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1. What is the adverb for the given word below? Misogynous A. Misogynousness B. Misogynity

C. Misogynously D. Misogynous

Ans. C. 2. Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?

A. 47

48 B.

1

4

C. 13

48 D.

35

48

Ans. B. P Ram = 1/6; p Ramesh = 1/8 P(only at) = p(Ram) × p(not Ramesh) + p(Ramesh) ×

p(n0 × Ram) = 1 7 1 5

6 8 8 6

12 1

40 4

3. Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Dhoni, as well as the other team members of Indian team, _____ present on the occasion. A. were B. was

C. has D. have Ans. B. 4. An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O and P,

in that order. The cumulative distances travelled and the

corresponding electricity consumption are shown in the table below

The stretch where the electricity consumption per km is minimum is

A. M B. N C. O D. P Ans. D.

5. Choose the word most similar in meaning to the given

word: Awkward A. Inept B. Graceful

C. Suitable D. Dreadful Ans. A. 6. In the following sentence certain parts are underlined

and marked P, Q and R. One of the parts may contain

certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose D as your Answer: if there is no error The student corrected

all the errors the instru answer bookthat on the

P Q

ctor marked

R

A. P B. Q C. R D. No Error Ans. B. The is not required in „Q‟

7. Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statement:

I. All film stars are playback singers. II. All film directors are film stars.

Conclusions: I. All film directors are playback singers. II. Some film stars are film directors. A. Only conclusion I follows B. Only conclusion II follows C. Neither conclusion I nor II follows D. Both conclusions I and II follow

Ans. D. 8. Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year’s Budget. The artists expressed their deep anguish at their request not

being approved, but many of them remain optimistic about funding in the future. Which of the statement(s) below is/are logically valid and can be inferred from the above statements? i. The artists expected funding for the arts to increase this year.

ii. The Chief Minister was receptive to the idea of increasing funding for the arts. iii. The Chief Minister is a prominent artist. iv. Schools are giving less importance to arts education nowadays. A. iii and iv B. i and iv C. i, ii and iv D. i and iii Ans. B.

9. If a2 + b2 + c2 = 1 then ab + bc + ac lies in the interval

A. 2

1,3

B. 1

,12

C. 1

1,2

D. 2, 4

Ans. B. 10. A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and

the deer cover 8 metre and 5 metre per leap respectively, what distance in meters will the tiger have a run before it catches the deer? A. 800 B. 600 C. 500 D. 450 Ans. A.

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Tiger - 1leap ⇒ 8 meter

Speed = 5leap/hr = 40m/min Deer → 1leap = 5meter

speed = 4hr = 20m/min

Let at time ‘t’ the tiger catches the deer. ∴ Distance travelled by deer + initial distance between

them

50 × 8 400m = distance covered by tiger.

40 × t = 400 + 20t

t = 400

200 = 20 min

total distance 400 + 20 × t = 800ms

Q. 11 — Q. 25 carry one mark each. 11. For the given fluctuating fatigue load, the values of stress amplitude and stress ratio are respectively

A. 100 MPa and 5 B. 250 MPa and 5 C. 100 MPa and 0.20 D. 250 MPa and 0.20 Ans. C. From the figure,

max min250 , 50MPa MPa

Stress Amplitude, max min

2a

=

1

2(250 − 50) =

100MPa Stress ratio (R ratio) is the ratio of the minimum stress experienced during a cycle to the maximum stress experienced during a cycle.

Stress Ratio,

max

500.20

250

minR

12. For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation OO’ passing through the centre of gravity. A. Solid Cylinder

B. Rimmed wheel

`

C. Solid sphere

D. Solid cube

Ans. B. The mass moment of inertia is denoted by I and is given for a single particle of mass m as

2I mr

where O-O is the axis around which one is evaluating the mass moment of inertia, and r is the perpendicular distance between the mass and the axis O-O Now, since the mass of all the objects given is same, mass moment of inertia is directly proportional to r2. Therefore for maximum mass moment of inertia maximum mass should be located as much away from the centre as possible which in present options will be for rimmed wheel. 13. A gear train is made up of five spur gears as shown in the figure. Gear 2 is driver and gear 6 is driven member. N2. N3, N4. N5 and N6 represent number of teeth on gears 2, 3, 4, 5, and 6 respectively. The gear(s) which act(s) as idler(s) is/are

A. Only 3 B. Only4 C. Only 5 D. Both 3 and 5 Ans. C. The idler gear performs following two functions: 1) Change the direction of rotation of the output shaft, 2) An idler gear can assist to reduce the size of the input/output gears whilst maintaining the spacing of the shafts. From the figure we can see only gear 5 acting as idler gear. 14. In the figure, link 2 rotates with constant annular velocity C02. A slider link 3 moves outwards with a constant relative velocity where Q is a Point on slider 3 and P is a point on link 2. The magnitude and direction of Coriolis component of acceleration is given by

