(fx ) - · PDF file... Express 2x +2x+ into Factorial Notation. (l) ... Write a program to convert an infix expression to postfix expression. (b) ... E A C K F H D B G

(DCS/DIT 211)

B.Tech. DEGREE EXAMINATION, MAY 2012.

(Examination at the end of Second Year)

Computer Science and IT

Paper I — MATHEMATICS – III

Time : Three hours Maximum : 75 marks

Answer Question No. 1 Compulsorily. (15 × 1 = 15)

Answer ONE question from each Unit. (4 × 15 = 60)

1. Write short notes on the following :

(a) State the Fourier conditions for a Fourier expansion.

(b) Find the Fourier series of ( ) xxf = in ππ <<− x .

(c) Write the Half-Range Fourier sine series and Half-Range Fourier cosine series.

(d) Find nb in the Fourier series of ( ) xxf = in ( )ππ ,− .

(e) Find the Finite Fourier Transform of ( ) xxf = in ( )l,0 .

(f) State the convolution theorem for Fourier Transform.

(g) State the shifting property for Fourier Transform.

(h) If 20 =y , 41 =y , 82 =y , 324 =y . Find 3y .

(i) If 22 xUE x = and 1=h . Find xU .

(j) Find xeE

∆2

.

(k) Express 222 ++ xx into Factorial Notation.

(l) State Simpson’s th

8

3Rule.

(m) Why Runge-Kutta method is better than Taylor’s series method?

(n) Write the Taylor’s series for solution of first order ordinary differential equation.

(o) Write the Newton’s Backward difference formula.

UNIT I

2. (a) Find the Fourier series to represent 2xx − from π−=x to π=x .

(b) Find the Half-Range cosine series for the function ( ) ( )21−= xxf in the interval

lx <<0 . Hence deduce that

+++= L222

2

5

1

3

1

1

18π .

Or

(c) Expand ( )

<<−

<<−=

12

1,

4

32

10,

4

1

xx

xxxf as the Fourier series of sine terms.

(d) Find the complex form of the Fourier series of ( ) xexf −= in 11 ≤≤− x .

UNIT II

3. (a) Find the Fourier cosine transform of ( )21

1

xxf

+= . Hence derive the Fourier sine

transform of ( )21 x

xx

+=φ .

(b) Find by Newton’s method, the real root of the equation 1cos3 += xx .

Or

(c) Express ( )

>

≤≤=

π

π

x

xxf

,0

0,1 as a Fourier sine integral and hence evaluate

( ) ( ) λλλ

λπdxsin

cos1

0

∫∞

−.

(d) Apply Gauss-Seidal Iteration method to solve the equation 17220 =−+ zyx ;

18203 −=−+ zyx ; 252032 =+− zyx .

UNIT III

4. (a) Given the following tabular data. Evaluate ( )9f using Newton’s divided difference

formula

x : 5 7 11 13 17

( )xf : 150 392 1452 2366 5202

(b) Find the missing values in the following table :

x : 45 50 55 60 65

( )xf : 3.0 – 2.0 – –2.4

Or

(c) Use Stirling Formula to evaluate tan 16°, given the following data :

θ : 0° 5° 10° 15° 20° 25°

tan θ : 0 0.0875 0.1763 0.2679 0.3640 0.4663

(d) Certain corresponding values of x and x10log are given below :

x : 300 304 3005 307

x10log : 2.4771 2.4829 2.4843 2.4871

Find 310log10 by Lagrange’s formula.

UNIT IV

5. (a) A solid of revolution is formed by rotating about the X-axis, the area between the

X-axis, the lines 0=x and 1=x and a curve through the points with the following

co-ordinates.

x : 0.00 0.25 0.50 0.75 1.00

y : 1.0000 0.9896 0.9589 0.9089 0.8415

Estimate the volume of the solid formed using Simpson’s rule.

(b) Using the Runge-Kutta method of Fourth order, compute ( )2.0y and ( )4.0y from

2210 yxdx

dy+= ; ( ) 10 =y by taking 2.0=h .

