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Q. 1 He is known for his unscrupulous ways.He always sheds __________ tears to deceive(a) fox’s(b) corcodile’s(c) corcodile(d) foxAns: c

Q.2 Jofra Archer, the England fast bowler, is________ than accurate.(a) more fast(b) faster(c) less fast(d) more fasterAns: a

Q.3 Select the word that fits the analogy:Build : Building :: Grow : _________

(a) Grown(b) Grew(c) Growth(d) GrowedAns: c

Q.4 I do not think you know the case wellenough to have opinions. Having said that, Iagree with your other point.What does the phrase “having said that” meanin the given text?(a) as opposed to what I have said(b) despite what I have said(c) in addition to what I have said(d) contrary to what I have saidAns: b

Q.5 Define [x] as the greatest integer lessthan or equal to x, for each x ϵ (-∞,∞). If y = [x].Then area under y for x ϵ [1,4] is ___________.(a) 1(b) 3(c) 4(d) 6

Ans: d

Q.6 Crowd funding deals with mobilisationof funds for a project from a large number ofpeople, who would be willing to invest smalleramounts through web-based platforms in theproject.Based on the above paragraph, which of thefollowing is correct about crowd funding?(a) funds raised through unwillingcontributions on web-based platforms(b) funds raised through large contributionson web-based platforms.(c) funds raised through coercedcontributions on web-based platforms.(d) funds raised through voluntarycontributions on web-based platforms.Ans: d

Q.7 P,Q, R and S are to be uniquely codedusing α and β. If P is coded as αa and Q as a αβ,then R and S, respectively, can be coded as____________.(a) βα and αβ(b) ββ and αα(c) αβ and ββ(d) βα and ββAns: d

Q. 8 The sum of the first n ters in thesequence 8, 88, 888, 8888, ... is _________.

(a)

(b)

(c)

(d)


Ans: d

Q. 9 Select the graph that schematicallyrepresents BOTH y = xm and y = x1/m properly inthe interval 0 ≤ x ≤ 1, for integer values of m,where m> 1.

(a)

(b)

(c)

(d)Ans: a

Q. 10 The bar graph shows the data of thestudents who appeared and passed in anexamination for four schools P, Q, R and S. Theaverage of success rates (in percentage) ofthese four schools is _______.

(a) 58.5%(b) 58.8%(c) 59.0%(d) 59.3%Ans: c

Q.11 Multiplication of real valued squarematrices of same dimension is(a) associative(b) commutative(c) always positive definite(d) not always possible to computeAns: a

Q. 12 The value of

(a) c(b) c + 1

(c)

(d)Ans: c

1

11

1 0lim01

c x

c xx

e formxe


Applying ‘L’ Hospital rule

=

1

111lim

c x

c xc xx

cee x e

=1

lim1 1 1x

c c ccx c c

Q. 13 The Laplace transform of a function f(t)

is L(f) = . Then, f(t) is

(a) f(t) =

(b) f(t) =

(c) f(t) =

(d) f(t) =Ans: c

L(f)= 2 2

1s

12 2

1 1( ) sinf t L ts

Q. 14 which of the following function f(z), ofthe complex variable z, is NOT analytic at all thepoints of the complex plane?(a) f(z) = z2

(b) f(z) = ez

(c) f(z) = sin z(d) f(z) = log zAns: dlog z is not analytic at all points.

