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1 SECTION - 1. This question consists of TWENTY-FIVE sub-questions ( ) of ONE ark each. For each of these sub-questions, four possibe aternatives (,, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer b darkening the appropriate bubbe against the question nuber on the eft hand side of the Objective Response Sheet (ORS). You a use the answer book provided for an rough work, if needed. 1.1 The divergence of vector r r = i r + j r + zk r is (a) i r + r j + k r (b) 3 (c) 0 (d) 1 1. Consider the sste of equations given beow: + = + = 5 This sste has (a) one soution (c) infinite soutions (b) no soution (d) four soutions 1.3 What is the derivative of f ( z) = at = 0? (a) 1 (b) -1 (c) 0 (d) Does not eist 1.4 The Gauss divergence theore reates certain (a) surface integras to voue integras (b) surface integras to ine integras (c) vector quantities to other vector quantities (d) ine integras to voue integras 1.5 For a spring-oaded roer-foower driven with a disc ca, (a) the pressure ange shoud be arger during rise than that during return for ease of transitting otion (b) the pressure ange shoud be saer during rise than that during return for ease of transitting otion (c) the pressure ange shoud be arge during rise as we as during return for ease of transitting otion (d) the pressure ange does not affect the ease of transitting otion 1.6 The shape of the bending oent diagra for a unifor cantiever bea carring a unifor distributed oad over its ength is (a) a straight ine (b) a hperboa (c) a eipse (d) a paraboa

2 1.7 In the figure shown, the spring defects b δ to position ( the equiibriu position) when a ass is kept on it. During free vibration, the ass is at position at soe instant. The change in potentia energ of the spring-ass sste fro position to position is δ Free ength k (a) 1 k (b) (c) 1 ( ) k δ 1 k g + (d) 1 k g partice P is projected fro the earth surface at atitude 45 with escape veocit v=11.19 k/s. the veocit direction akes an ange α with the oca vertica. The partice wi escape the earth s gravitationa fied (a) on when α = 0 (b) on when α = 45 (c) on when α = 90 (d) irrespective of the vaue of α N Earth P 45 α ν 1.9 ars and C, each of negigibe ass, support oad P as shown in the figure. In this arrangeent, C P (a) bar is subjected to bending but bar C is not subjected to bending (b) bar is not subjected to bending but bar C is subjected to bending (c) neither bar nor bar C is subjected to bending (d) both bars and C are subjected to bending 1.10 The area oent of inertia of a square of size 1 unit about its diagona is (a) 1 3 (b) 1 4 (c) 1 1 (d) 1 6

3 1.11 Which of the foowing stateent is correct? (a) Fwhee reduces speed fuctuations during a cce for a constant oad, but fwhee does not contro the ean speed of the engine if the oad changes. (b) Fwhee does not reduce speed fuctuation during a cce for a constant oad, but fwhee does not contro the ean speed of the engine if the oad changes. (c) Governor contros speed fuctuations during a cce for a constant oad, but governor does not contro the ean speed of the engine if the oad changes. (d) Governor contros speed fuctuations during a cce for a constant oad, and governor aso contro the ean speed of the engine if the oad changes. 1.1 The SI unit of kineatic viscosit (ν) is (a) /sec (b) kg/(-sec) (c) /sec (d) 3 /sec 1.13 static fuid can have (a) non-zero nora and shear stress (b) negative nora stress and zero shear stress (c) positive nora stress and zero shear stress (d) zero nora stress and non-zero shear stress 1.14 gas having a negative Joue-Thopson coefficient (µ < 0), when throtted, wi (a) becoe cooer (b) becoe warer (c) reain at the sae teperature (d) either be cooer or warer depending on the tpe of gas 1.15 Luped heat transfer anasis of a soid object sudden eposed to a fuid ediu at a different teperature is vaid when (a) iot nuber < 0.1 (b) iot nuber > 0.1 (c) Fourier nuber < 0.1 (d) Fourier nuber > The Rateau turbine beongs to the categor of (a) pressure copounded turbine (c) veocit copounded turbine (b) reaction turbine (d) radia fow turbine 1.17 For the circuar tube of equa ength and diaeter shown beow, the view factor F 13 is the view factor F 1 in this case wi be (a) 0.17 (b) 0.1 (c) 0.79 (d) 0.83 D 1 3 L=D

