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- 1. USN o() O Time: 3 hrs. PART _ A a. Expand (x) : x sin x as a Fourier series in the interval (-n, n), Hence dedube the following: Third Semester B.E. Degree Engineering Mathematics - lll Note: Answer FIVE full questions, selecting at least TWO questions from each parl 'i :lr:. ).. i l' ':: Max. Mark$'rl00 .,,..,.,, ,., O ,i. ..:i :11_ _ri:l; .lf l!:... '. .ri' (07 Marks) (! U) 0.) cd C) ERao- ;= kl o Eln oo Il trao .=N gtr c)tr -E q) €E o3 8E BS bd clO o.6b0ttltd rcX BEdl -i }B Es d_g FT5(s uiO 9H e3tr! .i_j Lr d:l eE>1= bov roo o= =c!14 6J tr>v VL Q*:r,,' a -)'., irll L Ft. ,, 'i, i H,: L.) <,; - J' c.i () z ricrt o aH b. .TC222tt -=l -r- ' 2 1.3 3.5 5.7 n-2 I I 1 ' 4 1.3 3.5 5.7 Find the half-range Fourier cosine series for the fung$gn lu- o<xs% i,,,,..,.^.":1"';" r(*)={ o/ ':n ; / Lo,U-*1,% <x<.[ j,. Where k is a non-integer positive constant.., (06 Marks) c. Find the constant term and the first two harmonics in the Fourier series for f(x) given by the followine tablwmg taDle. x: 0 n13 2n13 lt ErtB 5nl3 2n F(x) 1.0 r.4 1.9 1.7 'c.5 1.2 1.0 '" "'OU'' a. Find the Fourier trans$'ftrn"of the function (x) : xe-alxl b. Find the Fourier sine transforms of the lsinx. 0<x<a Functions f(x) - i [ 0, x)a c. Find the inverse Fourier sine Transform of " .. . 1 F- (d)'! i.-uo a > 0. ',r. C[, Find various possible solution separable variab le method. Obtain solution of heat equation of one dimensional wave e( o'u c, 92 bvluatton a( = ax, J (07 Marks) (07 Marks) (07 Marks) (06 Marks) (07 Marks) 02u F subject to condition u(0,1) :0, u (.[ ,t) : 0, (06 Marks) subject to condition u (0, y) : u( L,y):0, u (x, 0) :0, &,,:' b. au r:2 0t u (x, 0): (x) c. Solve Laplace equation #*#=O u(x,a):sintt) 1 of 3 (07 Marks)
- 2. The pressure are constants P and volume V Fit this eouatio of a gas are to the follov lOMAT3T related by the equation PV' : K, where r and K4a. 5a. b. c. 6a. are constants. rlt tnls equatlon to tne rollow P: 0.5 1.0 1.5 2.0 2.5 3.0 V: 1.62 I .00 0.75 0.62 0.s2 0.46 ing set of observations (in appropriate units) b. c. Solve the following LPP by using the Graphical method : Maximize: Z-3*, +4x, Under the constraints 4x, + 2x, <80 2xr+5x, <180 X1, x2 2 0. Solve the following using simplex method Maximize : Z=2x+4y, subject to ttre Constraint : 3x *y 122, 2x+3y <24, x ) 0, y 2 0. ,rlr''ii,l .tt. I (07 M*rks)" (06 Marks) (07 Marks) (06 Marks) Rule, dividing the interval into 3 equal parts. (07 Marks) initial conditions (07 Marks) PART _ B Using the Regular - Falsi method, find a real root (correct to three decimal places) of the equation cos x : 3x - 1 that lies between 0.5 and 1 (Here, x is in radians). (07 Marks) By relaxation method ,,.u{'*,-' ' Solve :-x*6y+272:85, 54x+y+z: l-IQi&('+ 15y+62:72. (06Marks) Using the power method, find the largest eiffi value and corresponding eigen vectors of the Io -2 21 d*'*" I I .,1u.. F matrix A_l_2 3 _ll r,'*o I I .,:+ L2 -1 3J ',,,.' taking [1, 1, 1]r as the initial;#@n vectors. Perform 5 iterations. (07 Marks) ,rr"trrlo1,;;; From the data given in*ffi"?otlowing Table ; find the number of students who obtained i) Less than 45 ii) between 40 and 45 marks. Marks H_ +o 40-s0 s0-60 60-70 70 80 No. of Studen&l 31 42 51 35 31 (07 Marks) that approximates to theUsing the Lagrange's formula, find the interpolating polynomialb. function described b the following table:nctrcn oescrl x 0 1 2 .