The document contains questions from an engineering mathematics exam covering topics such as Taylor series, differential equations, Laplace transforms, vector calculus, probability, and statistics. Students are asked to solve problems, prove theorems, derive equations, and perform other mathematical calculations related to these topics. The exam is divided into two parts with multiple choice and numerical answer questions.

1. USN 1OMAT41
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I a. UsingTaylorseries method, solve the problem 9=*'y-1, y(0) = I atthe point x:0.2.
ox
Consider upto 4tl' degree terms. (06 Marks)
b. UsingR.K.methodoforder4,solve 9=:*+{, y(0)$.=l atthepointsx:0.1 andx:0.2
dx 2""
by taking step length h : 0.1. 'nTJ" (07 Marks)
c. Given that g = x - y2, y(0): 0, y(0.2) :0.02,y(0.4) :0.0795,y(0.6) : o.1762.Compute
dx
4 a. Find the bilinear transformation that maps the points z: -7, i, -l onto the points w : 1, i, -1
respectively. (06 Marks)
b. Find the region in the w-plane bounded by the lines x : 7,y: 1, X + y:1 under the
transformation w : ,'.Iodi"ute the region with sketches. (07 Marks)
)z
c. Evaluate I i ,- - dz where c is the circle lzl:3. (07 Marks)
| (z+l)(z-2)
Fourth Semester B.E. Degree Examination, Dec.2015 lJa,n.20l6
Engineering Mathematics - lV
Time: 3 hrs. Max. Marksr100
Note: l. Answer FIVE full questions, selecting
at leust TWO questions from each part.
2. Use of statistical tables is permitted.
PART - A
: 0.8 by Adams-Bashforth predictou*oorrector method. Use the corrector formula
(07 Marks)
a. Evaluate y and z atx:0.1 from the Picards second approximation to the solution of the
following system of equations given by y - I and z: 0.5 at x : 0 initially.
(06 Marks)
b. Given y" - xy' - y = 0 *itt tt. 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 equation y" : 2yy' and
y and y'arq*gqvemed by the following values. y(0):0, y(0.2) :0.2027, y(0.4) :0.4228,
y(0.6):q-6.$41, y'(0): l,y'(0.2): 1.041, y'(0.4) :1.179, y'(0.6): 1.468. (Apply corrector
only
ffie)i (07 Marks)
dvdz:
?=2.
==
x'(y+z)
dx dx
a. Derive Cauchy Riemann equations in Cartesian form.
b. Find an analyic function (z): u + iv. Given u = x' -y' +-J- .
x- +y-
l-.1 .2 I
c. If f(z) is a regular tunction of z, show tnat | {, *i , i tffrl i= 4lf'@)l'
Lox oy )
(06 Marks)
(07 Marks)
(07 Marks)
I of 2

2. 5a.
b.
PART _ B
Solve the Laplaces equation in cylindrical polar coordinate system
differential equation.
probability that the item was produced by machine C.
1OMAT41
leading to Bessel
(06 Marks)
(07 Marks)
(06 Marks)
If o and B are two distinct roots of J,(x) : 0 then prove that JxJ,(ox)J,,(Px)dx:00
ifa+B. (oTMarks)
c. Express the pollmomral, 2x3 -x' -3x+2 interms of Legendre polynomials. (07 Marks)
State and prove addition theorem of probability. (06 Marks)
Three students A, B, C write an entrance examination. Theirchances ofpassing aret/z,Yr,'/+
respectively. Find the probability that,
i) Atleast one of them passes.
ii) A11 of them passes.
iii) Atleast two of them passes. (07 Marks)
c. Three machines A, B, C produce respectively 60%,30%#Q% of the total number of items
of a factory. The percentages of defective outputs of thffifirree machines are respectively
zyo, 30 and 4oh. An item is selected at random affii is found to be defective. Find the
7 a. The pdfofa randondom vanaDle x ls glven
x -J 1 -l 0 I 2 J
P(x) k 2k 3k 4k 3k 2k k
ariable by the following table:
Find: i) The value of k
iv) Mean of x
ii)P(x> 1) iii)P(-1 <x<2)
v) Standard deviation of x.
