Question Paper Code :ABS11T08
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
MATHEMATICS-II
(Common for All Branches)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
Unit – I
1
a)
Find the rank of the matrix A=
 2 −2 0

4 2 0
 1 −1 0

 1 −2 1
6

2
by reducing it into canonical form.
3

2
b) Find the characteristic polynomial of the matrix
a)
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Verify Cayley- Hamiltons theorem and hence find A – 1
A=
2
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Prove that the following set of equations are consistent and solve them
3x + 3y + 2z = 1 , x + 2 y = 4 , 10 y + 3 z = – 2 , 2 x – 3 y – z = 5
b) Find the matrix P which transforms the matrix A =
to diagonal form
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and hence calculate A4 .
3
a)
Unit – II
Show that the Eigen values of a Skew- Hermitian Matrix are either zero or purely
imaginary.
b) Find the nature of the quadratic form, index and signature of
10 x 2 + 2 y 2 + 5 z 2 – 4 xy – 10 xz + 6 yz by reducing it into sum of squares.
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4
5
a)
Find the Eigen values and Eigen vectors of the Matrix A=
b) Reduce the Quadratic Form 7 x 2 + 6 y 2 + 5 z 2 – 4 xy – 4 yz into canonical form.
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Unit – III
Form the partial differential equation by eliminating the arbitrary function f from
z = f( x2 - y 2) . State the details pertaining to type ,linearity etc., of the equation
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a)
b)
Solve
6
a)
∂3 z
+ 18 x y 2 + Sin ( 2x-y) = 0
2
∂x ∂y
Form the partial differential equation by eliminating the arbitrary function f from
x2 + y2 + z2 = f( xy )
b) Find the general solution of the partial differential equation ( y + z) p +(z + x) q = x + y
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Cont..2
::2::
Unit – IV
7
a)
Expand f(x) =
1
(π − x ) as a Fourier series with period 2π , to be valid in the interval
2
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0 to 2π .
x<0
0

b) Find Fourier integral representation of the function f(x) = 1 0 ≤ x ≤ 1 Hence show
0
x >1

π
x
Sin( )
2
∫0 x dx =
2
that
8
a)
π
2
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.
Expand f(x) = x sin x as a Fourier cosine series in the range 0 < x < π . Reduce that
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1 1
1
1
π
+
−
+
− ..... =
2 1.3 3.5 5.7
4.
Find Complex form of Fourier representation for the function f(x) =
b)
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 x , -π < x < π 

.
 0, elsewhere. 
Unit – V
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9
a)
Find the Fourier transform of f(x) defined by f(x) = x if |x| ≤ a
0 if |x| > a
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b) Find the Fourier cosine transform of f(x) defined by f(x) = x
, 0<x<1
2–x , 1<x<2
0
, x > 2
10

z

Evaluate Z – 1  2

 z + 11z + 24 
b) Solve the difference equation using z-transforms:
u n+2 – 3 u n+1 + 2 un = 0 given that u0 = 0 and u1 = 1.
a)
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Question Paper Code :ABS11T02
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
ENGINEERING PHYSICS
(Common for Computer Science and Engineering, Information Technology, Electronics and Communication
Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
4
Unit – I
What is cohesive energy? With the help of a suitable model for inter atomic forces
derive an expression for the cohesive energy.
b) Distinguish between hydrogen and Vander Waals bondings in solids.
a) Show that FCC is the most closely packed out of the three types cubic structures by
working out the packing factors.
b) Describe the crystal structure of CsCl.
a)
Unit – II
a) Derive Bragg’s law of X-ray diffraction.
b) Describe with suitable diagram, the powder method of determination of crystal
structure
a) What are nano materials? Explain how the reduction in size effects the properties of
materials.
b) Discuss any four applications of nano materials in detail.
5
a)
6
b)
a)
b)
7
a)
b)
8
a)
b)
9
a)
10
Unit – III
What is Debroglie’s hypothesis. Show that Debroglie wavelength of an electron
accelerated with a potential difference of V volt is λ = ( 1.227/ v ) nm.