| J 4 f(x) 1 J 6 1l 18 27 Hence find f (0.5) and f (3. 1). I Evatuate i- =oxby using Simpson ''t (%^ {1+x Hence find an approximate value of loeJ, . ^) ^ 1 7 a. Solve the one - dimensional wave equation + = o=l dx' dt- Subject to the boundary conditions u (0, t):0, u (1, t): 0, t > u(x, o): sin nx, *(*,0) = o, o < x< 1. ' a' 2 of 3 0 and the
- 3. b. Consider the heat equation 2*= + under the following conditions: 0x' 0t i) u(0, 1):u (4,t)-0, t 2 0 Employ the Bendre - Schmidt method with h : I to find the solution of the equation for .. 0<t < 1. (o6Martis) ^) -) Solve the two - dimensional Laplace equation + -+ -0 at the interior pivotal points of Ox' dy' the square region shown in the following figure. The values of u at the pivotal points on the 1OMAT31 _ .o::r,::,, 'r,,,, (07 MafkS) I ooo 9Oo find Zr (nP) and (07 Marks) (06 Marks) c. t 4"{QxlS, *-#nl1 # "t $L .ntu . ,'s rr ., ,,.; boundary are also shown in the figure. looo ooo 2 000 2200 I Ooo 9oooO ,: i! Fig. Q7 (c) ',.'- a. State and prove &"b recurrence relation of Z- Transformation hence t- Lw*e'll Zr [cos rt, , ) ) ,] C. Solve the difference equation yn+: - 2y n*r - 3yn - 3" + 2n Given yo : yr : 0. *:l.rB** 3 of3 (07 Marks)
- 4. "rl5 S"m Cv Note: Answer any FIVE full questions. Express the complex number (5 - 3i)(2 + i) in rhe form x + iy. 4+2i Find the modulus and the amplitude of I + cosO + i sinO. Find the cube roots of I + i. i Find the nth derivative of eu^ cos(bx + c). d(u, v, w) o(x,y,z) 5 a. Obtain the reduction formula for where n is a positive integer. Max. Marks:100 MATDIP3Ol Third Semester B.E. Degree Examinatiorr June/July 2Ol5 Advanced Mathematics - I Time: 3 hrs. 2a. b. 4a. b. c. Find the nth derivative of (x+l)(2x+3) c. If x=tan(1og y) provethat 11 +x2) yn+r* (?nx- l) yn*n(n- 1) y,-r =0. a. Find the angle of intersection of the curves rn = an cosn0, rn = bn sinn0. b. Find the Pedal equation of the curve r = a (1 - cos 0). c. Using Maclcaurin's series expand log(t + x) upto the term containing x4. USN c) () o(ll c, v, (g C) o) L. fiebo* =-i ;n -* ll coo.; J- .= c.,l (6s xan tsc) (l)g -q c) oB 8z Ed cEO orobotr(g(€ o }EG] r E(6 -e" A '8s agtro. oi (J= }Uq '?E |. (,) 6.Y>r q- trao (D= dl L., g) ,,' F ?...',t x.q" o)'11. U t't* 'j >1 o< -i c-i C) o z cn ti o a. b. c. (06 Marks) (07 Marks) (07 Marks) (06 Marks) (07 Marks) (07 Marks) (06 Marks) (07 Marks) (07 Marks) (06 Marks) (07 Marks) (07 Marks) (06 Marks) (07 Marks) (07 Marks) (06 Marks) (07 Marks) (07 Marks) If u = f(x + ct) + g(x - ct) show that #: C # If u - rf l,I,:) prove r;at xu* * yuy * zr,=e. Y'''x)-.t'. If u = x * t, n ; V + z, w = z + x find the value of Jcos" xdx b. -.', + ;,i C' 6a. b. c. 'ria4 '-Evaluate [-!a*. 'n Ju' - x' Evaluate i i .i:. *'*',dzdydx . 00 0 Define beta and gamma functions and prove that f(n + 1) = nf(n). rl2 tl2 I show thar J,ffie oe x I ffi.do = n. 00 Prove that 0(m, n) = {m) r(n) ' I-(m + n) L of 2 I
- 5. b. c. Solve Solve Solve a. Solve b. Solve c. Solve dv = -cos(x+y+l). ox (*' - y2) dx - xydy = g. dv-J +vcotx- 4xcosecx.aJ clx (D'- 6D2 + llD-6)y=0. (D'+ 2D + 1) = x2 + e**. (D'+D+ l)y=sin2x. MATDrP301 (06 Marks) (07 Marks) (07 Mr*p) ((H Marks) (07 Marks) (07 Marks) ***** 2of2
