R GATE 2019 - d1ykm90fp7q29d.cloudfront.net · GATE 2019 ME 2nd Feb 2019 Forenoon Session...

GATE 2019

MEnd2 Feb 2019

Forenoon Session

Note:-Don't forget to predict your rank using our rank predictor tool

BY

KREATRYX

Detailed Solutions

R

Klassroom 2020 Program for GATE-EE in Kalu Sarai, New Delhi

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https://www.kreatryx.com/gate-2019-rank-predictor/

ME Set-1 (Solutions)

© Kreatryx. All Rights Reserved. 1 www.kreatryx.com

Aptitude

Q.1 _______ I permitted him to leave, I wouldn't have had any problem with him being absent, ______ I?

(a) Had, would (b) Have, would

(c) Had, wouldn't (d) Have, wouldn't

Answer: (a)

Solution:

Had I permitted him to leave, I wouldn’t have had any problem with him being absent, would I?

Q.2 The minister avoided any mention of the issue of women's reservation in the private sector. He

was accused of ________ the issue.

(a) Belting (b) Skirting

(c) Collaring (d) Tying

Answer: (b)

Solution:

Skirting means going around or avoiding any direct issue

Q.3 A worker noticed that the hour hand on the factory clock had moved by 225 degrees during her

stay at the factory. For how long did she stay in the factory?

(a) 4 hours and 15 min (b) 3.75 hours

(c) 8.5 hours (d) 7.5 hours

Answer: (d)

Solution:

Each number on clock has 036030

12

Shifting by 0225 implies225

7.530

number

Since hour hand moves by 7.5 numbers, the stay in factory was 7.5 hours

Q.4 John Thomas, an_________ writer, passed away in 2018.

(a) Eminent (b) Prominent

(c) Dominant (d) Imminent

Answer: (a)

Solution:

John Thomas, an eminent writer passed away in 2018

Q.5 The sum and product of two integers are 26 and 165 respectively. The difference between these

two integers is__________

(a) 3 (b) 6

(c) 2 (d) 4

Answer: (d)

Solution:

Let two numbers be x & y

x+y= 26



xy= 165

165y

x

165x 26

x

2x 26x 165 0

x 11 x 15 0

x= 11 or 15

Hence, the difference= x y 4

Q.6 Congo was named by Europeans. Congo's dictator Mobuto later changed the name of the country

and the river to Zaire with the objective of Africanising names of persons and spaces, However, the

name Zaire was a Portuguese alteration of Nzadi o Nzere, a local African tern" meaning 'River that

swallows Rivers', Zaire was the Portuguese name for the Congo river in the 16th and 17th centuries.

Which one of the following statements can be inferred from the paragraph above?

(a) As a dictator Mobuto ordered the Portuguese to alter the name of the river to Zaire

(b) Mobuto's desire to Africanise names was prevented by the Portuguese

(c) Mobuto was not entirely successful in Africanising the name of his country

(d) The term Nzadi o Nzere was of Portuguese origin

Answer: (c)

Solution:

Mobuto was not entirely successful in his effort because he used Portuguese alteration of an African

term

Q.7 A person divided an amount of Rs. 100,000 into two parts and invested in two different schemes.

In one he got 10% profit and in the other he got 12%. Tithe profit percentages are interchanged with

these investments he would have got Rs.120 less. Find the ratio between his investments in the two

schemes.

(a) 11 : 14 (b) 9 : 16

(c) 37 : 63 (d) 47 : 53

Answer: (d)

Solution:

Let first part=x

Second part 100000 x

Amount obtained 10 12

1 x 1 100000 x100 100

= 1.1x+ 112000- 1.12x

= (112000- 0.02x)

Exchanging profit percentage, amount obtained

12 10

1 x 1 100000 x100 100

=110000+ 0.02x

Since now he get 120 less

(112000- 0.02x)- (110000+ 0.02x)= 120

2000- 120= 0.04x



188000x 47000

4

Ratio 47000

47 : 5310000 47000

Q.8 Under a certain legal system, prisoners are allowed to make one statement. If their statement

turns out to be true then they are hanged. If the statement turns out to be false then they are shot.

One prisoner made a statement and the judge had no option but to set him free. Which one of the

following could be that statement?

(a) I will be shot

(b) You committed the crime

(c) I did not commit the crime

(d) I committed the crime

Answer: (a)

Solution:

If prisoner says, I will be shot & he is shot then statement is true & hence he must be hanged but if he

hanged then his statement becomes false & he must be shot

So, both outcomes are impossible

Q.9 M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X

and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily

FALSE?

(a) W is the wife of P

(b) R is the father of Y

(c) M is the grandmother of Y

(d) W is the wife of R

Answer: (a)

Solution:

Since P & R have children X & Y respectively.

