gate mechanical engineering 2012

7/21/2019 GATE Mechanical Engineering 2012

1/22

Q No 1

5

Carry One

Mark

ach

1. Which one of the following is NOT a decision taken during the aggregate

production planning stage?

A) Scheduling of machines

B) Amount of labour to be committed

C) Rate

at

which production should happen

D) Inventory to be carried forward

Answer: -

B)

2 A CNC vertical milling machine has to cut a straight slot of 10mm width and 2mm

depth by a cutter of 10mm diameter between points (0,0) and 100,100) on the

XY plane dimensions

in

mm). The feed rate used

for

milling is 50mm/min.

milling time for the slot in seconds) is

A)

120

B)

170

C) 180

D)

240

Answer: - A)

3.

A solid cylinder of diameter

100mm

and height 50mm is forged between two

frictionless flat dies to a height of 25mm. The percentage change

in

diameter is

A) 0

B)

2.07 C) 20.7

D)

41.4

Answer: - D)

Exp:- From incompressibility we

get

rrdi h

1

= t d ~ h

2

d2

= lx l

d

2

= 1 x ~ = 141.42

d

d

Percentage change in

diameter=

2

1

x100

=

41.42

d

4. The velocity triangles at the inlet and exit of the rotor of a turbo machine are

shown. V denotes the absolute velocity of the fluid, W denotes

the

relative

velocity of the fluid, and

U

denotes the blade velocity. Subscripts 1 and 2 refer to

inlet and outlet respectively. I f

V

2

=

W

1

and

V

1

= W

2

then the degree of reaction

is

A) 0

Answer: - C)

B) 1

C) 0.5

D) 0.25

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2/22

5.

W hich one of the

fol lowin

g

con

figurations

has the highest

f in effect

iveness?

A) Thin

clo

sely spaced fi

ns

B) Thlnr

w id ely spaced

fins

C)Thick widely

spaced fi n

s

D) Thlckr

closely spaced

fins

Answer

: - A )

6.

An idea I gas

of mas s m and

ternperature

T

1

undergoes

a reversible

isotherm a

process fro

m

a

n in i t ia l pr

essure P

1

to

a

final pressure

P

2

. The heat

loss dur ing th

e

process is

Q.

The entropy change D.S

of

the

ga s

is

A)

mR

in P

2

)

B) m n

C) mRin

P

2

)- g

D)

Zero

A n

sw er: -

B

)

7.

In the m e

chanism g ive

n below

if

the

angu Ia r ve

loc i ty

of

the e

ccentr ic circu

Ia

r

disc

is

1ra

d/sr the

angular v

elocity rad/s) of the

fo l lowe

r link f

or

the

instant

show n in

the

f ig u re is

A ) 0.0

5

Answ

er: -

B)

B)

0.1

A ll d im ension

s are in

mm

C) 5.0

D) 10.0

8.

A circular so

lid disc of

un i f

o r m th ickness

20mm r rad iu s

200mm

and

mass 20kgr is

used as

a flywheel . If

it ro tates

at 600rpmr the k

inetic energy

of

the

f lywhee

lr in

Jou

les is

A)

395

B) 790

C) 1580

D) 3160

A nswer: -

B )

1

Exp:

K.E.

of

flywheel

= : Iw

2

I _ mR

2

_ 20

x 0.2

2

_

0

4

k

2

- - 2-

- 2 -

g

m

_

27tN _ 2 X 7tX600 _

6

2 83

d

/

w

- . ra

s

60

60

K.E

=

. .

x o.4x

62.83

2

=

790J

2

9. A cantilever

beam

of le n gth L is s

ubjec ted

to

a

m

oment M

at

the

f ree end

. The

mom

ent of inert

ia

of th

e beam

cross sect io

n about the n

eutral axis is

I and the

Young mod

ulus is E. The

m agn i tude

of

the

maxim

um deflect ion is

A) ML

2

B) ML

2

C)

