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Hyderabad |Delhi |Bhopal |Pune |Bhubaneswar |Bengaluru |Lucknow |Patna |Chennai |Vijayawada |Visakhapatnam |TirupatiACE Engineering Academy

: 2 : GATE_2016_Forenoon Session


GENERAL APTITUDE

1-5 carry one mark each

01. 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

Ans: (C)

Sol: In if clause (type2) ‘were’ is in the past tense so the so main clause should be in the conditional

clause (past tense). Therefore ‘C’ is the best answer

02. He turned a deaf ear to my request.

What does the underlined phrasal verb mean?

(A) ignored (B) appreciated

(C) twisted (D) returned

Ans: (A)

Sol: ‘turned a deaf ear’ means ignored

03. 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

Ans: (C)

Sol: Where there is a will there is a way. It is a quotation

04. (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

Ans: (A)



Sol: (x% of y) + (y% of x) =x y

y x100 100

xy xy

100

2xy

100

= 2% of xy

05. 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

Ans: (A)

Sol: The new number formed by reversing the digits is greater than the original number is possible in

options A and B only.

Options ‘A’:Sum of two digits in the number = 3 + 9 = 12

After reversing the two digits number = 93

The difference between the new number formed and original number = 93 – 39 = 54

option ‘A’ is correct.

Option ‘B’:original number = 57

After reversing, the number is formed = 75

The difference between these two numbers = 75 – 57 = 18

It is not.





06-10 Carry two marks each

06. 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

Ans: (D)

Sol: The amounts invested in the companies of, P and Q in 2006 = 8 : 9

The rate of interest of company ‘P’ in 2006 = 6%

The rate of interest of company ‘Q’ in 2006 = 4%

The amounts received after one year by P and Q companies in 2006 year

P Q

6% of 8 : 4% of 9

68

100 :

49

100

4 : 3

07. 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?

7

9

8

10

7.56.5 66.5

89.5

8

98

4

2000 2001 2002 2003 2004 2005 2006

PQ



(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.

Ans: (D)

Sol: ‘Today, historians correlate greatness of a king at his time with the availability of evidence.’ This

statement leads to the best inference i.e. option ‘D’

08 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.

Ans: (B)

Sol: From given facts, the following venn diagram is possible.

H = Humans

M = Mammals

E = Engineers

BH = Build houses

From above diagram, statement III is true.

09. 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

BH

E

M

H



Ans: (D)

Sol: Base perimeter of square pyramid = x = p

Slant height 2x

l

Lateral surface area of pyramid

21 Base perimeter (p) slant height (l)

2x

p21

l

2x

x21

4x2

= 0.25x2

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

Ans: (C)

Sol: Ananth takes 6 hours to read a book

Bharath takes 4 hours to read a book

L.C.M = 12

The number of pages read by Ananth and Bharath must be 12 (or) multiple of 12 only.

If Ananth read 12 number of pages in 6 hrs

1 hr =12

6 = 2 pages

If Bharath read 12 number of pages in 4 hrs

x/2

x/4x/4



1 hr =12

4 = 3 pages

Option ‘A’

it is not

Option ‘B’

it is not

Options ‘C’

After 3 hours is the number of pages to be read by Ananth, twice that to be read by Bharath.

3 hrs

Ananth Bharath

Read6 pages

Not read6 pages

Read9 pages

Not read3 pages

2 : 1

2 hrs

Ananth Bharath

Read4 pages

Not read8 pages

Read6 pages

Not read6 pages

8 : 6

4 : 3

1 hrs

Ananth Bharath

Read2 pages

Not read10 pages

Read3 pages

Not read9 pages

10 : 9





01 – Q. 25 carry one mark each.

01. The eigenvalues of the matrix are

01

10

(A) i and –i (B) 1 and –1 (C) 0 and 1 (D) 0 and –1

Ans: (A)

Sol: + = 0; = + 1

= i = – i

02. The number of solutions of the simultaneous algebraic equations y = 3x + 3 and y = 3x+5 is

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

Ans: (A)

Sol: y = 3x+5 & y = 3x+3 are parallel to each other

No solution is zero solution

03. At x = 0, the function isL

x2sin)x(f

(– < x < , L >0)

(A) continuous and differentiable.

