Q. 1 – Q. 5 carry one mark each.

Q. 1 – Q. 5 carry one mark each.

Q.1 “The dress _________ her so well that they all immediately _________ her on her

appearance.”

The words that best fill the blanks in the above sentence are

(A) complemented, complemented (B) complimented, complemented

(C) complimented, complimented (D) complemented, complimented

Q.2 “The judge’s standing in the legal community, though shaken by false allegations of

wrongdoing, remained _________.”

The word that best fills the blank in the above sentence is

(A) undiminished (B) damaged (C) illegal (D) uncertain

Q.3 Find the missing group of letters in the following series:

BC, FGH, LMNO, _____

(A) UVWXY (B) TUVWX (C) STUVW (D) RSTUV

Q.4 The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the

following statements is true?

(A) The circle has the largest area.

(B) The square has the largest area.

(C) The equilateral triangle has the largest area.

(D) All the three shapes have the same area.

Q.5 The value of the expression

1

1+log𝑢 𝑣𝑤+

1

1+log𝑣𝑤𝑢+

1

1+log𝑤 𝑢𝑣 is _________.

(A) -1 (B) 0 (C) 1 (D) 3

Q. 6 – Q. 10 carry two marks each.

Q.6 Forty students watched films A, B and C over a week. Each student watched either only

one film or all three. Thirteen students watched film A, sixteen students watched film B

and nineteen students watched film C. How many students watched all three films?

(A) 0 (B) 2 (C) 4 (D) 8

2018

Q.7 A wire would enclose an area of 1936 m2, if it is bent into a square. The wire is cut into

two pieces. The longer piece is thrice as long as the shorter piece. The long and the short

pieces are bent into a square and a circle, respectively. Which of the following choices is

closest to the sum of the areas enclosed by the two pieces in square meters?

(A) 1096 (B) 1111 (C) 1243 (D) 2486

Q.8 A contract is to be completed in 52 days and 125 identical robots were employed, each

operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How

many additional robots would be required to complete the work on time, if each robot is

now operational for 8 hours a day?

(A) 50 (B) 89 (C) 146 (D) 175

Q.9 A house has a number which needs to be identified. The following three statements are

given that can help in identifying the house number.

i. If the house number is a multiple of 3, then it is a number from 50 to 59.

ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.

iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

What is the house number?

(A) 54 (B) 65 (C) 66 (D) 76

2018

Q.10 An unbiased coin is tossed six times in a row and four different such trials are conducted.

One trial implies six tosses of the coin. If H stands for head and T stands for tail, the

following are the observations from the four trials:

(1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __.

Which statement describing the last two coin tosses of the fourth trial has the highest

probability of being correct?

(A) Two T will occur.

(B) One H and one T will occur.

(C) Two H will occur.

(D) One H will be followed by one T.

2018


Q.1 Vector triple product ( ) a b c of three vectors a, b and c is given by

(A) ( ) ( ) a c b a b c (B) ( ) ( ) b c a a c b

(C) ( ) ( ) a b c a c b (D) ( ) ( ) b c a a b c

Q.2 A real-valued function y of real variable x is such that 5 .y x At 0,x the function is

(A) discontinuous but differentiable (B) both continuous and differentiable

(C) discontinuous and not differentiable (D) continuous but not differentiable

Q.3 Considering the coordinate system shown in the figure, a force of magnitude 10 kN has

x-component of 6 kN. Possible y-component (s) of the force is/are

x

y

o

(A) +8 kN only (B) +5 kN only

(C) +8 kN and 8 kN (D) +5 kN and 5 kN

Q.4 When austenite decomposes upon cooling into two phases— ferrite and cementite, the

reaction is called

(A) Eutectic (B) Eutectoid (C) Peritectic (D) Peritectoid

Q.5 Match the geometric tolerances with their correct symbols:

P. Flatness 1.

Q. Perpendicularity 2.

R. Concentricity 3.

S. Roundness (Circularity) 4.

(A) P – 1, Q – 3, R – 4, S – 2 (B) P – 3, Q – 1, R – 4, S – 2

(C) P – 3, Q – 1, R – 2, S – 4 (D) P – 3, Q – 2, R – 1, S – 4

2018

Q.6 Which one of the following instruments makes use of the principle of interference of light?

(A) Optical flat (B) Auto-collimator

(C) Optical projector (D) Coordinate measuring machine

Q.7 In ASME process chart, the symbol represents

(A) operation (B) inspection (C) delay (D) transport

Q.8 Which one of the following is the most appropriate control chart for measuring the variability

of individual readings within a sample?

(A) -chartX (B) R-chart (C) p-chart (D) c-chart

Q.9 The machines and auxiliary facilities are located according to processing sequence of the

product (produced in very large quantities) in

(A) Process Layout (B) Fixed Position Layout

(C) Product Layout (D) Cellular Layout

Q.10 Which one of the following defects is NOT associated with the casting process?

(A) Hot tear (B) Porosity (C) Blister (D) Central burst

Q.11 In an oxy-acetylene gas welding process, oxygen and acetylene are mixed in a ratio of 1.5:1

(by volume). The flame is

(A) neutral (B) carburizing (C) reducing (D) oxidizing

Q.12 Each of three firms P, Q and R manufactures 100 lakhs components. The number of defective

components produced by P, Q and R are 30, 42 and 47, respectively. The firm(s) in

conformance with Six Sigma standard is/are

(A) only P (B) P and Q (C) P, Q and R (D) Q and R

Q.13 To make holes of 0.5 mm diameter and 30 mm depth in a mild steel component, the most

suitable process is

(A) chemical machining (B) electrochemical machining

(C) abrasive jet machining (D) plasma arc machining

Q.14 Which one of the following processes is NOT used for producing powders?

(A) Atomization (B) Ball milling (C) Sintering (D) Electrolysis

2018

Q.15 The process in which molten thermoplastic is forced between rolls to produce thin sheets is

called

(A) blow moulding (B) compression moulding

(C) calendering (D) extrusion

Q.16 The diagonal elements of a 3-by-3 matrix are 10, 5 and 0, respectively. If two of its

eigenvalues are 15 each, the third eigenvalue is _______

Q.17 Weights (in kg) of six products are 3, 7, 6, 2, 3 and 4. The median weight

(in kg, up to one decimal place) is _______

Q.18 The probabilities of occurrence of events F and G are P(F) = 0.3 and P(G) = 0.4, respectively.

The probability that both events occur simultaneously is P(FG) = 0.2. The probability of

occurrence of at least one event P(FG) is _______

Q.19 A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has

a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy

(in J) of the flywheel is _______

Q.20 A cylindrical wooden block of length 50 cm is floating in water in such a way that its axis is

vertical. The densities of wood and water are 800 kg/m3 and 1000 kg/m3, respectively. The

submerged depth, i.e., depth of immersion (in cm) of the cylinder is _______

Q.21 A machine consists of three components P, Q and R connected serially. The reliabilities of

P, Q and R are 0.97, 0.86 and 0.93, respectively. To increase the reliability of the machine,

two additional stand-by units of Q are attached. The overall reliability (up to two decimal

places) of the machine is _______

Q.22 The mean time between failures of a machine is 400 hour. If the availability of the machine

is 80%, the mean time to repair (in hour) is _______

2018

Q.23 Processing times on a single machine for 3 jobs are given below. All the jobs are available

at time t = 0.

Job 1 2 3

Processing time (minute) 15 3 6

The mean flow time (in minute) as per the shortest processing time (SPT) sequence

is _______

Q.24 In a two-pass wire drawing process, there is a 40% reduction in wire cross-sectional area in

1st pass and further 30% reduction in 2nd pass. The overall reduction (in percentage)

is ______

Q.25 A double-start thread with a pitch of 2 mm is to be cut using a lathe machine. The pitch of

the leadscrew of the lathe is 6 mm. The job rotates at 60 revolution per minute (RPM). The

RPM of the leadscrew is ______

2018


Q.26 Consider the analytic function 2 2( ) 2f z x y i xy of the complex variable ,z x iy

where 1.i The derivative ( )f z is

(A) 2 2x i y (B) 2 2x iy (C) x iy (D) 2 2x i y

Q.27 In order to evaluate the integral

1

0

e dx x with Simpson’s 1/3rd rule, values of the function

ex are used at x 0.0, 0.5 and 1.0. The absolute value of the error of numerical integration is

(A) 0.000171 (B) 0.000440 (C) 0.000579 (D) 0.002718

Q.28 A rigid link PQ of length 1.0 m is pinned at P. It rotates about P in a vertical plane with a

uniform angular acceleration of 1.0 rad/s2. At an instant when the angular velocity of the link

is 1.0 rad/s, the magnitude of total acceleration (in m/s2) of point Q relative to point P is

(A) 1.41 (B) 1.73 (C) 2 (D) 2.83

Q.29 In a shaft-hole system, the dimensions with tolerances (in mm) are as follows:

Shaft: 20 x

x

Hole: 0.0320 y

where both x and y are positive real numbers. Which one of the following will provide an

interference fit?

(A) x = 0.05, y = 0.040 (B) x = 0.04, y = 0.035

(C) x = 0.04, y = 0.032 (D) x = 0.02, y = 0.035

Q.30 A machine is procured at a price of Rs. 47000 with a 2-year warranty. After two years, the

annual maintenance cost (AMC) in Rs. is given by the following formula:

AMC = 2 2000, for 2i i ,

where i is the number of years elapsed since the machine was purchased. Neglect the scrap

value of the machine, inflation, interest, etc. For minimizing the average cost, the machine

should be replaced at the end of the year

(A) 2 (B) 4 (C) 7 (D) 10

Q.31 In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per

hour. The time for servicing a car is exponential with a mean of 15 minutes. The expected

waiting time (in minute) in the queue is

(A) 10 (B) 15 (C) 25 (D) 30

2018

Q.32 Actual and forecasted demands of a product are as follows:

Period 1 2 3 4 5

Actual demand 180 170 165 170 200

Forecasted demand 190 190 190 190 190

The forecast error measured in terms of mean absolute deviation (MAD) and mean absolute

percentage error (MAPE), respectively, are

(A) 13 and 7.84% (B) 13 and 9.85% (C) 17 and 7.84% (D) 17 and 9.85%

Q.33 In a mass production firm, measurements are carried out on 10000 pairs of shaft and hole.

