion of f(x) = ππ <<− xinxx cos

5. a) Form the partial differential equation by eliminating ‘a’ and ‘b’ from log(az-1)= x+ay+b.

b) Solve p+q = sinx + siny

6. A tightly stretched string with fixed end points x=0 and x = l is initially at rest in its

equilibrium position. If it is vibrating by giving to each of its points a velocity

),( xlx −λ find the displacement of the string at any distance x from one end at any

time ‘t’.

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Code No: X0121/R07

7. a) Prove that [ ])( xfF − = )(sF

b) Find the Fourier transform of ��

��

>

<=

ax

axxf

,0

,1)( and hence evaluate

dss

sxCosasSin .∞

∞−

8. a) If ,)1(

1252)(

4

2

−

++=

z

zzzu evaluate u2 and u3

b) Solve the difference equation yn+2+3yn+1+2yn= 0, y0=1, y1= 2 by z-transform.

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Code No: X0121/R07


MATHEMATICS - II

(Com. to CE, CHEM, MMT, AE, BT)




1. a) Find the non singular matrices P and Q such that the normal form of A is PAQ

where

��

�

�

��

�

� −

=

3451

1541

1631

A and hence find its rank.

b) Find the value of λ for which the system of equations 3x-y+4z=3; x+2y-3z = -2,

6x+5y+ λ z = -3, will have infinite number of solutions and solve them with that λ value.

2. Show that the sum of the eigen values of a square matrix is equal to its trace and the

product of the eigen values is equal to its determinant.

3. Reduce the quadratic form 323121 222 xxxxxx −+ to canonical form. Also find its

nature, rank, index and signature.

4. a) Find the Fourier series of ππ <<−+= xxxxf ,)( 2 and hence deduce the series

12.......

3

1

2

1

1

1 2

222

π=−+−

b) Given ��

≤≤+

≤≤−−=

π

π

xx

xxxf

0,1

0,1)(

Is the function even or odd ? Find the Fourier series for f(x).

5. a) Form the differential equation by eliminating the arbitrary function φ from

0)2,( 2222 =−++ xyzzyxφ .

b) Solve )()()( 222 yxzqxzypzyx −=−+− .

6. If a string of length l is initially at rest in equilibrium position and each of its points is

given the velocity ,sin 3

0l

xv

π find the displacement y(x, t).

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Code No: X0121/R07

7. a) Find the Fourier transform of x

e−

b) Find the Fourier sine and cosine transforms of )..5.2( 25 xx ee −− +

8. a) Find )1

(n

z∠

and hence evaluate ��

��

�

+∠��

��

�

+∠ )2(

1

)1(

1

nzand

nz

b) Solve the difference equation yn+2+3yn+1+2yn=0, y0=1, y1=2 by z – transform.

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Code No: X0121/R07


MATHEMATICS - II

(Com. to CE, CHEM, MMT, AE, BT)




1. a) For what value of k the matrix

��

�

�

��

�

�

−

−

399

222

0111

1344

k

k has rank 3.

b) Test for consistency the set of equations and solve them if they are consistent.

x+2y+2z = 2; 3x-2y-z = 5; 2x-5y+3z=-4; x+4y+6z=0.

2. Verify Caley-Hamilton theorem for the matrix

��

�

�

��

�

�

−

−−=

311

151

113

A and hence find A-1

.

3. Reduce the quadratic form 2x2+2y

2+2z

2-2xy-2yz+2zx to canonical form by orthogonal

transformation and hence find rank, index, signature and nature of the quadratic form.

4. a) Find the Fourier series to represent the function f(x) given by

��

<<

<<−−=

π

π

xk

xkxf

0,

0,)(

Hence show that .4

......7

1

5

1

3

11

π=+−+−

b) Find the half range sine series for f(x) = ),( xx −π .0 π<< xin

5. a) Solve p+3q = 5z+tan(y-3x)

b) Solve p2+q

2 = npq

6. The points of trisection of a tightly stretched string of length l with fixed ends are pulled

aside through a distance ‘a’ on opposite sides of the position of equilibrium, and the string is

released from rest. Obtain an expression for the displacement of the string at any

subsequent time and show that the midpoint of the string is always at rest.

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Code No: X0121/R07

7. a) Express ��

>

≤≤=

π

π

x

xxf

,0

0,1)( as Fourier sine integral and hence evaluate

.)sin()cos(1

0

λλλ

πλdx

−∞

b) Find Fourier cosine transform of f(x) = 2x

e−

8. a) If )()(,)1(

)( 43

3

22

nzandnzfindz

zznz

−

+=

b) Evaluate ��

��

�

−−

−

))((

21

bzaz

zz using convolution theorem.