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A. 2 𝜔2𝑉𝑄/𝑃; direction or 𝑉𝑄/𝑃 rotated by 90° in the direction of

𝜔2 B. 𝜔2𝑉𝑄/𝑃direction of 𝑉𝑄/𝑃 rotated by 90° in the direction of 𝜔2

C. 2 𝜔2𝑉𝑄/𝑃; direction of 𝑉𝑄/𝑃 rotated by 90° opposite to the

direction of 𝜔2 D. 𝜔2𝑉𝑄/𝑃; direction of 𝑉𝑄/𝑃 rotated by 90° opposite to the

direction of 𝜔2

Ans. A. The magnitude of Coriolis component of acceleration is given by

22 QP

V ; and its direction is given as direction of Qp

V rotated

by 90°in the direction of 2

15. The strain hardening exponent n of stainless steel SS 304 with distinct yield and UTS values undergoing plastic deformation is A. n<0 B. n=0 C. 0<n<1 D. n=1 Ans. C. The strain hardening exponent n of stainless steel SS 304undergoing plastic deformation lies between 0 & 1. It decides the plastic deformation behaviour of the material. 16. In a machining operation, if the generatrix and directrix both are straight lines, the surface obtained is A. Cylindrical B. helical C. Plane D. surface of revolution Ans. C. Machine tools produce geometrical surfaces on the job with the help of some tool work motions i.e. generatrix and directrix (two vectors). Now you take a point and then let it move along a straight line along a straight path and then this straight line will be traversed in a perpendicular direction suppose it is moved in this direction. So this straight line now precedes goes like this along this direction. So the resultant of this moment of the straight line along this path will be the flat surface or a plane. This straight line is called generatrix and the other direction along which this straight line or generatrix travel is called directrix simply D directrix. Thus in a machining operation, if the generatrix and directrix both are straight lines, the surface obtained is a plane. 17. In fill mould (cavity-less) casting process, the pattern is made of A. expanded polystyrene B. wax C. epoxy D. plaster of Paris Ans. A. In fill mould (cavity-less) casting process, the pattern is made of expanded polystyrene since expandable polystyrene is a thermoplastic material that can be molded into a variety of complex, rigid shapes. 18. In the notation (a/b/c): (d/e/f) for summarizing the characteristics of queuing situation, the letters b and ‘d' stand respectively for A. service time distribution and queue discipline B. number of servers and size of calling source

C. number of servers and queue discipline D. service time distribution and maximum number allowed in system Ans. A. In Kendall’s notation for representing queuing model:

( / / ) : ( / / )a b c d e f ,

a arrival (or interarrival) distribution,

b departure(or service time)distribution, c number of parallel service channels in the system,

d service discipline, e maximum number of customers allowed in the system.

f calling source or population

19. Couette flow is characterized by A. steady. incompressible, laminar flow through a straight circular pipe B. filly developed turbulent flow through a straight circular pipe C. steady, incompressible, laminar flow between two fixed parallel plates D. steady. incompressible, laminar flow between one fixed plate and the other moving with a constant velocity Ans. D. Couette flow is the laminar flow of a viscous fluid in the space between two parallel plates, one of which is moving relative to the other. 20. The thermodynamic cycle shown in figure (T-s diagram) indicates

A. reversed Carnot cycle B. reversed Brayton cycle C. vapor compression cycle D. vapor absorption cycle Ans. B. Reverse Brayton cycle consists of two reversible isobaric and two reversible adiabatic process executed in anticlockwise direction since they are power consuming cycles. 21. The ratio of momentum diffusivity (v) to thermal diffusivity (α), is called A. Prandtl number B. Nusselt number C. Biot number D. Lewis number Ans. A. Prandtl number is defined as the ratio of momentum diffusivity (v) to thermal diffusivity (𝛼). Its value decides whether momentum diffusion (convection) is more effective or thermal diffusion(heat conduction). 22. Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is

𝐶𝑟 = 𝐶𝑚𝑖𝑛

𝐶𝑚𝑎𝑥 . The effectiveness (ε) of the condenser is

A. 1−exp [−𝑁𝑇𝑈(1+𝐶𝑟)]

1+𝐶𝑟 B.