(B) not continuous and not differentiable.

(C) not continuous but differentiable.

(D) continuous but not differentiable.

Ans: (D)

Sol: 2 xf x sin

L

at x = 0 is having graph

It is continuous at x = 0 but not differential at x = 0

-2L -L 0 L 2L



04. For the two functions 23 xy3xy,xf and 2 3x, y 3x y y g

which one of the following options is correct?

(A)f

x x

g

(B)f

x y

g

(C)f

y x

g

(D)f

y x

g

Ans: (C)

Sol:f

6xy; 6xyy x

g

f

y x

g

05. The function 4z1z

Zf 2

2

is singular at

(A) z = 2 (B) z = 1 (C) z = i (D) z = 2i

Ans: (D)

Sol: To get singular points let z2+4 = 0

z2 = – 4

z = 2 i

06. A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is

(A)1N

21

(B)

1N

21

1

(C)

N

21

(D)

N

21

1

Ans: (C)

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

x,e8

1xf

8

1x

X

2

Then

1

X dxxf

(A) 0 (B)21

(C)e1

1 (D) 1



Ans: (B)

Sol:

1

2

1x

2

12

e22

1t

2

1x

dt

2

dx dx = 2dt

dte22

2

0

t2

1 2

Vt

2

1 2 t2 = 2V

=

0

2

1V

2

dVVe

2

1 2t dt = 2 dV

V2

dVdt

=2

1Ve

2

1

0

2

1V

08. The elastic modulus of a rigid perfectly plastic solid is

(A) 0 (B)1 (C)100 (D)infinity

Ans: (A)

Sol: Modulus is slope of curve (i.e zero) in elastic region

09. 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.

Stress

Strain



Ans: (C)

Sol: Hardness of a material will be measured by indentation technique.

If a material undergo more strain (deflection) in elastic region means stiffness is low.

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

Ans: (B)

(A) (B)

(C) (D)



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

Ans: (B)

Sol: For the highest position the distance between the cam center and follower = (r+5) mm

For the lowest position it is (r –5) mm

So the distance between the two positions

= (r+5) – (r–5) = 10 mm

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 _______

Ans: (3)

Sol: V 2 g h 2 10 5 10m / s

Q = AV = 510–610

= 510–5 m3/sec = 0.05 liter/sec = 0.05 60 = 3 lit/min

P

5 mm





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

by:

(A)1

3

vv

(B)1

2

vv

(C)2

3

vv

(D)3

1

vv

Ans: (C)

1

4

32

V

P



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________

Ans: (0.25)

Sol: Ratio of forceu22

u11

max2

max1

tx4

tx4

F

F

25.04

1

260

130

tx

tx

22

11

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

(A) Cellulose (B) Nylon (C) Polyester (D) Polyvinyl chloride

Ans: (A)

Sol: cellulose is made by C, H,O atoms can be extracted from trees.

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

Ans: (B)

Sol: During sintering the solvent added at mixing stage will evaporate and produce porosity which

comes the reduction in density of the component.

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 10o. The back rake angle (in degrees) is _______

Ans: (100)

Sol:

Turning operation,

i = inclination angle = 10,



f = 0.25 mm/rev, t1 = 0.25 = f cos Cs

f

25.0Ccos s 1

25.0

25.0 Cs = 0

= 90 – Cs = 90 – 0 = 90

tan b = sin tan i + cos tan

= sin90 tan10 + cos 90 tan

= 1 0.176 + 0 = 0.176

b = tan–1(0.176) = 10

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.


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

Ans: (A)

Sol: In EDM, dielectric fluid is used. Hence ‘Q’ is wrong.

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

Ans: (B)

Sol: CAPP will takes inputs from design but not from MRP. Hence “P” is wrong.



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

Ans: (B)

Sol: Fundamental deviation for shaft “h” is always “zero” irrespective of grade of tolerance.