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Code No: X0222/R07


FLUID MECHANICS AND HYDRAULIC MACHINERY

(Com. to EEE, MM)




1. a) Discuss the influence of the following fluid properties on fluid motion

i) Viscosity

ii) Specific gravity

iii) Surface tension

iv) Bulk modulus (8M)

b) The space between two parellel plates kept 3mm apart is filled with an oil of dynamic

viscosity 0.2 Pa.s. What is the shear stress on the lower fixed plate, if the upper one is moved

with a velocity of 1.50 m/sec? (8M)

2. a) What are the criteria to distinguish laminar flow from turbulent flow? (6M)

b) Determine whether the following velocity components satisfy the continuity equation.

i) u = cx, v = -cy

ii) u = -cx/y , v = c log xy (10M)�

3. a) Describe the Reynold’s experiment with the help of a neat sketch. (6M)

b) Two reservoirs with a difference in water surface elevations of 10 m are connected by a

pipe line ABC which consists of two pipes of AB and BC joined in series. Pipe AB is 10cm in

diameter, 20m long and has a value of f =0.02. Pipe BC is of 16cm diameter, 25m long and

has f=0.018. The junctions with the reservoirs and between the pipes are abrupt. Calculate the

discharge considering all minor losses. (10M)

4. a) A nozzle of size 10 cm diameter issues a jet of water with a velocity of 50m/sec. The jet

strikes a moving flat plate perpendicularly at the centre. The plate is moving with a velocity of

15m/sec in the direction of the jet. Calculate

i)The force exerted on the plate

ii)The work done

iii)Efficiency of the jet (8M)

b) Derive the equation for the impact of jet striking a moving inclined plate in the direction of

the jet (8M)

5. a) What are the different heads and efficiencies associated with hydroelectric power plants?

(8M)

b) Differentiate between impulse turbine and reaction turbine with examples (8M)

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Code No: X0222/R07

6. a) What is draft tube? Why is it a part of reaction turbines? (8M)

b) Explain the phenomenon of water hammer. What is a surge tank? Where is it located in a

power plant? (8M)

7. a) What are the types of similarities between a prototype and a model? (8M+8M)

b) A hydraulic turbine develops 8000 kW under a head of 30 m at 250 rpm. What is the

specific speed of the turbine? What would be the speed and power under a head of 18m?

8. a) What are the performance characteristics of centrifugal pumps? (10M)

b) How many impellers are required in a multistage pump to lift 5000 litres/minute against a

head of 200m, at a speed of 800 rpm? The specific speed of the impeller is not to exceed 700.

(6M)

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Code No: X0222/R07



(Com. to EEE, MM)




1. a) List out the physical properties of fluids. Define them and write their units (10M)

b) If the surface tension at air water interface is 0.073 N/m, what is the pressure difference

between inside and outside of an air bubble of diameter 0.01 mm? (6M)

2. a) Define and explain stream line, path line and streak line in fluid mechanics. (8M)

b) For the following flow find the equation of the streamline passing through (1,1)

V = 3xi – 3yj (8M)

3. a) Derive the Darcy Weisbach equation. (6M)

b) Two reservoirs are connected by a pipe line ABC which consists of two pipes of AB and

BC joined in series. Pipe AB is 10cm in diameter, 20m long and has a value of f =0.02. Pipe

BC is of 16cm diameter, 25m long and has f=0.018. The junctions with the reservoirs and

between the pipes are abrupt. What difference in water levels shall exist to maintain a

discharge of 15 lit/sec. (10M)

4. a)A jet of water strikes with a velocity of 50 m/sec a flat fixed plate inclined at 30 degrees

with the axis of the jet. The cross sectional area of the jet is 100 cm2. Find the force exerted by

the jet on the plate and the ratio in which the jet gets divided after striking. (8M)

b) Derive the equation for the impact of jet striking a curved plate at the centre when the plate

is stationary. (8M)

5. a) What are the elements of hydroelectric power stations? Explain them in detail (8M)

b) What is a mass curve? What is its use? Explain with neat sketches (8M)

6. a) Explain the working of a Pelton wheel with neat sketches? (8M)

b) A Francis turbine works under a head of 8.5 m at a speed of 300 rpm. A power of 100 kW

is developed with a discharge of 3 m3/sec. The runner diameter is 2.2 m. Find the speed,

discharge and power if the head is increased to 18m. (8M)

7. a) How do you achieve the governing of turbines? Explain with neat sketches. (8M)

b) Discuss the different characteristic curves of turbines? (8M)

8. a) What is a centrifugal pump? How are the centrifugal pumps classified? (8M)

b) A fluid is to be lifted against a head of 120m. The pumps that run at a speed of 1200 rpm

with rated capacity of 300 litres per second are available. How many pumps are required to

pump the water if specific speed is 700. (8M)

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Code No: X0222/R07



(Com. to EEE, MM)




1. a) Define and discuss the following fluid properties

i) Specific gravity

ii) Viscosity

iii) Surface tension

iv) Vapour pressure (8M)

b) A cylindrical shaft of 90mm diameter rotates about a vertical axis inside a fixed cylindrical

tube of length 50 cm and 95 mm internal diameter. If the space between the tube and the shaft

is filled by a lubricant of dynamic viscosity 2.0 pose, determine the power required to

overcome viscous resistance when the shaft is rotated at a speed of 240 rpm. (8M)

2. a) Explain how the fluid flows are classified? Explain the sketches where necessary. (8M)

b) Find the equation of stream line passing through (2, 2) for the fluid flow V = -y2i – 6xj

(8M)

3. a) Differentiate between major loss and minor losses. List and discuss the minor losses

b) A reservoir discharges water into the atmosphere through a compound horizontal pipe line

ABC. The compound pipe consists of two pipes as noted below. A is junction point with the

reservoir.

