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3. e.rn dE*;
USN
2a.
c.
MATDIP3Ol
Max. Marks:tr00
(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
{07 Marks)
(07 Marks)
. (06 Marks)
(07 Marks)
(07 Marks)
(06 klarks)
(07 Marks)
(87lvlarks)
(07 lV[arhs)
(07 N4arks)
_*:=::_;
Thind Sernester B.E. Degree Examination, Dec.2015 lJan"20l6
Advanced Mathematics - I
Note: Answer any FIVE fall questions.
Time: 3 hrs.
1a.
b.
c.
Express the following in the form a * ib,
311
--+ " and also find the conjugate.
i+i 2-i l-i
Show that (a+ib)'+(a-ib)' = 2(a2 +6z1nrz cos(ntan-r(b/a)).
Find the fourth roots of i -i16 and represent them on an argand plane.
Find the nth derivative of,cos 2x cos 3x.
If y="asiir1x thenprove that (1-x')yn*, -(2n+l)xy"*, -(n'+u')y, =0.
Find the nth derivative of
b.
L.
()
o!
-O
a!
'=
P _42
g)i
5E
()d
r[i
dJ
gQB
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ts
:q
oj
9.=
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> (ts
c oL)
()=
2<
o
L.J <.^;
;
Z
d
f
(x-1X2x+3)
3 a. Find the angle between the radius vector and the tangent to the curve r:a(l-cosO) at the
T
oolnt 0=-.aa
J
Find the pedal equation to the curve r = a(l + cos 0) .
Obtain the Maclaurin's series expansion of the function e* sin x.
4a.
b.
(,.
If u =e^'''. then prove that x** rP=rulogu .
ox oy
/
tf u = f[I,I,11. pror. that x9. r9+ r91 = o.
yr'*)' &'ay 0z
If u=x'+y'+z', Y =xy+yz+zx, w=x+y+2, find .tr'iu'* '1.
I x'y.z.l
5 a. Obtain the reduction formula for I" = j.or' xdx where n is a positive integer. (tl6 Marks)
0
,to nJ.o*i
b. Evaluate , J. J. xydydx
ttt
c. Evaluate, [[ lf* +y+z)dxdydz.JJJ
000
I of2

4. r
6a.
b.
C.
Prove that F(m,n) = 9P-f(m + n)
4
Evaluate: I*''' $- x)"'dx .
0
@
Evaluate: I xue-'^dx .
J
0
MATDIP3OI
(05 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
i07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)
{07 Marks)
a. Solve:
b. Solve:
c. Solve:
jll .osin2y=xrcos2y.
clx
(ev + ycosxy)dx + (xev + x cosxy)dy = Q .
x2ydx-(^'+y')dy=0.
8a.
b.
sorve:
gJ-69++r 19-6v = o.
dx' dx' dx
Solve : (D' - ily: e* + sin 2x .
Sotrve : (D2 +D+-l)y= 1+x+x'.
8*8{<8
2 of2

5. USN 10cs33
Third Semester B.E. Degree Exani .2015lJan.20l6
Logic Design
.g Time: 3 hrs. Max. Marks:lQP
9
E Note: Answer any FIVEfull questions, selecting atleast TWO questionsfrom
"o"hffiE -^.-_, PART. A ...
E I a. What is Logic gate? State and prove De Morgan's theorems. (07 Marks)
E b. Describe positive and negative logic. Prove 'positive OR" logic equal to "Negative AND"
3 logic. (05 Marks)
E c. Implement the following function by using : i) Nand gates only it) NOR gates only.ar
S Y:((A+B).C).D (osMarks)
il
i 2 a. Find the minimal SOP and minimal POS of the following Boolean function using K - Map.
