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Model Test Paper - IVGATE Mechanical Engineering

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Q. 1 - Q. 25 carry one mark each.

Q.1 An elastomeric bearing with 220 mmb = and 30 mma = is shown in figure. For a maximum lateral load 19 kNP = and a maximum displacement 12 mmd = , the shearing modulus G and the shear stress t respectively, are

(A) 1.08 MPa, 43 kPa2 (B) 0.54 MPa, 431 kPa

(C) 1.08 MPa, 862 kPa (D) 1.08 MPa, 6 kPa21

Q.2 Which of the following is the largest allowable diameter of a 3 m long steel rod ( 77 )GPaG = if the rod is to be twisted through 30c without exceeding a shearing stress of 80 MPa ?

(A) 17.85 mm (B) 11.9 mm

(C) 5.95 mm (D) 8.9 mm

Q.3 Coriolis component acceleration exists whenever a point moves along a path that has

(A) linear motion

(B) rotational motion

(C) tangential acceleration

(D) centripetal acceleration

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Q.4 The angular velocity of gear 2 is 800 rpm in the direction shown. What will be the angular velocity of gear 8 ?

(A) rpm72 (B) rpm42

(C) rpm93 (D) rpm56

Q.5 A block is placed on an inclined surface as shown in figure. If 35cq = and 400 NP =, what will be the magnitude of the friction force and state whether it is in equilibrium or not ?

(A) 315 N, No (B) 246 N, No

(C) 246 N, Yes (D) 315 N, Yes

Q.6 A plate-type clutch has the following properties 30 cmro = , 23 cmri = , engagement force of 534 N (normal force) and turns at 2000 rpm. The friction disc has a coefficient of friction of 0.3. What will be the power that can be transmitted by this system ?

(A) 13.3 kW (B) 7.20 kW

(C) 8.9 kW (D) 11.6 kW

Q.7 Match List I (Properties of fluids) with List II (Definition/ Result) and select the cor-rect answer using the codes given below :

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List-I List-II

a. Ideal fluid 1. Viscosity does not vary with rate of deformation

b. Newtonian fluid 2. Fluid of zero viscosity

c. /m r 3. Dynamic viscosity

d. Mercury in glass 4. Capillary depression

5. Kinematic viscosity

6. Capillary rise

Codes a b c d(A) 1 2 4 6(B) 1 2 3 4(C) 2 1 3 6(D) 2 1 5 4

Q.8 A tank is constructed of a series of cylinders as shown in figure. A mercury manometer is attached to the bottom of the tank. What will be the manometer reading h ?

(A) 37.6 m (B) 3.76 m

(C) 0.0376 m (D) 0.376 m

Q.9 A pump delivers 18.0 / .minL of water at a net head of 1.6 m at its best efficiency point. If the maximum pump efficiency is %70 , the power (bhp) required to run the pump is

(A) 403 W (B) 6.72 W

(C) 3.3 W (D) 197 W

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Q.10 Consider two metal plates pressed against each other. Other things being equal, which of the measures below will cause the thermal contact resistance to increase ?

(A) Cleaning the surfaces to make them shinier.

(B) Pressing the plates against each other with a greater force.

(C) Filling the gab with a conducting fluid.

(D) Coating the contact surfaces with a thin layer of soft metal such as tin.

Q.11 An automobile engine delivers 60 kW of power to the wheels while consumes fuel at a rate of 28 /L h. The fuel has a heating value of 44000 /kJ kg and a density of 0.8 /g cm3. What will be the efficiency of this engine ?

