This document contains information about an engineering mathematics exam for a fourth semester bachelor's degree program. It provides details about the exam such as the duration, maximum marks, and instructions to answer questions from each part of the exam. The document then lists the questions in two parts - Part A and Part B. Part A contains questions on topics like Taylor series, Runge-Kutta method, Adams-Bashforth method, systems of differential equations, and Bessel functions. Part B contains questions on Laplace's equation in cylindrical coordinates, Legendre polynomials, probability, distributions, hypothesis testing, and curve fitting.

1. USN 1OMAT4l
Fourth Semester B.E. Degree Examination, Dec.2015 lJan.20l6
Engineering Mathematics - lV
Time: 3 hrs. Max. Marks:100
Note: l. Answer FIVE futl questions, selecting 1r'
"'
at least Tl,l/O questions from euch part.
2. Use of statistical tables is permitted.
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PART - A *:;",'
I a. using Taylor series method, solve the problern *= *'y-1, y(0)L*rT, the point x:0.2.
ox
Consider upto 4th degree terms.
b. Using R.K. method of order 4, solve 9 = :* *{,
dx 2'
by taking step length h : 0.1.
c. Given thrt +: x - y2, y(0) : 0, y(0.2) :0.02,y(0.4) : 0.0795,y(0.6) :0.I762.Compute
dx
y at x: 0.8 by Adams-Bashforth predictor-corrector method. Use the corrector formula
twice. (07 Marks)
a. Evaluate y and zatx:0.1 from the Picards second approximation to the solution of the
following system of equations given by y: 7 and. z: 0.5 at x : 0 initially.
dvdzl
*=2. ::=x'(y+z)
dx dx
(06 Marks)
b. Given y"-xy' -y=.9" with the initial conditions y(0): 1, y'(0):0. Compute y(0.2) and
y'(0.2) by taking h: 0.2 and using fourth order Runge-Kutta method. (07 Marks)
c. Applying Milne's method compute y(0.8). Given that y satisfies the equatiotr y" : 2yy' and
y and y' arggvemed by the following values. y(0) : 0, y(0.2) : 0.2027, y(0.4) : 0.4228,
y(0.6) : 0.6841, y'(0) : l,y'(0.2): 1.041 ,y'(0.4): 1.119, y'(0.6) :1.468. (Apply corrector
only on66). (07 Marks)
,ff CauchyRiemann equations in Cartesian form.
U.'' FinO an analyic function (r): u + iv. Given u = x2 -y' +-J- .
'" x-+y-
c. If f(z) is a regular tunction of z, show that [++*l ,t,rrt '= 4lf'e)l'
I dx' dv- |
LJI
(06 Marks)
y(0): I atthepointsx:0.1 andx:0.2
t*|: (07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
4 a. Find the bilinear transformation that maps the points z: -1, i, -1 onto the points w: 1, i, -1
(06 Marks)
1 under the
(07 Marks)
(07 Marks)
respec tive ly.
b. Find the region in tlre w-plane bounded by the lines x :1,y: 1, X + y:
transformation w : ,'.lndicate the region with sketches.
c. Evaluate L ,",'. ^.dz where c is the circle lzl: 3.
r, (z + 1)(z - 2
I of2

2. PART - B
Solve the Laplaces equation in cylindrical polar coordinate system
differential equation.
toMar+r
leading to Bessel
(06 Marks)
5a.
b.
c.
6a.
b.
If o and B are two distinct roots of Jn(x) : 0 then prove that
JxJ"(crx)J,(Fx)dx=0
o ('
ifo+B. 1o7gti#9
Express the polynomial, 2x3 -x' -3x+2 interms oflegendre polynomials.
