Isro Papers

Mechanical - 2006-1 Set-A

1 In_nodular iron, graphite is ln.the.form ofa) Cementite _b) Free carbon c) Flakes d) Spheroids

2 Hardness of steel depends ona) Amount of carbon it containsb) The shape and distribution of the carbides in ironc) Method of fabricationd) Contents of alloying elements

3 Too high welding current in arc welding would result ina) Excessive spatter, under cutting along edges, irregular deposits, wasted

electrodesb) Excessive piling up of weld metal, poor penetration, wasted electrodesc) Too small bead, weak weld and wasted electrodesd) Excessive piling up of weld metal, overlapping without penetration of

edges, wasted electrodes

4 Which of the following processes would produce strongest components?a) Hot rolling b) Extrusion c) Cold rolling d) Forging

5 If a quantity Q is dependent on three other quantities q-, q2 and q3 related

such that Q = K x (qlrl x (qor2 x (q3r3 then overall error og =

a) nl(8qI)+n2(8q2)+n3(8q3) b) _!__ 8q1 +_1 8q2 +_!__ 8q3q1 q2 q3 n} q} n2 q2 n3 q3

c) 8q} + 8q2 + 8q3q} q2 q3

6 Which of the following has maximum hardnessa) Austenite b) Pearlite c) Troostite d) Martensite

7 The main advantage of line organization is itsa) Effective command and control b) Defined responsibilities at all levelsc) Rigid discipline in the organization d) All of the above

8 The mathematical technique for finding the best use of limited resourcesin an optimum manner is known asa) Operation research b) Linear programmingc) Network analysis d) Queuing theory

9 Which of the following errors are generally distributed in accordance withthe Gaussian distributiona) Controllable errors b) Calibration errorsc) Avoidable errors d) Random errors

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PL3 Is the deflection under the loa-d P of a ~antilever beam (le~gth L,3EImodulus of elasticity E, moment of inertia 1). The strain energy due tobending is

p2L3

a) 3EIp2L3

b)-6EI

p2L3

d)-48EI

11 A mass m attached to a light spring oscillates with a period of 2 sec. Ifthe mass is increased by 2 kg, the period increases by 1 sec. The valueof m isa) 1 kg b) 1.6 kg c) 2 kg d) 2.4 kg

12 A short column of external diameter 0 and internal diameter d carries anexternal load W. The greatest eccentricity which the load can havewithout producing tension on the cross section of the column isa) (O+d)/S b) (02+d2)/S c) (02+d2)/SO d) (02+d2)/Sd

-' -13 If the radius of wire stretched by a load doubled, then its Young's

modulus willa) Be doubledc) Become four times

b) Be halvedd) None of the above

14 Longitudirial stress in a thin cylinder subjected to internal pressure isa) Half of the hoop stress b) Twice the hoop stressc) Equal to the hoop stress d) One-fourth the hoop stress

15 Maximum deflection in cantilever due to pure bending moment M at itsend is

ML2a) 2EI

b) ML23EI

d) ML26EI

16 If Poisson's ratio for a material is 0.5, then the elastic modulus for thematerial isa) 3 times its shear modulusc) Equal to its shear modulus

b) 4 times its shear modulusd) Indeterminate

17 A cantilever beam of negligible weight iscarrying a mass M at its free end, and is alsoresting on an elastic support of stiffness k1as shown in the figure below. If k2 representsthe bending stiffness of the beam, thenatural frequency (rad/s) of the system is


.. - .. --_ ..--------_._._-_ .._--,---_ .


18 The figure shows 3 small spheres thatrotate about a vertical axis. Theperpendicular distance between the axisand the center of each sphere is given.Mass of highest rotational inertia aboutthat axis, is

3SKg1m

2m 9Kg

3m4Kg

a) 36 b) 4 c) 9 d) All same

19 Which of the following relationships between the force F on a particleand the particles position x implies simple harmonic oscillationa) F=-7X b) F=-200x2 c) F=10x d)F=5x2

20 A mass of 100 kg is held between two springs asshown in figure. The natural frequency ofvibration of the system in cycles/second is

a) 10 b) 2_ ,Jr Jr1 d) 20c) - ~..........,~~,~

2Jr Jr

20 kN/m

21 The bending equation is written as• I / s M /2 £2

a) -=-=- b) -=-=-M y R I Y R2M _ / _ £ M2 /2 £2

c) ----- d) -=-=-I y R I y R

22 Hydraulic testing of boilers is done at pressuresa) Below and above atmosphereb) Slightly above atmospheric pressurec) At half the working pressure of boilerd) At 1.5 to 2 times the working pressure

23 100 m of water column is equal toa) 1000 kN/m2 b) 100 kN/m2 c) 10 kN/m2 d) 1 kN/m2

24 Gantry girders are invariably designed to resista) Transverse loads only b) Lateral loads onlyc) Transverse and lateral loads d) Transverse, lateral and axial load

25 If the rotating mass of a rim type flywheel is distributed on another rimtype flywheel whose mean radius is half the mean radius of the former,then energy stored in the later at the same speed will bea) Four times the first one b) Same as the first onec) One fourth of the first one d) One and a half times the first one


--- ---- ---------------- .