So, X is a child of P & Y is a child of R

Since Y is legitimate child of W

So, W is married to R

Hence 1st statement is false

Q.10 A firm hires employees at five different skill levels P, Q, P, S, T. The shares of employment at

these skill levels of total employment in 2010 are given in the pie chart as shown. There were a total of

600 employees in 2010 and the total employment increased by 15% from 2010 to 2016. The total

employment at skill levels P, Q and R remained unchanged during this period. If the employment at

skill level S increased by 40% from 2010 to 2016, how many employees were there at skill level T in

2016?



(a) 60 (b) 30

(c) 35 (d) 72

Answer: (a)

Solution:

Number of employees in 2016=1.15 600=690

Employment at P, Q & R leave=20+25+25= 70%

Number of employees at P, Q, R

70600 420

100

This remains same in 2016= 420

Employees at S level in 201025

600 150100

Employees at S level in 2016= 1.40 150= 210

Employees at T level in 2016= 690- (420+210) =60



Technical

Q.1 A spur gear with 20° full depth teeth is transmitting 20kW at 200rad/s. The pitch circle diameter of

the gear is 100 mm. The magnitude of the force applied on the gear in the radial direction is

(a) 0.36kN (b) 0.73kN

(c) 1.39kN (d) 2.78kN

Answer: (b)

Solution:

P T 320 10 T 200

T 100 N-m

NF cos r T

NF cos20 0.05 100

NF 2128.355 N

Radial load, R N

F F sin

RF 2128.355 sin20 727.94 N 0.727 kN

Q.2 A slender rod of length L, diameter d (L>>d) and thermal conductivity1

k is joined with another rod

of identical dimensions, but of thermal conductivity2

k , to form a composite cylindrical rod of length

2L. The heat transfer in radial direction and contact resistance are negligible. The effective thermal

conductivity of the composite rod is

(a) 1 2

1 2

2k k

k k (b)

1 2k k

(c) 1 2

1 2

k k

k k (d)

1 2k k

Answer: (a)

Solution:

1 2 eq

L L 2L

k A k A k A

2 1

1 2 eq

k k 2

k k k

1 2

eq

1 2

2k kk

k k



Q.3 During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean

stress of +140MPa, and a minimum stress of -70MPa. The R-ratio (minimum stress to maximum stress)

for this cyclic loading is_________ (round off to one decimal place)

Answer: -0.2

Solution:

max min

mean 2

min70 MPa (given), mean

140 MPa given

max

max max

70140 280 70 350 MPa

2

min

max

70R 0.2 R 0.2

350

Q.4 4 A block of mass 10kg rests on a horizontal floor. The acceleration due to gravity is 29.81m s . The

coefficient of static friction between the floor and the block is 0.2. A horizontal force of 10N is applied

on the block as shown in the figure. The magnitude of force of friction (in N) on the block is ________

Answer: 10

Solution:

Limiting force L sF N

Required to move the block 0.2 10 9.81 N mg

19.62 N

The force applied is less than the limiting force, the magnitude of force of friction acting on the block

will be equal to the force applied.

Friction force = 10 N

Q.5 The position vector OP of point P (20, 10) is rotated anti-clockwise in X-Y plane by an angle 030

such that point P occupies position Q, as shown in the figure. The coordinates (x, y) of Q are

(a) (12.32, 18.66)

(b) (18.66, 12.32)

(c) (22.32, 8.26)

(d) (13.40, 22.32)

Answer: (a)

Solution:

x cos sin 20

y sin cos 10



cos30 sin30 2030

sin30 cos30 10

17.32 5 12.32

10 8.66 18.66

Q.6 The lengths of a large stock of titanium rods follow a normal distribution with a mean of

440mm and a standard deviation of 1mm. What is the percentage of rods whose lengths lie

between 438mm and 441mm?

(a) 99.75% (b) 86.64%

(c) 81.85% (d) 68.4%

Answer: (c)

Solution:

440 mm

1mm

Upper limit 441 440

11

Lower limit 438 440

21

So total will be 81.85%

Q.7 Consider an ideal Vapor compression refrigeration cycle. If the throttling process is replaced by an

isentropic expansion process, keeping all the other processes unchanged, which one of the following

statements is true for the modified cycle?

(a) Coefficient of performance is the same as that of the original cycle.

(b) Coefficient of performance is higher than that of the original cycle.

(c) Refrigerating effect is lower than that of the original cycle.

(c) Coefficient of performance is lower than that of the original cycle.

Answer: (b)

Solution:

In case of isentropic expansion, we get more refrigerating effect.