1−exp [−𝑁𝑇𝑈(1−𝐶𝑟)]

1−𝐶𝑟 exp[−𝑁𝑇𝑈( 1−𝐶𝑟)]

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C.𝑁𝑇𝑈

1+𝑁𝑇𝑈 D. 1-exp(-NTU)

Ans. D.

for boiler & condenser maxC therefore min

max

0r

CC

C

The effectiveness of heat exchanger is

1 exp[ (1 )]

1 exp[ ]1 exp[ (1 )]

r

r r

NTU CNTU

C NTU C

Since 𝐶𝑟=0

23. Using a unit step size. The value or integral ∫ 𝑥Inx2

1dx by

trapezoidal rule is_______ A) 0.541 B) 0.693 C) 0.641 D) 0.725 Ans. B. Let y = xlnx Unit step size h = 1 As per trapezoidal rule

0 1 2

0 11

1 22

2 2

1 1

2( ..................)2

( ln ) 0

( ln ) 2ln 2 1.386

1ln (0 1.386) 0.693

2

n

xx

xx

hydx y y y y

y y x x

y y x x

ydx x xdx

24. If P(X) = 1/4, P(Y) = 1/3, and P(X ∩Y) = 1/12, the value of P(Y/X) is

A. 1

4 B.

4

25

C. 1

3 D.

29

50

Ans. C. Conditional probability gives

1( ) 12( )

1( ) 3

4

Y P X YPX P X

25. The lowest eigen value of the 2×2 matrix[4 21 3

] is _______

Ans. 2

2 – (Sum of diagonal elements) + (sum of all elements in the

matrix) = 0

2 7 10 0

5 2 0

2,5

Thus lowest eigen value of given matrix is 2

26. The value of lim𝑥→0 (− sin 𝑥

2 sin 𝑥 + 𝑥 cos 𝑥)is __________

A. -0.333 B. -0.455 C. 0.231 D. 0.545

Ans. A. Let

0

sin

2sin cos

0

0

xy

x x x

y

Applying L Hospital rule

0

sin cos 1lim

2sin cos 2cos cos sin 3x ox

x x

x x x x x x x

27. A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m. and it has wall thickness of 10 mm. The magnitude of maximum in-plane shear stress (in MPa) is_________ A. 22 B. 24 C. 25 D. 29 Ans. C.

Major Principal Stress=hoop stress= 12

h

Pd

t

Minor Principal Stress=longitudinal stress= 24

l

Pd

t

Maximum in-plane shear stress = 1 2

2 8

Pd

t

=

3500 10 4

8 .01

25MPa

28. A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respectively

A. 433 N and 250 N B. 250 N and 433 N C. 353.5 N and 250 N D. 250 N and 353.5 N Ans. A.

Applying lami’s theorem we get

29. Which of the following statements axe TRUE for damped vibrations? P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion

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Q. Logarithmic decrement method is used to determine the amount of damping in a physical system. R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion. S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity: A. P and Q only B. P and S only C. P, Q and R only D. Q and S only Ans. C. In case of viscous damping, drag force is directly proportional to the relative velocity. All other options are correct. 30. A drill is positioned at Point P and it has to proceed to point Q. The coordinates of Point Q in the incremental system of defining position of a point in CNC part program will be

A. (3, 12) B. (5, 7) C. (7, 12) D. (4, 7) Ans. D. The coordinates of Point Q in the incremental system in CNC part program to position the drill from point P to that are (4,7) since in incremental system new reference get change to point P. 31. Which two of the following joining processes are autogeneous? (i) Diffusion welding (ii) Electroslag welding (iii) Tungsten inert gas welding (iv) Friction welding A. (i) and (iv) B. (ii) and (iii) C. (ii) and (iv) D. (I) and (iii) Ans. A. A fusion welding process using heat without the addition of filler metal to join two pieces of the same metal is referred to as autogeneous. Here diffusion welding & friction welding are autogeneous. 32. Three parallel pipes connected at the two ends have flow-rates 𝑄1,𝑄2and𝑄3 respectively, and the corresponding frictional

head losses are ℎ𝐿1, ℎ𝐿2and ℎ𝐿3 respectively. The correct expressions for total flow rate (Q) and frictional head loss across the two ends (hL) are A. 𝑄 = 𝑄1 + 𝑄2 + 𝑄3; ℎ𝐿 = ℎ𝐿1 + ℎ𝐿2 + ℎ𝐿3 B. 𝑄 = 𝑄1 + 𝑄2 + 𝑄3; ℎ𝐿 = ℎ𝐿1 = ℎ𝐿2 = ℎ𝐿3 C. 𝑄 = 𝑄1 = 𝑄2 = 𝑄3; ℎ𝐿 = ℎ𝐿1 + ℎ𝐿2 + ℎ𝐿3 D. 𝑄 = 𝑄1 = 𝑄2 = 𝑄3; ℎ𝐿 = ℎ𝐿1 = ℎ𝐿2 = ℎ𝐿3 Ans. B.