26 A thin circular disc is rolling with a uniform linear speed, along a straight .path on a plane surface .. Consider the following statements-in thisregard:1. All points of the disc have the same velocity2. The center of the disc has zero acceleration3. The center of the disc has centrifugal acceleration4. The point on the disc making contact with the plane surface has zero

accelerationOf these statementsa) 1 and 4 are correctc) 3 alone is correct

b) 3 and 4 are correctd) 2 alone is correct

27 If a number of forces act on a rigid body, each force may be replaced byan equal and parallel force acting through a fixed point, together with acouple. For the rigid body to be in equilibriuma) Both resultant force and couple must be zerob) The resultant couple on the body must be zeroc) The resultant force at the fixed point must be zerod) None of the above need be zero ..

28 Whirling speed of a shaft coincides with the natural frequency of itsa) Longitudinal vibration b) Transverse vibrationc) Torsional vibration d) Coupled bending torsional vibration

29 A fixed gear having 200 teeth is in mesh with another gear having 50teeth. The two gears are connected by an arm. The number of turnsmade by the smaller gear for one revolution of arm about the center ofthe bigger gear isa) 4 b) 3 2c) -

4d) 5

30 With symbols having the usual meanings, the single degree of freedomsystem, mx + d + kx = F sin ax representsa) Free vibrations with damping b) Free vibrations without dampingc) Forced vibrations with damping d) Forced vibrations without damping

31 In the two - rotor system shown in the figure,(11<b), a node of vibration is situated

a) Between 11 and lz but nearer to 11c) Exactly in the middle of the shaft

b) Between 11 and h but nearer to hd) Nearer to 11 but outside

32 Which one of the following is not a friction clutch?a) Disc or plate clutch b) Cone clutchc) Centrifugal clutch d) Jaw clutch


----~-..--- ..._-"._-- --_ ..._ ..-----------


33 Polar moment of inertia (Ip) of a circular disc is to be determined bysuspending it by a wire and noting the frequency of osciUations-(1)a) I a_1_ b) Ipaf2 c) Ipaf d) I a!

p /2 p /

34 Pick up the wrong statement. A flywheela) Is used to limit the inevitable fluctuation of speed during each cycleb) Controls the mean speed of rotationc) Stores up energy and gives up whenever requiredd) Regulates the speed during one cycle of a prime mover

35 Purpose of using differential gear in automobile is toa) Help in turning b) Control speedc) Avoid jerks d) Obtain rear movement

36 The acceleration of Simple Harmonic Motion of a pendulum isproportional toa) Length of pendulumc) Angular velocity

b) Time periodd) Displacement

37 A person walks up a stalled escalator in 90 seconds. When standing onthe same escalator, now moving, he is carried up in 60 seconds. Howmuch time would it take him to walk up the moving escalator?a) ~O sec b) 36 sec c) 45 sec d) 54 sec

38 A stone of mass m at the end of a string of length I. is whirled in a verticalcircle at a constant speed. The tension in the string will be maximumwhen the stone isa) At the top of the circlec) Quarter-was down from the top

b) Half-way down from the topd) At the bottom of the circle

39 Speed of particle executing simple harmonic motion with amplitude a ishalf of the maximum speed. At that instant, displacement of the particleis

aa) -2

b) -J3 a2

) 2ac --J3d) 3..fia

40 Two satellites, of masses m and 2m, are on the same circular orbitaround earth. If the velocity of the lighter satellite is v», what is thevelocity of the heavier satellite?

) 1 b) Voa -v2 0

1d) -v4 0

41 Nu = CRemprn represents heat transfer undera) Free convection b) Forced convectionc) Combined convection d) None of the above



42 If the inner and outer surfaces of a hollow cylinder (having. radllr- and r2and length L) are at temperatures t1and t2then rate of radial heat flow willbea) k t1 - t2

2JrL 1 r.og-r,

b) _1 __t1 -t22JrLk 1 r2og-

r1

43 For infinite parallel planes with emissivities £1 and &2' the interchangefactor for radiation from surface 1 to surface 2 is given bya) &'&2 b) _1 + _1 c) &1 + &2 d) &1&2

&'+&2-&'&2 &1 &2

44 For a closed system, difference between the heat added to the systemand work done by the gas, is equal to the change ina) Internalenergy b) Entropy c) Enthalpy d) Temperature

