3rd Semester (June-2016) Computer Science and Information Science Engineering Question Paper

1. USN
BodS-, cs *.f&.p),
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Third Sernesten B.E. Degree g*u*ifui*r,*6#
18ryrAT31
2016rw
Tirne: 3 hrs.
2a.
Engineerlng Mathemi
Note: ,Answer any FIVE fwll questionsu selectirug
atleast TWO questions from each part"
Max. Marks:100
(S7 Marks)
{06 Ndarks)
in the Fourier
(07 Marks)
(S7 Marks)
(06 Marks)
{CI7 Marhs)
the method of separation of
(87 Marks)
(S6 Marks)
P.ART-_-A
function {x) : x{Zw * x) in 0 < x S 2n. Hence deduce that
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I a. Find the Fourier series for the
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b. Find the half-range cosine series for the function t{x) : (x * 112 in 0 < x < 1.
c. Obtain the constant term and the co-efficient of the 1't sine and cosine terrns
series of y as given in the tollowing table
Solve the integral equation :
ro(
irtr, .orc0d0=]t^"'
0Sus'.
n.n..evaluare I *t o,
d t 0. u>l j t
Find the Fourier transform of f(x) : .'1*1.b.
c.
cl-
Find the infinite F-ourier cosine transform of e-"' .
Solve two dimensional Laplace equation ur* * ur, : 0 by
variables.
c. Solve the boundary vatrue
b. Obtain the D'Alembert's solution of the wave equation utt : C2u*, subject to the conditions
u(x. 0) : fl x) ,nC $t x.o) = 0 .
at
problem *=.'d+ , ( x( I subjcct ro the condirious
'atdk
tutu
-(0, t) :0; ;{L,t) = 0, u(x, 0) : x.
Ax ax'
(07 Marks)
4 a. Find the equation of the best fit straight line for the following data and hence estirnate the
value of the dependent variable corresponding to the value of the independent variabtre x
with 30. (o? Marks)
b. Solve by graphical method :
MaxZ:x*i.5y
Subject to the constraints x + 2y < 160
3x )- 2y < 240
x>0;y>0.
Solve by sirnplex methocl :
max z: 3x + 5y
subject to 3x * 2y <18
x<4
y<5
'x'Y)0'
{&6 Marks)
w
x 0 I 2
a
-) 4 5
v 9 18 24 28 26 2A
x 5 10 15 LJ 25
v It) I9 23 1_O 1fl
1 of2
(87 Marks)

2. IOMAT31
PAR.T _ B
a. Using the method of false position, find a real root of the equation x trog,ox - I.2:0, correct
to 4 decimal places. (07 Marks)
b. By relaxation methocl, solve :
10x+2y+z:9; x+10y-z:-22; -2x+3y+l0z:22. (06N{arks)
c. Find the largest Eigen value and the corresponding Eigen vector for the rnatrix
f*-))1| " - 'l
l-Z 3 -l iusingRayleigh'spowermethod;takingxo: [1 i 1]r. Perform5 iterations.
tt
L2 -r 3l
6 a. Find the cubic polynomial by using Newton's
(07 Marks)
forward interpolation formtrla which takes the
fotrtrowing values.
Hence evaluate f(4). {07 N{arks)
that approximate the functionUsing Lagrerirge's formuia, find the interpolating polynomial
described by the following table.
c.
TA,
F{ence find (3).
5.2
Evaluate Ikrg" x d* using Weddler's ruie by taking 7 ordinates.
J"t
1
Sotrve u,, * uly : 0 in the following squere Mesh. Carry out two iterations.
ol+qfs
t1
t2_
lo
u(5, 0 : 0 and initial condition u(x, 0) : {.,:0". Tt
[5(5 - x) for
taking h:.1, k: 0.2 upto t : 1.
Find the solution of the equation u,,, : 2Lr1 when u(0, t)
x(4 - x) taking h: 1. Find values upto t :5"
Find the inverse Z - transfbrrnation of
Solve the diflference equation : yn+2
Z - transforrnation.