The total flow rate 1 2 3Q Q Q Q across the main pipe &

frictional head loss across its two ends are

1 2 3L L L Lh h h h

33. A rigid container of volume 0.5 𝑚3contains 1.0 kg of water at 120°C (𝑣𝑓 = 0.00106 𝑚3/𝑘𝑔. 𝑣𝑔= 0.8908 𝑚3/𝑘𝑔). The state of

water is A. compressed liquid B. saturated liquid C. a mixture of saturated liquid and saturated vapor D. superheated vapor Ans. C. The specific volume of water during constant pressure will remain 𝜗 = (𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟)/(𝑚𝑎𝑠𝑠 of water) = 0.5/1 = 0.5m3/kg. Since specific volume of water lies between 𝑣𝑔 & 𝑣𝑓 at 120°C,

therefore the state of water is wet state i.e. a mixture of saturated liquid and saturated vapour. 34. Let 𝜙 be an arbitrary smooth real valued scalar function and V be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?

35. An air-standard Diesel cycle consists of the following processes: 1-2: Air is compressed isentropically. 2-3: Heat is added at constant pressure. 3-4: Air expands isentropically to the original volume. 4-1: Heat is rejected at constant volume.

If and T denote the specific heat ratio and temperature, respectively, the efficiency of the cycle is

A. 1 −𝑇4− 𝑇1

𝑇3− 𝑇2 B. 1 −

𝑇4− 𝑇1

𝛾(𝑇3− 𝑇2)

C. 1 −𝛾(𝑇4− 𝑇1)

𝑇3− 𝑇2 D. 1 −

𝑇4− 𝑇1

(𝛾−1)(𝑇3− 𝑇2)

Ans. B.

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th 𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒

ℎ𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑=

ℎ𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑−ℎ𝑒𝑎𝑡 𝑟𝑒𝑗𝑒𝑐𝑡𝑒𝑑

ℎ𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑=

3 2 4 1 4 1

3 2 3 2

( ) ( ) 1( )1

( ) ( )

P V

P

c T T c T T T T

c T T T T

Q. 36 — Q. 65 carry two marks each. 36. The value of moment of inertia of the section shown in the figure about the axis-XX is

A. 8.5050 × 106 𝑚𝑚4 B. 6.8850 × 106 𝑚𝑚4 C. 7.7625 × 106 𝑚𝑚4 D. 8.5725 × 106 𝑚𝑚4 Ans. B.

2 2 2

(120 60) (30 40) (30 40)( ) ( ) ( )xx x y A x y B x y CI I Ad I Ad I Ad

Since yd =0 for rectangular section A & for hollow rectangular

sections B & C

yd =(15 + 15)=30 mm. Putting these values in the above

equation we get

3 3

2

6 4

120 30 3060 2 30 30 30

12 12

6.885 10

xxI

mm

37. Figure shows a wheel rotating about O2. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is ________

a) 1200 b) 1100 c) 1400 d) 1500 Answer ||| 1400 Distance between points A & B= AB=300mm Velocity of point A=

2

80 /

80

A

A

V m s

V r

O A

Velocity of point B=

2

140 /

140

B

B

V m s

V r

O B

2

2

2 2

140 7

80 4

4

7

O B

O A

O A O B

Also O2B - O2A= BA=300mm Solving these two equations we get diameter of wheel(in

mm)=(2 O2B)= 2 700 1400mm

38. Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at 0 and a mass m at end P. The natural frequency of vibration of the system is

A. 𝑓𝑛 =1

2𝜋√

𝑘

4𝑚 B. 𝑓𝑛 =

1

2𝜋√

𝑘

2𝑚

C. 𝑓𝑛 =1

2𝜋√

𝑘

𝑚 D. 𝑓𝑛 =

1

2𝜋√

2𝑘

𝑚

Ans. A. For Equilibrium, moment about point O must be zero.

0OM

2 0

2

s

s

mg a kx a

mgx

k

Thus deflection of spring = 2

s

mgx

k

From similar triangles,

2

42

s

s

x

a a

mgx

k

Static deflection of mass is 4

2 s

mgx

k

4 4

1

2 4

n

n

g g k k

mg m

kf

m

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39. The number of degrees of freedom of the linkage shown in the figure is

