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- 1. USN 1OMAT41 Fourth Semester B.E. Degree Examination, Decemb er 2Ol2 Engineering Mathematics - lV Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting at least TWO questionsfrom each port. d o o PART _ A !n o. I a Using the Taylors series method, solve the initial value probt.* rt !I - xy - 1, y(0) : I at ox () the point x:0.1 (06 Marks) () ! b. Employ the fourth order Runge-Kutta method to solve q.t =tl-"r, y(0) : at the points 3s dx v- +x- 1 x:0.2 and x :0.4. Take h :0.2. (07 Marks)!,- 6e-.o col c. Given 9= *, + y, y(0) : dx 1, y(0.1) : I .1169,y(0.2) : 7.2773,y(0.3) : I.5049.Find y(0.4) =oo (c+ using the Milnes predictor-corrector method. Apply the corrector formula twice. (07 Marks)gd otr-E o) 2 a. Employing the Picards method, obtain the second order approximate solution of the following problem at x : 0.2. dy dz y(0):1, z(0):-1. dx=x+YZ *=V+zx, , , (06 Marks)a=oo) b. Using the Runge-Kutta method, find the solution at x : 0.1 of the differential equation dy , d 1 , -x *! under the conditions y(0): 1, y(0):0. Take step lengthh:0.1. dx dx -2xy =1>d (07 Marks)!d c. Using the Milnes method, obtain an approximate solution at the point x : 0.4 of the3ao{=o-A problem +.:*9-6y=0. y(0): l.y(0):0.1. Given that y(0.1): 1.03995. dx dx -Joj y(0.2): 1.138036, y(0.3) : 1.29865, y(0.1) :0.6955, y(0.2):1.258, y(0.3) : 1.873.,;o (07 Marks)o=6E!o 3 a. lf f(z): u * iv is an analytic tunction, then prove that (+l rtr) ll .Pt rtr) ll =lr,1rsl .=-Eo.i>,t dx / ry )oo"coo (06 Marks)o=sotr> b. Find an analytic function whose imaginary part is v = e* {(x - y)cosy -2xy sin y} .=o5L (07 Marks)lr< c. If (z) : u(r, 0) + iv(r, 0) is an analytic function, show that u and v satisfy the equation-N Aa 16o lA2a +---+-i^J=U.o (OTtVtarks)o ^2 or t or r- oa-ZH 4 a. Find the bilinear transformation that maps the points 1, i, -1 onto the points i, 0, -io respectively. (06 Marks) b. Discuss the transformationW: e. (07 Marks) c. Evaluate ItT n,,l,"ot11oz , where C is the circle lzl:3. (07 Marks) ! tr-t)(z-2)
- 2. 1OMAT41 PART * B5 a. Express the polynomial 2x3 -x -3x+2 in terms of Legendre polynomials. (06 Marks) b. Obtain the series solution of Bessels differential equation **+ *++ (x-r)y = 0 in dx dx the form y: AJ,(x) + BJ-"(x). (07 Marks) c. Derive Rodriques formula h(x) = r, (07 Marks) #(x-1).6a. State the axioms of probability. For any two events A and B, prove that P(A u B) = P(A) + P(B) - P(A n B) . (06 Marks) b. A bag contains 10 white balls and 3 red balls while another bag contains 3 white balls and 5 red balls. Two balls are drawn at ransom from the first bag and put in the second bag and then a ball is drawn at random from the second bag. What is the probability that it is a white ball? (07 Marks) c. In a bolt factory there are four machines A, B, C, D manufacturing respectively 20Yo,l5o/o, 25% 40% of the total production. Out of these 50 , 40 , 3o/o and 2Yo respectively are defective. A bolt is drawn at random from the production and is found to be defective. Find the probability that it was manufactured by A or D. (07 Marks)7 a. The probability distributio! gle i1119 r@m a variable X is given by the following table: Xi 1 -1 0 1 2 J p(xi) 0.1 k 0.2 2k 0.3 k Determine the value of k and find the mean, variance and standard deviation. (06 Marks) b. The probability that apen manufactured by a company will be defective is 0.i. If 12 such pens are selected, find the probability that (i) exactly 2 will be defective, (ii) at least 2 will be defective, (iii) none will be defective. (07 