45 The condition for reversibility of a cycle is

a) Cyclic fdQ < 0 b) Cyclic fdQ > 0T T

) C I· fdQ 0 d) Noneof thesec ycuc T=

46 The state of a real gas if changed from pressure Ph temperature T1topressure P2temperature T2. The change in enthalpy, h2-h1 , is given bya) fCpdT

b)

c)

d)

47 One hundredth of a kilogram of air is compressed in a piston-cylinderdevice. At an instant of time when T = 400 K, the rate at which work isbeing done on the air is 8.165 kW, and heat is being removed at a rate of1.0 kW, the rate of temperature rise will bea) 10 Kls b) 100Kls c) 1000Kls d) 10000Kls


...... -._---_ ..-.._-_ ......... __ ..--_._ ..


48 The volume V versustemperature T graphs for acertain amount of a perfect gas at two pressureP1 and P2 are as shown in the figure. It can beconcluded that

. -··-·--h~--····.·.·---:-··--········P2t . .... .v' . /.Yy

T-

a) The pressure P1 is greater than the pressure P2b) The adiabatic index for P1 is higher than that for P2c) P1 represents monoatomic gas and P2 represents diatomic gasd) None of the above

49 In the polytropic process pv" = Constant, if n=1 the process will be ata) Constant volume b) Constant pressurec) Constant temperature d) Adiabatic

50 In case of ideal triatomic gas, the ratio of specific heats CplCv would bea)1 b) 1.33 c) 1.40 d)1.41

51 The formation of frost on cooling coils in a refrigeratora) Increases power consumption b) Improves C.O.P. of the systemc) Increases heat transfer d) Reduces power consumption

. 52 An.air-conditioned room has one of the walls, which is 5m x 3m of 3.75 cmthick brick. The conditioned space is maintained at 27°C when theoutside temperature is 47°C. Variation of thermal conductivity withtemperature of the wall is given by k = 1+ 2 x 10-4 T, where T is in degreeKelvin, and k is in W / mO K. The heat gained by the conditioned spacethrough this wall isa) 849.6 W b) 84.96 W c) 800 W d) 0

53 A mild steel tank of wall thickness 12 mm contains water at 100°C. Theatmospheric temperature is 20°C. The thermal conductivity of mild steelis 50 W/mK, andthe heat transfer co-efficients for inside and outside thetank are 2850 and 10 W/m2 K, respectively. Calculate the rate of heat lossper m2 of tank surface and the temperature of the outside surface of thetank.a) 300.5 W/m2, 45.50Cc) 602.6 W/m2, 80.6oC

b) 495.2 W/m2, 67.6oCd) 795.2 W/m2, 99.52oC

54 In order to burn 1 Kg of CH4 completely the minimum number ofkilograms of Oxygen needed is (take atomic weight of H, C, 0 as 1,12,16respectively)a) 3 b) 6 c) 5 d) 4



55 The vector field F =xi-y} -(where -i and) are unit vectorstis-----------a) Divergence free, but not irrotationalb) Irrotational, but not divergence freec) Divergence free and irrotationald) Neither divergence free nor irrotational

56 dFor flow through a horizontal pipe, the pressure gradient-E in the flow

dxdirection isa) +ve b) 1 c) Zero d) -ve

57 The transition Reynolds number for flow over a flat plate is 5 x 105• Whatis the distance from the leading edge at which transition will occur forflow of water with a uniform velocity of 1m/s? (For water, the kinematicviscosity, u=O.858xIO-6m2/s) -a) 1m b)0.43m c)43m d)103m

58 Between section 1 and 2 of a pipe a pump, a heater, a very rough pipeand an orifice plate are placed. The Bernoulli equation can be appliedbetween 1 and 2 if .a) Orifice plate and heater are removedb) Heater pump and heater are removedc) Heater and pump are removedd) Heater, rough pipe and orifice plates are removed

59 A one dimensional flow is one whicha) Is uniform flowb) Is steady uniform flowc) Takes place in straight linesd) Involves zero transverse component of flow

60 A piece weighing 3 kg in air was found to weigh 2.5 kg when submergedin water. Its specific gravity isa) 1 b) 5 c) 6 d) 7

61 .The actual velocity at vena contracta for flow through an orifice from areservoir of height H=a) ~2gH b) Cv~2gH c) ~2gH ICv d) Cd~2gH

62 The horizontal component of force ona curved surface is equal to thea) Product of pressure at its centroid and areab) Weight of liquid retained by the curved areac) Force on a vertical projection of the curved surfaced) Weight of liquid vertically above the curved surface



·63 The maximum depth from which a centrifugal pump can.draw.water. isa) Dependent on the speed N of the pumpb) Dependent on the power of the pumpc) Around 10md) Dependent on N2