Describe an experiment to verify the dual nature of matter wave with a neat diagram.
Explain the salient features of Kronig - penny model.
Explain the classification of solids into metals, semiconductors and insulators based on
the band theory with neat diagrams.
Unit – IV
Define electric polarization. Explain various types of polarizations in dielectrics.
A parallel plate capacitor of area 650mm2 and a plate separation of 4 mm has a charge
of 2X10-10 C on it. When a material of dielectric constant 3.5 is inserted between the
plates. Find the resultant voltage across the capacitor.
Explain the origin of magnetic moment at the atomic level.
Explain Meissner effect.
Unit – V
How is a metastable state different from short lived state in excited atoms? Explain the
necessity of metastable state in production of lasers.
b) Explain the emission of laser light with a three level energy diagram.
c) Discuss in detail about the functioning of a He-Ne laser.
a) Derive expressions for
i. acceptance angle and the
ii. numerical aperture of an optical fibre
b) Discuss the applications of optical fibres in various fields.
c) Calculate the numerical aperture and acceptance angle of an optical fibre with core and
cladding indices 1.55 and 1.50.
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Question Paper Code :AHS11T01
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
TECHNICAL ENGLISH
(Common for Electrical and Electronics Engineering, Mechanical Engineering, Aeronautical Engineering,
Civil Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
4
a)
Unit – I
childhood
Give details of C.V.Raman’s
and his academic achievements
up to post graduation.
b) Read the following short paragraph and fill in the blanks with suitable ‘Articles’ (A, An,
The) :Sometime later, Raman took up __1__ directorship of Indian Institute of Science, in
Bangalore, where he stayed until he retired in 1948. He gave equal time to research
and organizational work there. He did __2___ lot of important research and nurtured
many good students during his time there. Though his tenure was not without
controversy, he never gave in to __3__ temptation of leaving ___4____ country for
__5__ better life.
a) Enumerate the services Mother Teresa rendered as a Humanitarian.
b) Add negative ‘pre- fix’ to the following words. Each question carries one mark.
i. Sufficient
ii. Proportion
iii. Reasonable
iv. Partial
v. Similar
Unit – II
a) Do you think the title ‘Connoisseur’ is apt for the story? Give reasons.
b) Do as directed:
i. Write the antonym of the word: Reveal
ii. Write the synonym of the word: Immaculate
iii. Write one word substitute: One who goes on foot
iv. Use this idiom/phrasal verb in your own sentence: knock down
v. Correct the sentence: They has misunderstood my letter.
a) “Success of third millennium generation depends on excellent communication skills”
Substantiate the statement with reference to Telecom as one of the mediums for
communication system.
b) Do as directed:
i. Choose appropriate word: The Sun is ----- (stationary/stationery).
ii. Write one word substitute: Rule by officials
iii. Write the antonym of the word: Give up
iv. Write the synonym of the word: Lament
v. Choose the appropriate verb: Lily practice/practices dance every day.
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Cont...2
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5
6
7
8
9
10
Unit – III
What was the secret promise the writer made to himself before he left the village,
hamlet of Chachuran?
b) Do as directed:
i. Write the antonym of the word: latter
ii. Write the synonym of the word: countenance
iii. Write one word substitute: murder of a mother
iv. Use this idiom in your own sentence: A man of letters
v. Correct the sentence: The churches here are many centuries old.
a) Give an account of Martin Luther King’s dream?
b) Do as directed:
i. Write the antonym of the word: diffidence
ii. Write the synonym of the word: indigenous
iii. Write one word substitute: belief that there is no God
iv. Arrange the jumbled sentences: while living among them/ I was/ and help the
poor/ to leave the convent.
v. Use the suitable verb: The theme of the drama ---------(reflect/reflects) our
culture.
