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(Please write your Exam RoZZ No.)

Exam RoZZNo.....•...........••..••

END TERM EXAMINATION THIRD SEMESTER (B.TECH.) DECEMBER-2012

Ipaper Code: ETMA201 Time: 3 Hours Note: Attempt

(a) (b) (c) (d)

any five questions including question/rom

Q.no.l which is compulsory. Select one each unit.

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

(3)

1Ti2

(3) (3) (4)

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

Find the Fourier Sine transform

of ~. x

(a) Find the Laplace Transform of the periodic function L[fl(t)]= ~(s)

LUfJx)f2 Q3

and

equation

+b,

where

f(t) = [

O
t

2c - t then

17)

c < t < 2c show

that

.

(7)

d2 ~

+ 4y = u(t - 2) , where u is unit step function

dr-

(7)

el

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

2

(3)

L[f2(t)]= F2(s)

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

(a) Solve the differential

if z == ax+ by+a

hi .a

I.

(b) If

2

(3)

UNIT-I Q2

(b) Find the Laplace Transform of

I

c. in

Ql

Subject: Applied Mathematics ' Maximum Marks :75

I e- tsin 2t

tdt .

(7)

3

Q4

cd

UNIT-II

(a) Find the Fourier Series to represent

a half-range cosine series for 0
ie

Q5

= X as

f(x)

(b) Express

(a) Find the Fourier Sine and Cosin~ transforms Fourier

Series

[1

O
f(x) in the

interval

of f(x) =

.0

for the

function

(7)

x>a (- 'Ii, 'Ii) , where

-Jr
Jr+X

f(x)

=[

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

xl;] = nJn

w

(b) Show that

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Q7

Q8

(7)

O
Jr-X

w Q6

xJ

-

II [Pn(x)Ydx

(a) Prove that

the

partial

(7)

n+1 .

(7)

=_2_.

(b) Show that

+1

2n

-J

(a) Form

differential

~- (x Bei' x) == xBer x.

UNIT-IV equation

by

the

elimination

a2z . (b) Save I -----=smxcos2y. Q9

(a) Solve

(D 2

DD'-2D'

2

)z = (y - l)e

au 2

(b) Solve the wave equation x=rr,

$

from

(7)

axoy

-

of

(7)

a2 z

2

(7+7)

dx

Ix + my + nz= ¢(x 2 + y2 + Z2 ) .

ax

(7) (7)

.n

(b) Find the

- Jr < X < Jr.

f(x) = xsinx,

the function

--

at

2

(7)

x . 2

au ax 2

== a --

1

under

au = 0, when t=O and u(x,O) = X, 0 < X <

at

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

the condition 'Ii _

u=O when x=O and (7)

~.

CD

(Please write your Exam Roll No.)

Exam Roll No

.

END TERM EXAMINATION THIRD SEMESTER

DECEMBER-2012

Paper Code: ETEC203 Subject: Signal & Systems Time: 3 Hours Maximum Marks :75 Note: Attempt five questions including Q. no. 1which is compulsory. Select one question from each unit. (a) Prove that an integer (b) Determine (c) Determine

discrete time sinusoidals whose frequency are separated by multiple of 2n are indentical. (4) whether the following signal is Power or energy x(n)~2eJ2n.(4) whether the following signal is periodic or non-periodic (4)

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

3

c. in

Q1

4

(dl Sketch the following sequence h(K), its reverse h(-K) shifted sequences 2 K = 0,1 h(K+3) and h(-K-2) h(K) =

K = 2,3 .

l°

otherwise

(4)

hi .a

..

J1

(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:(i) Stability and ROC for discrete time signal. (ii)DTFT and Z transform.

el

(5)

Q2

(a) consider

cd

UNIT-I

a

LTI system

with

impulse

hen) =

response

(i)3

u(n).

ie

Determine the steady state response for large 'n' to the excitation x(n) =cos Jrllu(n) .

(a) An LTI system has the impulse response

hen) =

.n

the following convolution

w

Q3

(6.5)

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

(6)

'4 (3)"

w

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

w

(b)A system is described

Q4

by

output when input x(n) is

xn()

2' (1)"

Jr

4u(n).

.Jr

=cos-n+S\ll-n. 3

Determine

= u(n).

(6)

y(n)=x(n)+~(y-l)-~y(n-2). 4 8

Find the (6.5)

UNIT·II (a) Determine the discrete fourier series representation sequence

u(n).

for the following (6)

4

(b) Determine the fourier series representation shown.

of the square wave as

(6.5) P.T.O.

I

/2.---

[-2-]

-T J

c. in

Q5

OR (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)

k

()

( C\.)

hi .a

?L\tJ

()

-I

(...6 )

el

"

,~

UNIT-III

I

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

cd

Q6

magnitude and phase characteristics

x~n~N-l

. Plot the

elsewhere

for N=5.

