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1

Mechanical Engineering

Q. No. 1 to 25 Carry One Mark Each

1. A mass m of a perfect gas at pressure p1 and volume V1 undergoes an isothermal process. The

final pressure is p2 and volume is V2. The work done on the system is considered positive. If R

is the gas constant and T is the temperature, then the work done in the process is

(A) 21 1

1

Vp V ln

V (B) 1

1 1

2

pp V ln

p (C) 2

1

VRT ln

V (D) 2

1

pmRT ln

p

Key: (B)

Exp: Isothermal work done, W pdV

For isothermal, pV= C

2

1

1 1

V

1 1

V

2 11 1 1 1 1 1 2 2

1 2

p V pV C constant

dVso, W p V

V

V pW p V n p V n ( p V p V )

V p

2. Which one of the following statements is TRUE for the ultrasonic machining (USM) process?

(A) In USM, the tool vibrates at subsonic frequency.

(B) USM does not employ magnetostrictive transducer.

(C) USM is an excellent process for machining ductile materials.

(D) USM often uses a slurry comprising abrasive-particles and water.

Key: (D)

3. The standard deviation of linear dimensions P and Q are 3 m and 4 m, respectively. When

assembled, the standard deviation (in m ) of the resulting linear dimension (P+Q) is ________

Key: 5 to 5

Exp: Given that

Standard deviate of P is 3 m Variance of P is 9 m

Standard deviation of Q is 4 m Variance of Q is 16 m

Variance of P + Q = Var (P+Q) = Variance P + Variance Q

= 9 + 16= 25

Standard deviation of P + Q = + Variance = + 25 = 5

4. The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive

power becomes.

(A) 2P (B) 4P (C) 8P (D) 16P

Key: (D)

Exp: Emissive power of black body 4

bE T

Given 4

b 1E P T




2

4 4

b b2 2

now T 2T

E 2T 16 T E 16P

5. The state of stress at a point is x y z xz zx yz zy xy yx0 and 50MPa .

The maximum normal stress (in MPa) at that point is _________

Key: 49.9 to 50.1

Exp: It is a pure torsion case in 2D

xy yx 50MPa

xy yx 1

for pure Torsion,

So maximum Normal stress 1 50MPa

6. The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other

eigenvalue is ___________

Key: 5 to 5

Exp: Given that det of 2×2 Matrix is 50 and are Eigen Value is 10.

Other Eigen value is 5 det product of eigenvalues

7. Which one of the following statement is TRUE?

(A) Both Pelton and Francis turbines are impulse turbines.

(B) Francis turbine is a reaction turbine but Kaplan turbine is an impulse turbine.

(C) Francis turbine is an axial – flow reaction turbine.

(D) Kaplan turbine is an axial – flow reaction turbine.

Key: (D)

8. Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of

getting at least one head is ____________

Key: 0.75 to 0.75

Exp: Total No of outcomes when two coins are tossed is 4 and sample space

S HH,HT,TH,TT

Favorable out comes for existence of at least one head are HH, HT, TH.

Required probability = 3

0.754

9. A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free

end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear)

(A) 2 3P L

6EI (B)

2 3P L

3EI (C)

3PL

3EI (D)

3PL

6EI

Key: (A)

xy0,

xy0,

1




3

Exp: x

L 2 2 2

x

0

2 3

M P.x

M dx P x dxU

2EI 2EI

P LU

6EI

10. It is desired to make a product having T-shaped cross-section from a rectangular aluminium

block. Which one of the following processes is expected to provide the highest strength of the

product?

(A) Welding (B) Casting (C) Metal Forming (D) Machining

Key: (C)

11. The heat loss from a fin is 6W. The effectiveness and efficiency of the fin are 3 and 0.75,

respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base

temperature, is __________.

Key: 7.9 to 8.1

Exp: Given LossQ 6W

act loss

max

max

3, 0.75

Q Q

Q Heat loss keep entire fin as base temperature

6Q 8W

0.75

12. For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per

hour. Which one of the following service rates will provide a steady state finite queue length?