-l C/^ I ^ l
-S
lf 'l n rn 11 L A/1 / < 11 /nof,f,^-r-.(a, b, c, d) : E. (6, 7,9, 10,13) + d(1, 4,5, fi). (08 Marks)
b. Using Q.M method simplify the following expression aqd realize it by using Nand logic
€ only. (a, b, c, d) : ,(0, 3, 5,6,7,11, 14). . (10 Marks).E only. (a, b, c, d):r(0,3, 5,6,7,11, 14). ,,.t. , (10Marks)
i c. Write a note on Static Hazard. (02 Marks)o
o
E A(x, y, z):2m(1,2,4,6) ; B(x;ay,p).':Xm (0,1,6,7) ; C(x, y,z): Im(2,6).EJI;
E 4 a. With logic diagram and truth tqb&'6xphin the working of master slave (J, K) flip flop.
.9 *.** (06 Marks)
E b. Draw the logic truth tablq@timing diagram of positive edge triggered D - flip flop.
o' (06 Marks)
S . d'n,'ot" '-
c. Write the verilog copgfrl positive edge triggered J.K flip flop. (03 Marks)d u. wfltE r.Irc veruog so$dryd,or posr[rve eugs trrggereo J.r ilrp rop. (uJ lvrarKs,
€ d. With neat diagram, explain the working principles of Switch De bouncer circuit. (05 Marks)
IE
E PART. B
F 5 a. Write a n$tdffi classifications of Registers. (04 Marks)(r
3 b. With n"@Ylagram and timing diagram, explain the working of Serial in - Serial out
E 3 a. Construct 8:1 multiplexer using only 2:1 multiplexer. (06 Marks)E 3 a. Construct 8:1 multiplexer using only 2:1 multiplexer. (06 Marks)
f b. Mention the three differences between decoder and demultiplexer. (03 Marks)
! c. Write the four comparisons between PLA and PAL. (04 Marks)
E d. Implement the following function using PLA : (07 Marks)
Explain with neat diagram, successive approximation A/D converter.
Explain with neat diagram, counter method of A/D conversion.
Write short notes on :
i) Binary loader ir) Differences between D/A and A"/D converters.
$ " ^.^^ .""r-q'-
* regi$ffiJFor explanation construct 4bit register using J.K flip flops. (10 Marks)
-E c. ffiffi v9ril9! qodg fo_r : i) Switche.i tail couiter ii) Shift registers of 5 bits
h., ^tp"lrbtructed
using D-flip flops. (06 Marks)
e.i 6 * M Write the comparison between Synchronous and Aslnchronous counter. (04 Marks)
*#ryqb. Design : i) a divide by 78 counter using 7493 and 7492 IC ii) modulo 120 counter
&d%q .t-' - -.--Q-,
. dq'* using 7490 and74921c. (08 Marks)
tu'*J c. Design a mod 6 counter using J.K flip flops and K - map simplification method. (08 Marks)
i#ffi# c. Design a mod 6 counter using J.K flip flops and K - map simplification method. (08 Marks)
|
* 7 a. Explain the difference between Mealy model and Moore model. (05 Marks)
b. Design a Mealy type sequence detector to detect a serial i/p sequence of 101. (10 Marks)
c. How does state transition diagram of a Moore machine differ from Melay machine?
(05 Marks)
(06 Marks)
(06 Marks)
(08 Marks)
8a.
b.
c.

6. USN 10cs32
Third Semester B.E. Degree Examinat[on, Dec.2015/Jan.20l6
Electronic Gircuits
,UW
Time: 3 hrs. Max. Marks00
Note: Answer FIVEfull questions, selecting
a at least TWO questions from each part.
E
o.
E p,q.nr - aUI
{ I a. What is an operating point? How to choose an operating point for faithful amplification ofc)
input signal? (06 Marks)8an
d E b. Derive the expressions for the operation point in voltage divider bias configuration. Use
H= accurate method for analysis. (08 Marks)
H 5 c. For the circuit shown in Fig.Ql(c), calculate Ig, Ic, V.., V., Vs and Ve. Assume B
: 100
F"]l and Vss : 0.7V (06 Marks)bo ,'
coo
.S .cdf
xbogo
otr
€g
oB
8*
o;l
bd
do
PE
!5
}E
Ed
-bts
6 .lJ
.9aA; 2 a. Bring out the difference between Bipolar Junction Transistors and Field effect Transistors
=G
4& 4 !{& (05Nlarks),o-
5 5 b. Explain;lft,Sbnstruction and working of N - channel depletion mode MOSFET along with
d € its clmr-Steiistic curves . (10 Marks)d.9 its clgt4reteristic curves. (10 Marks)o=
e E c. Li#(hnd briefly explain some applications of field effect transistors. (05 Marks).rn'L
E E P*s,*LiDq.S
ii 3 a- ;pbfine the following terms with reference to photo sensors (08 Marks)
6 ! *-.i'"aa
i E , "". *1 ii) Response time
F E.^ * * iii) Noise equivalent power
!*#4r''' iv) Spectral Response.