- 6. USN Time: 3 hrs. Note: Answer any FIW full questions, selecting atleast TWO questions from each part. PART - A Explain various types of shallow foundations. Also show the elevation of wall. _,*";*'i c. Explain with a neat sketch Ashlar chamferetl,,Shne masonry. 1.,,** - 3 a. Explain with neat sketches, variousgy,fo#of Lintels. b. What are the advantages of arch pv,pr-d lintel? c. What are the loads coming ove.g a.%rftel and how they are estimated? !,.,:i.n|,.rri{ipsd _Er{bfly explain the requirements of a good stair. l-"Write a note on different types of stairs. F Plan a stair case for a residential building in which the room size for 3m x 4.5mand height between floor finishes is 3.30m. Draw neat sketches. What are the objects of plastering and pointing? Explain different types of plaster finishes. Describe types of paints available in marker and their specific usage. Write short notes on: Types of glasses. Use of plastics in buildings. Formworks. Damp proofing in building. 10cv32 Max. Marks:100 (05 Marks) (10 Marks) (05 Marks) (10 Marks) (05 Marks) (05 Marks) Building Materials and Gonstruction Technology a, o o(B L (! U) cl €o ((, (l) Esibo- IJ<.- y5 Ea =a-oo ll troo .=N d$ ETotr €gtr'troB Ee 9s bd GIO o.oo0c .S c, BH ss= 'ocg -2" f'8s =(d d8.trLi 5d'oj tt) l) -cl it6().t lE r(l) 3=>H tr- bo ()= '= cl ,. I] 6) 5*ElI .,4, o< -: ei (l) o z H o F la. b. c. What is subsoil exploration? Explain any one method. .,,-.,..-'., "' (05 Marks) Design a strip footing for a brick wall 230mm thick, and 3.2m highahoveground level. The wall carries a superimposed toad of 100kN per metre run. Thg-sciiil,,*has unit weight of 18 kNI/m3, angle of repose 30o, SBC of 180 kN/m2. The footiry-:is provided with cement concrete base which has unit weight of 24 kN/m3 and rnos*i'hf's of rupture of 480 kn/m2. Take unit weight of brick masonry as 19.5 kN/m3. *L.", (10 Marks) a. Explain with sketches various types of closer bricks. ;. (05 Marks) b. Sketch plans of consecutive two layers of Eng#-ia,b"Iond for one and half brick thick wall. 5a. b. 4 a. Sketch a Queen post t*B,trffie of timber, which has to support tile roofing. Name the.r.Yx ''i components of the trusq_tMnature of force in them. (08 Marks) b. Explain the requireruoM of a good floor. (06 Marks) c. Explain with a q#, skbtch flat slab flooring. (06 Marks) PART - B h of a wooden door with shutter, name the parts. (08 Marks) (12 Marks) (05 Marks) (05 Marks) the staircase is (10 Marks) (06 Marks) (06 Marks) (08 Marks) on: i) Revolving door; ii) Collapsible door; iii) Rolling shutter. 6a. b,.rl 5+:i:' '1 a. b. c. a. b. c. d. (20 Marks)
- 7. USN lOCV/EV/CT33 Third 20t5 Time: 3 hrs. Max. Marks:10:0 Note: 7. Answer any FIW full questions, selecting atleust TWO questions from euch part. : 2. Missing data, if any, may be suitably assumed. ,,,., , ,:,,., ' PART _ A Define: i) Stress ii) Strain (04 Marks) Derive the relation between modulus of rigidity and Young's modulus of Elasticity and c. The modulus of rigidity for a material is 5lGPa. A 1Omm dianreter rod of the material was subjected to an axial load of 10kN and the change in diameter was observed to be 3 x 10-3mm. Calculate the Poisson's ratio and the modulus.,of elasticity. (08 Marks) 1a. b. C) o () U) cS (.) (g 0) ! ER -7= (c !, ;rt io tt qoo .