(A) 6 per hour (B) 10 per hour (C) 12 per hour (D) 24 per hour

Key: (D)

Exp: 12 / hour

For steady state finite queue length

So, 24 / hour

13. For the stability of a floating body the

(A) centre of buoyancy must coincide with the centre of gravity

(B) centre of buoyancy must be above the centre of gravity

(C) centre of gravity must be above the centre of buoyancy

(D) metacentre must be above the centre of gravity

Key: (D)

Exp: Stability of floating body is measure with the help of Meta center.

Floating body to be stable, Meta center must be above C.G

I

MG BG

,

For stability MG > 0

x xL

Px




4

14. The divergence of the vector yi xj __________

Key: 0 to 0

Exp: Let F yi xj

divergence of F y x 0x y

15. For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along

the length is M(x) = 5x2+10x, where x is the distance (in mm) measured from the free end of

the beam. The magnitude of shear force (in N) in the cross-section at x =10 mm is ________.

Key: 110 to 110

Exp:

2

x 10mm

dS.F (B.M)

dx

dS.F 5x 10x

dx

S.f 10x 10 S.F 10 10 10 110N

16. A sample of 15 data is a follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of

the data is

(A) 4 (B) 13 (C) 17 (D) 20

Key: (C)

Exp: We know that mode is the value of the data which occurred most of

17 is mode

17. If a mass of moist air contained in a closed metallic vessel is heated, then its

(A) relative humidity decreases (B) relative humidity increases

(C) specific humidity increases (D) specific humidity decreases

Key: (A)

Exp: Given that mass of moist air contained in a closed metallic vessel is heated, means its specific

humidity is constant.

So, from the psychometric chart,

We can say that at constant specific humidity, as temperature increases relative humidity

decreases i.e., 2 1

So, Answer is (A)

1 2

12

Relative humidity

100%

DBT




5

18. In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100mm and

160mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counter-

clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding

to the configuration shown in the figure is _____________

Key: 0.99 to 1.01

Exp: sin 2

V r sinn

o

if 90

sin180V r sin90 0.1 1 sin90 1m sec

2n

19. A machine component made of a ductile material is subjected to a variable loading with

min max50 MPa and 50 MPa. If the corrected endurance limit and the yield strength for

the material are '

e y100 MPa and 300MPa, the factor of safety is __________

Key: 1.99 to 2.01

Exp: max

min

y

e

50MPa

50MPa

300MPa

100MPa

max minmax

max minv

max v

yt e

50 500

2 2

50 5050

2 2

1

F.S

0 50 1

300 100 F.S

F.S 2

20. The crystal structure of aluminium is

(A) body-centred cubic (B) face-centred cubic

(C) close-packed hexagonal (D) body-centred tetragonal

Key: (B)

21. A steel bar is held by two fixed supports as shown in the figure and is subjected to an increases

of temperature T 100 C. and 200GPa, respectively, the magnitude of thermal stress (in

MPa) induced in the bar is __________.




6

Key: 218 to 222

Exp: Thermal Stress,

3 6

Th E T 200 10 11 10 100 220MPa

22. The Laplace transform of tte is

(A)

2

s

s 1 (B)

2

1

s 1 (C)

2

1

s 1 (D)

s

s 1

Key: (B)

Exp:

at

t

2

L e f t F s a1L te ;

s 1 where F s L f t

23. Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is

denoted byw . The axial positions x1 and x2 on the plate are measured from the leading edge

in the direction of flow. If x2 > x1, then

(A) 1 2

w wx x0 (B)

1 2w wx x

0 (C) 1 2

w wx x (D)

1 2w wx x

Key: (C)

Exp: w w1 2

w

y 0 y 0 y 01 2

u u u

y y y

24. A mass m is attached to two identical springs having spring constant k as shown in the figure.

The natural frequency of this single degree of freedom system is

(A) 2k

m (B)

k

m

(C) k

2m (D)

4k

m

Key: (A)

Exp: Equivalent stiffness keq = k + k = 2k

Natural frequency, eq

n n

k 2k

m m

25. Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in

cementite (Fe3C) is _________.