Q. 15 The members carrying zero force (i.e.zero – force members) in the truss shown in thefigure, for any load P > 0 with no appreciabledeformation of the truss (i.e. with no

appreciable change in angles between themembers), are

(a) BF and DH only(b) BE, DH and GC only(c) BF, DH, GC, CD and DE only(d) BF, DH, GC, FG and GH onlyAns: c

Q. 16 A single-degree-of-freedom oscillator issubjected to harmonic excitation F(t) = F0cos(ωt) as shown in the figure.

The non-zero value of ω, for which theamplitude of the force transmitted to theground will be F0, is

(a)

(b)

(c)

(d)Ans: c


fT = fO (Given)

transmissibility

1OT

O O

fff f

2

22 2

211

21

zn

zn n

22 2 22 21 1z zn n n

Taking (-ve) sign

2

1 1n

2

2n

2n

2 n

2km

Q. 17 The stress state at a point in a materialunder plane stress condition is equi-biaxialtension with a magnitude of 10 MPa. If one uniton the σ – τ plane is 1 MPa, the Mohr’s circlerepresentation of the state- of stress is given by(a) a circle with a radius equal to principalstress and its center at the origin of the σ – τplane(b) a point on the σ axis at a distance of 10units from the origin(c) a circle with a radius of 10 units on theσ – τ plane(d) a point on the σ axis at a distance of 10units from the originAns: b

Q. 18 A four bar mechanism is shown below.

For the mechanism to be a crank-rockermechanism, the length of the link PQ can be(a) 80 mm(b) 200 mm(c) 300 mm(d) 350 mmAns: a(S + l) < (P +Q)(S+ 600) < (400 + 300)S = 8080 + 600 < 700680 < 700Low is satisfiedl = 800 mm

Q. 19 A helical gear with 200 pressure angleand 300 helix angle mounted at the mid-span of


a shaft that is supported between two bearingsat the ends. The nature of the stresses inducedin the shaft is(a) normal stress due to bending only(b) normal stress due to bending in oneplane and axial loading; shear stress due totorsion(c) normal stress due to bending in twoplanes and axial loading; shear stress due totorsion(d) normal stress due to bending in twoplanes; shear stress due to torsionAns: a or c

Q. 20 The crystal structure of γ iron (austenitephase) is(a) BCC(b) FCC(c) HCP(d) BCTAns: b

Q. 21 Match the following.

(a) P-2, Q-3, R-4, S-1(b) P-1, Q-1, R-3, S-2(c) P-3, Q-3, R-1, S-3(d) P-4,Q-3, R-2, S-1Ans: a

Q. 22 The base of a brass bracket needs roughgrinding. For this purpose, the most suitablegrinding wheel grade specification is(a) C30Q12V(b) A50G8V

(c) C90J4B(d) A30D12VAns: a

Q. 23 In the Critical Path Method (CPM), thecost-time slope of an activity is given by

(a)

(b)

(c)

(d)Ans: d

Q. 24 Froude number is the ratio of(a) buoyancy forces to viscous forces(b) inertia forces to viscous forces(c) buoyancy forces to inertia forces(d) inertia forces to gravity forcesAns: d

Q. 25 Match the following non- dimensionalnumbers with the corresponding definitions:

(a) P-1, Q-3, R-2, S-4(b) P-3, Q-1, R-2, S-4(c) P-4, Q-3, R-1, S-2(d) P-3, Q-1, R-4, S-2Ans: d


26. The velocity field of an incompressible flowin a Cartesian system is represented by

Which one of the following expression for v isvalid?(a) -4xz + 6xy(b) -4xy – 4xz(c) 4xz – 6xy(d) 4xy + 4xzAns: b

2 2 ˆ2 3V x x i vj k

Incompressible flow

2 2 ˆ2 30

n y i vj k v wn y z

4 0vny

4v ny

∂v = -4nδy

v = -4xy + f [n,z]

v = -4xy – 4xz

Q. 27 For an ideal gas, the value of the Joule-Thomson coefficient is(a) positive(b) negative(c) zero(d) indeterminateAns: c

Q. 28 For an ideal gas, a constant pressureline and a constant volume line intersect at a

point, in the Temperature (T) versus specificentropy (s) diagram. Cp is the specific heat atconstant pressure and Cv is the specific heat atconstant volume. The ratio of the slopes of theconstant pressure and constant volume lines atthe point of intersection is

(a)

(b)

(c)

