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Diploma in Civil Engineedng / Diptoma in Electrical & Mechanical Englneering Term-End Examination a June.2OOS BET-O11: MATHEMATICS-I Time : 2 hours MoximumMalks : 70 No,e t Attempt Q. No. I uhich is compulsory ond ony other lout questions. In all, soloe fioe questions. All questionscofty equal morks. Use oJ colculators is pemitted. l. {a) Simplib and express the result with positive components (3xz1ox--f-xax-a {3x')-' {b) Find whetheror not th€ lirst polynomialis a lactor of the second. n2 E ^24 --2 1. (c) Solve BET.O1 1 P.T.O. (d) In a circle with centre O and radius5 cm, AB is a chord of length6 cm. lf OM -t AB, find the lengthof oM. (el If circumference a circleis 44 cm., find its area. of (f) Computethe el€venthterm of the sanes 4+8.5+13+... b) Find a unit vectorperpendicllarto the vectorsi, f. (h) Find the principal value of ""'(-+) Evaluate sin230' + cos230' 0 Find the radianmeasurecorespondingto 15". (k) Find th€ equationof a straight[n€ passingthrough (4, 3) and slope2. Determinelhe equationof a circle if ils centreis (8, - 6) and radius 5 units. is BET'o1 I What is meaning of the lollowing box ln a flow chaft ? (n) Mention fout computerprogramminglanguag€. 14x1=14 2. (a) The first term ol an AP is 4, and the tenth term is the 31. Determine sumol the first 10 terms. (b) Express lollowingwithout logariihms: the log x = logP + 2 log Q-log K- 3 Simplifu, f l-6 ' l !*'v" l 5+5+4 3. (a) ll a2 + bz - 7 ab, prove ihai 2 log (a + b) = log 9 + log a + log b (b) Find th€ middlet€rm in ihe expression of / -3f I b/ ff 3+5+7+......nt€rms 5+8+11+......8terms then complte the l"llue oI n, a BET-o1 1 P.T.O. 4. (a) Provethat sn x) L (b) Show that sin 105' + cos 105' = cos45 ' tc) Findthe angleof elevation the sunat a time when ot a wrtical pole 12 mehes hrgh castsa shadow 20 metres longon the ground. 5+5+4 5. (u) Find the equations lineswhich passthrougha point ol (4, 5) and makean angleof 45" with the line 2x+y+1=0. (b) Find the equationof a line thai has x-interc€pt-3 and is perpendicular th€ line 3x + 5y = 4 to (c, Find the equationof a line passingthrough ihe point {1, 3) and maktng angleof 60'with the positi\re an direction ol x-axis. 5+5+4 6. ia) Find the co-ordinates of the ceDtre and radius of the *2*f-e"+10y-0 (b) Find the €ccentricity, foci, and centre for the ellipse 2f+s92=1 1 BET.O 1 In the adjoining{igure,AB and CD are h{o chordsol eachother at p a circle, inters€cting If z BAC = 40", ard t BpD = 110., find Z PBD. 7. (al r r. * l - z i + 3 f a n d b = z t * ss t , -i then find a x b. Veriiy that a nnd a x b are perpendjcular lo each otber, Find the value of ), so that the vectors zi-ai +2t ansl-r.i*st d are perpendicllar to each other Show thdt the vectors u=3t*4i anu=el._rzf a are parallel. BET.O1 1 1,000 Diploma in Civil Engineering,/Diploma in Electrical & Mechanical Engineering Term-End Examinatiorl ' June, 2OO5 BET-012: PHYSIGS Time : 2 hours MaximumMorks: 70 (i) Answer ang five questions. Quesfion no. 1 's compursory, (ii) All qlestions cofty equol marks.. (iii) Giue SI units of physicol quantities in numerical You can use o colculotot. l. any seuen parts : Ans.r./er 2x7 (a) Define intensityof soundwaves,and write its units. (b) Draw shess - strain curve for a steel wire. (c) The resistance an electricheater is 25 Q and its of ends are connected to the poles of.a 90 V dry battery. Calculate the current flow in the heater BET.O12 P.T.O. ld) Why paramagnetic and diamagnetic substances cannot be used to make permanentmagnets? Convert 120" on Celsiusscaleinto Fahrenheitscale. (f) Define Diopter. igl Draw ray diagram for image formed when the obj€ct is kept between F and C in froi,t of a concave (h) Give t',{/o applications of Pascal's Law. 2. (a) Name the lactors allecting velocig ol sound wave in a gaseousmedium, Discuss them. 6 (b) An ai! column with a tuning fork of frequency v = 256 Hz resonates with column lengths of 334 cm and 101.8 cm. Calculate the speed of sound in air. 4 tcl Dellne surlace iension and give iLs SI unit How does the ,"alue of surface tension depend on temperature? 2, 1, 1 3. (a) Whai is a paramagnetic substance ? Give one example. State txo properiies of paramagn€tic substances. 1 ,1 , 2 (b) Define one calorie of h€at. How is it related with Joule? 2,2 Calculaie mean kinetic energy for one gram mole oI hydrogen ai S.T.P. Given density of hydrog€n at S.T.P. is 0 09 kg m-3. 6 BET-o12 4. la) State Kirchhoff's law of black body radiation. 2 (b) A \teel wire of lenglh 4 ? h and cross-seclion 3 0x10_5 m2 stretchesby the same amount as a copper wire of iength 3 5 m and cross-section 4'0X10 5 mz under a given load. What is the rdtio of the Young's modulusoI ste€lio that of copper ? 6 Define ihe term magnification in lenses. Calculate the focal length ol a convex lens that can be used to throw 29 times magnifiedimage.ol an object on a screen20 cm away. 2,4 Explain construction and working of a compound microscop€,with a neat labelleddiagram. 1,5 (b) A wire 2 crn long and 0.40 mm in diameter has a resisianceof 4 O. Caiculatethe resistivityof the material oI th€ wire. 4 (c) A charge q is moving with a velocig 1, in a region wbere both the magneiic field.B and electric field E are simuitaneously present. Whai is the Lor€ntz lorce acting on the charge ? 2 (d) What is the principle of a galvanometer ? 