Or

(c) Using modified Euler’s method, find an approximate value of ‘y’ when 3.0=x ,

given that yxdx

dy+= and 1=y when 0=x .

(d) Using Picard’s process of successive approximation, find the value of ‘y’ for 1.0=x ,

xy

xy

dx

dy

+−

= , ( ) 10 =y .

————————

(DCS/DIT 212)




Paper II — BASIC ELECTRONICS


Answer Question No. 1 compulsorily.

(14 × 1 = 14)

Answer ONE question from each Unit.

(4 × 14 = 56)

1. Write brief note about the following :

(a) What are semiconductor? Give examples.

(b) What is p-type semiconductor?

(c) What is fewer break down?

(d) What is forward bias and reverse bias in a PN junction?

(e) Why transistor called a current controlled device?

(f) What is stability factor?

(g) What is meant FET?

(h) What are the different types of power MOSFET?

(i) Differentiate BJT and UJT

(j) What is negative feed back?

(k) Define semitivity.

(l) Draw the equivalent circuit of crystal oscillator.

(m) Which feed back decreases the gain of the amplifier?

(n) What are the classifications of oscillator?

UNIT I

2. (a) Derive the expression for the barriers potential Vo at the Junction of a P-N diode.

(b) Explain the situation for the occurrence of the phenomenon of Avalanche

breakdown in semiconductor diodes and discuss the consequences.

(c) Draw the equivalent circuit of a semiconductor diode and briefly explain, how

diode act as a switch.

Or

3. Explain the input and output characteristics of C/E Configuration in NPN transistors.

UNIT II

4. (a) With a neat sketch explain the drain source characteristics and transfer

characteristics of enhancement type MOSFET.

(b) Why we call FET as a voltage controlled device?

Or

5. (a) Discuss the internal working phenomina of a L.C.D

(b) Explain the working and construction of a CRT with a neat sketch. Give the

detailed description of all parts in a CRT.

UNIT III

6. (a) Explain what type of feed back employed is oscillators.

(b) Draw the circuit of colpitts oscillator and explain the working of it.

(c) Give the normal frequency range of operation of colpitts oscillators.

Or

7. (a) Explain voltage series and shunt feed back amplifier an example.

(b) Explain the current series and shunt

feedback amplifier.

UNIT IV

8. (a) Explain and derive the condition for DC characteristics of an operational

amplifier.

(b) Explain about a basic differential amplifier.

Or

9. (a) Explain briefly about voltage controlled oscillator.

(b) Explain briefly about I.C. Voltage regulator.

——————————

(DCS/DIT 213)




Paper III — DIGITAL LOGIC DESIGN


Answer Question No. 1 compulsorily. (5 × 3 = 15)


1. (a) Define sequential circuit design.

(b) Explain 2's complement with example.

(c) Explain about Johnson counter.

(d) Explain PLA.

(e) Explain S:R flip flop

UNIT I

2. Explain 4-Variable k-maps with example.

Or

3. Explain about logic gates in detail.

UNIT II

4. (a) Explain Multiplexers

(b) Explain Decimal adder

Or

5. Design a 4-bit combinational circuit using ex-or gates.

UNIT III

6. Explain about SR, JK, T,flip-flops and edge-Triggered flip-flop.

Or

7. Explain about Binary counter.

UNIT IV

8. Define Memory and explain about ROMO RAM.

Or

9. Write short notes on

(a) PAL

(b) PLD

——————

(DCS/DIT 214)

B.Tech. DEGREE EXAMINATION, MAY 2012



Paper IV — DATA STRUCTURES


Answer Question No. 1 compulsorily. (1×15 = 15)


1. (a) List out and define the performance measures of an algorithm.

(b) How do you push and pop elements in a linked list?

(c) What are the advantages of double linked list over single linked list?

(d) What is ADT?

(e) Give the best, average and worst case time efficiency of quick sort.

(f) Construct expression tree for the expression A + (B – C)*D*(E + F).

