code no: rt21013 r13 set - 1 ii b. tech i semester regular examinations, dec - 2015€¦ · ·...

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Code No: RT21013

II B. Tech I Semester Regular Examinations, Dec - 2015

STRENGTH OF MATERIALS - I (Civil Engineering)

Time: 3 hours Max. Marks: 70

Note: 1. Question Paper consists of two parts (Part-A and Part-B)

2. Answer ALL the question in Part-A

3. Answer any THREE Questions from Part-B

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PART –A

1. a) Derive the relation between E, K and ν following usual notations.

b) Define point of contra flexure, Shear force and bending moment

c) State the assumptions of simple bending

d) Define shear centre and demonstrate with an example

e) State mohr’s theorems and their significance

f) Discuss the necessity and mechanics of compound cylinders (4M+4M+3M+4M+3M+4M)

PART –B

2. A central steel rod 18 mm diameter passes through a copper sleeve 24 mm inside and 39 mm

outside diameter. It is provided with nut and washers at each end, and the nuts are tightened

until a stress of 10 N/mm2 is set up in the steel. The whole assembly is then placed in a lathe

and a cut is taken along half the length of the tube , removing the copper to a depth of 1.5 mm

(a) Calculate the stress now existing in the steel (b) If an additional end thrust of 5000 N is

applied to the ends of the steel bar calculate the final stress in the steel. Take young’s modulus

for steel as twice that of copper. (16M)

3. Draw Shear Force Diagram and Bending Moment diagram for the beam shown below (16M)

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E DA

2m

B

10 kN/m

2m

C

3m 2m

50 kN

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Code No: RT21013

4. a) State the assumptions made in deriving bending equation.

b) An I-section has the following dimensions: flanges 150 × 10 mm and overall depth = 260

mm, thickness of web 10 mm. It is used as a cantilever beam over a span of 3 m to carry a

load of 40 kN/m over its entire span. Find the maximum bending stresse induced.

(6M+10M)

5. The T section of a beam has the following size:

Width of the flange 140 mm and depth of the flange 35 mm. Width of the web

30 mm and depth of the web is 130 mm. The beam is subjected to a vertical shear force of

60 kN. Calculate the shear stress at the junction of the web and the flange. (16M)

6. A cantilever beam of span 7 m carries a point load of 15 kN at a distance of 4 m from the right

end. Compute (a) the slope (b) the deflection under the load (c) the maximum deflection and its

location. Take E = 1.5 x 105 N/mm

2 and I = 5 x 10

8 mm

4. (16M)

7. A cylindrical drum 400 mm in diameter has a thickness of 8mm. If the drum is subjected to an

internal pressure of 2 N/mm2, determine the increase in the volume of the drum. Take young’s

modulus of elasticity, E=1.6x105N/mm

2 and poisson’s ratio, υ=0.25. (16M)

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Code No: RT21013







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PART –A

1. a) Derived the elongation in a tapered circular bar under an axial load of P

b) Describe the different kinds of beams and their end reactions

c) Derive the section modulus equation for rectangular and circular sections

d) Determine the shear center for a T-section

e) Explain moment area method with an example

f) Derive change in volume of a thin cylindrical shell subjected to an internal pressure p

(4M+3M+4M+4M+3M+4M)

PART –B

2. A steel tube 2.4 cm external diameter and 1.8 cm internal diameter encloses a copper rod 1.5

cm diameter to which it is rigidly joined at each end. If at a temperature of 100C there is no

longitudinal stresses calculate the stresses in the rod and the tube when the temperature is

raised to 2000C. Es=210 kN/mm

2 and Ec=1000 kN/mm

2. Coefficient of linear expansion for

steel is 11(10-6

)/0C and for copper 18(10

-6)/

0C (16M)

3. A 23 m long cantilever beam is 14 m long. The beam carries a load of

10 KN at 5 m from the fixed end, and a distributed load the intensity of which varies linearly

from zero at each end to 6 KN/m at free end. Draw the shear force and bending moment

diagrams. Find the magnitude and position of maximum bending moment. (16M)

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Code No: RT21013

4. Unsymmetrical I-section shown in

2.5 m to carry uniformly distributed

bending stress across the depth marking the values at salient point.

5. A beam of triangular section having base width 25 cm and height of 35

shear force of 5 kN. Sketch the shear stress distribution along the depth of the beam

6. A girder of uniform section and constant depth is freely supported over a span

of 2.5 meters. Calculate the central deflection and

beam under a central load of 22

7. A thick spherical shell of 350

2N/mm2. Determine the necessary thickness of the

material is 2.8 N/mm2.

section shown in below Figure is used as a simply supported beam

uniformly distributed load of 5 kN/m over entire span. Draw

bending stress across the depth marking the values at salient point.

lar section having base width 25 cm and height of 35

ketch the shear stress distribution along the depth of the beam

A girder of uniform section and constant depth is freely supported over a span

of 2.5 meters. Calculate the central deflection and slopes at the ends of the

beam under a central load of 22 kN. Given: I XX = 8 × 10-6

m4 and E = 190 GN/m

350 mm inside diameter is subjected to an internal pressure of

Determine the necessary thickness of the shell, if the permissible s

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simply supported beam of span

kN/m over entire span. Draw the variation of

(16M)

cm is subjected to a

ketch the shear stress distribution along the depth of the beam (16M)

A girder of uniform section and constant depth is freely supported over a span

slopes at the ends of the

0 GN/m2 (16M)

mm inside diameter is subjected to an internal pressure of

the permissible stress in the shell

(16M)

SET - 2

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Code No: RT21013







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PART –A

1. a) Derive the volumetric strain and change in volume for a rectangular parallel-piped

b) Derive the relation between SF, BM, and rate of loading at a section

c) Derive and plot the variation of bending stress for a hollow rectangular section

d) Find the shear centre for an rectangular section

e) Apply moment area method to a cantilever beam carrying point load at the center and find

the deflection at the tip

f) Derive the relation for volumetric strain and volume change for a thick spherical shell

(4M+3M+4M+3M+4M+4M)

PART –B

2. A rod 1m long is 10 cm2 in area for a portion of its length and 5 cm

2 in area for the remainder.