2 6. (a) Whai are secondary cells ? Explain their worldng principle. 2,2 {b) Calculai€ the operating magnetic lield required ior accelehting protons if the ndius of the cyclotron dees is 50 cm and its oscillator lrcquency js 16 MHz. cj,,eD e - 7.6 x 10-19 C; - = 1.67 x lO-27 kg. 4 BET-o12 P.T.O. (c) State FaEday's laws ol electrolysis. Eiplain the importance of Faraday constant in el€ctroiysjs. 3, 1 (d) Why are the passengers advised to remove ihe ink {rom their pens \rhile going up in an aeroplane ? 2 7. Write short note$on any ,&o of ihe following : 7x2 (a) Determinaijonof Mechanical of Equlvalent heat {b) Daniel Cell lc) Archimedes'principle {d) Tele.cope 't,000 BET-012 trEroGl Diploma in Clvil Engineering / Diploma in Electrical & Mechanical Engineering Term-End Examination June, 20O5 BET-013 CHEMISTRY : Time: 2 hours Maximum Morks ' 70 (i) Question No. I is compulsor!,. . (ii) Ansuer ony fo questions/rom Quesiions No. " 2to7. (iii) All questionscarrg equol marks. (iu) Use ol calculator is allowed. r, (a) Define ionizationenergy.How does it vary acrossthe periods in the periodic table ? (b) Ljst any four charact€ristics non-metals. of (c) What is red mud ? Explain briefly (d) lce floats on liquid water. Give reasons. {e) Ditferentiate bet'r./eena Calorie and a British Thermal Unit. (0 Wtit€ the us€sof molybd€numdisulphide. (s) Define glass transition t€mperatute- How is it important ? 2x7 BET-o13 P.T.O. 2. (a) What is modem periodlclaw ? Descdbevariousparis of the modem perjodictable. (b) Giv€ the eleckonic configurationsof the following Ms l'12),Fe '26), As(33), Sn(50) List five generalpropertiesof d block elem€nts. 5, 4, 5 3. (a) Discussany two meihodsol pr"paration of hydrogen gas and list its five uses. 'Complete (b) the following reactions (il '- NH4NO3 (.) (i0 3 NO2 ki + H2O (i) '-------+ How is nitric acid produced by Oshrald proc€ss ? List t o usesoI nitric acid. 5, 2, 7 4. b) Write any iwo or€s ol iron. How is iron extracted using a blast fumace ? Illustrate your answer with the help o{ the chemieal reactions involved and a labelled diagram. (b) Give compositionand usesof lollowing alloys , Brass,Gold (18 carat) 1o,4 What is meant by demineralisation of '&arer ? Describe ihe proc€ss of demin€ralisation using ion ex€hangeresins. 013 BE'T 2 (b) What is boiler corrosion ? Suggest iis preventive Explain ReverseOsmosisprocesso{ desalinationof braikish wat€r. 6,4, 4 6. (a) Illustrai€Otto Hoffmann's by-productoven process to nanulacture metal)u gi.al coke. (b) Discuss Fischer Tropsch process to produce synthetic De{ine cloud and pour pojnis of lubricants. How are rhese deternined ? Stap 'herr (ignifi(dnce in lubricaiion. 5,3,6 z. (a) What do you mru by polgmers ? Write the an mechanismof free radicalpolgmerisation. {b) What is w canizationof rubbers? \CJ Give composition.propertiesand usesof pyrex glass and optical glass. (d) What is clay ? Explain the term plasticity and describe methods to obtain '€quired plasticig. 4,2,4,4 BET-o13 1,000 Diploma in Civil Engineerlng / Diploma in Electrical & Mechantcat Engineering Term-End Examination JuDe,2OO5 : BET-O14 APPLIED MECHANICS Tirhe | 2 hows Moximum Morks: 70 Note I Atterhpt Q. M. I rahich is cofipvttotg and ony othet lour questions. In oll, sahreftoe qvestions. All questionscarty equol motks.UseoJ cqlculator is permitted. l. (a) Select tbe righl answer from the given four alternatives. 10x1=1O (i) A particle of mass m has momentum p, !t's kinetic ene4g ruill be {a) n1p (b) 2p2 p2 (c) m (d) pz 2fi BET.O14 P.T.O. {ii) A particle moves in a circular path of radius r. In half the period ol revolution, its displacement and distance co\reted are lal 2\ 2nr {u) ll' f,, lcl 2\ ft ld) r, ft (iij) The re$ltani o( t'.ro Jorces P and Q aciing ar an angb e is equd to r-;_----;- {a) {P' + Qf + 2PQsine t-;--_-;_- (b) iP' + Qt + 2PQcose t;--;- (c) {P" + Q' - 2PQsin0 - -;- f; (d) \jP' + Qz - 2PQcose {ie) The efliciency of a tifting machineis the rafio of {a) its outputto input (bl work done by it to the viork done on lt ic) adr,antage lts r,€locity its mechanical to ratio (dl AUof the above BET-OI4 {v) A lifting machine ha\,ing an efficiency less thah 50% is known as (a) reversiblemachine (b) id€al machine (c) noh-.e!€rsible0achine (d) None of the above (vi) Th€ velocity raiio of a simple wteel and .!de with D and d as the diameters of effort wheel and load axle is (a) D+d {b) D-d (c) Dd (d) D/d (vii) The iime of tlight of a proiectiie on a horizo al plaoe is ,^, 2u sin cr (b) 2u coso g usind {c) s (d) BET-O14 P.T.O. {uit The maximumdisplacement a body moving of with simple harmonic motion from its mean position is called {a) oscillation {b) amplitude (c) beat (d) None of the above (ix) The dope on the rcad surfaee generalb providedon the curvesis known as (a) angleof frictton {b) angleof repose {c) angleof banking (d) None ol the abor€ (xl The kinericenergyo[ a body of mass I kg is 12.5 kg m2 s_2.Its momentumln llnits of kg (a) 25 (b) 5 (c) o ld) 1.2.s (b) Fi in the blank: 4x1-4 'P' If the resultantof two forces and 'Q' acting {i) at an angle0 makesan angleof cr with P, then BET-O14 (ii) The coefficient of static fricton is aways than coefficient of d!'namic friction. (ii') Th€ centroid of an equilateral triangle of sid€ 'h' is located from any of its three sides at a distance h, {i') A ball dropped lrom the top of a tower reaches the ground in 6 seconds. The height of the to\lrer $ 2. An electriclight