(g) Give any two operations on AVL trees.

(h) What is B+ trees?

UNIT I

2. (a) Explain in detail the types of analysis that can be performed on an algorithm.

(b) Write an algorithm to perform transpose of a matrix and analyze time.

Or

3. (a) Write a program to insert an integer into sorted circular linked list of intgers?

(b) Explain various operations in double linked list.

UNIT II

4. (a) Write a program to convert an infix expression to postfix expression.

(b) What is recursion? Write a program to find the first 10 Fibonacci numbers using

Recursion.

Or

5. (a) Write a program to delimiter matching.

(b) Explain linear search and measure its complexity.

UNIT III

6. (a) Write shell sort algorithm and discuss its time complexities.

(b) Sort 18, 15, 22, 322, 319, 110, 88, 99, 212 elements using shell sort

(with shell size = 4) show all the intermediate result.

Or

7. (a) Explain about merge sort with suitable example

(b) Compare different sorting algorithm time complexities.

UNIT IV

8. (a) A binary tree has 9 nodes. The in-order and post order traversal of tree yields the

following sequence of the nodes. Draw the binary tree.

In-order: E A C K F H D B G

Post-order: F A E K C D H G B

(b) Write sort notes on AVL trees.

Or

9. Draw a binary search tree for the following input list 60, 25, 75, 15, 50, 66, 33, 44. Trace

the algorithm to delete the nodes 25, 75, 44 from the tree.

——————

(DCS 215)



Computer Science

Paper V – OBJECT ORIENTED PROGRAMMING


Answer Question No. 1 compulsory. (1 × 15 = 15)


1. (a) Define polymorphism.

(b) What is data hiding?

(c) What is use of inline function?

(d) What is purpose of this operator?

(e) Define early binding.

(f) Give the advantages of pointers.

(g) What is meant by stream?

(h) What is role of file( ) function? When do we use this function?

(i) What is an explicit constructor?

(j) What is meant by generic class?

(k) Give any two exceptions.

(l) Define template.

(m) Why does C++ have type modifiers?

(n) When do we use protected visibility specifier to a class member?

(o) What is virtual function?

UNIT I

2. What is constructor? Explain about different types of constructors. Give the limitations

of constructor.

Or

3. (a) Explain about different types of operators used in C++.

(b) Explain about friend function with suitable example.

UNIT II

4. (a) What is operator overloading? What are the rules for overloading the operators?

(b) Write a C++ program to overload the

‘==’ operator to compare two strings.

Or

5. (a) Differentiate early binding and late binding.

(b) Explain pure virtual functions with example.

UNIT III

6. What is manipulator? How to design our own manipulator? Give an example.

Or

7. (a) Differentiate procedure oriented and object oriented programming languages.

(b) What is used of new and delete operators? How these are invoked?

UNIT IV

8. What is an exception? How to handle exceptions in C++?

Or

9. (a) Explain about different string handling functions in string String class?

(b) How to create generic classes? Give the advantages of generic class.

——————

(DCS 216)



Computer Science

Paper VI — ENVIRONMENTAL STUDIES


Answer Q. No. 1 which is compulsory. (15 × 1 = 15)


1. Write brief notes on the following :

(a) Energy needs.

(b) Tribals.

(c) Mineral Resources.

(d) Food web.

(e) Wildlife Conflicts.

(f) Soil Pollution.

(g) Nuclear Hazards.

(h) Watershed Management.

(i) Acid Rain.

(j) Global warming.

(k) Waste Product.

(l) AIDS.

(m) Human Rights.

(n) Marine Pollution.

(o) Ozone Layer.

UNIT I

2. Briefly explain about water resources and their benefits.

Or

3. Critically examine the role of individuals in conservation of natural resources.

UNIT II

4. What are the features of Forest Ecosystem?

Or

5. Examine the threats to biodiversity.

UNIT III

6. Outline the causes and remedies of water pollution.

Or

7. Briefly write about Environment Protection Act.

UNIT IV

8. Suggest measures for the reduction of Population Growth in India.

Or

9. What is the relationship between Environment and Human Health?

———————–––

(DCS 221)



Computer Science

Paper I — MATHEMATICS – IV



Answer ONE question from each unit. (4 × 15 = 60)

1. (a) Write the Cauchy-Riemann equations in polar form.