The strain energy of the stepped bar is 40% that of a bar 10 cm2 in area 1m long under the

same maximum stress. What is the length of the portion of 10 cm2 in area

3. Draw the SFD and BMD for the beam loaded as shown in the Figure1

Figure1

4. a) State the assumptions involved in the theory of simple bending

b) Derive the section modulus for a box section

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SET - 3 SET - 3 R13

16 kN/m

450

2 kN 0.8 kN/m 2 kN

3 kN 600

2m 2m 2m 3m 3m 3m

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Code No: RT21013

5. A beam of square cross section150 mm is placed in such away that its diagonal is the neutral

axis. It is subjected to a sheer force of 6 kN. Sketch the variation of shear stress along the depth

of the beam.

6. A horizontal steel girder having uniform cross-section is 14 m long and is simply supported at

its ends. It carries two concentrated loads as shown in Figure 2. Calculate the deflections of the

beam under the loads C and D. Take E = 250 GPa and I = 150x106mm

4.

Figure 2

7. A compound cylinder formed by shrinking one tube to another is subjected to an internal

pressure of 80 MN/m2 . Before the fluid is admitted the internal and external diameters of the

compound cylinder are 160 mm and 280 mm respectively and the diameter at the junction is

220 mm. If after shrinking on, the radial pressure at the common surface is 02 MN/m2

determine the final stresses developed in the compound cylinder.

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DA BC

6.5 m 3 m 4.5 m

12 kN 8 kN

14 m

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Code No: RT21013







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PART –A

1. a) Derive the expression for equivalent static load when a weight falls through a height h on the

flange attached at the end of a circular bar.

b) What is the convention for shear force and bending moment? Show with the help of

diagrams

c) Derive the variation of bending stress across a diamond section and plot the same

d) What is shear center? Locate the shear center for a channel section

e) Derive the expression for deflection under point load P situated at a distance a from one

end of a simply supported beam.

f) Prove that the net force on the longitudinal diametral section of a thin cylinder subjected to

internal pressure p equals the projected area times the applied pressure

(4M+4M+3M+3M+4M+4M)

PART –B

2. Determine the percentage change in volume of a steel bar 7.6 cm square section1 m lond when

subjected to an axial compressive load of 20 kN. What change in volume would a 10cm cube

of steel suffer at a depth of 4.8 km in sea water? E = 205kN/mm2 and G = 82 kN/mm

2

3. A 23 m long cantilever beam has a span of 16 m. The beam carries a load of 13 KN at 6 m

from the fixed end, and a distributed load the intensity of which varies linearly from zero at

fixed end to 6 KN/m at right free end. Draw the shear force and bending moment diagrams.

Find the magnitude and position of maximum bending moment.

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Code No: RT21013

4. AnI-section has flanges of size 190 × 10 mm and its overall depth is 350 mm. Thickness of

webis 10 mm. It is used as a cantilever beam over a span of 5 m to carry a load of 50 kN/m

over its entire span. Find the bending stresses at the mid span.

5. An I-section with rectangular ends has the following dimensions.

i) Flanges: 13 cm x 2.2 cm ii) Web : 33 cm x 1.3 cm

Sketch the variation of shearing stress in the section for a shearing force of 10 kN

6. A overhang beam has two supports 4 a apart and has over hang portions of length a on either

side of the supports. It is carrying a load of 4W at the center, and a load of W at its extremes.

Determine the slope and deflection of the beam at the supports.

7. A pipe of 300 mm internal diameter and 60 mm thickness carries a fluid at a pressure of 15

MN/m2. Calculate the maximum and minimum intensities of circumferential stresses across the

section. Also sketch the radial stress distribution and circumferential stress distribution across

the section.

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Code No: RT21024


COMPLEX VARIABLES AND STATISTICAL METHODS (Electrical and Electronics Engineering)





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Note :- Statistical tables are required

PART –A

1. a) Is 3( )f z z= analytic? (4M)

b) State Cauchy's Integral Theorem. (3M)

c)

Find the residues at the singular points of 2

9

( 1)

z i

z z

+

+.

(4M)

d) Find the fixed points of the transformation ( )2

w z i= − . (4M)

e) Define Population and Sample with examples. (3M)

f) Define one-tailed and two-tailed tests. (4M)

PART –B

2.

a) Show that for ( )

( ) ( )3 3 3 3

2 2

– , 0

0 , 0

x y i x yz

f z x y

z

+ + ≠

= +

=

the Cauchy-Riemann

equations are satisfied at the origin but the derivative of ( )f z at origin does not

exist.

(10M)

b) Find the analytic function ( ) f z u iv= + where sinxv e y= .

(6M)

3.

a) Evaluate

3

2

0

i

z dz

+

∫ along real axis from 0 to 3 and then vertically to 3 .i+

(8M)

b) Find the Laurent series of ( ) 2

1

4 3f z

z z=

− + , for 1 3 z< < .

(8M)

4.

a) Determine the poles of the function ( )( )2

1

2

zf z

z z

+=

− and the residue at each

pole.

(8M)

b) Use residue theorem to evaluate

2

05 3sin

dπ

θ

θ−∫ .

(8M)

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Code No: RT21024

5.

a)

Determine the image of the region 3 5z − = under the transformation1

wz

= .

(8M)

b) Determine the bilinear transformation that maps the points 1 0 ,z =

2 32 , 2 z i z i= = − into the points 1 2 31 , 0 , w w w= − = = ∞ respectively.

(8M)

6. a) Determine the probability that X will be between 66.8 and 68.3 if a random

sample of size 25 is taken from an infinite population having the mean

68 3.andµ σ= =

(8M)

b) The average zinc concentration recovered from a sample of zinc measurements in

36 different locations is found to be 2.6 grams per milliliter. Find a 95%

confidence intervals for the mean zinc concentration in the river. Assume that the

population standard deviation is 0.3.