fixture weighting15 N hangsfrom a point C by h^,ostringsAC and BC. The string AC is inclinedat 60'to the horizontal and BC at 45" to the vertical as shown in figur€ 1. Determin€the {orcesin the stringsAC and BC. 14 Figurc 1 BET-O14 P.T.O. 3. A truss shown in figure 2, is subjected t\xo point loads to at B and F Find the fo:cesin all the members the ttuss of and tabulatethe results 14 F- 3m ----+F- 3m -----i kN 1.5 >P I 4m Figure 2 F 4kN I 4. (a) Definecoefficient staticfrictionandangleof friction. of Showthat p = tan 0 wh€r€the lettershar,€thef usual meanings. (b) Two block A and B of weights 1 kN and 2 kN respectiveD in equilibriumposition as shown in are figure3. Fisurc3 II the coeffici€ntof friction behreenthe hvo block as well as the block B and the floor is 0 3, find ihe minimum {orce (P) requirei to move the block B. BET-O14 (a) Show that there are h,\'o angles ol projection for a projectile to have the same horizontal range. What will be the maximuh heights attained in the tJ/o cases ? Compare ihe t'.,,/ohejghis for 0 = 30" gnd 60". (b) A projectile is lired honzontallg with a velociiy of 98 ms-r from a hill 490 m high. Compute (i) time taken to reach the ground (ii) th€ distanceof ihe target from th€ hill, and (iii) the velocity with which the dy strikes the ground. 6. Find the moment of ineriia of a T s€ction . as shown in tigure 4 about X-X and Y-Y axesthrough the C.G. of the section. 14 F_ 150 mm ___l T 50 mm l_ ,50 mm. F- -n Figure 4 BET-O14 7 P.T.O. 7. (a) State Newlon's second law of motion and prove that impulse is equal io the chang€ in momentum produced. {b) Two masses 7 W d 12 kg are connected at the t1r,o ends of a light inextensible string that passes over a frictionl€ss pulley. Find the acceleration of the massesand the tension in the string when the masses are rcleased. a, (a) A block of mass 0 8 kg is dragged along a level surlac€ at constant acceleration by hanging a block of mass 0.2 kg as shown in figure 5. Calculate th€ tension in the siring and the acceleration of the system. 02kg Figure 5 14 aET-O Two blocksof masses = 2 kg andMz = 5 kg arc Mt moling in the same direction along a frictionless surface with speeds 10 mt1 and 3 mi1 respecth,ely, being abeadof Ml. An ideal spnng MZ with K = 1120 N m-r is attached the backsideof to block Mz as shoumin figure 6. Find the maximum the compressjorof the spring!^then block collide. -----' 10 mtl ---- 3 ms-i Rgure6 BET.O14 1,o00 Diploma in Civll Engineering / Diploma in Electrical & Mechanical Engineering Term-End Examination June,)oos BET-015 ENGINEERING : MATERIALS Time , 2 hours MaximumMorks: 70 Note t Attempt dlt questions. All questions carry equal 1. (a) Fiil in the blank ; 7x1=7 (i) Dull paiches developedon a paini sudace is - deiectol paint. (ii) White lead and zinc oxide are - in a parnt, (iii) is the defect formed due to improper sawing of timber. (iv) Outemost ring beiween the bark and sapwood whjch is rlot yet converled jnto wood is known (') is obtained by bumlng limestone containing lot of clay and other substance. (vi) Shale is a -_ type of material. (vit rocks are formed bv alteration oI original structure under heat and pressure. BET.' P.T.O (b) State hue/faLse {or the follc*/,Jingstatements : 7x1=7 (i) The second class bricks have a minimum crushing strength of 45 kghm2. (i4 A good timber should have regular annual rings. (iii) Blue siain is a def€ct of timber due to Fungi. (iv) A good sand should not have coarse and angular gYainso{ pure silica. (v) Sandstone is a sedimeniary rock. (vi) Dolomite is a soft rock. (vii) A good brick should have a crushing str€ngih of lessthan 105 kg,/cmz. '7x2=14 2. Answer any trr,o o{ the followins : (a) List the method of quarrying of stones and explain any tlro of ihem. (b) Discuss the qualirv o{ good bricks. (c) Explain the manulacturing tiles. of 3. Answer aoy trro of the {otlowing t 7x2=14 (a) What are the essentialqualities of good building sion€s ? (b) Dscuss the selectlon ol materials for cement qoncrete. (c) Explain the signilicanceof compactjonof concrete. How v,,ill you achleve this at a constyuctlon site ? BET.O15 4. Answer any lu,o ol the following : 7x2=14 la) What ts decayol timber ? Explain variouscausesof lt. (b) Explain the chamcteristics good timber. of (c) Discuss propertiesof disiempers. the 5. Write short noteson : 31xa=14 2 (a) Rapid HardeningCement (b) Blast Furnaica Slag Cement {c) Air-entrainingcemeni (d Lo;heat cement BET-. 1,000 Diploma in Civil Engineering / Diploma in Electrical & Mechanical Engineering Term-End Examination June,2OO5 BET-016: ENGINEERING DRAWING Time : 2 hours MoximumMarks: 70 Note : Port A is to be attempted on ansuer scrlpts ond Pott B on drawing she€is. Use oJ calculator is allowed. PART A Attempt ony elgh, questions. All the questions cofty equol morks. (5 morks each) l. What are aligned s!6tem and unidirectional system of dimensioning ? 2 . What is the dillerence between a plain-scale and a diagonal-scale? lndicate the formula for the length of scale. 3 . lnscritte a circle in a given Equilateral-Triangle. 4. Define Ellipse,Parabolaand Hlperbola by any method. BET.O16 P.T.O. Give the name of ihat curve which is traced out by a moving point on the circumference of a circle without slipping along a straight line and where it is used. 6. Define Projection and state the position of any object with respect to reference-planes {H.P and VP) in 3d Angle Projection. Projections of hro Points 'A' and 'B' are gi\€n in the figure. State the position of each point with respect to the planes of projection, giving the disiances in mm. 8. What do you undeEtandby Tracesof a lioe ? Explain in brief. 