a)
Unit – IV
Assume that you are the Branch Manager of an organization. Draft a Memo to an
employee asking for explanation for going on leave without prior permission.
b) Write a letter to the Personnel Manager of an organization thanking him for the offer
of appointment as a management trainee and confirming your acceptance of the
offer.
a) Write a letter of complaint to the General Manager of the BSNL for delay in providing
Broadband Internet connection to your house.
b) Draft a job application letter for the post of Software Programmer in AccudocInfotech Limited Bangalore. Give a brief profile of your professional qualifications and
experience.
a)
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Unit – V
Imagine that you are an officer in Meghalaya Forest Department. The Secretary of the 15M
department has asked you to report on the steps taken in the previous year to conserve the
forests in and around Shillong. Write a report presenting the facts and making
recommendations.
The Principal of a college has appointed a committee of two teachers and three students to 15M
suggest new directions in which student’s co-curricular and extra-curricular activities can be
developed. Write the Committee’s report.
Question Paper Code :ABS11T03
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
ENGINEERING CHEMISTRY
(Common for Computer Science and Engineering, Information Technology, Electronics and Communication
Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
4
5
6
7
8
9
10
Unit – I
Describe the construction of a lead – acid storage cell with the help of a neat diagram
and chemical equations.
b) Explain the function of a Hydrogen – Oxygen Fuel Cell
a) Write a note on Nickel – Cadmium cell
b) Calculate the EMF of a concentration cell at 250C consisting of two zinc electrodes
immersed in solutions of Zn2+ ions of 0.2M and 0.02M concentrations.
a)
a)
b)
a)
b)
Unit – II
Write explanatory notes a Internal Conditioning Method
Explain the Zeolite process of Softening of water
What is desalination? Describe the desalination of sea water by electro dialysis
Describe how hardness of water determined by EDTA complexometric method
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Unit – III
a) Differentiate between thermoplastics and thermosetting series.
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b) Write preparation, properties and applications of
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(i) Teflon
(ii) Buna – N
(iii) Nylons
a) What is an adsorption isotherm? Derive an expression for Langmuir adsorption 8M
isotherm. Mention its limitations?
b) Describe the compounding of a plastic material
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Unit – IV
a) Describe how the proximate analysis of coal carried out?
b) Explain the refining of petroleum. Give the details of important fractions
a) Discuss the relative merits and demerits of solid, liquid and gaseous fuels
b) What is combustion? Find the weight and volume of air required for the complete
combustion of 1 kg of a fuel.
a)
b)
a)
b)
Unit – V
Describe the manufacture of portland cement with a neat diagram
Explain the phase diagram of lead silver system
What is a lubricant? Explain the main functions of a lubricant
Explain the following characteristics of a good refractory
(i) Refractoriness
(ii) Thermal spalling
(iii) Dimensional stability
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Question Paper Code :ABS11T04
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
ENVIRONMENTAL SCIENCE
(Common for Electrical and Electronics Engineering, Civil Engineering, Mechanical Engineering,
Aeronautical Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
4
5
6
Unit – I
Explain the different areas of environmental conservation to which people belonging to
different disciplines can contribute.
b) Define natural resources. How will you classify natural resources? Explain major reasons
of the resource depletion.
a) Show that agricultural practices implemented to increase the field from the land lead to
the formation of unproductive land.
b) Explain the difference in consumption of resources by the countries of the developing
and developed world.
a)
a)
b)
a)
b)
Unit – II
Discuss about the energy flow in the ecosystem
Discuss about ecological succession
What are the major hot spots of biodiversity in our country?
What do you understand by the term biodiversity? Write briefly about different kinds
of diversity in organisms
Unit – III
a) Describe the sources, effects and methods for control of Thermal pollution.
b) Write about causes, effects and control measures of urban wastes.
a) What is sustainable development? What are the key aspects of sustainable
development?
b) Discuss various measures of sustainable development.