: 3 b. Explain the working of a photo diode along with its VI characteristics.
cg
=
&- 1+&
LiDq.S
i i 3 a. ffibfine the following terms with reference to photo sensors
i'i .. ' i i) Responsivity
c. Write a short note on Liquid crystal displays.
(07 Marks)
(05 Marks)C)
o
z
CB
!
o
4 a. With a neat diagram, explain the h - parameter model for common - emitter transistor
configuration. (08 Marks)
b. Explain bandwidth with reference to an amplifier. What are the factors affecting it?
(05 Marks)
c. Explain the importance of cascaded connection of amplifiers, with a diagram. (07 Marks)
Fig. Q1(c)
I of2

7. 5a.
b.
6a.
b.
c.
7a.
10cs32
PART _ B
Classify large signal amplifier and make a suitable comparison. (10 Marks)
With a block diagram explain the working of Negative feedback amplifiers. How ir,ffi{#
affected in these amplifiers? (10 ffid,rkg
p*,*l"qs
*
Explain Barkhausen criterion. -, 'oo Marks)
Determine the gain and phase shift for an oscillator circuit with a 1% positi{ffidback and
a two stage CE configuration. d*
* (04 Marks)
Explain the working of an Astable Multivibrator with necessary diagra@%r{d expression for
frequency of oscillations. dl$ (10 Marks)
t*
qf
What is voltage Regulation? With a neat circuit diagram e)ffildtr the working of a Buck
Regulator. (12 Marks)
Compare linear power supplies with switched mode power supplies. (03 Marks)
A regulated power supply provides a ripple rejection of - 80dB. If the ripple voltage in an
unregulated input were 2V, determine the output rippl"-- (05 Marks)
_ ,%q*
Discuss any five performance parameters of flrMrational Amplifier. (05 Marks)
Explain with neat diagrams, the working of'lok-pass and high pass filters using operational
amplifiers. (08 Marks)
For the relaxation oscillator circuit in Fig.Q8(c), determine the peak - to - peak amplitude
and frequency of the square wave output given that saturation output voltage of op-amp is
+ 12.5V at power supply voltages of t15V. (07 Marks)
O'ot1tp
*:FX**
b.
c.
8a.
b.
c.
e { 'r'
l0 k.vt-
Fig. Q8(c)
2 of2

8. USN
t.
I
(l.
4a.
b.
5a.
b.
1CIC535
(04 iVlarks)
{05 Marksi
Third Sernester B.E. Degree Exa i Dec.2015/Jan.20l6
Time: 3 hrs. Max. Marks:1OCI
PART - A
I a. Explain the functions supported by C to carry out dynamic memory anlocation with example.
(S6 &{arirs)
b. What is recursion? What are the various types of recursion? Write a recursive function to
implement binary search. (s? Marks)
c. Define the term "space and time complexity". Determine the tirne co.rnplexity of an iterative
and recursive functions that adds n elements of an array using tabular method. (07 Marks)
2 a. Write a note on dynamically allocated array's with example. (06 ['trarks]
b. How rvould you represent two sparse polynomials using array of stmcturr;s and also write a
function to add two polynomials and give the analysis of the function. (10 Marks)
c. For the given sparse matrix A and its transpose, give the tripiet representation 'A' is the
given sparse matrix and 'B' will be its transpose.
2s 0 0 ii 0 -10
0t2 3 00 0
Data Structures with G
Note: Answer FIVE full questioms, selecting
at least TWO questions frow ewch part.
3a.
ir.
a)
o
(J
!
o.
