II B.Tech I Semester (R07) Regular Examinations, Nov- 2009 MATHEMATICS-II

Code No: X0121
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
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) Reduce the matrix A=
1 0 2 8
2 4 3 0
1 2 1 0
to normal form and hence find its rank.
b) Solve the system of equations by matrix method.
1 2 3
1 2 3
1 2 3
2
4 2 6
3 18
x x x x
x x x
x x
2. a) Prove that the two Eigen vectors corresponding to the two different Eigen values are
linearly independent.
b) Determine the Eigen values of A-1 , where
1 0 1
A
1 2 1
2 2 3
3. (a) Find the Eigen values of the matrix
i i
i i
2
3 2
.
(b) Reduce the quadratic form to the canonical form by an orthogonal reduction
3x 2y 3z 2xy 2yz 2 2 2 2 3 2 2 .
4. a) Define a Fourier series and write the Dirichlet conditions for the expansion of f(x) as
a Fourier series.
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Code No: X0121
b) Find the Fourier series expansion of the function f(x) = x in
,
.
Deduce that
1 1 1 1 1
1 3 5 7 9 4
LL
.
5. a)Form the partial differential equation by eliminating the arbitrary function from
z = f y + x + y .
b) Solve the partial differential equation
2 2 p x + q y = z.
6. Solve by the method of separation of variables x 3
y
x y
z z
3y
=0
7. a) Express the function f(x)=
0 1
1 1
when x
when x
as a Fourier integral.
Hence evaluate
d
x
0
sin cos
b) Find the Fourier sine integral for f(x) =
x
e , (>0)
hence show that 2
x
e =
d
x
0
2 2
sin
8. a) If Z(n2) =
3
2
z 1
z z
,find ( ) 3 z n and ( ) 4 z n
b) Solve the differential equation , using z-transforms 3 2 0 2 1 n n n u u u given that
0, 1. 0 1 u 0 u 1
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SET - 1
Code No: X0121
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
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) Solve the equations 2x y z 10, 3x + 2y + 3z = 18 and x + 4y + 9z=16.
b) Find P and Q such that PAQ is in normal form
1 1 1
1 1 1
3 1 1
A
.
2. a) Verify Cayley-Hamilton theorem for A =
0 1 2
1 2 3
1 2 3
and find 1 A
b) If
2 3 1 0
A I
and
3 10 0 1
. Find the eigen values of 2I A 10I A .
3. (a) Prove that the Eigen values of a real symmetric matrix are all real.
(b) Find the Eigen values and Eigen vectors of the Hermitian matrix of the matrix
3 4 2
2 3 4
i
i
4. a) Find the Half – range cosine series expansion of ( ) sin( )
l
x
f x s in the range 0 x l
b) Find the Fourier series expansion of the function f(x) = x2 in
,
.
Deduce that
2
2 2 2
2
1 1 1 1
1 2 3 4 6
LL
.
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SET - 2
Code No: X0121
5(a) Form the partial differential equation by eliminating the orbitrary function f from
( )
x y
z
xy yz zx f
y z b) Solve the partial differential equation 2 2 2 2 x p + y q = 1
6. Solve by the method of separation of variables uxt =
e t
cosx with u(x,0)=0 and
u(0,t)=0
7. a) Using Fourier cosine integral representation of an appropriate function, shows that
k
dw
wx kx
2
cos
0
2 2
k w
e
, x>0, k>0.
b) Find the Fourier transform of f(x) =
for x a
for x a
0
1
8. a)If f(z)=
4
2
( 1)
5 3 12
1
1
z
z z
, find the values of f(2) and f(3).
b) Find
( 2)( 1)
3
2
2
1
z z
z
z
2 of 2
SET - 2
Code No: X0121
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
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) Reduce the matrix
1 2 3
7 10 12
A
3 4 4
.into normal form and find its rank.
b) Solve the system of equations x + y + w = 0, y + z = 0, x + y + z + w = 0 and
x + y + 2 z = 0.
2. a) Find the eigen values and eigen vectors of the matrix A =
1 0 5
0 2 0
5 0 1
.
b) Verify Cayley-Hamilton theorem for A =
3 5 6
2 4 5
1 2 3
. Hence find A-1 .
3. (a) The eigen values of a Skew-Hermitian matrix are either purely imaginary or zero.
(b) Prove that
i
i
3
3
2
1
is a unitary matrix. Find its eigen values.
4. a) Define Even and odd functions and write the Dirichlet conditions for the expansion
of f(x) as a Fourier series.
b) Express f(x) =
x
in
,
as Fourier series.
Deduce that
2
1 1 1 1
1 3 5 7 8
2 2 2
2
LL
.
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Code No: X0121
5. a)Form the partial differential equation by eliminating the arbitrary constants
log az – 1 = x + ay + b
b) Solve
2 2 2 x (z - y) p + y (x - z) q = z y – x .
6. solve the wave equation
7. a) Find the Fourier transform of f(x) =
0 1
1 2
1
if x
x if x
b) Find the Fourier sine and cosine transforms of f(x) = e
ax
.
8. a. Find the Z- transform of exp(-a n), a>0
b. Find the Z- transform of the sequence defined by un = 2n n 0
= 0 n >0
c. Find the Z-transform of unit impulse
0 0
1 0
( )
n
n
n
2 of 2
SET - 3
Code No: X0121
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
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) Solve the system of equations using matrices
x y 2z 2, 2x 4y 6z 5, 2x 6z 9.
b)Find the rank of
1 2 3 2
2 5 1 2
3 8 5 2
5 12 1 6
A
.