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8
Unit – IV
Green environmental issues like clean development mechanism, carbon credits and carbon 15M
foot printing are involved in protecting the environment. Elaborate them with examples.
a) With suitable example discuss on the role of information technology in protecting the
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environment and human health from the pollution and natural disaster.
b) Discuss the scope, concepts, benefits and status of ISO 14000 series of environmental
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management standards.
9
a)
7
10
Unit – V
“People have no faith in Pollution Control Boards in the Protection of environment"
Discuss.
b) Write the importance of Environmental Protection laws in protecting air, water, forests
and wild life
a) What are the major limitations to successful implementation of our environmental
legislation?
b) Write an account on the objectives, key elements and methods involved in
environmental impact assessment with an example.
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Question Paper Code :ACS11T01
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
COMPUTER PROGRAMMING
(Common for Mechanical Engineering, Aeronautical Engineering and Civil Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
4
5
6
7
8
9
10
Unit – I
a) Define flowchart? Mention the different types of symbols used in writing a flow chart.
b) Mention and define any four system softwares
a) Define an algorithm? Write an algorithm to find the biggest of given three
numbers?
b) Explain the information processing cycle in the computer in detail?
Unit – II
In what way ’if statement’ is different from switch statement? Write a program using
Switch statement to manipulate student grade system.
Note: Read M1, M2, M3 subjects and find average and divide grades based on that.
b) How multidimensional array is passed to function , how are the formal argument
declaration written?
a) What is a function? What are the different types of functions? Explain function with no
argument and no return type with an example.
b) Explain how matrices can be represented using two dimensional arrays. Explain with
code how Transpose of a matrix can be done
a)
Unit – III
Explain how strings are declared and initialized in ‘C’?
What is void pointer? Explain with example.
What is pointer? Write a c program to read one two dimensional matrix using pointers.
Write a c program to find given string is palindrome or not without using string library
string.
b) What are the arithmetic operators that are permitted on pointers?
c) Write about dynamic memory allocation functions.
a)
b)
c)
a)
a)
b)
a)
b)
Unit – IV
What is a structure? Explain how to define and initialize the structure?
Write short notes on pointer to structures?
Illustrate the working of array of structure with an example?
What is a union? Write a program in C to demonstrate the use on unions in structures?
Unit – V
a) What is a file? What are the different types files? Explain the possible modes of opening
binary files?
b) Write c program to reverse the first n characters in given file.
c) Explain the general format of fseek() function with illustrative examples?
a) Explain the possible modes of opening text files? In all these modes what happens when
the file doesn’t exist and the file already exists?
b) Write a c program to find whether given file is palindrome or not.
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Question Paper Code :ACS11T02
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
DATA STRUCTURES THROUGH C
(Common for Computer Science and Engineering, Information Technology, Electrical and Electronics
Engineering, Electronics and Communication Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
Unit – I
a) State the various methodologies for analyzing the algorithms.
b) Code a recursive algorithm in C to compute the product of two positive integers m and
n using only addition.
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a)
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Code in C, for performing find all elements (k) in a tree and show that its run time O
(log n +s), where n is the number of elements in the tree and s is the number of items
returned in the search.
b) Write a function in C, that tests whether given two arrays of same size contain same
data. The function should return true if all the data is same, false even if one element is
different.
Unit – II
Write the procedure and sort the following sequence using
i. Selection Sort
ii. Radix Sort
Sequence: S Y E U Q T S A O D N I E B V C
4
Explain in detail about Merge Sort and derive the best and worst case complexities. Apply
the merge sort to the following sequence:
44 66 -88 77 55 -33 22 99 0 11 88 33 -99 -22 -77
5
a)
6
Unit – III
Consider the following arithmetic expressions,
i. A+B-C+D
ii. A%B*C/D
Construct a linked-list version of stack and convert the expressions into postfix.
b) Write a single function that initializes pushes and pops values from a fixed size stack.
a)
Consider the code:
int vals[5] = {10, 20, 30, 40, 50};
int *ptr;
ptr = vals;
Write a function to simulate operations of queue on the ptr.
b) Consider the code:
char *pStr = (char*) malloc(512);
Write a function to make use of the above code and initialize the compartments of a
queue.