(8M)

7. a) A storekeeper wanted to buy a large quantity of bulbs from two brands A and B

respectively. He bought 100 bulbs from each brand A and B and found by testing

brand A had mean life time of 1120 hrs and the S.D of 75 hrs and brand B had

mean life time 1062 hrs and S.D of 82 hrs. Examine whether the difference of

means is significant. Use a 0.01 level of significance.

(8M)

b) An urban community would like to show that the incidence of breast cancer is

higher than in a nearby rural area. If it is found that 20 of 200 adult women in the

urban community have breast cancer and 10 of 150 adult women in the rural

community have breast cancer, can we conclude at the 0.01 level of significance

that breast cancer is more prevalent in the urban community?

(8M)

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PART –A

1. a) Is 2( )f z z= analytic? (4M)

b) State Residue theorem. (3M)

c) Find the residues at the singular points of

2

4 z

z z

−

−.

(4M)

d) Find the fixed points of the transformation

z iw

z i

+=

−.

(4M)

e) Find the value of the finite population correction factor for n = 10 and

N = 1000.

(3M)

f) Define Type-I and Type-II errors in testing of hypothesis. (4M)

PART –B

2.

a) Show that for ( )

( )2

2 4

, 0

0 , 0

xy x iyz

f z x y

z

+≠

= + =

the Cauchy-Riemann equations are

satisfied at the origin but the derivative of ( )f z at origin does not exist.

(10M)

b) Find the analytic function ( ) f z u iv= + where sin cosu x hy= .

(6M)

3. a) Integrate ( ) 2f z x ixy= + from ( ) ( )1 ,1 2 , 8A to B along

the curve 3 , .x t y t= =

(8M)

b) Use Cauchy’s integral formula to evaluate

( )( )

2

1 2

z

C

edz

z z− −∫ where is the

circle 3 .z =

(8M)

4.

a) Determine the poles of the function ( )2

2

1zf z

z z

+=

− and the residue at each pole.

(8M)

b) Use residue theorem to evaluate ( ) ( )2 2

1 9

dx

x x

∞

− ∞+ +

∫ .

1 of 2

(8M)

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Code No: RT21024

5.

a) Find and sketch the image of the region 1 0 , 0

2x y

π− ≤ ≤ ≤ ≤ under .zw e=

(8M)

b) Determine the bilinear transformation that maps the points 1 0 ,z =

2 31 , 2 z z= = into the points 1 2 3

1 11 , ,

2 3w w w= = = respectively.

(8M)

6. a) Find ( 66.75)P X > if a random sample of size 36 is drawn from an infinite

population with mean 63 9.andµ σ= =

(8M)

b) Determine a 95% confidence interval for the mean of a normal distribution with

variance 2σ = 0.25 , using a sample of 100n = values with mean 212.3.x =

(8M)

7. a) Two independent samples of size 9 and 8 had the following values of the

variables :

Sample I 17 27 18 25 27 29 27 23 17

Sample II 16 16 20 16 20 17 15 21

Do the estimates of the population variance differ significantly? Use a 0.05 level

of significance.

(8M)

b) In a study to estimate the proportion of residents in a certain city and its suburbs

who favor the construction of a nuclear power plant, it is found that 63 of 100

urban residents favor the construction while only 59 of 125 suburban residents

are in favor. Is there a significant difference between the proportion of urban and

suburban residents who favor construction of the nuclear plant? Use a 0.05 level

of significance.

(8M)

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Code No: RT21024







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PART –A

1. a) Check analyticity by using Cauchys-Riemann Equations for ( )f z z z= . (4M)

b) State Laurent’s theorem. (3M)

c)

Find the residues at the singular points of 2

4

( 1)z +.

(4M)

d) Find the invariant points of the transformation

2 1

2

izw

z i

−=

+.

(4M)

e) Explain interval estimators of mean. (3M)

f) Write procedure for test of hypothesis concerning one mean for large sample. (4M)

PART –B

2.

a) Show that ( )

( )2 5

4 10

, 0

0 , 0

x y x iyz

f z x y

z

+≠

= + =

is not analytic at 0 ,z = although

the Cauchy-Riemann equations are satisfied at the origin.

(10M)

b) Find the analytic function ( ) f z u iv= + where cosxu e y= .

(6M)

3.

a) Evaluate ( )1

2

0

i

x iy dz

+

+∫ along the paths y x= and 2y x= .

(8M)

b) Find Taylor’s expansion of ( )3

2

2 1zf z

z z

+=

+ about the point z i= .

(8M)

4.

a) Determine the poles of the function ( )( ) ( )

2

21 2

zf z

z z=

− + and the residue at

each pole.

(8M)

b) Use residue theorem to evaluate ( )( )

2

2 21 4

xdx

x x

∞

− ∞ + +∫ .

1 of 2

(8M)

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Code No: RT21024

5.

a) Find and sketch the image of the region

3 50.5 0.5 ,

4 4x y

π π− ≤ ≤ ≤ ≤ under

.zw e=

(8M)

b)

Determine the bilinear transformation that maps the points 1 0 ,z =

2 31 , z z= = ∞ into the points 1 2 31 , , 1 w w i w= − = − = respectively.

(8M)

6. a) Determine the probability that X will be between 22.39 and 22.41 if a random

sample of size 36 is taken from an infinite population having the mean

22.4 0.048.andµ σ= =

(8M)

b) The contents of 7 similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8, 10.0,

10.2, and 9.6 liters. Find a 95% confidence interval for the mean of all such

containers, assuming an approximate normal distribution.

(8M)

7. a) In a random sample of 100 tube lights produced by company A, the mean life

time of tube light is 1190 hours with standard deviation of 90 hours. Also in a

random sample of 75 tube lights from company B the mean life time is 1230

hours with standard deviation of 120 hours. Is there a difference between the

mean lifetimes of the two brands of tube lights at a significance level of 0.05?

(8M)

b) Two samples of sodium vapor bulbs were tested for length of life and the

following results were returned :

Size Sample mean Sample S.D.

Type I 8 1234 hrs 36 hrs

Type II 7 1036 hrs 40 hrs

Is the difference in the means significant to generalize that type I is superior to

type II regarding length of life? Use a 0.05 level of significance.