AB: Diameter = 10cm, length =25m, f = 0.02

BC: Diameter = 12cm, length = 35m, f= 0.02

The water level in the tank is 10m above the centre line of the pipe. Calculate the discharge

considering all the minor losses. (8M+8M)

4. a) A jet of water of diameter 40 mm moving with a velocity of 30m/sec strikes a curved fixed

symmetrical plate at the center. Find the force exerted by the water on the plate, if the jet is

deflected through an angle of 120 degrees at the outlet of the curved plate. (8M)

b) Derive the equation for impact of jet striking a curved plate at one tip and leaving at the

other tip, when the plate is stationary (8M)

5. a) What are the types of hydroelectric power plants? Explain in detail (8M)

b) What are the criteria on which the turbines are classified? (8M)

6. a) What is the type of Francis turbine? Explain its working with neat sketches. (6M)

b) Discuss the significance and uses of the draft tubes? Derive the equation for the efficiency

of a draft tube. How are they classified? (10M)

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Code No: X0222/R07

7. a) What is specific speed? What are its uses? (6M)

b) Why is governing of turbine required? Discuss how the turbines are governed with neat

sketches. (10M)

8. a) What is the principle of working of a reciprocating pump? Explain the working of

reciprocating pump with neat sketches. (8M)

b) Water is to be pumped to a height of 90m. The pumps that run at a speed of 1000 rpm with

rated capacity of 200 litres per second are available. How many pumps are required to pump

the water if specific speed is 800? (8M)

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Code No: X0222/R07



(Com. to EEE, MM)




1. a) What are the fluid properties that influence fluid flow phenomena? List and discuss them

(10M)

b) The velocity distribution in a viscous flow over a plate is given by

u = 4y – y2, for y � 2m

where u = velocity in m/sec at a point distant y from the plate. If the coefficient of dynamic

viscosity is 1.5 Pa.s determine the shear stress at y = 0 and at y= 2.0m (6M)

2. a) Describe stream line and stream tube with the help of neat sketches. (6M)

b) For steady incompressible flow verify whether the following values of u and v are possible.

i) u = 4xy + y2 , v = 6xy + 3x

ii) u = 2x2 + y

2 , v = - 4xy

iii) u = -x/(x2 + y

2) , v = -y/(x

2 + y

2) (10M)

3. a) List out the minor losses in closed conduit flow and discuss their significance (6M)

b) A 6 cm diameter pipe has a discharge of 450 lit/min. At a section the pipe has a sudden

expansion to a size of 9 cm diameter. If the pressure just upstream of the expansion is 20 kN/

m2, calculate the pressure just after the expansion. Assume the pipe to be horizontal.

(10M)

4. a) A jet of oil of specific gravity strikes a fixed curved symmetrical plate at its center and

leaves at the outlet tips. The diameter of the jet is 62 mm and the velocity of the jet is 45

m/sec. If the jet is deflected by 100 degrees, calculate the force exerted on the curved plate.

(8M)

b) How do estimate the impact of a jet striking a moving normal plate in the direction of the

jet (8M)

5. a) What is a mass curve? What are its uses? (6M)

b) Discuss the classification of turbines with neat sketches. Specify the features and

advantages of different types. (10M)

6. a) Explain the working of a Kaplan turbine with neat sketches. (6M)

b) What is a draft tube? What are its types? Explain its use and derive the equation for its

efficiency. (10M)

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Code No: X0222/R07 �

7. a) What are different unit quantities? Derive the equations (8M)

b) A reaction turbine develops 7000 kW under a head of 45m with a speed of 150 rpm. What

is the specific speed of the turbine? What will be the power and speed when the turbine works

under a head of 20m. (8M)

8. a) What is indicator diagram of a reciprocating pump? Explain the working of a reciprocating

pump with a neat sketch. (8M)

b) Determine the number of the impellers required for a multistage centrifugal pump to deliver

3000 litres per minute to a height of 200m at a speed of 800 rpm. The specific speed value is

not to exceed 600. (8M)

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Code No: X0321/R07


PRODUCTION TECHNOLOGY

(Com. to ME, AME)




�

1. a) Large castings are not made by investment casting. Explain. (8M)

b) Name a casting process which requires no drafting. Explain why it is so. (4M)

c) State any four common green sand casting defects and give their causes and remedies.

(4M)

2. a) Explain how you maintain uniform solidification of a casting. (4M)

b) What precautions are to be taken to avoid distortion, cold shut and cavity formation?