The mean diameters of the shaft and the hole are 37.53 mm and 37.59 mm, respectively. The

corresponding standard deviations are 0.03 mm and 0.04 mm. The mean clearance and its

standard deviation (both in mm), respectively, are

(A) 0.06 and 0.07 (B) 0.06 and 0.06 (C) 0.06 and 0.05 (D) 0.07 and 0.01

Q.34 A pressure die casting set-up was tested by injecting water (density 1000 kg/m3) at a pressure

of 200 bar. Mould-filling time was found to be 0.05 s. Afterwards, the actual casting is made

by injecting the liquid metal (density 2000 kg/m3) at an injection pressure of 400 bar. Neglect

all losses (friction, viscous-effect, etc.). The approximate mould-filling time (in s) is

(A) 0.05 (B) 0.075 (C) 0.1 (D) 0.2

Q.35 The value of the surface integral (9 2 ) dS

x y z S i j k n over the surface S of the sphere

2 2 2 9,x y z where n is the unit outward normal to the surface element d ,S is ______

Q.36 Consider the differential equation 2

2

d2 8 0

d

yy

t

with initial conditions:

at 0,t 0y and d

10.d

y

t

The value of y (up to two decimal places) at 1t is ______

Q.37 One kg of air (that can be considered a calorically perfect gas with characteristic gas constant

R = 287 J/kg-K and specific heat ratio 1.4 ) undergoes a constant-volume process from

an initial static pressure of 1 bar to a final static pressure of 4 bar. The increase in entropy

(in J/kg-K) of air is ______

2018

Q.38 If 2 22( )u x y and v axy represent the x- and y-components of the two-dimensional

velocity field of an incompressible flow, the value of the constant a is ______

Q.39 A spherical pressure vessel (made of mild steel) of internal diameter 500 mm and thickness

10 mm is subjected to an internal gauge pressure of 4000 kPa. If the yield stress of mild steel

is 200 MPa, the factor of safety (up to one decimal place) is ______

Q.40 A square cross-section wooden column of length 3140 mm is pinned at both ends. For the

wood, Young’s modulus of elasticity is 12 GPa and allowable compressive stress is 12 MPa.

The column needs to support an axial compressive load of 200 kN. Using a factor of safety

of 2.0 in the computation of Euler’s buckling load, the minimum cross-sectional area

(in mm2) of the column is ______

Q.41 Length, width and thickness of a plate are 400 mm, 400 mm and 30 mm, respectively. For

the material of the plate, Young’s modulus of elasticity is 70 GPa, yield stress is 80 MPa and

Poisson’s ratio is 0.33. When the plate is subjected to a longitudinal tensile stress of 70 MPa,

the increase in the volume (in mm3) of the plate is ______

Q.42 In a V-thread, a wire is fitted such that it makes contact with the flank of the thread on the

pitch line as shown in the figure. If the pitch p of the thread is 3 mm and the included angle

is 60, the diameter (in mm, up to one decimal place) of the wire is ______

0.25p

O

Pitch line

60°

2018

Q.43 A project consists of three activities P, Q and R. The durations of activities follow Beta

distribution. The predecessors and durations of activities are as per the following table:

Activity Predecessors Optimistic time

(month)

Most likely time

(month)

Pessimistic time

(month)

P — 2 3 10

Q P 3 5 13

R Q 3 4 5

The expected project completion time (in month) is ______

Q.44 A company has two manufacturing plants (C1 and C2) and two distribution centres (D1 and

D2). The capacities of C1 and C2 are 100 and 200 units, respectively. The demand for D1 and

D2 are 190 and 110 units, respectively. The costs per unit (in Rs.) of transportation at different

routes are as per the following matrix:

D1 D2

C1 22 21

C2 20 27

The minimum total cost (in Rs.) of transportation is ______

Q.45 The annual demand of an item is 19845 units and the production rate is 100 units per day.

The per-unit production cost (excluding setup cost) is Rs. 50, the per-unit holding cost is

Rs. 10 per year and setup cost is Rs. 520 per setup. To minimize the total annual cost, the

optimum quantity to be produced per setup is ______

Q.46 A production line operates 7 hours a day in a 5-day week. The processing times for various

job elements are as follows:

Job element p q r s t

Processing time (s) 5 10 12 3 15

If the line is designed for an output of 8400 units per week, the theoretical minimum number

of work stations required is ______

Q.47 In a work sampling study of a worker, the information available are as follows: total time of

study: 30 hour, number of items produced: 320, total number of observations: 1000, number

of observations when worker is found working: 850 and average performance rating: 105%.

Company policy is to give allowance of 10% of total time on the job. The standard time

(in minute per item, up to one decimal place) for manufacturing the item is ______

2018

Q.48 The breakeven point of a manufacturing company is 50000 units. The fixed cost is

Rs. 200000 and the variable cost per unit is Rs. 20. The selling price per unit (in Rs.) of the

product at this breakeven point is ______

Q.49 A 10 mm thick plate is rolled to 7 mm thickness in a rolling mill using 1000 mm diameter

rigid rolls. The neutral point is located at an angle of 0.3 times the bite angle from the exit.

The thickness (in mm, up to two decimal places) of the plate at the neutral point is ______

Q.50 A cylindrical workpiece is turned at a feed of 0.1 mm/rev with a perfectly sharp tool. In ASA

system, the side and end cutting edge angles are 15° and 5°, respectively, as shown in the

figure. The peak-to-valley roughness (in µm, up to one decimal place) of the machined

surface is ______

5o

15o

Feed = 0.1 mm/rev

Q.51 The worktable in a CNC machine is driven by a leadscrew with a pitch of 2 mm. The

leadscrew is directly coupled to a stepper motor of step angle 1.8°. The number of pulses

required to move the worktable by 50 mm is ______

Q.52 During orthogonal machining of a job at a cutting speed of 90 m/min with a tool of 10° rake

angle, the cutting force and thrust force are 750 N and 390 N, respectively. Assume a shear

angle of 35°. The power (in W) expended for shearing along the shear plane is ______

Q.53 In an electrochemical machining of aluminium with plane parallel electrodes, the current

density is 70 A/cm2. Cross-sectional area of each electrode is 3 cm2. The current efficiency

(i.e., the fraction of current used for dissolution of metal) is 80%. Gram atomic weight,

valency and density of aluminium are 27 gram, 3 and 2700 kg/m3, respectively. Take

Faraday’s constant as 96500 Coulomb. The volumetric material removal rate (in mm3/min)

is ______

Q.54 Two metallic sheets are spot welded by passing a current of 8000 A for 0.2 s. Assume that a

cylindrical nugget of 8 mm diameter and 3 mm depth is formed. The density of the nugget

is 7500 kg/m3, effective resistance of the total system is 222 micro-Ohm and heat required

to produce 1.0 gram of nugget is 1400 J. The percentage of heat actually utilized in producing

the nugget is ______

2018

Q.55 In a planar 2-degree-of-freedom robot, Link 1 of 30 cm length is connected to base by a

revolute joint and Link 2 of length 20 cm is connected to Link 1 with a revolute joint as

shown in the figure. The work-envelope area (in cm2), covered by point P, is ______

Joint 1

Joint 2

Link 2

Lin

k 1

P

Base

2018

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Q.1 If I were you, I __________ that laptop. It’s much too expensive.

(A) won’t buy (B) shan’t buy

(C) wouldn’t buy (D) would buy Q.2 He turned a deaf ear to my request.

What does the underlined phrasal verb mean?

(A) ignored (B) appreciated (C) twisted (D) returned Q.3 Choose the most appropriate set of words from the options given below to complete the following

sentence. _________ ___________ is a will, _________ is a way.

(A) Wear, there, their (B) Were, their, there

(C) Where, there, there (D) Where, their, their Q.4 (x % of y) + (y % of x) is equivalent to .

(A) 2 % of xy (B) 2 % of (xy/100) (C) xy % of 100 (D) 100 % of xy Q.5 The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits

is greater than the original number by 54, find the original number.

(A) 39 (B) 57 (C) 66 (D) 93

2016


Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested

with them. The rates of interest offered by these companies may differ from year to year. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.

If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:

(A) 2:3 (B) 3:4 (C) 6:7 (D) 4:3

Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the

form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the availability of evidence today. Which of the following can be logically inferred from the above sentences?

(A) Emperors who do not leave significant sculpted evidence are completely forgotten. (B) Ashoka produced stone carved edicts to ensure that later historians will respect him. (C) Statues of kings are a reminder of their greatness. (D) A king’s greatness, as we know him today, is interpreted by historians.

7

98

10

7.56.5 66.5

8

9.5

89

8

4

2000 2001 2002 2003 2004 2005 2006

P Q

2016

Q.8 Fact 1: Humans are mammals. Fact 2: Some humans are engineers. Fact 3: Engineers build houses. If the above statements are facts, which of the following can be logically inferred?

I. All mammals build houses. II. Engineers are mammals. III. Some humans are not engineers.

(A) II only. (B) III only.

(C) I, II and III. (D) I only. Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the

lateral surface area of the pyramid?

(A) x2 (B) 0.75 x2 (C) 0.50 x2 (D) 0.25 x2

Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.

(A) 1 (B) 2 (C) 3 (D) 4

2016


Q.1 The eigenvalues of the matrix

0 11 0

are

(A) i and i (B) 1 and 1 (C) 0 and 1 (D) 0 and 1 Q.2

The number of solutions of the simultaneous algebraic equations 3 3 and 3 5 is

(A) zero (B) 1 (C) 2 (D) infinite Q.3 At x = 0, the function

sin , ∞ ∞, 0

is

(A) continuous and differentiable. (B) not continuous and not differentiable. (C) not continuous but differentiable. (D) continuous but not differentiable.

Q.4 For the two functions

, 3 and , 3 which one of the following options is correct?

(A) (B) (C) (D)

Q.5 The function

is singular at

(A) 2 (B) 1 (C) (D) 2 Q.6 A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is

(A) (B) 1 (C) (D) 1

2016

Q.7 A normal random variable X has the following probability density function

√

, ∞ ∞ Then d

(A) 0 (B) (C) 1 (D) 1

Q.8 The elastic modulus of a rigid perfectly plastic solid is

(A) 0 (B) 1 (C) 100 (D) infinity Q.9 Consider the following statements:

(P) Hardness is the resistance of a material to indentation. (Q) Elastic modulus is a measure of ductility. (R) Deflection depends on stiffness. (S) The total area under the stress-strain curve is a measure of resilience. Among the above statements, the correct ones are

(A) P and Q only. (B) Q and S only. (C) P and R only. (D) R and S only.

2016

Q.10 A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the

weight of the beam.

The correct Free Body Diagram of the beam is

(A)

(B)

(C)

(D)

Q.11 Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated

in the plane of the paper about point P lying 5 mm away from its center. The radius of the cam is 20 mm. The distance (in mm) between the highest and the lowest positions of the flat face follower is

(A) 5 (B) 10 (C) 40 (D) 45

5 mm

P

2016

Q.12 A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm2 area forms at the bottom of the tank. Considering the coefficient of discharge of the hole to be unity and the acceleration due to gravity to be 10 m/s2, the rate of leakage of water (in litre/min) through the hole from the tank to the atmosphere, under the given conditions, is _______.

Q.13 The figure below shows an air standard Diesel cycle in p-V diagram. The cut-off ratio is given by:

(A) (B) (C) (D)

Q.14 The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium

sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet is________.

Q.15 Which one of the following is a natural polymer?

(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride Q.16 In powder metallurgy, sintering of the component

(A) increases density and reduces ductility. (B) increases porosity and reduces density. (C) increases density and reduces porosity. (D) increases porosity and reduces brittleness.

Q.17 A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and

the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is 10. The back rake angle (in degrees) is _______.

4

p

V

2 3

1

2016

Q.18 Consider the following statements.

(P) Electrolyte is used in Electro-chemical machining. (Q) Electrolyte is used in Electrical discharge machining. (R) Abrasive-slurry is used in Ultrasonic machining. (S) Abrasive-slurry is used in Abrasive jet machining. Among the above statements, the correct ones are

(A) P and R only (B) Q and S only (C) Q, R and S only (D) P and Q only Q.19 Consider the following statements.