9, Define 'plane' and make a list of different typgs of planes with simple sketches. lO. What are ihe differentpositlonswhlch a solidcan takewith respectto the Reference-planes and V.P) ? {H.P shape? ExplainIn brief 11. How canwe developany calindrical with sketches. 12.Ditfercntiate between 'lsometric-view' and 'lsometric-projection'. Indicate the ratio beftreen Isometric Iength and Actual length also. BET-O16 PART B Attempt ong two questions. quesfions A/l coftIesequol morks.(15 markseach) 13. Construct a parabola by Rectanglemethod when the abscissa {Axis) - 60 mm and the double-ordinate = (Base) 100 mm. 14. A line 'PQ' 60 mm longhasits end 'P' in both H.P arld VP It is inclined 45'to H.P and 30'to VP Drawthe at projectionsof line and determineits Tracesalso. 15. A PentagonalhJramid, edge of base 30 mm and height 70 mm has its ole €dge ol the baseon the horizontal plane (H.P). Draw ihe projections the RJramidwhen its of axismakes angleof 60'to the horizontal an plane(H.P.). 16. Two viewsof a coneare givenin figure.Draw its lsometric BET.O16 1,000 Diploma in Civil Engineering / Diploma ln Electrical & Mechanical Engineering Term-End Examination June, 2OO5 BET-017 COMPUTER : BASTCS Time : 2 hours Moximun Mdrks: 70 Note : (il Question no. 1 is compursory. lii) Attempt any fout'questions out oJ the remaining questions numbered 2 to 7. 1, Fill in the blanksllom the choicesbelow: 14 . (t) First dialog box that appears after opening of MS Word is .-- -- . (ii) You can use styles to .- yow documents in Microsoft Word. (iii) You use the - -- toolbox to apptg common characterand paragraph{ormar' ro splecledlext (iv) The unit o{ slze measurement of fonts is called (v) For s€lecting a particularprintef you have to cJick defalit printer. BET.O17 P.T.O. (vi) ls us€d to insert the contenis o{ clipboard into the documeni. {vii) Marking a block of texi is done b9 dragging it with (viii) A passage of text is del€ied by seiecting it and pressing- keY. (ix) The short-cut key to open an existing file is _ {x) displaysihe contents of and name oi the active celi. (xi) In the Page Sefup oI MS Excel, . -- has the option to selectthe area to b€ printed (i.e- range ol cellsor rows or colurrns), (xii) In MS Excel _-- ate included in ihe worl,sh€ets and can be moved, copied and /eslzed as any other graphicalobject lt can be viewed along with the data and many charis can be inselled (xlil) - is tbe name given to the main computer equipmentand its periph€raldevices. (xlv) Insiructions to compuiei ate given through .n"o;l- (0 (a)Alt, (b)poini, (c)Ctrl+O,ld) format,(e)mouse, del' (g) tip cf ihe clay, (h) Embedded charts, (l) prosram' 0 fotmula bar, (k) hardware, (l) Set 3s, (m) She€{tab' {n) cursor, 10)paste, (p) iormat 7 BET.O] 2, Attempi an9 tDo oI ihe following : 2x7=14 (i) Whai is a computer ? Describe the general of architecture a computer. (it) What are MailMerge and data source ? What ? iheir advantages (iiii What are ihe steps r'nvolvedin copying a worksh€et to a new worksheei ? 3. Attempi any tlrJo of the fojlowing : 2x7=14 (i) How will you create a custom list in MS Excel ? {ji} Lisf and explain the contents ol fo[nattjDg tooJ bar. Make necessary assumptions. (iii) Where can one lind pictures to be insert€d in a document ? 4. Attempt any one of the following : 14 (i) Cr€at€ a slide show that shows the dajly time schedule an afmy personnel6n a week day, (max of with the name, tiile slides,morning and of 5 slides), evening duties, name of regiment etc. Write content oI each slid€ on the answer sh€et. Mak€ necessary assumplons. (ii) How do Explain, in detail, ihe Windowsaccessori€s. you prini in Windows ? BET-017 P.T.O 5. Att€mpt any tuo of the lollowing j 2x7=14 (i) Explain differeni tlpes of chartsjn Excel. 1i1) What is a footnot€ ? (iii) What is the role of "F1" key jn Windows ? 6. Attempt any l(ro of the folLowtng , 2x7=14 (i) What does Jormaftingof a floppy disk mean ? (ii) What are the lunctions in MS Excel ? cjve h/,/o examples- (iii) DiflerentiatebetweenFIND and REPTACEfunctions. 7. Attempt any one of the followins , 14 (i) Ust the steps followed for finding a document in a computer by searching. (iij Is it possible to convert text into table using Microsoft Word ? Justify youl answer wrtD an exampl€. BET.O17 1,000 Diploma in Civil Engineering / Dlploma in Electdcal & Mechanical Engineering Term-End Examination June,2OO5 BET-021 MATHEMATICS.II : Time : 2 hours MaximumMorks, 70 Nole : Question r'o. 1is coitpulsory. Attempt anyfour qu€stiohs out' oJ the rcmdining questions numbered 2 to 7. Use oJ colculotor is permittecl. 1. (a) Select the correct answer from ihe four given altematives each pari given betow : lor _ ,t,, -.' {,) rr y = ro9 IlaD y). lhprr i, eq]|/'l t" dr lal 2 sec2x (b) 2 cosec2x (c) 2 secsx (d) 2 cosecrx BET.O21 P.T.O. The point on tha curve y2 = x, the tangent at ,J.,bichmahes ar, angle o{ 45', wiih x-axis will be given by 1\ . ,u, 1 1 aJ lr. . f1 1\ tb) \.t t) (c) (2,4) ' [+' ;] The right circular cylinder o{ given guriace {including the ends) shail have maximum volume jf the ratio of lts height to its diametet is la) 2 ,o) ; (c) 15 (d) 1 lf i(x) = xz + 3x + 4, tlren i(A) - (a) A2+3A+41 (b) A2+3A+4 (c) A2 + 34 (d) (A+41(A+l) where A is a squar€matrix BET-021 The mode of the following sequenceof numbers 25, r5, 23, 40, 27, 25, 23, 25, 2D is la) 25 (b) 20 lc) 23 (d) None of the above l 4 3l (vi) Inverseof I I is L-7 1J f r 1l 4 3 l ,. | Ial I I I* - r l . 