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Cont…2
:: 2 ::
7
Unit – IV
Convert the following message into the nodes of the linked-list and sort the elements.
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Memory errors can be broadly classified into Heap Memory Errors and Stack Memory Errors.
8
9
10
a)
Perform arithmetic operation on two binary numbers of 8-bits percolating the addition 8M
of carry from right to left bits. Use linked-list to store the bits of the two binary
numbers and calculate the sum.
b) Write a program to construct the circular-doubly-linked-list of nnn nodes with names of 7M
people and pick a name randomly asking the position of any person, where the input
integer is mandatorily of 3 digits, if the input over boards get an appropriate integer in
the cycle corresponding to the position in the list.
Unit – V
a) What are the properties of binary tree? With an example, how do you represent the
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binary tree using an array?
b) Construct a binary tree for the post order and in order sequences of a binary tree given. 7M
Pre order : H, D, B, A, C, F, E, G, L, J, I, K, N, M, O
Post order : A, C, B, E, G, F, D, I, K, J, M, O, N, L, H
Write a ‘C’ program to implement BFS traversal for given graph. Consider the following 15M
cyclic digraph. Assume the adjacency list is in sorted order: for example, when iterating
through the edges pointing from 0, consider the edge 0→1 before 0→6 or 0→7.
Compute the topological order by running the DFS-based algorithm and listing the vertices
in reverse post order.
Question Paper Code :AEE11T01
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
BASIC ELECTRICAL ENGINEERING
(Common for Computer Science and Engineering and Information Technology)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
Unit – I
a) Write short notes on independent and dependent sources.
b) For the circuit shown in fig. 1 below, determine the current through 6 ohms resistor
and the power supplied by the current source.
Fig. 1
a) State and explain the Krichoff’s current law with example.
b) Write Voltage – Current relationship in inductor and capacitor
c) Find the equivalent resistance across A – B of the circuit shown in Fig. 2
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Fig. 2
3
Unit – II
Derive necessary equations for converting a delta network into a equivalent star
network
b) In the figure 3, find the value of K that will cause VY to be zero. Use nodal analysis.
a)
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Fig. 3
Cont…2
4
:: 2 ::
a) Explain the procedure with an example to solve a network using nodal equation by
inspection.
b) Use mesh analysis to find current I in the circuit shown figure 4.
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Fig. 4
5
6
Unit – III
a) Find the form factor and peak factor of the half wave rectified sine wave.
b) A voltage of 200 V at 50 Hz is applied across RLC series circuit, comprising of 15 Ω
resistance, 0.25H inductance and 122 µ F capacitance. Determine
(i) Impedance (ii) Current (iii) power factor and (iv) power in watts.
a)
In a circuit shown figure 5, if the value of R=L/C, then prove that the impedance of
entire circuit is equal to R only and is independent of frequency of supply. Find the
value of impedance for L=0.02 H and C=100 µ F.
Fig. 5
b) A parallel circuit shown figure 6 below has a total power 2000 W. Obtain the complete
power triangle.
Fig. 6
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7
8
Unit – IV
a) Explain (i) Coefficient coupling (ii) Dot rule
b) Two coils with inductances in the ratio of 5:1 have a coupling co-efficient K=0.5. When
these coils are connected in series aiding, the equivalent inductance is 44.4 mH. Find
L1, L2 and M.
a)
Define
(i) Self induced emf
(ii) self inductance
(iii) Mutually induced emf
(iv) Mutual inductance
b) In the Figure 8, find the voltage drop across the capacitor and the resistor.