b. In a certain factory turning 9,,$.razar blades there is a small probability of 1/500 for any
blade to be defective. The blades are supplied in packets of 10. Use Poisson distribution to
calculate the approximat,ps*fnber of packets containing, i) One defective, ii) Two defective,
in a consignment of 10000 packets. (07 Marks)
c. In a normal distribution3lo/o of items are under 45 andS%o of items are over 64. Find the
mean and standard deviation of the dishibution. (07 Marks)
a. A sample of 100 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
from a population with mean life of 40000 kilometers? (Use 0.05 level of significance)
Estahlish 99% confidence limits within which the mean life of tyres expected to lie. (Given
a!@t 26.s5 : l.96,Zo.ot:2.58) (06 Marks)
h.-{}hen individuals are chosen at random from a population and their heights in inches are
i',,,, ,r't foundtobe 63, 63,66,67,68,69,70,70,71,71. Testthehypothesisthatthe meanheightof
the universe is 66 inches. (Given that ts s5
: 2.262 for 9 d.f ) (07 Marks)
c. Fit a Poisson distribution to the following data and test the goodness of fit at 5% level of
significance. Given that ylor: 7.815 for 4 degrees of freedom.
*{<**{<
x 0 2 J 4
Frequencv t22 60 l5 2 I
2 of2
(07 Marks)

3. fQ*es
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Advanced Mathematics - ll
Time: 3 hrs.
Note: Answer any FIVE full questions.
1 a. Find the direction cosines of the line which is perpendicular to
cosines (3, -1, l)an(-3,2,4).
Find the image of the point ( l, -2, 3) in the plane 2x + y * z: 5
Find the shortest distance between the lines
x-15 _y-29 _r*5
8 -5
3 a. Find the constant 'a' so that the vectors 2i- j+ k, i + 2j-3k
b. If cos ct, cos B, cos y are the direction cosines of a line, then prove the following:
i) sin'cr +sin'B +sin'y =2
ii) cos 2cr + cos 2B * cos 2y = - | (07 1{arks)
c. Find the projection of the line AB on the line CD where A = (1, 2, 3), B : (1, 1, 1),
C : (0, 0, 1), D : (2,3,0i). (s7 N{arksi
2 a. Find the equation of the plane through (1, -2,2), (-3, 1, -2) and perpendicular to the plane
)v -v -r-r-6 -0. (6dMarks)
MATDIP4OI
Fourth Semester B.E. Degree Examination, Dec"2015 lJan.2A76
Max. Marks:100
the Iines with dircction
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]:
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Find the unit normal vector to both the vectors
sine of the angle between them.
Find the angle between the surfaces *'+y'+z'=9 and
(2, -1,2).
Find the diiectional derivative of $ = xy'+ yz3 atthe point (1,
normal to the surface xlogz - y' = -4 at (-1,2, l).
(07 Marks)
and 3i + aj + 5k are coplanar.
(06 Marks)
(07 Marks)
4i-j+3k and -2i+ j-zk. Find also the
(07 Marks)
{$7 Marks)
(86 &{arks}
(07 Marksl
is irrotational and find $
4 a. Aparticlemoves alongthecurve x=t3+1, y =t2,2:2t+ 5 wheretisthetime. Findthe
components of its velocity and acceleration at time t: 1 in the directionot 2i+3j+ 5k.
(06 Marks)
x = z2 + y' -3 at the point
({}7 Marks)
-2, -l) in the direction of the
a. Frove that div(curlA; = g.
)+
b. Find div F and curlF where
c. Show that the vector fr = 13r'
+
such that p.= grad$.
F = V(x3 + yt + z3 -3xyz) .
- zyi)i + (3y' - 2zx)j + (3zz - 2xy)k
1 of2
(07 l4arks)

4. "T
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a. Find:
b. Find:
c. Find:
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L
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cos2t
cos2 t),
at .- cos
t"
4s+5
cos 3t) .
ii) L{te-' sin 3t} .
