Mechnaical_1

8/10/2019 Mechnaical_1

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Mechanical Engineering ‐ Excerise‐1

1. Given that the determinant of the matrix

1 3 0

2 6 4

1 0 2

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥−⎣ ⎦

is – 12, the determinant of

the matrix

2 6 0

4 12 8

2 0 4

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥−⎣ ⎦

is

(A) – 96 (B) –24 (C) 24 (D) 96

2.

0

sin

1 cos x

x x

Lt x→

−

− is

(A) 0 (B) 1 (C) 3 (D) not defined

3. The argument of the complex number1

1

i

i

+− , where 1i = − , is

(A) – π (B) 2

π− (C)

2

π (D) π

4. The matrix form of the linear system 3 5dx

x ydt

= − and 4 8dy

x ydt

= + is

(A) 3 5

4 8

x xd

y ydt

−⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥

⎩ ⎭ ⎣ ⎦ ⎩ ⎭ (B)

3 8

4 5

x xd

y ydt

⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥−⎩ ⎭ ⎣ ⎦ ⎩ ⎭

(C) 4 5

3 8

x xd

y ydt −⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥

⎩ ⎭ ⎣ ⎦ ⎩ ⎭ (D) 4 8

3 5

x xd

y ydt ⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥−⎩ ⎭ ⎣ ⎦ ⎩ ⎭

5. Which one of the following describes the relationship among the three vectors,

, 2 3 and 5 6 4 ?i j k i j k i j k + + + + + +



(A) The vectors are mutually perpendicular

(B) The vectors are linearly dependent

(C) The vectors are linearly independent

(D) The vectors are unit vectors

6. A circular rod of length ‘L’ and area of cross‐section ‘A’ has a modulus of elasticity

‘E’ and coefficient of thermal expansion ‘α’. One end of the rod is fixed and other

end is free. If the temperature of the rod is increased by ΔT, then

(A) stress developed in the rod is E α ΔT and strain developed in the rod is α ΔT

(B) both stress and strain developed in the rod are zero

(C) stress developed in the rod is zero and strain developed in the rod is α ΔT

(D) stress developed in the rod is E α ΔT and strain developed in the rod is zero

7. A metallic rod of 500 mm length and 50 mm diameter, when subjected to a tensile

force of

100

kN

at

the

ends,

experiences

an

increase

in

its

length

by

0.5

mm

and

a

reduction in its diameter by 0.015 mm. The Poisson’s ratio of the rod material is

_______

8. Critical damping is the

(A) Largest amount of damping for which no oscillation occurs in free vibration

(B)

Smallest amount

of

damping

for

which

no

oscillation

occurs

in

free

vibration

(C) largest amount of damping for which the motion is simple harmonic in free

vibration



9

1

1

(D)

. A cir

cent

and t

(A) z

(C) V

0. For t

I. M

II. A

Indic

(A) B

(C) I i

1. A rig

figur

are g

Smallest

vibration

ular obje

r having

he floor is

ro

opposite

he given s

ting spur

evolute j

ate the co

oth I and I

s false

an

id link PQ

. The ma

iven. The

amount o

t of radiu

elocity V.

o the dire

atements

gear teeth

int is an e

rrect ans

I are false

II is

true

is 2 m lo

nitude a

agnitud

f damping

r rolls wi

The velo

ction of m

:

is an exa

ample of

er.

(B) I is tru

(D) Both

I

g and ori

d directio

of VP (in

for which

hout slip

ity at the

(

otion (

ple of hi

lower pai

e and II is

and II are

ented at

n of veloc

/s) at thi

the moti

ing on a h

point of

B) V in the

D) V verti

her pair

alse

true

0o to the

ity VQ , an

instant i

n is simpl

orizontal l

contact b

direction

ally upwa

horizont

the direc

e harmoni

evel floor

tween th

of motion

d from th

l as show

tion of ve

c in free

with the

e object

e floor

n in the

locity VP





(A) G is located below B (B) G is located above B

(C) G and B are coincident (D) independent of the locations of G and B

16. In a power plant, water (density = 1000 kg/m3) is pumped from 80 kPa to 3 MPa.

The pump

has

an

isentropic

efficiency

of

0.85.