(8M)

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Code No: RT21024







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PART –A

1. a) Check analyticity by using Cauchys-Riemann Equations for

( ) (cos sin )xf z e y i y= + .

(4M)

b) State Taylor’s theorem. (3M)

c) Find the residues at the singular points of tan z . (4M)

d) Find the invariant points of the transformation

3 5

izw

z i

− −=

+.

(4M)

e) Define point estimator and unbiased estimator. (3M)

f) Write 2χ statistic for test of goodness of fit. (4M)

PART -B

2. a) Show that ( ) f z xy= is not analytic at 0 ,z = although the Cauchy-

Riemann equations are satisfied at the origin.

(10M)

b) Find the analytic function ( ) f z u iv= + where 3 23u x xy= − .

(6M)

3. a) Integrate ( ) 2f z x ixy= + from ( ) ( )1 ,1 2 , 4A to B along

the curve 2 , .x t y t= =

(8M)

b) Use Cauchy’s integral formula to evaluate

( )2

2 2

z

C

edz

z π+∫ where C is the circle

4 .z =

(8M)

4.

a) Find the residue of ( )( )

31

zze

f zz

=−

at its pole. (8M)

b) Use residue theorem to evaluate

21

dx

x

∞

− ∞+∫ .

(8M)

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Code No: RT21024

5.

a) Determine and Plot the image of the region 2 3z< < and arg

4z

π< under

2w z= .

(8M)

b)

Determine the bilinear transformation that maps the points 1 1 ,z = −

2 3 , 1 z i z= = into the points 1 2 30 , , w w i w= = = ∞ respectively.

(8M)

6. a) Determine the probability that X will be between 75 and 78 if a random sample

of size 100 is taken from an infinite population having the mean 276 256.andµ σ= =

(8M)

b) A random sample of 8 envelopes is taken from the letter box of a post office and

their weights in grams are found to be: 12.1, 11.9, 12.4, 12.3, 11.5, 11.6, 12.1,

and 12.4. Find 95% confidence limits for the mean weight of the envelopes

received at that post office.

(8M)

7. a) A manufacturer claims that the average tensile strength of thread A exceed the

average tensile strength of thread B by at least 12 kilograms. To test his claim,

50 pieces of each type of thread are tested under similar conditions. Type A

thread had an average tensile strength of 86.7 kilograms with known standard

deviation of 6.28Aσ = kilograms, while type B thread had an average tensile

strength of 77.8 kilograms with known standard deviation of 5.61Bσ =

kilograms. Test the manufacturers claim at 0.01 level of significance.

(8M)

b) In two independent samples of sizes 8 and 10 the sum of squares of deviations of

the sample values from the respective sample means were 84.4 and 102.6. Test

whether the difference of variances of the populations is significant or not. Use a

0.05 level of significance.

(8M)

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Code No: RT21034


MANAGERIAL ECONIMICS AND FINANCIAL ANALYSIS (Com. to ME, ECE, CSE, IT, ECC, MTE)





~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART –A

1. a) Identify nature of managerial economics through its definitions (4M)

b) Identify formula for any one method of measuring demand elasticity and describe

variables used in it.

(4M)

c) What are the uses of Cobb-Douglas production functions and where it can be

applicable?

(4M)

d) What are the different phases in business cycle and explain with the help of graph (4M)

e) Explain the convention of “Conservatism” in accounting (3M)

f) What is IRR and identify suitable formula for Internal Rate of Return (3M)

PART –B

2. a) What is the importance and uses of Managerial Economics to Engineers? How

can use these concepts to Manufacturing Sector?

(8M)

b) What are the objectives & uses of demand forecasting? How do you predict

demand for Steel Manufacturing?

(8M)

3. a) List different internal & external economies of scale of for Chemicals Production

Units like Ranbaxy Labs Ltd. & Dr. Reddy Labs Ltd.?

(8M)

b) Determine BEP, P/V Ratio and Sales level for a profit of Rs.15.00 Lakhs, if Fixed

Cost is Rs.25.00 Lakhs, Sales is Rs.175.00 Lakhs and Variable Cost is Rs.170.00

Lakhs.

(8M)

4. a) Differentiate features Monopolistic & Oligopolistic Markets (8M)

b) Explain in detail different stages of business life cycle, how recessionary trends

influence Capital Goods Sector?

(8M)

5. a) What is a Business Cycle and explain different stages of business cycle? (8M)

b) Differentiate Memorandum & Articles of Association? (8M)

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Code No: RT21034

6. a) Journalise following transactions in the Books of M/S. Telugunadu Industries

Ltd., for the month of Oct-15

Date Transaction Description Amount Rs.

01-10-2015 Business Commenced with Cash 5,00,000/-

03-10-2015 Deposited in Costal Andhra Bank 3,00,000/-

07-10-2015 Purchased Goods from M/s. LCB Ltd. 25,00,000/-

09-10-2015 Sold Goods to M/s. ANL Ltd. 50,00,000/-

15-10-2015 Purchased Motor Vehicle from M/s.TML Ltd. 10,00,000/-

21-10-2015 Purchased Office Furniture from M/s. Godrej

Ltd.

2,00,000/-

30-10-2015 Withdrawn Cash for office purpose 1,00,000/-

31-10-2015 Paid Salaries & Rent in Cash 75,000/-

(8M)

b) Determine Current Ratio, Quick Ratio, Cash Ratio & Working Capital Ratios

with the help of following information:

Description Amount Rs.

Cash & Bank Balances 11,50,000/-

Marketable Securities 5,00,000/-

Prepaid Expenses 1,50,000/

Outstanding Expenses 2,25,000/

Short Term Investments & Term Deposits 8,00,000/

Debtors & Bills Receivables 25,00,000/

Creditors & Bills payables 10,00,000/

Provision for Divided & Taxation 1,45,000/

Short Term Bank Loans 4,00,000/

Inventory 2,75,000/

(8M)

7. a) Compare merits & demerits of Pay Back Period & Accounting Rate of Return

Methods

(8M)

b) Determine Accounting Rate of Return(ARR) for the following two projects, if

Company follows Straight Line Method of Depreciation and consider scrap value

Description Project-A

Cash Flow Rs.