MATDIP4Ol
(06 Marks)
(07 Marks)
(07 Marks)
(06 Marks)
(07 Marks)
(07 Marks)
7 a. nind: f'{ (s-1)'(s+2)j'
l' "-f I
Find: i) L-'{ =
"'' !.' ls'-4s+l3J
Find: L-{.'}
Is'(s+l)J
8 a. Using Laplace transforms, ,o1r. -d'Y -2+* y: e" with y(0) : 0, y'(0) : 1. (10 Marks)
ox ox
b. Using Laplace transformation method solve the difftrential equation y" +2y' -3y=sint,
Y(0) = Y'(0) =0. (l0Marks)
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Fourth Semester B.E. Degree Examination, Dec"20XS/Jaur.ZSXti
Gomputer Organization
Note: ,Answer FIVE full qaestions, selectireg
at least TWO qwestions.from ewch part.
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4 a. Explain with block diagrarn a general 8 bit parallel interface.
b. Describe how a read operation is performed on the FCI bus.
a. Explain the tunction of procesror r.ffifu block diagrarn. {08 Marks}
b. Derive the basic performance equation. Discuss the measures to imlrrove the perfi:rmance.
(08 $[anks)
c. List the different systems used to represent of signed number and give one exarnple for each.
{0.{ hlarks)
2 a. What is an addressing mode? Explain only four addr:essing rnodes wirlh an example for each.
{10 Marks}
b. Registers R.r and R2 of computer, contain the decimal values 1200 and 46CI0. Whai is EA of
the memory opened in each of the following instructions?
i) Load 20 (Rr), Rs ii) Move # 3000, Rs
iii) Store R5, 30(R1, R2) iv)Add - (Rz) Rs v) Subtract (Rr)+" R5 (&5 N{arirs)
c. What is subroutine linkage? Explain with an example subroutine linkage using linkage
register. (S5 Flarks)
3 a. What is interrupt? Explain polling and vectored intemrpts. ({t? s,i{arks)
b. What is bus arbitration? Explain the centralized arbitration with a neat diagrarn" (07 Marks)
c. Wliat is DMA? Explain the registers in a DMA interface. (s6 Marks)
PART _ B
Draw the organization of a 1K x 1 memory cell and explain its working.
Show rvith diagram the memory hierarchy with respect to speed, size and cost.
With a block diagram explain about direct mapping cache memrory.
Discuss the Booth's multiplication algorithm, with an example.
With figure, explain circuit arrangements for binary division.
multithreading.
c. Exptrain single instruction stream, multiple data strearn (SIMD).
Illustrate the steps for non - restoring division algorithm on the follovring data :
dividend : 1000, divisor: ltr. {s5 ilzflarks)
a. List out the actions needed to execute the instruction acid (R:), Rr. Write and explain
sequence of control steps for the execution of the same. {0811{arks)
b. Write a control sequence for on unconditional branch instructions. (04 Marks)
c. Explain the 3 bus organization of the processor. (88 &{arks}
a. With a neat diagram, explain the organization of a shared ffilemory muLltiprocessor. (08 N{arks}
b. What is hardware multithreading? Explain the differerrt approaches to hardware
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Fourth Semester B.E. Degree Examination, Dec.2015lJan"20l6
Graph Theory and Gombinatorics
Time: 3 hrs. Max. Marks:100
Note: Answer any FIVE full questions, selecting
atleast TWO questions from each part"
PART _ A
I a. Determine the order lVl of the graph G: (V, E) in the following cases :
0 G is a cubic graph with 9 edges
ii) G is regular with 15 edges
iii) G has l0 edges with2 vertices of degree 4 and all othervertices of degree 3. (07l!{arks}
b. Define isomorphism of any two graphs. Show that the foltowing graphs are not isomorphic.
(06 Marks)
Fig.Q1(b)
c. Prove that : Any connected graph G is Euler if and only if all the vefiices of G are of even
degree. (07 Marks)
,!^
Ld. Define:
i) Planar graph
ii) Non - planar graph
Show that the complete graph Ks is a non * planar graph. (07 Marks)
Write down the steps involved in the detection of planarity by method of elementary
reduction. (06 Marks)
Determine chromatic number and chromatic polynomial for the graph given O.ro*,.*,
Marks)
b.
C.
Prove that A connected graph is a tree if and only if it is minimally connected. (07 Marks)
Find all the spanning tress of the graph shown below :
Fig.Q3(c)
Obtain the optimal prefix code for the word VISVESVARAYA.