(A) 38.4% (B) 32.8%

(C) 49.3% (D) . %21 9

Q.12 A curve passes through the points given by the following table:

x 1 2 3 4 5

y 10 50 70 80 100

By Trapezoidal rule, the area bounded by the curve, the x-aixs and the lines x 1= , x 5= is(A) 255 (B) 275

(C) 305 (D) 310

Q.13 The singularity of esinz at z 3= is

(A) a pole (B) a removable singularity

(C) non-isolated essential singularity (D) isolated essential singularity

Q.14 The rank of an n row square matrix A is ( )n 1- , then

(A) adjA 0! (B) adjA 0=

(C) adjA In= (D) adjA In 1= -

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Q.15 Carbon dioxide is compressed from 0.3 m3 to 0.1 m3. During the process, the pres-sure and volume are related by p av 2= - , where 8 kPa ma 6-= . What will be the work done on the carbon dioxide during this process ?

(A) . kJ26 7 (B) . kJ39 9

(C) 53.3 kJ (D) . kJ66 8

Q.16 In a iron cooling curve, at which temperature the delta iron converts into gamma iron ?

(A) 1400 Cc (B) 768 Cc

(C) 910 Cc (D) 1535 Cc

Q.17 A gating ratio of 1 : 2 : 5 is used to design the gating system for aluminium alloy casting. The gating ration 1 : 2 : 5 represents

(A) Sprue base area : Runner area : Ingate area

(B) Sprue base area : Ingate area : Runner area

(C) Pouring basin area : Runner area : Ingate area

(D) Runner area : Sprue base area : Ingate area

Q.18 Using the given data points tabulated below, a straight line passing through the origin is fitted using least squares method. The slope of the line is

x 1.0 2.0 3.0

y 1.5 2.2 2.7

(A) 0.9 (B) 1.0

(C) 1.1 (D) 1.5

Q.19 In the permeability test, a sand specimen of height 5.08 cm and diameter 5.08 cm is used. If 2000 cm3 of air is allowed to pass through the specimen for a period of 120 seconds under a pressure of /gm cm7 2, the permeability number will be

(A) 71 (B) 53.70

(C) 82 (D) 35.80

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Q.20 The clearance in blanking operation, is provided

(A) 50% on punch and 50% on die.

(B) only on die.

(C) only on punch.

(D) on die or punch depending upon designers choice.

Q.21 In oxy-acetylene gas welding, for complete combustion, the ratio of oxygen to acety-lene is

(A) :11 (B) :.5 11

(C) :2 1 (D) :2.5 1

Q.22 If , . , . , .e e e e1 2 72 7 39 20 090 1 2 3= = = = and .e 54 604 = , then by Simpsons rule value

of e dxx0

4# is(A) 5.387 (B) 52.78

(C) 53.17 (D) 53.87

Q.23 Which of the following distribution is followed by the number of arrivals in a given time in a single-server queueing model ?

(A) Beta distribution

(B) Normal distribution

(C) Poisson distribution

(D) Negative exponential distribution

Q.24 Match List-I with List-II and select the correct answer using the codes given below the lists :

List-I List-II

P. Transportation Problem 1. Stage coach

Q. PERT 2. Hungarian method

R. Dynamic Problem 3. Critical path

S. Assignment Problem 4. Vogels approximate Method

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Codes : P Q R S(A) 4 3 1 2(B) 3 4 2 1(C) 4 1 3 2(D) 3 1 2 4

Q.25 In the ABC method of inventory control, Group A constitutes costly items. What is the usual percentage of such items of the total items ?

(A) 10 to 20% (B) 20 to 30%

(C) 30 to 40% (D) 40 to 50%

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Q. 26 - Q. 55 carry two marks each.

Q.26 Match List I (Welding processes) with List II (Features) and select the correct an-swer using the codes given below the list :

List-I List-II

P. Electric resistance welding 1. Arc is produced between two electrodes.

Q. Oxy-fuel gas welding 2. Heat produced is equal to I Rt2 .

R. Atomic hydrogen arc welding 3. It is mostly suitable for flat-position welding.

S. Submerged arc welding 4. Employing an exothermal chemical reaction for the purpose of developing high temperature.

T. Thermit welding 5. Source of heat is a gas-flame.Codes : P Q R S T(A) 4 2 1 3 5(B) 2 5 1 3 4(C) 2 4 3 1 5(D) 4 2 3 5 1

Q.27 What will be the stress at point B , (a) for the loading shown in figure, (b) if the 60 kN loads applied at points 2 and 3 are removed ?

