Exam RoZZNo.....•...........••..••

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END TERM EXAMINATION(Please write your Exam RoZZ No.)

THIRD SEMESTER(B.TECH.) DECEMBER-2012

Ipaper Code: ETMA201 Subject: Applied Mathematics ITime: 3 Hours ' Maximum Marks :75

Note: Attempt any five questions including Q.no.l which is compulsory. Select onequestion/rom each unit.

Ql (a) Find the Laplace Transform of sint cost.(b) Find the values of 1Ti2 and jO:'(c) Define the unit step function and Impulse function.(d) Show that Pn (1) == 1.

(e) Construct a first order partial differential equation, ifa and b are arbitrary constants,

(f) Find the Fourier Sine transform of ~.x

(3)(3)(3)

(4)

z == ax+ by+a2 + b2, where

(3)

(3)

UNIT-I

where u is unit step function

Q2

Q3

(a) Find the Laplace Transform of the periodic functionI.

(b) If L[fl(t)]= ~(s) and L[f2(t)]= F2(s)

LUfJx)f2 (t - x)dx}==~ (s).F2(s) .

d2(a) Solve the differential equation ~ + 4y = u(t - 2) ,

dr-

f(t) = [ t2c - t

then

O<t<cc < t < 2c

show

17)

that

(7)

(7)

(7)

y(O)=Oand y'(O)=l.

(b) Find the Laplace Transform of I e-2ttsin 3tdt .

UNIT-IIQ4 (a) Find the Fourier Series to represent the function f(x) = xsinx, - Jr < X < Jr. (7)

(b) Express f(x) = X as a half-range cosine series for 0<x<2. (7)

Q5 (a) Find the Fourier Sine and Cosin~ transforms of f(x) = [1.0

(b) Find the Fourier Series for the function f(x) in the

[

Jr+X -Jr<x<Of(x) =

Jr-X O<X<Jr

O<x<a

x>ainterval (- 'Ii, 'Ii) ,

(7)

where

(7)

Q6UNIT-III

(a) Find the relation between Beta and Gamma functions.

(b) Show that xl;] = nJn - xJ n+1 .

(7)

(7)

Q7 (a) Prove that II [Pn(x)Ydx =_2_.-J 2n + 1

(b) Show that ~- (x Bei' x) == xBer x. (7+7)dx

UNIT-IVQ8 (a) Form the partial differential equation by the elimination of $ from

Ix + my + nz= ¢(x 2 + y2 + Z2 ) . (7)

(b) S I a2z a2 z .ave -----=smxcos2y. (7)ax 2 axoy

Q9 (a) Solve (D 2 - DD'-2D' 2 )z = (y - l)e x . (7)

a2u 2 a2u(b) Solve the wave equation -- == a -- under the condition u=O when x=O andat2 ax1

x=rr, au = 0, when t=O and u(x,O) = X, 0 < X < 'Ii _ (7)at************

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~ .

Exam Roll No .CD

END TERM EXAMINATIONTHIRD SEMESTER DECEMBER-2012

Paper Code: ETEC203 Subject: Signal & SystemsTime: 3 Hours Maximum Marks :75

Note: Attempt five questions including Q. no. 1which is compulsory.Select one question from each unit.

(Please write your Exam Roll No.)

Q 1 (a) Prove that discrete time sinusoidals whose frequency are separated byan integer multiple of 2n are indentical. (4)

(b)Determine whether the following signal is Power or energy x(n)~2eJ2n.(4)(c) Determine whether the following signal is periodic or non-periodic

( ) Jr . Jr (4)x n = cos - n + sm - n .3 4

(dl Sketch the following sequence h(K), its reverse h(-K) shifted sequences

J2 K = 0,1

h(K+3) and h(-K-2) h(K) = 1 K = 2,3 . (4)... l° otherwise(e) Using convolution sum, determine the output for a sequence input

{l,l,l} for a system with impulse response hen) =(±rU(n). (4)

(f) Derive the relationship between:- (5)(i) Stability and ROC for discrete time signal.(ii)DTFT and Z transform.