(o
E
{)
a)
!
?()
=^-
-,1cO"
troo
<d st
F.
QI
oO
50<
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>6
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:Y
tix
o _-I
O:
=e
:q
>1 '+
ooo
'E':
F>
rJ<
;
z
o
r:.
Sparse matrix A =
0
0
8l
0
0
0
0
0
UL}
00
00
0 -18
60
00
00
00
Define stack. Implement push and pop functions for stacks using arra'ys.
Write the postfix form of the following expressions using stack:
i) A$ts*C-D+E/F/(G+H)
i0 A-B(C*D$E) {odvtrarks)
What is the advantage of circular queue over linear queue? Write insert and delete functicns
for circular implernentation of queues. (05 Marks)
Eyaluate the fbllowing postfix expression 623 + -3 821+ * 2 $ 3 + using stack.
(S4l4arks)
Write C functions to implernent the insert and delete operations on a queue using linked list.
(08 Marks)
lMith the node structure show how would you store the given polynomiais a and b in linked
list? Write a C function for adding 2 polynomials using linked lists. (0tl Marks)
Write a note on doubly linked list. How is it different from single linked list? ($4 N{arks)
PART _ B
What is binary tree? State its properties. How it is represented usinS; array and iinked list?
Girre example. (08 hfarks)
Show the binary tree with the arithmetic expression A/B*C*D+E. Give the algorithm
for inorder, preorder, postorder traversals and show the result ofthese traversals. (08 tr{arks)
What is heap? Explain different types of heap. (84 Marks)
1 of2

9. ,-
10cs35
6 a. Define binary search tree. Draw the binary search tree for the following input 14, 15, 4,9,7,
18, 3, 5, 16, 4,20, 17,9, 14,5 {07 Marks)
b. Construct abinary tree having the following sequences:
i) Preordler seq ABCDEFGHI
ii) Inorde,r seq BCAEDGHFI (05 Marks)
c. Write a iterative search routine for a binary search tree. (05 Marks)
d. Define the following terms:
i) Forests
ii) Graphs
iii) Slinner trees. (03 Marks)
7 a. Briefly explain the following with examples:
i) FIBLT ii) WBLT (08 Marks)
b. Write short notes on:
i) Fr:iority queues ii) Binomial heaps iii) Priority heaps iv) Fibonacci heafl;.Marks)
I Write short notes on:
a. AVL treers.
b. Red-black trees.
c. Optimal binary search trees.
d. Splalr {1ss5. (20 Marks)
*{<*{<*
2 of2

10. :,ilI*
a-)
o
!
c"
-o
a)
a3
.J
OJX
-fidU
7r)
-*tl
(o<
o!
lo
E*
!,:
O(j
-6
+::
-c- Y,
o.!()i
?.2
6=
5.:>a '*
o0-
=o{
=dqo
F>
o
O<
;
Z
d
!
oq
Note: Answer FIVE full questions, sele,cting
st least TWO questionsfrom each purt"
PART _4
I a. Define symrnetric difference of two sets. Also prove by using Venr,L diagram for any three
sets A, B, C (AAB)aC = AA(BAC) (06 Marks)
b. (r) Write the dual statement for the set theoretic results,
u : U = (a n n)r (a^ u)r (" n n)u 6^ ")
-
(ii) Using the laws ofset theory simplify : @u n)n Cu n. (03 Manks)
c. A student visits an arcade each day after school and plays one lJame of'either Laser man,
Millipede or space conquerors. In how many ways can he play one game t:ach day so that he
plays each of the three types at least once during a given school week? (Monday through
Friday). (06 Marks)
d. An integer is selected at random frorn 3 through 17 inclusive. If A is rthe event that a nunaber
divisible by 3 is choosen and B is the event that the choosen numlber exceeds 10. Determine
Pr(A), Pr(B), Pr(A
^
B), Pr(A u B). (s5 Manks)
? a. Prove the following logical equivalence withLout rLrsingJ truth table"
hp ,. (-q r .)]
"
(q
^,
r)v (p n r)e r . ($6 h{arks)
USN
Third Semester B.E.