(b) When do we say that a function is Harmonic? Give an example of a Harmonic

function.

(c) Show that ( ) 2zzf = is not analytic at any point.

(d) If ,log zw = find dz

dw and find where w is non-analytic.

(e) Distinguish between an isolated singularity and an essential singularity of an

analytic function.

(f) Evaluate ( )∫+

−

+i

i

dzzz

32

1

2 along the line joining the points ( ),1,1 − ( )3,2 .

(g) State Cauchy’s integral formula.

(h) State Laurent’s series.

(i) State Liouville’s theorem.

(j) Determine the poles of ( )( )izz

zf−

=2

1 and find their order.

(k) Distinguish between singular point and a regular singular point.

(l) Write the generating function for ( )xPn .

(m) Find ( )xP2 .

(n) Find ( )xJ0 .

(o) Write orthogonal property of Bessel’s function.

UNIT I

2. (a) Determine the analytic function whose real part is ( )yyyxe x 2sin2cos2 − .

(b) The necessary and sufficient condition for the derivative of the function

( ) ( ) ( )zfyxivyxuw =+= ,, to exists for all values of z in a region R are

(i) ,x

u

∂∂

,y

u

∂∂

,x

v

∂∂

y

v

∂∂

are continuous functions of x and y in R.

(ii) x

v

y

u

x

v

x

u

∂∂

−=∂∂

∂∂

=∂∂

, .

Or

3. (a) If ψφ iw += represents the complex potential for an electric field and

,22

22

yx

xyx

++−=ψ determine the function φ .

(b) If ( )zf is a regular function of z, prove that ( ) ( ) 22

2

2

2

2

4 zfzfyx

′=

∂

∂+

∂

∂.

UNIT II

4. (a) State and prove Cauchy’s theorem.

(b) Verify Cauchy’s theorem for the integral of 3z taken over the boundary of the

rectangle with vertices ii +−+− 1,1,1,1 .

Or

5. (a) State and prove Cauchy’s integral formula.

(b) Expand ( ) ( ) ( )41 22 +−=

zz

zzf for

(i) 1<z .

(ii) 21 << z .

(iii) 2>z .

UNIT III

6. (a) State and prove Residue Theorem.

(b) Use Residue theorem, to evaluate ( ) ( )∫∞

∞−++

dxxx

x

41 22

2

.

Or

7. (a) Solve in series the equation .0=+′+′′ yyxy

(b) Solve in series the equation 02

2

=− ydx

yd.

UNIT IV

8. (a) Show that ( )[ ] ( )xJxxJxdx

dn

nn

n1−= .

(b) Express 322 23 −−+ xxx in terms of Legendre’s polynomials.

Or

9. (a) Prove that

( ) ( )[ ]xJxJxdx

dnn 1+ = ( ) ( )[ ]xJxJx nn

21

2+− .

(b) Show that

( ) ( ) ( ) ( )( )( )∫

−

+ +++

=′−1

1

12

3212

121

nn

nndxxPxPx nn

——————

(DCS 222)



Computer Science

Paper II — CIRCUIT THEORY




1. (a) Define voltage.

(b) What is an energy?

(c) What is an electrical network?

(d) State KVL.

(e) What is maximum power transfer theorem applied to A.C. circuits?

(f) What is the relation between power factor and power?

(g) What is passive power of a network?

(h) Why phasor representation is advantageous in A.C. circuits?

(i) When a network can be called as two-port network?

(j) Give the condition for reciprocity by Z-parameters.

(k) Give the significance of parallel resonance.

(l) What is phase sequence of a poly phase system?

(m) What are the advantages of delta connection?

(n) Give the applications of star connection.