2. Diagonalize the matrix
7 2 1
2 10 2
1 2 7
A
3. (a)Prove that the eigen values of a Skew-Hermitian matrix are purely imaginary or zero.
(b) Show that A =
0 0
0 0
0 0
i
i
i
is a Skew-Hermitian matrix and also Unitary. Find eigen
values and the Corresponding eigen vectors of A.
4. a) Find the half range sine series for f(x)=x( x ), in 0<x< . Deduce that
7 32
1
5
1
3
1
1
1 3
3 3 3 3
3
b) Find the Fourier series expansion of the function f(x) = x3 in
,
.
5. a)Form the partial differential equation by eliminating the arbitrary constants a, b from
2z x a y-a b.
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Code No: X0121
b) Solve the partial differential equation
2 2
p q
+ = z.
x y
6. Solve the boundary value problem
2
2
u
t
2u
t2 =
c2
2
2
u
x
2u
x2 ; 0<x<l; t>0
With u(0,t)=0; u(l,t)=0 and
u(x,0)=0, ut (x,0)=
sin3 (
x
l
)
7. a) Find the Fourier sine transform of x
1
.
b) Find the Fourier cosine transform of f(x) = e
2x
+ 4 e
3x
8.. a) Find z(ncosn ) if
2 ( 1)
( )
z 1
z
z n .
b) Solve the differential equation ,using z-transform n
k k k y 5y 6y 5 2 1 5 6 , given
y(0)=0,y(1)=0.
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SET - 4
Code No: X0222
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
FLUID MECHANICS AND HYDRAULIC MACHINERY
(Electrical and Electronics Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a)State Newton’s law of viscosity. What is the effect of temperature on viscosity of
various fluids?
b)A cylinder of 0.30m diameter rotates concentrically inside a fixed cylinder of 0.31m
diameter. Both the cylinders are 0.3m long. Determine the viscosity of the liquid which
fills the space between the cylinders if a torque of 0.98N-m is required to maintain an
angular velocity of 2 rad/s. [8+8]
2. a)Define streamline, streak line and a path line
b) The stream function for a particular flow is = x3 –y3. Show that the flow cannot be a
potential flow. [8+8]
3. a) List out the minor losses in closed conduit flow and discuss their significance
[6]
b) A 6 cm diameter pipe has a discharge of 450 lit/min. At a section the pipe has a sudden
expansion to a sixe 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
[10]
4. a)A jet of water 75mm in diameter issues with a velocity of 30m/sec and impinges on a
stationary flat plate normally. Find the force exerted by the jet on the plate.
[8]
b) Find the impact of jet striking a normal flat plate when the plate is stationary [8]
5. a) Give different classification of hydro electric power plants and explain at least two
power plants with neat sketches. [8]
b)Explain in detail mini and micro hydropower plants. [8]
6. a) Differentiate between inward and outward flow reaction turbines [8]
b) Design a Francis turbine having radial blades with width to diameter ratio at inlet and
outlet as 0.5 and 0.7 respectively. Head of 70m, speed 500rpm, brake power 300kW,
flow ratio 0.2, speed ratio 0.7, hydraulic efficiency 95% and overall efficiency 85%.
[8]
7. a) Explain unit speed, unit power and unit discharge. (6)
(b) Tests were conducted on a Francis turbine of 0.8 m diameter under a head of 9 m. The
turbine running at 240 r.p.m. developed 84.5 kW and the water consumption was 1.2
m3/s. If the same turbine is operated under a head of 16 m, predict its new speed,
discharge and power developed. (10)
8. Explain with neat sketches the working of a single- stage centrifugal pump. (16)
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SET - 1
Code No: X0222
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
FLUID MECHANICS AND HYDRAULIC MACHINERY
(Electrical and Electronics Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a)Classify fluids. What are the various properties of fluids? [6+10]
b)A cylinder of diameter 0.1m rotates in an annular sleeve of internal diameter 0.102m at
100rpm. The cylinder is 0.25m long. If the dynamic viscosity of the lubricant between the two
cylinders is 0.9 paise, find the torque needed to drive the cylinder against viscous resistance.
2. a)Define path line, streak line and the streamline. For what type of flow these lines are
identical? [8+8]
b)A two-dimensional flow field is given by = 3xy. Determine the stream function. Determine
the velocities at A(1,2) and B(2,2). What is the discharge between the streamlines passing
through these points?
3. a) Describe the Reynold’s experiment with the help of a neat sketch. [6]
b) Two reservoirs with a difference in water surface elevations of 10m 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. [10]
4. a)A jet of liquid with specific gravity of 0.85 strikes a fixed flat plate. The diameter of the jet is
100 mm and its velocity is 45 cm/sec. Find the force exerted by the jet on the plate [8]
b) Find the impact of jet striking an inclined flat plate when the plate is stationary [8]
5. a)What is the function of draft tube? List various types of draft tubes and explain them with
neat sketches [8+8]
b) How a storage tank helps in reducing in water hammer effect? Describe the various types of
surge tanks with necessary sketches.