4 1.18 In descending order of agnitude, the thera conductivit of (a) pure iron, (b) iquid water, (c) saturated water vapour and (d) auinu can be arranged as (a) a b c d (b) b c a d (c) d a b c (d) d c b a Shrinkage aowance on pattern is provided to copensate for shrinkage when (a) the teperature of iquid eta drops fro pouring to freezing teperature (b) the eta changes fro iquid to soid state at freezing teperature (c) the teperature of soid phase drops fro freezing to roo teperature (d) the teperature of eta drops fro pouring to roo teperature 1.0. The cutting force in punching and banking operations ain depends on (a) the oduus of easticit of eta (b) the shear strength of eta (c) the buk oduus of eta (d) the ied strength of eta 1.1. In ECM, the ateria reova is due to (a) corrosion (c) fusion (b) erosion (d) ion dispaceent 1.. Two pates of the sae eta having equa thickness are to be butt weded with eectric arc. When the pate thickness changes, weding is achieved b (a) adjusting the current (c) changing the eectrode size (b) adjusting the duration of current (d) changing the eectrode coating 1.3. owance in iits and fits refers to (a) aiu cearance between shaft and hoe (b) iniu cearance between shaft and hoe (c) difference between aiu and iniu size of hoe (d) difference between aiu and iniu size of shaft 1.4. Production fow anasis (PF) is a ethod of identifing part faiies that uses data fro (a) engineering drawings (c) bi of aterias (b) production schedue (d) route sheets 1.5 When using a sipe oving average to forecast deand, one woud (a) give equa weight to a deand data (b) assign ore weight to the recent deand data (c) incude new deand data in the average without discarding the earier data (d) incude new deand data in the average after discarding soe of the earier deand data

5 . This question consists of TWENTY-FIVE sub-questions (.1.5) of TWO arks each. For each of these sub-questions, four possibe aternatives (,, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer b darkening the appropriate bubbe against the question nuber on the eft hand side of the Objective Response Sheet (ORS). You a use the answer book provided for an rough work, if needed..1 The iniu point of the function ( ) ( 3 3) f = is at (a) = 1 (b) = -1 (c) = 0 (d).. The rank of a 3 3 atri C ( = ), found b utiping a non-zero coun atri of size 3 1 and a non-zero row atri of size 1 3, is (a) 0 (b) 1 (c) (d) 3 = n unbiased coin is tossed three ties. The probabiit that the head turns up in eact two cases is (a) 1 9 (b) 1 8 (c) 3 (d) Two heica tensie springs of the sae ateria and aso having identica ean d coi diaeter and weight, have wire diaeters d and. The ratio of their stiffness is (a) 1 (b) 4 (c) 64 (d) The aiu principa stress for the stress state shown in the figure is σ σ σ σ σ (a) σ (b) σ σ (c) 3σ (d) 1.5σ.6. The sun gear in the figure is driven cockwise at 100 rp. The ring gear is hed stationar. For the nuber of teeth shown on the gears, the ar rotates at ar Sun 0T ring 80T Panet 30T (a) 0 rp (b) 0 rp (c) rp (d) rp