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Fig. 7
9
Unit – V
a) Explain the properties of cut set matrix
b) Draw the oriented graph and develop the fundamental loop matrix of the network
shown in figure 8
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fig. 8
10
a)
Derive the relation:
i) Z in terms of Y
ii) h – parameters in terms of Z
b) Find the Z – parameters of the network shown in fig. 9
Fig. 9
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Question Paper Code :AEE11T02
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
BASIC ELECTRICAL AND ELECTRONICS ENGINEERING
(Common for Civil Engineering, Mechanical Engineering and Aeronautical Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
Unit – I
a) Explain briefly about i) Conductors ii) Semiconductors iii) Insulators
b) A conductor of length 2Km and resistivity of 3X10-8Ω- m is transmitting a current of
300A.Calculate its cross sectional area if the total voltage drop in the conductor should
not exceed 30V.
a)
Determine the total amount of power in the series circuit shown in figure 1
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Fig. 1
b) Explain and differentiate the types of Induced E.M.F’s
3
4
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Unit – II
Define
i. Average value
ii. RMS value
iii. Form Factor
iv. Crest Factor
b) Find the Form factor and Crest factor of the following wave forms
a)
a)
Explain
i.
ii.
iii.
iv.
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Apparent Power
Active Power
Reactive Power
Complex Power
Cont…2
:: 2 ::
b) A pure resistance of 50Ω is connected in series with a capacitor of 100µF across a 230V,
50Hz supply. Find the
i. Current
i. Power Factor
ii. Impedance
iii. Voltage across resistor
iv. Voltage across capacitor
v. Active Power
vi. Reactive Power
5
6
7
8
Unit – III
State Maximum power transfer theorem. Derive the expression for Maximum power
transferred to the load, in case of DC excitation.
b) Solve the voltage ‘V’ in the figure 2, using super position theorem. Verify the result
using nodal analysis
a)
Fig. 2
Derive the expression for the deflection in an electrostatic deflection system. Hence obtain
the expression for electrostatic deflection sensitivity
Unit – IV
Draw the circuit diagram of a full wave rectifier with centre tap connection and bridge
connection, and explain its operation.
a) Explain the volt-ampere characteristics of PN junction diode.
b) Draw the circuit diagram of half wave rectifier and explain its operation
Unit – V
a) Explain the operation of PNP transistor.
b) What is early effect? What are its consequences?
10 a) Explain the functioning of BJT in CB configuration. Also draw its input & output
characteristics
b) Compare CB, CE, CC configurations.
9
7M
8M
7M
15M
15M
7M
8M
8M
7M
9M
6M
Question Paper Code :ABS11T05
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
PROBABILITY, STATISTICS AND COMPUTATIONAL TECHNIQUES
(Electrical and Electronics Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
4
Unit – I
According to a particular survey 14.9% of those who have received a doctor’s degree in
engineering are blacks. Suppose that 6 people who have received their doctor’s degree
in engineering are randomly selected, find the probability that
i) exactly 2 are black
ii) At least two are black
iii) At most two are black
iv) None is a black
b) The weight of an electronic component is normally distributed with a mean of 6 ounces
and standard deviation of 0.25 ounce.
i)
find the probability that the electronic component weighs more than 6.5
ounces.
ii)
what must be the standard deviation of weight be in order for the company
to state that 99.9%of its electronic components are less than 6.5 ounces.
iii)
If the standard deviation stays at 0.25ounces, what must be the mean weight in
order for the company to state that 99.9% of its electronic components are less
than 6.5 ounces?
a)
a)
The diameter of a metal shaft for a precision instrument is assumed to be normally
distributed with a mean of 0.5mm and a standard deviation of 0.025 mm.
What is the probability that shaft diameter is greater than 0.31 mm?
What is the probability that shaft diameter is between 0.235 & 0.315 mm?
b) Show that the mean and standard deviation for Poisson distribution are identical.
Unit – II
A random sample of size 100 has a standard deviation of 5. What can you say about the
maximum error with 95% confidence.
b) A sample poll of 300 voters from district A and 200 voters of district B showed that 56%
and 48% were in favour of a given candidate. At 5% level of significance, test the
hypothesis that there is a difference in districts.
a)
a)
A sample of 64 students have a mean weight of 70 kgs. Can this be regarded as a
sample from a population with mean 65 kgs and standard deviation of 25kgs.
b) Two random samples gave the following results the nicotine contents in milligrams in
two samples of tobacco.