Q2

UNIT-I

(a) consider a LTI system with impulse

Determine the steady state response forx(n) =cos Jrllu(n) .

(b) Use circular convolution for determiningx[n] = {2,3,5,6}; h[n] = {-2,4,3,2} .

OR

response hen) = (i)3 u(n).

large 'n' to the excitation(6.5)

the following convolution(6)

(6.5)

Q3 (3)"(a) An LTI system has the impulse response hen) = '4 u(n). Determine

the O/P of the system at n~-l, n~6 when input x(n) = u(n). (6)

(b)A system is described by y(n)=x(n)+~(y-l)-~y(n-2). Find the4 8

(1)"output when input x(n) is 2' 4u(n).

Q4UNIT·II

(a) Determine the discrete fourier series representation for the following

()Jr .Jr

sequence xn =cos-n+S\ll-n. (6)3 4

(b) Determine the fourier series representation of the square wave asshown. (6.5)

P.T.O.

I

/2.---

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[-2-]

-TJ

(...6 )" ,~

()-Ik()

( C\.)

ORQ5 (a) What is Gibbs phenomenon? Explain its importance. (2.5)

(b) Obtain the Fourier Series representation of the following waveforms.Sketch the magnitude and phase spectra. (10)

?L\tJ

UNIT-III

Q6

Q7

{I x~n~N-l

Find the DTFT of a signal 4(n) given by x(n) =. 0 . Plot theelsewhere

magnitude and phase characteristics for N=5. (12.5)OR

(a) Determine the frequency responses at 0=0 and O=n for the system

described by the difference equation yen)= ~y(n -1) -~y(n - 2) + x(n) .(8.5)·66

(b) Find the Nyquist rate and the Nyquist interval for each of the following

met)-_[sin ~O 1lt J 2signals;- (i) met)= 5cos1000ntcos4000nt (ii) --1"-- (4)

(6)

(12.5)Q8

Q9

UNIT-IV

1 ( 1)n-IFind the Z-transform of x(n) = 2(n2 + n)"3 u(n -1) .

OR(a) Find the inverse laplace transform of the following:-

(') X() S2 +6s+7 R () 1 (00) X() 'S3 +2s2 +6R () O'1 s= 2 es>- 118= 2 es>.s +3s+2 s +3s

(b)The O/P y(t) of continuous time LTI system is 2e-3t when ifPx(t)=u(t). compute (i) impulse response h(n) (ii) olp when x(t)=e-tu(t). (6.5)

************

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Exam Roll No ..............•..••....@END TERM EXAMINATION

(Please write your Exam Roll No.)

THIRD SEMESTERj!J.TECH.! DECEMBER-2012~er Code: ETEC205 -=~_-._~=__-=-.~~=~~~_--=-_-.~-_u~-b-!i-e-c-t:-C--i,.,-c-u-i-ts-&-S-y-s-t-e-m-s~1Time: 3 Hours Maximum Marks :75

1 Note: Attempt any five questions including Q.no.l which is compulsory. I

Q. No. l(a) Find the z-parameters of the T-network shown in Fig.I.(all resistances are in ohms) (5)5 12

1~.~

l' FI& 1 2/ "

(b) The transfer function ofa network is given by M(s) = V(s) = s+3 .When i(t) is the. " I(s) (s+2t

unit step function, find the value ofv(t) in tbe steady state. (5)

(c) In a two terminal network, the open circuit voltage at the load terminal is lOOYand theshort circuit at the same terminal "givesSA current. Find the load current, if a load of 80oh~ resistance is connected at the load terminal. . (5)

(d) Find the current i. in the network (5)

Fig.2.

(e) For the network shown in Fig.3, the switch is closed at t;' O.If the curr.ent in Land

. di(t)l dP (t)1voltage across Care 0 for t < 0, find i(O), -- and --2- .

dt 1=0' dt 1=0+

(5)

Q.No.2(a) Write the equation for the waveforms shown in Fig.4(a)&(b)

flu

(6)

(!}

FigA.~

(b) What do you understand by Tree and Co-Tree of a graph? Explain the method todevelop incidence matrix for a graph with the help of a's.uitable example. (6.5) P,T~(9.