6 .7. For the oading on truss shown in the figure, the force in eber CD is D C E F 1kN 1kN (a) 0 kn (b) 1 kn (c) kn (d) 1 kn.8. odies 1 and shown in the figure have equa ass. surfaces are sooth. The vaue of force P required to prevent siding of bod on bod 1 is od P 45 od 1 (a) P = g (b) P = g (c) P = g (d) P = g.9. The asseb shown in the figure is coposed of two assess rods of ength with two partices, each of ass. the natura frequenc of this asseb for sa osciations is (a) g (b) g ( cosα ) (c) g cos ( α ) α α (d) ( g cosα ).10. Mass M sides in a frictioness sot in the horizonta direction and the bob of ass is hinged to ass M at C, through a rigid assess rod. This sste is reeased fro rest with θ =30. t the instant when θ = 0, the veocities of and M can be deterined using the fact that, for the sste (i.e., and M together), M C (a) the inear oentu in and directions are conserved but the energ is not conserved θ

7 (b) the inear oentu in and directions are conserved and the energ is aso conserved (c) the inear oentu in direction is conserved and the energ is aso conserved (d) the inear oentu in direction is conserved and the energ is aso conserved.11. ccic heat engine does 50 kj of work per cce. If the efficienc of the heat engine is 75%, the heat rejected per cce is (a) 16 3 kj (b) kj (c) 37 1 kj (d) 66 3 kj.1. singe-acting two-stage copressor with copete intercooing deivers air at 16 bar. ssuing an intake state of 1 bar at 15 C, the pressure ratio per stage is (a) 16 (b) 8 (c) 4 (d).13. The horizonta and vertica hdrostatic forces F and F on the sei-circuar gate, having a width ω into the pane of figure, are F h F r Gate width w (a) F = ρghrω and F = 0 (b) F = ρghrω and F = 0 (c) F = ρghrω and F = ρgωr / (d) F = ρghrω and F = πρgωr / r r i j is.14. The -D fow with veocit ν = ( + + ) + ( 4 ) r (a) copressibe and irrotationa (c) incopressibe and irrotationa (d) incopressibe and not irrotationa (b) copressibe and not irrotationa.15. sa stea whiste (perfect insuated and doing no shaft work) causes a drop of 0.8 kj/kg in the enthap of stea fro entr to eit. If the kinetic energ of the stea at entr is negigibe, the veocit of the stea at eit is (a) 4 /s (b) 40 /s (c) 80 /s (d) 10 /s

8 .16. For air at a given teperature, as the reative huidit is increased isothera, (a) the wet bub teperature and specific enthap increase (b) the wet bub teperature and specific enthap decrease (c) the wet bub teperature increases and specific enthap decrease s (d) the wet bub teperature decreases and specific enthap increases.17. Water (Prandt nuber 6) fows over a fat pate which is heated over the entire ength. Which one of the foowing reationship between the hdrodnaic boundar aer thickness (δ) and the thera boundar aer thickness (δ t ) is true? (a) δ t > δ (b) δ t < δ (c) δ t = δ (d) Cannot be predicted.18. In a spark ignition engine working on the idea Otto cce, the copression ratio is 5.5. The work output per cce (i.e., area of the P-V diagra) is equa to V c J, where V c is the cearance voue in 3. The indicated ean effective pressure is (a) 4.95 bar (c) bar (b) 5.50 bar (d) bar.19. The height of the down-sprue is 175 and its cross-sectiona area at the base is 00. The cross-sectiona area of the horizonta runner is aso 00. assuing no osses, indicate the correct choice for the tie (in seconds) required to fi a od cavit of voue (Use g = 10 /s ). (a).67 (b) 8.45 (c) 6.7 (d) For rigid perfect pastic work ateria, negigibe interface friction and no redundant work, the theoretica aiu possibe reduction in the wire drawing operation is (a) 0.36 (b) 0.63 (c) 1.00 (d).7.1. During orthogona cutting of id stee with a 10 rake ange too the chip thickness ratio was obtained as 0.4. the shear ange (in degrees) evauated fro this data is (a) 6.53 (b) 0. (c).94 (d) Resistance spot weding is perfored on two pates of 1.5 thickness with 6 diaeter eectrode, using current for a tie duration of 0.5 seconds. ssuing the interface resistance to be Ω, the heat generated to for the wed is (a) 565 W-sec (c) 500 W-sec (b) 8437 W-sec (d) W-sec