Marks) c. In a normal distribution, 3lo/o of the items are under 45 and 8o/o are over 64. Find the mean and standard deviation, giventhat A(0.5):0.19 and A(1 .4):0.42, where A(z) is the area under the standard normal curve from 0 to z >0. (07 Marks)8 a. A biased coin is tossed 500 times and head turns up 120 times. Find the 95o/o confrdence limits for the proportion of heads turning up in infinitely many tosses. (Given that z": 1.96) (06 Marks) b. A certain stimulus administered to each of 12 patients resulted in the following change in blood pressure: 5, 2, 8, -1, 3, 0, 6, -2, 1, 5, 0, 4 (in appropriate unit) Can it be concluded that, on the whole, the stimulus will change the blood pressure. Use to.os(11):2.201. (07 Marks) c. A die is thrown 60 times and the frequency distribution for the number appearing on the face x N glven the followins table table: x I 2 J 4 5 6 Frequency 15 6 4 7 1l t7 Test the hypothesis that the die is unbiased. (Given that yf;or(5) = 1 1.07 and X3o, (5) = 15.09 ) (07 Marks)
- 3. / USN t0cY42 Fourth Semester B.E. Degree Examination, December 2Ol2 Goncrete Technology Time: 3 hrs. Max. Marks:100 Note: 7. Answer uny FIVEfull questions, selecting atleust TWO questions from each part . o o 2. Use of IS - 10262 - 2009 is permitted. o L a PART _ A E I a. What are the chemical compositions of cement? How the cement is manufactured give flow 4) chart. (10 Marks) (! (.) b. Explain the terms normal consistence initial and final setting time. (10 Marks) oX 2 a. Explain the importance of size shape and texture of aggregate. (10 Marks) -*ll b. Explain the role of admixture in concrete making. Write briefly about the accelerators and troo (10 Marks) retardors. 6$ -il gc) og eO 3 a. What is meant by workability of concrete? What are the factors affecting the workability of o> the concrete. (10 Marks) b. Explain briefly the suggrigation and bleeding of concrete. (10 Marks) a: oo) 4a. Why curing is necessary. Explain briefly the different types of curing. (10 Marks) botr $(d b. What are the processes of manufacturing of the cement concrete? Explain briefly. (10 Marks) E(o PART _ B J?() OE 5a. Explain the influence of water/cement ratio on the strength of the concrete. (08 Marks) oA b. Explain how the compressive and tensile strength of the concrete is determined. (08 Marks) c. What do you mean by non - destructive testing of concrete? Explain any one of them. o_i (04 Marks) /io o= ai !o 6a. What are the factors that influence the strength of concrete? (06 Marks) 5 .:? Explain the different types of shrinkage that take place in concrete. (06 Marks) >= b. bo" trbQ c. Write a note on creep of concrete. (08 Marks) o= go =d tr> o 7a. What is meant by concrete - mix - designs? Write the steps involved in the method of mix - -, < design (lS - 10262 -2009) (14 Marks) * a.l o b. What are the factors reducing the durability of the concrete. (06 Marks) o Z 8 Write short notes : o E a. Light weight concrete b. Mineral - admixtures c. Fibre - reinforced concrete d. Compaction of concrete. (20 Marks)