(A) 8.33 MPaB as =^ h , . MPa7 64B bs =-^ h (B) 8.33 MPaB as =-^ h , 7.64 MPaB bs =^ h

(C) . MPa6 25B as =^ h , . MPa8 23B bs =^ h (D) . MPa7 64B as =^ h , . MPa6 25B bs =^ h

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Q.28 A solid circular steel shaft of 86 mm diameter is subjected to combined bending and twisting moment. The ultimate tensile and shear stress of the shaft are 700 MPa and 500 MPa, respectively. If the bending moment is 3000 N m- and factor of safety is 6, the torque generated by the shaft is

(A) 10000 N m- (B) 9000 N-m

(C) 12000 N-m (D) 11000 N-m

Q.29 A steel spur pinion has a module of 1.25 mm, 18 teeth cut on the 20c full-depth system and a face width of 12 mm. At a speed of 1800 /minrev , this pinion is expected to transmit a steady power of 0.5 kW. If velocity factor and the modified Lewis factor are .0 74 and .0 309, respectively, what will be the resulting bending stress ?

(A) 68.76 MPa (B) 75.64 MPa

(C) 58.45 MPa (D) 82.51 MPa

Q.30 A velocity field of a flow is given by ( 1) ( 2)y yV i j= - + - , where V is in /m s and x and y are in meters. What will be the equation of stream line passing through the point ( , )5 3 ?

(A) ( )lny x y 2 2= + - + (B) ( 2) 2lny x y= + + +

(C) ( )lnx y y 2 2= + - - (D) ( 2) 2lnx y y= + - +

Q.31 What will be the force in member AC of the truss with the loading and support system as shown in figure when the members of the truss are all of length L ?

(A) 0.577 TF ^ h (B) 0.289 CF ^ h

(C) 0.577 CF ^ h (D) 0.289 TF ^ h

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Q.32 The function xx1 is a decreasing if

(A) x e< (B) x e>

(C) x e= (D) xe1>

Q.33 Consider the following two statement :

Assertion (A): The function ( )f x x x x x x41

31

21

214 3 3 2= - - - + has an extreme value at

x 1= .Reason (R): '( )f 1 0=The correct option is(A) Both A and R individually true and R is the correct explanation of A

(B) both A and R individually true but R is not the correct explation of A

(C) A is true, but R is false

(D) A is false, but R is true.

Q.34 For flow of air at 15 Cc and 1 atm over a 0.3 m wide plate at 65 Cc with a velocity of /m s3 , match the following quantities (List-I) with corresponding computed values (List-

II) at 0.3 mx = . Take air properties as: 1.127 /kg m3r = , 1.918 10 /kg m s5m # -= - and .Pr 0 7255= .

List-I List-II

a. Hydrodynamic boundary layer thickness (in m)

1. .0 0058

b. Average friction coefficient 2. 0.0065

c. Local shear stress due to friction ( in /N m2)

3. 0.00726

d. Thermal boundary layer thickness (in m)

4. 0.0294

Codes: a b c d(A) 4 1 2 3(B) 2 3 4 1(C) 4 3 2 1(D) 2 1 4 3

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Q.35 The demands of a product in the month of March, April and May turned out to be 20, 25 and 26 units respectively. The forecast for March is 20 units and smoothing constant a is 0.2. What will be the forecast for the month of June, using exponential smoothing method ?