Assuming

that

the

temperature

of

the water remains the same, the specific work (in kJ/kg) supplied to the pump is

(A) 0.34 (B) 2.48 (C) 2.92 (D) 3.43

17. Which one of the following is a CFC refrigerant?

(A) R744 (B) R290 (C) R502 (D) R718

18. The jobs arrive at a facility, for service, in a random manner. The probability

distribution of number of arrivals of jobs in a fixed time interval is

(A) Normal (B) Poisson (C) Erlang (D) Beta

19. In exponential smoothening method, which one of the following is true?

(A) 0 ≤ α ≤

1 and

high

value

of

a is

used

for

stable

demand

(B) 0 ≤ α ≤ 1 and high value of a is used for unstable demand

(C) α ≥ 1 and high value of a is used for stable demand

(D) α ≤ 0 and high value of a is used for unstable demand

20. For machining a rectangular island represented by coordinates P(0,0), Q(100,0),

R(100,50) and S(0,50) on a casting using CNC milling machine, an end mill with a

diameter of 16 mm is used. The trajectory of the cutter centre to machine the

island PQRS is

(A) (‐8, ‐8), (108, ‐8), (108,58), (‐8,58) , (‐8, ‐8)



(B) (8,8), (94,8), (94,44), (8,44), (8,8)

(C) (‐8,8), (94,0), (94,44), (8,44), (‐8,8)

(D) (0,0), (100,0), (100,50), (50,0), (0,0)

21. Which one of the following instruments is widely used to check and calibrate

geometric features of machine tools during their assembly?

(A) Ultrasonic probe (B) Coordinate Measuring Machine (CMM)

(C) Laser interferometer (D) Vernier calipers

22. The major difficulty during welding of aluminium is due to its

(A) high tendency of oxidation (B) high thermal conductivity

(C) low melting point (D) low density

23. The main cutting force acting on a tool during the turning (orthogonal cutting)

operation of a metal is 400 N. The turning was performed using 2 mm depth of cut

and 0.1

mm/rev

feed

rate.

The

specific

cutting

pressure

(in

N/mm

2

) is

(A) 1000 (B) 2000 (C) 3000 (D) 4000

24. The process of reheating the martensitic steel to reduce its brittleness without any

significant loss in its hardness is

(A) normalising (B) annealing (C) quenching (D) tempering

25. In solid‐state welding, the contamination layers between the surfaces to be welded

are removed by

(A) alcohol (B) plastic deformation

(C) water jet (D) sand blasting



2

2

2

2

3

3

6. The i

coun

(A) 0

7. If y =

dy

dx

8. In th

dens

(A) 0

9. Usin

subi

0. The

The

1. A bl

figur

coeff

need

ntegral ∫

ter clock

f(x) is the

2 at x = 1

e followin

ity. The st

.18

the trap

tervals, t

tate of st

aximum

ck R of

. Block R

icient of

ed to mo

(C

ydx x−

ise directi

(B)4

π−

solution o

0, f(15) =

g table, x

ndard de

(B) 0.

zoidal rul

e definite

ess at a p

ensile str

ass 100 k

is tied to

tatic frict

e the bloc

) y is eval

n. The in

f 2

2 0

d y

dx=

______

is a discr

iation of

6

e, and divi

integral +

−∫

oint is giv

ss (in MP

g is place

the wall

ion for al

k S is

luated alo

egral is e

(C) 2

π−

with the

te rando

is

(C) 0.5

ding the i

| | x dx is_

n by σx =

a) at the p

on a bl

y a mass

l surfaces

ng the cir

ual to

oundary

m variabl

nterval of

_____

‐6 MPa,

oint is___

ck S of m

less and i

is 0.4, th

cle 2 x y+

(

conditions

and p(x)

(D) 0.6

integratio

y = 4 MPa

___

ass 150 k

nextensibl

e minimu

2 1

4= trav

) 4

π

y = 5 at x

is the pr

n into thr

and τxy =

as show

e string P

m force F

ersed in

= 0, and

bability

e equal

‐8 MPa.

n in the

. If the

(in kN)



3

3

3

3

3

(A) 0

2. A pai

a

spe

3. Cons

with

attac

____

4. An i

nor

1000

5. A bl

and

horiz

velo

6. A sli

a uni

parti

equa

.69

r of spur

ed

reduct

ider a ca

length 0.

hed at th

___

eal wate

al to its p

kg/m3, th

ck weighi

kinetic fri

ontal forc

ity (in

m/

er crank

form ang

lly balan

l to crank

(B) 0.

ears with

ion

of

5:1.

tilever be

1 m. The

e free tip,

jet with

th and ex

e diamete

ng 200 N i

tion are

e (in new

) of

the

bl

echanis

lar veloci

ed by a r

radius. N

8

module 5

The

num

am, havin

frequenc

is 100 H

olume fl

erts a forc

r (in mm)

s in conta

0.4 and 0

ton) P =

ock attain

has slide

y of 10 ra

evolving

eglect th

(C) 0.9

mm and a

er

of

teet

g negligib

of vibra

. The fle

w rate o

e of 1000

f the wat

t with a l

.2, respec

0t, wher

d after

1

r mass of

d/s. The

ass of 6

mass of

center di

h

on

pinio

le mass a

ion of th

ural rigidi

0.05 m3

N. Consid

er jet is __

evel plane

tively. Th

t denot

seconds

0 kg, stro

rimary in

kg at the

connectin

(D) 1.37

tance of

n

is

_____

nd unifor

beam,

ty (in N.