(4M)

c) Bring out the difference between the solidification of pure metals and metal alloys?

(4M)

d) How do you decide the shape of a riser? Explain. (4M)

3. a) What are the disadvantages of bare wire electrode as filler materials? (4M)

b) Explain the principle of arc welding with all the elements in the circuit. (4M)

c) What is meant by HAZ? Explain why it is to be minimized. (4M)

d) Discuss the applications of Thermit welding. (4M)

4. a) Describe the differences between Brazing and Soldering. (4M)

b) Explain the principle of brazing and its applications. (4M)

c) Explain any two non- destructive tests applied in welding with neat sketches. (8M)

5. a) Explain the possible defects in rolling and suggest suitable remedies. (8M)

b) On a certain mill the rolling load for 25% reduction is 7KN/mm of width.

What is the rolling load when front and back tensions of 120 and 150MPU are

applied? �0 = 13KN/mm2 and � = 2�. (8M)

6. a) What principles are normally considered in the design of drop forgings? (8M)

b) What is spring back effect and how it does affect the bending process? Explain with a

sketch. (8M)

7. a) Distinguish between forward extrusion and backward extrusion processes. (8M)

b) Explain why normal anisotropy is important in determining the deep drawability

of materials. (8M)

8. Write short notes on the following:

i) Processing of plastics

ii) Hot and cold spinning

iii) Friction welding (16M)

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Code No: X0321/R07



(Com. to ME, AME)




�

�

1. a) What are the undesirable effects that could result from turbulence of the metal

in the gating system and mould cavity? Explain. (8M)

b) Sketch a graph of Specific volume Vs Temperature for a metal that shrinks as

it cools from the liquid state to room temperature. On graph, mark the area

where shrinkage is compensated for by risers? (8M)

2. a) What are crucible furnaces? Where are they preferred and why? (8M)

b) Explain the reasons for using the flux in melting of metals in cupola. (8M)

3. a )Mention the causes and remedies for magnetic arc blow. (8M)

b) Explain the effect of polarity on penetration in DC arc welding with a neat sketch.

(8M)

4. a)What are the low temperature joining processes? Explain briefly. (8M)

b) Why is brazing an appropriate method for joining dissimilar metals with widely

different melting points? (8M)

5. a)Explain the effect of rolling variables on rolling load and rolling process. (8M)

b) What is the significance of recrystallization temperature in metal working? (8M)

6. a) Discuss the types of presses and press tools with their applications. (10M)

b) Describe the process of making seamless tubes. (6M)

7. a)Why are the fabrication processes applied to plastics often different from those applied

to metals? Explain. (8M)

b) What are some of the ways that plastic sheet, plate and tubing can be cast? (8M)

8. Write short notes on the following:

i) Forging defects

ii) Drawing and its types

iii) Design of welded joints (16M)

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Code No: X0321/R07



(Com. to ME, AME)




�

1. a) What is the difference between the solidification of pure metals and metal alloys?

Explain. (8M)

b) What are composite moulds? Why are they used? Where are they used? (8M)

2. Explain with the help of neat sketches, the construction and working of the following types

of crucible furnaces:

i) Coke fired pit furnace

ii) A gas fired crucible furnace

iii) An oil fired tilting furnace (16M)

3. a) Explain with a neat sketch forge welding process. (4M)

b) Write the applications, advantages and limitations of projection welding. (12M)

4. Discuss the relative advantages and the disadvantages of friction welding, induction

welding, explosive welding and laser welding. (16M)

5. a) How do you estimate the rolling load? (6M)

b) Sketch and explain the sequence of operations involved in rolling a square section

to I-beam. (10M)

6. a) Why is lubrication often a major concern in metal forming? Explain. (8M)

b) What are the various press tool components? Explain them. (8M)

7. a) Describe the extrusion process and discuss its controlling parameters. (8M)

b) Explain the design considerations in spinning process. (8M)

8. a) List a few components manufactured by the injection moulding and justify why they are

manufactured by this process. (6M)

b) Describe the advantages of cold forming of plastics over other processing methods.

(4M)

c) Explain blow moulding method of processing plastics. (6M)

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�

�

Code No: X0321/R07



(Com. to ME, AME)




�

1. a) Why is match plate pattern much easier to use than a standard pattern? Explain.

(8M)

b) What are the undesirable effects that could result from turbulence of the metal

in the gating system and mould cavity? Explain. (8M)

2. Describe crucible melting and cupola operation with neat sketches. (16M)

3. Discuss the relative advantages and the disadvantages of forge welding, resistance welding,

thermit welding and plasma welding. (16M)

4. a) What are the low temperature joining processes? Explain briefly. (8M)

b) List and discuss the destructive tests applied in welding. (8M)

5. a) Compare the properties of cold and hot worked parts. (8M)

b) What is effect of strain rate on the formed components? (4M)

c) Explain the methods of eliminating work hardening effect. (4M)

6. a) What do you mean by die-angle and discuss its functions in wire drawing. (8M)

b) Explain the working of hydraulic press with neat sketch. (8M)

7. a) Describe deformation in extrusion and explain possible defects and suitable remedies

(6M)

b) Discuss impact extrusion and hydrostatic extrusion processes with neat sketches.