Project-B

Cash Flow Rs.

Initial Cost of Investment 125000 150000

I Year 35000 45000

II Year 40000 55000

III Year 45000 40000

IV Year 50000 65000

V Year 20000 35000

Salvage Value 20000 25000

(8M)

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Code No: RT21034







~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART –A

1. a) Identify different scope areas of managerial economics? (4M)

b) Compare Point & Arc Elasticity of Demand (4M)

c) Explain Law of Variable Proportion? (4M)

d) List various features of Joint Stock Company. (4M)

e) Compare the convention of “Consistency & Full Disclosure” in accounting (3M)

f) List & identify formula for Net Present Value & Profitability Index (3M)

PART –B

2. a) What is the law of Demand? What are the different factors influencing Demand? (8M)

b) What are the objectives & uses of elasticity demand? Differentiate Promotional &

Cross Elasticity of demand?

(8M)

3. a) Explain the law of diminishing marginal utility with the help of suitable graph

under different stages of return of scale?

(8M)

b) Determine BEP, P/V Ratio and Sales level for a profit of Rs.25.00 Lakhs, if Fixed

Cost is Rs.15.00 Lakhs, Sales is Rs.190.00 Lakhs and Variable Cost is Rs.180.00

Lakhs.

(8M)

4. a) Differentiate features Perfect & Monopoly Markets (8M)

b) List different methods of pricing and explain any four of them in detail.

(8M)

5. a) Compare features & limitations of Partnership to that of Sole Trader form of

business.

(8M)

b) Differentiate features of Private Limited Company to that of Public Limited

Company?

(8M)

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R13 SET - 2

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Code No: RT21034

6. a) Prepare Three Column Cash Book following transactions in the Books of M/s.

Mahanadu Manufacturers Ltd., for the month of Oct-15


01-10-2015 Opening Balance of Cash 5,00,000/-

03-10-2015 Costal Andhra Bank Balance 3,00,000/-

07-10-2015 Purchased Goods from M/s. LCB Ltd. on

Credit

25,00,000/-

09-10-2015 Sold Goods to M/s. ANL Ltd. on Credit 50,00,000/-

11-10-2015 Received a bank cheque from M/s. ANL

Ltd & requested for a discount of Rs. 1.00

Lakh accepted

49,00,000/-

13-10-2015 Paid to M/s, LCB Ltd 10,00,000/-

15-10-2015 Purchased Motor Vehicle from M/s.TML

Ltd. for Rs. 10,50,000/- Paid Down

Payment of Rs. 50,000/- through Bank

10,50,000/-

21-10-2015 Purchased Office Furniture from M/s.

Godrej Ltd. and paid through bank

1,00,000/-


28-10-2015 Paid Salaries & Rent in Cash 75,000/-

30-10-2015 Interest payable 50.000/-

31-10-2015 Income Tax Payable 3,00,000/-

(8M)

b) Determine Debt-Equity Ratio, Proprietary Ratio and Funds Proportion Ratios

with the help of following information:


Equity Capital 10,00,000/-

Profit & Loss A/C(Profit) 5,00,000/-

Reserves & Surplus 3,00,000/

Premium on Issue of Shares & Debentures 2,50,000/

Debentures 30,00,000/

Long Term Fixed Deposits Accepted 5,00,000/

Long Term Bank Loans 15,00,000/

Provision for Divided & Taxation 1,50,000/

Short Term Bank Loans 5,00,000/

Fixed Assets 45,75,000/

(8M)

7. a) Compare merits & demerits of Net Present Value Method & Internal Rate of

Return Methods

(8M)

b) Determine NPV, Profitability Index and Internal Rate of Return(IRR) for the

following project.


Cash Flow Rs.

PV Factor

15%

PV Factor

20%

Initial Cost of

Investment

225000 1.000 1.000

I Year 55000 0.870 0.833

II Year 45000 0.756 0.694

III Year 75000 0.658 0.579

IV Year 58000 0.572 0.482

V Year 29000 0.497 0.402

Salvage Value 24000 0.497 0.402

(8M)

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R13 SET - 2

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Code No: RT21034







~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART –A

1. a) Differentiate Producer Durable & Non Durable and Consumer Durable & Non

Durable Goods Demand?

(4M)

b) How demand is forecasted through method of least squares method? (4M)

c) Explain Returns to Scale with the help of graph? (4M)

d) List various features of Departmental Type of Undertaking. (4M)

e) List & explain various functions of accounting (3M)

f) List & explain various steps involved in Capital Budgeting (3M)

PART –B

2. a) What are different distinctions of Demand? (8M)

b) What is price elasticity of demand? Explain Relatively Elastic, Relatively

Inelastic, Unity Elastic.

(8M)

3. a) Explain the least cost input output combinations with suitable graphs? (8M)

b) Determine P/V Ratio, Fixed Cost and BEP with the help of following

information:

Description 2014-15 2015-16

Sales(Rs. Lakhs) 10.00 50.00

Profit(Rs. Lakhs) 2.50 22.50

(8M)

4. a) How Price & Output determined under Perfect Competition in Short Run for

Industry & Firm? Explain with the help of graphs.

(8M)

b) What are the objectives and situation behind pricing strategies and explain cost

based pricing methods.

(8M)

5. a) Compare Objectives, features & limitations of Co-operative type of

organisation.

(8M)

b) What are the objectives & limitations of state enterprises?

1 of 2

(8M)

R13 SET - 3

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Code No: RT21034

6. a) Prepare Three Column Cash Book following transactions in the Books of M/s.