(d)Ans: dacc to Tds equationTds = dU +PdVTdS = dU [ v = c]TdS = cVdT

If P = CTdS = dh - udPTdS = Cp dT

Q. 29 For three vectors

and areunit vectors along the axes the axes of a right –handed rectangular/Cartesian coordinate


system, the value of is______________.Ans: 6 to 6

Q. 30 A flywheel is attached to an engine tokeep its rotational speed between 100 rad/sand 110 rad/s. If the energy fluctuation in theflywheel between these two speed is 1.05 kJthen the moment of inertia of the flywheel is______________ kg.m2 (round off to 2 decimalplaces).Ans: 0.98 to 1.02

2 2max max min

12

E I

1.05× 103 × 2 = I [1102 - 1002]I = 1 kg/m2

Q. 31 A balanced rigid disc mounted on a rigidrotor has four identical point masses, each of 10grams, attached to four points on the 100 mmradius circle shown in the figure.

The rotor is driven by a motor at uniformangular speed of 10 rad/s. If one of the massesgets detached then the magnitude of theresultant unbalance force on the rotor is__________ N (round off to 2 decimal places).Ans: 0.09 to 0.11

Unbalance tonef = mrω2

210 0.1 101000

= 0.1 N

Q. 32 A sheet metal with a stock hardness of250 HRC has to be sheared using a punch and adie having a clearance of 1 mm between them.If the stock hardness of the sheet metalincreases to 400 HRC, the clearance betweenthe punch and the die should be __________mm.Ans: 1.0 to 1.3

C = 0.0032 t

.C Hardness No

2 2

1 1

HNCC HN

C2 = 1 ×400250

C2 = 1.2 mm

Q. 33 A company is hiring to fill fourmanagerial vacancies. The candidates are fivemen and three women. If every candidate isequally likely to be chosen then the probabilitythat at least one woman will be selected is__________ (round off to 2 decimal places).Ans: 0.90 to 0.955 men, 3 womenP[atleast one women selected for 4 vacanices]= 1 - P[none]


Q. 34 The compressor of a gas turbine plant,operating on an ideal intercooled Brayton cycle,accomplishes an overall compression ratio of 6in a two-stage compression process.Intercooling is used to cool the air coming outfrom the first stage to the inlet temperature ofthe first stage, before its entry to the secondstage. Air enters the compressor at 300 K and100 kPa. If the properties of gas are constant,the intercooling pressure for minimumcompressor work is ____________kPa (roundoff to 2 decimal places).Ans:T1 = 300 KP1 = 100 kPaC.R = 6 = rp

3

1p

P rP

3

1

6PP

P3 = 6 × 100= 600 kPa

P1 = H LP P

P2 = 3 1PP

= 600 100= 245 kPa

Q. 35 In a concentric tube counter-flow heatexchanger, hot oil enters at 1020C and leaves at650C. Cold water enters at 250C and leaves at

42oC. The mean temperature difference (LMTD)is _________0C (round off to one decimal place).Ans: 48.8 to 49.8Counter flow

∆Te = 40∆Ti = 60

∟MTD =60 40

6040

i e

e

T TT InInT

= 49.30C

Q. 36 The evaluation of the definite integral

by using Simpson’s 1/3rd (one-third) rule with step size h = 0.6 yields(a) 0.914(b) 1.248(c) 0.581(d) 0.592Ans: d1.4

1

| |x x dx

step size h = 0.6

x -1 -04 0.2 0.8 1.4

y -1 -0.16 0.04 0.64 1.96

Simpson’s 1/3rd rule1.4

1

| |x x dx 0.6 1 1.96 4 0.16 0.64 2 0.04

3

= 0.2[0.96 + 1.92 + 0.08] = 0.592

Q. 37 A vector field is defined as


Where, are unit vectors along the axesof a right-handed rectangular/ Cartesian

coordinate system. The surface integral

(where is an elemental surface area vector)evaluated over the inner and outer surfaces of aspherical shell formed by two concentricspheres with origin as the center, and internaland external radii of 1 and 2, respectively, is(a) 0(b) 2π(c) 4π(d) 8πAns: a

3

rFr

3. . 0rFr

By divergence theorem

Q. 38 Bars of square and circular cross-sectionwith 0.5 m length are made of a material withshear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and thecylindrical bar cross- section diameter is 4 cm.The specimens are loaded as shown in thefigure.