A. -3 B. 0 C. l D. 23 Ans. C.

Degree of freedom is given as

1

1

3( 1) 2

1

F N P

P N L

Where N=Total number of links in a mechanism,

1P = Number of pairs having one degree of freedom,

L = Number of loops in a linkage

Here N = 6, 1P = 7 & L = 2

1P = 6+2-1= 7

F = 3(6-1)-(27) = 15-14 = 1 40. For ball bearings, the fatigue life L measured in number of

revolutions and the radial load F are related by 𝐹𝐿1/3 = 𝐾 , where K is a constant. It withstands a radial load or 2 kN for a life of 540 million revolutions. The load (in kN) for a life of one million revolutions is _______ A. 16.28 B. 15.20 C. 12.80 D. 13.40 Ans. A. The fatigue life L of a ball bearing measured in number of

revolutions and the radial load F are related by,1

3FL K where K is a constant. When radial load F1 is 2kN , life of bearing L1 is 540million revolutions. The load for a life of one million revolutions L2 is F2 is calculated as:

1 13 3

1 1 2 2F L F L

Since both L1 & L2 are in million revolutions we have 1 1

3 32

2

(2 540 ) ( 1 )

16.28

F

F kN

41. In a rolling operation using rolls of diameter 500 mm, if a 25 mm thick plate cannot be reduced to less than 20 mm in one Pass, the coefficient of friction between the roll and the plate is ___________ A. 0.1412 B. 0.1520 C. 0.80 D. 0.40 Ans. A. Thickness of the plate before rolling hi = 25mm Thickness of the plate after rolling hf = 20mm Radius of rolls R = (500/2) = 250mm The coefficient of friction between the roll and the plate is given as:

25 20 10.14142

250 50

i fh hh

R R

42. Ratio of solidification time of a cylindrical casting (height = radius) to that of a cubic casting of side two times the height of cylindrical casting is ______ A. 0.5625 B. 0.520 O C. 0.6080 D. 0.4060 Ans. A. According to Chvorinov principle, solidification time of casting is

given as

2

s

Vt K

SA

Where, K= mould constant, V = volume of casting & SA = surface area of casting

For cylindrical casting = 1

22

22 2s

r ht K

r rh

Since height = radius

1

23 2

2 22 2 16s

r rt K K

r r

For cubical casting =2

23 2

26 36s

L Lt K K

L

Since length of cubical casting = 2(height of cylindrical casting) = 2 (radius of cylindrical casting)

2

22 22

36 36 9s

rL rt K K K

Now, Ratio of solidification time of a cylindrical casting to that of a cubic casting is calculated as:

1

2

90.5625

16

s

s

t

t

43. The annual requirement of rivets at a ship manufacturing company is 2000 kg. The rivets are supplied in units of 1 kg costing Rs. 25 each. If it costs Rs. 100 to place an order and the annual cost of carrying one unit is 9% of its purchase cost, the cycle length of the order (in days) will be_________ A) 75 B) 77 C) 80 D) 85 Ans. B. Annual demand of rivets = D= 2000kg/year Purchasing cost = C= Rs. 25 /unit Ordering cost = Co = Rs. 100/order

Holding cost = Ch = (.09 25) Rs. 2.25/unit/year

Now, EOQ = Q* = 2 2 2000 100

421.632.25

o

h

DC

C

units

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The cycle length of the order = T* = *

*

421.6370.2108

2000

Q

D

year = (0.2108 365) 76.94 77 days

44. Orthogonal turning of a mild steel tube with a tool of rake angle 10° is carried out at a feed of 0.14 mm/rev. If the thickness of the chip produced is 0.28 mm. the values of shear angle and shear strain will be respectively A. 28°20´ and 2.19 B. 22°20´and 3.53 C. 24°30´ and 4.19 D. 37°20´ and 5.19 Ans. A.

Back rake angle 10

Feed = f =0.14mm/rev Cut chip thickness = t2 = 0.28mm For orthogonal cutting , uncut chip thickness = t1 = f =0.14mm

Chip thickness ratio r = 1

2

0.140.5

0.28

t

t

Shear angle is given as

cos 0.5cos10tan

1 sin 1 0.5sin10

28.33

r

r

Shear strain

tan( ) cot tan(28.33 10 ) cot 28.33 2.186

45. In a CNC milling operation, the tool has to machine the circular arc from Point (20, 20) to (10, 10) at sequence number 5 of the CNC Part program. If the center of the arc is at (20, 10) and the machine has incremental mode of defining Position coordinates, the correct tool Path command is A. N 05 G90 G01X-10 Y-10 R10 B. N05G91 G03X-10 Y-10R10 C. N05G90G03X-20 Y-20 R10 D. N05 G91 G02X-20 Y-20R10

