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# 4th Semester (June; July-2015) Civil Engineering Question Paper

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4th Semester (June; July-2015) Civil Engineering Question Paper

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### 4th Semester (June; July-2015) Civil Engineering Question Paper

1. 1. USN lOMAT41 CJ (J 9 ? vt Cd ! 6) C6 c) a c)xbo# Q:a va EO 7n O{., "troo .E .cC\$ xaoY q.) ()tr -tr o) Lr L. oB E2 AEO-* b6 (s0 ooc Er-o }EC6-t t(g its!oql! d. g. tro, 6Gt o.i L. '!-'! o)= }UUl'rE c.H6= rr C) 6.v>) q- b{)o tr60 (J= o.u :; o< -,r' c.i C) o.i Z .!rr.iiii.Yi 9 :1ilr I (!i j t< r= Enginee ring Mathem atics - lV Time: 3 hrs. Max. Marksrl00 Note: Answer eny FIVE full questions, selecting atleast TWO questions from ea,ch part. PART. A a. Obtain y(0.2) using Picards method upto second iteration for the initial value problem Fourth Semester B.E. Degree Examination, June/July 2Ol5 + = x= -2y y(o) = l. dx b. c. 2a. ",,.' 06 Marks) Solve by Eulers modified method to obtair y( 1.2) given y' = ffi yQ) = 2. (07 Marks) , Using Adam Bash forth method obtain y at x = 0.8 given'. ' (07 Marks) dvr^ a=x-y' , y(0)=0 , y(0.2)=0.02 , y(0.4)+,0;0795and y(0.6)=0.1162.1J ox {'"}.., ,, i% .,,,,,-'..f Solve by 4'n order Runge Kutta method sim-ut#e'ous equations given by dx dv t"'l -=y-t , +:X*t withx= 1=!af t=0, obtainy(0.1) andx(0.1). dt dt :' (06 Marks) b. Solve di / du ' i - dx, -.|.AJ * y' =0, y(%= t, y'(0) = 0. Evaluate y(0.2) correct to four decimal places, using Runge Kutta method of fourth order. (07 Marks) c. Solve for x = 0.4 using Milnes predictor corrector formula for the differential equation y" + xy' + y = 0 with y(0) = l, y(0.1) = 0.995, y(0.2) = 0.9802 and y(0.3) = 0.955. Also z(0) =9, z(0.1)=-0.099s , z(0.2) --0.196, z(0.3) =-0.2863. (07 Marks) Verify whether f(r) = sinZz is analytic, hence obtain the derivative. (06 Marks) Determineiil.analyticfunctionf(z)whoseimaginarypartis*(07Nxarks) x-+y- Dgfine a harmonic function. Prove that real and imaginary parts of an analytic function are offior't. (07 Marks) ". ' Under the mapping w = e', find the image of i) I <x<2 ii) % . y . ;. (06Marks) Find the bilinear transformation which maps the points 1, i, -l from zplaneto2, i, -2 into w 3a. b. c. i ,\$;t3iu' i"' ' b. plane. Also find the fixed points. c. State and prove Cauchy's integral formula. (07 Marks) (07 Marks) (06 Marks) (07 N{arks) (07 Marks) PART - B a. b. c. Prove Jn(x) = * [J^ r(x) * Jn+r (x)]. Prove (n+1 ) P,(x) - (Zn+l) x P,(x) - n Pn-r(x). Explain the following in terms of Legendres polynomials. ^o+3x3-*'+5x-2 I of 2
2. 2. a. A class has l0 boys and 6 girls. Three students are selected at random one after another. Find the probability that i) first and third are boys , second a girl ii) first and second are of same sex and third is of opposite sex. If P(A) =0.4, P(B/A) = 0.9, P(B/[) = 0.6. Find P(A/B), P(A/B ). (06 Marks) (07 MarH\$b. c. c. Xn a bolt factory machines A, B and C manufacture Za/o, 35a/r, and 457o of the total.,gf"fteir outputs 5a/o, 4o/o and 27o are defective. A bolt is drarvn at