Which specimen(s) will fail due to the appliedload as per maximum shear stress theory?(a) Tensile and compressive loadspecimens

(b) Torsional load specimen(c) Bending load specimen(d) None of the specimensAns: a

area = 4 cm × 4 cm40 × 40 mm2

3280 10 50 /

40 40N mm

2max

50 25 / 202 2

N m MPa

32

max 3816 16 64 10 16 / 20

40N mm MPa

d

32

3320 10 30 /406

N mm

2max

30 15 / 202 2

N m MPa

Tensile and Compressive load specimen

Q. 39 The 2 kg block shown in figure (top view)rests on a smooth horizontal surface and isattached to a mass-less elastic cord that has astiffness 5 N/m.


The cord hinged at O is initially unstretched andalways remains elastic. The block is given avelocity v of 1.5 m/s perpendicular to the cord.The magnitude of velocity in m/s of the block atthe instant the cord is stretched by 0.4 m is(a) 0.83(b) 1.07(c) 1.36(d) 1.50Ans: cEnergy conservation

2 2 21 0

1 1 12 2 2mv mv kn

2 × (1.5)2 = 2 × v02 + 5 × (0.4)2

V0 = 1.360 m/s

Q. 40 The truss shown in the figure has fourmembers of length l and flexural rigidity El, and

one member of length and flexural rigidity4El. The truss is loaded by a pair of forces ofmagnitude P, as shown in the figure.

The smallest value of P, at which any of thetruss members will buckle is

(a)

(b)

(c)

(d)Ans: c

2 2

2 2

4 2

2

EI EIPll

Q. 41 A rigid mass-less rod of length L isconnected to a disc (pulley) of mass m andradius r = L/4 through a friction-less revolutejoint. The other end of that rod is attached to awall through a friction-less hinge. A spring ofstiffness 2k is attached to the rod at its mid-span. An inextensible rope passes over half thedisc periphery and is securely tied to a spring ofstiffness k t point C as shown in the figure.There is no slip between the rope and the pulley.The system is in static equilibrium in theconfiguration shown in the figure and the ropeis always taut.

Neglecting the influence of gravity, the naturalfrequency of the system for small amplitudevibration is


(a)

(b)

(c)

(d)Ans: c

Since the disc is in pure rolling on the string Byrotating the disc with angle results in rotating

the rod with angle (let us say) about hingepoint.Now for same deflection of point ‘B’L L

By energy methodTotal energy,

2

21 1 12 22 2 2 2total p

LE I k r k

2

221 1 22 2 2 4total p

LE I k r k

0totaldEdt

22 21 3 12 4 2 2 0

2 2 2 64kLmr k r

2 223 4 2 0

2 16 16 64m L L k kL

3 9 032 32m k

3 9 0m k

3 0km

3nkm

Q. 42 A strip of thickness 40 mm is to berolled to a thickness of 20 mm using a two-highmill having rolls of diameter 200 mm.Coefficient of friction and arc length in mm,respectively are(a) 0.45 and 38.84(b) 0.39 and 38.84(c) 0.39 and 44.72(d) 0.45 and 44.72Ans: dht = 40 mmho = 20 mmd = 200 mm

cos α = 1 DhD

α = 25.84tan α = μtan 25.84 = μμ = 0.48

Lp R = RDR100 20

= 2000= 44.72

Q. 43 for an assembly line, the productionrate was 4 pieces per hour and the averageprocessing time was 60 minutes. The WIP


inventory was calculated. Now, the productionrate is kept the same, and the averageprocessing time, the WIP inventory(a) decreases by 25%(b) increases by 25%(c) decreases by 30%(d) increases by 30%Ans: c