,3 +5r2 +82-4
* 6yn*r + 9yn :
(06 Marks)
(07 Marks)
(07 Marks)
0<x<1
and u1(x, 0) :0 solve by
1<x<5 "'
(06 Marks)
: 0 and u(4, t) : 0 and u(x, 0) :
(07 Marks)
(06 Marks)
givenyo:yr:0using
(07 Marks)
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Fig. Q7(a) o o'' a +'s'
b. The transverse disptracement of a point at a distance x from one end to any point 't' of a
^) ^)
vibrating string satisfies the equation : + = ZSd-- with boundary condition u(0, t) :
Af Ax"
c.
a. FindtheZ-transformationofthefotriowing:i)3n-4sin L+5a2 iiydLl. (o7Marks)
4n!
^2+Z _ZZ
b.
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3. USN
Time: 3 hrs.
Note: Answev any FIVE full qwesttions.
a. Express the compiex number
(1+i)(1+3i).
(1+ si)
b. Find the modulus and amplitude of I * cosO + i sin0.
c. Find the cube root of 1 - i.
Find the ntr'derivative of eu* cos (bx + c).
MATDIP3CIl
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Max. Marks:100
(G6 Marks)
(S7 Marks)
(CI7 Marks)
(S6 N{arks)
(07 Marks)
(07 Marks)
(06 Marks)
(07 &{arks}
(07 Marks)
(S6 Marks)
{S7 Marksi
(&7 Marks)
(85 Marks)
(07 Marks)
Third Semester B.E. Degree Exam ;-June/July
Advanced Mathematics - I
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2a.
b.
3a.
b.
4a.
b.
6x
Find the nth derivative of
(x-2)(x+2)(x-1)
If y: sin-lx, prove that (1 - x')yn,z - (2n+ l)x yn*r - n2yn : 0.
Find the angle of intersection of the curves 12 sin 20 : a2, rz cos20 : b2.
Find the nodal equation of the curve r(1 - cosO) :2a.
Expand log (secx) upto the term containing xa using Maclaurin's series.
l. show that u** * uyv = 0.xfu:xt-3of*x*e*cosy+
rf u = t(t.".21. pror. rhat x
Y z x)
ur*yuy*zu.:0.
, d(u,v,rv;
c" ltnd '" ',whereu:x*y*2, v:y+z)w:2.o(x,y,z)
5 a. obtain reduction formuia for
f
cos' x dx, where n is positive integer.
24
b. Evaluate f-I-a.J r. -;"''rr 14-X-
i Jr.' + y' + z'1dzdydr.
-h -a
l'I
c. Evaluate
I of2
(87 Marks)

4. 6a.
b.
Prove that: i) f(n+l) : n I(n) and
Prove that P(m, n; : I(*l r(')'.
f(m+n)
c" Show that I _$. l" JSro d0 = n .
o t/sin 0 i
dv -,'-(9x+Y+l)-.
dx
ye*Y dx + (xe*Y + 2y) dy: 0.
.9I*rcotx=cosx.
dx
ii) I(n *1): nr for a positive integer n.
MATDIP3Ol
(06 Marks)
(07 Marks)
{07M'arks)
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(06 Marks)
(07 Marks)
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(06 Marks)
(07 Marks)
(07 Marks)
'l a" Solve
Sotrve
Solve
8a.
b.
b.
c"
Solve -d? o9 * 9y = 5.-,' .
dx' dx
Solve (D'- 4D + 13)y: cos 2x.
Solve (D' + 2D + l)y : * + 2x.
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*****
2 of2

5. USN
Time: 3 hrs.
2a.
b.
Third Semester B.E. Degree
.10cs32
ne/July 2016
I{ax. Marks:100
Electronic Gircuits
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Note: Answer any FIVE full qaestions, selecting
stleast TWO qwestions.from each part.
PA.ITT _ A
I a. With the help of commcn - emitter amplifier configuration, explain the criteria for selection
of a suitable operating point and the factors affecting its stability. (08 Marks)
b. Fig. Q1(b)(i) shows the transistor as an inverting switch with the desired output waveform
for the given input waveform as shown in Fig. Q1(bxiil. Find the value of,Vcc, Rc and R6
given that B:80, I61.u11 : l0 mA, the output voltage Vorl when the transistor is off is i2 V,
Ven:0.7V. (0E Marks)
3a.
b.