6. a)A pipeline 1200m long supplies water to 3 single jet Pelton wheels. The head above the nozzle
is 360m. The velocity coefficient for the nozzle is 0.98 and the coefficient of friction for the
pipeline is 0.02. The turbine efficiency based on the head at the nozzle is 0.85. The specific
speed of each turbine is 15.3 (in m, kW, r.p.m., units) and the head lost due to friction in the
pipeline is 12m of water. If the operating speed of each turbine is 560 r.p.m., determine the
total power, the diameter of each nozzle, the diameter of the pipeline, Volume of water used
per second. (8)
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Code No: X0222
b) A Kaplan turbine produces 60,000 kW under a net head of 25m with an overall efficiency of
90% Taking the value of speed ratio Ku as 1.6, flow ratio ! as 0.5 and the hub diameter as 0.35
times the outer diameter, find the diameter and speed of the turbine.
(8)
7. What are the characteristic curves of a hydraulic turbine? How are they useful to practical
engineer? (16)
8. The outer diameter of an impeller of centrifugal pump is 400 mm and outlet width
50 mm. The pump is running at 800 r.p.m and is working against a total head of
15 m. The vanes angle at outlet is 400 and manometric efficiency is 75%. Determine
(i) velocity of flow at outlet, (ii) velocity of water leaving the vane, and (iii) angle
made by the absolute velocity at outlet with the direction of motion at outlet, and
(iv) discharge. (16)
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SET - 2
Code No: X0222
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
FLUID MECHANICS AND HYDRAULIC MACHINERY
(Electrical and Electronics Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) Define kinematic and dynamic viscosity. What is the effect of temperature on
viscosity? Explain.
b)The space between two parallel plates 5mm apart is filled with an oil of relative density
0.9. A force of 2N is required to drag the upper plate of area 900 cm2 at a constant
velocity of 0.8m/s. Assume straight line velocity distribution and calculate the dynamic
viscosity and kinematic viscosity. [8+8]
2. a) Define stream function. What are the conditions for flow to be irrotational?
b)A stream function =2xy. Show that the function satisfies the continuity equation and
that the flow is irrotational. Workout the corresponding velocity potential function[6+10]
3. a)Derive the Darcy Weisbach equation. [6]
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. [10]
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 plate is 100 cm2. Find the
force exerted by the jet on the plate and the ratio in which the jet gets divided after
striking. [8]
b) Derive the equation for the impact of jet striking a curved plate at the centre when the
plate is stationary. [8]
5. a) Classify the water turbines based on action of water on moving blades and explain
them.
b)What are the types of water turbines used in high head hydro electric power plant and
why? Describe the various factors to be considered while selecting a water turbine [6+10]
6. a)The velocity of whirl at inlet to the runner of an inward flow reaction turbine is (3.15
H )m/s and the velocity of flow at inlet is (1.05 H )m/s. The velocity of whirl at exit
is (0.22 H )m/s in the same direction as at inlet and the velocity of flow at exit is (0.83
H )m/s, where H is the head in meters. The inner diameter of the runner is 0.6 times the
outer diameter. Assuming hydraulic efficiency of 80%, compute the angles of the runner
vanes at inlet and exit. [8]
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SET - 3
Code No: X0222
b)A reaction turbine works at 450 r.p.m under a head of 120m. Its diameter at inlet is
1.2m and the flow area is 0.4 m2. The angles made by the absolute and relative velocities
at inlet are 20o and 60o respectively with the tangential velocity. Determine the volume
flow rate, the power developed and the hydraulic efficiency. Assume whirl at outlet to be
zero. [8]
7. (a) What is specific speed? State its significance in the study of hydraulic machines. [8]
(b) A turbine develops 8000 kW when running at 100 r.p.m. The head on the turbine is 30
m. If the head is reduced to 18 m, determine the speed and power developed by the
turbine. [8]
8. Explain the working principles of reciprocating pump with sketches. [16]
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SET - 3
Code No: X0222
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
FLUID MECHANICS AND HYDRAULIC MACHINERY
(Electrical and Electronics Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a)Distinguish between:
i)Compressibility and vapour pressure
ii)Surface tension and capillarity
b)Derive an expression for the capillary rise of a fluid having surface tension " and
contact angle # between two vertical parallel plates placed a distance t apart. If the plates
are of glass, what will be the capillary rise of water having " =0.073N/m, #=00 and t=
1mm. [8+8]
2. a) Define steady, unsteady, uniform and non-uniform flow. What is vortex flow?
b) Calculate the unknown velocity components so that they satisfy continuity equation:
u=2x2; v = xyz; w=?
u=(2x2 + 2xy); w = (z3-4xz-2yz); v=? [8+8]
3. a) Differentiate between major loss and minor losses. List and discuss the minor losses
[8]
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. [8]
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.[8]
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 [8]
5. Draw the neat layout of hydro electric power plant and explain briefly at least eight
components of it
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SET - 4
Code No: X0222
6. a) Prove that the maximum efficiency of Pelton wheel occurs when the ratio of bucket
velocity u to the jet velocity V is expressed as  = ]
2(1 cos )
1 cos
[
u
1 2
1
K K
V c c K
s s
Where
the loss due to bucket friction and shock is expressed as
g
K V u
2
( )2
1 and that due to
bearing friction and windage loss as (K2
g
u
2
2
); 1 K and K2 are constants and being the
bucket angle at outlet.(Neglect volumetric losses) [8]
b)A Pelton wheel has to be designed for the following data: Power to be developed=
6000kW. Net head available = 300 r.p.m.; Ratio of jet diameter to wheel diameter = 1/10;
and overall efficiency = 85%. Find the number of jets; diameter of the jet; diameter of
the wheel; and the quantity of water required. [8]
7. Define unit speed, unit discharge and unit power of a hydraulic turbine. Explain how a
plot of unit power and efficiency against unit speed at different gate openings can be used
to predict the performance of a turbine under any working condition. [16]
8. A single acting reciprocating pump has a 15 cm piston with a crank of radius 15 cm.
The delivery pipe is 10 cm diameter. At a speed of 60 r.p.m., 310 litres/s of water is
lifted to a total height of 15 m. Find the slip, coefficient of discharge and theoretical
power in kW required to drive the pump. [16]
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SET - 4
Code No: X0321
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PRODUCTION TECHNOLOGY
(Mechanical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Explain using simple sketches the following pattern types :
i. Skeleton pattern. ii. Cope and drag pattern.