Key: 6.3 to 7.0

Exp: Percentage of carbon by weight in cementite =12

100 6.67%56 3 12




7

Q. No. 26 to 55 Carry Two Marks Each

26. In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is

0.2mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the

maximum shear angle to the minimum shear angle during machining is ___________

Key: 1.45 to 1.53

Exp:

1

c

9

t 0.2mm

t 0.25mm to 0.4mm

1

c

o

c

o

c

max

min

tr costan , where r

1 r sin t

if t 0.25mm, r 0.8 & 42.08

if t 0.4mm, r 0.5 & 28.18

42.081.493

28.18

27. A cylindrical pin of 0.020

0.01025

mm diameter is electroplated. Plating thickness is 0.0052.0 mm.

Neglecting the gauge tolerance, the diameter (in mm, up to 3 decimal points accuracy) of the

GO ring gauge to inspect the plated pin is _________.

Key: 29.030 to 29.030

Exp: Diameter of GO end of ring gauge = 25.02 + 2(2.005) = 29.030mm

28. A helical compression spring made of wire of circular cross-section is subjected to a

compressive load. The maximum shear stress induced in the cross-section of the wire is 24

MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are

doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.

Key: 6 to 6

Exp:

max 3

1

1 2 2 1 2 1

331 1 2

3

2 2 1 2

2

2

8P.D

d

Given, 24MPa

P P , d 2d , D 2D

D d 24 1so, . 2

D d 2

24MPa

4

6MPa

29. In a counter-flow heat exchanger, water is heated at the rate of 1.5kg/s from 40°C to 80°C by

an oil entering at 120°C and leaving at 60°C. The specific heats of water and oil are

4.2kJ/kg.K and 2kJ/kg.K respectively. The overall heat transfer coefficient is 400 W/m2.K.

The required heat transfer surface area (in m2) is

(A) 0.104 (B) 0.022 (C) 10.4 (D) 21.84

Key: (D)

Exp: Given counter flow Heat Exchanger




8

Water –

i

o

c

c

c

c

p

m 1.5kg / s

T 40 C

T 80 C

C 4.2KJ / kg.K

Oil - i

o

o

h

h

p

T 120 C

T 60 C

C 2kJ / kg.K

Overall Heat Transfer Coefficient = 400 W/m2K

Area (A) =?

c o i

c o i

c p c c

c p c c

i o

i o

3

2 2

Q UA LMTD

m C T T UA LMTD

m C T TA

Un( / )

1.5 4.2 80 40 1021.83m A 21.83m

40 20400

40n20

30. The rod PQ of length L = 2 m, and uniformly distributed mass of M = 10 kg, is released

from rest at the position shown in the figure. The ends slide along the frictionless faces OP and

OQ. Assume acceleration due to gravity, g = 10 m/s2. The mass moment of inertia of the rod

about its centre of mass and an axis perpendicular to the plane of the figure is (ML2/12). At

this instant, the magnitude of angular acceleration (in radian/s2) of the rod is ____________

Key: 7.25 to 7.75

Exp: 2M 10kg, g 10m sec

2

2

2

c

2

I

ML

12

M 2 1 2M M 2MI M

12 12 2 32

2MT I Mg 0.5

3

210 0.5

3

157.5rad sec

2

I

o

i

h

o

c

T 60 C20

T 40 C

i

o

h

i

c

T 120 C40

T 80 C

1m

Mg

1

2

1m

I

0.5




9

31. A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a

load of 6kN as shown in the figure. Considering the effect of direct load and moment, the

magnitude of resultant shear force (in kN) on bolt C is.

