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 number 1 1 i i + − , where 1 i = − , is (A) – π (B) 2 π − (C) 2 π (D) π 4. The matrix form of the linear system 3 5 dx x y dt = − and 4 8 dy x y dt = + is (A) 3 5 4 8 x x d y y dt − ⎧ ⎫ ⎡ ⎤⎧ ⎫ = ⎨ ⎬ ⎨ ⎬ ⎢ ⎥ ⎩ ⎭ ⎣ ⎦⎩ ⎭ (B) 3 8 4 5 x x d y y dt ⎧ ⎫ ⎡ ⎤⎧ ⎫ = ⎨ ⎬ ⎨ ⎬ ⎢ ⎥ − ⎩ ⎭ ⎣ ⎦⎩ ⎭ (C) 4 5 3 8 x x d y y dt − ⎧ ⎫ ⎡ ⎤⎧ ⎫ = ⎨ ⎬ ⎨ ⎬ ⎢ ⎥ ⎩ ⎭ ⎣ ⎦⎩ ⎭ (D) 4 8 3 5 x x d y y dt ⎧ ⎫ ⎡ ⎤⎧ ⎫ = ⎨ ⎬ ⎨ ⎬ ⎢ ⎥ − ⎩ ⎭ ⎣ ⎦⎩ ⎭ 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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Mechanical Engineering ‐ Excerise‐1
1. Given that the determinant of the matrix
1 3 02 6 41 0 2
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥−⎣ ⎦
is – 12, the determinant of
the matrix
2 6 04 12 82 0 4
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥−⎣ ⎦
is
(A) – 96 (B) –24 (C) 24 (D) 96
2. 0
sin1 cosx
x xLtx→
−−
is
(A) 0 (B) 1 (C) 3 (D) not defined
3. The argument of the complex number11
ii
+−
, where 1i = − , is
(A) – π (B) 2π
− (C) 2π (D) π
4. The matrix form of the linear system 3 5dx x ydt
= − and 4 8dy x ydt
= + is
(A) 3 54 8
x xdy ydt
−⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥
⎩ ⎭ ⎣ ⎦ ⎩ ⎭ (B)
3 84 5
x xdy ydt
⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥−⎩ ⎭ ⎣ ⎦ ⎩ ⎭
(C) 4 53 8
x xdy ydt
−⎧ ⎫ ⎡ ⎤ ⎧ ⎫=⎨ ⎬ ⎨ ⎬⎢ ⎥
⎩ ⎭ ⎣ ⎦ ⎩ ⎭ (D)
4 83 5
x xdy 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 circ
cente
and t
(A) ze
(C) V
0. For th
I. Ma
II. A r
Indic
(A) B
(C) I i
1. A rig
figure
are g
Smallest
vibration
cular objec
er having v
the floor is
ero
opposite t
he given st
ating spur
revolute jo
ate the co
oth I and I
is false and
id link PQ
e. The mag
iven. The m
amount o
n
ct of radius
velocity V.
to the dire
tatements
gear teeth
oint is an ex
rrect answ
I are false
d II is true
is 2 m lon
gnitude an
magnitude
f damping
s r rolls wit
. The veloc
ction of m
:
h is an exam
xample of
wer.
(B) I is true
(D) Both I
ng and ori
nd directio
e of VP (in m
g for which
thout slipp
city at the
(
motion (
mple of hig
lower pair
e and II is f
and II are
ented at 2
n of veloc
m/s) at this
the motio
ping on a h
e point of
B) V in the
D) V vertic
gher pair
r
false
true
20o to the
ity VQ, and
s instant is
on is simple
orizontal l
contact be
e direction
cally upwar
e horizonta
d the direc
s
e harmoni
evel floor w
etween th
of motion
rd from th
al as show
ction of ve
c in free
with the
e object
e floor
wn in the
locity VP
1
1
1
1
(A) 2
2. Biot n
(A) co
(B) co
(C) in
(D) b
3. The m
with
(A) En
4. Cons
figure
The f
the c
at po
(A) 1
5. For a
‘B’, th
.14
number sig
onvective r
onductive
nertia force
uoyancy fo
maximum
a referenc
ntropy
ider a two
e below.
free stream
cylinder su
oint
complete
he conditio
(B) 1.8
gnifies the
resistance
resistance
e to viscou
orce to visc
theoretica
ce environm
(B) E
o‐dimensio
m velocity
rface temp
(B) 2
ly submerg
on of stabi
89
ratio of
in the fluid
in the soli
s force in t
cous force
al work obt
ment, is ca
Enthalpy
onal lamin
is U∞ and
perature T
ged body w
lity will be
(C) 1.21
d to condu
id to conve
the fluid
in the flui
tainable, w
alled
(C)
nar flow o
d the free
Ts. The loca
(C) 3
with centre
e
1
uctive resis
ective resis
d
when a sys
Exergy
over a long
stream te
al heat tran
e of gravity
(D) 0.96
stance in th
stance in t
tem intera
(D)
g cylinder
emperature
nsfer coeff
(D) 4
y ‘G’ and c
he solid
he fluid
acts to equ
) Rothalpy
r as shown
e T∞ is low
ficient is m
4
centre of b
uilibrium
n in the
wer than
minimum
uoyancy
(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