(6M)

c) Derive an equation for ideal extrusion pressure. (4M)

8. a) Are plastics are castable? If yes, explain various ways that plastic sheet, plate

and tube can be cast. (8M)

b) Why are the fabrication process applied to plastics often different from those applied

to metals? Explain. (8M)

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Code No: X0424/R07


ELECTRICAL TECHNOLOGY

(Com. to ECE, EIE, BME, ECC)




1. a) Derive emf equation for a d.c machine (8M)

b) What things distinguish motor action from generator action in a dc machine? (4M)

c) Explain the functions of brushes and commutator in a dc machine. (4M)

2. Derive mathematically torque-speed characteristic of various dc motors. Draw the curves

and discuss them. (16M)

3. a)Explain the constructional features of a single phase transformer and further classify the

transformers based on design (8M)

b) A 1-phase transformer has 400 primary and 1000 secondary turns. The net cross sectional

area of the core is 60 cm2. If the primary is connected to a 50Hz supply at 500V; determine

i) the peak value of the flux density in the core and

ii) the voltage induced in the secondary winding (8M)

4. A 7.5 kVA, 2400V/120V transformer was tested by short circuiting the low voltage side

and applying 100 V to the high voltage side. The measured power input was 145 W.

Determine the regulation when the load has 0.8 lagging power factor. (16M)

5. a) Explain the construction and working principle of a 3-Phase induction motor (8M)

b) A 4-pole, 50 Hz, 3-phase induction motor has a full load slip of 5%. Each rotor has a

resistance of 0.3� and a stand still reactance of 1.2�. Find the ratio of the maximum torque

to the full load torque and the speed at which the maximum torque occurs? (8M)

6. a) Explain the advantages of pitch factor and Distribution factor (6M)

b) A 500 kVA, 1.1 kV, 50 Hz three phase star connected alternator has an effective armature

resistance of 0.2� per phase. The synchronous reactance per phase is 1.5�. Calculate the

full load voltage regulation at

i) 0.8 lagging power factor and

ii) 0.8 leading power factor. (10M)

7. Explain the working principle and operation of the following with neat diagrams

i) A.C Servomotor and

ii) Stepper Motor (16M)

8. Write short notes on the following

i) Air Friction Damping

ii) Eddy current damping

iii) Fluid Friction Damping

iv) Secondary instruments with respect to Electrical instruments classification (4x4M)

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Code No: X0424/R07







1. a) Explain the construction of a dc machine and what materials are used for each component

of the machine (8M)

b) Classify the dc machine based on the excitation systems. (8M)

2. a) Derive an expression for the torque developed by a dc motor. (8M)

b) Find the useful flux per pole on no load of a 250V, 6-pole shunt motor having wave

connected armature winding with 110 turns. The armature resistance including brush is

0.2�.The armature current is 13.3 A at no load speed of 908 rpm. (8M)

3. a) Derive the emf equation of a 1-Phase Transformer (8M)

b) A single phase, 50 Hz core type transformer has core of cross section area 400sq.cms.The

permissible maximum flux density is 1 wb/m2. Calculate the number of turns on the high

and low voltage sides for a 3000/220V ratio. (Neglect series voltage drop) (8M)

4. a) What is an ideal transformer? Draw its no-load phasor diagram (8M)

b) The primary winding of a 50 Hz single phase transformer has 480 turns and is fed from

5400 V supply. The secondary winding has 20 turns. Find the peak value of flux in the core

and the secondary voltage. (8M)

5. a) Explain why the rotor of an induction motor rotates in the same direction as the stator

magnetic field. (6M)

b) A slip ring induction motor runs at 290rpm on full load when connected to a 50Hz supply

Calculate

i) The number of poles

ii) The slip

iii) The slip for full load torque if the total resistance of the rotor circuit is doubled. (10M)

6. a) Derive the emf equation of an Alternator. (8M)

b) A 3-phase, 16 pole alternator has a star connected winding with 144 slots and 10

conductors per slot. The flux per pole is 30 mWb. The speed is 375 rpm. Find frequency,

phase and line emf. (8M)

7. Explain different types of Stepper motors with neat diagram (16M)

8. a)Derive the expression for deflecting torque produced in a M.I attraction instrument (8M)

b) Compare PMMC instruments with M.I Instruments (8M)

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Code No: X0424/R07







1. a) Classify the dc machine based on excitation systems (8M)

b) Derive emf equation for a dc machine (8M)

2. a) Explain with neat diagram how you conduct Swinburne’s test on a dc machine. What

information you gather from this test (8M)

b) A shunt machine connected to 250 V mains has an armature resistance (including

brushes) of 0.12� and the resistance of the field circuit is 100�. Find the ratio of the speed

as a generator to the speed as a motor, the line current in each case being 80 A.