(05 Mari<s)
Indicate the code.
(08 Marks)
Fig.Q2(c)
I of2

7. Fig.Qa(a) Fig.Qa@) Fig.Qa(c)
b. Using the Kruskal's algorithm, find a minimal spanning tree of the weighted graph shown in
Fie.Qa&). (06 Marks)
c. For the network shown in Fig.Q4(c), determine the maximum flow between the vertices A
and D by identiffing the cut -set of minimum capacity. (05 Marks)
PART _ B
5 a. A woman has 11 close relatives and she wishes to invite 5 of them to dinner. trn how many
h
ways can she invite them in the following situations?
i) Two particular persons wili not attend separately
ii) Two particular persons wiltr not attend together.
Detenrdne the coefficient of :
i) xyz' in fhe expansion of (2x - y - 44
i, *'t'rt' in the expansion of (3x - 2y - 4z)7 .
Using the moves R(x, y) + (x + 1, y) and U : (x, y) -+ (x, y + 1), find
c&n one $0 :
i) Frorn (0, 0) to (6, 5) and not rise above the line y: x.
ii) From (2, l) ta (7 , 6) and not rise above the line y : x - 1.
ii| From (3, 3) to (n0, 15) and not rise above the line y: x + 5.
4a.
6a.
b.
a
7a.
b.
8a.
h
Determine the shortest path
directed graph(Fig. Q4(a)).
frorn the vertex 'a' to every
aa+*{<
2 of2
10cs42
other vertices in the foflowing
{CI8 Marks}
(07 l4anks)
(07 Marks)
in how many ways
(05 Marks)
(07 Marks)
each child gets atleast
{06 Marks)
(87 Marks)
Determine the number of positive integers n such that i < n < 100 and n is not divisibie by 2,
3, or 5. (07 Marks)
There are n pairs of Chiidren's gloves in a box. Each pair is of a different colour. Suppose
the right gloves are distributed at random to 'n' children and thereafter the left gloves are
atrso distributed to them at random. Find the probability that :
i) no child gets a matching pair
ii) evenF child gets a rnatching pair
iii) exactly one child gets a matching pair and
iv) atleast 2 children get matching pairs. (07 Marks)
Find the rook poiynomial for the 3 x 3 board y using the expansion formula. (06 Marks)
Find the g;enerating flunction for the following sequences :
i) 12,22,32.42.---- ii)02,1',2',3',4t,-----
ii) I ', 2r, 3', 4', vi) ol, lt, z' , 43, - - - - .
ln how mafy ways can we distribute 24 pencils to 4 children so that
3 pencils but not more than 8.
{Jsing gerrerating function, find the number of partitions of n: 5.
A bank pays a certain oh of anntal interests on deposits, compounding the interests once in
3 rnonths. If a deposit doubles in 6 years and 6 months, what is the annual % of interest paid
by the bank? (od Marks)
Solve therecurrence relation a.r.t+z- 6an11 * 9an:3 x2n -t7 x 3nforn )0, giv'en&0:1,
&t :4.
Solve the recurrence relation &n+l - &n:3n
function,
(87 Manks)
, n ) 0 with ao :1 by using method of,generating
(07 Marks)
Jd
Fig.Qa(a) Fig.Qa(c)

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b.
C.
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b.
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(08 M*rks)
F ourth Sernester B"E" Degree Exarnination, Dec.ZCI1S/Jam"2{}16
lUlicroprocessor
'X'irne: 3 hrs. Max. Marks:1t10
Note: ,Answer any FIVE fwll questions, selecting atleast TWO qaestians frotn each part
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a. Explain short, near and far jump instructions with examples.
b. I)issuss tire fcllowing instructions with examptres :
i) SHR ii) SHi- ii| RCR iv) TEST.
c. Briefly explain rhe string comparison instructions.
PART - B
5 a. Differentiate between Macros and Procedures.
b. Explain the basic rules for using Assembly language with C/C++ for
applicatir-rns with the ireip of examples"
c. Wliat is Inline Assembiy? Exptrain its need.
6 a. Explain the fi-mctions of following pinsin 8086.