,
,0, Marks)
State and prove addition theorem of probability. (06 Marks)
Three students A, B, C write an entrance examination. Theirchances of passing are'/2,/r.'/o
respectively. Find the probability that,
i) Atleast one of them passes. .. .,. L.{
ii) Allofthempasses. s. r
iii) Atleast two ofthem passes. "
q&"" (07 Marks)
Three machines A, B, C produce respectively 600A,30o/o, 'fh% of the total number of items
of a factory. The percentages of defective outputs of these three machines are respectively
2oh, 3o/o and 4oh. An item is selected at random and is found to be defective. Find the
probability that the item was produced by machins Q.'::'' (07 Marks)
7 a. The pdfofa ran the following table:
Find:i) The value of k ii) P(x > 1) iii) P(-l <x<2)
c.
b.
iv) Mean of x Elpndard deviation of x. (06 Marks)
In a certain factory turning out ffiar blades there is a small probability of 1/500 for any
blade to be defective. The-hladeb are supplied inpackets of 10. Use Poisson distribution to
calculate the approximafg:'@inber of packets containing, i) One defective, ii) Two defective,
in a consignment of 1_0d,pb packets. (07 Marks)
In a normal distributibi 3l% of items are under 45 and 8o/o of items are over 64. Find thec.
8a.
mean and standard deviation of the distribution. (07 Marks.l
A sample of.{00 tyres is taken from a lot. The mean life of tyres is found to be 39350
kilometers with a standard deviation of 3260. Can it be considered as a true random sample
frora*qppopulation with mean life of 40000 kilometers? (Use 0.05 level of significance)
E;S,turhlish 99Yo confrdence limits within which the mean life of tyres expected to lie. (Given
that Zo15 - 1.96, Zo ot : 2.58) (06 Marks)
b. Ten individuals are chosen at random from a population and their heights in inches are
found to be 63, 63,66,67,68,69,70,70,71, 71. Test the hypothesis that the mean height of
the universe is 66 inches. (Given that to os
: 2.262 for 9 d.f ) (07 Marks)
c. Fit a Poisson distribution to the following data and test the goodness of fit at 5oA level of
significance. Given that yl.*:7.815 for4 degrees of freedom.
{. ,< rk ,k rk
dom variable x is given o
x -3 1 0 1 2 -1
P(x) k 2k 3k 4k 3k 2k k
x 0 I 2 ., 4
Frequency t22 60 15 2 I
2 of2
(07 Marks)

3. US1
Frove that div(curlAl = 9.
) --)
Find divF and curlF where
Show that the vector f, = 13*'
+
suchthat p=grad$.
F = V(x3 + yr + z3 -3xyz) .
- 2yz)i+ (3y' - 2zx) i + (322 - 2xy)k
MATDIP4Ol
Max. Marks:100
the lines with directicn
(06 h{arks)
(06 Marks)
(07 Marks)
z-10:
-_-.-
ancl
-2, -l) in the direction of the
(07 ft4arks)
(06 Marhs)
{CI7 Marks)
is irrotational and find S
b. If cos cx,, cos B, cos y are the direction cosines of a line, then prove the following:
i) sin2 u+sin' B+sin2y :2
ii) cos 2cr + cos 2B + cos 2y = -1 (07 h{arks)
c. Find the pro.jection of the iine AB on the line CD where A = (1, 2, 3), B : (1, 1, 1),
C : (0, 0, i), D : (2,3,0). (07 Marks)
2 a. Find the equation of the plane through (1, -2,2), (-3, l,
2x-y-z-t6=0.
-2) and perpendicular to the plane
Fourth
Time: 3 hrs"
Note: Answer any FIVE full qwestiorus.
tr a. Find the direction cosines of the line which is perpendicular to
cosines (3, - l, l) an (-3,2, 4).
3a.
4a.
o
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.v
soa
'=
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a)6
a=
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dJ
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-c)>r
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q-
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fiti
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(r<
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a)
Z
d
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b.
b.
3 -15 7
x-15 y-29 z-5
=-:- {07 Marks)
8 -5
Find the constant 'a' so that the vectors 2i- j+ k, i + 2j-3k and 3i + a.j+ 5k are coplanar.
t' , ' , + ,l l-, , ,l
(o6Marks)
Frove that I a+ b. b+ c. c+ u l= Zl a, b. c |
. (s7 Manks)
L]L]
Find the unit normal vector to both the vectors 4i- j+ 3k and -2i+ j-2k. Find also the
sine of,the angle between them. {i}7 &4arks)
A particle moves along the curve x = t3 + 1 , y = t' , z : 2t + 5 where t is the time. Find the
components of its velocity and acceleration at time t : 1 in the direction of 2i + 3j + 6k .
b. Find the angle between the surfaces x'+ y'+z'=9 and x=22 +y'-3
(05 &{arks)
at the point
(S7 &Iarks)
Find the image ofthe point (1, -2, 3) inthe plane 2x + y - z : 5.