Indo-Japan Consultants Ltd., for the month of Oct-15


01-10-2015 Opening Balance of Cash 15,00,000/-

04-10-2015 Rayalaseema Bank Balance 30,00,000/-

05-10-2015 Purchased Goods on Credit 20,00,000/-

10-10-2015 Sold Goods on Credit 50,00,000/-

12-10-2015 Received a bank cheque from Mr. Srinivas 40,00,000/-

14-10-2015 Paid to M/s, LCB Ltd 10,00,000/-

16-10-2015 Purchased Motor Vehicle from M/s.SML Paid

Down Payment through cash

1,50,000/-

18-10-2015 Purchased Office Furniture from M/s. Godrej

Ltd. and paid through bank

1,50,000/-


22-10-2015 Paid Salaries & Wages though Bank 2,75,000/-

24-10-2015 Interest credited in bank 50.000/-

26-10-2015 Income Tax Paid 2,00,000/-

28-10-2015 Deposited Cash in Bank 25,000/-

30-10-2015 Received cheque from Mr. Pullarao 2,50,000/-

(8M)

b) Determine Interest Coverage and equity Ratio and Debt Ratio with the help of

following information:


EBIT 50,00,000/-

Taxation 50%

Long Term Institutional Loans( Repayable 5 Years) and 10%

Interest 10,00,000/

5 Years 12% Debentures 50,00,000/

Long Term Bank Working Capital Loan for 5 Years at an interest

of 30%

15,00,000/-

(8M)

7. a) How do you estimate cash flow? Compare merits & demerits of traditional

methods & DCF methods.

(8M)

b) Determine NPV, Profitability Index and Internal Rate of Return(IRR) for the

following project.


Cash Flow Rs.

PV Factor

15%

PV Factor

20%

Initial Cost of

Investment

900000 1.000 1.000

I Year 350000 0.870 0.833

II Year 400000 0.756 0.694

III Year 245000 0.658 0.579

IV Year 350000 0.572 0.482

V Year 220000 0.497 0.402

Salvage Value 120000 0.497 0.402

(8M)

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R13 SET - 3

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Code No: RT21034







~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PART –A

1. a) How knowledge of Economics, Management and Operations Research helpful in

decision making?

(4M)

b) List qualitative methods of demand forecasting and explain opinion poll

methods?

(4M)

c) Identify properties of Iso-Product Curves with the help of graph? (4M)

d) Differentiate Privatisation & Liberlisation concepts. (4M)

e) List & explain different types of errors in preparation of trial balance. (3M)

f) Nature of Capital Budgeting Project Decisions (3M)

PART –B

2. a) Explain law of Demand & Limitations with the help of graph? Also list different

factors influencing demand.

(8M)

b) Compare price, income, promotional & cross elasticity of demand?

(8M)

3. a) What is a production function? Explain different types of Short & Long Run

Production Function?

(8M)

b) Determine P/V Ratio, Fixed Cost and BEP with the help of following

information:

Description 2014-15 2015-16

Sales(Rs. Lakhs) 20.00 50.00

Profit(Rs. Lakhs) 5.00 10.00

(8M)

4. a) How Price & Output determined under Perfect Competition in long Run for

Industry & Firm? Explain with the help of graphs.

(8M)

b) What are the objectives and situation behind pricing strategies and explain cost

based pricing methods.

(8M)

5. a) Compare Objectives, features & limitations of Cooperatives. (8M)

b) What are the objectives & limitations of state enterprises?

(8M)

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R13 SET - 4

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Code No: RT21034

6. a) Journalise following transactions in the Books of M/s. Indo-Malasian

Constructions Ltd., for the month of Oct-15


01-10-2015 Business commenced with Cash 15,00,000/-

03-10-2015 Deposited Indo-Malaysian Bank 10,00,000/-

07-10-2015 Purchased Goods on Credit from M/s. Isuzu

& Co.

25,00,000/-

10-10-2015 Sold Goods on Credit to M/s. GMRIFL 30,00,000/-

11-10-2015 Received a bank cheque from M/s.

GMRIFL on Account

20,00,000/-

15-10-2015 Paid to M/s, Isuzu & Con On Account 12,00,000/-

16-10-2015 Purchased Motor Vehicle from M/s.MML 12,00,000/-

17-10-2015 Purchased Office Furniture from M/s.

Tumbi Ltd. and paid through bank

1,00,000/-


29-10-2015 Paid Salaries & Wages though cash 75,000/-

29-10-2015 Interest credited in bank 2,50.000/-

30-10-2015 Paid Freight through bank 1,00,000/-

30-10-2015 Deposited Cash in Bank 1,25,000/-

31-10-2015 Paid Rent through bank cheque to Mr.

Umamaheswar Rao

50,000/-

(8M)

b) Determine Stock Velocity & Debtors Velocity with the help of following

information:

Description

Opening Balance of Stock 5,00,000/-

Opening Balance of Debtors 15,00,000/-

Opening Balance of Bills Receivables 4,00,000/

Closing Balance of Stock 2,00,000/

Closing Balance of Debtors 25,00,000/-

Closing Balance of Bills Receivables 8,00,000/-

Sales 40,00,000/-

Gross Profit 20%

Credit Sales 60%

Days in a Year 360

(8M)

7. a) What are the different Methods of evaluating capital budgeting projects? (8M)

b) Determine Pay Back Period and Internal Rate of Return (IRR) for the following

project.


Cash Flow Rs.

PV Factor

12%

PV Factor

20%

Initial Cost of

Investment

1000000 1.000 1.000

I Year 250000 0.893 0.833

II Year 350000 0.797 0.694

III Year 200000 0.712 0.579

IV Year 450000 0.636 0.482

V Year 250000 0.567 0.402

Salvage Value 150000 0.567 0.402

(8M)

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R13 SET - 4

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Code No: R21016

II B. Tech I Semester Supplementary Examinations, Dec - 2015

MATHEMATICS - III (Com. to CE, CHEM, BT, PE)