1 I I L 7 l a 3l ( b i -'l f I " l-7 1_l ,[1 o] ( c ) ; 1 | zJ rl L0 '' f1 -3l ldr *l I "17 4l BET.O21 P,T.O. lvlr, - rs equal Io l' a. l ---r 5 5 (b) :+:i ., 3 4. tcl ;+;t (d) None of ih€ above {b) Siaie wh€therihe followingstatemenis true or are falseand justi{! your an$rer. (jl - 1e (--,2) .3 -cl lit) li'r' -: --= = 27 r+ 3 x+J - lriD r) y = t4x - 5f, rh,n lv = 4{4x 5)3 dx Fill in the blank. l"-2 x+ v l f 0 3l (i) rf I l=l lihen l'-s 4a-81 L4 12) x = _ y = _ z = - lrlI I ( i t L e t A = 1 4 5 6 1a n d = , B then lsl, AB= A+BT= t'l BET-021 (ii0 I sin 2x l - o * = (iv) Average ';alue may be termed 14x1=14 2. la) Elaluate Im- - -- It 2x' + y" - 6y - 9x - 0. determinerhe equarion ol the normal to ihe curve at the poini (1, 7). 7+7 3. la) Show that the tunction l*' x when +1 f(x)= j l2 x when =1 ls dlscontinuous x = 1. at (b) f 1 Lvatuate| - dx. /+/ J ex+1 ni2 4. (a) Evaluate I J 0 (b) Rnd the area bet$een the paratolas yz = 4ax and ,2 = 4ay. BET-021 P.T,O. 5. (a) Solve lor o suchihat the expression is =ffi rmagrnary. (b) lf {2+3i(3-4 = x + iy, evaluat€andy. x 7+7 1 1 2 5 1 6. (a) I I A - I land L-1 3 -41 -t 1l lt t l B=10 -1 4 l f i n dw h e t h t h em a t r i x er Lu , -1] expression for €ach of [t A + B, {ji) AB and liii) BA is possible/valid. State with reasons when a matrix expression is not \Elid,/possible. Determine the inverse of the matrix f r , -,1 i l A-l-1 3 0l f o -2 ,l ,*, 7. (a) Show that th€ variance of the first n positive iniegets i,,!rnz-tr 12 8Er-021 The following iable shows the mirrks obtained by 100 candidaiesin an examination. Calculate the mean and standarddeviation. 7+7 Marks No. ol Candidates 1- 10 3 11-20 21-30 26 31-40 4 1- 5 0 51 60 I BET-021 1,000 Diploma in Civil Engineering / Diptorna in Electrlcal & Mechanical Engineering Teml-End Examination June, 2O05 BET-02?. STRENGTH MATERTALS OF Time: 2 hours MaximumMorks: 70 Noae : Question no. 1 is computsory. Attempt on9 tow questions Jrcm the rcmaining. Assume suitable data whereuer necessoryand mention it clea y. Use ol colculotor is ottowed. l-. Choose corect answers the from iie givenalt€matives. 14x1=14 (i) The relation behre€n young,s ModuL,s E, Bulk modulusK, and Poisson'sratjo p is given by (a) E=2K(1 -2p) (b) E = 3K(1 + &) (c) E=3K{1 -2p) td) E=2Klt+p) 8ET-o22 P.T.O, (it The elastic modulus of steel is 18 iimes the €lastic modulus of concrete. The modulat ratio will be (a) e (b) 18 (c) 36 (d) None of the abov€ (iii) If the Young's modulus of elasticity of a material is n ic€ its modulus ot ngidiiy, the Poisson's raiio oI the material is (a) -1 (b) -05 (c) 05 (d) zero (iv) If a prismatic member with area of cross section A is subj€ctedto tensile load P, then the maximum shear str€ssand its inclination with the direction of the load, (a) P/A and 45" (b) P,u2Aand 45' lc) P/2A and 60' (d) P/A and 30" BEr-022 Compatibility condition in a compositebai ensures (a) strains in the components of the bar are equal (b) stressesin the compon€nts of the bar are equal (c) strains and stresses th€ compon€ntsof the in bar are equal (d) None of the above (vi) Maximum bending moment in a beam occurswhere (a) deflectionjs zero (b) shear force is maximunl (c) shear force is minimum (d) shear force changes sign (vit The variaiionof bendingmoment in the portion of a beam carryinglinearlyvarying load is (a) linear (bl parabolic (c) cubic (d) constant (viit) A poftion of the beam bet'r,,eentwo sdctians is said to be in pure bendingwhen there is (a) constant berding mofient and Ero sl.€ar [orce (b) constant shear force and zero bending rnoment (c) constant b€nding moment and constani shear ld) None of the above BEr-o22 P.T.O, (ix) Ii the length of a simply supportedbeam carrying a concentrated load at the centre ]s doubled, the defleciionat the centre will becone la) hro times (b) four tim€s (c) eight times (d) sixteen times {x) An isotropicmaterlalis one which has (a) same elastic properties in all three direcilons (b) same elastic properties in at least two dlrections (c) different elastic properties in all direciions (d) None o.f'!he above {x') Bucklingload for a column dependsupon (a) length of the column only (b) least lateral dimension only (c) both lensth and teast lateml dlmension (d) None of the above (xit Principal planesare the planes (a) which have maxlmum shear stresses (b) which ha'"€ zero sh€ar shesses (c) which ha!,€ maximum normal stresses (d) which have minimum normal stresses BEI.O22 (xiii) A propped canttlever is a,/an (a) stable and statistically determinate beam (b) unstable and statistically indeterminate beam (c) stable and statisiically indeterminate beam {d) unstable aDd siatisticallg determinate beam lxiv) If th€ load at the free end of a caniileverbeam is doubled la) sjope and deJlectjon al the fixed end will (b) slope and deflection at the fixed end will (c) slope and defleciion at the fixed end willremain unchanged (d) None of the above A iimber beam 200 mm wide and 400 mm deep is simply supported over a span of 4.0 m. Find th€ maximum uniformly disiributed load that the beam can carry, if ihe bendingsire.s is nor to exceed8 N/mm2. l4 If a 2.0 m long bar having a square cross s€ction of 300 mm side is subjected to a compressive force of 600 kN/mm2, find the changein votumeif elasticconstant E and r for the material are knour as 100 kN/mmz and 0.2 respectively. 