s strikes

ring the

_____

whose co

block is

s the tim

is ______

ke of 0.2

rtia force

crank, pl

g rod and

50 mm is

_

flexural

ith a 0.5

2) of the

flat plat

ensity of

efficients

acted up

e in seco

and rota

s of the sl

ced at a

crank. W

used for

rigidity,

kg mass

beam is

placed

ater as

of static

on by a

ds. The

tes with

lider are

distance

hen the



3

3

3

cran

nor

7. An

Conv

The

8. A rigi

= 2L

freq

(A)

9. A hy

2000

20

Som

angle (w

al to the

ffset sli

entionally

alue of Q

d uniform

3. Ends A

ency of t

2

k

m

rodynam

rpm. Bot

m and b

erfeld n

ith respec

lider axis i

er‐crank

, the Quic

R is ____

rod AB of

and B ar

e system i

ic journal

bearing

earing is

mber of t

t to slide

s ______

mechanis

Return R

__

length L

e support

s given by

(B) k

m

bearing is

ore diam

lubricate

e bearin

axis) is 3

m is sh

atio (QRR

nd mass

d by spri

subject t

eter and l

with an

is _____

0°, the u

wn in

is consid

is hinge

ngs of sp

(C)

2000 N l

ngth are

oil havi

_

balanced

he figur

red to be

at C suc

ing const

2k

m

oad at a r

40 mm. If

g viscosi

force (in

at an

greater t

that AC

nt k. The

(D)

tational

radial cle

y 0.03 P

newton)

instant.

an one.

L/3, CB

natural

5k

m

peed of

rance is

a.s, the



4

4

4

0. A 2

imm

the

/°C,

the r

1. 1.5 k

kJ/kg

tem

3277

2. Cons

figur

cons

is re

coeff

0 mm lo

vable rigi

oung’s m

espective

od is ____

g of wate

, hf = 50

erature o

.0 kJ/kg).

ider one

below)

ant heat

moved fr

icient of 2

ng, stress

d walls. T

dulus an

ly, the ma

___

is in satu

5 kJ/kg).

f water r

he heat a

imension

f thickne

lux, q" = 1

m the w

50 W/m2.

free rod

e temper

coefficie

gnitude o

rated liqui

Heat is a

aches 40

dded (in k

l steady

s

s 30 mm

× 105 W/

ll by con

. The tem

at room

ature of t

t of ther

f the lon

d state at

dded in

0°C (v =

) in the p

tate heat

and ther

2 is appli

ection w

perature (

tempera

he rod is

al expan

itudinal s

2 bar (vf

a constan

1.5493 m

ocess is _

conductio

al condu

ed. On th

ith a fluid

in °C), at

ture is h

niformly

ion are 2

ress (in

0.00106

t pressur

/kg, u =

_____

n across

a

tivity 15

other sid

at 25°C

= 0 is___

ld betw

raised by

0 GPa an

Pa) deve

m3/kg, uf

process

2967.0 kJ

wall

(as

s

/m.K. At

e of the w

and heat

___

en two

50°C. If

1× 10‐5

loped in

= 504.0

till the

kg, h =

hown in

x = 0, a

all, heat

transfer



43. Water flows through a pipe having an inner radius of 10 mm at the rate of 36 kg/hr

at 25°C. The viscosity of water at 25°C is 0.001 kg/m.s. The Reynolds number of the

flow is_______

44. For a fully developed flow of water in a pipe having diameter 10 cm, velocity 0.1

m/s and kinematic viscosity 10‐5 m

2/s, the value of Darcy friction factor is_______

45. In a simple concentric shaft‐bearing arrangement, the lubricant flows in the 2 mm

gap between the shaft and the bearing. The flow may be assumed to be a plane

Couette flow with zero pressure gradient. The diameter of the shaft is 100 mm and

its tangential speed is 10 m/s. The dynamic viscosity of the lubricant is 0.1 kg/m.s.

The frictional

resisting

force

(in

newton)

per

100

mm

length

of

the

bearing

is

_______

46. The non‐dimensional fluid temperature profile near the surface of a convectively

cooled flat plate is given by

2

W

W

T T y ya b c

T T L L∞

− ⎛ ⎞= + + ⎜ ⎟− ⎝ ⎠ , where y is measured

perpendicular to the plate, L is the plate length, and a, b and c are arbitrary

constants. TW and T∞ are wall and ambient temperatures, respectively. If the

thermal conductivity of the fluid is k and the wall heat flux is q", the Nusselt

number "

W

q L Nu

T T k ∞

=−

. is equal to

(A) a (B) b (C) 2c (D) (b + 2c)

47.