Discrete
T'ime: 3 hrs"
Degree Examin "?r}l5lJzrn.20l6
Mathematical Structures
b. Define Tautology. Examine whether
[(p
"
q) + r]++ [-o -+ -(p v q)] t a Tautotogy.
c. Establish the validity of the argument:
p+q
q+(r",s)
-r t, (-t .,, u)
p^t
..u
-
3 a. Write down the converse, inverse and contra positive of ,
"V*L* 2
+ 4x - 2l>Ol-+ (x, 3) r (r . -7)]
t0cs34
Ir{ax. Marks:100
the comrpound prcposition
(fi7 &6arks)
(07 Manksi
{03 Marks)
b. Let p(x) :x' -7x + 10=0, q(x) :x' -2x-3=0, r(x):x <Cl. De,terrnine the truth or falsity
of the statement for which the universe contains only the integers 2 and 5. If a statement is
false, provide a counter example.
i) Vx[p(x) + -r(x)] ii) vx[q(x) -+ r(x)]
iv) lx[p(x) -+ r(x)] (05 srarks)
c. Determine the truth value of each of the fotrlowing quantified statements for the set of all
non-zero integers:
0 !x,lyfxy=l] ii) Vx,lyfxy=11 iii) lx,=yll,2x+y=5)zr(x-3y=-B)]
iv) Ix,=y[(3x - y =I]) n (2x+ 4y = 311 v) !x, Vyfxy == 1]. (05 Manks)
d. Estabiish the validity of the following argument,
Vx, [p1x; v q(x)]
rl
rx. [--p(x)]
Vx, [--q(x) v r(x)]
Vx, [s(x) + -r(x)]
-:=x<tl-
I of2
(07 Marks)

11. 4 a. Define tiee well-or:dering principle.
111
-+._---f-_-F....+
5a.
l^
c.
d.
1tlcs34
By using mattrreinatical induction prove that,
n
(07 Marks)
(07 Marks)
2.5 5.8 I .lL (3n - 1)(3n + 2) 6n + 4
b. If F0, F,,IL."..." are Fibonacci numbers, prove that i F,' = F, X Fn*r .
The.Ackermann'rs numbers A-,n are defined recursively for m, ne N as follows:
Ao.n=n+1fnrn>0
A*,0 = A*_r,r :[or m>0
Ar,,,:A*-r,p where P=A-,n-r forrn,n>0. Provethat A,,, =n-12 forallne N.1Oe Marks)
PART - B.
Defrne equivalence relation and equivaience class with one example. (05 Marks)
Let A.:{1, 2,3,4,5}, R be a relation on A defined by aRb if and only if 'a' is a multiple of
'b'. R.epresent the relation R as a matrix and draw its digraph. (06 Marks)
Let A=ti,2,3, 4,5), A relation R on AxA by (",,y,)R(*r,yr) if and only if
xr * yr =xz * y, . Deterrnine the partition of A x A induced by R. (04 Marks)
Consider rtlhe Flass;e diagram of a FOSET (A,R) given below:
If B = {c, d, e}, find (if they exist)
(i) all upper bounds of ts (ii) all lower bounds of B
(iii) the least upper bound of B (iv) the greatest lower
a. LetfR+Rbedefinedby
f -'(- 6,5])
Fig. Q5 (d) bound of B' (04 Marks)
r'(-6), r-'([- 5,5]) and
(05l{arks)
(04 Marks)
(S5 Marks)
[:x-5 forx>o
f(x) ={ find f '(3).
t-3x+l forx<0
b. If f is a real valued function defined by f(x) = x' + I Vx e R.. Find the images of the
fotrlorving: (r) A, = {2,3} (ir) A, = {-2,0,3 (iii) A3 = {0, U (iv) Ao = {-5,3} (s5 Marks)
c. State the pigeon h,ole principle. Frove that in any set of 29 persons at least five persons must
have been born onthe same dav of the week. (04 Marks)
d What is Invediblis function? For the invertible functions f :A -+ B and g: B -+ C , prove
that (g o f)-' = f-' o g-'. (06 NIarks)
a. Definie su.bgroup of a group. Prove that H is a subgroup of a group G if and only if for all
a, be [I, ab-l e H . (06 Ndarks)
b. For a group G, prove that the function f : G +G defined by f(a) = a-r is an isomorphism if
and onlf if G is abehan.