(A) 20 units

(B) 22 units

(C) 26 units

(D) 28 units

Q.36 In a vertical double-acting steam engine running at 360 rpm, the cylinder diameter is 0.3 m, piston rod diameter is 40 mm and length of connecting rod is 0.7 m. When the crank has moved 120c from top dead centre, the pressure of steam at the cover end is 0.35 /N mm2 and that at the crank end is 0.03 /N mm2. If the weight of reciprocating parts is 500 N and length of stroke is 300 mm, the piston effort will be

(A) . kN41 34

(B) . kN23 85

(C) . kN59 6

(D) 31.8 kN

Q.37 The arm F of a reverted Epicyclic train shown in figure, carries two wheels A and D and a compound wheel B C- . Wheel A meshes with wheel B and wheel D meshes with wheel C . Number of teeth on A 40= , Number of teeth on D 24= and number of teeth on C 36= . If wheel A is fixed and arm F rotates at 300 rpm counter-clockwise, the angular speed of wheel D is

(A) 720 rpm (B) 600 rpm

(C) 450 rpm (D) 500 rpm

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Q.38 A Cannot heat engine is shown in figure. It receives energy from a reservoir at Tres through a heat exchanger where the heat transferred is given by Q k T TresH H= -o ^ h and TL is the low temperature at which it rejects heat. To design the heat engine for maximum work output, what should be the high temperature, TH , in a cycle ?

(A) T Tres L (B) T Tres L

(C) ( )T T /res L 1 3 (D) T Tres L2^ h

Q.39 The iron is electro-chemical machined by using copper electrode and sodium chloride solution. The supply voltage and current of the ECM used be 18 Volt (DC) and 5000 A respectively. Assume a tool-work gap of 0. 5 cm0 and the current efficiency h can be taken as 100 percent with sodium chloride electrolyte. If the specific resistance is 5.0 ohm cm- , the material removal rate and the electrode feed rate respectively, are

(Take A 56, Few = , v 2= , 7.8 /g cm3r = , F 96500= Coulomb)(A) 1.86 10 / , 1.60 /minm s mm7 3# - (B)1.86 10 / , . 60 /minm s mm0 16 3# -

(C) . 8 10 / , .60 /minm s mm4 1 37 3# - (D) . 8 10 / , . 6 /minm s mm4 1 0 36 3# -

Q.40 Consider a gas turbine engine with regeneration. The engine operates with two stag-es of compression and two stages of expansion. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. The pressure ratio across each stage of the compressor and turbine is .3 5 and the compressor and turbine efficiencies are 78 % and 86 %, respectively. The effectiveness of the regenerator is %72 . Assuming constant specific heats for air at room temperature, what will be the thermal efficiency of the cycle ?

(A) 43.6% (B) . %39 2

(C) 48.9% (D) 51.7%

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Q.41 The air has a dry-bulb temperature of 22 Cc and a wet-bulb temperature of 16 Cc . The enthalpy of the air at dry-bulb temperature is 2541.1 /kJ kghg = and at the wet bulb temperature are 67.17 /kJ kghf = and 2463 /kJ kghfg = . Also the saturation pressure of water at dry-bulb and wet-bulb temperatures are 2.6452 kPa and 1.819 kPa, respectively. Assuming the air pressure of 100 kPa, what will be the specific humidity of kilogram water per kg of dry air and the relative humidity ?

(A) 0.00903, 54.1% (B) 0.01354, 80.1%

(C) 0.01129, 67.6% (D) 0.00506, 30.3%

Q.42 Consider the seven jobs, each of which has to go through the machines A and B in the order AB . Processing times in hours are given in table below :

Jobs 1 2 3 4 5 6 7

Machine A 3 12 15 6 10 11 9

Machine B 8 10 10 6 12 1 3What will be the idle time for machines A and B , respectively, to minimize the total elapsed time ?(A) 1 hour, 16 hours

(B) 1 hour, 17 hours

(C) 2 hours, 15 hours

(D) 2 hours, 18 hours

Two Marks Numerical Answer Type Questions (Q. 43 to 47).

Q.43 The truss ABC shown in the figure supports a vertical load W at joint B . The dis-tance between supports is 7.0 m and joint B is restrained against displacement perpendic-ular to the plane of the truss. If each member is a slender circular steel pipe ( 200 GPaE =) with outside diameter 100 mm and wall thickness 6.0 mm, what will be the critical value Wcr of the load in kN ?