(8M)

3. Draw and explain the phasor diagram of a transformer under No-Load and load conditions

(16M)

4. a) Define voltage regulation of a transformer and develop an expression for calculating the

regulation (8M)

b) The primary and secondary winding resistances of a 40 kVA, 6600/250V single –phase

transformer are 10� and 0.02� respectively. The equivalent leakage reactance as referred to

the primary winding is 35 �. Find the full load regulation at 0.8 power factor leading

(8M)

5. a) Distinguish between Squirrel cage Induction motor and Slip ring induction motor

(5M)

b) A 3-phase induction motor with 6 poles runs at 980 rpm when connected to a 440V, 50Hz

supply. Calculate

i) The percentage slip

ii) Frequency of the rotor currents (6M)

c) Explain the torque –Slip characteristics with a neat diagram (5M)

6. Explain the O.C and S.C characteristics of a Synchronous Machine with a neat sketch. How

voltage regulation can be calculated by the use of their results? (16M)

7. a) Explain the construction and working of an a.c Servo motor? Draw the characteristics of

a.c servomotor (8M)

b) What do you mean by synchros and give some applications of synchros (8M)

8. Write short notes on the following

i) Indicating Instruments

ii) Integrating Instruments

iii) Recording Instruments

iv) Absolute instruments (16M)

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Code No: X0424/R07







1. a) Discuss various losses in a dc machine. (8M)

b) Explain briefly the purpose of the following

i) Armature winding ii) Armature core iii) Field winding

iv) Pole shoes v) pole core vi) Commutator (8M)

2. a) Derive an expression for the Torque developed by a dc motor. (8M)

b) A shunt generator has an induced voltage on open circuit of 127V. When the machine is

on-load the terminal voltage is 120 V. Find the load current if the field circuit resistance be

15� and the armature resistance 0.02�. Ignore armature reaction (8M)

3. a) Starting from first principle draw the approximate equivalent circuit of a transformer

(8M)

b) A single phase transformer has 180 and 90 turns respectively in its secondary and primary

windings. The respective resistances are 0.233� and 0.067�. Calculate the equivalent

resistance of

i) The primary in terms of the secondary winding

ii) The secondary in terms of the primary winding and

iii) The total resistance of the transformer in terms of the primary (8M)

4. Explain with neat diagram O.C and S.C tests conducted on a single phase transformer for

pre-determining the efficiency (16M)

5. a) Obtain the relation between rotor input, rotor output and rotor copper losses with respect

to a 3-phase Induction motor (8M)

b) A 6-pole , 50 Hz ,3-phase induction motor running full load develops a useful torque of

150 N-m at a rotor frequency of 1.5 Hz. Calculate the shaft power output. If the mechanical

torque loss in friction be 10 N-m, calculate

i) Rotor copper loss, ii) The input to the motor and iii) The Efficiency (8M)

6. a) What do you mean by synchronous reactance and Asynchronous impedance of an

alternator (8M)

b) A 4-pole, 3-phase, 50 Hz star connected alternator has 60 slots, with 2 conductors per slot

and having armature winding of the two-layer type. Coils are short pitched in such a way

that if one coil side lies in slot number 1, the other lies in slot number 13.Determine the

useful flux per pole required to generate a line voltage of 6000V. (8M)

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Code No: X0424/R07

7. a) Explain the construction and working principle of shaded pole motor. Also draw its

characteristics (10M)

b) List some of the applications where stepper motor is used (6M)

8. a) Derive the expression for deflecting torque produced in a PMMC Instrument with a neat

diagram (8M)

b) Explain the importance of Damping Systems in an indicating instrument and further

classify the Damping systems. (8M)

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Code No: X0521/R07


PROBABILITY AND STATISTICS

(Com. to CSE, IT, CSS)




1. a) For the given three events A, B and C, verify that

P(AUB/C) = P(A/C) + P(B/C) – )/( CBAP ∩ ?

b) Box 1 contains 1 white and 999 red balls. Box 2 contains 1 red and 999 white balls. A

ball is picked from a randomly selected box. If the ball is red, what is the probability that it

came from box 1?

2. a) From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random.

Let the random variable X denote the number of defective items in the sample. Find the

probability distribution of X when the sample is drawn without replacement?

b) Probability density function of a random variable X is

��

��

≤≤=

elsewhere

xforxSinxf

,0

0,2

1

)(π

Find the mean, mode and median of the distribution and also find the probability between

20 πand ?

3. a) In a binomial distribution consisting of 5 independent trails, probabilities of 1 and 2

success are 0.4096 and 0.2048 respectively. Find the parameter p of the distribution?

b) Find the probability that by guess-work a student can correctly answer 25 to 30 questions

in a multiple-choice quiz of 80 questions. Assume that in each question with four choices,

only one choice is correct and student has no knowledge of the subject?