(A) 13 (B) 15 (C) 17 (D) 30

Key; (C)

Exp:

2 2 2 21 2

1 1

A C 1

6Pr imary shear 2kN

3

Secondaryshear 1500 kN mm

P e 1500M 0.3

r r 50 50

R R C r 0.3 50 15kN

Resultant shear at 'C' 2 15 17kN.

Resultant shear 15 2 17kN.

32. The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m3

and 300K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the

vessel is 0.5bar. If the gas constant of air is R = 287 J/kg. K and the atmospheric pressure is 1

bar, the mass of air (in kg) in the vessel is

(A) 1.67 (B) 3.33 (C) 5.00 (D) 6.66

Key: (C)

Exp: 3

gauge

atm

abs g atm

V 2.87m ; T 300K

P 0.5bar

R 287J / kg.K

P 1 bar

P P P 1.5bar

5

PV mRT

PV 1.5 10 2.87So, m 5kg

RT 287 300

33. For the laminar flow of water over a sphere, the drag coefficient CF is defined as

2 2

FC F / U D , where F is the drag force, is the fluid density, U is the fluid velocity and

D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the

sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows

over another sphere of diameter 200mm under dynamically similar conditions, the drag force

(in N) on this sphere is _____________




10

Key: 19.9 to 20.1

Exp: Given that the condition is dynamic similarity, and in the given condition, Inertia and viscous

force plays major role, hence Reynold‟s number should be same for both model and prototype.

1 2

Re Re

In the first case: 3

1 1U 2m sec, D 100 mm, 1000 kg m

In the second case: 3

2 2U 2m sec, D 200mm, 1000 kg m

1 2

UD UD

Since same water is flowing over both sphere

1 2 1 2

1 1 2 2

2

2

,

U D U D

2 100 V 200

U 1m sec

So, Drage force in second case will be

22 2 2

2 F 2 2F C U D 0.5 1000 (1) 0.2 20N

34. A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is

compressed to make a rod of final length 10mm. Consider the longitudinal tensile strain as

positive and compressive strain as negative. The total true longitudinal strain in the rod is

(A) –0.5 (B) –0.69 (C) –0.75 (D) –1.0

Key: (B)

Exp: i f

fTrue

i

20mm 10mm

truestrain,

10n n 0.69

20

35. A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are

mounted on the same shaft. All the gears are mounted on parallel shafts and the number of

teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The

speed (in rpm) of the gear S is _________.

Key: 120 to 120

Exp: P Q R S

P

T 24, T 45, T 30, T 80

N 400rpm

P P Q QN .T N T




11

Q

Q Q S S

S

400 24N 213.33rpm

45

N T N T

213.33 45N 120rpm

80

36. In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg

and 1800 kJ/kg, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg and 124

kJ/kg, respectively. The specific steam consumption (in kg/k W.h) of the cycle is ______

Key: 3.5 to 3.7

Exp: Given that,

1 2

3 4

h 2803 kJ / kg, h 1800kJ / kg

h 121kJ / kg, h 124kJ / kg

T 1 2

p 4 3

net T P

net

W h h

2803 1800 1003kJ / kg

W h h

124 121 3kJ / kg

W W W 1000kJ / kg

3600Specific Steam consumption 3.6kg / kWh

W

37. A calorically perfect gas (specific heat at constant pressure 1000 J/kg.K) enters and leaves a gas

turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K

and 400 K. respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s

through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is.