(P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP). (Q) Production flow analysis helps in work cell formation. (R) Group technology takes input from choice of machining or cutting parameters. Among the above statements, the correct one(s) is (are)

(A) P only (B) Q and R only (C) P and R only (D) Q only Q.20 The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of

a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the fundamental deviation (in m) for the same is

(A) 22 (B) zero (C) 22 (D) 24 Q.21 The roughness profile of a surface is depicted below.

The surface roughness parameter Ra (in m) is _______.

2 µm

5 mm

2 µm

X

prof

ile

heig

ht

centre-line of the profile

2016

Q.22 The facility layout technique that uses relationship (REL) chart is

(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP. Q.23 For a random variable, X, let be the sample average. The sample size is n. The mean and the

standard deviation of X are µ and σ, respectively. The standard deviation of is

(A) (B) (C ) (D) √

Q.24 ST and NT denote the standard time and the normal time, respectively, to complete a job.

Allowance , where 0 1. Which one of the following relationships is correct?

(A) (B) 1 )

(C ) (D) 1

Q.25 The throughput rate of a production system is 20 units per hour. The average flow time is 30

minutes and the cycle time is 3 minutes. The average inventory (in units) in the system is

(A) 1.5 (B) 9 (C ) 10 (D) 11.33


Q.26 The range of values of k for which the function

4 6 8 has a local maxima at point x = 0 is

(A) 2 or 2 (B) 2 or 2 (C) 2 2 (D) 2 2

Q.27

lim → is equal to ______.

2016

Q.28 To solve the equation 2 sin by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be closest to

(A) – 8.101 (B) 1.901 (C) 2.099 (D) 12.101 Q.29 In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K)

is given as , where q is the heat input per unit length (in J/m) of weld, is the thermal

diffusivity (in m2/s) of the plate materials and is a constant independent of process parameters and material types. Two welding cases are given below. Case I: V = 15 V, I = 200 A, v = 5 mm/s, k = 150 W/mK, = 3000 kg/m3, C = 900 J/kg-K Case II: V = 15 V, I = 300 A, v = 10 mm/s, k = 50 W/mK, = 8000 kg/m3, C = 450 J/kg-K where, V is welding voltage, I is welding current, v is welding speed, and k, and C refer to the thermal conductivity, the density and the specific heat of the plate materials, respectively. Consider that electrical energy is completely converted to thermal energy. All other conditions remain same. The ratio of the peak temperature in Case I to that in Case II is

(A) (B) (C) 1 (D) 2

Q.30 A bar of rectangular cross-sectional area of 50 mm2 is pulled from both the sides by equal forces of

100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45o with the axis, shown as a dashed line in the figure, is ________________.

100 N 100 N

45o

2016

Q.31 A 1 m × 10 mm × 10 mm cantilever beam is subjected to a uniformly distributed load per unit length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point P is ____________.

Q.32 A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an

internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in mm) is________.

Q.33 An engine, connected with a flywheel, is designed to operate at an average angular speed of 800

rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be 6240 J. In order to keep the fluctuation of the angular speed within ±1% of its average value, the moment of inertia (in kg-m2) of the flywheel should be ____________.

Q.34 A 2 m × 2 m square opening in a vertical wall is covered with a metallic plate of the same

dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s2. The force (in kN) exerted by water on the plate is _____.

2 m

2 m

water

patm

patm

2 m × 2 m square plate

vertical wall

vertical wall

100 N/m

1 m

Point P

2016

Q.35 An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible

process its pressure reduces to . Following statements are made regarding the process. (P) Heat is transferred from the gas. (Q) Work done by the gas is zero. (R) Entropy of the gas remains constant. (S) Entropy of the gas decreases. Among the above statements, the correct ones are

(A) P and R only. (B) P, Q and R only. (C) Q and R only. (D) P, Q and S only. Q.36 A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end

of the fin is kept at a constant temperature tb. The fin loses heat by convection to the atmosphere which is at a temperature ta (ta< tb). Four options of temperature profiles are shown. Identify the correct option.

(A)

(B)

(C)

(D)

L

tem

pera

ture

tb

ta x 0

tb

taL x

tem

pera

ture

0 L

tb

ta x 0

tem

pera

ture

atmosphere at ta

tb

convection

x x = L

tb

taL

tem

pera

ture

x0

2016

Q.37 In a fully developed turbulent flow through a circular pipe, a head loss of is observed. The

diameter of the pipe is increased by 10% for the same flow rate and a head loss of is noted.

Assume friction factor for both the cases of pipe flow is the same. The ratio of is closest to

(A) 0.34 (B) 0.62 (C) 0.87 (D) 1.00 Q.38 Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P

has rectangular cross-section of 100 mm × 200 mm. Block Q is of square cross-section. Both P and Q were cast under the same conditions with all their surfaces enclosed within the mould. The solidification time of a casting is proportional to the square of the ratio of its volume to its surface area. The ratio of solidification time of the block P to that of the block Q is ______.

Q.39 A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile

stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly elastic. The elastic modulus of copper is 100 GPa. The resultant elongation (in mm) is ________.

Q.40 In a single-pass rolling operation, a 200 mm wide metallic strip is rolled from a thickness 10 mm to

a thickness 6 mm. The roll radius is 100 mm and it rotates at 200 rpm. The roll-strip contact length is a function of roll radius and, initial and final thickness of the strip. If the average flow stress in plane strain of the strip material in the roll gap is 500 MPa, the roll separating force (in kN) is _______.

Q.41 Two solid cylinders of equal diameter have different heights. They are compressed plastically by a

pair of rigid dies to create the same percentage reduction in their respective heights. Consider that the die-workpiece interface friction is negligible. The ratio of the final diameter of the shorter cylinder to that of the longer cylinder is __________.

Q.42 Two flat steel sheets, each of 2.5 mm thickness, are being resistance spot welded using a current of

6000 A and weld time of 0.2 s. The contact resistance at the interface between the two sheets is 200 and the specific energy to melt steel is 10×109 J/m3. A spherical melt pool of diameter 4 mm is formed at the interface due to the current flow. Consider that electrical energy is completely converted to thermal energy. The ratio of the heat used for melting to the total resistive heat generated is ______.

Q.43 A cylindrical bar of 100 mm diameter is orthogonally straight turned with cutting velocity, feed and

depth of cut of 120 m/min, 0.25 mm/rev and 4 mm, respectively. The specific cutting energy of the work material is 1×109 J/m3. Neglect the contribution of feed force towards cutting power. The main or tangential cutting force (in N) is ________.

2016

Q.44 A 60 mm wide block of low carbon steel is face milled at a cutting speed of 120 m/min, feed of 0.1 mm/tooth and axial depth of cut of 4 mm. A schematic representation of the face milling process is shown below. The diameter of the cutter is 120 mm and it has 12 cutting edges. The material removal rate (in mm3/s) is ______.

Q.45 In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with

abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the water jet at a rate of 0.6 kg/min with negligible velocity. Assume that at the end of the focusing tube, abrasive particles and water come out with equal velocity. Consider that there is no air in the abrasive water jet. Assuming conservation of momentum, the velocity (in m/s) of the abrasive water jet at the end of the focusing tube is _________.

Q.46 A single axis CNC table is driven by a DC servo motor that is directly coupled to a lead screw of 5

mm pitch. The circular encoder attached to the lead screw generates 1000 voltage pulses per revolution of the lead screw. The table moves at a constant speed of 6 m/min. The corresponding frequency (in kHz) of the voltage pulses generated by the circular encoder is_________.

Q.47 A helical gear with involute tooth profile has been machined with a disc-type form gear milling

cutter. The helical gear has 30 teeth and a helix angle of 30. The module of the gear milling cutter is 2. The pitch circle diameter (in mm) of the helical gear is_______________.

Q.48 A quality control engineer has collected 5 samples, each of size 30. The numbers of defective items

in the samples are given in the table below.

Sample number I II III IV VNumber of defective items 3 2 4 1 5

The upper three-sigma (3σ) control limit for the proportion of defective items in any sample is _____.

cutter

feed

work piece

60 mm

ϕ 120 mm

schematic representation (top view)

2016

Q.49 A job consists of two work elements, P and Q. Completion time (in minutes) of each work element was measured. A pilot study involved collecting a sample of 40 observations. The results of this pilot study are summarized in the table below.

Work element Mean completion time (in minutes) Standard deviation (in minutes) P 1 0.50 Q 1 0.05

For the main study, the minimum sample size for the sample mean time of any work element to be within 0.1 minutes of its true mean time with 95% confidence (corresponding standard normal value, . 1.96 is ______________.

Q.50 Consider a system with 10 identical components connected in series. The time to failure of each

component is exponentially distributed with a failure rate of 0.10 per 500 days. The reliability of the system after 400 days of operation is _____.

Q.51 For a process, the quality loss coefficient is 5. The target value on the dimension to be attained

through the process is 50 mm. If the maximum loss permissible (in monetary terms) is INR 80, the maximum allowable deviation (in mm) from the target is

(A) (B)

(C) 4 (D) √10

Q.52 Consider a network with nodes 1, 2, 3, 4, 5 and 6. The nodes are connected with directed arcs as

shown in the table below. The respective costs (in INR) incurred while traversing the directed arcs are also mentioned.

Directed arcs 1 2 1 3 2 4 2 5 3 2 3 4 35 45 46 56Cost (in INR) 3 9 3 2 2 4 8 7 2 2

The second shortest path from node 1 to node 6 (i.e. the path that has the second least total cost and does not use any part of the shortest path) has a total cost (in INR) of

(A) 7 (B) 8 (C) 15 (D) 19 Q.53 Five jobs need to be processed on a single machine. All the jobs are available for processing at time

t = 0. Their respective processing times are given below.

Jobs I II III IV V Processing times (in minutes) 13 4 7 14 11

The average completion time (in minutes) of jobs as per the Shortest Processing Time rule is

(A) 9.8 (B) 24.2 (C) 49.0 (D) 121.0

2016

Q.54 Transportation costs (in INR/unit) from factories to respective markets are given in the table below. The market requirements and factory capacities are also given. Using the North-West Corner method, the quantity (in units) to be transported from factory R to market II is

Factory Requirements (in units) P Q R S

Mar

ket I 3 3 2 1 50

II 4 2 5 9 20 III 1 2 1 4 30

Factory Capacity (in units)

20 40 30 10

(A) 30 (B) 20 (C) 10 (D) 0 Q.55 In a given year, a restaurant earned INR 38,500 in revenues. In that year, total expenses incurred

were INR 30,000 and the depreciation amount was INR 3,200. At 40% tax rate, the net cash flow (in INR) for that year was _____.

2016

Graduate Aptitude Test in Engineering

Notations :

Question Paper Name: PI : PRODUCTION AND INDUSTRIAL ENGINEERING 1st Feb Shift2Number of Questions: 65Total Marks: 100.0

Number of Questions: 10Section Marks: 15.0

Question Number : 1 Question Type : MCQ

Options :


Options :


2015

Prabhat_Verma

Typewritten text

Wrong answer for MCQ will result in negative marks, (-1/3) for 1 mark Questions and (-2/3) for 2 marks Questions.