Refrigerating effectCOP

Work supplied

So, original cycle

COP COP



Q.8 The table presents the demand of a product. By simple three-months moving average method,

the demand-forecast of the product for the month of September is

Month Demand

January 450

February 440

March 460

April 510

May 520

June 495

July 475

August 560

(a) 510 (b) 490

(c) 536.67 (d) 530

Answer: (a)

Solution:

By moving average method, we get

Forecast for month of September 495 475 560

5103

Q.9 A parabola 2x y with 0 x 1 is shown in the figure. The volume of the solid of rotation obtained

by rotating the shaded area by 360° around the x-axis is

(a)2

(b)

(c) 2

(d)4

Answer: (a)

Solution:

Assume a disc of width ‘dx’ & radius f (x)

2

2Volume of disc f x dx y dx x dx

1

0

Volume xdx2

Q.10 A flat-faced follower is driven using a circular eccentric cam rotating at a constant angular

velocity . At time t=0, the vertical position of the follower is y(0) =0, and the system is in the

configuration shown below.

The vertical position of the follower face, y(t) is given by

(a) e 1 cos2 t

(b) esin2 t

(c) e 1 cos t

(d) esin t



Answer: (c)

Solution:

y OB OB CD OB

AC AD OB

R ecos R e

e 1 cos

e 1 cos t

Q.11 For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of

constant cross-section, the Nusselt number at constant wall heat flux qNu and that at constant wall

temperature TNu are related as

(a)q T

Nu Nu (b)q T

Nu Nu

(c)q T

Nu Nu (d) 2

q TNu Nu

Answer: (c)

Solution:

q

Nu 4.36

T

Nu 3.36

q T

Nu Nu

Q.12 The length, width and thickness of a steel sample are 400mm, 40mm and 20mm, respectively. Its

thickness needs to be uniformly reduced by 2mm in a single pass by using horizontal slab milling. The

milling cutter (diameter: 100mm, width: 50mm) has 20 teeth and rotates at 1200rpm. The feed per

tooth is 0.05mm. The feed direction is along the length of the sample. If the over-travel distance is the

same as the approach distance, the approach distance and time taken to complete the required

machining task are

(a) 14mm, 18.4s (b) 14mm, 21.4s

(c) 21mm, 28.9s (d) 21mm, 39.4s

Answer: (b)

Solution:

Diameter of milling with (D) = 100 mm, length (L) = 400 mm

tf 0.05 mm

N 1200 rpm

Z 20 teeth

Depth of cut (d) = 2 mm

Approach d D d 2 100 2 14 mm

Time taken m

L 2A

f

where

m tf f N Z

Time taken 400 2 14

21.41200

0.5 2060

seconds



Q.13 Water flows through a pipe with a velocity given by4 ˆV x y jm st

, where j is the unit

vector in the y direction, t (>0) is in seconds, and x and y are in meters. The magnitude of total

acceleration at the point (x, y)= (1,1) at t = 2s is _______ 2m s

Answer: 3

Solution:

x

u u ua u v

x y t

y

v v va u v

x y t

So, x

u u ua u v 0

x y t

y y2

v v v 4 4a u v x y 1 a

x y t t t

ya at (1, 1) and t = 2 is 24 1 3 m/s and this will be equal to total acceleration.

Q.14 In a casting process, a vertical channel through which molten metal flows downward from

pouring basin to runner for reaching the mold cavity is called

(a) Blister (b) Sprue

(c) Pin hole (d) Riser

Answer: (b)

Solution:

The vertical channel through which molten metal flows downward from pouring basin to runner for

reaching the mold cavity is called sprue.

Q.15 Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the

figure.

The metal was loaded in uniaxial tension starting from O. Upon loading, the stress-strain curve passes

through initial yield point at P, and then strain hardens to point Q, where the loading was stopped,

From point Q, the specimen was unloaded to point R. where the stress is zero.

If the same specimen is reloaded in tension from point R, the value of stress at which the material

yields again is _______ MPa.

Answer: 210

Solution:

Value of the stress at which material will yield again is 210 MPa as seen from the figure.



Q.16 During a non-flow thermodynamic process (1-2) executed by a perfect gas, the heat interaction

is equal to the work interaction 1 2 1 2Q W

when the process is

(a) Isothermal (b) Adiabatic

(c) Isentropic (d) Polytropic

Answer: (a)

Solution:

From fist law

Q U W

Q W when U 0 which means process is isothermal.

Q.17 A cylindrical rod of diameter 10mm and length 1.0m is fixed at one end. The other end is twisted

by an angle of 10° by applying a torque. If the maximum shear strain in the rod is 3p 10 , then p is

equal to________ (round off to two decimal places),

Answer: 0.85 to 0.90

Solution:

Using maxT G

J R L

max maxG R

R L G L

max

maxG

3

max

0.005 100.872 10

1 180

P 0.872

Q.18 Consider the matrix

1 1 0

P 0 1 1

0 0 1

The number of distinct Eigen values of P is

(a) 3 (b) 1

(c) 2 (d) 0

Answer: (b)

Solution:

The given matrix is upper triangular & hence eigen values are diagonal elements which are all 1.