Find the shortest distance between the lines x - q
=
y +9
(2, -7,2).
c. Find the directional derivative of 0 = xy' + yz3 at the point (1,
normal to the surface xlogz-y' = -4 at (-1, 2, 1).
5a.
b.
(.-
'frL A - .)
h 7h4 Fr.
S emester B.E. D eg ree Exa rninalitiffirE'c "201 5 I J an.2 0 I 6
Advanced Mathematics - ll
I of2
(07 N4arks)

4. -I
a. Find:
b. Find:
c. Find:
7 a. Find:
b. Find:
OS
i
LT
)
:'
bt
L
r)
L
3tl
MATDIP4Ol
(06 Marks)
-' sin 3t) . (07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
ii) L{te
, -rlt, (
t
4s+5
(s-1)'(s+2) I
'
',," {;j#,,}, ) L-'|{"r(=)}
c. Find: L-ri .-t ].
Is'(s + l)J
8 a. Using Laplace transforms, ,ofu. {{ -2+r y = e'* with y(0) : 0, y'(0) : 1. (10 Marks)
dx' dx
b. Using Laplace transformation method solve the differential equation y" +2y'-3y =siflt,
Y(0) = Y'(0) = 0. (l.Marks)
***rkrk
2 of?

5. ({:,H*,lqi 1oEC44r
Y,,__*// gFourth Semester B.E. Degree Examinition, Dec.20l5lJan.20l6
Signals & Systems
Time: 3 hrs. Max. Marks:100
Note: Answer FIVE full questions, selecting ;,,1
at least TIYO questions fro* each part. ,*. * ,
;
: PART-A ,**,,.J r.., .a
€ I a. Sketch EVEN and ODD .o*pon.rtil?itffial x(t) shown in Fig. Q1 (a).
'. ;: too Marks)
i, 4 zttlo.
ElrE ,/-- -- f-- - 'z-
EY :10-n;5<n<10 *.s'r'"l
Hbog d : 0 ; ew (elsewhere / otherwise) fl.i,ri (04 Marks)orF oE
€ .g c. Determine whether the following signals are periodic or not. If periodic find the fundamental
: E period: {,* o
9,a
xc / /
=o /rTnl /',T11
E ! ii) x(t) = x,(t) + xr(t) + xr(t) with fundamental periods of 3.2,9.6 and 12.8 secs for x1, x2
OE
.8
=
and x: respectively. (06 Marks)
€ x A t ----L:----- --- Lr---- -:- --i 'ilr:- -1-- -,:-- F: nr /1 d, , 7
*:- ---r----'-'J' :
E E d. A continuous time signahx(t) is shown in Fig. QI (d). Sketch
E E i v/+r,r't
- t ,i *,
{l.g -z -L to
ER I
60: I
8=
: F" Fig. Ql (a)t "- r1g. Ql (a.)