(A) 6.14 (B) 7.00 (C) 7.50 (D) 8.00

Key: (B)

Exp: Given that,

p

1

2 L

in out

C 1000J / kgK

T 1100K, P 4.6MW

T 400K, Q 300kJ / s

E E

2 2

1 21 1 2 2 L

V Vh gz h gz Q P

2 2

1 2 1 2

1 2 L

V V , Z Z

So, h h Q P

p 1 2 L

3 6

mC T T Q P

300 10 4.6 10m

1000 1100 400

m 7kg / sec

4

32

1

T

S

P

LQ

21




12

38. Three masses are connected to a rotating shaft supported on bearings A and B as shown in the

figure. The system is in a space where the gravitational effect is absent. Neglect the mass of

shaft and rods connecting the masses. For m1 = 10kg, m2 = 5kg and m3 = 2.5 kg and for a shaft

angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is

_________.

Key: 0 to 0

Exp: 1 1

2 2

3 3

m 10kg, r 0.1m

m 5kg, r 0.2m

m 2.5kg, r 0.4m

x 1 1 1 2 2 2 3 3 3

o o o

o o

y 1 1 1 2 2 2 3 3 3

A B

F m r cos m r cos m r cos

10 0.1 cos0 5 0.2 cos120 2.5 0.4 cos240

1 0.5 0.5 0

F m r sin m r sin m r sin 0 5 0.2 sin120 2.5 0.4sin 240 0

R R 0kN

39. A strip of 120 mm width and 8mm thickness is rolled between two 300 mm-diameter rolls to

get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30

m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the

roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive

the two rolls is _________.

Key: 9.4 to 9.8

Exp: Width = 120mm

Initial thickness to = 8mm

Diameter of Roller = 300mm

Radius of Roller = 150mm

Final thickness = 7.2mm

i fh t t 8 7.2 0.8 mm

Power require to drive one roller

p pP T. F L .A.L . Here, PA L b

2

pP L .b phere, L R h

6 3

VP R h .b.

R

30200 10 0.8 10 0.12 4.8 kW

60

So, power require to drive 2 roller = 2P 2 4.8 kW 9.6 kW




13

40. A product made in two factories p and Q, is transported to two destinations, R and S. The per

unit costs of transportation (in Rupees) from factories to destinations are as per the following

matrix:

Destination

Factory R S

P 10 7

Q 3 4

Factory P produces 7 units and factory Q produces 9 units of the product. Each destination

requires 8 units. If the north-west corner method provides the total transportation cost as X (in

Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (X-Y),

in Rupees, is

(A) 0 (B) 15 (C) 35 (D) 105

Key: Answer is not matched with IIT Key

Exp:

By North West corner Rule

Total cost, x = 10×7+7×1+4×8 = Rs.105

By VAM

Total minimum Cost, y = 3×8+4×1+7×7=Rs.77

So, x–y = Rs.28

41. One kg of an ideal gas (gas constant R = 287 J/kg.K) undergoes an irreversible process from

state-1 (1 bar, 300 K) to state -2 (2 bar, 300 K). The change in specific entropy (s2 – s1) of the

gas (in J/kg. K) in the process is ___________

Key: –201 to –197

Exp: Given

1 2

1 2

m 1kg, R 287J / kg.K

P 1bar, P 2bar

T 300K, T 300K

22 1

1

Same Temperature

P 2S S R n 287 n 198.93J / kgKP 1

10 7

3 4

R S

P 7

Q 9

8 8

10 7

3 4

R S

P 7

Q 1 8

1 2

10 71

3 42

V 6 V 7

u 0 7 17

u 3 9 18 1

8 8

7 3




14

42. A 60 mm-diameter water jet strikes a plate containing a hole of 40mm diameter as shown in

the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected

vertically. The density of water is 1000 kg/m3. If velocities are as indicated in the figure, the