In an

air

‐standard

Otto

cycle,

air

is

supplied

at

0.1

MPa

and

308

K.

The

ratio

of

the

specific heats (γ) and the specific gas constant (R) of air are 1.4 and 288.8 J/kg.K,

respectively. If the compression ratio is 8 and the maximum temperature in the

cycle is 2660 K, the heat (in kJ/kg) supplied to the engine is _______



4

4

5

5

8. A re

certa

rese

(A) 0

9. An id

MPa,

both

high

enth

for r

Disre

0. Jobs

jobs

40 m

at th

(A)

1. A m

rod a

minu

ersible h

in amoun

voir at 40

.8

eal rehea

with reh

turbines i

pressure

lpy of wa

levant da

garding th

arrive at

ollows Po

inutes. Th

facility p

tal rod of

t any inst

tes. The t

at engine

t of heat

K. The n

(B) 1.

Rankine

at being

s 500°C a

turbine a

ter at the

a.

e pump w

facility a

isson dist

e service

er shift wil

(B) 14

3

initial len

nt is give

ue strain

receives

from a r

t work ou

ycle oper

one at 4

nd the en

nd 2247

exit from

ork, the c

an avera

ibution. T

time follo

ll be

th L0 is s

n by the e

ate (in mi

2 kJ of h

servoir a

tput (in kJ

(C) 1.4

tes betw

MPa. The

halpy of

J/kg at t

the pum

cle efficie

e rate of

he averag

s expon

(C) 7

5

bjected t

xpression,

n‐1) at the

at from

t 800 K. I

) of the cy

en the pr

temperat

team is 3

e exit of

is 191 kJ

ncy (in pe

5 in an 8

service t

ntial dist

a drawin

L(t) = L0(

end of on

reservoi

t rejects

cle is

(D) 2.0

essure lim

re of ste

185 kJ/kg

low pres

/kg. Use t

rcentage) i

hour shift.

ime of a j

ibution. I

(D) 10

3

g process.

+ t2), wh

minute i

at 1000

1 kJ of h

its of 10 k

m at the

at the ex

sure turbi

he followi

s ______

The arriv

b on the

le time (i

The lengt

re t is th

_______

K and a

at to a

a and 8

inlets of

it of the

ne. The

ng table

l of the

acility is

n hours)

h of the

time in



5

5

5

5

2. Duri

that

degr

oper

3. For t

(A) P

(C) P

4. If th

the t

5. An a

hole

core

____

g pure o

the thick

e rake a

tion is __

he given a

‐I, Q ‐III, R‐

II, Q ‐III, R

Taylor’s t

ol life (in

luminium

of 100 m

(density 1

________

thogonal

ess of th

ngle tool

_____

ssembly: 2

IV, S‐II

IV, S‐I

ool life ex

min) for

alloy (den

m diamet

600 kg/m3

____

urning o

e chip pr

is 0.2 m

5 H7/g8,

onent n i

aximum

sity 2600

r and 10

). The net

eration o

duced is

m/rev. Th

atch Gro

(B) P‐I,

(D) P‐II,

0.2, and

roduction

kg/m3) ca

mm len

buoyancy

a hollo

0.5 mm.

e shear

up A with

Q ‐IV, R‐III,

Q ‐IV, R‐III

he tool c

rate is __

sting is t

th is ma

force (in

cylindric

The feed

train pro

Group B

S‐II

I, S‐I

anging ti

_____

be prod

e in the

ewton) a

l pipe, it

given to

uced du

e is 1.5

ced. A c

asting usi

ting on th

is found

he zero

ring the

in, then

lindrical

ng sand

e core is



Key for Excerise‐1

Q.NO Key/ Range

1 A

2 A

3

C

4 A

5 B

6 C

7 0.29 to 0.31

8 B

9 A

10 D

11

D

12 B

13 C

14 B

15 A

16 D

17 C

18 B

19 B

20

A

21 C

22 A

23 B

24 A

25 B

26 C

27 34 to 36

28 D

29 1.10 to 1.12

30 8.4 to 8.5

31 D

32 29 to 31

33 0.064 to 0.067

34 56 to 57

35 4.8 to 5.0

36 29 to 31

37 1.2 to 1.3

38 D

39 0.75 to 0.85

40

499 to

501

41 4155 to 4160

42 620 to 630

43 635 to 638

44 0.06 to 0.07

45 15 to 16

46 B

47 1400 to 1420

48 C

49 40 to 42

50 B

51 0.9 to 1.1

52 2.8 to 3.0

53 D

54 5.9 to 6.1

55 7 to 8

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Mechnaical_1