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Q.44 In a double-pipe parallel-flow heat exchanger, ethylene glycol 2500 /J kg Ccp c-=^ h at 60 Cc and 0.3 /kg s is used to heat Glycerin 2400 /J kg Ccp c-=^ h at 20 Cc and the same mass flow rate. If the overall heat transfer coefficient is 380 /W m C2 c- and the heat transfer surface area is . m5 3 2, what will be the rate of heat transfer in kW ?

Q.45 Given figure shows that steam at a rate of 5 /kg s, enters in an isentropic steam turbine at 4 MPa. This steam is exhausted at 50 kPa, 100 Cc . Five percent of this flow is diverted for feed-water heating at 700 kPa. What will be the power produced by this turbine in kW ?

Q.46 A steel bar of 50 mm diameter was turned at 284 rpm and tool failure occurred in 10 minutes. The speed was changed to 232 rpm and the tool failed after 60 minutes of cutting time. To obtain a 30 minute tool life, what cutting speed in rpm should be used ?

Q.47 What will be the transportation cost of the following transportation problem ?

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.inCommon Data For Q. 48 and 49.An element in biaxial stress is subjected to stresses 60 MPaxs =- and 20 MPays = as shown in the fi gure.

Q.48 Using Mohrs circle, the stresses acting on an element oriented at a counterclockwise angle .22 5cq = from the x axis, are

(A) . MPa48 28x1s =- , . MPa8 28y1s = , 28. 8 MPa2x y1 1t =

(B) MPa20x1s =- , . MPa8 28y1s = , 28.28 MPax y1 1t =

(C) . MPa8 28x1s = , . MPa48 28y1s = , 28.28 MPax y1 1t =

(D) . MPa48 28x1s = , MPa20y1s =- , 28.28 MPax y1 1t =

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Q.49 What will be the maximum shear stresses and associated normal stresses using Mohrs circle ?

(A) 40 MPamaxt =- , 20 MPaavgs = (B) 20 MPamax avgt t= =

(C) MPa40max avgt t= = (D) 40 MPamaxt = , 20 MPaavgs =-

Common Data For Q. 50 and 51.The work-tool system is governed by the following equation, when machining steel with H.S.S. cutting tools. .26 035 VT f d. . .0 13 0 77 0 37=A min100 tool life was obtained under the following cutting conditions: Velocity 25 /minm= Feed 0.3125 /mm rev= Diameter of bar 2.50 mm=

Q.50 What is the effect on the tool life respectively, for a %20 increase in the cutting speed, feed and depth of cut, taking each separately ?

(A) 25 , 59.25 , 34.23min min min (B) 34.23 , 25 , 59.25min min min

(C) 25 , 34.23 , 59.25min min min (D) 59.25 , 34.23 , 25min min min

Q.51 What will be the effect on the tool life for a %20 increase in each of the above pa-rameters taken together ?

(A) 4.9 min (B) 6.2 min

(C) 8.7 min (D) 3.3 min

Statement For Linked Answer Questions 52 and 53.

Given the matrix A82

42=

-= G

Q.52 Eigen values are

(A) ( , )6 4 (B) ( , )4 2

(C) ( , )4 5 (D) ( , )6 3

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Q.53 Eigen vecotrs are

(A) [ , ],[ , ]1 1 2 1 (B) [ , ],[ , ]1 2 2 3

(C) [ , ],[ , ]1 1 2 2 (D) [ , ],[ , ]2 2 3 3

Statement For Linked Answer Questions 54 and 55.A 2 m high, 4 m wide signboard is attached to a 4 m wide, 0.15 m high rectangular concrete signpost (density 2300 /kg m3= ) by two 5 cm diameter, 4 m high (exposed part) poles as shown in figure below. The signboard is to withstand 150 /km h winds from any direction. The density of air to be 1.30 /kg m3, the drag coefficient for circular rod is

.C 0 3D = , for rectangular signboard .C 2 0D = and the flow is turbulent.