random found to be"'dHbCtive. What is the probabiiity that it is from machine B? ,**q' (07 Marks) a. A random variable x has the foll distribut Find k, mean and S.D of the distribution. (06 Marks) b. The probability that a bomb dropped hits the target is 0.2. Find the probability that out of 6 bombs dropped i) exactly 2 will hit the target ii) atleast 3 will hit the target. (07 Marks) Find the mean and variance of the exponential distribution. (07 Marks) A die is tossed 960 times and 5 appear 184 times. Is the die biased? (06 Marks) Nine items have values 45,47,50,52,48, 17,49,53,51. Does the mean of these differ significantly from assumed of mean of 47.5:',(, = 8 , to.os = 2.31). (07 Marks) c. A set of 5 similar coins tossed 320 t ives following tablS I ves w e. No. of head*,"r* ,,Q; I 2 3 4 5 6 27 72 tt2 7l 32 Test the hypcthesis that data folloiili binomial distribution (Given y - 5, Nl.r, = 11.07) (07 Marks) 8a. b. o ow on: x: -2 1 0 1 2 3 4 P(x) : 0.1 0.1 k 0.1 2k k k 88***
3. 3. tiE(.rn ev USN Time: 3 hrs. Note: Answer any FIVE full questions. Find the angle between 2 diagonals of a cube. the perpendicular drawn from A to BC. c. Find the equation of the plane in the Intercept form 1*I +? -1,, abc Provethat(dx6;' d:(d:d) 6 -fU.e )a. Provethat 1[F.G]: F. dG*oF. G. dt L -r ' dt dt Find the velocity and acceleration forthe curve i : (1+') i + (1 +hj and also find their magnitude. Fourth Semester B.E. Degree Examination, June/July 2015 Advanced Mathematics - ll MATDIP4Ol Max. Marks:100 ! ri: ." (06 Marks) (07 Marks) (07 Marks) (05 Marks) (15 Marks) (05 Marks) (15 Marks) o o a(€ ir = a () (.) dn, C)x bo- cdu -o ..' on ll .g?;i -r .= c{(!\$ nbo Y()' otr _c(.) o> 8q gs bU (sO o0tr 6d ,(tr CE -i '1' (6 t=9 As a9trt o.; al) Sr 'l 9E5a u: t-E s..! c) ?e >! uov tr DI) o- ii o* c,? U< -C G) z tr o, ifi la. b. If A(0 9 6), B(l 2 3) , C(7 - 25) are vertices of a triangle. Find the coordinates of the foot of 2a. b. Find the equation of the plane passing through the three pointS.(2,3,4) , (-3, 5, l) (4, -1,2). (06 Marks) Find the equation of the plane through the points (1, 2, -1) and perpendicular to the planes x + y -22: 5 and 3x- y + 4z: 12. (07 Marks) c. Find the equation of the plane through the points (-1, 2,0) and containing the plane 2x+ 3y+52-l:0and3x+y-z*2:0. =t - (O7Marks) a. Findtheunitvectorparalleltothesumofthevector A:2i+4j-5kand E:i+ 2j+3k. , , (06 Marks) b. Determine 1" suchthat A : i+i * [';'fl :2i- 4k. a : i + ],j + 3kare coplanar. (07 Marks) (07 Marks) (06 Marks) + (2t - 5)k at t : 1 (07 Marks) (07 Marks) Find the directional derivative of \$ - x2yz * 4xz2at (1, -2, -1) along 2i - j - 2k. (06 Marks) If F :(x+ y+ 1) i +j -(x+ y)k. Find F.curlF. (07Marks) Show that V.(V , A ) : 0. (07 Marks) c. a. b. 5a. b. c. b. a. c. tt*=fr,ia ,rd #=frx6 thenshowthat 1[dx6]: ,fr,x(ax6). Find L f(t) given that f(t) : {: ; o <t <4 L5; t>4 Find i) L[e3'sin5t sin3t] ii) L[ts cosh3t] iii) L;t3 e-3'1. Findr[E] Lt.l b. Find i)L'[ 4s+5 ii)''[ffi] iii)L.t-r] ce,trTBsl. LlSSrASr"t 4 B K t 3 C a o S (s-l)2(s+2) 1 of),