- 4. USN 10cv43 Fourth Semester B.E. Degree Examination, December 2Ol2 Structural Analysis - I Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting atleast TI,I/O questions from each parl (J () (.) PART _ A i: a I a. Distinguish between static and kinematic indeterminate structures, with example. (04 Marks) b. Derive an expression for the strain energy stored in a member due to bending. (06 Marks) 0) c. A cantilevers truss is loaded as shown in Fig. Q1(c). The cross sectional area of the members is as indicated in the figure. Find the strain energy stored due to loading. Take E :72 GPa. ()Eq (10 Marks);6 0?rT-*t -oa 1u ku.= C.lgil ,rr[ 6JC-C(l)o>3s Fig. Q1(c)a:oO 2 a. A cantilever of length 4 m is loaded as shown in Fig. Q2(a). Taking EI constant for the(60 whole length of the beam, calculate the deflection at the free end by moment - atea method.botr (08 Marks) /nlrl"t -6 A {{kln T)Lkn-v I!d A :t rrr-.*,oi=x9tro.orw ),r"-Li!5 Fig. Q2(a) Fig. Q2(b)oja= Determine the slope at A and deflection at C in the beam loaded as shown in Fig. Q2(b), byao b. conjugate beam method. Take EI constant.4 t= (12 Marks)LO5 .:r>:bo-E50 3a. Find the deflection under concentrated load for the beam shown in Fig. Q3(a), usingo= Castiglianos first theorem. Take E:2 x 108 kN/# and I : 14 x 10-6 ma (10 Marks)o.Btr>=ov!or<*N p=,5okHooZLo Fig. Q3(a) Fig. Q3(b) b. Find the vertical deflection at C for the shown in Fig. Q3(b). Using strain energy method. Take EI constant. (10 Marks)
- 5. 10cv43 Find the vertical deflection at F for the pin jointed truss shown in Fig. Q4, using unit load method. Assume cross sectional area of each member as 1000 mm2 and E : 200 GPa. (20 Marks) l0l+r Fig. 4 PART - B5 a. A three hinged parabolic arch hinged at the supports and at the crown has a span of 24 m and a central rise of 4m. It carries a conc6ntrated load of 50 kN at I 8 m from the left support and a udl of 30 kN/m over the left half portion. Determine the bonding moment, normal thrust and radial shear at a section 6 m from left support. (12 Marks) b. A suspension cable having supports at same level has a span of 40 m and maximum dip of 4 m. The cable is loaded with udl of 10 kN/m through its length. Calculate the maximum and minimum tension in the cable. Also find the length of the cable. (08 Marks)6 a. Draw BMD for the propped cantilever loaded as shown in Fig. Q6(a), by consistent deformation method. The supports at A and B remain at the same level after the load. (10 Marks) golttr {YH h K 3rt &r{ Fig. Q6(a) Fig. Q6(b) A fixed beam is loaded as shown in Fig. Q6(b). Draw BMD. (10 Marks) Analyse the continuous beam shown in Fig. Q7 by Clayperons theorem of three moments. Draw BMD, SFD and elastic curve. EI constant throughout (20 Marks) Enks ftk*, ktlrt ,to Itr Fig. Q7 A parabolic arch hinged at the ends has a span of 30 m and rise of 5 m. A concentrated load of 12 kN acts at 10 m from the left hinge. The second moment of area varies as the secant of the slope of the rib axis. Calculate the horizontal thrust and the reactions at the hinges. Also calculate maximum bending moment anywhere on the arch. (20 Marks) {<{<**x<
- 6. USN t0cY44 Fourth Semester B.E. Degree Examination, December 2Ol2 Surveying - Il Time: 3 hrs. Max. Marks:100 Note: l. Answer FIVEfull questions, selecting at least TWO questionsfrom each part. d 2. Assume any missing data suitably. o o I a PART _ A 1 a. Describe the procedure of measuring horizontal angle with a transit. (06 Marks) () b. State what errors are eliminated by repetition method. (04 Marks) () ! c. Explain the prolongation of a straight line using theodolite:oX i) Which is in adjustment ii) Which is in poor adjustment. (10 Marks) r.) 2 a. What are the fundamental lines of a theodolite state the desired relationship between them.= ll (10 Marks)ootroo.