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Q. No.3(a)

(b)

.- .Find whether the continuous time system described by yet) = X(t2)varying and linear or not?

Using Laplace transform, rmd the forced and natural responses of the system described

by d2

yet) +5 dy(t) + 6y(t) = dx(t) + 6x(t) , when the input is a unit step function anddt2 dt dt

the initial conditions of the system are y(O)=! and y' (0)== 2. (6.5)

(6)

L

The switch k (Fig.S) is in the steady state in position a for -<lO < t < O. At t = 0, it isconn~cted to position b. Find the expression for current iL (t), for t >0. _

r~:~~.~t'RI')lOOVIr 'OV1 41F

__ -->f vcr~)

Fig.6.

(b) AII~~ing transients to die out with switch S in position 'a', the switch Is then moved toposItion 'b' at t=0, as shown in Fig.6. Find expressions for Vc (t) and VR (t) for t > O. (6.5)

Q.No.4(a)

Q.No.5(a) Determine the-y-parameters for the network shown in Fig.7. (6)

+

1,_----'----- _Fig.?

(b).

Determine the IJ-parameters of the network shown in Fig.S. (6.5)

Q.No.6(a)

(b)

A voltage source VI whose internal resistance is R1 delivers power to a load ~2 + jX2 inwhich X2 is fixed but R1 is variable. Find the value of Rz at which the power delivered tothe load is a maximum. (6.5)State Thevenin's theorem. O~tain the Thevenin equivalent of the network across theterminal AB as shown in Fig.9. (all element values are in ohm). (6)

Fig.9.

Q.No.7(a)

(b)

Test whether (6)(I) the polynomial F(s) = S4 + S3 + 2s2 + 3s +2 is Hurwitz; and

(Ii) the function F(s) = ~ is positive real, where and K & it are positive constants.S2 +a -

For the network function yes)=:; 2(s+l)(s+3) synthesize in Foster-' and Cauer-I(8 +2)(s +4)

form. (6.5)

: o~•• _.

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END TERM EXAMINATIONTHIRD SEMESTER B.TECH. DECEMBER~20 12

Paper Code: ETIT209 Subject: Object Oriented ProgrammingUsing C++

Time: 3 Hours Maximum Marks :75I Note: Attempt any five question~ including Q. no.1which is compulsory, I

(Please write your Exam Roll No.) Exam Roll No .••......•...........•.

Q 1 (a) What are mutable variables?(b)What are nameless objects?(c)What is general purpose pointer?(d)When is scope resolution operator used?(e) Differentiate between pointer and reference variable.(f) What is the role of destructors in C++program?(g)What is static function?(h)What is the difference between function overloading and function

overriding?(i) Explain th~ concept of this pointer.(j) Which operators cannot be overloaded? (2.5xlO=25)

Q2 (a)What is meant by a constant member function? Explain with anexample. (4)

(b)What is role of an inline function? How does it differ from macro?Explain with examples. (4)

(c) Explain dynamic memory management for C++. (4.5)

Q3 (a) Write a program. to overJoad ++ operator for prefix and postfix use. (6)(b)What are default arguments? (3)(c) Why argument passed to a copy constructor is a reference variable? (3.5)

Q4 (a) Write a program to overload operator + to concatenate two stringsusing friend function. (6.5)

(b)Differentiate among private, public and protected access modifiers.Also, explain their meaning when a derived class inherits from a baseclass using public, protected or private keywords. (6)

Q5 (a)What is the difference between a virtual function and a pure virtualfunction? Explain with example. (6.5)

(b)What is a function template? Write a function template to find amaximum value from an array. (6)

Q6 (a) Write a C++ program to copy one me to another file after convertingthe lower case characters to upper case characters. (7.5)

(b)What is exception handling? Discuss try, catch and throw with thehelp of suitable example. (5)

Q7 (a) Write a program to implement stack using class template. (6.5)(b)What is a standard template library (STL)? Briefly explain sequepce

containers and asso.ciative containers. (6)

************

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EN'D TERM EXAMINATIONTHIRDSEMESTER DECEMBER-2012

,Paper Code: ETCS211 Subject: Data Structure ITime: 3 Hours Maximum Marks :75L Note: Attempt anyfive questions including Q.no.l which is compulsory. I

(Please write your Exam Roll No.)