Prabhat_Verma

Rectangle

Prabhat_Verma

Typewritten text

Q.1 to Q.5 carry 1 mark each & Q.6 to Q.10 carry 2 marks each.

Prabhat_Verma

Rectangle

Options :


Options :


Options :


2015

Options :


Options :

Question Number : 8 Question Type : NA

Correct Answer :280

2015


Options :


Options :

Number of Questions: 55Section Marks: 85.0


Options :


2015

Prabhat_Verma

Typewritten text

Q.11 to Q.35 carry 1 mark each & Q.36 to Q.65 carry 2 marks each.

Prabhat_Verma

Rectangle

Options :


Options :


Options :


2015

Options :

Question Number : 16 Question Type : NAT

Correct Answer :412 to 416


Correct Answer :85


2015

Options :


Options :


Correct Answer :0.4 to 0.5


Options :

2015


Options :


Options :


Options :


2015

Options :


Options :


Options :


Options :

2015


Options :


Options :


Options :


Options :

2015


Correct Answer :1.5


Options :


Correct Answer :9000


Options :

2015


Options :


Options :


Options :

2015


Options :


Correct Answer :2.5


Correct Answer :14

2015


Options :


Correct Answer :-17.5


2015

Options :


2015

Options :




Correct Answer :

2015

8820 to 8840


Correct Answer :-50 to -48







2015


Options :


Correct Answer :2.5


2015



Correct Answer :5


Correct Answer:343749 to 343751


2015

Correct Answer :80


Options :


Options :


Options :

2015


Options :


Correct Answer :6




2015

Options :

2015


Q.1 Choose the most appropriate word from the options given below to complete the following sentence. A person suffering from Alzheimer’s disease short-term memory loss.

(A) experienced (B) has experienced (C) is experiencing (D) experiences

Q.2 Choose the most appropriate word from the options given below to complete the following

sentence. ____________ is the key to their happiness; they are satisfied with what they have.

(A) Contentment (B) Ambition (C) Perseverance (D) Hunger Q.3 Which of the following options is the closest in meaning to the sentence below?

“As a woman, I have no country.”

(A) Women have no country. (B) Women are not citizens of any country. (C) Women’s solidarity knows no national boundaries. (D) Women of all countries have equal legal rights.

Q.4 In any given year, the probability of an earthquake greater than Magnitude 6 occurring in the

Garhwal Himalayas is 0.04. The average time between successive occurrences of such earthquakes is ____ years.

Q.5 The population of a new city is 5 million and is growing at 20% annually. How many years would

it take to double at this growth rate?

(A) 3-4 years (B) 4-5 years (C) 5-6 years (D) 6-7 years


Q.6 In a group of four children, Som is younger to Riaz. Shiv is elder to Ansu. Ansu is youngest in the

group. Which of the following statements is/are required to find the eldest child in the group? Statements

1. Shiv is younger to Riaz. 2. Shiv is elder to Som.

(A) Statement 1by itself determines the eldest child. (B) Statement 2 by itself determines the eldest child. (C) Statements 1 and 2 are both required to determine the eldest child. (D) Statements 1 and 2 are not sufficient to determine the eldest child.

2014

Q.7 Moving into a world of big data will require us to change our thinking about the merits of exactitude. To apply the conventional mindset of measurement to the digital, connected world of the twenty-first century is to miss a crucial point. As mentioned earlier, the obsession with exactness is an artefact of the information-deprived analog era. When data was sparse, every data point was critical, and thus great care was taken to avoid letting any point bias the analysis. From “BIG DATA” Viktor Mayer-Schonberger and Kenneth Cukier The main point of the paragraph is:

(A) The twenty-first century is a digital world (B) Big data is obsessed with exactness (C) Exactitude is not critical in dealing with big data (D) Sparse data leads to a bias in the analysis

Q.8 The total exports and revenues from the exports of a country are given in the two pie charts below.

The pie chart for exports shows the quantity of each item as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 5 lakh tonnes and the total revenues are 250 crore rupees. What is the ratio of the revenue generated through export of Item 1 per kilogram to the revenue generated through export of Item 4 per kilogram?

(A) 1:2 (B) 2:1 (C) 1:4 (D) 4:1

Q.9 X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is

1 km east of P. What is the distance between X and Q in km?

(A) 1 (B) √2 (C) √3 (D) 2 Q.10 10% of the population in a town is HIV+. A new diagnostic kit for HIV detection is available; this

kit correctly identifies HIV+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _______

Item 111%

Item 220%

Item 319%Item 4

22%

Item 512%

Item 616%

Exports

Item 112%

Item 220%

Item 323%

Item 46%

Item 520%

Item 619%

Revenues

2014


Q.1 The system of equations, given below, has

x+2y+4z=2 4x+3y+z=5

3x+2y+3z=1

(A) a unique solution (B) two solutions

(C) no solution (D) more than two solutions Q.2 Directional derivative of 22xz yϕ = − , at the point (1, 3, 2), becomes maximum in the direction of

(A) 4 2 3i j k+ − (B) 4 6 2i j k− + (C) 2 6 2i j k− + (D) 4 6 2i j k− −

Q.3 A metallic sphere of 0.1 m diameter has a thermal conductivity of 10 W/m-K. If the fluid flowing around it has a heat transfer coefficient of 10 W/m2-K and thermal conductivity of 0.4 W/m-K, the value of Biot number is ______

Q.4 A quantitative measure of maintainability is

(A) Downtime (B) Mean Time Between Failure

(C) Mean Time To Repair (D) System availability Q.5 Which one of the following techniques is used to analyze the cause and effect of product failure?

(A) Quality Function Deployment

(B) Fault Tree Analysis

(C) Value Analysis

(D) Failure Mode and Effect Analysis Q.6 As the product passes through different stages of product life cycle, the product variety

(A) increases (B) decreases and then increases

(C) remains the same (D) decreases

2014

Q.7 A machine has been purchased for Rs.100,000 and its useful life is estimated to be 10 years. Its scrap value at the end of 10 years is estimated as Rs.20,000. If the depreciation is determined using the declining balance method, the value of depreciation (in Rs.) during the first year is _______

Q.8 A company wants to determine the proportion of time workers are idle. In a pilot study, the proportion of idle time was found to be 0.16. If the company wants to be 95% confident (z-value = 1.96) that the estimated value is within 0.03 of the true proportion, the number of observations required in the study should be _______

Q.9 A manufacturing plant, working in 2 shifts of 8 hrs each, produces 30,000 switch boards using a set of 7 workstations in series. The cycle time, in seconds, is _______

Q.10 A simple random sample of 100 observations was taken from a large population. The sample mean

and the standard deviation were determined to be 80 and 12, respectively. The standard error of mean is _______

Q.11 The diameter of a shaft must be within a tolerance of 0.02 of the nominal diameter. Which control

chart is useful to determine that the process is in statistical control?

(A) p chart (B) c chart

(C) X and R chart (D) U chart

Q.12 Which one of the following is not a characteristic of JIT manufacturing system?

(A) Reduction of lot sizes (B) Efficient use of buffer inventory

(C) Small but frequent deliveries (D) Higher productivity

Q.13 Relationship between Young’s Modulus (E), Shear Modulus (G), and Poisson’s Ratio (μ), for a

material obeying the Hooke’s Law, is

(A) 𝐸𝐸 = 𝐺𝐺(2+μ)

(B) 𝐸𝐸 = 2𝐺𝐺(1+μ)

(C) (1 )E G µ= + (D) 2 (1 )E G µ= +

2014

Q.14 For a metal alloy, which one of the following descriptions relates to the stress-relief annealing process?

(A) Heating the workpiece material above its recrystallization temperature, soaking and then cooling in still air

(B) Heating the workpiece material below its recrystallization temperature, holding for some time and then furnace cooling

(C) Heating the workpiece material up to its recrystallization temperature and then rapid cooling

(D) Heating the workpiece up to its recrystallization temperature and cooling to room temperature alternately for a few cycles

Q.15 Generative Approach of Computer Aided Process Planning is NOT based on

(i) part coding using Group Technology (ii) part feature recognition and extraction (iii) database of standard process plans for

part families

(iv) geometric modelling of part

(A) (i) and (ii) (B) (i) and (iii) (C) (i),(ii) and (iii) (D) (i), (ii) and (iv) Q.16 Which one of the following methods is NOT used for producing metal powders?

(A) Atomization (B) Compaction

(C) Machining and grinding (D) Electrolysis Q.17 In an open loop, point-to-point controlled CNC drilling machine, a stepper motor, producing 200

angular steps per revolution, drives the table of a drilling machine by one angular step per each pulse generated by a pulse generator (shown in figure). Each angular step moves the table by one Basic Length Unit (BLU) along X axis with a lead screw having a pitch of 4 mm. If the frequency of pulse generator is doubled, the BLU will

(A) become double of previous value (B) become half of previous value (C) remain the same

(D) become zero

Pulse generator pulses Driver Stepper

motor

CNC drill table X axis

2014

Q.18 A spindle speed of 300 rpm and a feed of 0.3 mm/revolution are chosen for longitudinal turning operation on an engine lathe. In finishing pass, roughness on the work surface can be reduced by

(A) reducing the spindle speed (B) increasing the spindle speed (C) reducing the feed of tool (D) increasing the feed of tool

Q.19 Chills are used in casting moulds to

(A) achieve directional solidification (B) reduce the roughness of top surface of the cast product (C) increase the solidification time (D) reserve excess molten metal

Q.20 A moving mandrel is used in

(A) wire drawing (B) forging (C) tube drawing (D) bending Q.21 Brazing and Soldering are

(A) plastic joining methods (B) homogeneous joining methods (C) autogenous joining methods (D) heterogeneous joining methods

Q.22 Match the following:

Group I (Mechanism) Group II (Machines)

P Quick return 1 Lathe Q Apron 2 Shaping R Intermittent indexing 3 Gear hobbing S Differential mechanism 4 Milling

(A) P1-Q2-R4-S3 (B) P2-Q1-R4-S3 (C) P4-Q1-R2-S3 (D) P2-Q3-R1-S4

2014

Q.23 Reaming is a process used for

(A) creating a circular hole in metals (B) cutting a slot on the existing hole surface (C) finishing an existing hole surface (D) making non-circular holes in metals

Q.24 Find the correct combination of manufacturing processes to produce the part, shown in figure, from a blank (holes shown are with square and circular cross-sections).