2M L

2

D ) 4ML

2

2EI

EI

EI

EI

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3/22

Answer: - (A

)

Exp:- E d

2

y = M

dx2

upon lntigra tio

nr

EI

= Mx + C

1

Once again integratingr weget

Mx

El y

= - - +

C

1

X

+

C

2

2

For cantilev er

beam

at

x =

1

dy

= 0 x

= 0

y

= 0

dx

From th

is we

g

et C

1

= C

1

Or

Henc

e

Mx2

.

d fl

t

ML

2

y

=

2

EI ; max

1mum

e

ec

1 n

Ymax

=

2

EI

10

For a

long slender

column

of

un

iform cross s

ectionr the ra

t io

of

crit ical

buckling

load for th e ca

se

w

ith both

end s cia m pe

d

to

the case w

ith both ends

hinged is

A) 1

B

)

2

C) 4

D)

8

Answer: -(

C )

41t

2

EI

E xp :- C rltica I

Buckling load

for column fix

ed at both en

ds =

L

C

ritical Bucking

load for a c olu

mn hinged a

t both lands

2

;

1

11 . Atx=O, the fu nction f (x )

=X

3

+ 1

has

(A) A m a

x imum va lue

(C) A sing

ular i ty

Answ

e r: - ( D )

(B) A

m in imum v alu

e

(D) A p

oint

of

inflec

tion

Ex

p:- The

function

f x)=

x

3

+1

has

a

poin

t of in

flection at x =

0 since in

the graph

sign of

the curvatur

e

i.e.

1

the co

ncavity) is cha

nged.

y

.

~ ~ ~ ~

X

0

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4/22

12. For the spherical surface, x

2

+ y

2

+ z

2

-1 the unit outward normal vector at the

point

1-, ._1,o)

is given by

(A) _ _j+ __ __ J (B) __ __i __ __ J

(C)

k (D) _ _j+ __ __ j + __ __ k

J2 J2 J2 J2 J3 J3 3

Answer: - A)

Exp: -Given

spherical surface

is

x

2

+

y

2

+

z

2

= 1 and point is

. k

,

0)

Normal vector outward to x

2

+ y

2

+ z

2

-1=

0

at ..k ,

0} s

1 .

1 .

Ok 1 .

1 .

..{21+

..{2]+

.

=

..{21+ ..{2]

1 . 1 .

-1 -1

Hence the outward unit normal vector =

~

+ ~ : ] = }z i +

5:

j

13. Match the following metal forming processes with their associated stresses in the

workpiece.

List I

p

Coining

Q

Wire Drawing

R Blanking

s Deep

drawing

(A) P-4, Q-1, R-2,

S-3

(C) P-1, Q-2, R-4,

S-3

Answer: - A)

1

2

3

4

List II

Tensile

Shear

Tensile and compressive

Compressive

(B) P-4, Q-1, R-3,

S-2

(D) P-1, Q-3, R-2,

S-4

14. In abrasive

jet

machining, as the distance between the nozzle tip

and

the work

surface increases, the material removal rate

A) Increases continuously

B) Decreases continuously

(C) Decreases, becomes stable and then increases

D) Increases, becomes stable and then decreases

Answer: - D)

~ 0 0 4 0

15.

In

an interchangeable assembly, shafts

of

size 25. ooo-

0

010

m m mate with holes

of

~ 0 0 3 0

size

5 . o o o ~ o . o z o

m m . The maximum interference in microns) in the assembly is

A) 40 B) 30 C)

2 D)10

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5/22

Answ

er: - C)

Maximum in

terference=

m aximum siz

e of sh

aft-

m

inim um size

of hole

= 25.040-2

5 .020

=201 lm

16. Du

ring normalizin

g process

of steel, the spe

cimen is heate

d

A) Between

the upper and

lower crit ical t

em perature a

nd cooled in s

ti l l air

B) Above

the upper critical

tempera ture a

nd cooled in

furnace

C) Above

the upper crit ica

l tem pera ture

and cooled in

sti l lai

r

D ) Betwee

n the upper a

nd lower cr i t ic

al tempera tur

e and cooled

in fu rnace

Answ

er: - C)

17

. Oil f lows

through a 2

00m m d iame

ter horizontal

cast Iron pip

e friction fa

ctor,

f=O. 0225)

of length 500

m . The vo lum

etric f low ra

te Is 0.