Sample
size
sample mean sum of squares of deviation
1
10
15
90
2
12
14
108
Test whether the samples came from the normal population.
Cont…2
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8M
7M
8M
7M
8M
7M
8M
:: 2 ::
5
Unit – III
a) Find the real root for x3-x-4=0, using False position.
b) From the following table find
x
y
6
8
9
10
1
2
7.4036 7.7815
3
4
8.1291 8.4510
5
6
8.7506 9.0309
a) Find the real root for
using Newton Raphson method.
b) Find y(1.6) using Newton’s forward difference formula from the table
x
y
7
0
6.9897
7M
8M
1
3.49
1.4
4.82
1.8
5.96
7M
8M
2.2
6.5
Unit – IV
a) Fit a least square straight line to the following data.
x:
2
7
9
1
5
12
y:
13
21
23
14
15
21
b) A river is 80 feet wide. The depth d in feet at a distance x feet from one bank is given by
x:
0
10
20
30
40
50
60
70
80
d:
0
4
7
9
12
15
14
8
3
a)
Fit a least square quadratic curve to the following data
x:
1
2
3
4
y:
1.7
1.8
2.3
3.2
b) Evaluate by Simpson’s 3/8th rule.
Unit – V
Use Milne’s method to find y(0.8) and y(0.1) from
y(0.2), y(0.4) and y(0.6) from Runge-Kutta method
7M
8M
8M
7M
y(0)=0. Find the initial values
a) Solve
for x=0.4given that y=0 at x=0 using Taylor’s series method
b) Using Euler’s method solve for y at x=2 from
y(1)=1 taking h=0.5
15M
7M
8M
Question Paper Code :ABS11T06
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
COMPUTATIONAL TECHNIQUES
(Electronics and Communication Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
1
2
3
Unit – I
Using Newton – Raphson method, find the real root of the equation x log10 x =1.2
correct to 4 decimal places.
b) Solve the following system of equations by Gauss-Jacobi’s method (Carry out 4
Iterations)
8x – 3y + 2z = 20
4x + 11y – z = 33
6x + 3y + 12z = 35
a)
Use the Regula-Falsi method to find a real root of the equation x3 – 2x – 5 = 0 correct to
three decimal places.
b) Solve the following system of equations by Gausi-Seidel method to obtain the solution
correct to three places of decimal.
x + y + 54z = 110
27x + 6y – z = 85
6x + 15y + 2z = 72
a)
a)
Unit – II
Find the interpolating polynomial f(x) for the following data
7M
8M
7M
8M
7M
x
0 2 4
6
8
10
y=f(x) 0 4 56 204 496 980
b) The following table gives distances in miles of the variable horizon for the given heights
in feet above earth’s surface
8M
x
200
250
300 350 400
y=f(x) 15.04 16.81 18.42 19.9 21.27
Find y for x = 218
4
a)
The area of a circle (A) corresponding to diameter (D) is given below:
7M
D 80
85
90
95
100
A 5026 5674 6362 7088 7854
Find the area corresponding to diameter 105 using an appropriate interpolation
formula.