(A) Drilling and milling on column and knee type universal milling machine

(B) Die-sinking and CNC Wire-cut EDM process

(C) Die-sinking and CNC drilling

(D) CNC Wire-cut EDM process only Q.25 In an open die forging, a circular disc is gradually compressed between two flat platens. The

exponential decay of normal stress on the flat face of the disc, from the center of the disc towards its periphery, indicates that

(A) there is no sticking friction anywhere on the flat face of the disc

(B) sticking friction and sliding friction co-exist on the flat face of the disc

(C) the flat face of the disc is frictionless

(D) there is only sticking friction on the flat face of the disc

2014


Q.26 If 3 2 42x y zϕ = then 2ϕ∇ is

(A) 2 4 2 4 3 2 3 12 4 20xy z x z x y z+ + (B) 2 2 3 4 3 2 2 2 4 24x y z x z x y z+ + (C) 2 4 3 4 3 2 2 12 4 24xy z x z x y z+ + (D) 2 2 4 3 2 2 4 4 24xy z x z x y z+ +

Q.27 Using the Simpson’s 1/3rd rule, the value of ydx∫ computed, for the data given below, is _______

x 1 3 5 y 2 6 4

Q.28 If the equation sin(𝑥𝑥) = 𝑥𝑥2 is solved by Newton Raphson’s method with the initial guess of x=1, then the value of x after 2 iterations would be _______

Q.29 If 2 kg mass of water, with a specific heat of 4.18 kJ/kg-K, is heated from 20°C to 40°C in an open container, then the change in entropy of water, in kJ/K, is ______

Q.30 A gas at a pressure of 500 kPa and volume of 0.75 m3 is contained in a cylinder-piston assembly. When the piston moves slowly in the cylinder, the pressure inside the cylinder varies as V – 1.2. If the final volume of gas becomes doubled, then the work done by the gas, in kJ, is _______

Q.31 Two geometrically identical metallic bars are joined end to end (as shown in Fig.). Bars P and Q have thermal conductivities of 5 W/m-K and 10 W/m-K respectively. The free end of the Bar P is kept at 40°C, while that of Bar Q is at 10°C.

The junction temperature (in °C) for steady state heat flow is _______

Q.32 A metallic sphere of 1 kg mass, with surface area of 0.0314 m2, is maintained at an initial temperature of 50°C. The fluid circulating around the sphere is maintained at a temperature of 10°C. Specific heat of metallic sphere is 314 J/kg-K and the heat transfer coefficient between the fluid and the sphere is 10 W/m2-K. The time taken (in seconds) for the sphere to cool down to 20°C is ________

2014

Q.33 An element, shown below, is subjected to stresses: σx = 5 kN/mm2, σy = 3 kN/mm2 and τ = 1 kN/mm2. The magnitudes and direction of principal stresses σ1, σ2 (in kN/mm2) and φ (in degrees) are

(A) 5.41, 2.58, –22.5 (B) 5.41, 2.58, –45 (C) 5.0, 3.0, –22.5 (D) 4.0, 4.0, –22.5 Q.34 Each axis of NC machine is driven by a stepper motor drive with a lead screw. The pitch of lead

screw is p mm. The step angle of stepper motor per pulse input is α degrees/pulse. The ratio of gear drive in stepper motor drive is g (number of turns of the motor for each single turn of the lead screw). The number of pulses required to achieve a linear movement of x mm is

(A) 360

g xp

α (B)

360g xp

(C) 360

g xp

(D) 360g x

pα

Q.35 A uniformly distributed load (q) of 1500 N/m is applied on a simply supported beam LMN with an

overhang of 0.5 m. Which one of the following statements is FALSE?

(A) Reaction forces at L and M are 1 kN and 2 kN

(B) Bending moment is zero at the points L, N and at a point in between L and M

(C) The bending moment is zero at points L and N only

(D) The shear force is zero at points L, N and at a point in between L and M

2014

Q.36 A CNC instruction G91G01X30Y40F100 commands the movement of tool along the path at a feed rate of 100 mm/min (G91- incremental format and G01- linear interpolation). The feed rate of the tool (in mm/min) along the X axis will be _______

Q.37 Elastic moduli of a fibre reinforced plastic composite and fibres are 200 GPa and 400 GPa, respectively. The longitudinal fibres are taking up 50% of the load. Assuming the area fraction equal to the volume fraction, the volume fraction of the fibres will be _______

Q.38 The processing times and the due dates of 4 independent jobs processed by a single machine in a shop are given in the table. The average lateness of the jobs (in days) following the Shortest Processing Time (SPT) rule is _______

Job Processing Time (in days)

Due Date (in days)

1 4 6 2 7 9 3 2 18 4 8 15

Q.39 The annual requirement of a raw material item is 10,000 units. The holding cost of inventory for the item is 80 paise per unit per year and the ordering cost is Rs. 40 per order. The order quantity presently is 800 units per order. Assume that there are no other costs. Which one of the following observations is CORRECT?

(A) The order quantity is optimal and total ordering cost is equal to total holding cost. (B) The order quantity is optimal and total ordering cost is more than total holding cost. (C) The order quantity is not optimal and total ordering cost is equal to total holding cost. (D) The order quantity is not optimal and total ordering cost is more than total holding cost.

Q.40 In a single-server queuing system, arrivals are Poisson distributed with a mean of 16 per hour and the exponential service time is 3 minutes per person on the average. What would be the expected number of persons in the queue (Lq) for the queue disciplines of First-come-first-serve (FCFS) and Last-come-first serve (LCFS)?

(A) 4.0, 4.0 (B) 4.0, 3.2

(C) 3.2, 4.0 (D) 3.2, 3.2

2014

Q.41 A project consisting of five activities needs crashing. The details of crashing that was carried out are given in the table.

If the overhead cost of the project is Rs. 200 per day, then the net change in project cost (in Rs.) because of crashing is _______

Activity Normal Time (days)

Shortest Time (days)

Cost in Rs. for Reduction/day

Actually Crashed by (days)

1-2 6 4 100 1 day 1-3 7 5 100 2 days 1-4 10 7 100 1 day 2-4 4 3 200 Not Crashed 3-4 5 4 200 1 day

Q.42 Two systems, P and Q, contain 3 components each. Reliability of the components is measured for 1000 hours operations and time-to-failure distributions for all the components are found to be exponential. System P components are connected in a series parallel structure with each component having a reliability of 0.8. System Q components, on the other hand, are connected in series with each component having a reliability of 0.9. See the configuration of the systems below. The reliabilities of System P and System Q will be respectively

(A) 0.768, 0.729 (B) 0.512, 0.729 (C) 0.5, 0.271 (D) 0.232, 0.271 Q.43 Marks obtained by 100 students in an examination are given in the table.

Sl. No. Marks Obtained Number of Students

1. 25 20 2. 30 20 3. 35 40 4. 40 20

What would be the mean, median, and mode of the marks obtained by the students?

(A) Mean 33; Median 35; Mode 40 (B) Mean 35; Median 32.5; Mode 40

(C) Mean 33; Median 35; Mode 35 (D) Mean 35; Median 32.5; Mode 35

0.8 0.8

0.8

System P System Q

0.9 0.9 0.9

2014

Q.44 In a given day in the rainy season, it may rain 70% of the time. If it rains, chance that a village fair will make a loss on that day is 80%. However, if it does not rain, chance that the fair will make a loss on that day is only 10%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day?

(A) 3/10 (B) 9/11 (C) 14/17 (D) 27/41

Q.45 For the linear programming problem given below, find the number of feasible corner point solutions. Is the optimal solution degenerate? Maximize z = 2x1 + 3x2 Subject to: x1 + 2x2 ≤ 60; 2x1 + x2 ≤ 30; x1 – x2 ≥ – 10; x1 ≥ 0; x2 ≥ 0

(A) 4; No (B) 4; Yes (C) 5; No (D) 5; Yes Q.46 A manufacturing company must select a process for its new product, VS-5, from among two

alternatives. The following cost data have been gathered.

Cost Process X Process Y Fixed Rs. 10,000 Rs. 40,000 Variable Rs. 5/unit Rs. 2/unit

If the objective is to select a process with the least total cost for a given demand, which one of the following is the most appropriate choice?

(A) Below 10,000 units, Process X; Above 10,000 units, Process Y

(B) Below 10,000 units, Process Y; Above 10,000 units, Process X

(C) Below 20,000 units, Process X; Above 20,000 units, Process Y

(D) Below 20,000 units, Process Y; Above 20,000 units, Process X Q.47 The following data refers to a manufacturing plant.

Current Year Previous Year

Revenue generated (in Rs.) 200,000 220,000 Number of units produced 1000 1200

Piece rate of workers (in Rs.) 22 18 Assuming the previous year to be the base year, the labor productivity index for this plant is _______

2014

Q.48 A manufacturing company producing ball bearings has conducted a time study for 10 cycles of a job consisting of three elements. The details are shown in the table below.

Job elements Average elemental time (in minutes)

Performance rating factor

1 0.12 0.8 2 0.34 1.1 3 0.48 1.2

If the permissible allowance is 15%, then the standard time (in minutes) is _______

Q.49 A control chart for number of non-conformities per unit is to be constructed for a manufacturing process. Sixteen non-conformities were recorded while inspecting 30 units. How should the Upper Control Limit (UCL) and the Lower Control Limit (LCL) be set for this control chart?

(A) UCL = 1.81, LCL = 0.70 (B) UCL = 2.71, LCL = 0.00

(C) UCL = 0.533, LCL = – 0.533 (D) UCL = 3.10, LCL = – 1.46

Q.50 For a given volume of a riser, if the solidification time of the molten metal in riser needs to be quadrupled, the surface area of the riser should be made

(A) one-fourth (B) half (C) double (D) four times Q.51 A 80 mm thick steel plate with 400 mm width is rolled to 40 mm thickness in 4 passes with equal

reduction in each pass, by using rolls of 800 mm diameter. Assuming the plane-strain deformation, what is the minimum coefficient of friction required for unaided rolling to be possible?

(A) 0.111 (B) 0.158 (C) 0.223 (D) 0.316 Q.52 In an arc welding operation, carried out with a power source maintained at 40 volts and

400 amperes, the consumable electrode melts and just fills the gap between the metal plates to be butt-welded. The heat transfer efficiency for the process is 0.8, melting efficiency is 0.3 and the heat required to melt the electrode is 20 J/mm3. If the travel speed of the electrode is 4 mm/s, the cross-sectional area, in mm2, of the weld joint is _______

Q.53 A hard ceramic marble, having density (ρ) of 3000 kg/m3 and diameter (d) of 0.025 m, is dropped accidentally from a static weather balloon at a height of 1 km above the roof of a greenhouse. The flow stress of roof material (σ) is 2.5 GPa. The marble hits and creates an indentation on the roof. Assume that the principle of creation of indentation is the same as that in case of abrasive jet machining (AJM). The acceleration due to gravity (g) is 10 m/s2. If V is the velocity, in m/s, of the

marble at the time it hits the greenhouse, the indentation depth ( 10006

d Vρδσ

= × × × ), in mm,

is _______

2014

Q.54 An HSS drill of 20 mm diameter with 5 mm cone height is used to drill a through hole in a steel work-piece of 50 mm thickness. Cutting speed of 10 m/min and feed rate of 0.3 mm/rev are used. The drilling time, in seconds, neglecting the approach and over travel, is _______

Q.55 The alignment test “Spindle square with base plate” is applied to the radial drilling machine. A dial indicator is fixed to the cylindrical spindle and the spindle is rotated to make the indicator touch the base plate at different points. This test inspects whether the

(A) spindle vertical feed axis is perpendicular to the base plate

(B) axis of symmetry of the cylindrical spindle is perpendicular to the base plate

(C) axis of symmetry, the rotational axis and the vertical feed axis of the spindle are all coincident

(D) spindle rotational axis is perpendicular to the base plate

2014

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

Q.1 The fixed cost and the variable cost of production of a product are Rs. 20000 and Rs. 50 per unit, respectively. The demand for the item is 500 units. To break even, the unit price of the items in Rs. should be

(A) 50 (B) 75 (C) 90 (D) 100 Q.2 Therbligs refer to the

(A) basic types of fixtures used in machining. (B) fundamental motions used in manual work. (C) basic types of waste in manufacturing process. (D) fundamental types of material handling systems.