Answer any FIVE Questions

All Questions carry Equal Marks

~~~~~~~~~~~~~~~~~~~~~~~~~

1. Prove that i) 1 1(2 1) ( ) ( 1) ( ) ( )n n nn xP x n P x nP x

+ −+ = + +

ii) Prove that 1/2

2( ) (sin )J x x

xπ=

(15M)

2. a) Find the regular function w u iv= + where 2 2[( )cos 2 sin ]xu e x y y xy y

−= − + . (8M)

b)

If

3

6 2

( ), 0

( )

0, 0

x y y ixz

f z x y

z

−≠

= +

=

prove that ( ) (0)

0f z f

z

−→ as 0z → along any

radius vector but not as 0z → along the curve 3y ax=

(7M)

3. a) i) Expand cosh5x in a series of powers of hyperbolic cosines of x.

ii) Expand 5sinh x in a series of powers of hyperbolic sines of multiples of x.

(8M)

b) If cos( ) cos sin ,x iy iθ θ+ = + show thatcos2 cosh 2 2x y+ = .

(7M)

4. a) Let C denote the boundary of the square whose sides lie along the lines

2, 2x y= ± = ± where c is described in the positive sense.

i) ( / 2)

( )oc

Tan zdz

z x−∫ ( 2)ox < ii)

2

cos

( 8)c

zdz

z z +∫

(8M)

b) Evaluate

2

2

0

i

z dz

+

∫ along (i) the real axis from z = 0 to 2 and then vertically to

(2+i) ii) The imaginary axis to i and then horizontally to (2+i).

(7M)

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SET - 1 R10

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Code No: R21016

5. a) Expand

( 1)( 2)( )

( 1)( 4)

z zf z

z z

− +=

+ + in the region i) 1 4z< < ii) 1z <

(8M)

b) Explain different types of singularities with examples

(7M)

6. a) Show by the method of contour integration

that2 2 2 3

0

cos(1 ) , ( 0, 0)

( ) 4

mamxdx ma e a b

x a a

π∞

−= + > >

+∫ .

(8M)

b) Find the poles and residues at each pole of tanh z .

(7M)

7. i) If a>e, use Rouche’s theorem to prove that z ne az= has n roots inside the

circle 1z = .

ii) State and prove that Fundamental theorem of Algebra.

(15M)

8. a) Find the bilinear transformation which maps the points , ,0i∞ in the z-plane into

1, ,1i− − in the w-plane

(8M)

b) Show that the transformation

2 3

4

zw

z

+=

− change the circle 2 2 4 0x y x+ − = into

the straight line 4u+3=0.

(7M)

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SET - 1 R10

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Code No: R21029


ELECTRO MAGNETIC FIELDS (Electrical and Electronics Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Describe the concept of electric field and derive the expression for the electric field

due to a point charge.

b) Determine the field strength at a point situated 6cm away from two equal charge of

Q1 = +109C and other charge of Q2 = 10

9C, if the distance between them is 9m.

2. a) Derive the expression for electric field intensity due to an electric dipole,

b) Prove that the potential due to an electric dipole satisfies Laplace’s equation

3. a) Derive the point form of Ohm law for conductors.

b) Explain about the conduction and convection current densities.

4. a) State and explain Biot-Savart’s law.

b) Derive the expression for magnetic field intensity at the center of a circular wire?

5. a) Prove that .IH.dI∫ =

b) A single phase circuit comprises two parallel conductor X and Y, each 1 cm

diameter and spaced 1m apart. The conductors carry currents of +100 and -100A,

respectively. Determine the field intensity at the surface of each conductor and also

in space exactly midway between X and Y.

6. a) Derive the Lorenz force equation for moving changes is magnetic field.

b) A straight solid wire segment carrying a current 2 U y A extends from A (0, 1, 2) to

B (0, 4, 2) is free space. This wire is subjected to the magnetic field of an infinite

current filament lying along z- axis and carrying 25A is the Uz direction. Find the

vector torque on the wire segment about as origin at (i) PA (0,0,2), (ii) PB (0,0,0), (iii)

Pc (0, 2, 0).

7. a) Derive the expression for determination of energy stored in a magnetic field.

b) Derive an expression for the mutual inductance if two straight filamentary circuits of

length L and of infinitesimal cross section which are parallel to each other and a

distance D apart.

8. a) Write down the Maxwell’s equations in integral form and explain their significance.

b) Show that the total displacement current between the condenser plates connected to

an alternating current voltage source is exactly the same as the value of charging

current flowing in the leads.

1 of 1

R10 SET - 1

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Code No: R21043

II B. Tech I Semester Supplementary Examinations, Dec - 2015 PROBABILITY THEORY AND STOCHASTIC PROCESSES

(Electronics and Communications Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) State and prove total probability theorem. (8M)

b) A bin contain the 100 resistors as detailed below

R/Tolerance 10 Ω 47 kΩ 1 kΩ Total

5% 5 20 10 35

10% 10 15 20 45

20% 10 5 5 20

Total 25 40 35 100

If a resister is picked randomly with replacement, find i) p (20% resister)

ii) p(10 Ω and 1k Ω) iii) p (4 kΩ and 10%) iv) p (5% and 1 kΩ)

(7M)

2. a) A sample space is defined by .5,4,32,1 ≤≤= sS A random variable is defined

by X= 2 for 65.35,5.32053,5.20 ≤≤=<<=≤≤ sforXandsforXs

i) Is X discrete, continuous, or mixed?

ii) give a set that defines the values X can have

(7M)

b) A random variable X is Gaussian with aX=0 and σ =1

i) What is the probability that 2>X ?

ii) What is the probability that X>2?

(8M)

3. a) Find mean and variance of exponential random variable. (7M)

b) A random variable X is uniformly distributed on the interval ( )ππ ,− X is

transformed to the new random variable Y = T(x) = a Tan(X), where a > 0. Find

the probability density function of Y.

(8M)

4. a) Random variables X and Y have the joint density

)3/()4

(

, )()(12

1),(

yx

YX eyuxuyxf−−

=

Find (i) 51,4,2 ≤<−≤< YXP (ii) 2,0 −≤<−∞∞<< YXP

(7M)

b) Random variables X and Y have respective density functions

( ) ( ) ( )[ ] and1

axuxua

xf x −−=

( ) ( ) by

y eybuyf−

=

where a>0 and b>0. Find and sketch the density function of W= X + Y if X and Y

are statistically independent.

(8M)

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R10 SET - 1

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Code No: R21043

5. a) Two Gaussian random variables X and Y have variance 49 22== YX and σσ

respectively, and correlation coefficient ρ. It is known that a coordinate rotation

by an angle 8/π− results in new random variables Y1 and Y2 that are

uncorrelated. Determine ρ.

(8M)

b) Two random variables having joint characteristic function

XY(ω 1, ω 2)= exp(−2ω2

1−8ω2

2). Find moment’s m10, mo1, m11.

(7M)

6. a) Given the random process by

X(t)=A cos(w0t) + B sin(w0t)

where w0 is a constant, and A and B are uncorrelated zero-mean random variables

having different density functions but the same variance. Show that X(t) is wide

sense stationary but not strictly stationary.

(8M)

b) Let X (t) be a stationary continuous random process that is differentiable. Denote

its time derivative by ( ).tX& Show that ( )[ ] .0=tXE &

(7M)

7. a) If X(t) is a stationary process, find the power spectrum of ( ) ( )tXBAtY 00 += in

terms of the power spectrum of X(t) if A0 and B0 are real constants.

(7M)

b) A random process is given by where A is a real

constant, is a random variable with density function ( and is a random

variable uniformly distributed over the interval (0, ) independent of . Show

that the power spectrum of is SXX ( = [ ( ( ]and also

find .

(8M)

8. A system’s power transfer function is

( )4

2

256

16

ωω

+=H

a) What is its noise bandwidth?

b) If white noise with power density nW/Hz is applied to the input, find

the noise power in the system’s output.

(15M)

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R10 SET - 1

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Code No: R21053


MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE AND ENGINEERING (Com. to CSE, IT, ECC)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Write the following statements into symbolic form and verify for the validity of

conclusion.

i) All men are mortal. ii) Socrates is a man. iii) Therefore Socrates is a mortal.

(4M)

b) Show that ￢(p ∨ (￢p ∧ q)) and ￢p ∧￢q are logically equivalent by developing a

series of logical equivalences

(5M)

Show that ∀x(P(x) ∧ Q(x)) and ∀xP(x) ∧ ∀xQ(x) are logically equivalent

(6M)

2. a) Use Fermat’s little theorem to compute 52003

mod 7, 52003

mod 11, and 52003

mod 13. (8M)

b) Construct a formula for the sum of the first n positive odd integers. Then prove your

conjecture using mathematical induction.

(7M)

3. a) Draw Venn diagrams for each of these combinations of the sets A, B, C, and D.

i) (A ∩ B) ∪ (C ∩ D) ii) A ∪ B ∪ C ∪ D iii) A − (B ∩ C ∩ D

(9M)

b) Let A = a, b, c, B = x, y, and C = 0, 1. Find i) A × B × C. ii) C × B × A.

(6M)

4. a) Find the adjacency matrix and incidence matrix for Km,n, Kn? (8M)

b) Show that a graph G is self complementary if it has 4n or 4n+1 vertices (n is non

negative integer).

(7M)

5. a) Find the number of edges in the following trees: i) tree with 10,000 vertices

ii) full binary tree with 1000 internal vertices iii) full 3-ary tree with 100 vertices

(8M)

b) What is the Chromatic number of Kn and Cn? Color K5 and C5 graphs?

(7M)

6. a) Define the terms with examples: Group, Abelian Group, Semi Group, Monoid (8M)

b) Show that set G = 1, 2, 3, 4, 5 is not a group under addition and multiplication

modulo 6.

(7M)

7. a) Suppose that there are 1807 freshmen at your school. Of these, 453 are taking a

course in computer science, 567 are taking a course in mathematics, and 299 are

taking courses in both computer science and mathematics. How many are not taking

a course either in computer science or in mathematics?

(8M)

b) Describe the circular permutation. Find the number of circular 3 – permutations of 5

people

(7M)

8. a) What is the solution of the recurrence relation an = 6an−1 − 9an−2 with initial conditions

a0 = 1 and a1 = 6?

(8M)

b) Solve the recurrence relation using generating function

an - 6an-1 = 0 for n ≥ 1 and a0 = 1

(7M)

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R10 SET - 1

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Code No: X0225


ELECTRO MAGNETIC FIELDS (Electrical and Electronics Engineering)