f" ? b. Determine whether the following signal x1n) isnNeRGY or POWER signal:
'S+ x(n)=1' o<n<5
.= c'A+
-10-n.{(n{1fl {,,,1,,,,
E E ' x(n)=."'(+)*"(?)sE t)
tr
E F ^;'"''. txlto d' f "". " I
;5 rl---
bE ku:" -1
B.U : I
!!tE ;, l
E E ,* L;--
!€ *-&* ,/1H E r*^
it nM
€ E i) x(t)u(l- t) n*i*^
'
x!i
E' e ii x(t)[u(t) - qMM)]E9 *s
eE iii) x(t)[u(t 4;tf
: rftll (06 r]rarks)
lS ^u%.'. lxl+)v;lt
>1r fl]g0;0 * w
o = ,t.&
E S {*iu s
5 0" *#-: #f"#3 k-"L,,W Fig. Ql (d)
irud
o"q * 2 a. Determine and sketch the convolved output of the system whose input x(t) and impulse
-.:6i": " response h(t) are given as follows:
g ,,i _ )
E x(t) = e-3'{u(t) - u(t - 2)}; h(t) : e-'u(t) (10 Marks)
E b. State and prove the Associative property of convolution sum. (04 Marks)
e c. Find the unit step response of the following systems given by their impulse responses:
H
'E i) h(t; =.-l'l ir) h(n): [l']'utrl (06 Marks)
2) /
1 of3

6. t0EC44
3 a. Determine whether the following systems defined by their impulse responses are causal and
stable
i) h(t; = e-3'u(t - 1;
ii) h(n): 4-"u(2-n)
Find the total response of the system given by differential equation, " &;
y'(t)+3y'(t) +2y(t)=2x(t) withy(0): -1, y'(0)=L and x(t)=cos(t)u(t) *.ffiMr
Realize Direct Form - I and Direct Form - II block diagrams for the systffSlen b1
b. Find the total response of the system given by differential equation,
Realize Direct Form - I and Direct Form - II block diagrams for the syst@ffien by the
(04 Marks)
4a.
(12 Marks)
(08 Marks)
a$
,risffi
ffiarxs;
b.
difference equation: y(n) + lVtn - 1) - y(n - 3) = 5x(n - 1) + 3x(n - 2)*fo' 4 -fry*
State and prove the following properties of DTFS: r
., . u,r
i) Frequency shift .t,d
ii) Convolution ,tr "
iii; Perseval's theorem *,
Consider the periodic waveform: #,*,
x(t):4+2cos3t+3sin4t :t',
i) Find the complex Fourier coefficients. *r,h, *
ii) Using Parseval's theorem, find the power siiectrum.
iii) Find the total average power.
,PAnr - g
5 a. Find DTFT of the following .ig,ru
i) x(n) = {,, r.
i.
r, ,}
ii) x(n) = (O.s)^-'u{n)
iii) x(n) : n(0.5)2'u(n)
b. Using convolution
X(eio ) = ----l-':.' (1 - ae-j0)2 '
i) x,(t) = sin C(200t)
ii) x, (t) = sin C2 (2001)
iii) x,(t) = sin C(200t) + sin C'zQ00t)
theorem, find the inverse DTFT
lul. t.
. )'i.r , i ! n.!ar ...+ 1 .. inn?5l*!E!;
(08 Marks)
of X("jn), given
(08 Marks)
.::t .'. . -:. ,l-,r^l,i.iiri**
(08 Marks)
! 1 ,1:f :-,:1r1i!:11{"*,rr,"r. sfigfEf-t
j rrl
c. Find inverse Fourier transform of X(ro) =
fia + z)'
(04 Marks)
6 q- Find the frequency response and impulse response of the system having the output y(t) for
***
.' the input x(t) as given below:
wq T x(t) = e-'u(t) ; y(t) = e-2'u(t) + e-3'u(t) (06 Marks)**{[*
,j"fiq" b. Find the Fourier Transform representation for the periodic signal x(t)=3+2cosnt and
^"{" draw the spectrum. (06Marks)
c. Specify the Nyquist rate and Nyquist intervals for the following signals:
2 of3

7. r r ^$"h'x(n) = 6(n) + -5(n - 1) -:5(n - 2) f,*''
48'nl
?U
Y(n)=S(n)-ja(n-t). f-'4 iJ
b. A LTI discrete time system is givon,6y the system function H(z) =
FndZ-transform of given x(n). Sketch ROC, poles and zeros of x(z)
x(n) = d-l)'u(n) - 2[3'u(-n - r)] (04 Mar-ks)
2) L ,J
.f*-;
b. Determine the signal x(n) whose z-transform is given by, x(z) = log(1 - az-' ); lzl > td 161
using properties of z-transform. ,
(Qa Mark$
Find inverse z-transform of the following: 'i* * '
#
,$#
-Zr-r
i)x(z)=#;RoC.lZl,l:Usepartialfractionexpansion**j,,o+u*'
&*"-#
ii)x(z)=#;RoC.lZl.1.U,.longdivisionmethod.(08Marks)zz -52+r /.