Q.3 Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their

arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is

(A) 3 (B) 4 (C) 5 (D) 6 Q.4 Circular blanks of 10 mm diameter are punched from an aluminum sheet of 2 mm thickness. The

shear strength of aluminum is 80 MPa. The minimum punching force required in kN is

(A) 2.57 (B) 3.29 (C) 5.03 (D) 6.33 Q.5 A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire

method. The diameter of the best size wire in mm is

(A) 0.866 (B) 1.000 (C) 1.154 (D) 2.000 Q.6 Match the CORRECT pairs.

Processes Characteristics / Applications

P. Friction Welding 1. Non-consumable electrode Q. Gas Metal Arc Welding 2. Joining of thick plates R. Tungsten Inert Gas Welding 3. Consumable electrode wire S. Electroslag Welding 4. Joining of cylindrical dissimilar materials

(A) P-4, Q-3, R-1, S-2 (B) P-4, Q-2, R-3, S-1 (C) P-2, Q-3, R-4, S-1 (D) P-2, Q-4, R-1, S-3

Q.7 In a rolling process, the state of stress of the material undergoing deformation is

(A) pure compression (B) pure shear (C) compression and shear (D) tension and shear

Q.8 Consider one-dimensional steady state heat conduction along x-axis (0 ≤ x ≤ L), through a plane

wall; with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.

(A) The direction of heat transfer will be from the surface at 100°C to the surface at 0°C. (B) The maximum temperature inside the wall must be greater than 100°C. (C) The temperature distribution is linear within the wall. (D) The temperature distribution is symmetric about the mid-plane of the wall.

2013

Q.9 A cylinder contains 5 m3 of an ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is

(A) 804.7 (B) 953.2 (C) 981.7 (D) 1012.2 Q.10 A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m

and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is

(A) PQ (B) QR (C) RS (D) SP Q.11 Let X be a normal random variable with mean 1 and variance 4. The probability P{ X<0} is

(A) 0.5 (B) greater than zero and less than 0.5 (C) greater than 0.5 and less than 1.0 (D) 1.0

Q.12 Choose the CORRECT set of functions, which are linearly dependent.

(A) xsin , 2sin x and 2cos x (B) cosx , xsin and xtan

(C) cos 2x , 2sin x and 2cos x (D) cos 2x , xsin and xcos

Q.13 The eigenvalues of a symmetric matrix are all

(A) complex with non-zero positive imaginary part (B) complex with non-zero negative imaginary part (C) real (D) pure imaginary

Q.14 The partial differential equation 2

2

x

u

x

uu

t

u

∂∂=

∂∂+

∂∂

is a

(A) linear equation of order 2 (B) non-linear equation of order 1 (C) linear equation of order 1 (D) non-linear equation of order 2

Q.15 Match the CORRECT pairs.

Numerical Integration Scheme Order of Fitting Polynomial

P. Simpson’s 3/8 Rule 1. First Q. Trapezoidal Rule 2. Second R. Simpson’s 1/3 Rule 3. Third

(A) P-2, Q-1, R-3 (B) P-3, Q-2, R-1 (C) P-1, Q-2, R-3 (D) P-3, Q-1, R-2

2013

Q.16 A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from 1E to 2E along the length of the rod, the normal stress developed at the section-SS is

(A) A

P (B)

( )( )21

21

EEA

EEP

+−

(C) 1

2

AE

PE (D)

2

1

AE

PE

Q.17 For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the

pressure drop p∆ over a length L and the wall shear stress wτ are related by

(A) L

Dpw 4

∆=τ (B) 2

2

4L

Dpw

∆=τ (C) L

Dpw 2

∆=τ (D) D

Lpw

∆= 4τ

Q.18 For a ductile material, toughness is a measure of

(A) resistance to scratching (B) ability to absorb energy upto fracture (C) ability to absorb energy till elastic limit (D) resistance to indentation

Q.19 A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same

material, which is 8 times heavier than the original casting, will be

(A) 10 (B) 20 (C) 24 (D) 40 Q.20 A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The

rotational speed of the workpiece is 160 rpm. The material removal rate in mm3/s is

(A) 160 (B) 167.6 (C) 1600 (D) 1675.5 Q.21 In the 3-2-1 principle of fixture design, 3 refers to the number of

(A) clamps required (B) locators on the primary datum face (C) degrees of freedom of the workpiece (D) operations carried out on the primary datum face

Q.22 In simple exponential smoothing forecasting, to give higher weightage to recent demand

information, the smoothing constant must be close to

(A) −1 (B) zero (C) 0.5 (D) 1

S

P P

S

L

L/2

E1 E2

2013

Q.23 A company manufactures 1000 toys every day. On an average, 10% of the toys are defective and 40% of the defective toys can be reworked into defect-free ones. The average number of defect-free toys manufactured daily is

(A) 900 (B) 920 (C) 940 (D) 960 Q.24 The type of control chart used to monitor the amount of dispersion in a sample is

(A) c-chart (B) p-chart (C) x -chart (D) R-chart Q.25 Which one of the following is modeled based on adaptation capabilities of biological systems?

(A) Relational database (B) Fuzzy system (C) Simulated annealing algorithm (D) Genetic algorithm

2013

Q.26 to Q.55 carry two marks each. Q.26 A company plans to purchase a machine whose uptime needs to be atleast 95%. They have

shortlisted two models of the machine with the following operational characteristics:

Machine MTBF (hr) MTTR (hr) Model M 60 4 Model N 48 2

The company should buy

(A) only Model M (B) only Model N (C) either Model M or N (D) neither Model M nor N

Q.27 A manufacturer produces bars designed to be of 10 mm diameter with a tolerance of ±0.1 mm.

Historical data indicates that manufactured bars have an average diameter of 9.98 mm with a standard deviation of 0.15 mm. The process capability index is

(A) 0.08 (B) 0.12 (C) 0.18 (D) 0.27 Q.28 Let (P) denote the linear programming formulation of a transportation problem with m sources and

n destinations. Then, the dual linear program of (P) has

(A) nm× variables and nm× constraints (B) nm× variables and nm + constraints (C) nm + variables and nm + constraints (D) nm + variables and nm× constraints

Q.29 Following data refers to an automat and a center lathe, which are being compared to machine a

batch of parts in a manufacturing shop.

Automat Center Lathe Machine Set-up Time in min 120 30 Machine Set-up Cost in Rs./min 800 150 Machining Time per piece in min 2 25 Machining Cost in Rs./min 500 100

Automat will be economical if the batch size exceeds

(A) 28 (B) 32 (C) 61 (D) 75

Q.30 Cylindrical pins of 020.0010.025

++ mm diameter are electroplated in a shop. Thickness of the plating is

0.230± micron. Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is

(A) 25.042 (B) 25.052 (C) 25.074 (D) 25.084 Q.31 During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current

of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be

(A) 0.11 (B) 0.23 (C) 0.30 (D) 0.52

2013

Q.32 Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below: Specific enthalpy (kJ/kg) Velocity (m/s) Inlet steam condition 3250 180 Exit steam condition 2360 5 The rate of heat loss from the turbine per kg of steam flow rate is 5 kW. Neglecting changes in potential energy of steam, the power developed in kW by the steam turbine per kg of steam flow rate, is

(A) 901.2 (B) 911.2 (C) 17072.5 (D) 17082.5 Q.33 A simply supported beam of length L is subjected to a varying distributed load sin (3π x/L) Nm−1,

where the distance is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

(A) zero (B) π3L (C) πL (D) πL2

Q.34 The probability that a student knows the correct answer to a multiple choice question is 3

2. If the

student does not know the answer, then the student guesses the answer. The probability of the

guessed answer being correct is 4

1. Given that the student has answered the question correctly, the

conditional probability that the student knows the correct answer is

(A) 3

2 (B)

4

3 (C)

6

5 (D)

9

8

Q.35 The solution to the differential equation 02

2

=−dx

duk

dx

ud where k is a constant, subjected to the

boundary conditions u(0) = 0 and u(L) = U, is

(A) L

xUu = (B)

−−=

kL

kx

e

eUu

1

1 (C)

−−= −

−

kL

kx

e

eUu

1

1 (D)

++=

kL

kx

e

eUu

1

1

Q.36 The value of the definite integral 1

ex∫ ( ) dxxln is

(A) 9

2

9

4 3 +e (B) 9

4

9

2 3 −e (C) 9

4

9

2 3 +e (D) 9

2

9

4 3 −e

Q.37 The following surface integral is to be evaluated over a sphere for the given steady velocity vector

field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.

dAS

).(4

1∫∫ nF

where S is the sphere, 1222 =++ zyx and n is the outward unit normal vector to the sphere. The value of the surface integral is

(A) π (B) 2π (C) 43π (D) 4π

2013

Q.38 The function ( )tf satisfies the differential equation 02

2

=+ fdt

fd and the auxiliary conditions,

4)0( ,0)0( ==dt

dff . The Laplace transform of )(tf is given by

(A) 1

2

+s (B)

1

4

+s (C)

1

42 +s

(D) 1

24 +s

Q.39 A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a

mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg-m2 is

(A) 25 (B) 50 (C) 100 (D) 125 Q.40 A single riveted lap joint of two similar plates as shown in the figure below has the following

geometrical and material details. If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is

(A) 83 (B) 125 (C) 167 (D) 501 Q.41 Two cutting tools are being compared for a machining operation. The tool life equations are:

Carbide tool: 30006.1 =VT

HSS tool: 2006.0 =VT where V is the cutting speed in m/min and T is the tool life in min. The carbide tool will provide higher tool life if the cutting speed in m/min exceeds

(A) 15.0 (B) 39.4 (C) 49.3 (D) 60.0 Q.42 In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes

through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be

(A) (7.5, 5) (B) (10, 5) (C) (7.5, −5) (D) (10, −5)

plate width w = 200 mm plate thickness t = 5 mm number of rivets n = 3 rivet diameter dr = 10 mm rivet hole diameter dh = 11 mm allowable tensile stress of plate σp = 200 MPa allowable bearing stress of rivet σc = 150 MPa

P

t t

w w P

2013

Q.43 In water jet machining, the water jet is issued through a 0.3 mm diameter orifice at a pressure of 400 MPa. The density of water is 1000 kg/m3. The coefficient of discharge is 1.0. Neglecting all losses during water jet formation through the orifice, the power of the water jet in kW is

(A) 25.3 (B) 50.6 (C) 75.9 (D) 101.2 Q.44 A linear programming problem is shown below.

Maximize 3x + 7y Subject to 3x + 7y ≤ 10 4x + 6y ≤ 8 x, y ≥ 0 It has

(A) an unbounded objective function (B) exactly one optimal solution (C) exactly two optimal solutions (D) infinitely many optimal solutions

Q.45 Consider a two machine flow shop where jobs are first processed in Machine X and then in Machine Y, in the same sequence. The processing times of four jobs (1, 2, 3 and 4) on the machines are:

Job Processing time (in min)

Machine X Machine Y 1 6 5 2 3 4 3 7 6 4 5 4

The sequence of jobs on the machines that minimizes make span is

(A) 2−3−1−4 (B) 1−2−3−4 (C) 2−1−3−4 (D) 3−1−4−2 Q.46 Match the CORRECT pairs.