Q.54 The drag forces acting on the signboard and 2 poles respectively, are

(A) 18.06 ,kN 136 N (B) 180.6 ,kN 13.6 N

(C) 136 ,N 18.06 kN (D) 180.6 ,kN Zero

Q.55 What will be the minimum length L of the concrete block for the panel to resist the winds ?

(A) 18.5 m (B) 37.1 m

(C) 8.5 m (D) 3.71 m

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General Aptitude (GA) Questions

Q. 56 - Q. 60 carry one mark each.

Q.56 Look at this series: 8, 22, 8, 28, 8, . . . What number should come next?

(A) 09 (B) 29

(C) 32 (D) 34

Q.57 Choose the correct word that means the opposite or most nearly the opposite.

Nimble(A) sturdy (B) sluggish

(C) thoughtless (D) relaxed

Q.58 Find the sentence that has a mistake in grammar or usage. If you find no mistakes, mark choice d.

(A) It has not rained since last April.

(B) The jurors walked solemnly into the room.

(C) Had we known, we would not have come.

(D) No mistakes.

Q.59 The protesters were concerned that the proposed legislation would have a(n) ______ effect on the states nature preserves.

(A) scintillating (B) deleterious

(C) insipid (D) punctilious

Q.60 Coffee stains made the note ________.

(A) ilegible (B) illegible

(C) ilegable (D) illegable

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Q. 61 - Q. 65 carry one mark each.Originating in the 1920s, the Pyramid scheme is one of the oldest con games going. Honest people are often pulled in, thinking the scheme is a legitimate investment enterprise. The first customer to fall for the Pyramid scheme will actually make big money and will therefore persuade friends and relatives to join also. The chain then continues with the con artist who originated the scheme pocketing, rather than investing, the money. Finally, the pyramid collapses, but by that time, the scam artist will usually have moved out of town, leaving no forwarding address.

Q.61 This paragraph best supports the statement that

(A) it is fairly easy to spot a Pyramid scheme in the making.

(B) the first customer of a Pyramid scheme is the most gullible.

(C) the people who set up Pyramid schemes are able to fool honest people.

(D) the Pyramid scheme had its heyday in the 1920s, but its making a comeback.

Statement For Linked Answer Questions 62 and 63.The table lists the size of building lots in the Orange Grove subdivision and the people who are planning to build on those lots. For each lot, installation of utilities costs $12,516. The city charges impact fees of $3,879 per lot. There are also development fees of 16.15 cents per square foot of land.

Lot Area (Sq. Ft.) Builder

A 8023 Ira Taylor

B 6699 Alexis Funes

C 9004 Ira Taylor

D 8900 Mark Smith

E 8301 Alexis Funes

F 8269 Ira Taylor

G 6774 Ira Taylor

Q.62 The area of the smallest lot listed is approximately what percent of the area of the largest lot listed ?

(A) 25% (B) 50%

(C) 75% (D) 85%

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Q.63 How much land does Mr. Taylor own in the Orange Grove subdivision?

(A) 23,066 sq. ft (B) 29,765 sq. ft

(C) 31,950 sq. ft (D) 32,070 sq. ft

Q.64 SBI lent Rs. 1 lakh to farmer Kishan Singh @ %6 per annum of simple interest for 10 years period. Meanwhile bank offered a discount in rate of interest according to Govt. policy for farmers. Thus the rate of interest decreased to %4 . In this way Kishan Singh had to pay total amount .1 48 lakh.

After how many year Kishan Singh got the discount in rate of interest ?(A) 2 years (B) 3 years

(C) 4 years (D) 5 years

Q.65 In the figure, ABCD is a rectangle and points E , F , G and H are midpoints of its sides. What is the ratio of the area of the shaded region to the area of the un-shaded region in the rectangle ?

(A) :1 1 (B) :1 2

(C) :1 3 (D) 1 : 4

END OF THE QUESTION PAPER

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