= c(€$ rr b0 y() c>t -g c) 9- oB E2 (h= q;O dO o"oo0d cO(g vo >! -(rg Ed 513Q- o- 5, tro. o; (hu o: 5oatE r0) 5.v oo-trb0 C)= =s) =c)o! U< * (.1 C) P z F 2 a. A reinforced concrete column 300mm x 300mm has, 20mm in diameter. Calculate the safe load the rclumn COncrete 5.2 N/mm2 un6 E.t..r - 1g . , . 'i'."' "' tr -concrete b. A compound bar made of steel plate 60rqr" wide and 10mm thick to which the copper plate 60mm wide and 5mm thick are rigidly connected to each other. The length of the bar is 0.7m. If the temperature is raised-,by 80oC. Determine the stress in each metal and the change in the length. . Take: E, : 200 GPa cr. i '12 * l0-6PC E"u: 100 GPa ",',cf,s, : 17 x 10-6/oC. 4 reinforcement bars of steel each can take if the permissible stress in (08 Marks) (12 Marks) 3 a. Derive exnrelsiffifrincipal stresses and their plaaes for two dimensional stress systems. (08 Marks) b. At a point i{e strained material, the state of the stress is as shown in the Fig.Q.3(b). Calculate$qviirrmal and the shearing stress on the plane AC. Also furd the principal stresses and their$anes. Determine the maximum shear stress and their planes. (12 Marks) Fig.Q.3(b) l0o {nafr IDO r'r!'lt {r, L0 nt/*" , 4a. b. Define: i) Shear force ii) Bending moment iii) Point of contra flexure. (06 Marks) A beam ABCD, 8m long has supports at 'A' and at'C' which is 6m from 'A'. The beam carries a UDL of 1OkN/m between 'A' and 'C' at point B a 30kN concentrated load acts 2m from the support A and a point load of 15kN acts at the free end'D'. Draw the SFD and BMD giving salient values. Also locate the point of contra-flexure if any. 6o u/u*nL I of 2 (14 Marks)
- 8. 5a. b. PART _ B Derive Bernoulli-Euler bending equation + = I - =t . ^ I v R 1ocv/EV/qT33 (06 Marks) (06 Marks) (10 Marks) (04 Marks) (06 Marks) The cross section of a beam is shown in Fig.Q.5(b).The shear force on the section is 410kN. Estimate the shear stresses at various points and plot the shear distribution diagram. (14 Marks) '0rn.4 T O.ltrn IA o.88 I 0- l- o,s,,n J t'*'Q,,: ' i. ' a. Derive the equation EI# = M* with ur*f ';ttation. shear stre s'g'ier,tlain ing s ame. ,.:'r: 8 a. Oistffi,iliJh bet*een short column and long column. b. Explain: ,,,.,i),,,"'"' Effective length of column .-"' r0 Slenderness ratio ,, ,,,i:,. " iii) Buckling load. b. Determine the Euler's crushing load for a hollow cylindrical cast iron column 150mm external diameter and 20mm thick. If it is hinged at both the ends and 6m long compare this load with the crushing load as given by Rankine's formula. Use the constants: E: 80 GPa. .t *( * * {< a to.ts rn b. A beam of constant C/S 10m long,is"-fteely supported at its ends and loaded with 2 loads of 60kN each at 3m from either end. Fihd the slope at the support and the deflection under any one load. Take EI constant. (14 Marks) a. List the assumptions made fn'the theory of pure torsion. (04 Marks) b. Explain: i) Polar modulus; ii) Torsional rigidity; iii) Polar moment of inertia. (06 Marks) c. A solid shaft is to tmresmit 340 kN-m at 120rpm. If the shear stress of the material should not exceed 8OMFa','Find the diameter required. What percentage saving in weight would be obtained if th-is Shhft is replaced by a hollow one whose dr : 0.6do, the length, material and f. : 550MPa e( = 1 600 ) of ) (10 Marks)