Explain the gate triggering characteristics of an SCR. (04 Marks)
Draw and explain the working of D-MOSFET with the help of <irain current and
transconductance curve. When the voltage is applied to the gate of a P-Cliannel
D-MOSFET, does the current flow depieted or enhanced? (12 Marks)
Fig. Q2(b) shows a circuit using E - MOSFET given that the threshold voltage for the
MOSFET is 2 V and l6ionl : 6 mA for V651on1 : 5V, determine the volume of the operating
point. (SB Marks)
t5v
t i,(-sr*
What are photodiodes? Explain with VI characteristics. (05 Marks)
Determine the cut-off wave length for silicon and germanium photodiodes, given that their
Bandgap energies are 1.1 ev and. 0.72 ev, respectively, at 25oC. How will the cut off wave
length change when the operating temperature change form 25'C to 200'C? (05 Marks)
c. Write short note on :
i) Cathode ray tube display
ii) Ernerging display technologies.
'-"1'fL
' 1<:,
ti;.G'
Exdhi
Fig. Qi(b)(i) Fig. Q1(b)(ii)
L of2
(10 Marks)

6. 10cs32
4 a. Explain how the h-parameters are detennined by making use of transistor's input and outprit
6 a. Explain Earkhausen r:riteria with suitable circuit diagrarns and essential conditions.
(05 Marks)
b. Explain with a neat connection diagram and waveforms how IC555 timer is used as the
astable mutrtivibrator. (S8 Marks)
c" A step input of amplitude 8 volts is applied to a RC low - pass circuit shown in Fig. Q6(c)(i)
and Fig. Q5(cXii) betrow. Determine the output voltage at end of : i) 2misec ii) 5nr/sec
iii) Find upper cut-off frequerlcy f,, and rise time t.. (07 Marks)
Fie. Q6(c) (i) Fig. Q5(cxii)
characteristlcs.
b. Carryout the analysis of a transistor amplifier operating in corrmon emitter
configuration with suitabie derivations.
PART _ B
5 a. Distinguish between class A, class B, Class C, class D, ciass AB amplifiers
conduction angle, operating region, application and efficiency.
b. Explain all four feedback topologies with appropriate circuit diagrams.
o. Are arnplif?er has a open * loop voltage gain Au : i000 t 100. It is required
ampiifier whose voltage gain varies by no more than t 0.1%.
i) Find the value of feedback factor $
ii) Find gain with feedback.
7 a. Write a note on 3 teminal voltage regulator.
b. Deternaine the regulated output voltage for LM 317 voltage regulator shown
v"
&a-o -st*.
Fig. Q7(b)
c. What are switching reguiators? Describe the basic topology of Boost regulator.
and practical Op-Amps.
Discuss performanc e parameters o f operational amplifi ers.
Explain Op-Amp as peak detector circuit.
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rt
(tr0 Marks)
fixed bias
(10 Marks)
interms of
(05 Marks)
(10 Marks)
to have an
(05 Marks)
(05 Marks)
Fig. Q7(b).
(05 Marks)
(10 Marks)
(10 Marks)
(05 Marks)
t>F
*{.

7. Third Semester B.E. Degree Examih'afr6n, June/July 2016
Logic Design
Note: Answer any FIYE full qaestions, selecting
atlesst TWO qwestions frono each part.
10cs33
Max. Marks:100
(08 Marks)
(08 Marks)
(04 Marks)
(10 Marks)
(06 Marks)
(04 Marks)
(10 Marks)
Tirne: 3 hrs.
la.
b.
PART _ A
Name universal gates. Realize basic gates using NAND gate only.
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a.
Prove that symmetrical signal has a duty cycle of 50o/o and find the frequency, low and high
2 a. Find the SOP of the following Boolean function using K - rnap :
i) (p q r s) : Xm(6, 7 ,9, 10,1 1, 13) + d(0, 1, 8, 12)
ii) (a b c d) : 7rm (1,2, 4,9, 10, 12) + d(0, 3, 5). (08 Marks)
b. Simplify (A B c D; : rm(0, r, 2, 3, 5, 8, 12, 14, i5) using euine - Mcclusky method.