4. 4. MATDIP4Ol 8 a. Using Laplace transform solve : g' * 4y* 3y = st ; y(0) : 0 y'(0) : l. (10 Marks) dt, 'dt -r J-'' - J -/ - b. Solve using Laplace transformation method y" + 2y' - 3y: sin t, y(0): y'(0): 0. (10 Marks) 2 of2
5. 5. L 13 td ?t- C U 0 L I o) o (.) d ! = U) 0) (l, c) l-r E9oo- .;i> EO =a-9 .. bo ll loo .= C.l Cg\$ HbD HC) ()tr -E q) EE -.E 3E bU OEo0tr(lld :o }Htq5 'O ct nts 5lJ E(€ d_g ts6 5.8 s,i O 0,)= 5()atE lr 0) 3P>l= boe trbo ()= Lr. g =c)()*.i oa' -.it',c^i () z 1a. b. c. USN Fourth Semester B.E. Degree Examination, Goncrete Technology Time: 3 hrs. Note: l. Answer FIVE fuU questions, selecting at least TWO questions from each parl 2. fJse of IS - 10262 - 2009 is permitted. **-,"?i# PART - A -....,.-..).''..:- ,. " '" '1ii What are the various laboratory tests conducted on cement? * " '*'!05 Marks) Explain the importance of conducting the soundness test on cement aqd.'Qe procedure of conducting the soundness test. I1 (10 Marks) Explain with the flow chart the manufacture of cement by wet proce\$g.". i (05 Marks) .. ,;.r, 2 a. Explain the importance of shape and texture of aggregate used,inlffincrete. (10 Marks) b. Which are various tests conducted on coarse aggregates fo1.dpftnhining its strength? .,-.,,,;'.# (05 Marks) c. Explain bulking of aggregates. ,,,ffi* (05 Marks) 3 a. What is an admixture? What is the effect of air entraiffi'bnt on the properties of concrete? . ., ti,..,. b. Write short notes on accelerators and retarder"r:ira' 't.'f '.:r.ltlE 4 a. Define workability andJist the factors-a{fe0ting workability. (08 Marks) b. List the various tests to measure wo,rlEffiity and explain KEE BEE consistorneter test. 6a. b. 7a. b. t' -' '''-''t,.'J 'q 'ilir- t ',ih,'ttPART - B 5 a. What are factors affecting *&etr.ngth of concrete? b. ExplainJfoe aecelerated,qXdht test orl concret6 bubes. c. WIte short notes on_B-ffistrength of concrete. Explain briefly thi* &dtors affecting modulus of elasticity of concrete. Discuss the fr-cfol8 affecting creep. 'if,"'.,q lir.".,Jr Explain-ffie*different methods of controlling sulphate attack on concrete. Dise-us;'the durability of concrete in sea water. j*,',..1...,# 8 _*"D*e,s'ign a concrete mix by IS method for M30 grade concrete as per IS rc262-2009. .*,t-,;1,- a) Grade : M30 h# b) Cement : OPC - 43 Grade , c) Maximum Nominal size of aggregate : 20mm d) Minimum cement content : 320 Kg/*' e) Max. w/c Ratio :0.45 0 Workability : 100mm slump g) Exposure condition : severe (Reinforced concrete) h) Method of concrete placing : pumping i) Degree of super vision : Good j) Type of aggregate : Crushed Angular k) Max. Cement content :450 Kg/m3 l) Chemical admixture : Super plasticizer. (12 Marks) (08 Marks) (12 Marks) (04 Marks) (08 Marks) (08 Marks) (10 Marks) (10 Marks) (10 Marks) (10 Marks) Max. Marks:100 I of 2
6. 6. Test Data for materials: i) Specific Gravity of cement : 3.15 ii) Specific Gravity of C.A :2.74 iii) Specific Gravity of F.A :2.74 iv) Water Absorption for l0cY42 (20 Marks) 1) C.A 2) F.A v) Free surface 1) C.A 2) F.A 0.s% 1.0% moisfure NIL (Absorbed moisture also NIL) NIL vi) Fine Aggregate conforms to grading zone - I 1) oftable 4 of IS 383 2) Coarse Aggregate *{<rt** IS sieve size (mm) Analysis of coarse Aggregate fraction ffi *f U iff.rent Fractions Remarks I II II 40% Combined t00% 20 10 4.7 5 2.36 r00 0 lop,..# 7l'4,.' -r*#40 rlPr% O 60 0 40 28.s 3.7 100 28.s 3.7 Conforming To Table 2 of IS 383 2 of2