14 BEl-022 P.T.O 4. A beamABCD 20 m long is loaded shownin figure. as Th€ beamis supported B and C. Draw B.M. and S.F. ai diagram principal indicating numerical values. 14 tzm-t------."............_ --1- 12n 6^ -, A compound bar is constructed fast€ningthree bars by 50 mm wide by 12 mm thick together io form a bar 50 mm wide and 36 mm thick The middle bar is of airrninlum atloy {oI which E = 70 kN/mm2 and the oulside bars are of brasswith E = 100 kN/mm2. If the bars are initiallylastenedat 18oC and temperature the whole of of the assembly then raisedto 50' C, delerminethe stresses is q€t up in lhe brassand lhe aluminrurn. o, dnd o . may be taken as 18 x 10-6 Kr and 22 x 1O-5 K:1 respectively. l4 6. A beam of triangularcrosssectionoI basewidth 120 mm and heigbt 100 mm is subiected io shear torce of 5 kN. Find ih€ maximum shearstr€ssat th€ n€utralaxis. 14 A solid shaft has to transmit 90 kW power at 160 RPM. Find the suitablediameter {or ihe shatt if the maximum torque transmitted in each r€volutjon exce€dsthe mean by 25%. Take allowable shear stress as 70 N,/mmz. 14 BEl-O22 A steel bar of.ectangu)arsection 40 x 60 mm pinned ai each end is 3 m long. Determinethe buckiingload when it is subjected to axial comprcssion and also calculate axial stress using Euler's expression.Determine,the mininum length for which Euler'sequalionmay be valid. 14 Take pyoportionality limii as 250 MPa ahd E . 200 GPa {2 \ 105 N/mn21 BET422 1,000 Diploma in Civil Engineering / Diploma in Electrical & Mechanical Engineering Term-End Examination June, 2OO5 OF BET-023: ELEMENTS SURVEY Time , 2 hours Moxinum Morks : 70 Note . Question no. 7 is c!mpulsory. Attempt ony four questions lrom the rcmaining. All questions carry equal marks. use of colculator is permitted 1. Select the most appropriate an$,/er for each of the following multiple choice obj€ctive type quesiions given below. 2x7=14 (i) Geodet:c suweying is dilferent lrom Plane 5urveying (a) the curvature of th€ €arth (b) the la€e difference of elevation betreen various po,n$ (c) coverage of very large area (d) undulations of the iopography BET-023 P.T.O. (it Number of link in a 30 m metric chain is (a) 100 (b) 150 (c) 180 (d) 200 (iii) 'Ranging' is the process of (a) Iixing rangingrods on d suney line (b) aligning the chain in a straight line behveen tro (c) iaking olfsets from a chain ljne (d) chaining over a mnge of mountains (ivl Which of the following is not used for measuring n,rhon.li."l:r ^flc,lc ? (a) Line Ranser (b) Sieel Tape (c) Optical Square (d) Cross Staff (v) Local attraction in compasssuruegingmay exist due (a) incorfeci levelling of magneiic needle (b) loss of magneiismof the needle (c) friction of the needle at the pivot (d) presence of magnetic substancesnear the BET.O23 {vi) Il th€ R.L. of a B.M. is 100.0 m, the backsight is 1.215 rn and the foresight 1.8?0 m, the R.L. of is the torwardsfation is la) 99 345 m (b) 100 345 m (c) 100.655m (d) 103 085 m {vit The instrumeni usedfor accurate centering plane in tabie surveyjs la) Spirjt level (b) Alldade (c) Plumbing fork {d) Trough compass 2. Dilferentiate between the following ierms : 3!x4=1s 2 (i) Plan and Map (ii) Plane Survey and Geodetic Survey (ii0 Main Station and Tie Siatton (iv) Backsight and Foresight 3. {a) A 30 m chain was found to b€ 3 cm too long after ' chaining 1800 m. The same chain was observedtc) be 5 cm too long alter chainingthe total distanceof 4000 m. Assumingthat the chain was correct at the commencement of work, find the true iength of the total distancechained. BET.O23 P.T.O. {b) WiL\ the help ol a n€at sketch, describ€the 3-4-5 offsei method for obtainingperpendicularoffset to a cbain )ine. 10+4=14 4. (a) Deline the {ollowing , (i) Magneticdeclination (ii) Local attraction (b) Convert the following reduced bearings io whote circle b€arings: (i) s 54'32 W (it s 39" 52',W 7+7=14 Following readings were taken during a levelling exetcise. The inshment was shifted atter 5s and 8th reading. Enter the r€adings in the regular li€ld-book format and find RLs o{ the statiom, if the RL of stariing slation is assumed to be 105.000. 2430. 3546. 3113, 2106, 0945. 2.598. 2744. 7 615, 0 974, 0 823 and 0 178. 14 6 . State the thtee point problem. Explain how it is solved by the gaphical method. )4 Describe in brief the temporary adjustments oJ a theodolite. Explain how would you measure the bearingof a line with a theodolite. 