64 Two pipe lines at a differentpressures, PA and PB, eachcarrying the same liquid ofspecific gravity of 51 areconnected to a U tube with aliquid of specific gravity of 52resulting in the level differences thh h2 and h3 as shown in the hlfigure. The difference in pressure 1head between points A and B interms of head of water is S1

a)c)

h1 S2+ h2S1+ h3S1h1 S1 - h2S2 - h3S1

b) h1 S1+ h2S2 - h3S1d) h1 S1+ h2S2 + h3S1

65 List I gives·4 dimensionless numbers and List II gives the types of forces,which are one of the constituents describing the numbers. Match list Iwith List II and select the correct answer using the codes given below thelists:

a)b)c)d)

List IA. Euler numberB. Froude numberC. Reynolds numberO. Webber number

List II1. Pressure force2. Gravity force3. Elastic force4. Surface tension5. Viscous force

A2312

C4455

D5544

B3221

66 A single-stage impulse turbine with a diameter of 120 cm runs at 3000rpm. If the blade speed ratio is 0.42, then, the inlet velocity of steam willbea) 79 m/s b) 188 m/s c) 450 m/s d) 900 m/s



67 For laminar flow over a flatplate, the thickness of the boundary-layer at adistance from the leading edge is found to be 5 mm. The thickness of theboundary layer at a downstream section, which is at twice the distance ofthe previous section from the leading edge, will bea) 10 mm b) 5J2 mm c) 5/ J2 mm d) 2.5 mm

68 If Uco = free stream velocity, u = velocity at y, and 5 = boundary layerthickness, then in a boundary layer flow, the momentum thickness B isgiven by

a) B= f~(I-~)dYo u; o;

c) B= f U

2

2 (1--U-JdYtv: o;

s U ( u2 Jb)B= f- 1--2 dy

o U", U",

d) B = f (1--U-JdYo Uoo

69 An automobile moving at a velocity of 40km/hr is experiencing a windresistance of 2kN. If the automobile is moving at a velocity of 50km/hr,.the power required to overcome the wind resistance isa) 43.4kW b) 3.125 kW c) 2.5 kW d) 27.776 kW

70 A constant-head water tank has, on one of its vertical sides two identicalsmall orifices issuing two horizontal jets in the same vertical plane. Thevertical distance between the centers of orifices is 1.5 m and the jettrajectories intersect at a point 0.5 m below the lower orifice. What is theapproximate height of water level in the tank above the point ofintersection trajectories?a) 1.0 m b) 2.5 m c) 0.5 m d) 2.0 m

71 A unit vector perpendicular to the vectors a = 2i - 3}+ k and b = i + } - 2k,is

a) ~(-i+}+k)

c) ~(i+j+k)

b) ~(i+ j-k)

d) (i+}+k)

72 The region of the z plane for which Iz - a I = l(Re a "* 0) isz+a

a) x-axis b) y-axisc) The straight line z = lal d) None of the above

If =. f3 ' yare the roots of equations x3+ PX2+QX+P=O,73

Then the value of tan" cc +tan-1 f3 + tan-1y is

a) n n] 2 b) nn c) Znr: d) nJr4

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---_ .. ----- ------... _-_ .._ ..__ ..-.-. __ --- - - .----- - .._


.....~.--.-.- ..---. -~-. ~ l--·a···· b + c

74 The value of the determinant 1 b c +a is1 c a+b

a) 0 b) 1 c) (a+h+c) d) 3

75 I I dxdThe value of J J Y is

o 0 ~ (1 - x 2 )(1 _ y 2)

b) 7r

4d) 7r

2

76 Solution of (D2 + 16)y = cos4x, is

a) y = Acos4x + Bsin4x +.!cos4x8

c) y=Acos4x+Bsin4x+.!sin4x8

b) y = Acos4.x+ Bsin4x+ ; sin4x

d) y=ACOS4x+Bsin4x+; cos4x

77 Laplace transform of t2 +2t+3 is-2 2 3a) -----S3 S2 S

2 2 3c) -+-+-

S3 S2 S

2 2 3b) -+---

S3 S2 S

-2 2 3·d) -+---

S3 S2 S

78 Equation of a straight line passing through the point (-1,2) and makingequal intercepts on the axes isa) x-y=l b) x-2y=1 c) x+y=l d) x-y=2

79 A bag contains eight white and six red marbles. The probability ofdrawing two marbles of same colour is

) 8c2·6c2 b) 8c2 6c2a --+--1~ 1~2 l~

c) 8c2·6c2 d) 8c2 + 6c2

14c2·14c2 14c2 12c2

80 TheAlgebraic multiplicity ofthe matrix A = [~ -~3 I}sa)l b) 2 c) 3 d) 4


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