7. 7. USN Time: 3 hrs. load, using conjugate beqffittrod. Determine the deflection energy method. f- gtr, --4+-d'n J Fie.Q2(b) the bent shown in Fig. Q3(a), lDht'l Fig.Q3(a) under 60 ld{ loads in the beam shown 10cv43 Max. Marks:100 (10 Marks) by real work method (10 Marks) in Fig.Q3(b), by strain (10 Marks) ":.fn*. Fourth Semester B.E. Degree Examinatib\$s 2015 Structural Analysis - I Note: 7. Answer any FIW faU qaestions, selecting atleast TWO questions from each parL a. b. c. b. C) () '-E a (.) ICg l< U1 '<,C) .g o E9 6v ao ll tr-09 .=c{ .(s\$ L bi0 ol5q) o> Eq BS bd o€b0trcrd EX >ii-(t64 1rd -bts 5rj i() HB 5.8oj EH 3 c,)tE tr.;i Li0) ?1, >1= bo-tro0rt a !E:, ; .F - d ':!. "rt. ts&9 -',o.,-Lol X l.r -ir 1. I x: irir ! Fi... .,'! .. .^ ,Ft 1, .d -?,,4."'"-1ri. ; z (6 E 2. Missing data, if any, may be suitably assumed. PART - A .,F,.- "rr,rf Distinguish between statically determinate and indeterminate structures wrHji'amnt3.. ,__., * ".*,ii (08 Marks) Find degree of indeterminacy of following structure shown in Fig. Q1€B["-- (06 Marks) Fie.Q1(bxi) Fig.Ql (bxii) u' f,,.,,t Fie.Q 1(b)(iii) (06 Marks) Calculate the deflection (10 Marks) SWlnr 9r**4ot c \$r) *_'",rrr "' Fig.e2(a) b. For the beam shown in Fig. pffOl. Determine slope at left support and deflection at 100 kN A cantilever beam of length 4 m is loaded ur qii.d,p,n in Fig .Q2(a). and slope at free end by moment area methq,&#aking EI is constant. Fig.Q3(b)
8. 8. 4a. b. Determine the reaction at prop for a propped cantilever beam carrying length throughout span" Take EI is constant using strain energy method. Analyse the fixed beam by strain energy method and draw SFD and Fie.Qa(b). 10GV43 of UDL of dunit (08 Marks) BMD. Shown in (12 Marks) . ..i Fig.Qa0) PAR.T _ B 5 a. A three hinged parabolic arch has a span of 20 mts and rise of 5 mts. {rrearri.s a udl of 2 kN/m over the left half of the span and a point load of 721d.{ at 5 ryq"'hom the right end. Find the BM, normal thrust and radial shear at a section 4 mts from tffi.pfrA. (12 Marks) b. A cable is suspended between two points A and B 100 mts apaffiffit'h central dip of 8 mts. It carries udl of 20 kN/m. Find : i) length of the cable ii) maxiar,\$m'and minimum tension in the cable *-,H (08 Marks) a. Draw SFD and BMD for the propped cantilever bea\$aNpad'6d as shown in Fig. Q6(a). Using consistent deformation method. t*sl (10 Marks) .*A -,fig'Q6(a) b. Analyse the fixed beam shown ik&;.p6(b). draw BMD and SFD by consistent deformation method. *.d"r, " (10 Marks) '1? "illi1;l lir1*-h\$ ;1 &.u&# by Clape5rron's three moment theorem. (20 Marks) Find the horizontal thrust for the two hinged arch as shown in Fig.QS. The moment of inertia at any section is Ic sec 0 where 0 is the slope at section and Ic is MI at the crown. Neglect the effect of rib shortening. Draw BMD. Fig.Q8 *{<**rk 2 of2 /ra--ss- Za- (20 Marks)