/.:',-,\~r)Exam Roll No ::':,;;' .

Q2

Q3

Q5

Ql (a) Time complexity to solve a problem P by four different algorithms given asA = 0(2 N ), B = O(N 312 ), C = O(N log2N ) and D = O(N * log 2 N) . Arrange them in

increasing order.(b) Briefly discuss about any two strategies for memory representation of sparse matrix.(c) How doubly link list solves the problem associated with single link list?(d) What is the minimum number of stacks of size 'N' required to implement a queue of

size 'N'? Justify your answer.(e) What is the maximum height of any AVL-tree with 11 nodes? Assume that the

height of a tree with a single node is O.(f) Numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 inserted into a initially empty binary search tree

in given order. What will be the in-order traversal sequence of the resultant tree?(g) Let G be a complete undirected graph on 5 vertices. If vertices of G are unique then

what is the number of distinct cycles of length 3 in G?(h) Differentiate between external and internal sorting.(i) What is the number of swaps required to sort N elements using selection sort, in the

worst case? '(j) B-tree of order 4 is built by 10 successive insertions. What is the maximum number

of node splitting operations that may take place? ' (2.5x10=251

(a) What is recursion and how it is implemented? (2.5)(b) Write an algorithm to reverse a given single link list. (5)(c) Write an algorithm to convert Infix notation into Postfix notation by using stack. (5)

(a) Briefly discuss about storage implementation of two dimensional array. (2.5)(b) Write an algorithm to implement circular queue using array. (5)(c) Write an algorithm to delete a node situated at mid position in a given doubly link

lisL (5)Q4 (a) Does the minimum spanning tree of a graph give the shortest distance between any

two specified nodes? Why or why not? (2.5)(b) Write an algorithm to return height of a given binary tree. (5)(c) For any binary tree if in-order traversal is: M B F D K I J C G A N and post-order

traversal is: M F K D B J G C N A I. Write pre-order traversal for this tree. (5),(a) To perform search over a graph which strategy is better breadth first search or

depth first search? Justify. (2.5)(b) Explain single source shortest path algorithm by using a suitable example. Derive

its runtime complexity. (5)(c) For a given undirected graph G=(V, E), if nodes are VI, V2, ...• , VIQ.Two nodes VI and

VJ are connected if and only if 0 < II- JI < 3. Each edge (VI, VJ) is al'lsigned a weight

(I+J). What will be the cost of the minimum spanning tree (MST)of G? (5)

Q6 (a) For a given set of N distinct elements how many binary search trees are possible? (2.5)(b) Perform heap sort for following given data in order: 1,2,3,4, 5,6,7,8,9, 10, 11,

12, 13, 14, 15. (5)(c) Write an algorithm to find a cycle in a given graph by using depth-first or breadth

first search. (5)

Q7 (a) What is the number of comparisons required in merging two ordered files A and B ofsizes M and N respectively? Prove your answer. (2.5)

(b) Create AVLtree using following data given in order: 3, 2, 1, 4, 5, 6, 16, 15, 14. IS}(e) Write quick sort algorithm and also derive its run time complexity. '(5)

Q8 (a) Construct 2-3-4 tree (B-tree with a minimum degree of two) in which each data itemis a letter. The alphabetical ordering of letters used in constructing the tree are B,H, I, L, N, P, Q, T, U, V, X, Z, G. (2.5)

(b) Write short notes on any two of the following:- (51'2=10)(i) Hashing (ii)File organization Techniques(iii)Topological Sorting (iv)Threaded binary Tree

************

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