Hence, there is only 1 distinct eigenvalue.

Q.19 Which one of the following welding methods provides the highest heat flux 2W mm ?

(a) Tungsten inert gas welding



(b) Oxy-acetylene gas welding

(c) Plasma arc welding

(d) Laser beam welding

Answer: (d)

Solution:

Laser Beam welding provides a high heat flux on the order of 9 210 W/ mm and above

Q.20 A solid cube of side 1m is kept at a room temperature of 032 C . The coefficient of linear thermal

expansion of the cube material is 5 01 10 C and the bulk modulus is 200MPa. If the cube is

constrained all around and heated uniformly to 042 C , then the magnitude of volumetric (mean) stress

(in MPa) induced due to heating is ______

Answer: 60

Solution:

Block is heated from all the direction, is countsained from all sides, fo we can else, V

V3 T

k

because it become a case of hydrostatic stress.

V3k T

9 53 200 10 1 10 10 660 10 Pa

60 MPa

Q.21 The natural frequencies corresponding to the spring-mass systems I and II areI

andII

respectively. The ratio I

II

is

(a) 2

(b) 4

(c) 1

2

(d)1

4

Answer: (c)

Solution:

eq

1 1 1

k kk



eq 1

kk

2 and eq 2

k 2k

1

k 2k and

2m m

1

2

k

1 12m

4 22k

m

Q.22 Air of mass 1kg, initially at 300K and 10bar, is allowed to expand isothermally till it reaches a

pressure of 1bar. Assuming air as an ideal gas with gas constant of 0.287kJ/kg.K, the change in entropy

of air (in kJ/kg.K, round off to two decimal places) is _________


Solution:

Isothermal expansion takes place

2 2

P 2 1

1 1

T Ps c ln Rln T T

T P

10.87 ln kJ/kgk

10

s 0.66 kJ/kgk

Q.23 Evaluation of4

3

2

x dx using a 2-equal-segment trapezoidal rule gives a value of _____

Answer: 63

Solution:

For 2 equal segment, we consider a point x = 3 between 2 & 4.

4

3

2

1 1x dx f 2 2f 3 f 4 8 2 27 64 63

2 2

Q.24 For the equation 2dy7x y 0

dx , if 3y 0

7 , then the value of y(1) is

(a)3

73

e7

(b)3

77

e3

(c)7

33

e7

(d)7

37

e3

Answer: (c)

Solution:

This is a linear differential equation

Integrating Factor = 32

7x7x dx

3e e 3 37 7

x x23 3

dye 7x e y 0

dx

37x

3d

e y 0dx



3 37 7

x x3 3e y c y c e

Since y (0) = 3

7

3c

7

37x

33

y e7

7

33

y 1 e7

Q.25 As per common design practice, the three types of hydraulic turbines, in descending order of

flow rate, are

(a) Pelton, Francis, Kaplan

(b) Francis, Kaplan, Felton

(c) Kaplan, Francis, Felton

(d) Felton, Kaplan, Francis

Answer: (c)

Solution:

In descending order of flow rate, the three types of hydraulic turbines can be arranged in the following

way

Kaplan > Francis > Pelton

Q.26 A gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when 6 operating

at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5, while maintaining the

same inlet conditions. Assume air as a perfect gas with specific heat ratio 1.4 . If the specific work

output remains the same for both the cases, the isentropic efficiency of the turbine at the pressure

ratio of 5 is _______ (round off to two decimal places)


Solution:

1 2

isen

1 2

T T0.7

T T

and

1/

1 1

2 2

T p

T p

isen for case 2 1 3

1 3

T T

T T



Given, inlet conditions is same

1 2 2

1 1 2

12

1

1

T T T0.7 0.7T 1 T T

TTT 1

T

Similarly, 3

2 1 1 3

1

TT 1 T T

T

Equating the above equation [1 2 1 3

T T T T it is given specific work output is equal]

1 2 10.2857 0.2857

1 10.7T 1 T 1

3 5

20.5114,

Q.27 In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are 45° and

10°, respectively. The feed during cylindrical turning is 0.1mm/rev. The centre line average surface

roughness (in µm, round off to one decimal place) of the generated surface is _______

Answer: 3.7 to 3.8

Solution:

Center line avg surface roughness h

4

where s e

f 0.1h

tanC cotC tan45 cot10

0.1h 0.01498 mm

1 5.6712

h 14.989 m

Center line roughness h 14.989

3.747 m4 4

Q.28 A car having weight W is moving in the direction as shown in the figure. The centre of gravity