Ans. B. For programming in incremental co-ordinates G90 code is used. Since for circular interpolation in clockwise direction G03 is used. In incremental mode of programming since reference is changed X-10 & Y-10 is applicable 46. A Prandtl tube (Pitot-static tube with C=1) is used to measure the velocity of water. The differential manometer reading is 10 mm of liquid column with a relative density of 10. Assuming g = 9.8 m/𝑠2, the velocity or water (in m/s) is ______. A) 1.12 B) 2.43 C) 1.328 D) 1.80 Ans. C. In Prandtl tube velocity of water flowing through pipe is calculated as

1

102 ( 1) 1 2 9.8 0.01 ( 1) 1.328 / sec

1

m

V

W

SV C gx m

S

47. Refrigerant vapor enters into the compressor of a standard vapor compression cycle at - 10°C (h = 402 kJ/kg) and leaves the

compressor at 50°C (h = 432 kJ/kg). It leaves the condenser at 30°C (h = 237 kJ/kg). The COP of the cycle is ________ A) 4.5 B) 5.5 C) 6.5 D) 5.0 Answer ||| 5.5 Enthalpy of refrigerant entering into compressor h1 = 402 kJ/kg Enthalpy of refrigerant leaving the compressor = h2 = 432 kJ/kg Enthalpy of refrigerant leaving the condenser &expansion device= h3 = h4 = = 237 kJ/kg

COP of the cycle = 1 3

2 1

( )R 402 2375.5

( ) 432 402i

h hE

W h h

48. Steam enters a turbine at 30 bar, 300°C (u = 2750 kJ/kg, h = 2993 kJ/kg) and exits the condenser as saturated liquid at 15 kPa (u = 225 kJ/kg. h = 226 kJ/kg). Heat loss to the surrounding is 50kJ/kg of steam flowing through the turbine. Neglecting changes in kinetic energy and potential energy, the work output of the turbine (in kJ/kg of steam) is ________ A) 2600 B) 2620 C) 2717 D) 2537 Ans. C. Enthalpy of saturated liquid at exit from the condenser =h4=226 kJ/kg Enthalpy of steam at exit from the turbine= h2=h4 + Qrej = (226 + 50) = 276 kJ/kg Enthalpy of steam at entry into the turbine = h1 = 2993 kJ/kg Work output of the turbine = h2 – h1 =(2993 - 276) = 2717 kJ/kg

49. Air in a room is at 35°C and 60% relative humidity (RH) The pressure in the room is 0.1 MPa The saturation pressure of water at 35°C is 5.63 kPa. The humidity ratio of the air (in grain/kg of dry air) is___ A) 21.74 B) 22.20 C) 25.17 D) 20.37 Ans. A.

DBT of air = 35 C

Air pressure = Pt = 0.1MPa = 100 kPa Saturation pressure of water = Pvs = 5.63 kPa Relative Humidity of air =

0.605.63

3.378

V V

VS

V

P P

P

P kPa

Humidity ratio of the air =

3.378

0.622 0.622 .02174100 3,378

V

t V

P

P P

kg/kgda =21.74 gm/kgda

50. A solid sphere 1 of radius ‘r’ is placed inside a hollow, closed hemispherical surface 2 of radius ‘4r’. The shape factor 𝐹2−1 is

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9 | P a g e

A. 1/12 B. 1/2 C. 2 D. 12 Ans. A. If F1-1 = Radiation from surface 1 to surface 1 F1-2 = Radiation from surface 1 to surface 2 F1-1 + F1-2 = 1 Since F1-1 = 0 (because sphere is solid surface) F1-2 = 1

As per reciprocity theorem 1 1 2 2 2 1AF A F

2 2 2

2 1

22

2 1

2 1

4 1 2

4 3 4

1

12

r R R F

r r F

F

51. The value of 2[ 3 8 4 6 ]c

x y dx y xy dy (where C is

the boundary of the region boundary by x = 0, y = 0 and x + y = 1) is ………………………… A) 7/4 B) 5/3 C) 4/3 D)2/3 Ans. B.

Let M = 23 8x y & N = 4 6y xy

In the boundary x varies from 0 to 1, accordingly y varies from 0 to 1-x As per Green’s Theorem

2

1 1 11

2

00 0 0

12

0

[ 3 8 4 6 ]

6 16 5

5 1

c

xx

dN dMx y dx y xy dy dxdy

dx dy

dN dMdxdy y y dxdy y dy

dx dy

x dy

Let 1-x =t ,-dx=dt As x varies from 0 to 1 ,t varies from 1 to 0.

1 0

2 2 3

0 1

5 55 1 5 1

3 3x dx t dt

52. For a given matrix 𝑃 = [4 + 3𝑖 −𝑖

𝑖 4 − 3𝑖], where 𝑖 = √−1 ,

the inverse of matrix P is

A. 1

24[4 − 3𝑖 𝑖

−𝑖 4 + 3𝑖] B.