(o) Define time constant of a RLC parallel network.

UNIT I

2. (a) Explain KCL and give a physical example.

(b) A solenoid 50 cm long and 10 cm is dia in wound with 1500 turns. Find (i) the

inductance (ii) the energy store in the magnetic field when a current of 4A flows in

the coil.

Or

3. (a) Derive an expression to find the energy stored in a capacitor.

(b) Determine the current supplied by each source.

UNIT II

4. (a) Explain compensation theorem.

(b) Define the loop currents in the circuit given below.

Or

5. (a) Develop the phasor diagram of a RLC series circuit.

(b) Find the current in the resistor R3 of the circuit given as, using super position

principle.

UNIT III

6. (a) Determine Y-parameter of a conventional ‘T’ network.

(b) Find the value of L for which the circuit given below in resonant at a frequency of

W = 5000 rad/sec

Or

7. (a) Determine the condition of resonance in the parallel RLC circuit.

(b) Compute the open circuit impedance parameter of the circuit given below.

UNIT IV

8. (a) Explain the advantages of polyphase system.

(b) Calculate the active and reactive components of current in each phase of a star

connected, 5000 V, 3-phase system supplying 3000 Kw at a p.f. of 0.8.

Or

9. (a) Explain flow power factor can be measured by using the readings of two-wattmeter

method.

(b) A 3 phase 4-wire, 208 V, RYB system supplies a star connected load in which

Ω= o1010RZ ; Ω= o3015YZ and Ω−= 3010BZ resp. Find the line currents.

——————————

(DCS 223)



Computer Science

Paper III — COMPUTER ORGANIZATION


Answer Question No. 1 compulsorily.

(15 × 1 = 15)

Answer ONE question from each Unit.

(4 × 15 = 60)

1. (a) Define Three-state Bus Buffers.

(b) Write instruction set completeness.

(c) Define pipeline register.

(d) Define hit ratio.

(e) What is RISC?

(f) What is DMA?

(g) What is an Interrupt cycle?

(h) Give an example of computer arithmetic addition.

(i) Define subroutine call and return.

(j) What are the uses of start and stop bits in Asynchronous serial transfer.

(k) Define Associative Mapping.

(l) What are the uses of DASD?

(m) Differences between Hardwired and Microprogrammed control.

(n) What is memory space in virtual memory?

(o) What is I/O interface?

UNIT I

2. (a) Explain Logic Micro operations with example.

(b) Explain shift micro operations with example.

Or

(c) Explain Instruction cycle.

(d) Explain Interrupt cycle.

UNIT II

3. (a) Explain design of control unit.

(b) Explain address sequencing.

Or

(c) Explain RPN with example.

(d) Explain register stack.

UNIT III

4. (a) Explain Booth Multiplication Algorithm.

(b) Explain the division algorithm.

Or

(c) Explain Memory Hierarchy.

(d) Explain briefly Virtual Memory.

UNIT IV

5. (a) Explain source and destination initiated stroke for data transfer.

(b) Briefly explain programmed I/O and Interrupt – initiated I/O.

Or

(c) Explain Handshaking Method.

(d) Explain in brief input-output processes.

———————–––

(DCS 224)



Computer Science

Paper IV — DISCRETE MATHEMATICAL STRUCTURES


Answer question No. 1 Compulsorily. (15 × 1 = 15)


1. (a) 7,6,5,4;7,3,2,1 == BA and 9,8,7,6,5,4,3,2,1=U then find '' BA ∆ .

(b) xxA / is positive integer and 25 2x≥ ; 9,5,4,2=B find AB− .

(c) Is QPP ∨>− tautology.

(d) State the converse of “if 2+4=6 then I am not a president of India”

(e) 5,4,2,3,2,1 == BA then how many binary relations can we define from A to B.

(f) Define compliment of a relation.

(g) Define Matrix of a relation R on A to B.

(h) Give an example of Transitive relation

(i) Define a symmetric relation.

(j) Define Hassee diagram.