(12 Marks)
3 a. Design a16: l multiplexerusingtwo 8: l multiplexersand one2: l multiplexerswith
expressions. (06 Marks)
b. With relevant diagram explain n-bit magnitude comparator. (08 Marks)
c. Give HDL implernentation for 4 : I MUX using 'case' statement. (06 Marks)
4 a. What do you mean by characteristic equation of 'Flip-flop'? Draw the logic diagram, truth
table and explain working of 'JK - Flip - Flop' and implement the same using NAND gate.
(12 Marks)
b. With state table and state transition diagram, analyse the behaviour of sequential circuit
shown in Fig. Q4(b). (08 Marks)
L*v
Fig. Qa&)
PART _ B
a. With a neat logic and timing diagram, explain the working of a 4 - bit SISO register.
duty cycles for asymmetrical signai if it is high for 3 ms and low for 4 ms.
c. Explain the structure of VHDL/Verilog program.
b. Design two 4 - bit number serial adder.
c. Write verilog HDL code for 4 * bit SXPO shift register.
Design synchronous modulus - 5 (mod -5) counter using JK - Flip*Flop.
t* - .,.-,.. .
l..l L. o"r
6a.
b. Explain, design of 4 * bit binary ripple - up counter using negative edge triggered JK - flip-
flops with block diagram and timing diagrarn. (10 Marks)
L of2

8. 8a.
b.
10cs33
a. With neat diagram explain and compare Mealay and Moore rnachine. (10 Marks)
b. Reduce state transition diagram (Moore model) of Fig. Q7(b) by i) Row elimination method
ii) implication table method. (10 Marks)
Discuss the two drarrvbacks of resistive divider used in cohverting D/A. Draw the schematic
for a 4-bit binary ladder and explain how the digital to analog conversion is achieved using
it.
Discuss the working of following A/D converters :
i) Successive approximation A/D
i, Counter type A/D.
(10 Marks)
(10 Marks)
Fig. Q7(b)
2 of2

9. USN
a. Write the open statement "Some straight lines are parallel
symbolic form and find its negation.
b. Test the validity of the following argument :
All employers pay their employees
Anil is an employer
.'. Anil pajzs his employees.
10cs34
Max. Marks:100
(06 Nfarks)
(05 Marks)
or all straight lines interest" in
(84 Marks)
(06 Marks)
(05 Marks)
(05 Marks)
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Third Semester B.E. Degree Exa June/July 2016
Time: 3 hrs.
Discrete Mathematical $tructures
Note: Answer an_v FIYE full questiorcs, selecting
atleqst TWO questiorus fro*n each purt"
statement "If Ram can solve the puzzle then Ram can solve the problem".
d. Estabiish the validity of the argurnent
(qr-r)vs
-qv(rr^.-q)
." r-)s.
PART _ A
Define subset, disjoint sets and complement of a set with an example for each (06 Marks)
In a survey of 260 college students the following data were obtained :
64 had taken raathematics course, 94 had taken computer science, 58 had taken business,
26 had taken both mathematics and computer science, 28 had taken mathematics and
business, 22had taken computer science and business and 14 had taken all the three types of
courses.
D How many students were surveyed who had taken none of the three types of courses?
ii) How many had taken only computer science course? (07 Marks)
c. Three students write an examination. Their chances of passing ur" $, * and { respectively.
Find the probability that : i) all of them pass ii) at least one of them passes and iii) at least
two of them pass. (07 Marks)
a. Define conjunction and disjunction with an example. (04 Marks)
b. Prove that (p -+ (q vr)) e ((p
^
- q) + r) is a tautology using the truth table. (05 N{anks)
c. Define converse and inverse of a conditional. State the converse and inverse of the following
c. Prove by contradiction that"if n2 is an odd integer then n is odd".
d. Provethat forallrealnumbers xandyif x+ y> 100thenx) 50 ory> 50
4 a. State the induction principle. Prove by induction that 6nrz r72n+t is divisible by 43 for each
positive integer n. (0d Marks)
b. For the sequence {an} defined recursively by a1 :8, &2:22, an:4 (a, r - an-z) for n > 3
prove that an : (5 + 3n)2" ' for n >'1. (07 Marks)
c. If Fo, Fr ,Fz - - - - - are Fibonacci numbers prove that f { = Fn+2 -1.
i=0
I of2
(07 Marks)

10. PART _ B
5 a. Define Cartesian product of two sets. For non ernpty sets A, B, C prove that
Ax(B -C):(AxB)-(AxC).