(CG) of the car is located at height h from the ground, midway between the front and rear wheels. The

distance between the front and rear wheels is I. The acceleration of the car is a. and acceleration due

to gravity is g. The reactions on the front wheels fR and rear wheels r

R are given by



(a)f

W W hR a

2 g l

;

r

W W hR a

2 g l

(b)f r

W W hR R a

2 g l

(c)f r

W W hR R a

2 g l

(d)f

W W hR a

2 g l

;

r

W W hR a

2 g l

Answer: (d)

Solution:

V r fF 0 R R W …… (1)

Taking moment about P.

fR ma h w 0

2

f

WR mah

2

f

W W hR a

2 g

From (1), r

W W hR a

2 g

Q.29 If one mole of2

H gas occupies a rigid container with a capacity of 1000 litres and the temperature

is raised from 27°C to 37°C, the change in pressure of the contained gas (round off to two decimal

places), assuming ideal gas behaviour, is ______Pa. (R=8.314J/mol-K)

Answer: 80 to 85

Solution:

1P V nRT,

1P 1 1 8.314 300 31000 1m

1P 2494.2 pa

Now, 2 2

P V nRT

2P 1 1 8.314 310 1 2

1 2

V V

n n

2P 2577.34 pa

Change in pressure 2 1

P P 2577.34 2494.2 Pa

83.14 Pa

Q.30 Five jobs (J1, J2, J3, J4 and J5) need to be processed in a factory. Each job can be assigned to any

of the five different machines (M1, M2, M3, M4 and M5). The time durations taken (in minutes) by the

machines for each of the jobs, are given in the table. However, each job is assigned to a specific

machine in such a way that the total processing time is minimum.

The total processing time is __________minutes.



M1 M2 M3 M4 M4

J1 40 30 50 50 58

J2 26 38 60 26 38

J3 40 34 28 24 30

J4 28 40 40 32 48

J5 28 32 38 22 44

Answer: 146

Solution:

40 30 50 50 58

26 38 60 26 38

40 34 28 24 30

28 40 40 32 48

28 32 38 22 44

Subtracting lowest element of each row from corresponding row

10 0 20 20 28

0 12 34 0 12

16 10 4 0 6

0 12 12 4 20

6 10 16 0 22

Subtracting lowest element of each column from corresponding column



min cost 28 30 28 22 38 146

Q.31 In orthogonal turning of a cylindrical tube of wall thickness 5mm, the axial and the tangential

cutting forces were measured as 1259N and 1601N. respectively. The measured chip thickness after

machining was found to be 0.3mm. The rake angle was 10° and the axial feed was 100mm/min. The

rotational speed of the spindle was 1000rpm. Assuming the material to be perfectly plastic and

Merchant's first solution, the shear strength of the material is closest to

(a) 920MPa

(b) 722MPa

(c) 875MPa

(d) 200MPa

Answer: (b)

Solution:

Orthogonal turning (given)

t f sin 90

t f …… (1)

Now, mf f N

mm rev min100 f 1000 f 0.1

min min rev

From (1), t 0.1

and ct 0.3 mm given

c

t 0.1r 0.33

t 0.3

Axial force x T

F F sin

T1259 N F

and cF 1601 N given

Shear strength s

s

F

bt / sin

…… (2)

Now, s c T

F F cos F sin …… (3)

For finding , use r cos 0.33cos10

tan tan1 rsin 1 0.33sin10

19.021

Put 19.021 in (3)



s c TF F cos 19.021 F sin 19.021 1103.2533 N

Using (2) s

1103.2533719.132 MPa

5 0.1 / sin19.021

Q.32 A circular shaft having diameter 0.01

0.0565.00 mm

is manufactured by turning process. A 50µm thick

coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is 5 m . The minimum

hole diameter (in min) to just provide clearance fit is

(a) 65.01 (b) 65.12

(c) 64.95 (d) 65.10

Answer: (b)

Solution:

Minimum hole diameter just to provide clearance fit is equal to the maximum diameter of shaft

possible which is equal to 65.01 2 0.05 2 0.005 mm

maximum diameter of shaft 65.12 mm

Q.33 Two immiscible, incompressible, viscous fluids having same densities but different viscosities are

contained between two infinite horizontal parallel plates, 2 in apart as shown below. The bottom plate

is fixed and the upper plate moves to the right with a constant velocity of 3m/s. With the assumptions

of Newtonian fluid steady and fully developed laminar flow with zero pressure gradients in all

directions, the momentum equations simplify to

2

2

d u0

dy

If the dynamic viscosity of the lower fluid2

,

is twice that of the upper fluid,1

then the velocity

at the interface (round off to two decimal places) is _______ m/s

Answer: ()