Group I Group II P. Man-machine chart 1. Determines standard time of jobs Q. Learning curve 2. Finds the preferred method of doing work R. Time study 3. Measures work improvement S. Motion study 4. Shows idle times

(A) P-2, Q-3, R-4, S-1 (B) P-3, Q-2, R-4, S-1 (C) P-4, Q-1, R-3, S-2 (D) P-4, Q-3, R-1, S-2

Q.47 A firm produces 120 units of product in every 8 hour shift. Four operations as given below are needed to manufacture each unit of product.

Operation Precedence Processing time (in min) P none 1 Q P 2 R P 4 S Q, R 3

The above operations are to be assigned to workstations, such that one or more operations are performed in each workstation. Only one unit of product will be processed in each workstation at a time. The minimum number of workstations that will achieve the production target, without violating the precedence constraints, is

(A) 1 (B) 2 (C) 3 (D) 4

2013

Common Data Questions Common Data for Questions 48 and 49: A disc of 200 mm outer and 80 mm inner diameter is faced at a feed of 0.1 mm/rev with a depth of cut of 1 mm. The facing operation is undertaken at a constant cutting speed of 90 m/min in a CNC lathe. The main (tangential) cutting force is 200 N.

Q.48 Neglecting the contribution of the feed force towards cutting power, the specific cutting energy in J/mm3 is (A) 0.2 (B) 2 (C) 200 (D) 2000

Q.49 Assuming approach and over-travel of the cutting tool to be zero, the machining time in min is

(A) 2.93 (B) 5.86 (C) 6.66 (D) 13.33 Common Data for Questions 50 and 51: The demand for soap at a retailer is 40 kg per day. The retailer buys soap from a company in bulk at the cost of Rs. 50 per kg. The retailer incurs a cost of Rs. 200 to place an order to the company, and a holding cost of Rs. 0.1 per kg per day to store the soap. The lead time between the placing and receiving of orders is 3 days. The retailer’s current ordering policy is to order 200 kg every 5 days.

Q.50 To avoid stock out situations, the retailer needs to place orders when the inventory level (in kg) drops to (A) 40 (B) 60 (C) 80 (D) 120

Q.51 If the retailer uses an optimum order policy to minimize the total cost, the saving in Rs. in the total

cost as compared to the current policy will be

(A) 10 (B) 20 (C) 40 (D) 50

2013

Linked Answer Questions Statement for Linked Answer Questions 52 and 53: A project consists of seven activities, whose durations are independent normal random variables, as shown in the table below. Activities are identified by their beginning node i and ending node j.

Activity (node i – node j)

Mean duration (in days)

Standard deviation (in days)

1 − 2 6 1 1 − 3 9 2 2 − 3 2 0.5 2 − 4 8 0.5 3 − 4 7 1 3 − 5 8 1 4 − 5 4 1

Q.52 The critical path of the project, based on the mean activity duration, is (A) 1−2−3−4−5 (B) 1−2−3−5 (C) 1−3−5 (D) 1−3−4−5

Q.53 Let Φ denote the cumulative distribution function of the standard normal random variable. The

probability that all activities on the critical path, based on the mean activity duration, are completed in 22 days is

(A) Φ−1(0.333) (B) Φ−1(0.816) (C) Φ−1(1.664) (D) Φ−1(2.235) Statement for Linked Answer Questions 54 and 55: In orthogonal turning of a bar of 100 mm diameter with a feed of 0.25 mm/rev, depth of cut of 4 mm and cutting velocity of 90 m/min, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at the chip-tool interface. The main (tangential) cutting force is 1500 N.

Q.54 The orthogonal rake angle of the cutting tool in degree is (A) zero (B) 3.58 (C) 5 (D) 7.16

Q.55 The normal force acting at the chip-tool interface in N is

(A) 1000 (B) 1500 (C) 2000 (D) 2500

2013

General Aptitude (GA) Questions

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

Q.56 Were you a bird, you ___________________ in the sky.

(A) would fly (B) shall fly (C) should fly (D) shall have flown Q.57 Choose the grammatically INCORRECT sentence:

(A) He is of Asian origin. (B) They belonged to Africa. (C) She is an European. (D) They migrated from India to Australia.

Q.58 Complete the sentence:

Universalism is to particularism as diffuseness is to _______________.

(A) specificity (B) neutrality (C) generality (D) adaptation Q.59 What will be the maximum sum of 44, 42, 40, ...... ?

(A) 502 (B) 504 (C) 506 (D) 500 Q.60 Which one of the following options is the closest in meaning to the word given below?

Nadir

(A) Highest (B) Lowest (C) Medium (D) Integration

Q.61 to Q.65 carry two marks each.

Q.61 A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is

(A) 36 (B) 30 (C) 24 (D) 18 Q.62 The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of

the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

(A) 16,500 (B) 15,180 (C) 11,000 (D) 10,120 Q.63 Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random.

What is the probability that the selected number is not divisible by 7?

(A) 13/90 (B) 12/90 (C) 78/90 (D) 77/90

2013

Q.64 After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history.

Which one of the following assertions is best supported by the above information?

(A) Failure is the pillar of success. (B) Honesty is the best policy. (C) Life begins and ends with adventures. (D) No adversity justifies giving up hope.

Q.65 Find the sum of the expression

8180

1...............

43

1

32

1

21

1

+++

++

++

+

(A) 7 (B) 8 (C) 9 (D) 10

2013


Q.1 20

1 coslimx

x

x

is

(A) 1/4 (B) 1/2 (C) 1 (D) 2

Q.2 For the spherical surface 2 2 2 1x y z , the unit outward normal vector at the point

(1 1

, ,02 2

) is given by

(A) 1 1ˆ ˆ2 2

i j (B) 1 1ˆ ˆ2 2

i j

(C) k̂ (D) 1 1 1 ˆˆ ˆ3 3 3

i j k

Q.3 Consider the function ( )f x x in the interval 1 1x . At the point x = 0, f(x) is

(A) continuous and differentiable.

(B) non-continuous and differentiable.

(C) continuous and non-differentiable.

(D) neither continuous nor differentiable.

Q.4 At x = 0, the function 3( ) 1f x x has

(A) a maximum value (B) a minimum value

(C) a singularity (D) a point of inflection Q.5 The area enclosed between the straight line y = x and the parabola y = x

2 in the x-y plane is

(A) 1/6 (B) 1/4 (C) 1/3 (D) 1/2 Q.6 For a long slender column of uniform cross section, the ratio of critical buckling load for the case

with both ends clamped to the case with both ends hinged is

(A) 1 (B) 2 (C) 4 (D) 8 Q.7 A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is

increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same,

the percentage change in the circumferential (hoop) stress is

(A) 0 (B) 1 (C) 1.08 (D) 2.02 Q.8 A cantilever beam of length L is subjected to a moment M at the free end. The moment of inertia of

the beam cross section about the neutral axis is I and the Young’s modulus is E. The magnitude of

the maximum deflection is

(A)

2

2

ML

EI (B)

2ML

EI (C)

22ML

EI (D)

24ML

EI

Q.9 A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a

flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is

(A) 395 (B) 790

(C) 1580 (D) 3160

2012

Q.10 In the mechanism given below, if the angular velocity of the eccentric circular disc is 1 rad/s, the

angular velocity (rad/s) of the follower link for the instant shown in the figure is

(A) 0.05 (B) 0.1 (C) 5.0 (D) 10.0 Q.11 Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and

leaves as a saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the

saturated liquid and vapor at 15 kPa are hf = 225.94 kJ/kg and hg = 2598.3 kJ/kg respectively. The

mass flow rate of steam is 10 kg/s. Kinetic and potential energy changes are negligible. The power

output of the turbine in MW is

(A) 6.5 (B) 8.9 (C) 9.1 (D) 27.0 Q.12 An ideal gas of mass m and temperature T1 undergoes a reversible isothermal process from an

initial pressure P1 to final pressure P2. The heat loss during the process is Q. The entropy change S

of the gas is

(A) 2

1

lnP

mRP

(B) 1

2

lnP

mRP

(C) 2

1 1

lnP Q

mRP T

(D) zero

Q.13 For an opaque surface, the absorptivity , transmissivity and reflectivity are related by

the equation:

(A) (B) 0 (C) 1 (D) 0 Q.14 Which one of the following configurations has the highest fin effectiveness?

(A) Thin, closely spaced fins (B) Thin, widely spaced fins

(C) Thick, widely spaced fins (D) Thick, closely spaced fins Q.15 Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of

length 500 m. The volumetric flow rate is 0.2 m3/s. The head loss (in m) due to friction is (assume

g = 9.81 m/s2)

(A) 116.18 (B) 0.116 (C) 18.22 (D) 232.36 Q.16 A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies

to a height of 25 mm. The percentage change in diameter is

(A) 0 (B) 2.07 (C) 20.7 (D) 41.4

Note: All dimensions are in mm.

45

25

5

2012

Q.17 In an interchangeable assembly, shafts of size 010.0040.0

000.25

mm mate with holes of size

020.0030.0

000.25

mm. The maximum interference (in microns) in the assembly is

(A) 40 (B) 30 (C) 20 (D) 10

Q.18 A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a

cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm).

The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is

(A) 120 (B) 170 (C) 180 (D) 240

Q.19 Match the following metal forming processes with their associated stresses in the workpiece.

Metal forming process Type of stress

1. Coining P. Tensile

2. Wire Drawing Q. Shear

3. Blanking R. Tensile and compressive

4. Deep Drawing S. Compressive

(A) 1-S, 2-P, 3-Q, 4-R (B) 1-S, 2-P, 3-R, 4-Q

(C) 1-P, 2-Q, 3-S, 4-R (D) 1-P, 2-R, 3-Q, 4-S

Q.20 During normalizing process of steel, the specimen is heated

(A) between the upper and lower critical temperature and cooled in still air.

(B) above the upper critical temperature and cooled in furnace.

(C) above the upper critical temperature and cooled in still air.

(D) between the upper and lower critical temperature and cooled in furnace.

Q.21 In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the

material removal rate

(A) increases continuously.

(B) decreases continuously.

(C) decreases, becomes stable and then increases.

(D) increases, becomes stable and then decreases.

Q.22 Which one of the following is NOT a decision taken during the aggregate production planning

stage?

(A) Scheduling of machines (B) Amount of labour to be committed

(C) Rate at which production should happen (D) Inventory to be carried forward

Q.23 Which one of the following is NOT associated with the process of new product development?

(A) QFD (B) FEMA (C) KANBAN (D) DFMA

2012

Q.24 A process needs to be standardized for method and time. Which one of the following represents the

sequence of work study experiments?

(A) Time study followed by method study

(B) Only time study

(C) Time study and method study simultaneously

(D) Method study followed by time study

Q.25 Reduction in the variability of manufactured product characteristics will definitely result in

observations close to

(A) the upper control limit in X chart.

(B) the lower control limit in X chart.

(C) the lower control limit in R chart.

(D) the center line in R chart.

2012

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

Q.26

2 4

2 2 5

1

x y z

x y z

x y z

The system of algebraic equations given above has

(A) a unique solution of x = 1, y = 1 and z = 1.

