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[3 Hours] [ Total Marks: 80 $+'(1) Question no. 1 is compulsory. I '/'a-(2) Attempt any three of the remaining O-

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I t*V+Vrla* +x2dy where c is the closed curvb of the region touo(#bY )r:x and )r: x2' . : "SCD) Use Cayiey-Hu*iitoo iheorem 1s ffnd.As- 4A1 -7f+77A2'rr'i0('|in tenns 5

.oorAwhere* [l i] ^, ,5i-

(c) A continuous random variable has probability densi$Enction 5

f(x): 6(x-x) 0<x<1 Find mean and variance' 6)(d) A random sample of 900 items is found to havq;sean of 65.3cms. Can 5

itbe regarded as a sarnple from_a large poputffinhhose moar is 66.2cms.

and standard deviation is 5 cms at 5% leveMf siqnificance.,(y--

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QP Gode: {2404

N.B.

1.

2. (a) Calculate the value of rank correlatiorl$fficienl from the folowing data

regarding marks of 6 students in ics and accountancY in a test

(b) lf l0% of bolts prod a machine are detective. Find the probability

(c)

) In aJ@ratory experiment two samples gave the following results.

d;" size mean sum of squares of deviations

)\ ,12

1013

'15

l490108

Test the equality of sample variances at 5o/o level of significance.

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A ts -6 2fShow that the 6frt" A:l -^6 ;^ -?iJrruw ,,,", .:bo'^.^ _ ^ L2 _4 3

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is diagona[kdble. Find the transforming matrix and the diagonal matrix.

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at random atmost one will be defective.

8

6

a

2 QP Gode : { 2404

(b) Find the relative maximurn or minimum of the function. 6 c^\V-,

z: xr2+xr2+L2-6xr -10xr-14xr+103 qt(c) prove ttrat F: Sr2cosx4z3)i +(2ysirx -4)i +(3x*+2)k is a conservative field" t C\'

Find the scalar potential for p and the workdone in moving an object in . O.dthis field from (0, 1, -1) ta 1|, ^t,21 .$=-

,v(a) The.weights of 4000 students are found to be normally distributq{ with

mean 50kgs. and standard deviation 5kgs. Find the. probahilif tl-A$E:dent4. V

\/IJ'#;T ffi ffi?'i*"";*,i=iD^ T*; io; ;t u*; r;o'(ii) betrveen 45 and 60 kgs. 'i.

^.}.-(b) Y,::*tr's

Dever*e"r: *.:t"- -3fJJN.eds r,vhere F: +xi+3y3-22fr. and s is.the t,rfl. bounded by, _s-

(c) Based on the- following data, canyou say that4fre is no relation between

5. (a)

(b)

(c)

smoking and literacy. X,smokers ,arra*nkeF

LiteratesIlliterates

8345

s7 -o68 ,?

A random variable X foilows distribution with variance 3 calculate

p(X:2) and p(X24)

.V' r-Use Stoke,stheorem.$Bvaluate J f .dr u,here F:x2i+xyj and c is the

A;bounCary of thg.Qtungt. ;<:0, 5C, -Fit,'y:b

Find the equati# of the two lines of regression and hences find correlation'-\-)

co efficient Jfo-m the following data.,^.S

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6. (a) Two independent samples of sizes 8 and 7 gave the following results ' 6 c

SarnPle 1: 19 17 15 21 16 18 16 14

sam;le ,: 1s t4 t5 19 15 18 16 OO*"

Isthediflerencebetweensamplemeanssignificant. -.S,l)

(c) use the Kuhn-Tucker conditions to solve the following N'r rsMaximise z:2xr2-742+l2xrx,

_CO.Subject to 2x,*5xr<98

-q}-x,xr>0

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SUg:SURflQ.P. NO :12434

(3 Hours)

N.B, : (l) Question No 1 is compulsory.

(2) Attempt any three from the remaining questions.

(3) Attempt sub question in order only.

(4) Assume suitable data , if required and state the same clearly.

(5) Figures to right indicate fulI marlis.

"f'

i. Solve zrny iouroithe follbwing. .aS 20

(a) Draw aneatsketch of simple circular curye & show all elemerlqro(b) Explain use of computer in surveying.'

. + dS(c) ExplainprinciPles ofEDM <e'(d) Explain field method to determine the constant of a taffimeter ?

(e) Differentiate between land survey and constructiong{eV ?

rr2. (a) Describe the principle of tacheometry and dffientiate between fixed hair 8

method and movable hair method of tu.t .offi(b) A fixed hair tacheometer fitted with an a@raYtic lens with instrument constant 12

of 100, was used to determine the sl point P &Q.The following

reading were taken. If the staffwas fr$}d vertically, compute the gradient from P

&Q

Inst.Station

Staffstation

,.urro:{ )\Reading of' Stadia hair

Reading ofaxial hair

Verticalangle

A P

v .:60.91s 2.s8sa.750 3.7i5,

1,7s02.240

+ 150

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-o-3. (a) What is transiRi?trrves ? Why it is provided, explain different types oftransition

curye. ^Q'(b) Two tango$d intersect at chainage 7250 m. The angie of intersection is 1500.- Calcu,pfall data necessary for setting out a curye of radius 250m by the

.' al"fl&fon angle method. The peg intervals may be taken as 20m.*fr<S' 4. tu) C$hat dou understand by setting out work? Explain in detail the procedure for

, *f setting outwork for abuilding.

NE A gradient of -2.5% meets a gradient of +3.0% at a chainage of i350 m and

Srt elevation of 140rn. A vertical curve of length 200m is to be set out with pegs at

C 20m interval. Caluculate the elevation of Pegs by chord gradient method.

aS'P GN-Gon,85o3-{4. (TtrRNovER)

10

10

10

10

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ITotal Marks : 80

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Q.P. NO t12434

,25. (a) Compare a conventional theodolite with electronic theodolite.

(b) What is precise levelling? Which instruments are required for it? Explain how it 10 J.is conducted in the field? 19'

.d6. Write short notes on - td^

(a) Total Station i'| S ",()'

(b) GPS and Rernote sensing {9(c) Subtense barmethed XS(d) Use of laser in surveying - Cf

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