9 .3. Fift observations of a production operation reveaed a ean cce tie of 10 in. the worker was evauated to be perforing at 90% efficienc. ssuing the aowances to be 10% of the nora tie, the standard tie (in seconds) for the job is (a) (b) 7.3 (c) 9.0 (d) ethod of ocation in a jig or fiture woud coective restrict the work piece in n degrees of freedo, where the vaue of n is (a) 6 (b) 8 (c) 9 (d) 1.5. In an NC achining operation, the too has to be oved fro point (5,4) to point (7,) aong a circuar path with center at (5,). efore starting the operation, the too is at (5,4). The correct G and M code for this otion is (a) N010 G03 X7.0 Y.0 I5.0 J.0 (b) N010 G0 X7.0 Y.0 I5.0 J.0 (c) N010 G01 X7.0 Y.0 I5.0 J.0 (d) N010 G00 X7.0 Y.0 I5.0 J.0 SECTION This section consists of TWENTY questions of FIVE arks each. ttept NY FIFTEEN questions. nswers ust be given in the answer book provided. 3. Sove the differentia equation, with the foowing conditions: d d + = (i) at = 0, = 1 π (ii) at =, = π 4. The figure shows an eectric otor driving a achine under stead conditions b eans of three straight tooth spur gears having 5, 3 and 6 teeth. The diaetra pitch is 4 teeth/c and the pressure ange is 0. For the direction of otor rottion shown, deterine the radia oad acting on the shaft carring the ider. Motor 000 rp 15 N- 5T Ider 3T 90 6T

10 5. Water (p = 1000 kg/ 3 ) fows horizonta through a nozze into the atosphere under the conditions given beow. (assue stead state fow). Water 1 Nozze 1,V 1,P 1,V,P t inet: 1 = 10-3 ; V 1 = /sec; P 1 = Pa(gauge) t outet: 1 = 10-4 ;P = P at Deterine the eterna horizonta force needed to keep the nozze in pace. 6. nuber of cod roing passes are required in a two-high roing i to reduce the thickness of a pate fro 50 to 5. The ro diaeter is 700 and the coefficient of friction at the ro work interface is 0.1. it is required that the draft in each pass ust be the sae. ssuing no front and back tensions, deterine (a) the iniu nuber of passes required and (b) the draft in each pass. 7. Stea at 300 kpa and 500 C (h = kj/kg) enters a stea turbine and eits at atospheric pressure and 350 C (h = kj/kg). Heat osses in the turbine are 50 kw and the ass fow rate is 0.5 kg/s. deterine the power output of the turbine if kinetic energ osses are negigibe. 8. Two soid workpieces, (i) a sphere with radius R and (ii) a cinder with diaeter equa to its height, have to be sand cast. oth work-pieces have the sae voue. Show that the cindrica work-piece wi soidif faster than the spherica work-piece. 9. spring ass dashpot sste is shown in the figure. The spring stiffness is k, as is, and the viscous daping coefficient is c. the sste is subjected to a force f o cosωt as shown. Write the equations of otion which are needed to deterine. (No need to deterined.) =0 k c F 0 cos(ωt) 10. four-stroke engine deveops 18.5 kw at 50 rp. The turning oent diagra is rectanguar for both epansion and copression strokes. The turning oent is negative during copression stroke and is zero during suction and ehaust strokes. The turning oent for the epansion stroke is.8 ties that of the copression stroke. ssuing constant oad, deterine the oent of inertia of the fwhee to keep the tota fuctuation of the crankshaft speed within 1% of the average speed of 50 rp.