=N b. A dumpy level was kept midway between two points A & B 100m apart. The readings on cS* staff held at A & B were 2.340 m and 1.795 m. The instrument was then kept at C, 20 m hboY()(JC from A along BA produced. The readings on the staff held at A & B were 1.985 m and_co 1.435 m respectively. Calculate the correct readings at A & B with the instrument at C. Is the line of collimation inclined upward or downward? (10 Marks)?1, ^a= 3 a. A theodolite was set up at a distance of 150 m from tower. The angle of elevation to the topo() of the tower was 10o8 while the angle of depression to the foot of the tower was 3o12. The staff reading on the B.M. of R.L. 50.217m with the telescope horizontal was 0.880 m. Find50c the height of the tower and the R.L. of the top of the parapet. (06 Marks)E:,6 b. What are the applications of total station? (02 Marks)!6=-o(B c. To find the elevation of the top(P) of a hill, a flag staff of height 1 .5m was erected and the-+o following observations were made from two stations A & B at considerably differentoi= elevations 156m apart. The angle of elevation from A to the top 6f the flag staff was 38"24o-atra. and that from B to the same point 2612 . A vane 1.2m above the foot of a staff held on Ao-l was sighted fromB andthe angle of elevationwas observedto be 954. The height of the9i;ao instrument axis at A was 1.494 and the R.L. of the instrument axis at B was 45.00m. FindatE the horizontal distance P from B and the R.L. of P. (12 Marks)!ob0ocb0 Differentiate between fixed hair method and movable hair method. (06 Marks)o= Following observations were taken with a tacheometer fitted with an anallactic lens having ao.Btr>:o value of constant to be 100 and staff held vertical.o Inst. Station Staff station R.B. Vertical angle Staff readines.Lr< 0 P N37"W 4 12, 0.910, 1.510, 2.110aOlo a N 23E 5" 42, 1.855, 2.705,3.555o Determine the gradient between points P & Q. (10 Marks)Z c. Two vertical angles to vanes fixed at 1m and 3m above the foot of the staffheld vertically at!oo. if R.L. of instrument axis is 235.665 m above the datum. I of2
- 7. t0cY44 PART _ B5a. Derive the expressions for the following elements of a simple curve. , External distance ii) Mid ordinate (04 Marks) b. A curve has a radius of 400m and a deflection angle of 40o. The chainage of point of intersection 1804.25 m. Compute the necessary data to setout simple curve by offsets from chords produced. Take Peg interval as 20 m. (08 Marks) c. Two straight lines with a total deflection angle of 72o30 are to be connected by a compound curve of two branches of equal length. The radius of the first arc is 350 m and that of the second arc is 500m and chainage of vertex is 1525m. Find the chainages of two tangent points and that of point of compound curvature. (08 Marks)6a. Explain with neat sketches the different triangulation systems. (06 Marks) b. Define the following : i) Satellite station ii) Reduction to centre. (04 Marks) C. From an eccentric station S 9m to the west of the main station B, the following angles were measured ZBSC : 33"1540 and ZASC : 67o562C,. The stations S and C are to the opposite sides of the line AB. Calculate,the correct angle ABC if the lengths AB & BC are 3,896.8 m and 4,470.72 m respectively. (10 Marks)7a. What is super elevation? Derive an expression for the amount of super elevation. (06 Marks) b. With the help of neat sketches, explain types of vertical curves. (06 Marks) c. A circular curve of radius 300m on a railway line gauge 1.5m is to be provided with transition curves at both ends. The super elevation is to be restricted to 15 cm. The design should be such that the rate of change of radial acceleration is 0.3 m/sec3. Calculate the length of the transition curve and design speed of vehicles if no lateral pressure is to be exerted on the rails. Also calculate the shift and spiral angle of the transition curve.