21. The roughness profile of a surface is depicted below.

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

Ans: (0)

Sol:

a

hR

n

032

162162

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

(A) CRAFT. (B) Travel chart. (C) Partial Set Covering. (D) ALDEP.

2 m

2 mProf

ile h

eigh

t

centre-line ofthe profile X

5 mm



Ans: (D)Sol: ALDEP – BASED ON REL REQUIREMENTS

23. For a random variable, X, let X 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 X is

(A) n (B) (C )n

(D)n

Ans: (D)

Sol: Standard deviation,n

s

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

Allowance = LL ST, where 0 < LL<1. Which one of the following relationships is correct?

(A) LL1NT

ST

(B) ST=NT(1+LL) (C ) LL1NT

ST

(D) ST=NT(1–LL)

Ans: (A)

Sol: RA = Relaxation allowance = LL ST

ST = NT + RA

ST = NT + LL ST

ST (1 – LL) = NT

LL1

NTST

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

Ans: (C)

Sol: Average2

production.minproduction.max

units102

020



Q. 26 – Q. 55 carry two marks each.

26. The range of values of k for which the function 4322 x8x6x4k)x(f

has a local maxima at point x = 0 is

(A) k < –2 or k >2 (B) k –2 or k 2 (C) –2 < k < 2 (D) –2 k 2

Ans: (A)

Sol: f(x) = 32x3+18x2+2(k2–4)x

f(x) = 96 x2 + 36x + 2 (k2–4)

f(0) = 2(k2–4) < 0

k2 – 4 < 0

k < –2 (or) k > 2

27.2x5

0x x1e

lim

is equal to ______.

Ans: (25)

Sol: =5x 5x

x 0

e 1 e 1Lt 5 5

5x 5x

=5x 5x

x 0 x 0

e 1 e 1Lt 5 Lt 5

5x 5x

= 5 1 51 = 25

28. To solve the equation 2sinx = x 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



Ans: (B)

Sol: f(x) = 2sin x – x

f (x) (2sin x x)h

f (x) 2cos x 1

= – 0.099

x1= 2+h = 2 – 0.099 = 1.901

29. In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in

K) is given as

qc

T 1 , 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 C1 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)31

(B)21

(C) 1 (D) 2

Ans: (A)

Sol:k

C

61 105.55

9003000

150



62 1088.13

4508000

50

531 106

105

20015

r

VIq

532 105.4

1010

30015q

1

2

2

1

2

1

q

q

T

T

6

6

5

5

105.55

1088.13

105.4

106

3

1333.0

55.555.4

88.136

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 450 with the axis, shown as a dashed line in the figure, is ________________.

Ans: (1)

Sol:

max

100 / 501MPa

2 2

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 ____________.

100 N 100 N

45o



Ans: (300)

Sol:1

M 100 1 50N m2

3

2

M 50 10300 MPa (Tension)

Z 10 106

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________.

Ans: (5)

Sol: P = 500 kPa = 0.5 MPa

h = 100 MPa,D = 2m

h

PD

2t

0.5 2000100

2 t

thickness, t = 5mm

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 ____________.

Point P100 N/m

1m



Ans: (44.45)

Sol: Given mean speed N = 800 rpm

2 Nrad / sec

60

Fluctuation of energy E = 6240 J

Fluctuation of speed = 1%

Moment of inertia I = ?

We know E = I 2Cs

22s

E 6240I

C 2 N0.02

60

= 44.45 kg-m2

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 _____

Ans: (120)

Sol:

F gAh 1000 10 2 2 (2 1)

= 120 kN

2m

2m

water

vertical wall

2m 2msquare plate

vertical wall

Patm

Patm



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 P1 . 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.


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

Ans: (D)

Sol: At constant volume to decrease pressure, temperature has to be decreased. So heat has to be

transferred from the gas.

As the change in volume is zero, work done by the gas is zero. Entropy of the gas decrease as

system is losing heat.