0 MN / MX ii) ALE, iii) BHE iv) iNTR".
PART - A
Draw and explain the prograrnming model of 8086 through Pentium processors. (s5 Marks)
Expiain with neat block diagram the working principle of 8085 Architecture. (08 Marks)
Discuss the Flag registers of 8086 with exarnples. (85 &tar!rs)
Briefly explain the concept of Memory paging in 803E5 microprocessor, with suitable
schematio diugru*. (08 Marks)
Expiain the execution of PUSFI and POF lnstruction, with respect to Stack Addressing
mode. (85 Mxrks)
Discuss the Importance of protected mode memory addressing. (06 Marks)
Write 8085 ALP for Reverse a string and check is it palindrome. (05 n,'tarhs)
Explain the following Instructions with examples :
i) XI-AT ii) LEA iii) CMP iv) SAHF
c. What are Assernbler Directives? Explain any four directives rvith suitable examples"
b. V/ith neat diagram, explain minimum mode of 8086 systeni.
c. Expiain Bus tirerings for Read and Write operation for rninineum rnode
(S6 Ii(arxs)
({}8 Marks)
(06 S{arks)
($6 Marks)
(05 Vtarks)
16 bir DOS
({}8 t/trsrks)
(06 Ntarks)
(08 Marks)
{07 &{ar}ls}
of 8085 system.
(SS ft4arks)
a. Explain any two rnethods of Address decoding technique with schematic diagrarn.
(08 S{arks)
b. Design an 8085 based systenn v'rith the following specifications :
i) 8085 in Minimum mode ii) 64 Kbyte EPROM ii| 64 Kbyte RAM.
Draw the completer schematic diagram ofthe design trndicating memory rnap. (sB &{r,rks)
c. Differentiate between Memory mapped L/O and Direct V0. (s4 Marks)
a. Explain with neat block diagram the working operation of 8255 PIPI. (08 Marks)
b. Discuss the basic DMA controller operation in Microprocessor system. {t}6 Mart<s)
c. Expiain any three types 8086 lrrtemrpts. ({,i5 l'trarks}

9. Ms{"{f certRAL
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USN 1OCS43
Fourth Semester B.E. Degree Examination, Dec.2015 lJan.20l6
Design and Analysis of Algorithms
Time:3hrs.
'* ':: -
'i''"''''.d,S;Max. Ma
-'.Q'.g Note: Answer any FfWfull questions, selecting .%"* atleast TWO questions from each part. .,,
-A
a------"'--r -
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ds
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'H *,;VI , qr*
d E I a. What is an algorithm? Explain the notion of algorithm with,.gp$6ffi1e. (06 Marks)
H= b. Explain the asymptotic notations with examples. " tr (06 Marks)
t :" c. Write an algorithm for selection sort. Analyze its efficien- (q8Marks)
Ea - ./rr
-E ll^ h#
:E f 2 a. What is divide and conquer? Explain the genera[4netfrild of divide and conquer. (06 Marks)
H ; b. Write an algorithm for merge sort. Analyze itsFhffiiency. (08 Marks)
I fr c. ApplyquicksortonfollowinglistanddrawQffisivecalltree:5,3,1,9,8,2,4,7.
: .E , (06 Marks)
aE ,*Ofr g "^.-)E 'E 3 a. What is minimum cost spanningrfldlApply Prim's qsnd Sfuskal's. alggrithm on Fig. Q3(a).!aR
Ht *Y/- ;: (loMarks)
ts a4 EI-oE:
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A.t" ^ ffiWrite Dijkstra's shortest path algorithm. Apply Dijkstra's algorithm on Fig. Q3(b) to obtains; .-uJ'.'rr!vsrJelrsoDuvrlwDuyqvL,qrSvrrLura!^PyrJurJrDLr.(LD.Lrts,rrll1rrrJul"rE.vJu,,LUuulal.lu
t g U.& shortest paths. (10 Marks)
E E..rS$' n
5r{+vr
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g
Fie.Q3(b)
I of2

10. 4 a. Explain dynamic programming.
digraph Qa@).
Find transitive closure using
Fig.aQ(a)
"b:"'find'a11'pair shortest'paths using Floid's algorithm for the graph Fig. Qa@).
Find the optimal
programming.