(b) How does the grain size distribution of the molding sand affect it’s strength ?
2. (a) Give the classification of centrifugal casting. Discuss the applications of each class.
(b) Discuss the various types of gates that are normally used.
3. ( a)Draw neat sketch of submerged arc welding and explain the various equipment used
in it.
(b)What are the basic types of oxyacetylene flames used in oxyfuel gas welding and
cutting operations? Explain briefly.
4. a)What are the various steps involved in friction welding process? Explain them with
simple sketches.
b)Explain the various welding discontinuities caused by inadequate or careless
application of established welding technologies.
5. Explain the metal deformation process: Rolling, Forging, extrusion and Drawing and
differentiate them with their function.
6. Describe the methodology involved in manufacturing of Pipe and tube
7. (a) Compare and contrast the processes of direct extrusion and indirect extrusion.
(b) What is cold impact extrusion? Explain how it is done.
8. (a) Write the properties and applications of the following thermoplastic materials:
Polyethylene; Polystyrene; Teflon; Nylon
(b) Explain the following:
Fillers; Stabilizers; Plasticizers
1 of 1
SET - 1
Code No: X0321
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PRODUCTION TECHNOLOGY
(Mechanical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) What are composite moulds? Why are they used? Where are they used?
(b) What are different types of gates used in sand moulding process?
2. Suggest suitable modifications to an existing cupola to obtain (i) Fuel economy
(ii) Higher tapping temperature (iii) Improved quality of liquid metal
3. a)Explain the plasma arc welding process with the help of neat sketches.
b)Explain the general guidelines to be considered while designing welded joints.
4. a)What are the various destructive testing techniques to test the welded joints quality?
Explain briefly any two types.
b)Draw and explain the shape of fusion zone in friction stir welding process as a function
of force and speed
5. What are the effects on recrystallisation of temperature, time, and reduction in
thickness in cold working process?
6. Write about Hot spinning process with neat sketch
7. (a) What is Sleeve method of direct extrusion? Explain. With a neat sketch, show how it
is done.
(b) Write brief notes on the following types of extrusion:
Tube extrusion; Stepped extrusion
8. (a) Define and explain what is a polymer, and classify them.
(b) What are Plasticizers and fillers? Explain them briefly.
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SET - 2
Code No: X0321
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PRODUCTION TECHNOLOGY
(Mechanical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. (a) Why is match plate pattern is much easier to use than a standard pattern? Explain.
(b) What are the undesirable effects that could result from turbulence of the metal
in the gating system and mould cavity? Explain.
2. (a) State the differences between true-centrifugal casting, semi-centrifugal casting,
centrifuging. Which method is used for cast iron pipe production.
(b) Discuss the various elements that comprise the gating system.
3. a)Draw the simple sketch of metal arc welding process and explain the equipment used in
the process.
b)Draw the simple sketches of the following weld joints:
i) Butt joint ii) Corner joint iii) T joint iv) Lap joint
4. a)What are the various nondestructive testing techniques? Explain any one method
briefly
b)List the various brazing methods used in the industries. Explain any two methods
briefly.
5. Describe the advantages and limitations of hot working with reference to micro and
mechanical structure
6. Discuss about the advantages and limitations of Hot spinning process
7. (a) Write brief notes on the following types of extrusion:
Impact extrusion; Hydrostatic extrusion
(b) With a neat sketch, describe the process of indirect extrusion.
8. (a) Write short notes on the following used in plastics:
Plasticizers; Catalysts; Solvents
(b) Distinguish between addition polymerization and condensation polymerization.
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SET - 3
Code No: X0321
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PRODUCTION TECHNOLOGY
(Mechanical Engineering)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) Explain different pattern materials used with their merits and demerits.
b) Explain the function of sprue well in gating system with neat sketch
2. (a) Discuss the shell molding process with the help of neat sketch.
(b) Give the relevance of the following with reference to a casting
i. Sprue
ii. Runner
iii. Ingate
3. a)What is the main application of spot welding process? Discuss the sequence of
operations in resistance spot welding process with the help of simple sketches.
b)What are the functions of electrode coatings?
4. a)What is TIG welding process? With the help of neat sketch, explain the process of TIG
welding.
b)What are the different types of solders used in soldering technique? Discuss their
applications.
5. Describe “Theory of rolling” and mechanics of rolling
6. Explain the principle of operation of Press used for sheet metal working for cutting
operation
7. (a) Define extrusion, and describe its characteristics.
(b) Distinguish between hot extrusion and cold extrusion wrt their advantages and
limitations.
8. (a) Write short notes on the following used in plastics:
Flame Retardants; Lubricants; Dyes and pigments
(b) Differentiate between natural resins and synthetic resins.