2m

3

s. The head l

oss

in m) du

e to friction

is assume

g=9.

81mls

2

A) 116.18

B)

0.116

C) 18.22

D) 23

2.3 6

Answer:

- A)

Exp:-

0.022

5x500x

0

2

2

fL V

2

rrx 0.2

H

= =

4

=116.18m

2gD

2x9.81x0

.4

18. For an opaque surface, the absorptivity a), t ransit iv i ty

( t)

and re f lect iv i ty p) are

relate

d by the equa

tion

A)

a

p

= 1;

B)

p a t =

0 C)

a

p

= 1

D)

u

p

= 0

Answ

er: - C)

19.

Steam en

ters an adiab

atic turbine o

pera t ing

at

st

eady state wi

th n enthalp

y o

f

3

251.0kJikg a

nd le

a

ves

s a saturated

m

ixture

a

t

15

kPa with qua

lity dryness

fraction) 0.9. The enthalpies of

the

saturate d liquid and

va

pour at 15kPa are

ht=225.94

kJ ikg and hg=

2598.3kJ ikg

respect i vely. T

he mass flow

rate of steam

is

1

0kg ls. Kinetic

and potentia

I energy chan

ges are neg ll

glble. The pow

er outpu t of

the tur

b ine in

MW

is

:

A)

6. 5

B) 8. 9

C) 9.1

D ) 27.0

An sw er: -

B)

.

Exp:- Po

wer = m,x h

1

- h

2

) = 10 x

3251- 225.

94 + 0. 9x 2598. 3

- 225.94)

= 890010

Is

= 8.9MW

20. The

following are

the data for tw

o crossed he

licalgears use

d

fo

r speed r

eduction:

Ge

ar I :Pitch circ

le d iameter in

th e plane

of rotation 80mm

and helix an

gle 300.

G

ear II: Pitch

circle d iamete

r in th

e

plan

e o

f

rotation

120mm and

helix angle

22.50.

f the input speed is

1440rpm

, the output spee

d in rpm Is

A )

1200

B)

9 C

) 87 5

D) 72

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6/22

Answer: - (B

)

Exp: - For

helical gears

V I

It

t

. d

1

cos

80 cos 30

N

2

e

o

c y ra 10

=

=

d

2

COS


7/22

24. Consider the function f(x) = lxl in the interval -1 :o;; x :o;; 1.

At

the point x=O, f (x) is

(A) Continuous and differentiable

C) Continuous and non-differentiable

Answer: - (C)

(B) Non-continuous and differentiable

(D) Neither continuous nor differentiable

Exp:- Given function is f(x) =

lx

1

1

x

1

is continues at x = 0 but not differentiable

25. lim (

1

- x) is

X-+0

X

A)

1/4

Answer: - (B)

Exp:- It

x ~ O

B)

1/2

C) 1

x ~

2sin

2

1) sin

2

1)

1 1

It = 2 It = 2

X

= -

x

x

x

J

4 2

- x4

2

Q No 6

Carry

Two Marks Each

D) 2

26. Calculate the punch size in mm, for a circular blanking operation for which details

are given below:

Size

of

the blank 25mm

Thickness of the sheet

Radial clearance between punch and die

Die allowance

A)

24.83

Answer: - (A)

(B) 24.89

2mm

0.06mm

0.05mm

(C) 25.01 (D) 25.17

Exp:- Diameter

of

punch= Diameter of Blank- 2 x radial clearance- die allowance

= 25-2x0.06-0.05= 24.83 mm

27.