Q. 44 A small metal bead (radius 0.5 mm),initially at 1000C, when placed in a stream offluid at 200C, attains a temperature of 28oC in4.35 seconds The density and specific heat ofthe metal are 8500 kg/m3 and 400 J/kg.K,respectively. If the bead is considered aslumped system, the convective heat transfercoefficient (in W/m2.K) between the metal beadand the fluid stream is(a) 283.3(b) 299.8(c) 149.9(d) 449.7Ans: br = 0.5 mm, Cp = 400 J / kg k, δ = 8500 kg/m3

t = 4.35 secV RP C

i p

T T hAeT T C V

28 20 3000 4.35100 20 8500 400 0.5

he h = 299.95 W/m2K

Q. 45 Consider two exponentially distributedrandom variables X and Y, both having a meanof 0.50. Let Z = X + Y and r be the correlationcoefficient between X and Y. If the variance of Zequals 0, then the value of r is ____________(round off to 2 decimal places).Ans: -1.00 to -0.98

Q. 46 An analytic function of a complex

variable z = x + iy (i = ) is defined as

Where is a real function. The value ofthe imaginary part of f(z) at z = (1 + i) is _______(round off to 2 decimal places).Ans: 1.99 to 2.01

Q. 47 In a disc-type axial clutch, the frictionalcontact takes place within an annular regionwith outer and inner diameters 250 mm and 50mm, respectively. An axial force F1 is needed totransmit a torque by a new clutch. However, totransmit the same torque, one needs an axialforce F2 when the clutch wears out. If contactpressure remains uniform during operation of anew clutch while the wear is assumed to beuniform for an old clutch, and the coefficient of


friction does not change, then the ratio F1/ F2 is__________ (round off to 2 decimal places).Ans: 0.85 to 0.89T = μW RmTnew = μ ×W × Rnew

Tnew = μ ×Wnew ×3 30 12 20 1

23

R RR R

Told = μ ×W × Rold

Tnew = Told3 30 1 12 20 1

23 2

onew old

R R R RW WR R

0.871new

old

WW

Q. 48 A cam with a translating flat-facefollower is desired to have the follower motion

Contact stress considerations dictate that theradius of curvature of the cam profile shouldnot be less than 40 mm anywhere. Theminimum permissible base circle radius is________ mm (round off to one decimal place).Ans: 47.9 to 48.1y(θ) = 4 [2πθ – θ2]

(0≤θ≤2π)

4 2 2dy Vd

= 8 (π – θ)(for y to be max)

0dVd

8dVad

[θ, = π]

min mincurvature BaseR R y a

40 = RBase + [0 - 8]min

40 = RBase – 8(RBase = 48 mm )

Q. 49 A rectangular steel bar of length 500mm, width 100 mm, and thickness 15 mm iscantilevered to a 200 mm steel channel using 4bolts, as shown.

For an external load of 10 kN applied at the tipof the steel bar, the resultant shear load on thebolt at B, is ___________ kN (round off to onedecimal place).Ans: 15.9 to 16.1

110 2.5

4 4PP kN

orP2 =

2 2 21 2 3

10 400 14.144 50 2A B C D

Per f f f f kNr r r

e BR S = 2 214.14 2.5 29 14.14 2.5 cos 45o

= Re SB = 16.005 kN


50 The barrier shown between two watertanks of unit width (1 m) into the plane of thescreen is modeled as a cantilever

Taking the density of water a 1000 kg/3, and theacceleration due to gravity as 10 m/s2,thecantilever is ___________ kN-m (round off tothe nearest integer).Ans: 104 to 106

δω = 1000 kg/m3

g = 10 m2

width (w) = 1 m

f1 = δg ∆ 1h= 1000× 10× [ 1 × 4] × 2f1→ 80 kNf2 = δg ∆ 1d= 1000× [ 1 × 1] × 0.5 = 5 kN

CP1 = 4 ×1 43 3

CP2 = 1 ×1 13 3

So MA = 8043

- 513

320 15 315 1053 3 3

kN m

Q. 51 The magnitude of fraction force at joinC o the hinge-been shown in the figure is____________ kN (round off to 2 decimalplaces).