1

25[

𝑖 4 − 3𝑖4 + 3𝑖 −𝑖

]

C. 1

24[4 + 3𝑖 −𝑖

𝑖 4 − 3𝑖] D.

1

25[4 + 3𝑖 −𝑖

𝑖 4 − 3𝑖]

Ans. C. Let A =

11

12

21

22

11 12

21 22

1

4 3

4 3

(4 3 )

( )

( )

(4 3 )

16 9 1 24

4 3

4 3

4 3

4 3

4 31

4 324

T T

i i

i i

C i

C i i

C i

C i

A

C C i iAdjA

C C i i

i i

i i

i iAdjAA

i iA

53. Newton-Raphson method is used to find the roots of the equation. 𝑥3 + 2𝑥2 + 3𝑥 — 1 = 0. If the initial guess is 𝑥0 =

1, then the value of x after 2𝑛𝑑 iteration is ____ A) 0.20 B) 0.25 C) 0.25 D) 0.30 Ans. D.

3 2

0

2 3 1 0

1

x x x

x

As per Newton-Raphson Method

01 0

0

( )

( ')

(1 2 3 1) 11

3 4 3 2

f xx x

f x

Similarly

12 1

1

( )

'( )

1 1 3( 1)

1 1 98 2 2 0.3043432 2 46

2 34

f xx x

f x

12 1

1

( )

'( )

1 1 3( 1)

1 1 98 2 2 0.3043432 2 46

2 34

f xx x

f x

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54. Laplace transform of the function f (t) is given by 𝐹(𝑠) =

𝐿{𝑓(𝑡)} = ∫ 𝑓∞

0(𝑡)𝑒−𝑠𝑡 𝑑𝑡. Laplace transform of the function

shown below is given by

A. 1−𝑒−2𝑠

𝑠 B.

1−𝑒−𝑠

2𝑠

C. 2−2𝑒−𝑠

𝑠 D.

1−2𝑒−𝑠

𝑠

Ans. C.

0

stF s L f t f t e dt

Now, 𝑓(𝑡) = 2 for 0<x<1

1

0

2 22

sst e

F s e dts

55. A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots.

Helical slots are such that one turn of helix is completed over a distance of 0.5 m. If velocity of bullet when it exits the barrel is 20 m/s, its spinning speed in rad/s is_____ A) 254 B) 251 C) 240 D) 244 Ans. B. Horizontal distance travelled in one turn of helix = s=0.5m Velocity of bullet at exit =v=20 m/s

Time taken by bullet in one turn of helix =.5 1

sec20 40

s

v

During one turn of helix

Angular displacement radian

Initial angular velocity 0i

Time taken=1/40 sec Using equation of motion under rotation

21

2

1

2

22 40 251.32 / sec

i

f

f

t t

t

radt

56. For the overhanging beam shown in figure, the magnitude or maximum bending moment (in kN-m) is________

A) 45 B) 49 C) 40 D) 44 Ans. C. For overhanging beam to remain in equilibrium

20 (10 4) 60

0

( 4) (20 6) (10 4 2) 0

50

60 60 50 10

A B

A

B

B

A B

R R

M

R

R kN

R R kN

At any point between A & B, shear force =10 -10x and it will be10x and it will be zero at x=1m from A Also shear force changes sign at x=4m from A i.e. B So bending moment will be maximum at x=1m or x= 4 m

1

4

( ) (10 1) 10

( ) (10 4) (10 4 2) 40

x m

x m

BM kNm

BM kNm

So bending moment is maximum at x=4m or at point B = -40kNm 57. The torque (in N-m) exerted on the crank shaft of a two stroke engine can be described as 𝑇 = 10000 + 1000𝑠𝑖𝑛2𝜃 − 1200 𝑐𝑜𝑠 2𝜃, where 𝜃is the crank angle as measured from inner dead center Position. Assuming the resisting torque to be constant, the Power (in kW) developed by the engine at 100 rpm is ____ A) 104 B) 145 C) 140 D) 102 Ans. A. The torque on the crankshaft is given as

10000 1000Sin2 1200 os2T C

Since the torque is a function of 2 , the cycle is repeated after

every 180 of the crank rotation.

0 0

1 1(10000 1000sin 2 1200cos 2 )

110000 10000

meanT Td d

Nm

Now, Power developed by the engine =

2 10010000 104.72

60T kW

58. A cantilever bracket is bolted to a column using three M12×1.75 bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in MPa) is______

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11 | P a g e

A) 490 B) 445 C) 340 D) 446 Ans. A.