4. a) Determine the expected number of random samples having their means

i) Between 22.39 and 22.41

ii) greater than 22.42

iii) less than 22.37

iv) less than 22.38 or more than 22.41 for the following data N= 1500; n=36, Ns =300, σ

= 0.48 and µ = 22.4 ?

b) The mean life time of light bulbs produced by company is 1500 hours and SD of 150

hours. Find the probability that lighting will take place for

i) at least 5000 hours

ii) at most 4200 hours

if three bulbs are connected such that when one bulb burns out, another bulb will go on.

Assume that life times are normally distributed?

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Code No: X0521/R07

5. a) A research worker wants to determine the average time it takes a mechanic to rotate the

types of a car and he wants to be able to assert with 95%. Confidence that the mean of his

sample is off by at most 0.5 minutes. If he can presume from past experience that σ =1.6

minutes how large a sample will have to take?

b) In a study of an automobile insurance a random sample of 80 body repair costs had a

mean of Rs. 472.36 and the S.D. of Rs. 62.35. If x is used as a point estimate to the true

average repair costs, with what confidence we can assert that the maximum error doesn’t

exceed Rs.10?

6. a) If 80 patients are treated with an antibiotic 59 got cured. Find a 99%. Confidence limits

to the true population of cure?

b) Write about null hypothesis and testing of null hypothesis?

7. a) A random sample of size 16 values from a normal population showed a mean of 53 and a

sum of squares of deviations from the mean equals to 150. Can this sample be regarded as

taken from the population having 56 as men? Obtain 95% confidence limits of the mean of

the population?

b) A pair of dice are thrown 360 times and the frequency of each sum is indicated below

Sum: 2 3 4 5 6 7 8 9 10 11 12

Frequency: 8 24 35 37 44 65 51 42 26 14 14

would you say that the dice are fair on the basis of the chi-square test at 0.05 level of

significance?

8. In a maintenance shop, the inter –arrival times at tool crib are exponential with an average

time of 10minutes. The length of the service time is assumed to be exponentially distributed

with mean 6 minutes. Find

i) Estimate the fraction of the day that tool crib operator will be idle?

ii) The probability that were will be six or more operator waiting for the service?

iii) The manager of the shop will install a second booth when an arrival would expect to

have to wait 10 minutes or more for the services. By how much must the rate of arrival be

increased in order justify a second booth?

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Code No: X0521/R07







1. a) Show that if AB=φ , then )()( BPAP ≤ ?

b) Five persons in a group 20 are Engineers. If three persons are selected at random,

determine

i) The probability that all are engineers and

ii) The probability that at least one being an engineer?

2. a) A player tosses 3 fair coins. He wins Rs.500 if 3 heads appear, Rs. 300 if 2 heads appear,

Rs. 100 if 1 head occurs. On the other hand, he loses Rs. 1500 if 3 tails occur. Find the

expected gain of the player?

b) For the continuous probability function xeKxxf

−= 2)( when ,0≥x find

i) K

ii) mean

iii) variance

3. a) The mean of binomial distribution is 3 and the variance is .4

9 Find

i) The value of n

ii) )7( ≥xp

iii) ?)61(( <≤ xP

b) A sales tax officer has reported that the average sales of the 500 business that he has to

deal with during a year is Rs. 36,000 with a standard deviation of 10,000. Assuming that the

sales in these business are normally distributed, find

i) The number of business as the sales of which are Rs. 40,000.

ii) The percentage of business the sales of which are likely to range between Rs. 30,000 and

Rs. 40,000.

4. a) If the population is 3, 6, 9, 15, 27

i) List all possible samples of size 3 that can be taken without replacement from the finite

population?

ii) Calculate the mean of each of the sampling distribution of means?

iii) Find the standard deviation of sampling distribution of mean?

b) A manufacture claims that any of his list of items cannot have variance more than 1 cm2.

A sample of 25 items has a variance of 1.2 cm2. Test whether the claim of the manufacturer

is correct?

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Code No: X0521/R07

5. a) Ten bearings made by a certain process have a mean diameter of 0.5060 cm with a

standard deviation of 0.0040 cm. Assuming that the data may be taken as a random sample

from a normal distribution, construct a 95% confidence interval for the average diameter of

the bearings?

b) Write short notes on Bayesian Estimation?

6. a) Random samples of 400 men and 600 women were asked whether they would like to have

a flyover near their residence. 200 men and 325 women were in favour of the proposal.

Test the hypothesis that proportions of men and women in favour of the proposal are same,

at 5% level?

b) Write short notes on type I and type II error?

7. a) A machine is designed to produce insulating washers for electrical devices of average

thickness of 0.025 Cm. A random of sample of 10 washers was found to have a thickness of

0.024 cm with a SD of 0.002 cm. Test the significance of the deviation. Value of t for 9

degrees of freedom at 5% level is 2.262?

b) From the following data, find whether there is any significant liking in the habit of taking

soft drinks among the categories of employees?

Soft drinks Clerks Teachers Officers

Pepsi

Thumsup

Fanta

10

15

50

25

30

60

65

65

30

8. a) Discuss Queuing Theory. Explain its applications?

b) General structure of a Queuing system?