Ans: 19.95 to 20.05

0RightBM

4 RC × 4 × 2RC = 20 kN

Q. 52 A slot of 25 mm × 25 mm is to be milledin a workpiece of 300 mm length using a sideand face milling cutter of diameter 100 mm,width 25 mm and having 20 teeth.For a depth of cut 5 mm, feed per tooth 0.1 mm,cutting speed 35 m/min and approach and overtravel distance of. 5 mm each, the timerequired for milling the slot is _________minutes (round off to one decimal place)Ans: 7 to 935 = π × 0.100 × N


N= 111.408 rpm

t =0 300 50 5 52

0.1 20 11.418

DL A

f N

= 1.6157 min per passFor 25 mm depth of cut 5 pass needed. Because

5 mm depth is given25 55

Total matching time = 1.6157 × 5= 8.078 min

Q. 53 The following data applies to basic shaftsystem:Tolerance for hole = 0.002 mm,Tolerance for shaft = 0.001 mm,Allowance = 0.003 mm,Basic size = 50 mm.The maximum hole size is __________ mm(round off to 3 decimal places).Ans: 50.005 to 50.005Basic shaft system

Tolerance for hole = 0.002 mmTolerance for shaft = 0.001 mmAllowance = 0.00 mmBasic size = 50 mmminimum hole size = 50 + 0.003 + 0.002= 50.005

Q. 54 A steel part with surface area of 125cm2 is to be chrome coated through anelectroplating process using chromium acidsulphate as an electrolyte. An increasing currentis applied to the part according to the followingcurrent time relation:

l = 12 + 0.2twhere, l = current (A) and t= time (minutes).The part is submerged in the plating solution fora duration of 20 minutes for plating purpose.Assuming the cathode efficiency of chromiumto be 15% and the plating constant of chromiumacid sulphate to be 2.50 × 10-10mm3/A.s, theresulting coating thickness on the part surface is_________ μm (round off to one decimal place).Ans:I = 12 + 0.2t

Infinity small time ‘dt’

dQ = 2.50× 1022

.mmA S

× 12 + 0.2t × dt

connect ‘B’ to ‘min’dQ = 2.50× 102× 60 × 12 + 0.2t× dt

considering cathode efficiency is 15%dQ = 2.50× 102× 60 × [12 + 0.2t] dt × 0.15In 20 minQ =

20 2

02.50 10 60 12 0.2 0.15dQ t dt

= 63 mm3

As area as 125 cm2

Plat thickness =63 0.00504

125 100mm

=5.04 mm

Q.55 In a turning process using orthogonaltool geometry, a chip length of 100 mm isobtained for an uncut chip length of 250 mm.The cutting conditions are: cutting speed = 30m/min, rake angle = 200.The shear plane angle is ______ degrees (roundoff to one decimal place).Ans: 22 to 25length of chip = 100 mmUncut chip length = 250 mmCutting speed = 30 m/minα = 20o

Shear plane angle is --------------- 0


r =100 0.4250

t lctc l

tanφ =cos 0.4cos 20 0.4354

1 sin 1 0.4 sin 28

or dr d

φ = tan-1 0.43φ = 23.5o

Q. 56 The thickness of a steel plate withmaterial strength coefficient of 210 MPa, has tobe reduced from 20 mm to 15 mm in a singlepass in a two-high rolling mill with a roll radiusof 450 mm and rolling velocity of 28 m/min. Ifthe plate has a width of 200 mm and its strainhardening exponent, n is 0.25, the rolling forcerequired for the operations is __________ kN(round off to 2 decimal places).Note: Average Flow Stress = Material Strength