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SET - 4
Code No: X0424
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
ELECTRICAL TECHNOLOGY
(Com.to ECE,EIE,BME,E.CON.E,ECC,ICE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) Explain the construction features of a DC machine with the help of neat
sketches? (10M)
b) State the purpose of magnetic yoke in a DC machine? (6M)
2. a) Explain the principal of operation of DC motor with neat sketches? (8M)
b) Derive an expression for torque developed in the armature of DC motor?
(8M)
3 a) Draw and explain the no load phasor diagram for a single phase transformer?
(8M)
b) A single phase transformer has 1000 turns on the primary and 200 turns on the
secondary. The no load current is 3 Amp at a pf of 0.2 lagging. Calculate the
primary current and power factor when the secondary current drawn is 280
Amp at a p.f. of 0.8 lagging. (8M)
4. a)Discuss how do you perform open circuit test and short circuit tests on a
single phase transformer in the laboratory. How do you find the regulation of the
transformer? (8M)
b)In no load test of single phase transformer, the following test data was obtained:
Primary Voltage: 220V, Secondary Voltage: 110V
Primary current: 0.5 A, Power input: 30W.
Resistance of the primary winding = 0.6 ohm
Find the following:
(i) Turns ratio (ii)magnetizing component (iii) working component (iv)iron loss.
(8M)
5. a)Explain how the rotating magnetic field is developed in a 3- induction Motor?
(10M)
b) A 3- , 6 pole, 50Hz cage motor is running with a slip of 4%.
Find (i) Speed of rotating field relative to stator winding
(ii) Motor speed
(iii)slip speed (6M)
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SET - 1
Code No: X0424
6. A 3-phase, 16-pole alternator has the following data: (16M)
Number of slots=192; Conductors/slot =8(conductors of each phase are
connected in series); coil span=160 electrical degrees; speed of the alternator
=375 r. p. m; flux / pole=55 mWb. Calculate the phase and line voltages.
7. Explain the constructional details of shaded pole 1- induction motor. (16M)
8. (a) Explain how the instruments are classified? (12M)
(b) A moving coil consists of 100 turns wound on a square former (4M)
having a length of 3 cm. The flux density of 0.06 wb/m2. Calculate the deflecting
torque action on the coil when it carries a current of 12mA.
2 of 2
SET - 1
Code No: X0424
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
ELECTRICAL TECHNOLOGY
(Com.to ECE,EIE,BME,E.CON.E,ECC,ICE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a)What is DC generator and explain the basic principle of a DC generator? (8m)
b) Derive the expression for emf generated in a DC machine? (8M)
2. a) Write short notes on
(i) back emf (4M)
(ii) Types of dc motors (4M)
b) Derive an expression for speed equation of a DC motor? (8M)
3. a)What is meant by equivalent reactance of a single phase transformer? How is it
calculated in terms of primary and secondary terms? (8M)
b)A 75 kVA, 11000/440 V, 50 Hz transformer has primary and secondary
resistance of 7.8 and 0.0085 ohms and the primary and secondary reactance’s of
9.4 and 0.0123 ohms respectively.
Calculate
(i) Equivalent impedance referred to primary
(ii) Equivalent impedance referred to secondary
(iii) Total copper loss. (8M)
4. a)Explain the procedure for performing the short circuit test on a
single phase transformer? What is the information obtained from
this test?
(8M)
b)In a 25 kVA, 2000/200V, 50Hz single phase transformer, the
iron and full load copper losses are 350 and 400 W respectively.
Calculate the efficiency at unity power factor on full load and
half load.
(8M)
5. 3- , 6 pole, 50Hz cage motor is running with a slip of 4%. (16M)
Find (a) Speed of rotating field relative to stator winding
(b) Motor speed
(c) slip speed
(d) Frequency of the emf induced in the rotor
(e) Speed of rotation of rotor mmf relative to rotor winding
(f) Speed of rotor of rotor mmf relative to stator winding
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SET - 2
Code No: X0424
6. Derive Average E.M.F per phase and RMS E.M.F per phase of an Alternator.
Also obtain the line voltage of an alternator if it is star connected. (16M)
7. (a) What are Synchros? Explain the constructional features & classification
of Synchros? (12M)
(b) What are the applications of Stepper motors? (4M)
8. What are the requirements of indicating instruments? (16M)
SET - 2
Code No: X0424
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
ELECTRICAL TECHNOLOGY
(Com.to ECE,EIE,BME,E.CON.E,ECC,ICE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) Describe all the types of DC generators in detail. (12M)
b) A 6 pole wave wound DC generator running at a speed of 300 rpm generate an
induced emf 535 V. calculate the flux per pole if it has 650 conductors? (4M)
2. a) Explain the characteristics of
(i) DC shunt motor (ii) DC series motor (iii) DC compound motor (10M)
b) Mention the application of DC motors (6M)
3. a)What is a transformer? Differentiate between step up and step down
transformers. (8M)
b)A transformer with a 10:1 ratio and rated at 50kVA, 3000/300V, 50 Hz is used
to be kept constant at 300V. (8M)
4. a)Derive the condition for maximum efficiency of a single phase transformer
(8M)
b)A4 kVA, 200/400V, 50Hz single phase transformer is supplying full load
current at 0.8 power factor. The following are the test results:
O.C. Test (LV Side) :200V, 0.8A,70W (L.V.Side)
S.C. Test (HV Side): 20V, 10A, 60W (H.V. Side)
Calculate efficiency, secondary voltage and current into primary at the above
load. (8M)
5. The power input to the rotor of a 440V, 50Hz, 3-phase, 6-pole induction motor.
is 50kW.It is observed that the rotor emf makes 120 complete cycles per minute.