~~~~~~~~~~~~~~~~~~~~~~~~~

1. a) Obtain the expression for electric field intensity on the axis of a uniformly charged

circular disc.

b) Derive the relation between potential and electric field intensity.

2. a) Derive an expression for electric field intensity due to an electric dipole.

b) Given the potential filed, V = (50 Sin θ/r) V, in free space, determine whether

satisfies Laplace’s equation.

3. a) Drive an expression for energy stored and energy density in an Electrostatic field

b) Derive the boundary conditions at the interface between two perfect dielectrics.

4. Derive the expressions for magnetic field intensity and magnetic flux density due

to circular coil.

5. a) i) A very long and thin, straight wire located along the z-axis carries a current I in

the Z-axis direction. Find the magnetic field intensity at any point in free space

using Ampere’s law

b) Prove the Maxwell’s equation from Ampere’s law

6. a) An iron ring with a cross sectional area of 3 cm square and mean circumference of

15cm is wound with 250 turns wire carrying a current of 0.3A. A relative

permeability of ring is 1500. Calculate the flux established in the ring

b) Derive an expression for a torque on a closed rectangular loop carrying current ‘I’.

7. a) A solenoid is 50 cm long, 2 cm in diameter and contains 1500 turns. The

cylindrical core has a diameter of 2 cm and a relative permeability of 75. This is

coil is co-axial with a second solenoid, also 50 cm long, but 3 cm diameter and

1200 turns. Calculate ‘L’ for the inner solenoid and L for the outer solenoid.

b) Obtain an expression for energy density in inductor

8. a) State and prove poynting theorem.

b) State Maxwell‟s equation for static fields. Explain how they are modified for time

varying electric and magnetic fields.

1 of 1

R07 SET - 1

code no: rt21013 r13 set - 1 ii b. tech i semester regular examinations, dec - 2015€¦ · ·...

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