Solution: 2

2

d u0

dy

1

duC

dy

1 2u C y C

The velocity profile is linear

Shear stress at interface will be same

1 2

1 2

1 2

du du

dy dy

i i

1 1

3 V V 02

1 1



i i3 V 2V

iV 1 m/s

Q.34 The rotor of a turbojet engine of an aircraft has a mass 180kg and polar moment of inertia 10

kg.m2 about the rotor axis. The rotor rotates at a constant speed of 1100 racks in the clockwise

direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800km per

hour takes a turn with a radius of 1.5km to the left. The gyroscopic moment exerted by the rotor on

the aircraft structure and the direction of motion of the nose when the aircraft turns, are

(a) 162.9N.m and the nose goes down

(b) 162.9N.m and the nose goes up

(c) 1629.6N.m and the nose goes up

(d) 1629.6N.m and the nose goes down

Answer: (d)

Solution:

Gyroscopic couple p pI 10 1100

p

V

R where

5V 800

18 and R 1500 m

Gyroscopic couple 5 1

10 1100 80018 1500

1629.629 Nm

the engine rotates in the clockwise direction and the aeroplane takes a left turn, the nose will go

down.

Q.35 In a four bar planar mechanism shown in the figure, AB =5cm. AD =4cm and DC =2cm. In the

configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular

velocity of 10rad/s. The magnitude of angular velocity (in rad/s) of bar DC at this instant is

(a) 15

(b) 25

(c) 0

(d) 10

Answer: (b)

Solution:

This is a previous year GATE question on the same concept.

for this case, B c

V V

AB CD5 2

CD

10 5

2

2

CD25 rad / s



Q.36 The value of the following definite integral is _______ (round off to three decimal places)

e

1

xlnx dx

Answer: 2.0 to 2.2

Solution:

e

e 2 2 2 2 2 2 2

1 1

x 1 x x x e e 1 e 1x ln x dx ln x dx ln x ln 2.097

2 x 2 2 4 2 4 4 4 4

Q.37 A steam power cycle with regeneration as shown below on the T-s diagram employs a single

open feed water heater for efficiency improvement. The fluids mix with each other in an open feed

water heater. The turbine is isentropic and the input (bleed) to the feed water heater from the turbine

is at state 2 as shown in the figure. Process 3-4 occurs in the condenser. The pump work is negligible.

The input to the boiler is at state 5. The following information is available from the steam tables:

State 1 2 3 4 5 6

Enthalpy (kJ/kg) 3350 2800 2300 175 700 1000

The mass flow rate of steam bled from the turbine as a percentage of the total mass flow rate at the

inlet to the turbine at state 1 is _______

Answer: 20

Solution:

Using energy balance

2 4 5mh 1 m h h

in 2800 1 m 175 700

2625 m 525

m 0.2 i.e. 20%



Q.38 A harmonic function is analytic if it satisfies the Laplace equation.

If 2 2u x,y 2x 2y 4xy is a harmonic function, then its conjugate harmonic function v(x, y) is

(a) 2 24xy 2y 2x Constant

(b) 2 22x 2y xy Constant

(c) 2 24xy 2x 2y Constant

(d) 24y 4xy Constant

Answer: (c)

Solution:

x

uu 4x 4y

x

By Cauchy – Riemann equation

x yu u

v

4x 4yx

2v 4xy 2y f x

'

x

uv 4y f x

x

Since, x y

uv u

y

'4y f x 4y 4x

'f x 4x

2f x 2x c

2 2v 4xy 2y 2x c

Q.39 At a critical point in a component, the state of stress is given asxx

100MPa ,xy

220MPa ,

xy yx80MPa and all other stress components are zero. The yield strength of the material is

468MPa. The factor of safety on the basis of maximum shear stress theory is ________ (round off to one

decimal place).

Answer: 1.8

Solution:

Finding 1,2

from the given data

2

x y x y 2

1,2 xy2 2

2

2100 220 100 22080

2 2

160 100

1 2260 MPa, 60 MPa

On the basis of maximum shear stress theory



Maximum of yt1 2 1 2

S, ,

2 2 2 2N

Maximum of 468

100, 130, 302N

468130

2N

N 1.8

Q.40 A single block brake with a short shoe and torque capacity of 250N.m is shown. The cylindrical

brake drum rotates anticlockwise at 100rpm and the coefficient of friction is 0.25.

The value of a, in mm. (round off to one decimal place), such that the maximum actuating force P is

2000 N, is _______

Answer: 210 to 215

Solution:

f N 0.25 N

Taking moment about A

aP 2.5a N a f 0

4

0.25N

P 2.5 N4

2000 2.5 1.0625 N

N 4705.88 N

T 250 N-m N a

a 0.2125 m 212.5 mm

Q.41 The set of equations

x y z 1

ax ay 3z 5

5x 3y az 6

Has infinite solutions, if a=



(a) -4 (b) -3

(c) 4 (d) 3

Answer: (c)

Solution:

Equation can be expressed in matrix form as

1 1 1 x 1

a a 3 y 5

5 3 a z 6

Equations have infinite solution if A 0

1 1 1

a a 3 0

5 3 a

2 21 a 9 1 a 15 1 3a 5a 0

22a 24 2a 0 2a a 12 0

a 4 and a 3

Out of this only a = 4 gives infinite solution because then

(i) + (ii) = (iii)

Hence equations becomes linearly dependent & number of linearly independent equations are less

than number of variables.