- 9. USN 10cv34 Third Semester B.E. Degree Examination, June/July 201..5 Surveying - I Max. Marks:10Orime:3hrs. Note:r. #iliiffioril"?#,itri,IXi;,iyy r* 5q E ,. Missing data" if any, may be suitably assumrr. _ atY E PART_A J q : r a. List the different methods of surveying. what are their objertives q.iIS "l "W**; $ t. Bring out the difference between 'Precision' and 'Accuracy'. ;V (06 Marks) g i c. What is map? State the numbering method in a map. - $" (0s Marks) gi 2 a. BrieftheworkingprincipleofanEDM. aP (06Marks) f f b. With a neat skerch describe the concept of "Reciproqffiafging". (06 Marks) .g+ c. The length of a line measured with 20.0 m chaii$ffas 1341.0m. The same line when E $ measured with 30.0 m chain which was Z0^dih too short was found to be 1350.00 m. E * Determine the enor in 20.00 m chain. r-e' g E € elror ln zu.tru m cham. Q* (08 Marks) t E 3 a. Explain with a neat skerch, the workirglt'and use of an "Optical Square". (06 Marks) .g E b. Write the procedure to overcomei&ft8stacle for chain surveying r',,hen both vision and ? E chaining is obstructed. OY (06 Marks) E f c. Two stations 'P' and 'Q' wereqktd on southem side bank of a river flowing west to east pt. E S 'P' is wastewords of pi'q'ro(* m apart. The bearings of a tree 'R' on the northem side of gE the bank is otservea to ti&i ro:si *a:g8o respectively from'P' and 'e'. Catcutate the ; € width of the river. .$' (0s Marks) €'= cy ng 4 a. Distinguishbetr$pi 9 = i) wCB an6OH B F iti oip a{l@t-tination 3 ; iii) Y$bearingand truebearing with reference to compass surveying. (06 Marks) E E t. Statg$*''PrismatiCCompass" is different from'surveyors Lmpass'. (06Marks) E E c. F6(1$fing is a closed traverse ABCDA conducted clockwise. Fore bearings of the lines are.' = ffiifo*t ' determine the values of included angle and apply the checkl-i C) 6.v<; *L.# S;o ., lLinelABlBClCDlDAl Ef w ffi EL.Oi' (osMarks) Line AB BC CD DA FB 400 70 21c- 280' ;c-,:] PARr-B ! S a. Explain 'Bowditch's rule' adopted for adjusting a closed traverse. (08 Marks) 7 b. The fore and book bearings of a closed traverse is given below. Correct the bearing for local 5 attraction, bv ideutifying the stations affected by local attraction. (u tvlarks) 6oi Line AB BC CD DA FB 32" 30', L24" 30', 1810 O', 289" 30', BB 214"30', 3030 15', 10 0' 1080 45',
- 10. 10cv34 a. Define the following terms with respect to leveling. : i) Bench mark ii) Backsight iii) Change point vi) Fore sight v) Reduced level vi) Height of collimation. (06 Marks) b. What are the 'Temporary Adjustments' of a Dumpy level? (06Ikfu) c. Following observations refer to a'Reciprocal Leveling'. Calculate the elevation ofp21&"ffi i1 that of 'A' is 100.150 m, by deterring the collimation error. ffiffi.r.1^h s"-*? M inst at Staff reading on Remarks A 1.824 2.748 AB = 1000.00 B 0928 1.606 's 7a. b. Enumerate the characteristics of contour lines. M " (08 Marks) The following readings were taken with a dumpy level %#t'oping ground at a common interval of 5.0 m. The RC of first point is 200.00. Rule offiffduge of level book and enter the readings. Calculate the reduced levels of all the poingqndthe gradient between first and last point. 