Find x(o) if x(z) is given by,
.- z+2
t) .-
' (z-0.8)'
i1) (04 Marks)
(08 Marks)
3 - 4z-l
| -3.52-1 + l.5z-2
.
rr si:#r{r#}#!flH
l|:
.. r i ; r,6"t:4. ltli*.: ,r :
,,i,**t:i,*r*i$i&S
8 a. A causal system has input x(n) and output y(n). Find the impulse response of the system if,
z+7
3(z-t)(z + 0.9)
3 of3
Speci$ the ROC of H(z) and'rdetermine h(n) for the following conditions:
i) the system is stable -, ;.
'
i) the system is causql o. (06 Marks)
c. Solve the followingffierence equation using unilateral z-transform for the given input and
j}-#,'liii$fr'$W,, *nn x(n) = u(n) and y(-1) : 1. (0o wtarte ";4^ s /)F
lbi Iq. t/
r&*
^*
-&ta & *a
"'-i. s
}(.'&q
{
d*" %d
L}
Ih. t

8. USN 10E,S43
Fourth S emester B.E. Degree ExamifrAflon, D ec.20 1 5/Jan .2016
Gontrol Systems
Time: 3 hrs. Max. Marks:lGQ
Note: Answer any FIVE full questions, selecting , *u*',
atleast TWO quesfionsfrom eachpart. d%,
'
d ^.^-
€ PART-A *ry;*E - -:n ,r . , r 1 , 1 , # 'e%'*
E I a. Briefly explain the requirements of a good control system. _
q.+ry (06 Marks)
E U. Show thaithetwo sysiems shown in Fig.qr6Xi) and Fig.Q1(b)(ii) a*eh;f6gous system by
€ comparing their transfer functions
s h
(06 Marks)
o-
(ittr
-g ^AAAA--..--*=,, 1 no,
14)
13^
Ei V; * vz- n,i, ,"-I I lc r *"?,2'
=:
.* +
f; i., Fig.Ql(b)(i) * tk:J ' Fie.Q1(b)(ii)
E ; c. For the mechanical system shown in Fig.Q[S), i) Draw the mechanical network ii) write
; E the differential equations. iii) draw forcg- volfage analogous electric network. (08 Marks)6 ;
a-------
r
;ffiF/
dvninE-:fron. I)
9,e A Ks
.= 6 |l-a#1-_..], b7-
eB X lr, l*E€ 4 ;trf
$; ^X e: t ^- l*,
€ E ot r I
E€ ) ',,4-+ ts ,*--p
i'/7777747-
E i '#tr* Fig.Ql(c)
A-
*x ".*
g + 2 a. Illustrate ffi#/to perform the following in connection with block diagram reduction
; S techniqqeg.
g E i)- F{*,ffi"e take - off point aft,er a summing point-a tE ..{
H E it}%ffiifting take - off point before a summing point
E # *i'ii)=" Removing minor feedback loop. (06 Marks)
ilb b" - What is signal-flow graph representation? Briefly explain the properties of signal flow
H oo t&dr
E E .".-a graph. (06 Marks)
E P - .
b. Draw a block diagram for the electric circuit shown in Fig.Q2(c) and obtain the transfer
g H .
r,*h"
!t,@:k tunction :4?. (08 Marks)
" a Ei(s)
-j c.i'
; R,, C>
E
E eftfr I In, *n,gtctff--i
Fig.Q2(c)
1 of3

9. 3 a. Show that the steady state error
with -ve feedback.