Since r for P & Q =2 230 250 251.8mm

The primary and secondary shear forces are

' ' '

1'' ''

2 2 2 2

1 2

90003000

3

9000 250 3037500

( ) (30 30 )

Q P R

P R

P P P N

Pe rP P N

r r

Neglecting the maximum shear force developed ar bolt P is P

= '

PP +''

PP = (3000+37500) N = 40500N

pA = 2 22 212 1.75 82.51

4 4 4cd d p mm

Maximum shear stress at bolt P =

40500490.8

82.51p

PMPa

A

59. A shaft of length 90 mm has a tapered portion of length 55 mm. The diameter of the taper is 80 mm at one end and 65 mm at the other. If the taper is made by tailstock set over method the taper angle and the set over respectively are A. 15°32´ and 12.16mm B. 18°32´ and 15.66 mm C. 11°22´ and 10.26 mm D. 10°32´ and 14.46mm Ans. A.

Taper angle= 2

80 65

2tan

55

7.765

Taper angle= 2 2 7.765 15.53

Set over =

1

(80 65)90 12.27

2 2 55

D dL mm

L

60. The dimensions of a cylindrical side riser (height — diameter) for a 25 cm × 15 cm × 5 cm steel casting are to be determined. For the tabulated shape factor values given below, the diameter of the riser (in cm) is______

A) 11.2 B) 24.5 C) 12.6 D) 10.6

Ans. D. shape factor = (length + width/thickness)=(25 + 15)/5 = 8 From the given table

3

2

3

0.50

0.50(25 15 5) 937.5

937.54

937.54

10.60

R

C

R

V

V

V cm

d h

d

d cm

The diameter of the riser is 10.60cm 61. For the linear programming problem: Maximize 𝑍 = 3𝑋1 + 2𝑋2 Subject to −2𝑋1 + 3𝑋2 ≤ 9 𝑋1 − 5𝑋2 ≥ −20 𝑋1, 𝑋2 ≥ 0 The above problem has A. unbounded solution B. infeasible solution C. alternative optimum solution D. degenerate solution Ans. A. 𝑋1 − 5𝑋2 ≥ −20 may be reduced as

1 2

1 2

5 20

120 4

X X

X X

1 2

1 2

2 3 9

14.5 3

X X

X X

Plotting these two equations in cartesian co-ordinates & applying the given conditions we will get unbounded solution. 62. Which of the following statements are TRUE, when the cavitation parameter σ = 0? (i) the local pressure is reduced to vapour pressure (ii) cavitation starts (iii) boiling of liquid starts (iv) cavitation stops (a) i, ii and iv (b) only ii and iii (c) only i and iii (d) i, ii and iii Ans. B. cavitation number, σ, is defined as

2

( )

1

2

vp p T

LU

where U , p and ( )T are respectively a reference velocity,

pressure and temperature in the flow (usually upstream

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12 | P a g e

quantities), ρL is the liquid density and vp ( )T is the saturated

vapor pressure. Now, when

0

( )vp p T

Thus boiling occurs & cavitation starts. 63. One side of a wall is maintained at 400 K and the other at 300 K. The rate of heat transfer through the wall is 1000 W and the surrounding temperature is 25°C. Assuming no generation of heat within the wall, the irreversibility (in W) due to heat transfer through the wall is______ A) 274 B) 248 C) 360 D) 244 Ans. B. The energy rate equation of the wall is

* 1 * 1

298 2981000 1 1000 1

400 300

248.33

o o

in out

T TQ Q I

T T

I

I W

64. A brick wall (k =0.9𝑤

𝑚.𝑘) of thickness 0.18 m separates the

warm air in a room from the cold ambient air On a particular winter daw the outside air temperature is —5°C and the room needs to be maintained at 27°C. The heat transfer coefficient

associated with outside air is 20 (𝑊

𝑚2𝑘).Neglecting the

convective resistance of the air inside the room, the heat loss, in

(𝑊

𝑚2), is

A. 88 B. 110 C. 128 D. 160 Ans. C. The heat transfer rate is given as

2 2

2

2

2

300 268*

0.18 1

0.9 20

274.4

300*

0.18

0.9

300 274.4*128

0.18

0.9

w w

w

w

T TQ

A A

T K

TQ

A

Q W

A m

65. A mixture of ideal gases has the following composition by mass:

If the universal gas constant is 8314 J/kmol-K. The characteristic gas constant of the mixture (in J/kg-K) is A) 274 B) 245 C) 340 D) 244 Ans. A. Let x be the total mass of gas in kg Moles of N2, O2, & CO2 are

Molecular mass of ideal gas = total mass of gas/total no. of moles

1

0.60 0.30 0.10 0.033

28 32 44

xM

x

Characteristic gas constant =

8314274.362 /

1/ 0.033

URR J kgKM

***