14 BET,O23 1,000 Diploma in Civil Engineering / Diploma in Electrical & Mechanical Engineering Term-End Examination June, 2O05 'gET.OZl : E/M ENGINEERING Time: 2 hours MaximumMarks: 70 Note : All questions compulsory. UseoJ calculator are is permitted. l. Selectthe correct answerfrom the given four alternati\res for the following multiple choice quegtions : 14x1=14 (i) In cold countries, water pipes sometimes burst, (a) the pipe contracts {b) water expands on freezing (c) when water {reezes, pressure jncreases (d) when water freezes, it takes heat lrcm pipes (ii) Heat required to raise the temperature of a body through 1" C is known as (a) specificheat capacity (b) water equr\,?lent (c) molar s!,eci{ic beat (d) thermal capacity BET-o24 P.1.O. c- (iii) the lue of is aq \al zPro (b) benreen 0 and 1 (c) negative (d) great€r than 1 {iv) It lhe Iempevaturc of lbe source js increased, efliciency of a Carnot engine (a) increases (b) decreases (cl remains constanl (d) lirst increases and then remains constant processoccursat constant Ah adiabaLic (a, temperature (b) pressure (c) heat {d) None of the above (vi) The capacityof lift and cranesls definedin terms of (a) the height to be lifted (b) carryingload in kg or tonnes (c) horsepower of the motor (d) None of the above BEl{24 {vii) When a capacjtor js connected to a batiety la) an allernatjng currmi flows in the circu]i {b) no curent ilows al all (c) a current flows for some timc and finally it decreas€sto zero (d) cunent keeps on increasing and teaches maximum after sorne time (viir) A bird sitting on a high power lin€ (a) gets killed instandy (b) gets a mild shock (c) is not affected practically (d) gets a fatal shock {n} Figue 1 shows cunents in a part of electrical cirqji. The current i is (a) 1A (b) 13 A (c) 17 A (d) 37A e,ttAZq P.T.O. tx, Four conductorsof equal length and of resistance 10 O each are connectedin the form of a squar€. The eq{rivalent resistancebetween hro opposite cornersof tie squareis (a) 2'5 I (b) 10 o (c) 20 o (d) 40 c) lxi) An inductor may sior€ energyin {a) its electrictield (b) iis coiis (c) its magneticfield (O both in electricand magneticlields (xii) In a losslesstransformer, an alternating current of 2 A is llowing in the primary coil. The number of tums in the primary and secondary coilsare 100 and 20 respectilely. The ,.,alue of cufient in the secondary is coil (a) 0.08 amperes (b) 0.4 arnperes (c) 5 amperes (d) 10 amperes BEr-O24 (iit In seriesLCR AC circuit, the phase angle bet een cur.ent and voltage is la) Any ang@ben een u ano t t {b} I2 ' (c) r toJ l1ny angte betweenu ano (xiv) Which of the following quantities remains constant in a slepdown lransformer? {a) Cunent (b) Voltage (c) Power _ {d) None of the above Answerany t.oo of the following : (a) A Carnot heat pump opemtes between the temperaturelevels - 5" C and 25" C. If the power consumptionol the heat pump is 5 KW determine; {i) the rate at which energy is iejected at 25" C, (ii) the coefficient of performance. {b) What are the five major air pollutants coming out of an IC engin€ ? Explain in detail. 7 Differentiaie between the fuel systems in a Diesel engine and a Peirol engine. 7 BET-o24 P.T.O. Answer any t.!o ot the following : (a) Derive expression for work done during an isothermalchange. (b) Why sholrld you have trees in the exteior area of the building? Justily your answer (c) What are the proiection systemsavailable in the high rise buildings for avoiding fire hazards ? 4, Answer any l!.,o o{ ihe followjng : (aJ Three capacitorsof 1 pF, 2 yF, and 3 pF are joined in series first and then in parallel. Calculate the rdiio ol equivalent ca!,acitance in the two cases, (b) Calculate the potential differ€nce bet'reen th€ points A and B ftom the data as shown in figure 2. Figure 2 BEf 024 (c) A 100 Q resistor, 100 mH inductor a and 100 frF capacitor are all connectedin parallel acrossa 200 V, 50 Hz a.c. source. Findthe currentsupplied by the sourceand its relativephaseWith r€spectio the voltage. 5. Anst er any ttr)o oJ the following (a) A powel transmissionline feeds input power at 2300 V to a stepdown transformer,with its primary windings having 4000 turns. What should be the numb€r of turns in the secondarywindingsin order to get output power at 230 V ? tbi A 250 V DC series motor runsat 500 rpm, when taking a cunent of 25 A. The r€sistanceof the armature 0.5 e and ihat of the field is 0.3 O. If is the current remains constant, calculaiethe necessary additional resistance reducethe speed to to 250 rpm. (c) An 8-pote, 50 Hz tnductjonmoior runs ai 720 rpm whenon lull load.Calculate the (i) slipof the rotor (ii) speedof the statorfieldwjth relerence stator to {ili) speedof the statorfieldwith rel€rence rotor to (iv) frequenc,of rotor curr€nts M speed at rotor field rviih relerence to rotor conductors {vi) speed of rotor field with reference to stator conduitors. Ber-o24 1,000 Diploma in Civil Engineering/ Diploma in Electrical & Mechanical Engineering Term-End Examination June, 2OO5 BET-026; WORKSHOP TECHNOLOGY Time : 2 hours Maximun Marks : 70 Note : Question no. I is compulsory. Attempt six questions Jram Port A ond tbo questions Jrcm Part B l. (2 Atiempt any seuen questions mark each).Choosethe correct answerslrom amongstthose giv€n below : 2x7=14 (a) The knot which can be easilyseparated from the out body of wood is known as (i) Dead knot (ii) Live-knot (b) The tool which is usedfor drawing hro,parallellines dl a limp on a woodensurface i 'np erlnp rc r^ lnown as (i) Markns Knife (ii) Marking Gauge (iii) Monise Gauge BET.O26 P.T.O. (c) For the preparationof oifpaint. litharge ts us€d as a (i) Base (ii) Drier (iij) Vehicle (d) The abiliiy of sand particl€s to stick iogether is (i) Cohesiveness (ii) Adhesiveness (iii) Collapsibility ie) Dunns welding,Borax is usedas a (i) Filler meial (ii) Parent metal (iii) Flux (fl Hard Solder usuallymelts at a temperatureoi about (t 600'c (ii) 400'c tiii) 350'c (s) Hammers are generallgmade of (i) Casi iron (ii) Wrousht-iron (iii) Cast-steel (h) Auger is used as a (i) Measuring tool [ii) Bonns too] (iii) Markins tool BET-026 For Oxy-Acetylenew€lding process, oxygen gas is filled in the cylinderat a pressureof (i) 90 ks,/cm2 100 ks/cm2 lii) 125 ks/cmz - 14o ke/cmz (iri) I75 kg,/cm2 190 kg/cmz A cylindrical shape in a mould can be developed (i) Trtangle (ii) Circle (iii) Rectangle PART A Attempt any six queslions.AII the questionscarry equo/morks(6 narks each). 