In

a single

pass

rolling process using 410mm diameter steel rollers, a strip of

width 140mm and thickness 8mm undergoes 10 reduction of thickness. The

angle of bite in radians is

A)

0.006 (B) 0.031 (C) 0.062 (D)0.600

Answer: - (C)

Exp:-

~ H

=

D(1-cosa)

~

0.1x8

COSet

1 =

D 410

Ia

3.571

a 5 7 x ~ radians

Ia = 0.062 radians

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8/22

28. In aDC

arc welding

operation, the

voltage-arc

length chara c

teristic was ob

tained

a

s Vare = 20 +5

1 where the ar

c length I was

varied betwe

en

Sm

m and

7mm. Here

Varc

denotes the

arc voltage

in Volts. The

arc cu

rr

e

n

tw

as varied fro

m 400A

to

S

ODA Assuming li

near power so

urce charac te

ristic, the op

en circuit vo lt

ag e and

s

hort circuit cu

rrent for thew

elding operati

on are:

A) 45

V, 450A

B) 7SV,

SS

OA

C)

95V, 950A

D) lSOV, l

SOOA

Answ

er: -

C)

Exp:

Varc

= 20 5

I =

Smm

, Var

m = 45 V

1= 7mm, varc:fl =55

v

where V

0

is op

en c ircuit volta

ge

and 1

5

is sho r

t c i rcu i t curre

nt)

v

45 =V

0

-

x

s

oo

s

v

5

5 = V

0

- g x 4

00

I s

Upon solving

1)

and

2)

w

e

get

V

=

95

volts

Is

= 950A

29. A la

rge tank w ith

a nozzle a tt a

ched contain

s three Im mis

cible

in

viscid

fluids

as

sh

ow n. Assu m

in g that th e

changes in

h

11

h

2

and

h

3

are neg l

ig i ble, the

in stantaneou s

d ischarge vel

ocity is:

.

--

- - . - - . - - .

__

_ r

D )

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Answe

r: - (A)


9/22

E xp :- Ap

plying Bernou

lli 's equat ion, a

t exit we ge

t,

Pl v;

P

2 i

-

gzl =

- gz2

P3 2

P

3

2

We kn

ow that Z

1

=

Z

2

, V

1

=

0 P

2

= Patm

H

ence

it

reduce

to

pl

V

P

3 2

v 2 =

~

p3

But P

=

P1

ghl

+ P2

gh2

+

p3gh3

Upon subst i tu

t ing we g

et

v 2

=

2

gh 3 [1

+

plh

l +

p2h2J

p2h3 p3h3

30.

Water (c P

=

4.

18kJ kgK) at

8ooc enter

s a coun te r flo

w heat excha

nger with a

ma ss f low

ra te o

f

O.S

kg/s. Air cp =

1kJ/kg K ) e

ntersat

3ooc with a mass

flow

ra t eof 2.09kg/s

. I f the ef f

ectiveness

of the h e

a

t exch

ange r is 0.8,

the LMTD ( in

OC is

(A )40

(B)

20

(C) 10

(D)

5

Answer: -

(C)

Exp:-

E = ~ X ~

- th

e

miR ~

- tc )

31

0

.

8

= 4.18 x

0.5 x 80- t;,.

2.09 x 1

80-

30)

t ht =

40C

mhcp th,

-

t,.,

= mccp, (tc, - tc,)

O.S

x 4.18 x

40 =2.09x1

x tc ,- 30)

t

ct

=

70C

9

1

=

9

2

=

10

C : LMTD

=

1

0C

A so lid

s teel cube co

nstrained on

a II six face s is

heated so tha

t th e tern pe

rature

ri s

es uni formly

by.L\.T. I f t

he thermal coe

fficient o f th e

material is

a Young's

m

odu lu s is E

and the Poiss

on's ratio is v

, th etherm al

s

tr

ess develo

ped in the

be du e to

heating is

(A) _ a .L\.