(12.5)

OR

(a) Determine the frequency responses

ie

Q7

described by the difference equation ·66

at 0=0 and O=n for the system yen)= ~y(n -1) -~y(n

- 2) + x(n) .(8.5)

.n

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

w

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

Q9

Find the Z-transform

1 ( 1 of x(n) = 2(n2 + n)"3

)n-I u(n -1) .

OR (a) Find the inverse laplace transform of the following:(1')

X()s=

2

(4)

UNIT-IV

w w

Q8

J

2

(12.5)

(6)

+6s+7 R es>() 1 (00)118=X() 'S3 +2s +6R es>. () O' 2 2 s +3s+2 s +3s (b) The O/P y(t) of continuous time LTI system is 2e-3t when ifP x(t)=u(t). compute (i) impulse response h(n) (ii) olp when x(t)=e-tu(t). (6.5) S2

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

@

(Please write your Exam Roll No.)

Exam Roll No ..............•..••....

END TERM EXAMINATION

-=~_-._~=__-=-.~~=~~~

THIRD SEMESTERj!J.TECH.! DECEMBER-2012

~er Code: ETEC205 _--=-_-.~-_u~-b-!i-e-c-t:-C--i,.,-c-u-i-ts-&-S-y-s Time: 3 Hours Maximum Marks :75 Note: Attempt any five questions including Q.no.l which is compulsory. I

1

Find the z-parameters of the T-network shown in Fig.I.(all resistances are in ohms) (5) 5 12

1~.~ l'

2/ "

FI& 1

The transfer function ofa network is given by M(s)

.

"

= V(s) = I(s)

s+3

.When i(t) is the

(s+2t

hi .a

(b)

c. in

Q. No. l(a)

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 the short circuit at the same terminal "givesSA current. Find the load current, if a load of 80 oh~ resistance is connected at the load terminal. . (5)

(d)

Find the current i. in the network

cd

el

(5)

(e)

ie

Fig.2.

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

. di(t)l voltage across Care 0 for t < 0, find i(O), -1=0'

dt

.

(5)

1=0+

w

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.n

dt

dP (t)1 and --2-

Q.No.2(a)

Write the equation for the waveforms shown in Fig.4(a)&(b)

(6)

flu

(!}

FigA.

~ (b)

What do you understand by Tree and Co-Tree of a graph? Explain the method to develop incidence matrix for a graph with the help of a' s.uitable example. (6.5)

P,T~(9.

.- . Find whether

Q. No.3(a)

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 2 by d yet) + 5 dy(t) + 6y(t) dx(t) + 6x(t) , when the input is a unit step function and dt2 dt dt the initial conditions of the system are y(O)=! and y' (0)== 2. (6.5)

(b)

=

The switch k (Fig.S) is in the steady state in position a for -0. _

Q.No.4(a)

(6)

r~:~~ . ~t' R I' ) lOOVIr 'OV1

L

-->f vcr~)

c. in

__ 41F

Fig.6.

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

Q.No.5(a)

Determine the-y-parameters

(b)

.

of the network shown in Fig.S.

cd

Determine the IJ-parameters

+

(6.5)

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

w

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(b)

_

(6)

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Q.No.6(a)

Fig.?

for the network shown in Fig.7.

el

1,_----'-----

hi .a

(b)

Fig.9.

Q.No.7(a)

Test whether

(6)

(I) the polynomial F(s) (Ii) the function

F(s)

=

S4

=~

S2

(b)

For the network function form.

+ S3 + 2s + 3s + 2 is Hurwitz; and

+a

2

is positive real, where and K & it are positive constants.

-

yes)=:; 2(s+l)(s+3) (8 +2)(s +4)

synthesize in Foster-'

and Cauer-I (6.5)

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Exam Roll No .••......•...........•.

(Please write your Exam Roll No.)

END TERM EXAMINATION THIRD SEMESTER

B. TECH.

DECEMBER~20 12

Paper Code: ETIT209

I

Q1

(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 an example. (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 strings using friend function. (6.5) (b) Differentiate among private, public and protected access modifiers. Also, explain their meaning when a derived class inherits from a base class using public, protected or private keywords. (6) (a) What is the difference between a virtual function and a pure virtual function? Explain with example. (6.5) (b) What is a function template? Write a function template to find a maximum value from an array. (6)

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cd

el

hi .a

c. in

I

Subject: Object Oriented Programming Using C++ Time: 3 Hours Maximum Marks :75 Note: Attempt any five question~ including Q. no. 1 which is compulsory,

w

Q6

Q7

(a) Write a C++ program to copy one me to another file after converting the lower case characters to upper case characters. (7.5) (b) What is exception handling? Discuss try, catch and throw with the help of suitable example. (5) (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) ************

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

(Please write your Exam Roll No.)

::':,;;'

.

EN'D TERM EXAMINATION THIRDSEMESTER

DECEMBER-20 12

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

L Ql

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

given as them in

hi .a

c. 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)

Q3

(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 < < 3. Each edge (VI, VJ) is al'lsigned a weight

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, Q5

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cd

el

Q2

w

Q6

II- JI

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

(5)

(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 of sizes 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 item is 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 ************