magnitude of horizontal force (in N) required to hold the plate is _________

Key: 627 to 629

Exp: Force in X–direction = Rate of change of momentum

i f x directionP P

1 21 2

x direction

1 1 2 2 1 2

2

1 2

2 2

m V m V

V A V A V V V

V A A

1000 20 20 0.06 0.044

628.32N

43. The arrangement shown in the figure measures the

velocity V of a gas of density 1 kg/m3 flowing

through a pipe. The acceleration due to gravity is

9.81 m/s2. If the manometric fluid is water (density

1000 kg/m3) and the velocity V is 20 m/s, the

differential head h (in mm) between the two arms of

the manometer is ____________

Key: 19 to 21

Exp: Given

3 2

g

3

m

1kg / m , g 9.81m / s

1000kg / m , V 20m / s

m

2

m

V 2gH Where H h 1

VSo, h 1

2g

2

20h 1000 1

2 9.81

h 0.0204m 2.04cm h 20.4mm

1D 6cm

120m / s V

2D 4cm

220m / s V




15

44. A metal ball of diameter 60mm is initially at 220 °C. The ball is suddenly cooled by an air jet

of 20°C. The heat transfer coefficient is 200 W/m2.K and 9000kg/m

3, respectively. The ball

temperature (in °C) after 90 seconds will be approximately.

(A) 141 (B) 163 (C) 189 (D) 210

Key: (A)

Exp: D = 60mm = 0.06m

2 3

i

p

T 220 C, h 200W / m K, 9000kg / m

T 20 C, C 400J / kgK, K 400W / mK

t 90sec T ?

p

h.A 200 90 3.t.VC 0.03 9000 400i

f f

f

T T 220 20e e

T T T 20

T 141.3 C

45. A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm,

respectively. The friction lining in the disc is made in such a way that the coefficient of

friction varies radially as 0.01r, where r is in mm. The clutch needs to transmit a friction

torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is

_________

Key: 0.49 to 0.51

Exp:

i o

2 2 3

r 20mm, r 40mm, 0.01r

T 18.85kN mm

p ?

P p2 rdr

T p2 r dr p 0.01r 2 r dr 0.0628r .dr

4040 43

20 20

4 43

rT 0.0628p r dr 0.0628p

4

40 2018.85 10 0.0628p

4 4

p 0.5MPa

46. The surface integral S

F.ndS over the surface S of the sphere 2 2 2x y z 9, where

F=(x+y) i+ (x+z) j+(y+z) k and n is the unit outward surface normal, yields ______.

Key: 225 to 227

Exp:

F x y i x z J y z k

divF x y x z y z 1 0 1 2x y z

By divergence theorem,

^

2 2 2

S V

F.ndS divFdV where V is volume of given surface of sphere x y z 9

V

4 272dV 2V 2 72 226.1947

3

dr

r

ir

0r




16

47. Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1

is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of

the total acceleration (in m/s2) of point P of the block with respect to fixed point O is

________

Key: 243 to 244

Exp: Acceleration of the block,

v 6m / sec, 20rad / sec

2 22 2 2

r cr

2

cr

22

r

2 2 2

r

a a a r 2v

r OP,

a 2v 2 6 20 240m / s

a r 20 0.1 40

a 240 40 243.31m / sec

48. During the turning of a 20mm-diameter steel bar at a spindle speed of 400 rpm, a tool life of

20 minute is obtained. When the same bar is turned at 200 rpm, the tool life becomes 60

minute. Assume that Taylor‟s tool life equation is valid. When the bar is turned at 300 rpm, the

tool life (in minute) is approximately.

(A) 25 (B) 32 (C) 40 (D) 50

Key: (B)

Exp: Taylors Tool life equation,

n

n n

1 1 2 2

n

2 1

1 2

n

3 3

n

3 1

1 3

0.63

3

3

3

VT C

V T V T

T V

T V

60 400

20 200

n 0.63

at N 300rpm, T ?

T V

T V

T 400

20 300

T 31.57 min utes

T 32min utes




17

49. Consider the matrix A = 50 70

70 80

whose eigenvectors corresponding to eigenvalues 1and 2

are 2

1 2

1

70 80x and x .