10cs34
(07 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
c.
6a.
b.
'I a.
b.
b. IfA: t|,2,3,4 andR.isarelationonAdeflnedbyR:{(i,2)(1,3)(2,4)(3,2)(3,3)(3,4)}
find R2 and R3. Draw-their digraphs. (06 Marks)
Find the nurnber of equivalence relations that can be defined on a finite set A with I A I
: 6.
(07 Marks)
Let A : R B : {x/x is real and x > 0}. Is the function f : A -+ B defined by (a) : a2 an onto
d.
function? a one to one function? (05 Marks)
Let A : {1,2,3, 4} f and g be functions from A to A given by :
f : {(i, 4) (2, L) (3,2) (4,3)) g: {(1, 2) (2,3) (3, 4) (4, 1)} prove that f and g are
inverses of each other. (05 Marks)
Draw the F{asse diagram representing the positive divisors of 36. (G5 lVlarks)
Let A : dL,2,3, 4, 5, 5,l).R be the equivalence relation on A that induces the partition
A: {1,2U {3} U {4,5,7} U {6}. FindR. (051rarks)
A binary symmetric channel has probabiiity p : 0.05 of incorrect transmission. If the word
c:011011iOi is transmitted what is the probability that i) single error occurs ii) a double
error occurs iii) a triple emor occurs? {06 Marks)
The parity check matrix for an encoding function E:Z) + Z8 is given by :
(t o I I o o)
ltH=lr r 0 0 l 0l
[i o r o o t)
i) Determine the associated generator matrix
ii) Does this code correct all single errors in transrnission?
i) Define cyclic group
ii) Prove that the group @*,*) is cyclic. Find all its generators.
State and prove Lagrange's theorem.
Frove that the set Z with binary operations 0 and O defined by :
x @ y:;1* y- 1
xOy:x*y-xy
is a commutative ring with unity.
Prove that every finite integral domain is a field.
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b.
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USN 10cs35
Third Semester B.E. Degree Examination, June/July 2016
Data Structures with G
Time: 3 hrs. Max. Marks:100
Note: Answer any FIVE full questions, selecting
atleast TWO questions fro* each part"
PART _ A
Write a recursive function to print the permutation of a string (ABC) passed to it as an
argument. (06 Marks)
What is the purpose of using free( )? With an example explain the problem that occur when
free( ) is not used. (04 Marks)
c. Obtain the step count for the C - function to add two matrices of M x N size using counting
method and tabular method.
void add-matrix(int a[][MAX-SIZE], int b[ ]IMAX-SIZEI, int c[ ][MAX-SIZE], int m, int n)
{ int i, j;
for(i:0;i<m; i++)
{
for0:0;j<n;j++;
{
cttlLll : at'lLtl + b[i]Lll ;
II
)
la.
b.
)
I
d. Explain how memory can be dynamically allocated using realloc( ).
(04 Marks)
(06 Marks)
a. Explain how address calculation is done in row major ordering for a Z-dtmensional affay.
Also generalize for n-dimension. (04 Marks)
b. Describe unions used in C. How is it different from structures? (06 Marks)
c. Design an algorithm to add two polynomials using ADT polynomial. (05 Marks)
d. With the help of an example, explain sparse matrix. How the sparse matrix is represented in
memory. Design the algorithm to transpose a given matrix represented as triples in a l-D
array. (05 Marks)
3 a. Write an algorithm to evaluate a postfix expression. Use a stack to evaluate the followinq
postfix arithmetic expression. Show the changing status of the stack in tabular form.
(AB + C -B A + C $-Xor given A : 1, B : 2,C : 3. (06 Marks)
Differentiate between stack and queue. How are they related to LIFO and FIFO concept?
(06 Marks)
Write a program to check whether a given string is palindrome or not using stack. (04 Marks)
What is the disadvantage of queue which is implemented using arcay and how to overcome
b.
c.
d.
I of2
(04 Marks)

12. 4a.
5a.
b.
c
6a.
b.