Fig.Qa@)
solution for the following instance o
Item Weieht Y&e
1 2 12
2 1N^; 10
3 (r 20
4 t 2, 15
yw:5
a. Explain different decrease
PAR.T _ B
approaches using example.
b. Differentiate between D BFS.
10cs43
Warshall's algorithm for the
(06 Marks)
a*
.dd'lil,
d,y
.r r
d
using dynamic
(06 Marks)
(06 Marks)
(04 Marks)
(10 Marks)
(06 Marks)
(06 Marks)
(06 Marks)
(08 Marks)
c. Write'Hoiiryi66l?s
In the text : JIM
^6)** ap'o{"
r/
ffidtu.k
problem
for string matching. Find the pattern : BARBER.
IN A BARBERSHOP.
7 ,. ,$$s back tracking? Draw the state space tree for 4 - queen's problem.
qfb$/hat is branch and bound method? Apply branch and bound to the following
. -
' assignment problem :
.^] Job 1 lob2 Job 3 Job 4
$$- f? ': i il ltir;I 5 8 t 8 lPersonc
, L 7 G g 4 Jrersond
c. Explain approximation algbrithm for traveling salesman problem.
8 a. Yfhat is PRAM? Explain PITAM algorithm with example.
b. Explain various computational models.
c. What is list ranking? Explain different types of list rarking.
!f:itf**
2 of?
6 a. What b decisbiHef Draw the decision tree for three element selection sort and estimate
its lower (10 Marks)
(10 Marks)
(08 Marks)
instance of
(06 Marks)
b. Explain ing with examples :
1 lems ii) NP problems iii) NP -,'conplete problems.

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, Time:3 hrs.
Jan.20l6
iii) Process status
Max. Marks:100
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Degree Examination,
Unix and Shell Programming
Note: Answer FIVE full questions, selecting
at least Tl4/O questions from each part.
b.
c.
2a.
b.
4a.
b.
c.
PART _ A
Explain the Architecture of UNIX operating system with a neat diagram.
Describe the salient features of UNIX operating system.
Write a note on man command.
Explain the different types of files supported in UNIX.
Which command is used for listing file attributes? Explain significance of each
output.
Explain with a neat diagram the three modes of Vi - editor-
(08 Marks)
(04 Marks)
(06 Marks)
fleld in the
(08 Marks)
(06 Marks)
(06
(08 Marks)
(08 Marks)
(06 Marks)
(06 Marks)
(08 Marks)
(08 Marks)
x.U.s t .#i*+r,s;'l'lhE
iii;i*.W,-is 50% of
(08 Marks)
(06 Marks)
(08 Marks)
(06 Marks)
(06 Marks)
What are standard input, standard output and standard error? Explain in detail with example.
ine the telm process. E4plain the mechaqi$opsp.o..ss creation in LINIX.
{ab$efelbwinq command with an exam6ilh"*-
f)'' ffi-"fig jobs-in background (& and ffiirl
ii) Execute later (at and batch) r #
Write a note on sort and find.o**ur&J
Differentiate between Hard link and Soft link in UNIX with example.
Explain the following commands with example
'a
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Ba
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c. Explain
i) Head ii) tail iii),Pr (06 Marks)
.,t,,** PART _ B
ffiween a wild card and regular expression? Explain 'grep' command
ith,exarple.
Regular Expressions? Explain any four ERE set used by grep and egrep.
ing and context addressing in sed with example.
Shell programming? Write a shell program to create a menu which displays,
of files
f''1
b.
c.
a.
b.
c.
,1pin itrett features of 'while' and 'for' with syntax.
ain the use of test and
[ ],.!o evalu4!9,,gp expression in shell.
{i:i+r!'S:ll',1:rii,, i
is AWK? Explain"any three built - in function in AWK.
Write an AWK sequence to find HRA, DA and Netpay of an employee, where DA
basic, HRA is l2Yo ofbasic and the Netpay is the sum of HRA, DA and Basic pay.
Briefly describe built in variables in AWK.
Explain with example the string handling function supported by perl.
Explain Lists, Arrays and Associative Arrays with respect to perl.
Write a perl script to convert decimal number to binary number.
l"C,qggrrt user of the system and
ii) Current date
v) Quit to UNIX
3
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What is the dii ::.
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