108S43
.* = groffi using simple closed loop system
(06 Marks)
b. The block diagram of a simple servo system is shown in Fig. Q3(b). Compute the values of
K and T to give overshoot of 20% and peak time of 2 sec. (06 Marks)
Sq**
:, 1
CCs) d,, ",/ * -l
"
Fie.Q3(b) ,...
u
iJ*
c. Referring to Fig.Q3(c), find the following : i) transfer tunctiorrl P iD €, Wn iii) % Mp,
d*,
* F(s)
T. andTr. where K:33 N/m, B:15 N-Vrn, M:3 tg.(# (08Marks)
+ t+)
"t*"Pig.Q3(c)t,"l1"..l
What is stable and unstable systffi? What is the difference between absolute and relative4a.
b.
stable systems? (06 Marks)
than -1. (06 Marks)
c. The open fer function of a unity feedback, open loop control system is given by
G(s) =
K(S'+ 10)
-#,1)findtheva1ueofKsothatthesteadyStateerrorforaunitys'(s' + 2s +10)
and angle of departure. (06 Marks)
pqgabo,{ic input is < 0.1 ii) for the value of K found in part i) verify the closed loop system is
q+S-le or not. (08 Marks)
t"q l$,
*s
" ffiP* pARr - B..
',--#'t K
"r,,5a.ConsiderthesystemwithG(s)H(s)=*,furdwhethers:_0.75ands:_1+j4
_ )S# s(s + 2)(s + 4) '
Q - is on the root locus using angle condition. (04 Marks)
b.ForasystemhavingG(s)H(s)=#.Findtheva1idbreakawaypointS
c. Show that the part of the root locus of a system with G(s)H(9 =
ffi
is a circle having
center (-3, 0) and radius at Ji.Qsing both graphical and analytical method). (10 Marks)
frnPlnliry
2 of3

10. What is lead and lag network?
do qnain.a.ppro ac[, ..
108S43
(04Marks). r- '3:{a-',:1,+'a
of lead qrd lag compensator. , .(05 yarko
(06 Marks)
(08 Marks)
$$I
6a.
b.
c. For a control system having G(s) = ,, K *0'5t)
.= ,. , draw bode plot, with K =e s(l+ 2s)(1+ 0.05s + 0.125s')
4 and find gain margin and phase margin. (10MaI[O
7 a. Draw polar plot of : i)
*
G(s)H(s) - loo
^:fti""m;(s+2)(s+4)(s+8)' C};-
J
b. State and explain Nyquist stability criterion. ?,^
t (04 Marks)
c.ForthegivensystemG(s)=ffisketchtt,.Nvq.}id'dtanddetermine
whether the system is stable or not. * , J ;
tt* (10 Marks)
'* .*"
8 a. Construct the state model using phase variables if the sy:tq*nis described by the differential
equation
'
d'v(t)
*
4d'zvlt)
.qP +2y(t)= su(t)ffi;,}* state diagram. (06 Marks)
dt' dt'
b. List the properties of the state transition mafi'
r;mr.
c. Obtain the state transition matrix for : A = lfrW, I
.
!zbN/ - Jl
fti,q*d**dr
"qr ?
1" *
& d {<{<*,1.*
-*d*,w-3t"+ "+.;!"
i:.. 4
&.**W
-*s**iuk#
nffit*
t
r $
e"-o.. h
ff*
3 of3

11. CElt?r' i'
LlsRs''"
USI
b.
8a.
b.
r0EC45
(10 h{arhs}
{04l4arks}
(05 i!{arks}
(06 &4arksi
(&4 Marks)
{tr0 N'Iarks}
(10 Marks)
(18 Marks)
(05 NIarks)
(85 Nlarks)
Fourth Sermester B"E" Degree Exam Dec.2015l&an"?$tr 6
Tirne: 3 hrs. fu{ax. Marks:tr00
PART _A
tr a. Mention the styles/ types of HDI- Description. Explain any 2 types with an example of half
FundamentaEs of HDL
Note: Answer FIVE fwll qwestions, selectimg
at least TWO qaestions from each part
adder in both VHDL and verilog.
'b" Vlention the Data types used in VHDL and verilog
c. Distlnguish between Verilog and VHDL.
examptre.
c. What are vector data types? Explain them in VHDL and verilog.
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2 a. Write a dataflow description for 4bit ripple carry adder in VHDL and verilog. (10 Marks)
b. Explain the signal declaration and variable assignment statement used in F{DL with at:
3 a. Write bekravioral description af 2 : I multiplexor using,if-ense in /HllL and veritrcg.
b. Write behavioral description of half addressing VHDL.
c. Write VI{DL and verilog codes far 4 x4 bit Booth algorithrns.