11 11. Use the area oent ethod to find the vertica defection of the unifor bea at the foowing points: (a) idde of the bea (point O) (b) eft end of the bea (point ) The feura rigidit of the bea is EI. P o P a a a a 1. Too ife testing on a athe under dr cutting conditions gave n and C of Taor too ife equation as 01 and 130 /in, respective. When a cooant was used, C increased b 10%. Find the percent increase in too ife with the use of cooant at a cutting speed of 90 /in. 13. Identica straight turning operation was carried out using two toos: (S) and (S). Show that the first too wi give better surface finish in ters of peak-to-vae height. 14. Water fows through a 0.6 diaeter, 1000 ong pipe fro a 30 overhead tank to a viage. Find the discharge (in iters) at the viage (at ground eve), assuing a Fanning friction factor f = 0.04 and ignoring inor osses due to bends etc. 15. coposite wa, having unit ength nora to the pane of paper, is insuated at the top and botto as shown in the figure. It is coprised of four different aterias,, C and D. Insuated H =H D C D H H C T 1,h 1 T,h L 1 L L 3 Insuated The diensions are: H = H D = 3, H = H C =1.5, L 1 = L 3 = 0.05, L = 0.1 The thera conductivit of the aterias are: K = K D = 50 W/-K, K = 10W/-k, K C = 1 W/-k. The fuid teperatures and heat transfer coefficients (see figure) are: T 1 = 00 C, h 1 = 50 W/ -K, T = 5 C, h = 10 W/ K.

12 ssuing one-diensiona conduction, (a) sketch the thera circuit of the sste, and (b) deterine the rate of heat transfer through the wa. 16. raton cce (air standard) has a pressure ratio of 4 and inet conditions of one standard atosphere pressure and 7 C. Find the air fow rate required for 100 kw power output if the aiu teperature in the cce is 1000 C. ssue γ=1.4 and C p = 1.0 kj/kg-k. 17. Francis turbine running at 00 rp deveops a power of 5000 kw under a head of 5. deterine the speed and power output under a head of bet drive shown in Figure (a) has an ange of wrap of 160 on the saer pue. dding an ider as shown in Figure (b), increases the wrap ange to 00. The sack side tension is the sae in both cases and the centrifuga force is negigibe. what percentage is the torque capacit of the bet drive increased b adding the ider? (use coefficient of friction µ = 0.3.) (a) (b) 19. The kg ass C oving horizonta to the right, with a veocit of 5 /s, strikes the 8 kg ass at the ower end of the rigid assess rod. The rod is suspended fro a frictioness hinge at and is initia at rest. If the coefficient of restitution between ass C and ass is one, deterine the anguar veocit of the rod iediate after ipact. 5 /s 1.6 C 0. echanic has an engine fro a 1970 ode car which works on the basis of Otto cce. The engine dispaces 1.8 iters, has a copression ratio of 10.:1 and has si cinders. The pistons in the origina engine are 10 in diaeter. The echanic bores the cinder and repaces the piston with new pistons that are arger in diaeter than the originas. (a) Keeping a other factors sae, what wi be the percentage change in power output? (b) what percentage wi the engine efficienc change?

13 1. copan is offered the foowing price breaks for order quantit Order quantit and above 100 Price (Rs.) Order cost is Rs.60 per order whie the hoding cost is 10% of the purchase price. Deterine the econoic order quantit (EOQ) if the annua requireent is 1000 units.. The shaft shown is supported on bearings at and. This shaft carries three eccentric asses (each of ass ) in panes parae to - pane at C, D and E. e the eccentricit of ass at C is e and eccentricit of asses at D and E is. the shaft rotates at speed ω. In the figure, θ D and θ E indicate the anguar positions of asses at D and E in - pane with respect to that of ass at C. Negecting gravit effect, deterine θ D and θ E to provide static baance. so deterine the ratio of agnitudes of dnaic bearing reactions at and for the obtained vaues of θ D and θ E. θ D e e/ D θ E E e/ ω z C

OSCILLATIONS. dt x = (1) Where = k m

OSCILLATIONS. dt x = (1) Where = k m OSCILLATIONS Periodic Motion. Any otion, which repeats itsef at reguar interva of tie, is caed a periodic otion. Eg: 1) Rotation of earth around sun. 2) Vibrations of a sipe penduu. 3) Rotation of eectron