50 70

respectively. The value of T

1 2x x is_________

Key: 0 to 0

Exp: 50 70

A70 80

Eigen vectors are 2

1 2

1

70 80X ; X

50 70

Where 1 2, Eigen values of A

2T

1 2 1 2 1

2 1 1 2

80X X 70 50 70 80 50 70

70

70 5600 70 3500 70 9100

70 130 9100 9100 9100 0

1 2sum of eigen values

Trace 50 80 130

50. The radius of gyration of a compound pendulum about the point of suspension is 100mm. The

distance between the point of suspension and the centre of mass is 250mm. Considering the

acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound

pendulum is _________.

Key: 15 to 16

Exp: k 100mm 0.1m

L 250mm 0.250m

g 9.81m / sec

22

n 2

I mk m 0.1

mgL m 9.81 0.250W 15.66rad / sec

I m 0.1

51. Consider the differential equation 3y'' x 27y x 0 with initial conditions y(0) = 0 and

y'(0) 2000. The value of y at x = 1 is ________.

Key: 93 to 95

Exp:

2 2

c 1 2 p

c 1 2

1 1

3y '' x 27y x 0, y 0 0, y ' 0 2000

Auxillaryequation, 3m 27 0 m 9 0 m 0 3i

y c cos3x c sin3x and y 0

y c cos3x c sin3x

y 0 0 c 0 0 c 0

2

2

y c sin3x

y' 3c cos3x




18

2 2

2000y' 0 2000 2000 3c c

3

2000 2000y sin3x, y 1 sin3 94.08

3 3

52. If f(z) = (x2+ay

2) + ibxy is a complex analytic function of z = x + iy, where i = 1, then

(A) a = –1, b= –1 (B) a = –1, b = 2 (C) a = 1, b = 2 (D) a = 2, b = 2

Key: (B)

Exp: Given 2 2f z x ay i bxy is analytic

2 2

u x,

x y y x

value u x ay , bxy

u2x by

x x

u2ay bx

y y

Clearly for b = 2 and a= –1 above Cauchy-Riemann equations holds

53. A project starts with activity A and ends with activity F. The precedence relation and durations

of the activities are as per the following table:

Activity Immediate Predecessor Duration

(days)

A - 4

B A 3

C A 7

D B 14

E C 4

F D,E 9

The minimum project completion time (in days) is ______

Key: 30 to 30

Exp:

Minimum project completion Time = Length of longest path = 4+3+14+9=30 Days.

54. Maximize Z = 5x1+3x2

Subject to

x1+2x2 10,

x1–x2 8,

x1, x2 0.

In the starting Simplex tableau, x1 and x2 are non-basic variables and the value of Z is zero.

The value of Z in the next Simplex tableau is _________.

1 2

3

4

5 6F

9

A

4C, 7

B3 14

D

4

E




19

Key: 40 to 40

Exp:

max

st

nd

26 2Z at ,

3 3

1 Table at 0,0 Z 0

2 Table at 8,0 Z 40

55. The principal stresses at a point in a critical section of a machine component are

1 2 360MPa, 5MPa and 40 MPa. For the material of the component, the tensile

yield strength is y 200 MPa. According to the maximum shear stress theory, the factor of

safety is

(A) 1.67 (B) 2.00 (C) 3.60 (D) 4.00

Key: (B)

Exp:

y1 3 w1 3

2 2 FOS

20060 40

FOS

FOS 2

General Aptitude

Q. No. 1 - 5 Carry One Mark Each

1. If you choose plan P, you will have to _______ plan Q, as these two are mutually _________.

(A) forgo, exclusive (B) forget, inclusive

(C) accept, exhaustive (D) adopt, intrusive

Key: (A)

2. P looks at Q while Q looks at R. P is married, R is not. The number of people in which a

married person is looking at an unmarried person is

(A) 0 (B) 1 (C) 2 (D) Cannot be determined

Key: (B)

3. If a and b are integers and a – b is even, which of the following must always be even?

(A) ab (B) a2 + b

2 + 1 (C) a

2 + b + 1 (D) ab – b

Key: (D)

Exp: According to the given relation of a–b = even, there is a possibility of odd-odd (or) even-even

is equal to even. From the options, Option (D) is correct. Since, odd × odd–odd (or) even × even–even → is always even number.