4 a. With Logic diagram, write structural desoription for 2 x 4 decoder with 3 state output both
{SE Marks}
{04 h{arks)
{08 Marks)
in VFIDL and verilog.
b. Mention different types of binding. Discuss binding between
i) 2 modules in verilog ii) between library and component in VFIDL.
PART_- B
5 a. Write VHDL description of an N - ilit - ripple carry adder using procedures and verilog
description using tasks.
b. Write veritrog function to find greater of 2 signed numbers.
c" Write a note on VHDL file processing
6 a. With a block diagram and function table of SRAM, write FIIDL codes for 16 x 8 SLAM.
(12 iVEartcs)
b. Write a VF{DI- code for addition of two 5 x 5 matrices, using a package. (08 N{ar[<s)
7 a. How do you invoke VHDL entity from verilog module? Explain with an example.
(SE N{arks)
With the help of block dia explain mixed language description of 9 birt adcler. (12 Marks)
What is meant by synthesis? List and explain the steps involved in syrthesis. (0s Marks)
ilesrgn gate levetr sis and write VH
lnput Outputs
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00 (ceirt) 0-7 z: temperature
0i (offset) 0-7 z: temperatwe *4
l0 (hatrf) 0-7 z: temperature I 2
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Time: 3 hrs.
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Fourth Semester B.E. Degree ec"20151Jan"2016
Linear IGs and Applications
Max" Marks:100
Note: 7. Answer uny FIVE full questions, selecting
aileast TWO qaestions.from euch purt.
2. Missing data, tf any, naay be asswmed switwbly.
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{05 1{arks)
: R3 : 2.2K a*d Rz : 220 K.
(X{} Marks)
inverting summing aiaptrifier
{S4 N{arks)
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PART _ A
With a neat circuit diagram, explain the basic op-amp circuit.
The non - inverting amplifier uses pA 741 op-amp with Rr
Determine maximum possible output offset voltage due to :
il input offset voltage of 5 mV
ii) input bias current of Ig 1*u*y
: 500rlA
iii) Input offset current of I;16s;: 200 rlA
iv) iv) resistance toierance of + 10%.
Obtain the expression for output voltage for the two input
circuit.
o.
Draw a neat circuit diagram of a capacitor coupled voltage follower and explain its operation
with necessary design steps. (SB fi4arks)
Design a high irnpedance capacitor - coupled non-inverting amplifier to have a lorv cr;toff
frequency of 200 Hz. The input and output voltages are to be 16 mV and 4V respectively
and minimum load resistance is 10 KQ. Select R, : 1 Me) and C1 : 0.1 pF. (sG Nlarks)
Explain how the upper cutoff frequency can be set for in',rerting amplifier with the help of
neat circuit diagram and also explain design steps.
3 a. Define loop gain, loop phase shift, pole frequency and phase margin.
b. Explain miller effect compensation.
c. For the circuit shown in Fig. Q3(c), calculate :
i) Full power bandwidth of tr V peak input and op-amp slew rate of 250 V/ps
ii) Maximum peak output voltage obtain for input signal of ill0 KHz ar:ld with slew rate of
05V/r rq {{}4 {arks)
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(S4 h'narksi
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List the precautions to be observed for op-amp circuit stability.
I of 2
(06 N{arks}

13. a. Design the current source circuit shown in Fig. Q4(a) to produce a
iaad. Use a+ l2Y supply and an LM 108 op-amp.
10EC46
100mA output to a 40 fl
(06 Marks)
(08 Marks)
(06 Marks)
(06 Marks)
(06 Marks)
b.
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b.
c.
6a.
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Sketch the circuit of a current amplifier with floating load. Explain circuit operation and
derive an equation for current gain. (06 Martr<s)
What are the advantages of precision rectifier over ordinary rectifier? Exptrain the working
ofa full wave precision rectifier. (08 Marks)
PART _ B
With relevant diagram, explain the operation of negative clamper circuit using op-lffiFnauruO
Design a triangular waveform generator to produce a *2Y, 1K*12 oufirut. Use a +l5V
supply. Also calculate the minimum-op-amp slew rate.