(k) Draw the digraph for the relation ).3,3()2,2()1,2()2,1(),1,1(=R

(l) Define n-degree.

(m) Solve nn aa 41 =+ for 0≥n and 70 =a .

(n) Define Euler path.

(o) How many strings of length 4 can be formed using SUCCESS.

UNIT I

2. (a) Prove the following :

(i) ( )BAABA ∩−=−

(ii) ( ) ( )BAABA ∩=−−

(b) Construct the truth table for ( )( ) ( ) ( )( )RQRPRQP >−∨>−>−<>−∨ .

Or

3. (a) Write the following sentences into predicate logic statements and verify the

conclusion.

All trees are graphs.

Some graphs are trees.

AND-OR graph is a graph.

MST is a tree.

Therefore, MST is a graph.

(b) Prove the tautology ( ) ( )( ) ( ) ( ) xQxxPxxQxPx ,,, ∃∧∃>−∧∃

UNIT II

4. (a) Prove that ( )52 +nn is a factor of 6 using mathematical induction.

(b) Determine the integral solutions of 324321 =+++ XXXX where 0>iX .

Or

5. (a) In how many ways can 24 pencils be distributed among four children such that each

children gets at least 3 but not more than eight.

(b) Prove that 122 1211 ++ + nn is divisible by 133.

UNIT III

6. (a) Solve the recurrence relation nn aa 43 1 =+ for 0≥n and 50 =a .

(b) Find the recurrence relation and the initial condition for the sequence 2,10,50,250....

and also find general term.

Or

7. (a) Solve the recurrence relation 096 21 =+− −− nnn aaa for 2≥n and 10 =a , 21 −=a using

generating functions.

(b) Solve the recurrence relation nnn aa 21 +=+ for 1,0 0 =≥ an .

UNIT IV

8. (a) Find the transitive closure of the diagraph whose adjacency matrix is

1010

0101

0010

1001

(b) Find the in-degrees and the out-degrees of the vertices of the following digraph.

Or

9. (a) Draw the Hasse diagram for the relation “a divides b’’ on D36 a set of divisors of 36.

(b) Determine the matrix of the partial order whose Hasse diagram is given below.

———————

(DCS 226)



Computer Science

Paper VI – MICROPROCESSORS


Answer question No.1 compulsorily.

(15)

Answer ONE question from each unit.

(4 × 15 = 60)

1. Write short notes on the following

(a) What is ALE signal?

(b) What are assembler directives?

(c) If HOLD input and NMI input are simultaneously activated, which one is service

first? Justify your answer.

(d) What is the major difference between an 8086 operating in minimum and

maximum modes?

(e) What is XLATB instruction of 8086?

(f) What is the function of BHE?

(g) What is an addressing mode?

UNIT – I

2. (a) Write the functional block diagram of 8086 and explain how 8086 is reset with

power-on and manual operation and write the

after-effect of resetting 8086.

(b) Explain the function of segment registers of 8086.

Or

(c) Explain the Data and Addresses naming directives of 8086.

(d) List the major steps in developing an assembly language program.

UNIT – II

3. (a) Write an ALP to find out number of even and number of odd numbers from a

given series of 16 bit hexadecimal numbers.

Or

(b) Write an ALP for the addition of two 3 × 3 matrices. The matrices are stored in the

form of lists row wise. Store the result of addition in the third list.

UNIT – III

4. (a) Explain the basic 8086 system timing with a diagram.

(b) Explain the stack structure of 8086 in detail.

Or

(c) Explain the interrupt structure of 8085 and hardware interrupt applications.

UNIT – IV

5. (a) Explain about 80186’s programmable interrupt controller.

(b) Explain READ and WRITE modes of operation using DMA controller in 8086

system.

Or

(c) Explain the design procedure to interface memories to 8086.

(d) Explain about 80188 processor.

––––––––––––

Documents

(fx ) - · PDF file... Express 2x +2x+ into Factorial Notation. (l) ... Write a program to convert an infix expression to postfix expression. (b) ... E A C K F H D B G