Calculate
(i)Slip
(ii) Rotor speed
(iii) Rotor copper losses per phase
(iv)Mechanical power developed
(v)Rotor resistance per phase if the rotor current is 50A (16M)
1 of 2
SET - 3
Code No: X0424
6. A 3-phase, 10 pole alternator has 2 slots per pole per phase on its stator with 10
conductors per slot. The air gap flux is sinusoidally distributed and equals to 0.05
wb. The stator has a coil span of 1500 electrical degrees. If the alternator is
running at 600 r. p. m., calculate the e. m. f generated per phase at no load. (16M)
7. (a) Explain about various types of Capacitor motors? (10M)
(b) Explain the applications of Synchros. (6M)
8. Explain the operation of ammeters and voltmeters in the ac circuits? How
they are classified? (16M)
SET - 3
Code No: X0424
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
ELECTRICAL TECHNOLOGY
(Com.to ECE,EIE,BME,E.CON.E,ETM,ECC,ICE)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1 a) what is a separately and self exited DC generators, Explain them with help of
neat sketches? (8M)
b) A separately exited generator when running at 1200 rpm supplies a current of
200 A at 125 V to a circuit of constant resistances .What will be the current when
speed drops to 1000 rpm if the field current is unaltered? Armature resistance is
0.04 ohms and the total voltage drop at brushes is 2 V. Ignore the change in
armature reaction. (8M)
2. a) What is the necessary of a starter for DC shunt motor? Explain the operation
principle of 3-point starter with neat diagram? (10M)
b) What are the different methods speed control of DC motor give the advantages
and disadvantages in brief. (6M)
3. a)Explain briefly the operation of a transformer and sketch phasor diagram on no
load? (8M)
b) A 250/2500V transformer is fed from a 250V supply. The total winding
resistance and reactance ads referred to low voltage side is 0.1 and 0.5 ohms
respectively. The resistance representing core loss is 400 ohm and magnetizing
reactance is 250 ohm. A load of impedance (600+j 300") is connected across the
secondary terminals.
Calculate (i) input current (ii) secondary terminal voltage and (iii) primary
power factor (8M)
4. a) What are the different losses occurring in a transformer on load? How can these
losses are determined experimentally? (8M)
b)A 200/1000V, 50Hz single phase transformer gave the following test
results:
O.C. Test (LV Side) : 200V,0.7A, 70W
S.C. Test (HV Side): 15V, 10A, 85W
Calculate the parameters of the equivalent circuit referred to the LV Side.(8M)
5. Explain the constructional details of a 3-phase Induction motor. (16M)
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SET - 4
Code No: X0424
6. a) What is the significance of pitch factor and distribution factor? Derive the
expression for above factors. (8M)
b) A 200 kVA, 480 V, 50 Hz ,Y-connected Synchronous Generator with a rated
field current of 5 A was tested, and the following data were obtained: (8M)
Open circuit terminal voltage: 540 V (line-to-line).
Short Circuit current :300A
When a DC voltage of 10 V was applied to two of its terminals, a current of 25A
was measured. Find the Value of Synchronous Reactance.
7. a) What are various types of stepper motors? (10M)
b) What are the salient features of Servomotors? (6M)
8. a) Give the constructional details of attraction-type moving iron instruments.
(8M)
b) Derive the expression for deflecting torque of attraction type MI instruments.
(8M)
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SET - 4
Code No: X0521
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PROBABILITY AND STATISTICS
(Com. To CSE, IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) If A and B are two events such that P(A)= 1/3 , P(B) =3/4 and P(A U B)=11/12
find P(A B) and P(B A).
b )A fair die is tossed twice. Find the probability of getting a 4,5, or 6 on the first toss
and 1,2,3,or 4 on the second toss.
2. a) The density function of a random variable X is f (x) e x , x 0
= 0 , otherwise.
Find E(X), E(
2 X ), Var (X).
b) Let X denotes the minimum of the two numbers that appear when a pair of fair dice
tossed. Determine the (i) Discrete probability distribution (ii) Expectation and (iii)
Variance
3. a) Out of 800 families with 5 children each, how many would you expect to have
(i) 3 boys (ii) at least one boy?
b) If X is a normal variate with mean 30 and standard deviation 5, find the probabilities
that (i) 26< X< 40 and (ii) X>45.
4. a) If the distribution of the weights of all men traveling by air between Hyderabad and
New Delhi has a mean of 163 pounds and a standard deviation of 18 pounds, what is the
probability that the combined gross weight of 36 men traveling on a plane between these
two cities is more than 6,000 pounds?
b) In a city A, 20% of a random sample of 900 school boys has a certain slight physical
defect. In another city B, 18.5% of a random sample of 1600 school boys had the same
defect. Is the difference between the proportions significant at 0.05 level of significance
5. The efficiency expert at a computer company tested 40 engineers to estimate the
average time it takes to assemble a certain computer component, getting a mean of
12.73 minutes and S.D of 2.06 minutes.
i) if X = 12.73 is used as a point estimate of the actual average time required to
perform the task, determine the maximum error with 99% confidence.
ii) Construct 98% confidence interval for the true average time it takes to do the
job.
iii) With what confidence can we assert that the sample mean does not differ from
the true mean by more than 30 seconds.
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Code No: X0521
6. a)A manufacturer claimed that at least 95% of the equipment which he
supplied to a factory conformed to specifications. An examination of
sample of 200 pieces of equipment revealed that 18 were faculty. Test his
claim at 5% level of significance.
b)In a big city 325 men out of 600 men were found to be smokers. Does
this information support the conclusion that the majority of men in this city
are smokers?