T ) E

(1 - 2v)

(B) _ 2a

.L\.

T

)

E

1-

2 v )

(C )

_ a.L\.T) E

(1 - 2v)

a .L\.T ) E

(D

) - 3 (1 - 2v )www.examrace.com

Answer: - (A

)


10/22

32. A so li

d circu Ia r sha

ft needs to be

designed to

t ransmIt a tor

que

of SO

Nm.

If

the

al

lowable shear

stress of the

material is 14

DMPa, assum

ing a factorof

safety

of

2, the min i

mum al lowabl

e design diameter

in mm is

(A) 8

(B) 1

6

(C) 24 (D)32

Answer: -

(B)

Exp

:- T

=

SON-

n; allowable=

140MPa

fo.s

=

2;

C

=allowab

le =70MP

a

sa fe f

T

We

know, Zp =tsafe

Z

p =

1td

3

~

d 3

= 16T

16

1t safe

d = 16

x SDx 10

3

7t

X7

d = 1S .

3 8 m m

'16mm

0 5

33. A for

ce

of 40D

N is

applied

to

the

brake drum

of O.Sm

d iam

eter in a ban

d brake

system as s

hown in th e

figure, where

the wrappin

g angle is

180o. f the

coeffic ie

n t

of

friction b

etween the dr

um and the b

and Is D. 2S,t

he braking tor

que

applie

d, in

Nm

is

(A) 1

.6

Ans

w e r: - ( B)

~ t i

-

-

4

oON

(B) S4.4

C

) 22. 1

(D) 1S .7

Exp

:- As the dru

m is rotat ing

in anti clockw

ise direction,

T

1

will be tight

side T2w

ill

be clac

k side.

T

l =

e..e

=

.2Sx

=

2.19

T2

T

2

= 182

.37S N

Bre a

king torque = (T

1

-

T

2

) r

=

S4.4 N - m

34.

A box conta

ins 4 red bal

ls and 6 black

balls. Three

balls are sele

cted random ly

from the

box one a

f te r anotherwitho

ut replac

ement. The p

robabil ity that

the

s

ele cted set con

tains one red

ball and two

black balls Is

(A

)

__ __

2

0

1

B)

12

C )

~

10

(D) . .

2

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Answer: -

D)


11/22

Red

Bla ck

Exp : - G iv

en,

4 6

Th e s

election will be

R

BB

or

BBR

of BRB

Pro

babil i ty

of

sele

ct ing

RBB

=

x

6

~

10 9 8

Prob

abil i ty

of

se le

ct ing

BBR

=

5

~

10

9 8

Probabllity of selectin g

BRB =

~ x:x

P Re

d=1)

=sum of

a bo

ve thre

e

pro b

abi l i t ies=

0.5

35

2 d

2

y dy

Consid e

r

the differential

equati o

n x -

+

x

4 y

= with the bo u

ndary

dx

2

d

x

condit ions

of

y(O )

=

0

and y 1)

=

1.

The com plete solut ion

of

the d if fe rent ia l

equat ion is

(B)

s i n ~ )

Answer: -

(A)

Exp : -

2

d

2

y

d

y

X -

X

4y = 0

dx

2

dx

Cau

chy s

D.

E

Y = x2

dy d

2

y

- =

2x -=2

d x

dx

2

m

2

4=

o

m

2

=

4

m

=

2

y(O )

= 0

y

1)

=

:

The

required so lut i

on is C

1

x

2

+

C

2

x

2

+ C

2

x

2

Hence the a

nswer is x

2

.