b) Use Lagrange’s interpolation formula to find f(4) given
8M
x
0 2 3
6
y=f(x) -4 2 14 158
Cont…2
:: 2 ::
Unit – III
5
a)
Evaluate
2
∫0
7M
e − x dx using Simpson’s rule taking h= 0.25
2
b) Fit a straight line of the form y=a+bx for the following data
8M
X 0 5 10 15 20 25
y 12 15 17 22 24 30
6
a)
Fit a second degree polynomial to the following data by the method of least squares
7M
X 0 1
2
3
4
y 1 1.8 1.3 2.5 6.3
2
b) Find dy , d y at x=1.5 for the following data
2
8M
dx dx
X 1.5 2.0
2.5
3.0
3.5
4.0
y 3.375 7.0 13.625 24.0 38.875 59.0
Unit – IV
7
Tabulate y(0.1),y(0.2) and y(0.3) using Taylor’s series method given that
dy 2
= y + x and
dx
15M
y(0)=1
8
a)
Find the value of y for x=0.4 by Picard’s method given that
dy 2
= y + x 2 , y(0) = 0
dx
b) Given y' = x + sin y , y ( 0 ) =1 . Compute y(0.2) and y(0.4) with h=0.2 using Euler’s
8M
7M
modified method.
9
Unit – V
Given the values of u(x, y) on the boundary of the square in the fig below, evaluate the
function u(x, y) satisfying the Laplace equation
15M
∂ u ∂u
+
= 0 at the pivotal points of
∂x 2 ∂y 2
2
2
this figure
10
∂u ∂ 2 u
Solve the equation
=
subject to the conditions u(x, 0) = sin πx, o≤ x ≤1;
∂t ∂x 2
u(0,t) = u(1,t) = 0. Carry out computations for two levels, taking h=1/3, k=1/36.
15M
Question Paper Code :AME11L03
VARDHAMAN COLLEGE OF ENGINEERING
(AUTONOMOUS)
Four Year B. Tech II Semester Regular Examinations July - 2012
(Regulations: VCE-R11)
ADVANCED ENGINEERING DRAWING
(Common for Civil Engineering, Mechanical Engineering, Aeronautical Engineering)
Time: 3 hours
Max Marks: 75
Answer ONE question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
---------------------------------------------------------------------------------------------------------------------------Unit – I
1
Draw the projections of a regular pentagon of 40 mm side, having its surface inclined at 30o 15M
to V.P and the side on which it rests on V.P, making an angle of 60o with H.P. Use auxiliary
plane method.
2
3
4
5
6
A cone of base 50 mm diameter and altitude 60mm is lying on one of its generators on H.P,
such that the top view of its axis makes an angle of 30o with reference line-xy. Draw its
projections using auxiliary plane method.
15M
Unit – II
A cube of 30mm edge, rests on one of its corners on H.P. such that, an edge containing this 15M
corner is inclined at 600 to H.P. and parallel to V.P. The other two edges passing through
that corner are equally inclined to H.P. Draw the projections of the cube.
A lamp shade is in the form of cone, the ends of which are 80mm and 160mm diameter and 15M
the vertical height is 150mm. It rests on H.P., on a point of its large end, with axis inclined at
400 to H.P. and 300 to V.P. The smaller end of the shade is nearer to V.P. Draw the
projections of the shade.
Unit – III
A vertical cylinder of 60 mm diameter, is penetrated by another cylinder of 45 mm diameter. 15M
The axes of the two cylinders are intersecting at right angles. Draw the projections of the
two
cylinders, showing the lines(curves) of intersection.
The pictorial view of an object is shown in figure-1. Draw its front, top and one of the profile 15M
views using first angle projection. All dimensions are in mm.
Figure-1
Cont…2
7
8
:: 2 ::
Unit – IV
Draw the isometric view of the object whose orthographic projections are as shown in figure
below. All dimensions are in mm
Draw the isometric view of the object whose orthographic projections as shown in figure
below. All dimensions are in mm.
15M
15M
Cont…3
:: 3::
9
10
Unit – V
A cube of 50mm edge, is resting on H.P. with a vertical face inclined at 300 to V.P. it is cut by 15M
a section plane parallel to V.P. and 10mm away from the axis. Draw its sectional front view.
A rectangular pyramid of base 30mm x 20mm and 45mm height, rests with its base on the 15M
ground. One of the longer edge of the base is parallel to P.P and 30mm behind it. The
station point is 50mm in front of P.P and 25mm to the left of the axis of the solid and 50mm
above the ground. Draw the perspective projection.