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.

x

tb

convection

atmosphere at ta

x=L

tb

ta

tem

pera

ture

0 x L

(A)

tb

ta

tem

pera

ture

0 x L

(B)



Ans: (B)

Sol: c

0 c

cosh m (L x)

cosh m L

2

2

d0

dx

, so angle of inclination of tangents for curve should increase with ‘x’

37. In a fully developed turbulent flow through a circular pipe, a head loss of h1 is observed. The

diameter of the pipe is increased by 10% for the same flow rate and a head loss of h2 is noted.

Assume friction factor for both the cases of pipe flow is the same. The ratio of1

2

h

h is closest to

(A) 0.34 (B) 0.62 (C) 0.87 (D) 1.00

Ans: (B)

Sol:

For turbulent flow2

5

fLQh

12.1d

2 1

551 1

h d 51h 0.62

d h 1.1d

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 ______.

tb

ta

tem

pera

ture

0 x L

(C)

tb

ta

tem

pera

ture

0x

L

(D)



Ans: (0.9016)

Sol:

LP = LQ= 500,

Block “P” is rectangular = 100200

Block “Q” is square

(Ac)P = (Ac)Q

100 200 = x2

mm42.141200100x

sP A

VM

411.291005005002002001002

500200100

sQ A

VM

974.304.141242.1415004

50042.1412

2

2

Q

P

Q

P

M

M

9016.0974.30

411.292

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 ________.

Ans: (0.81 mm)

Sol: Given l = 300 mm



max = 270 MPa

E = 100 GPa

max E

3270 100 10300

l =81010–3m = 0.81mm

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 _______

Ans: (2598)

Sol:

b = 200 mm, H0 = 10mm, H1 = 6mm,

R = 100 mm, N = 200 rpm

y = 500 MPa,

Roll separating force

H4

L1Lb

3

2y

204100HRL

by assuming maximum reduction

2.0R

H

82

610H

R.S.F

84

202.0120200500

3

2

= 2598076 N 2598.076kN



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 __________

Sol:

Let d1 = d2 = d

h1 = height of first cylinder

h2 = height of second cylinder

assume h1 < h2

let % reduction in height = 10%

Ist cylinder

1.0h

hh

0

f0

h0 – hf = 0.1 h0

hf = h0 – 0.1 h0 = 0.9 h0

A0h0 = Af hf

d02h0 = df

2 hf

f

00f h

hdd

0

00 h9.0

hd

= 1.054 d0 = 1.054 (d0)1

IInd cylinder

A0h0 = Afhf

d02h0 = df

2 hf

f

00f h

hdd

0

00 h9.0

hd = 1.054 (d0)2



Ratio 20

10

d

d

1d054.1

d054.1

20

10

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 ______

Ans: (0.2327)Sol: t = 2.5 mm , I = 6000A, = 0.2sec

R = 200

Heat required, (H.R/m3)= 10109 J/m3

nugget diameter = d = 4mm (sphere )

Heat generated = I2 R

= 60002 20010–6 0.2 = 1440 J

Heat required = volume heat required/m3

33 m/R.HR3

4

933 10101023

4

= 335.1032 J

generatedHeat

requiredHeatI.H

2327.01440

1032.335



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 ________

Ans: (1000)

Sol:

Orthogonal cutting

D = 100 mm, Vc = 120 m/min, f = 0.25 mm/rev

d = 4mm,

Specific cutting energy (Sp.C.E) = 109 J/m3

Specific cutting energy

MRR

doneWorkorpower

3C C6

C

F VJ / m

f d V 10

FC = Sp.C.E f d 10–6

9 610 0.25 4 10 1000

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 _____

feedwork piece

60 mm+

120 mm

cutter

schematic representation (top view)



Ans: (1527.8872)

Sol: b = 60 mm, V = 120 m/min

t = 0.1 mmtooth, d = 4 mm

End mill cutter, D = 120 mm

z = 12

fm = ft × z× N

= 0.1×12×120

10001201000

= 381.9718 rpm

MRR = bdfm = 604381.9718

= 9176.232 mm3/min = 1527.8872 mm3/sec

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 _________

Ans: (680)

