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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 + + + + + +
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(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
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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
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(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)
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(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
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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)
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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
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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
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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
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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 _______
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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
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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
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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