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1. a) In a certain group of computer personnel, 65% have insufficient knowledge of hard ware,

45% have inadequate idea of software and 70% are in either one or both of the two

categories. What is the percentage of people who know software among those who have a

sufficient knowledge of hard ware?

b) State and prove Baye’s theorem?

2. a) A sample of 4 items is selected at random from a box containing 12 items of which 5 are

detective. Find the expected number E of defective items?

b) If the probability density function of a random variable x is given by

��

��

�

≤

>−=

0,0

0,2

2)(

xfor

xforx

exKxf

Determine

i) K ii) The distribution function for X?

3. a) 20% of items produced from a factory are defective find the probability that in a sample

of 5 chosen at random

i) none is defective

ii) one is defective

iii) ?)41( << xP

b) If X is a normal variate, find the area A

i) to the left of Z = -1.78

ii) to the right of Z = -1.45

iii) Corresponding to 53.18.0 ≤≤− Z

iv) to the left of Z= -2.52 and to the right of Z= 1.83 ?

4. A random sample of size 64 is taken from a normal population with m= 51.4 and s =68.

What is the probability that the mean of the sample will

i) exceed 52.9

ii) fall between 50.5 and 52.3

iii) be less than 50.6?

b) A random sample of size 25 from a normal population has the mean 5.47=X and the

standard deviation S = 8.4. Does this information tend to support or refute the claim that the

mean of the population is 5.42=µ ?

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5. a) A random sample of size 100 is taken from a population with 1.5=σ . Given that the

sample mean is 6.21=X . Construct a 95% confidence interval for the population mean µ ?

b) If we can assert with 95% that the maximum error is 0.05 and P=0.2, find the sample

size?

6. a) 20 people were attacked by a disease and only 18 survived will you reject the hypothesis

that the survival rate if attacked by this disease is 85% in favour of the hypothesis that is

more at 5% level?

b) Explain the procedure generally followed in testing of hypothesis?

7. a) Find the maximum difference that we can expect with probability 0.95 between the means

of samples of sizes 10 and 12 from a normal population if their standard deviations are

found to be 2 and 3 respectively?

b) A firm manufacturing rivets wants to limit variations in their length as much as possible.

The lengths (in C ms) of 10 rivets manufactured by a new process is

2.15 1.99 2.05 2.12 2.17

2.01 1.98 2.03 2.25 1.93

Examine whether the new process can be considered superior to the old if the old population

has standard deviation 0.145 Cm?

8. a) Explain briefly the main characteristics of queuing system?

b) Explain Traffic intercity?

c) Explain (M/M/1) : )/ FCFSα Queuing model?

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Code No: X0521/R07







1. a) A bag contains 6 white and 4 red pens and a second bag contains 4 white and 8 red pens.

One of the bags is chosen at random and 2 pens are drawn. Find the probability that one is

white and the other is red?

b) If A and B are two events and the probability P(B) ≠ 1 prove that

[ ][ ])(1

)()()/( 1

BP

BAPAPBAP

−

∩−= ?

2. a) A continuous random variable X has probability density function 10;3)( 2 ≤≤= xxxf ,

find a and b such that

i) { } { }aXPaXP >=≤ and

ii) { } 05.0=> bXP ?

b) Find the mean and variance of the density function

30,9

2)( ≤≤= x

xxf ?

3. a) The probability that the life of a bulb is 100 days is 0.05. find the probability that out of 6

bulbs

i) at least one

ii) greater than four

iii) none will be having a life of 100 days?

b) Find the mean and standard deviation of a normal distribution in which 7% items are

under 35 and 89% are under 63?

4. a) The mean of certain normal population is equal to the standard error of the mean of the

samples of 64 from that distribution. Find the probability that the mean of the sample size

36 will be negative?

b) Find

i) 7),365.2( =< νwhentP

ii) 24,)318.1( => νwhentP

iii) 12,)179.2356.1( =<<− νwhentP

iv) 17),567.2( =−> νwhentP ?

5. a) Find 95% confidence limits for the mean of a normality distributed population from

which the following sample was taken 15,17,10,18,16,9,7,11,13,14?

b) Write short notes on Bayesian Estimation?

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6. a) In a random sample of 400 industrial accidents it was found that 231 were due at least

partially to unsafe working conditions. Construct a 99% confidence interval for the

corresponding true proportion?

b) Write about

i) Critical region

ii) left tailed test

iii) right tailed test?

7. a) The means of two random samples of sizes 9 and 7 are 196.42 and 198.82 respectively.

The sum of the squares of the deviation from the mean are 26.94 and 18.73 respectively.

Can the sample be considered to have been drawn from the same normal population?

b) The following are the samples of skills. Test the significant difference between the

means at 0.05 level

SAMPLE-I 74.1 77.7 74.4 74 73.8 -

SAMPLE-II 70.8 74.9 74.2 70.4 69.2 72.2

8. a) Explain about queuing theory characteristics?

b) Define preemptive discipline and non preemptive priority?

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