Coefficient ×

1

nTrue Strainn

Ans: 1164 to 1168

True strain (εT) = In15 0.287620

hf Inho

0 1

nTKn

=210× 0.250.2876

123.041 0.25

Mpa

f = 0 R h b

= 123.04 450 5 200 1167kN

Q.57 Two business owners Shveta ans Ashokrun businesses in two different states. Each ofthem, independent of the other, produces twoproducts A and B, sells them at Rs. 2,000 per kgand Rs. 3,000 per kg, respectively, and usesLinear Programming to determine the optimalquantity of A and B to maximize their respectivedaily revenue. Their constraints are as follows: i)for each business owner, the production

process is such that the daily production of Ahas to be at least as much as B, and the upperlimit for production of B is 10 kg per day, andii) the respective state regulations restrictShveta’s production of a to less than 20 kg perday, and Ashok’s production of A to less than 15kg per day. The demand of both A and B in boththe states is very high and everything producedis sold.The absolute value of the difference in daily(optimal) revenue of Shveta and Ashok is_________ thousand Rupees (round off to 2decimal places).Ans: 9.90 to 10.10Maximum Z = 2000n1 + 3000 n2

n1 ≥ n2n2≥ 10 A =n1 unitsn1< 20 B = n2 units.n1< 15Shveta’s Profit = [Put n1= 20 and n2= 10]= Rs 2000 × 20 + 3000 × 10= 40000 + 30000= 70000Ashok’s profit = Put (n1= 15, n2= 10)= Rs 2000 × 15 + 3000 × 10= 30000 + 30000= 60000Difference = 70000 – 60000= 10000 = 10k

Q.58 Consider two cases as below.Case 1: A company buys 1000 pieces per year ofa certain part from vendor ‘X’. The changeovertime is 2 hours and the price is Rs. 10 per piece.The holding cost rate per part is 10% per year.Case 2: For the same part, another vendor ‘Y’offers a design where the changeover time is 6minutes, with a price of Rs. 5 per prices, andholding cost rate per part of 100% per year. Theorder size is 800 pieces per year from ‘X’ and200 pieces per year from ‘Y’.


Assume the cost of downtime as Rs. 200 perhour. The percentage reduction in the annualcost for Case 2, as compared to Case 1 is___________ (round off to 2 decimal places).Ans: 8.19 to 8.23

Q. 59 Consider steady, viscous, fullydeveloped flow of a fluid through a circular pipeof internal diameter D. We that the velocityprofile forms a parabolic about the pipe centre

line, given by: V = - C2

2

4Dr

m.s, where C is

a constant. The rate of kinetic energy (in J/s) atthe control surface A- B, as shown in the figure,is proportional to Dn. The value of n is______________.

Ans: 8 to 8

V = - C2

2

4Dr

V = -C [r2 – R2 ]V = C [R2 – r2]

V = CR22

221 rR

2 2.

0 0

1 1 .2 2

R R

dAk mv vv dA

3

0

1 .2

R

v dA 32

3 62

0

1 .2 .R rC R r dr

R

323 6

20

2 1 .R rC R r dr

R

36 2 43 6

6 2 40

3 32 1 .R r r rC R r dr

R R R

2 2 2 23 6 32

2 8 42 2R R R RC R

23 62

8RC R

3 828

c R

3 8

8

28 2c D

So n = 8

Q.60 Air discharges steadily through ahorizontal nozzle and impinges on a stationaryvertical plate as shown in figure.