Sfate and prove Lagrange's theorem.U.
d"
8a.
A bfuLary syrnmetrric channel has probability P:0.05 of incon'ect transmission. if the word
C:011011101 is transmitted, what is the probability that, i) a double error occurs
ii) a triple eff,Jr occurs iii) three errors occur no two of them consecu.tive? (s5 Marks)
Find ali integers K and m for which (2,@, O) is a ring under the binary operations
x @ y: x 1- ),- K, x@y : x * Y- mx,. (SS Marks)
b. What is an integrerl domain? Prove that every field is an integral domain. (05 Marks)
c' Let Clbe a group code in Z;. If r e Zi is a received word and r is decoded as the code word.
C. , then prove that d(C., r) < d(C, r) for all c e C . (84 Marks)
d. Frove tha.t in Z,,laf is a unit if and only if gcd (a, n) : 1 and find all the units in Zrz.
I * {< {< *
(06 Marks)
2 of2

12. USN 1QCS36
Third Semester B"E" Degree Ex 'ec.20n5/Jam"2015
Object Oriented Progra g wEth G++
Time: 3 hrs. Max" Mae"ks:100
Note: Answey any FXVE full qwestiows, selecting
atlewst TWCI qwestions frone eack part.,
PART _ A
1 a. State the important features of object oriented programrning. Compare objeci crienteri
system with procedure oriented system. (CI8 Manks)
b. What is function overloading'/ lllustrate function overloading througtr swap function rvhich
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swaps two inieger, two doubXe and two character data.
c. Explain the lvorking of an inline function with example
{0E Marks)
(04 Marks)
(04 Marks)
can be use<i to
(S8 &tari<s)
{CI6 Marks}
(06 1V[arks)
(tr0 Marks)
2 a. Define tlie terin class and objects. Write a C++ prograrn to define a class cc'mplex with reatr
aud imaginary as data rnembers and get_data( ), add{ ) and display*Data( ) as member
function to read, add and display comptrex object. {08 Man-i<s)
b. Explain with example different types of constructors. (08 Marks)
c. Explain with an example the rotre of static data member in a class to count the nurnber of
cbject ereated in a program. (S4 Marks)
Expiain how "ilew" and "delete" operator manages menaory altrocation/de-allscation
dynamically. (08 Marks)
Mhat are friend functions? Why is it required? Explain with the help of a suitable
example" (05 Marks)
o. 'V/rite
a C+]- prograrn to arrange a set of integers and floating point vaiues in asceuding
order by using template functions. (S6 Marks)
4 a. What is inheritance? Explain with example different types of inheritance in C++. (lG &,!arks)
b. With an example, explain the effect of private, protected and public access specifier. When a
base class is inherited by a derived class? {tr0 Marks}
PAR.T _ B
5 a. With the illustration code, explain how the constructors and destructors are invotrved wher"l a
deriveei class object is created. (X0 B{arks}
b. What is the ambiguity that rnight arise in multiple inheritances? Fltiw to overcorne this?
Explain with an example. (06 1!{arks)
c. Explain rnethods of restoring the original access specification of a bar;e ctrass rncml:ers wilen
it is inherited as private.
5 a. What is virtual function? Explain with an example. How virtual function
irnptrement the runtime polymorphism?
b" Explain with an example pure virtual function.
c. Explain horv virtual functions are hierarchical witla an exanrple.
What are various lOStreams in C++? Give the stream ciass hierarchy.
Describe the use of following manipulators :
i) setw( ) ii) setfill( ) iii) setprecision( ) iv) setioflags( ) v) resetioflags( ).(ls Marks)
ffhat is exception handling? Explain with an example how exception is handled in C++.
{10 Marks)
What are standard template library? List and explain any five ntemLier function from rrectors
and lists class in STL. {trs stanies)
*{<*x*
td.
b"
Sa.
b.