Alternate Method:

Let a – b =2K a b 2K

2 2ab b b 2K b b b 2Kb b b b 2Kb b b 1 2Kb

Even; since 2Kb always even & b (b-1) also even, if with b is odd or even.

0,0

0,5

2x

0, 8

8,0

10,0

26 2,

3 3

1x




20

4. A couple has 2 children. The probability that both children are boys if the older one is a boy is

(A) 1/4 (B) 1/3 (C) 1/2 (D) 1

Key: (C)

Exp: No.of Favourablecases

ProbabilityTotal No.of Possible cases

The probability that both children are boys if the order one is a boy = 1

2

5. The ways in which this game can be played __________ potentially infinite.

(A) is (B) is being (C) are (D) are being

Key: (C)

Q. No. 6- 10 Carry Two Marks Each

6. “If you are looking for a history of India, or for an account of the rise and fall of the British

Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts

and the effects this mutilation will have in the respective sections, and ultimately on Asia, you

will not find it in these pages; for though I have spent a lifetime in the country, I lived too near

the seat of events, and was too intimately associated with the actors, to get the perspective

needed for the impartial recording of these matters.”

Which of the following closest in meaning to „cleaving‟?

(A) Deteriorating (B) Arguing (C) Departing (D) Splitting

Key: (D)

7. There are 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are required to form

pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must

necessarily be paired with someone. In how many ways can 4 such pairs be formed?

(A) 74 (B) 76 (C) 78 (D) 80

Key: (C)

Exp: If P is paired with y; they Q has 4 choices

R has 3 choices

S has 2 choices

Total 24 choices

(or)

If Q is paired with y; then P has 3 choices

R has 3 choices

S has 2 choices

Total 18 choices

(or)

If R is paired with y; then P has 3 choices

Q has 3 choices

S has 2 choices

Total 18 choices




21

(or)

If S is paired with y; then P has 3 choices

Q has 3 choices

S has 2 choices

Total 18 choices

Total number of ways = 24+18+18+18=78

8. In the graph below, the concentration of a particular pollutant in a lake is plotted over

(alternate) days of a month in winter (average temperature 10°C) and a month in summer

(average temperature 30°C).

Consider the following statements based on the data shown above:

(i) Over the given months, the difference between the maximum and the minimum pollutant

concentrations is the same in both winter and summer.

(ii) There are at last four days in the summer month such that the pollutant concentrations on

those days are within 1 ppm of the pollutant concentrations on the corresponding days in

the winter month.

Which one of the following options is correct?

(A) Only i (B) Only ii (C) Both i and ii (D) Neither i nor ii

Key: (B)

Exp: The difference between the maximum and the minimum pollutant concentrations

(i) in winter = 8-0=8 ppm ,

(ii) in summer = 10.5-1.5=9 ppm

(i) is false & (ii) is correct from the graph.

9. All people in a certain island are either „Knights‟ or „Knaves‟ and each person knows every

other person‟s identity. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

Which one of the following can be logically inferred from the above?

(A) Both P and Q are knights

(B) P is a knight; Q is a knave

(C) Both P and Q are knaves

(D) The identities of P, Q cannot be determined

Key: (D)




22

10. X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and

double the number of tractors, it takes 5days to plough the same field. How many days will it

take X bullocks alone to plough the field?

(A) 30 (B) 35 (C) 40 (D) 45

Key: (A)

Exp: Given Number of days required that X bullocks and Y tractors to plough a field = 8 days

(1) i.e, X Y 8D 8X 8Y 1day Number of days required that

Xbullocks and 2y tractors

2

to plough field 5 2

X 5i.e, 2Y 5D X 10Y 1D

2 2

From (1) & (2); we have

5X 11X8X 8Y 10Y Y

2 4

15XFrom 1 X Y 8D 8D X 30days

4

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