Exptrain the v,zorking of phase shift oscillator using op-amp.
3-terminal regulator.
c. Explain the operation of basic high voltage regulator using IC 723.
With relevant diagrarns, explain basic inverting and non-inverting colq)arator circuit with
V1g1: 0V. (06 Marks)
With a neat circuit diagram, explain the operation of inverting Schmitt trigger circuit and
discuss the desigll procedure. (1S Marksi
c. Using 741 op-arnp, design the first --order active low-pass filter to have a cutoff frequency of
1.2 KHz. (S4 Marks)
7 a. Briefly expnain the standard representation of 78XX series 3-terminai [C regulators and
enumerate the characteristics of this type of regulators. (08 Marks)
il. With the help of neat diagram, explain the operation of adjustable regulator using fixed
8 a. Explain the operation of a mono - stable multivibrator using 555 iC timers. (0d hdarks)
b. Explain the operation of phase - locked loop (PLL) with the help of neat btrock schernatic
diagrarn. {08 Marks}
c. What output voltage would be produced by DAC whose output range is 0 to tr0 V and whose
input binary number rs
i) 10 (2 bit DAC)
ir 0110(4bitDAC)
iii) 1 0 i i 1 I 00(forSbitDAC).
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Time: 3 irrs.
Microcontrollers
Note: Answer FIVE full questions, selecting
at lesst TWO questions from each trtart"
PART _ A
a. With neat diagram, with the programming model of 8051 with addresses of SFR's and ports.
Also give tr28 bytes RAM allocation. (12 Marks)
b. Interface 8051 to 8K external RAM and 32K external ROM and explain how 8051 access
thern? (88 Marks)
a. Explain difference addressing modes of 8051. Give an exannple for each of thern and
mention liraitations of each. (0T hfarks)
b. Explain the following instruction of 8051 with example (values).
i) xcr{D A1 @ Ri ii) Movc N @ A + pc iii) swAp A
iv) RL A v) MUL AB vn) DA A {89 Marlls}
c. Examine the foilowing code and analyse the result with ftrag register. Conter"lt
MOV Ar # -30d
MOV Rr, # -50d
ADD A, Rr {04 Marks)
a. Explain the different types of conditional and unconditional jurnp instruction of and
unconditional jump instruction of 8051. Specify the difference range associated with jump
instruction. (88 Marks)
b. Classify the CALL instruction in 8051. Explain each one. (06 Marks)
c" Write a program to generate and store Fibonacci terms, which are less then FFh. ($6 Marks)
a. What are assernbler directives? Explain any four of them. (05 Marks)
b. Write a program to find LCM (List Common Multipiier) of two nurnber rnr and mz.
i09 Marks)
i&6 Marks)
a. Explain TMOD and TCON register of 8051 timers. (ls Martrs)
b. For every 50 chocolates, vending machine is getting heated up, it requires minimum of l sec
break after every 50 chocolates. Provide solution for this real time problem" (10 Nlarks)
What is baud rate? Which timer of the 8051 is used to set the baud r:ate?
Explain SCON register with its bit patiern.
c. Explain the advantages of interfacing 8255 with 8051 pc.
I a. Explain MSP430 architecture withrreat block diagram.
b. Explain memory address space of MSP430 with neat diagrarn.
c. Write ALP to f,rnd larger element in a block af data using MSP430.
c. Explain C data types for 8051 with their data size in bits and data range.
PART _ B
Write a 8051 program to send the data message " MICROCONTR.OLLERS " of the length
l7 character at a baud rate24A0,8bit data, lstop bit serially. {CI8 Manks)
7 a. Coirrpare polling and Interrupt. Explain the six intemupt of 805 1, vrith priraary and interrupt
vector tabtre. (08 Marks)
b. Write a program to rnove stepper motor by 20steps is anticlockwise d,{rection interface.
({18 Marks}
(04 Marks)
(08 Marks)
(04 Marks)
(08 Marks)
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