(B) only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0).

(C) infinite number of solutions.

(D) no feasible solution.

Q.27 For the matrix A = 5 3

1 3

, ONE of the normalized eigen vectors is given as

(A)

1

2

3

2

(B)

1

2

1

2

(C)

3

10

1

10

(D)

1

5

2

5

Q.28 Consider the differential equation

22

24 0

d y dyx x y

dx dx with the boundary conditions of

0 0y and 1 1y . The complete solution of the differential equation is

(A) 2x (B) sin

2

x

(C) sin2

x xe

(D) sin2

x xe

Q.29 The inverse Laplace transform of the function 1

( )( 1)

F ss s

is given by

(A) ( ) sinf t t (B) tetf t sin)(

(C) ( ) tf t e (D) ( ) 1 tf t e

Q.30 A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one

after another, without replacement. The probability that the selected set contains one red ball and

two black balls is

(A) 1/20 (B) 1/12 (C) 3/10 (D) 1/2

Q.31 The state of stress at a point under plane stress condition is

σxx = 40 MPa, σyy = 100 MPa and τxy = 40 MPa.

The radius of the Mohr’s circle representing the given state of stress in MPa is

(A) 40 (B) 50 (C) 60 (D) 100

2012

Q.32 A force of 400 N is applied to the brake drum of 0.5 m diameter in a band-brake system as shown in

the figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and the

band is 0.25, the braking torque applied, in N.m is

(A) 100.6 (B) 54.4 (C) 22.1 (D) 15.7 Q.33 Water (Cp = 4.18 kJ/kg.K) at 80°C enters a counterflow heat exchanger with a mass flow rate of

0.5 kg/s. Air (Cp = 1 kJ/kg.K) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness

of the heat exchanger is 0.8, the LMTD (in °C) is

(A) 40 (B) 20 (C) 10 (D) 5 Q.34 Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure.

If D1 and D2 are the diameters of the inner and outer tubes respectively, then the view factor F22 is

given by

(A) 2

1

1D

D

(B) zero (C) 1

2

D

D

(D) 1

2

1D

D

Q.35 A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming

that the changes in h1, h2 and h3 are negligible, the instantaneous discharge velocity is

(A) 1 1 2 23

3 3 3 3

2 1h h

ghh h

(B) 1 2 32g h h h

(C) 1 1 2 2 3 3

1 2 3

2h h h

g

(D) 1 2 3 2 3 1 3 1 2

1 1 2 2 3 3

2h h h h h h

gh h h

2

1

h3

h2

h1

3

400 N

1

2

2012

Q.36 In a DC arc welding operation, the voltage-arc length characteristic was obtained as

20 5arcV l where the arc length l was varied between 5 mm and 7 mm. Here Varc denotes the

arc voltage in Volts. The arc current was varied from 400 A to 500 A. Assuming linear power

source characteristic, the open circuit voltage and the short circuit current for the welding

operation are

(A) 45 V, 450 A (B) 75 V, 750 A (C) 95 V, 950 A (D) 150 V, 1500 A Q.37 In a single pass rolling process using 410 mm diameter steel rollers, a strip of width 140 mm and

thickness 8 mm undergoes 10 % reduction of thickness. The angle of bite in radians is

(A) 0.006 (B) 0.031 (C) 0.062 (D) 0.600 Q.38 A mould having dimensions 100 mm × 90 mm × 20 mm is filled with molten metal through a gate

as shown in the figure. For height h and cross-sectional area A, the mould filling time is t1. The

height is now quadrupled and the cross-sectional area is halved. The corresponding filling time is t2.

The ratio t2/t1 is

(A) 1

2 (B) 1 (C) 2 (D) 2

Q.39 A thin square plate ABCD with side of unit length is kept in the X-Y plane as shown in the figure.

The plate is first rotated by 30° in the anti clockwise direction about the Z-axis with A fixed at the

origin. The plate is then rotated by 90° in the anti clockwise direction about the X-axis with A fixed

at the origin. The final co-ordinates of C are

(A) (1.366, 0.366, 0.0) (B) (0.0, 1.366, 0.366)

(C) (1.366, 0.0, 0.366) (D) (0.366, 0.0, 1.366) Q.40 A sine bar has a length of 250 mm. Each roller has a diameter of 20 mm. During taper angle

measurement of a component, the height from the surface plate to the centre of a roller is 100 mm.

The calculated taper angle (in degrees) is

(A) 21.1 (B) 22.8 (C) 23.6 (D) 68.9

D

X

Y

A

Z

B

C

2012

Q.41 Match the following plastic products with their most appropriate materials.

Products Materials

1. Gears P. Polymethylmethacrylate (PMMA)

2. Helmets Q. Polyamides (PA)

3. Lenses R. Polyethylene (PE)

4. Food packaging S. Acrylonitrile-butadiene-styrene (ABS)

(A) 1-Q, 2-R, 3-S, 4-P (B) 1-S, 2-P, 3-Q, 4-R

(C) 1-P, 2-Q, 3-R, 4-S (D) 1-Q, 2-S, 3-P, 4-R

Q.42 In a shaping process, the number of double strokes per minute is 30 and the quick return ratio is 0.6.

If the length of the stroke is 250 mm, the average cutting velocity in m/min is

(A) 3.0 (B) 4.5 (C) 7.5 (D) 12.0

Q.43 For a linear programming problem, the set of constraints x+y ≤ 2, 3x+5y ≥ 15, x ≥ 0 and y ≥ 0 leads

to

(A) an infeasible solution.

(B) a unique optimal solution.

(C) multiple but finite optimal solutions.

(D) infinite optimal solutions.

Q.44 A milk vendor incurs an overstocking cost of Rs. 2 per litre and a shortage cost of Rs. 0.5 per litre.

The demand is uniformly distributed between 1 litre and 6 litres. Using the Newsvendor Model, the

maximum quantity of milk in litre(s) the vendor should order is

(A) 2 (B) 6 (C) 1 (D) 3

Q.45 The specification limits for the weight of a product are 13.1 kg and 15 kg. If the process has a

variance of weight 0.05 kg2, then the process capability index is

(A) 6.3 (B) 1.9 (C) 1.4 (D) 8.6

Q.46 On an average, there are 30 customers in a queue. If the arrival rate of customers into the system is

16 customers per hour and on average 32 customers leave the system per hour, then the average

number of customers in the system is

(A) 16.5 (B) 30.5 (C) 32.0 (D) 46.0

Q.47 Data for four jobs that need to be processed on a single machine are given below.

Job P Q R S

Processing time (days) 12 9 21 10

Due date (days) 20 40 30 19

All the four jobs are available at time zero. If the jobs are scheduled using the Earliest Due Date

(EDD) algorithm, then the job with maximum tardiness is

(A) P (B) Q (C) R (D) S

2012

Common Data Questions

Common Data for Questions 48 and 49:

Two steel truss members, AC and BC, each having cross sectional area of 100 mm2, are subjected to a

horizontal force F as shown in figure. All the joints are hinged.

Q.48 The maximum force F in kN that can be applied at C such that the axial stress in any of the truss

members DOES NOT exceed 100 MPa is

(A) 8.17 (B) 11.15 (C) 14.14 (D) 22.30

Q.49 If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is

(A) 0.63 (B) 0.32 (C) 1.26 (D) 1.46

Common Data for Questions 50 and 51:

Data for a plain milling operation are given below.

Length of workpiece 200 mm

Cutter diameter 100 mm

No. of teeth 4

Cutter speed 100 rpm

Feed 200 mm/min

Depth of cut 2 mm

Total clearance (entry

and exit)

5 mm

Q.50 Mean undeformed chip thickness (in microns) is

(A) 142 (B) 100 (C) 71 (D) 50

Q.51 Machining time for a single pass (in seconds) is

(A) 60 (B) 66 (C) 126 (D) 150

60º

45º

A

B

C F

2012

Linked Answer Questions

Statement for Linked Answer Questions 52 and 53:

In an EDM process using RC relaxation circuit, a 12 mm diameter through hole is made in a steel plate of

50 mm thickness using a graphite tool and kerosene as dielectric. Assume discharge time to be negligible.

Machining is carried out under the following conditions:

Resistance 40 Ω

Capacitance 20 μF

Supply voltage 220 V

Discharge voltage 110 V

Q.52 The time for one cycle, in milliseconds, is

(A) 0.55 (B) 0.32 (C) 0.89 (D) 0.24

Q.53 Average power input (in kW) is

(A) 0.373 (B) 0.137 (C) 0.218 (D) 0.500

Statement for Linked Answer Questions 54 and 55:

In a particular year, an organization earns cash revenues of Rs. 2,00,000. Total material and labour

expenses are Rs. 1,09,000. The depreciation claimed on the equipment is Rs. 25,000. The tax rate is 20%.

Q.54 The profit after tax (PAT) is

(A) Rs. 92,800 (B) Rs. 66,200 (C) Rs. 72,800 (D) Rs. 52,800

Q.55 The net cash flow is

(A) Rs. 97,800 (B) Rs. 77,800 (C) Rs. 66,000 (D) Rs. 72,800

2012

General Aptitude (GA) Questions


Q.56 Choose the most appropriate alternative from the options given below to complete the following

sentence:

Suresh’s dog is the one ––––––––– was hurt in the stampede.

(A) that (B) which (C) who (D) whom

Q.57 Choose the most appropriate alternative from the options given below to complete the following

sentence:

Despite several ––––––––– the mission succeeded in its attempt to resolve the conflict.

(A) attempts (B) setbacks (C) meetings (D) delegations

Q.58 Choose the grammatically INCORRECT sentence:

(A) They gave us the money back less the service charges of Three Hundred rupees.

(B) This country’s expenditure is not less than that of Bangladesh.

(C) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser

sum.

(D) This country’s expenditure on educational reforms is very less.

Q.59 The cost function for a product in a firm is given by 5q2, where q is the amount of production. The

firm can sell the product at a market price of 50 per unit. The number of units to be produced by

the firm such that the profit is maximized is

(A) 5 (B) 10 (C) 15 (D) 25

Q.60 Which one of the following options is the closest in meaning to the word given below?

Mitigate

(A) Diminish (B) Divulge (C) Dedicate (D) Denote

Q. 61 - Q. 65 carry two marks each.

Q.61 Given the sequence of terms, AD CG FK JP, the next term is

(A) OV (B) OW (C) PV (D) PW

Q.62 A political party orders an arch for the entrance to the ground in which the annual convention is

being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the height of the

arch in meters. The maximum possible height of the arch is

(A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters

2012

Q.63 Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list

Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list

R: Doubling each entry in a list doubles the mean of the list

S: Doubling each entry in a list leaves the standard deviation of the list unchanged

(A) P, Q (B) Q, R (C) P, R (D) R, S

Q.64 Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal

interviews to collect and collate economic data. Requirements: High School-pass, must be

available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

(A) Gender-discriminatory

(B) Xenophobic

(C) Not designed to make the post attractive

(D) Not gender-discriminatory

Q.65 An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies

60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.

The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.

Of Y’s shock absorbers, 72% are reliable.

The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y

is

(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720

2012

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Q. 1 – Q. 5 carry one mark each.

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