10cs35
Write a program that create a linked list consisting of nodes of the following struct type and
searches the record of a student whose roll_number is given by the user.
sturct student
{
char name [15];
int roll_no ;
struct student *next i
) ; (10 Marks)
List out the difference between singly linked list and doubly linked list. What are the
advantages of circular list? (05 Marks)
Explain how to reverse and invert a given singly linked list with an example and write its
C-function. (O5Marks)
PART _ B
Write a C - function to insert an item into a binary tree based on direction, (06 Marks)
b.
7a.
Define max-heap and min-heap. How will you represent a max-heap as an alray? Write an
algorithm to insert an element to a max-heap. Create a max-heap : 100 200 -10 -30 -60 80
90 300. (08 Marks)
List various types of threaded binary trees. Explain in-threaded binary iree. (06 Marks)
Suppose the following list of number is inserted in order into an empty binary search
tree(BST) 70 80 60 65 50 45 55,
D Construct the binary search tree
i, Find in order, pre-order and pos-order traversal of BST created
iii) ls the BST constructed at AVL tree? State reasons for your claim. Further if your answer
is negative balance the tree so that it becomes an AVL tree. (I0 Marks)
Explain the activities to be performed to delete a node from a binary tree and write
C-function to delete an item from the tree. (10 Marks)
Obtain the shortest(x) and weight(x) for each node in the following binary trees and iclentify
which is height - based leftist tree and which is weight*based leftist tree. (10 Marks)
Fig. Q7(a)
b"
8a.
b.
Construct an AVL tree by inserting the elements MAR, MAY, NOV, AUG, APRIL, JAN,
DEC; fuLy, FEB, JUNE, oCT, SEPT. (10 Marks)
Obtain the optimal binary search tree for the following items and associated probability.
Keys 10 15 2A 25
Probability 3 3 1 1. (toMarks)
Define RED-BLACK trees. Consider the red-black tree shown below and insert the item 50
into the tree and write the final red-black tree. (10 Marks)
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Third Semester B.E. Degree Ex
Object Oriented Programm
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Time: 3 hrs.
Note: Answer FIVE full questioms, selecting
at leust TWO quntiirnt from each purt.
PART _ A
Explain any three features of object oriented programming.
through a base class reference.
b. With examples explain pure virtual function and abstract classes.
What is function overloading? Write a C++ program to define three overloaded functior-rs to
find the sum of two integers, sum of two floating point numbers and sum of three integers.
c' What are inline functions? Illustrate inline functions with an examptre.
(08 Marks)
(06 Marks)
2 a. Define class and objects. Write a C++ program to create a class STUDENT with the
following specifications.
Data members: Name, Roll No. and Average Marks
Member functions: Read & Write
Use the above specification to read and print the information of 5 students. (10 Marks)
b. What are constructors? Explain the different types of constructors. Write a C++ program to
iilustrate the different types of constructors. (10 Marks)
3 a. What are friend functions? Write a C+r program to find the sum of two cornplex numbers
using friend functions. (10 Marks)
b. Write a C++ program to perform the addition of two location objects by overloading '+'
operator, using a class "LOCATION" with the data members longitude and latitude. Read
and display the location objects by overloading the operators << & >>. (10 Marks)
4 a. Explain the visibility of the base class members for the access specifiers:
i) Public ii) Private iii) Protected.
Illustrate the same with a program. (10 Marks)
b. Write a C++ program to illustrate multiple inheritance and multilevel inheritance. (10 Marks)
PART _ B
5 a. Illustrate with a C+* program the execution of constructors and destructors when single
inheritance is involved. (06 Marks)
b. Explain passing of parameters to base class constructors in multiple inheritance. (08 Marks)
c. Explain the need for virtual base classes. (06 Marks)
6 a. What is a virtual function? Write a C++ program to demonstrate calling of virtual function
7 a. What are streams in C++? Explain C++'s predefined streams? (08 Marks)
b. Explain width ( ), precision ( ) and fiIl( ) functions. (06 Marks)
c. What are IIO manipulators? Explain any five C++ manipulators used for output. (06 Marks)
8 a. What is exception handling? Write a C++ program that illustrates exception handling with
the help of keywords: try, throw and catch. (10 Marks)
b. What is STL? Briefly explain the use of containers, vectors, lists and Maps. (10 Marks)