Q.42 In a UTM experiment, a sample of length 100mm was loaded in tension until failure. The failure

load was 40kN. The displacement, measured using the cross-head motion, at failure, was 15mm; the

compliance of the UTM is constant and is given by 85 10 m N . The strain at failure in the sample is

________ %.

Answer: 2

Solution:

L 100 mm 0.1m

P 40 kN

Compliance 2

2

L mm/N

NAEm

m

Given compliance 85 10 m/N

3 8PL40 10 5 10

AE

m

3 840 10 5 100.02

L 0.1

% 0.02 100% 2%

Q.43 A uniform thin disk of mass 1kg and radius 0.1m is kept on a surface as shown in the figure. A

spring of stiffness 1

k 400N m is connected to the disk centre A and another spring of stiffness

2k 100N m is connected at point B just above point A on the circumference of the disk. Initially, both

the springs are un-stretched. Assume pure rolling of the disk. For small disturbance from the



equilibrium, the natural frequency of vibration of the system is __________rad/s (round off to one

decimal place).


Solution:

Moment of inertia of thin disc about 2 2

2mR 3mRC mR

2 2

Using conservation of energy method.

2 2 2

1 2

1 1 1I k x k y C

2 2 2

Relation between x and y, x y

2x yR 2R

and x R x R 2

2 2 2

1 22

1 3 x 1 1mR k x k 4x C

2 2 2 2k

Differentiating

1 2

3m xx k xx k 4xx 0

2

3

1 x 400x 400x 02

800 2x x 0

3

2

n n

160023.094 rad/sec

3

Q.44 A cube of side 100 mm is placed at the bottom of an empty container on one of its faces. The

density of the material of the cube is 3800kg m . Liquid of density 31000kg m is now poured into the

container. The minimum height to which the liquid needs to be poured into the container for the cube

to just lift up is ________mm.

Answer: 80

Solution:

Let, the height of the fluid be ‘h’, when cube just lifts up.

BF mg

f submerged b bodyV g V g

31000 a a h 800 a

h 0.8 100 mm

h 80 mm



Q.45 Consider an elastic straight beam of length L=10πm, with square cross-section of side a = 5mm,

and Young's modulus E =200GPa. This straight beam was bent in such a way that the two ends meet,

to form a circle of mean radius R. Assuming that Euler-Bernoulli beam theory is applicable to this

bending problem, the maximum tensile bending stress in the bent beam is _________MPa.

Answer: 100

Solution:

Using

M E

J Y R

L 10 2 R R 5m

So, E

a / 2 R

9200 10 0.005

5 2

100 MPa

Q.46 The wall of a constant diameter pipe of length 1m is heated uniformly with flux q" by wrapping a

heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is

incompressible and the flow is assumed to be laminar and steady all

through the pipe. The bulk temperature of the fluid is equal to 0°C at the inlet and 50°C at the exit.

The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow

thermally develops after some distance from the inlet. The following measurements are made:

Point P Q R

Wall temp C 50 80 90

Among the locations P, Q and R. the flow is thermally developed at

(a) P and Q only

(b) P, Q and R

(c) R only

(d) Q and R only

Answer: (d)

Solution:

For constant wall flux



T remains same after the flow is developed.

P QT | 30 C, T | 50 C ,

RT | 50 C

So flow is thermally developed at Q and R,

Q.47 A plane-strain compression (forging) of a block is shown in the figure. The strain in the direction

is zero. The yield strength yS in uniaxial tension/compression of the material of the block is 300MPa

and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started

yielding. At a point where x

40MPa (compressive) and,xy

0 the stress componenty

is

(a) 340MPa (tensile)

(b) 340MPa (compressive)

(c) 260MPa (tensile)

(d) 260MPa (compressive)

Answer: (b)

Solution:

1 2 1 2 SytMax , , ,

2 2 2 2 N

2

2

x y x y

1, 2 xy2 2

x y x y

2 2

x y x y

1 x2 2

x y x y

2 y2 2



x y yx SytMax , , , N 1

2 2 2 2 N

y y yt40 S300

and2 2 2 2

y y340 MPa 300 MPa

Larger of the 2 values will the y

y340 MPa

Q.48 A gas is heated in a duct as it flows over a resistance heater. Consider a 101kW electric heating

system. The gas enters the heating section of the duct at 100kPa and 27 °C with a volume flow rate of315m s . If heat is lost from the gas in the duct to the surroundings at a rate of 51kW, the exit

temperature of the gas is

(Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant

specific heatP

C 1kJ kg ;R 0.5kJ kg.K )