(08 Marks)8a. Plot the cross staff survey of a field ABCDFE from the field book measurements given in Fig.Q8(a) below and determine the area of the field. (10 Marks) Lb tofr F 16o kl9b I oso l4o D e 150 HUN Gtoo tzd, ob* Fig.Q8(a) b. A road embankment is 30m wide at the top with side slopes of 2 to 1. The ground levels at 100 m intervals along a line AB are as under: A 170.3, 169.1, 168.5, 168.1 166.5 B The formation level at A is 178.7m with a uniform falling gradient of 1 in 50 from A to B. Determine the volume of earthwork by prismoidal rule. Assume the ground to be level in cross-section. (10 Marks) **{<{<* 2 of2
- 8. / USN 06cv45 Fourth Semester B.E. Degree Examination, January 2013 Hydraulics and Hydraulic Machines Time: 3 hrs. Max. Marks:100 C Note: Answer FIVEfull questions, selecting o o at leust TLI/O questions from each part. PART _ A a) (n (J L a. Define the following: E9 d= D Most economical channel s/, 2 ii) Hydraulic depth de =n iii) Rapidly varied flow. (06 Marks) -^tl e€ b. Show that for most economical triangular channel section the crest angle is 90o. (06 Marks) .=N .g <- c. Determine the dimensions of an economicaltrapezoidal section of an open channel with side - ol) ts() slope 2H:1V laid at a slope of 1 in 1600 to carry a discharge of 36 m3/s. Take C : 50. otr FO (08 Marks) 3s a. Distinguishbetween: i) Specific energy and total energy o= oo ii) Sequent depths and alternate depths iii) Gradual closure and sudden closure of value. (06 Marks) boc b. A stream carrying discharge of 2.4 cumec/m has velocity of 6 m/s is discharged from toe of .s c3 -o a dam on a horizontal bed. What will be the height of jump? Also calculate energy loss in >6 6- meters of water. (08 Marks) -4o c. What is the maximum pressure rise due to sudden closure of a valve in a pipe of 300mm 6rr diameter conveying water at 1.8 m/s? The pipe wall thickness is 18mm, Epipe: 210 GPa, ob1 Kwater :2.1 GPa. (06 Marks) o.. oi v1 -Y o= 3a. What is meant by dimensional homogeneity? Give example. (06 Marks) a,= b. Fluid of density p, viscosity p flows at an average velocity V through a pipe of diameter D. €i Show that the shear stress of pipe wall is !o 6." > (k tro! ,r=Orf[f] (08 Marks) o= o- Ai c In 1:40 scaled spillway model, the velocity and discharge are 2m/s and, 2.5m31s. Calculate =o 5! the corresponding velocity and discharge in the prototype. (06 Marks) J< -i Gi 4 a. Show that the efficiency of a jet striking normally on series of flat plates mounted on the o o periphery of wheel is 50%. (10 Marks) z b. A 75mm diameter jet moving with 30 m/s strikes a flat plate with its normal at an angle 45o to the axis of the jet. Determine the normal force on the plate, if the plate is stationary. Also o find hydraulic efficiency of the jet if the plate is moving with 15 m/s in the direction ofjet. (10 Marks) 7 of2
- 9. 06cv4s PART _ B A jet of water 5cm diameter strikes on a curved vane with 20 m/s. The vane being moving at5 a. to the direction of 10 m/s in the direction of the jet. The jet leaves the vane at an angle of 60o motion of vane at outlet. Determine: i) The force exerted on the vane in the direction of motion. (10 Marks) ii) Work done Per second bY the jet. b. A pelton wheel has to develop 13230 kW power under a net head of 800m while running at : : 600 rpm. If c,: 0.97, speed ratio 0.46, jet ratio 1/16, determine: i) pitch circle diameter; ii) th; diameter ofjeti iily ttre quantity of water supplied to the wheel; iv) the number ofjets required. Overall effrciency : 85oh. (10 Marks) (08 Marks)6a. with a neat