7. a) An auditor claims that he takes on an average 10.5 days to file income tax returns (I.T.
returns). Can this claim be accepted if a random sample shows that he look 13, 19, 15, 10,
12, 11, 14, 18 days to file I.T. returns? Use a 0.01 Level of significance.
b)The following random samples are measurements of the heat-producing capacity (in
millions of calories per ton) of specimens of coal from two mines:
Mine 1: 8,260 8,130 8,350 8,070 8,340
Mine 2: 7,950 7,890 7,900 8,140 7,920 7,840
Use the 0.02 level of significance to test whether it is reasonable to assume that the
variances of the two populations sampled are equal.
8. a) a)Explain briefly the main characteristics of Queueing system?
b)Explain Traffic intensity?
c)Explain (M/ M 1): ( / FCFS) Queuing model.
2 of 2
SET - 1
Code No: X0521
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PROBABILITY AND STATISTICS
(Com. To CSE, IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) State the axioms of probability. If A and B are independent events show that
( A
C
, B
C
), ( A, B
C
) and (A
C
,B ) are also independent.
b)Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that
they are both aces if the first card is (i) replaced (ii) not replaced.
2. a) ) Is the function defined as follows a density function f (x) e x , x 0
= 0 , x<0
If so determine the probability that the variate having this density will fall in the
interval (1,2)? Find the cumulative probability function F(2) ?.
b) The probability density function of a variate X is
4 5 6
9k 11k 13k
(i) Find P(X<4) , P ( X 5 ) , P ( 3< X 6)
(ii) What will be the minimum value of k so that P(X 2) > 0.3 ?
3. a) Two dice are thrown 120 times. Find the average number of times in which, the
number on the first die exceeds the number on the second die?
b) Suppose 10 percent of the probability for a normal distribution ( , ) 2 n is below 35
and 5 percent above 90. What are the values of and ?
4. a) If a 1-gallon can of paint covers on an average 513 square feet with a standard
deviation of 31.5 square feet, what is the probability that the mean area covered by a
sample of 40 of these 1-gallon cans will be anywhere from 510 to 520 square feet?
b) In a sample of 500 from a village in Andhra Pradesh, 280 are found to be rice eaters
and the rest wheat eaters. Can we assume that the both articles are equally popular?
1 of 2
X 0 1 2 3
P(X) k 3k 5k 7k
SET - 2
Code No: X0521
5. a) Assuming that = 20.0, how large a random sample be taken to assert with
probability 0.95 that the sample mean will not differ from the true mean by more
than 3.0 points?
b) What is the maximum error one can expect to make with probability 0.90. When
using the mean of a random sample of size n = 64 to estimate the mean of
population with 2 = 2.56.
6. On the basis of their total scores, 200 candidates of a civil service examination are
divided into two groups, the upper 30% and the remaining 70% consider the first
question of the examination. Among the first group, 40 had the correct answer.
Whereas among the second group, 80 had the correct answer on the basis of these
results, can one conclude that the first question is not good at discriminating ability
of the type being examined here?
7. a)Producer of ‘gutkha’, claims that the nicotine content in his ‘gutkha’ on the average is
1.83 mg. Can this claim accepted if a random sample of 8 ‘gutkha’ of this type have the
nicotine contents of 2.0, 1.7, 2.1, 1.9, 2.2, 2.1, 2.0, 1.6 mg? Use a 0.05 level of
significance.
b) In two large populations there are 30% and 25% respectively of fair-haired people. Is
this difference likely to be hidden in samples of 1200 and 900 respectively from the two
populations? Use a 0.05 Level of significance.
8. a) Write a note on Kendal and Lee’s notation for the identification of queues.
b)Assume that both arrival rate and service rate following Poisson distribution.
The arrival rate and service rate are 25 and 35 customers/hour respectively, at a single
window in RTC reservation counter. Find
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SET - 2
Code No: X0521
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PROBABILITY AND STATISTICS
(Com. To CSE, IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) A class has 12 boys and 8 girls. Three students are selected at random one after the
another. Find the probability that (i) first two are boys and third is girl (ii) first and third
are of the same sex and the second is of opposite sex.
b) A business man goes to hotels X,Y,Z 20%,50%,30% of the time respectively. It
is known that 5%, 4%, 3% of the rooms in X,Y,Z hotels have faulty plumbing .
What is the probability that business man’s room having faulty plumbing is assigned to
hotel Z.
2. a)Is the function defined by f(x) = 0, x < 2,
3 2
18
2x
,2 x 4
0 , x> 4
a probability density function ? Find the probability that a variate having f(x) as density function
will fall in the interval 2 x 3 ?
b)A Player tosses two fair coins. He wins Rs.100/- if head appears, Rs.200/- if two heads
appear. On the other hand he loses Rs.500/- if no head appears. Determine the expected
value E of the game and is the game favourable to the player?
3.a) (a) If X has the binomial distribution with mean 25 and probability of success 1/5,
find P( X 2 ), where and 2 are the mean and variance of the distribution?
b) Number of monthly breakdowns of a computer is a random variable having Poisson
distribution with mean equal to 1.8. Find the probability that the computer will function for a
month (i) without a breakdown (ii) with only one breakdown and (iii) with at least one
4. a) A random sample of size 25 from a normal population has the mean 47.5 and the
standrad deviation 8.4. Does this information support or refute the claim that the mean of
the population is =42.5?