Sol: Vw = 800 m/s

mw = 3.4 kg/min

ma = 0.6 kg/min

Vmmvmvm wawwaa

V60

4.36.0800

60

4.30

60

6.0

45.33 = V15

1

V = 45.33×15 = 679.95

= 680 m/sec



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________

Sol: p = 5 mm

1000 pulses 1 rev of motor

1 rev of lead screw

Velocity of table = 6 m/min

= 6000 mm/min

= 100 mm/sec

1000 pulses 1 rev of lead screw 5 mm

mm005.01000

5pulse1

BLU = 0.005 mm

Table speed = BLU × Rate of Pulses

Rate of pulses =005.0

100

= 20000 pulses/sec

= 20000 Hz

= 20 kHz

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 30o. The module of the gear milling

cutter is 2. The pitch circle diameter (in mm) of the helical gear is_________

Ans: (69.28)

Sol: mn = normal module = 2mm

Pitch circle diameter, nZ m 30 2d

cos cos30

= 69.28mm



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 V

Number 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

_____

Ans: UCL = 0.2643

Sol:samplesofnumbersizesample

defectivesofsump

305

51423

1.010

1

305

15

Standard error of proportion

n

p1pp

30

1.011.0

054772.030

9.01.0

Central line = p = 0.1

Upper control limit = p3p

= 0.1 + 30.054772 = 0.2643

Lower control limit = p3p

= 0.1 – 30.054772 = 0



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, Z0.025 = 1.96 is ______________

Ans: (96)

Sol: Standard deviation = s1 = 0.5 minutes

Error of study = h = 0.1 minutes

Z0.025 = 1.96

2

11

Z sh

h

2

1.0

5.096.1

= 96.04 observations

Standard deviation = s2 = 0.05 minutes

Error of study = h = 0.1 minutes

Z0.025 = 1.96

2

22

Z sh

h

2

1.0

05.096.1

= 1 observations

Larger of the two values is 96.

Hence study should be continued upto 96 observations.



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 _____

Ans: 0.449

Sol: Rs = e-nt

Failure rate,500

1.0

t = 400 days

n = 10 in series

449.0eR400

500

1.010

S

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)41

(B)101

(C) 4 (D) 10

Ans: (C)

Sol: 20

0AR

R = Quality loss coefficient

A0 = Economic consequence

0 = Functional limit or customer tolerance

R = 5 , A0 = 80,

R

A00 416

5

80



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 3→5 4→5 4→6 5→6

Cost (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

Ans: (C)Sol:

Path Duration

1-3-4-6 9+4+2 = 15

1-3-2-4-6 9+2+3+2 = 16

1-3-4-5-6 9+4+7+2 = 22

1-3-2-5-6 9+2+2+2 =15

1-3-2-4-5-6 9+2+3+7+2 = 23

1-2-4-6 3+3+2 = 8

1-2-5-6 3+2+2 = 7

1-2-4-5-6 3+3+7+2 = 15

3

4

2

3

5

61

9

24

3

2

27

82



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

Ans: (B)Sol: SPT RULE

Job Time Completion time (ci)II 4 4III 7 11V 11 22

I 13 35IV 14 49

Ci = 121

iC 121Mean completion Time 24.2 min

n 5

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

FactoryRequirements

(in units)

P Q R S

I 3 3 2 1 50

II 4 2 5 9 20Market

III 1 2 1 4 30

Factory capacity(in units) 20 40 30 10

(A) 30 (B) 20 (C) 10 (D) 0



Ans: (C)

Sol: Supply = 20+40+30+10 = 100 units

Demand = 50+20+30 = 100 units

Factory R to market II is 10 units.

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 _____

Ans: 8300Sol:

Amount (INR)Yearly revenue 38500Total expenses 30000Earning before taxes 8500Tax rate @ 40% 3400Earnings after taxes (EAT) 5100Depreciation 3200Net Cash flow = (EAT + Depreciation) 8300

FACTORY

P Q R S REQ

I

II

III

20

3

X4

1X

330

210

2X

2X

510

120

1X

9X

410

50

20

30

20 40 30 10

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