sketch, explain the functioning of a Kaplan turbine. b. A Francis turbine has to be designed for an overall output of375 kW under a head of 80m with 700 rpm. Determine the main dimensions of the runner, runner vane angles. Take hydraulic losses : l0o/o, flow ratio 0.15, ratio of inner to outer diameter:0.5, ratio of : = 0.82, area blocked by thickness of runner vanes : 5o/o, width to diameter at outlet 0.1, no: speed ratio : 0.6. (12 Marks) (06 Marks)7a. Define draft tube. What are its functions? (06 Marks) b. Derive expression for specific speed of a turbine c. A turbine is to operate at ahead of 25m under 200 rpm. The discharge is 10 cumec. If the efficiency isgOoh,determine the performance of turbine under a head of 20m. (08 Marks)8 a. Differentiate between : i) Pump and turbine. ii) Suction head and delivery head. (06 Marks) iil) Single stage pump and multistage pump (06 Marks) b. What is primary of a pump? How it is done? A centrifugal pump^tas to work against a manometric head of 25rn, rotating at 850 rpm and c. discharginf O.)S m3ls. Velocity o? flo* and vane angle at outlet are 2.5 m/s and 40". If Tlman: 95Yo, calutlate: i) diameter of impeller ; ii) width atoutlet. (08 Marks) ***rr* 2 of2
- 10. / USN 10cv46 Fourth Semester B.E. Degree Examination, Decemb er 2Ol2 Building Planning and Drawing Time: 4 hrs. Max. Marks:100 (.) o Note: 1. Part - A is compulsory o 2. Answer any TWOfull questionsfrom Part - B. ! PART _ A 6) C) I Draw the plan, elevation and sectional elevation for the line diagram of the building shown in (JX Fig. Q1. Also write the schedule of openings a. Plan of the building (25 Marks) cge b. Elevation (15 Marks) -.o c. Section @ A- A (15 Marks) o0 d. I t* Schedule of openings. (05 Marks) o ::J (.)tr -o =ts PART _ B d= A sequence RCC column 400 mm x 400 mm is resting on a flat RCC square footing. The o() column consists of 6 bars of 16 mm dia, with 2 legged 8 mm dia stirrups @ 200 mm c/c and 6O the footing reinforcement consists of 12 mm dia bars @ 150 mm c/c both ways. The size and botr d6 thickness of the footing are 1200 x 1200 mm and 750 mm respectively. Draw to a suitable ,d scale the following views, a. Plan of the footing (05 Marks) -?o b. Vertical section of the column with footings (10 Marks) OE c. Cross - section of the column. (05 Marks) o- 6. tro. o. o ..i o= a tii 3 a Drawto ascale of I : l0the elevationof fullypaneled doorforanopening of 1.2 m x 2.1 m. (15 Marks) !o 5E Y. b. Calculate carpet area, plinth area for the drawing shown in Fig. Q3(b). (05 Marks) ^: bo- cao o= o. :j tr> Prepare a bubble diagram and develop a single line diagram of a office building to a scale of o 1 : 100 with the following requirement. t/< D AEE room -i ..i ii) Technical staff room o o iii) Clerical staff room iv) Accountant and related staff room L v) Storekeeper and related staffroom o o. vi) Manager room vii) Drafting room viii) Toilet block for men and women (separately). (20 Marks)
- 11. p 10cv46The line diagram of residential building is shown in Fig. Q5. Prepare sanitary layout andelectrica I layout plans with usual notations. (20 Marks) 6 =-{ T BG> Q- ooi+1 t<. r r- a-H e.;l I T 5.O?=- g1 --A,)t=.s r.- .4 9. /: -2 -il-2-lo.l6 r-r v t N q HqLT- I l^, B q.r-+l 4-3* 11.-o | 2-o r 2-+ x1 r.G 5 er<-- - r.qxl.? 5 11-.D 51- BEP l t-?xa.3 3. o 1 -=ft $t F{ .-q_ _t Fie. Q3(b) {v} V. rs Ctre O{ Bep .4.=:A? B.s iA_3 D...D Fr-i t 6tq B A$ r-t a.r-r-c )- , I D.Ih ^aag 5-ox6.o A t$ *< tB+$..{ q-s L +.1 rt^ 1 -a rl l.q J -J) .g Il- t5 or BE$ B-3 x 9-- 3 s?r3

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