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Code No: X0521
(b) At a certain date in a large city 400 out of a random sample of 500 men were found
to be smokers. After the heavy taxation on tobacco another sample of 600 men in the
same city included 400 smokers. Was the observed decrease in the proportion of smokers
significant?
5. The mean of random sample is an unbiased estimate of the mean of the population 3,
6, 9, 15, 27.
(i) List of all possible samples of size 3 that can be taken with replacement from
the finite population.
(ii) Calculate the mean of each of the samples listed in (i) and assigning each
sample a probability of 1/10. verify the mean of these X is equal to 12. Which
is equal to the mean of these X is equal to 12. Which is equal to the mean of
the population i.e. E( X ) = 0 i.e., prove that X is an unbiased estimate of .
6.(a) In a sample of 1000 people in Karnataka 540 are rice eaters and the rest are wheat
eaters. Can we assume that both rice and wheat are equally popular in this state at
1% level of significance?
(b) A die was thrown 9000 items and of these 3220 yielded a 3 or 4. Is this consistent
with the hypothesis that the die was unbiased?
7. a)Random samples of specimens of coal from two mines A and B are drawn and their
heat-producing capacity (in millions of calories/ton) were measured yielding the
following results:
Mine A 8350 8070 8340 8130 8260
Mine B 7900 8140 7920 7840 7890 7950
Is there significant different between the means of these two samples at 0.01 level of
significance.
b)A coin was tossed 400 times and returned heads 216 times. Test the hypothesis that the
coin is unbiased. Use a 0.05 Level of significance.
8. a) a)Show that for a single service station, Poisson arrivals and exponential service time,
the probability that exactly n calling units are in the Queueing system is ,
, where is the traffic intensity.
b)Explain (M/ M 1): (! / FCFS) Queuing model.
2 of 2
SET - 3
Code No: X0521
II B.Tech I Semester (R07) Regular Examinations, Nov- 2009
PROBABILITY AND STATISTICS
(Com. To CSE, IT,CSS)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
1. a) The probability that India wins a cricket test match against West Indies is known to be
2/5. If India and West Indies play three test matches , what is the probability that (i)
India will lose all the three matches (ii) India will win at least one test match (iii) India
will win at most one match?
b)A problem is given to three students A,B,C whose chances of solving are
1
2 ,
1
3 and
1
4
respectively. What is the probability that the problem is solved?
2. a) The trouble shooting capability of an IC chip in a circuit is a random variable x with
distribution function given by
F(x) = 0 , for x 3
2
9
1
x, for x > 3
Where x denote the number of years . Find the probability that the chip will work
properly (i) less than 8 years (ii) beyond 8 years (iii) between 5 to 7 years.
b) A fair coin is tossed until a head or five tails occurs. Find the expected number of
tosses of the coin ?
3. a) An irregular six faced dice is such that the probability that it gives 3 even numbers in 5
throws is twice the probability that it gives 2 even numbers in 5 throws. How many sets of
exactly 5 trials can be expected to give no even number out of 2500 sets?
b)Fit a Poisson distribution to the following data
x 0 1 2 3 4 5 total
f 142 156 69 27 5 1 400
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Code No: X0521
4. a) The mean life of a sample of 10 electric bulbs was found to be 1456 hours with S.D. of
423 hours. A second sample of 17 bulbs chosen from a different batch showed a mean life
of 1280 hours with S.D. of 398 hours. Is there a significant difference between the means
of two batches?
b)A die is tossed 960 times and it fall with 5 upwards 184 times. Is the die unbiased at a
level of significance of 0.01?
5. a) What is the size of the smallest sample required to estimate an unknown
. proportion to within a maximum error of 0.06 with at least 95% confidence.
(b) It is desired to estimate the mean number of hours of continuous use until a
certain computer will first require repairs. If it can be assumed that = 48
hours, how large a sample be needed so that one will be able to assert with 90%
confidence that the sample mean is off by at most 10 hours.
6. An insurance agent has claimed that the average age of policy holders who issue
through him is less than the average for all agents which is 30.5 years. A random sample
of 100 policy holders who had issued through him gave the following age distribution.
Age 16 – 20 21 – 25 26 – 30 31 – 35 36 – 40
No. of persons 12 22 20 30 16
Calculate the Arithmetic mean and standard deviation of this distribution and use these
values to test his claim at 5% level of significance
7. a)The lifetime of electric bulbs for a random sample of 10 from a large shipment gave the
following data :
Item 1 2 3 4 5 6 7 8 9 10
Life in 1000s of hrs. 4.2 4.6 3.9 4.1 5.2 3.8 3.9 4.3 4.4 5.6
Can we accept the hypothesis that the average life time of bulb is 4000 hrs? Use a 0.05
level of significance.
b)A sample poll of 300 voters from district A and 200 voters from district B showed that
56% and 48%, respectively, were in favor of a given candidate. At a level of significance
of 0.05, test the hypothesis that there is a difference the districts.
8. A gourmet delicatessen is operated by one person, the owner. The arrival pattern of
customers on Saturdays appears to follow a Poisson distribution. With a mean arrival rate
of 10 people per hour. Customers are served on a FIFO basis, and because of the
reputation of the store they are willing to wait for service once they arrive. The time ii
takes to serve a customer is estimated to be exponentially distributed, with an average
service time of 4 min. Determine,
(a) the probability that there is a queue,
(b) the average size of the queue, and
(c) The expected time that a customer must wait in the queue.
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