6x6=36 2. What are the common us€s ol timber in building industri€s? 3. Describein brief the characteristics a good oil-paint. of 4. How is French'polish pr€pared ? Differenhatebetween Paint and Polish. 5. How are the tools of carpentry classified Explain wiih ? 6- What js "Settjng ol Saw Teeth" ? Why is it done ? BET-o26 P.T.O. 7 . Distinguishbetwe€n"Facingsand" and "Parting-sand. 6. Nam€ the common sheet metal working machinesas per their nature of work. 9 . What do you undersiandby Gas welding ? Make a list ol welding. tools and equipmenttequiredfor Oxy-Acetglene 10. Distinguishbetw€en solderingand brazing pfoc€sses.in brief. PART B Attempt anv tuo questions.All the questionscarry equal morks(10 morkseach). 10x2=2O 1 1 . Sketch and describethe constructionand working of the "Band-Saw . 12. Describewiih ihe help of sketch€s, different iypes of the "Gas W€ldingTechniques' . 1 3 . What do you mean by stakes ? Nam€ and sketch i\ro iypes of siakesgivingtheir usesin sheetmetal work. which 14. Explainin brief the uarjousiyp€s of air compr€ssors are gen€rally used at construction plant sites. BET-026 1,000 Diploma in Civil Engineering ,/ Diploma ln Electrical & Mechanical Engineering Term-End Examination June,2OO5 BET.037: FLUIDMECHANICS Time : 2 hours Maximum Marks : 7O Note : All questions ore compulsory. Use ol colculotor is permitted. l- Selectthe correctaltemative. 7x2=14 (i) Neunon'slaw of viscosityrelates (a) ihe shear stress and strain in a fluid (b) the shear stress, pre&ure and velocity (c) the shear stress and rate of strain (d) none of the above {ji) A uujd is a substance that (a) cannot withstand any shear lorce (b) cannoi remain at rest under the action ol a sh€ar force (c) flows in ihe absence of extemal lorces (d) is jncomp/essible and jnviscid BET-037 P.T.O, (ili) Capillarig rise and depression phenomena (a) are observed on9 ln vertical tubes (b) depend solely upon the surface t€nsion of the liquid (c) depend upon the surface tension of the liquid as well as the matedalof the tube (d) depend upon th€ pr€ssure dlfference behteen the liquid and the en\nronm€nt tiv) Relation behreen Co, C., and Cu is C (a) C, = :! c (b) c, = =! k) cd = ci" d\ a _ ta c \1/2 (v) The pressure at a point is equal in all directions (a) only when rhe lluid is inviscid (b) when the fluid i5 incompressible (c) when ihe fluid is at rest, regardlessof its nahrre (d) in a laminar flow BET-037 (vj) Ol the various methods of measuring discha€e through a pipe lin€, the one with the least loss of energy and direct r€adingis (a) by m€ans ol a venturimeter (b) by meansof an orilicemeter (c) by meansof a Ilow nozzle (d) by tra\,€rsing a piiot-static probe (vii] In parall€l-pipe systems (a) the pipes must be placed geomeirically parallel to each other (b) the flow mu.r be rhp samp rn all pines (c) the head loss acrosseach of the parallel pipes must b€ the same (d) none of the abov€ :s valid 2. Answer any tt,o of the Iollowing I 2x7=14 (a) Find the heighi through which water rises by capillary acUon in a glass iube ol 2 mm bore il ihe surface tension at the prevailing temperature is 0 075 N,zm. (b) Water Jlows through a horizontal venturimeter, 35 cm x 20 cm diameter, at the rate of 0.082 cumec.If the differenceof pressureis 0 32 m of water, calculate lhe coeffici€ni o{ the venlunmeter. (c) An oil of specificgravity 0 80 is flowing through a pipe of 100 mm diamei€r at a velocity of 1 m/sec. Determinewh€ther ihe llow i9 laminar or turbulentit ihe kinematic viscosity the o'l is 1 x lO E mz/s. of BET037 P.T . O 3. Ansrrer any tuo of the loilowing : 2^7=14 {a) li) A ptpe oI 25 cm diameter cauies water with a mean veloci9 ol 4 m/sec. Calculaie the discharge. {ii) ll the pipe is bifurcated jnta two pjpes al 72 crn diametereach, Jind the v€locityin each pipe. (b) A sharp'edg€dorifice of 6 cm diam€ter discharges water under a bead of 6 m. Find th€ valu€sot the coefficients of velocity, coeflicient of contraction, and coefticientof dischargeil ihe measuredrate of flolv is 0.016 cumecs.The diameterof the jet ai th€ vena-contracta 5 cm, is k) What is Euler's equaiion of motion ? Derive the equation along a s\eatnline and obtajD Bemoulli's made il any. €quationfrom it. List the assumptions 4. Answer any one of the lollowing , 14 (a) A 160 mm diameter pipe reduces in diameter abruptly to 120 mm diameter. If the pipe caries water at OO4 m3,/sec, calculate the loss of head acoss the contYaction. Take the coefficientof coniractionas 0 60. (b) Find the Ioss of head due to friction in a pipe carryjng water. The pipe is 400 m long and 20 cm in diamei€r. Th€ dischargeibrough the pip€ is O 05 cumecs. Takef=004. BET.O37 5. Answer any or€ of the following I (a) The cross'section an op€n channelis a trapezium of wiih a bottom widih of 5 m and sizeslopes1 vettical to 2 hoyizontal. Calculaie th€ discharge if the depth I ol warer is 2 m a-d S = __-. Use Chezys lormula II'UU c=45. 14 (b) Write short notes on any toat: nr3!=M (l) Viscosity (ij) Turbulent Flow (iii) Hydraulic Slope (iv) Venturimeier (v) Energy Gladient Ljne (vi) Intemal Mouthpiece BET-037 1,000