(a) 037 C (b) 053 C

(c) 032 C (d) 076 C

Answer: (c)

Solution:

k.e. p.e 0

From SFEE

1 2mh Q mh W i

Finding m

PV mRT 3100 10 V mx500 300

m 10 kg / s

So putting in equation (i)

1 2m h h W Q

3

p 1 210 c T T 50 10

3 3

210 1 10 300 T 50 10

2

2

300 5 T

T 305 K 32 C

Q.49 Match the following sand mold casting defects with their respective causes.

Defect Cause

P Blow hole 1 Poor collapsibility

Q Misrun 2 Mold erosion

R Hot tearing 3 Poor permeability

S Wash 4 Insufficient fluidity



(a) P-3, Q-4, R-2, S-1 (b) P-3, Q-4, R-1, S-2

(c) P-2, Q-4, R-1, S-3 (d) P-4, Q-3, R-1, S-2

Answer: (b)

Solution:

Blow hole poor permeability

Misrun Insufficient fluidity

Hot tearing poor collapsibility

Wash Mold erosion

Q.50

A project consists of six activities. The immediate predecessor of each activity and the estimated

duration is also provided in the table below:

Activity Immediate

predecessor

Estimate duration

(week)

P - 5

Q - 1

R Q 2

S P, R 4

T P 6

U S, T 3

If all activities other than S take the estimated amount of time, the maximum duration (in weeks) of

the activity S without delaying the completion of the project is _________

Answer: 6

Solution:

Max duration of S = 6 weeks

Q.51

Taylor's tool life equation is given by nVT C , where V is in m/min and T is in min. In a turning

operation, two tools X and Y are used. For tool X. n =0.3 and C=60 and for tool Y, n=0.6 and C=90.

Both the tools will have the same tool life for the cutting speed (in m/min, round off to one decimal

place) of _________

Answer: 38 to 41

Solution: nVT C



For X: 0.3VT 60 …… (1)

For Y: 0.6VT 90 …… (2)

From (1), we get,

1/0.3

0T

V

…… (3)

From (2), we get,

1/0.6

90T

V

…… (4)

Equating (3) & (4), we get 1/0.3 1/0.6

60 90

V V

2

60 90

V V

260V

90

V 40 m/min

Q.52 Consider a prismatic straight beam of length L=πm, Pinned at the two ends as shown in the

figure.

The beam has a square cross-section of side p =6mm.

The Young's modulus E = 200GPa, and the coefficient of thermal expansion 6 13 10 K . The

minimum temperature rise required to cause Euler buckling of the beam is _______ K.

Answer: 1

Solution:

2 min

2

e

EIP

L

For hinged beam e

L L m

4

92

2

0.006200 10P

12

And P

E TA

4

99 6

2

0.006200 10200 10 3 10 T

120.006

T 1K



Q.53

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the

interfaces. The center slab experiences a non-uniform internal heat generation with an average value

equal to 31000Wm , while the left and right slabs have no internal heat generation. All slabs have

thickness equal to 1 m and thermal conductivity of each slab is equal to 1 15Wm K . The two extreme

faces are exposed to fluid with heat transfer coefficient 2 1100Wm K and bulk temperature 30 °C as

shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties

are constant. If the left extreme face temperature1

T is measured to be 100 °C, the right extreme face

temperature2

T is __________°C.

Answer: 60

Solution:

1q (through conduction) q through convection on LHS

hA T

100 A 70

7000 A W

2q (through conduction) q through convection on RHS

hA T

3100 A T 30

Now, 1 2

q q 10000 1 A

37000 A 100 A T 30 10000 1 A

37000 100T 3000 10000

3T 60 C

Q.54 The variable x takes a value between 0 and 10 with uniform probability distribution. The variable

y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of

variables (x +y) being greater than 20 is

(a) 0.25

(b) 0.50

(c) 0

(d) 0.33



Answer: (a)

Solution:

If we plot both variables on each axis

Since y x 20, we plot a line y x 20 & shaded area gives probability

x yP x y 20 f x f y dx dy

10 20

0 20 x

1 1dy dx

10 20

10

0

120 20 x dx

200

102

0

1 x 10.25

200 2 4

Q.55 A truss is composed of members AB. BC. CD. AD and BD. as shown in the figure. A vertical 5 load

of 10kN is applied at point D. The magnitude of force (in kN) in the member BC is ________

Answer: 5

Solution:

Taking moment about A.

cR 2a 10 a

cR 5 kN

By lami’s theorem

BC cF R

sin135 sin135

BCF 5 kN

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