0.405, 1.990, 2.030,3.t20,3.700,0.910, 1.815'$dr50, 3.660, 0.430 , 1.455. (12 Marks) f)* q a. Explain the procedure adopted to measure plqffitance between two points by plane table surveying. J b. State the importance of orientation ,ppld". hbling. What are the orientation? ,*t-J c. Describe the method of 'nesectiff'Bessels graphical method". &*.& *,w/[' *r<*** fl&^ & *#',r*h,J KW(b &d -e+ t"#kr' rup &l #&pt V{, "m kw#+ d '%,. f altr .* # ,'q*fr #ft"ffi"qN rk#" - .w " -& dqte. dq-fg- ^#s. ,q. sd# .d.& '!&_ mutually inaccessible (06 Marks) methods available for (06 Marks) (08 Marks) 2ofZ
- 11. USN Third Semester B.E. Applied Time: 3 hrs. Note: Answer arry FIVE full questions, selecting atleast TWO questions from each part. PART - A Discuss the importance of geology in the field of civil engineering. With neat figure, describe the internal structure of the earth. Discuss any two of the following physical properties of minerals : i) Fracture ii) Lustre iii) streak. 3 a. Define soil. Discuss the erosion and conservation:ofsoil. b. Discuss the mechanical weathering of rocks, ,, ''.,,,_- " c. Explain Epigene and Hypogene geological agents. d. Define waterfall. a. What is earthquake? Discuss the causes of earthquake. b. Explain the Remedial measure of landslide. c. Explain continental shelf, continental slope. d. Explain with neat diagram, the Mid oceanic ridge. PART - B 5 Explain the following : a. Importance ofjoints in civil engineering b. Normal fault and reverse fault c. Unconformity d. Anticiinal and synclinal fold. 7 a. Explain the electrical resistivity method for ground water exploration. b. Write a note on artificial recharges of ground water. c. Write a note on confined and unconfined aquifers. d. Write a note on hydrological cycle. 8 Explain the following : a. Application of remote sensing in civil engineering b. Impact of mining on environment c. Application of GIS and GPS in civil engineering d. Quality of ground water in different terrain. 10cv/cT36 2015 Max. Marks:100 (06 Marks) (06 Marks) (04 Marks) (08 N{arks) (06 Marks) (04 Marks) (02 Marks) (08 Marks) (05 Marks) (04 Marks) (03 Marks) (20 Marks) (08 Marks) (05 Marks) (04 Marks) (03 Marks) La. b. c. 0.) o o l- cd a 6 0) 0) .aX a0- x- lrI c3 C' !l rr^r 6r,,co .=N d$ =O Ra aX oc) a0c($(s )e ?6 'O(g to tr- =d/q oi ?.= 6: soaa ti :-o 5.:>q- ^^c =c0 C.)= =9X 6.) J< - c.i C) o z :r d. Write physical properties chemical composition and uses of any two of the following : i) Quartz ii) Calcite iii) Galena. (04 Marks) a What are igneous rocks? Describe the mode of occurrence of igneous rocks. (08 Marks) b. Describe the prirnary structure of sedimentary rocks. i'." (06 Marks) c. What is metamorphism? Describe any four types of metamorphism. (06 Marks) a. Define dam? Discuss the geological consideration in selecting a suitable site for dam construction. (12 Marks) b. Discuss tunneling in anticlinal folded rocks. (04 Marks) c. Explain silting of reservoir and its control. (04 Marks) (20 Marks)

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