The inlet and outlet areas of the nozzle are 0.1m2 and 0.02 m2, respectively. Take air density asconstant and equal to 1.2 kg/m3. If the inletgauge pressure of air is 0.36 kPa, the gaugepressure at point O on the plate is _______ kPa(round off to two decimal places).Ans: 0.37 to 0.45


On applying continuity equationmo = δ1 A1 V1 = δ2 A2 V2

0.1 V1 = 0.0.02 V2

V2 = 1 1 10.1 10 50.02 2

V V V

Now on applying Bernoulli equation 1 –2section

2 21 1 2 2

1 22 2P v P vz zg g g g

[P2 = 0], Z1 = 0 = z2

22311 50.36 10

1.21 9.81 2 2vV

g g

V1 = 4.98 m/sV2 = 5 × 4.98 = 24.9 m/sNow applying Bernoulli equation 2 and 0sections

220 02 2

2 32 2P vP v z z

g g g g

2(24.9) 0.382

oo

p P kPag g

Q. 61 Air (ideal gas)enters a perfectly insulatecompressor is 6. Specific heat at constantpressure for air is 1005 J/kg.K and ratio ofspecific heats at constant pressure and constantvolume is 1.4. Assume that specific heats of airconstant. If the isentropic efficiency of thecompressor is 85 percent, the difference inenthalpies of air between the exit and the inlet

of the compressor is ________ kJ/kg (round offto nearest integer).Ans: 244 to 246

T1 = 310 K

Rp2

1

6, 0.85Hs

L

P P nP P

Cp = 1005 J/kg k = 1.005 kg/kg ky = 1.4

1

2 2

1 1

yyT P

T P

1.4 1

2 1.46310T

T2 = 517.225 K

2 112 1

isenisen

act

W h hW h h

2 112 1

0.85 PC T Th h

12 1

1.005 517.22 3100.85

h h

= 245 kJ/kg

Q. 62 One kg of air, initially at a temperature of1270C, expands reversibly at a constantpressure until the volume is doubled. If the gasconstant of air is 287 J/kg.K, the magnitude ofwork transfer is ____________ kJ (round off to2 decimal places).Ans: 114.6 to 115.0t1 = 1270C = 127 + 273 = 400 KV2 = 2V1 R = 287J/kg k.


W = PV

= mRT= 1 × 287 × 400287 4001000

kJ kkg k

= 114.8 KJ

Q. 63 For an ideal Rankine cycle operatingbetween pressure of 30 bar and 0.04 bar, thework output from the turbine is 903 kJ/kg andthe work input to the feed pump is 3 kJ/kg. Thespecific steam consumption is ___________kg/kW.h (round off to 2 decimal places).Ans: 3.98 to 4.02SSC [kg/kwR]

=3600

wtW

=3600

T PW W=

3600 4903 3 /

kgkw h

kg/kW.h

Q. 64 For a Kaplan (axial flow) turbine, theoutlet blade velocity diagram at a section isshown in figure.

The diameter at this section is 3 m. The hub andtip diameters of the blade are 2 m and 4 m,respectively. The water volume flow rate is 100m3/s. The rotational speed of the turbine is 300rpm. The blade outlet angle β is _______degrees (round off to one decimal place).Ans: 11.0 to 14.0Db = 2m Q = 100m3/secDo = 4 m N = 300rpmDS = 3m

tan β = 2

2

f

b

C VfC u

u2 =3 300 47.12 /

60 60DH m s

Q 2 224 a bd d Vf

100 = 2 224 2

4Vf

2 10.61 /Vf m s

tan β =10.61 12.547.12

o

Q. 65. The indicated power developed by anengine with compression ratio of 8, is calculatedusing an air-standard Ott cycle (constantproperties). The rate of heat addition is 10 kW.


The ratio of specific heats at constant pressureand constant volume is 1.4. The mechanicalefficiency of the engine is 80 percent.The brake power output of the engine is________ kW (round off to one decimal place).Ans: 4.4 to 4.6CR = 8Q 5 = 10 kwγ = 1.4ηmuch= 80%BP output = kw

mBPIP

4 111 netotto

S

Wr Q

1.4 111

8

0.564otto net

S

WQ

0.564 =10netW

Wnet = 5.64 kwhm × IP = BP0.80× 564 = BP4.5 kw = BP

q.1 heisknownforhisunscrupulousways. ans:dthegatecoach.com/admin/solutionfile/f9575550mechanical...

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