3

6. The sys

te m

of

algebra

ic equat ions g

iven below ha

s

X +

2y

+ Z = 4

2X

+ Y +

2Z = 5

X - Y + Z = 1

(A) A un i

que so lut ion

of x=1

y=1

an

d z=

1

D

) e-x sin ( 1t;

(B) O n

ly the two so lu

t ions

of x=1

y=1

and

z

=1)

and

x=2r y=

1

and z=O)

(C) In fi

nite num

ber of

s

olut ions

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D)

N

o feasible so l

ut ion


12/22

An

swe r: - (C)

E xp :-

The g ivene

quat ions are

X + 2y +

Z =

4

- (1)

2x

+

y

+2z =

5 - (2)

X

+

y

+ Z =

1

-(3)

Eliminating n f rom (1)

2) ,

we

have

y

=

1

-(4)

Elim

inating x fo rm

2) 3),

we

ha v e

y =

1

-(5)

Lines

4)

an

d

5)

are co inc

ident

H

ence

the

g ive

n equat ion ha

s infinite so lu t

ions

37. The ho

mogeneous s

ta te

of

stress

for a meta I

part

undergoin g

plast ic defo r

mat ion

I

s

T

= [150 a l

0

0 -

10

W he

re the stress

co

mponent

va

lues are in

MPa. Using von

Mises yield c

riterion,

the value

of

e

s t imated she a

r yield stress,

in

MPa

is

(A )

9.50

(B) 1 6 .07

(

C) 28 .52

D

)49.41

A

n sw e r: - (B)

Exp : -

eq

= { u - 0

22

)

2

+ 11

-

22 )

2

+

6 [ c

ri2

+ +

}

We know

, cr

11

= 10, cr

22

= 20,

0 33 =

-

10; 0 12

= 5; 0

23

= 0 13

= 0

Oeq

=

27.839 M P

a

0

S hear

stress

at

yie ld

Cy

=

Jj =16.

07 MPa

38. D eta

i ls pertaining

to an orthogo

nal me

tal

cu tt

ing process ar

e g iven below

Chip th ickness ratio 0.4

Unreform ed

th ickness

R

ake angle

C

utting speed

Mean th

ickness

of

pri

ma ry shearzo

ne

0.6mm

+10

0

2.5m/s

25 microns

The shear

stra in rate

in s-

1

dur ing

the process

is

(A

) 0 .1781 x 10

5

(B)

0.7754

x

10

5

www.examrace.com

C

) 1.0104 x 10

5

D) 4.397 x 10

5


13/22

A

nswe r: - C )

Exp:- r = 0.4

t

1

=

0.6mm

a

=

10

Vc =

2

.5m/s

tm = 25

L

m

rcosa

o

~ =

.

= 0 4 2 3 3

~

= 2 2

9

1 - rstn

a

.

V

co

sa

S hear stra1n

rate=

os

- a x t m

2.

5 x

cos1

0 =

1

.

010

4x

10

s

/S

co

s12.9 x 25 x 10

39 . In a

sing le pass d

r i l l ing opera t

ion, a through

hole of 15mm diam

eter

is

to

be

dr i l led in a st

eel p la te

of

50mm

thickness. D rill spindle speed is

500rpm,

feed is

0

.2mm/rev

and d

rill pointangle is

11so . Assumin

g

2mm

clear

ance

at

appro

ach

and e

x it,

the

t

otal drill time in se

conds is

A) 35

.1

B) 32 .4

C)

31 .2

D) 30.1

Answ er: - A )

E

xp:- T = Lh +A+

+C)

c

f

Lh = 5

0mm;A = = 2

m m ;C = D

o t ~ ) 7.5 x co t

59 )= 4 .5mm

2 2

N = 500

rpm; f = 0. 2m

m rev

Tc = 0.585min

or35.1

Seconds

40

.

Consider two infin

i te l y lo n

g

th in

concen

tr ic

tub

es

of circu lar

cros

s section as

shown in

the

fi gure.

If D

1

and

the

d

iameters

of

th

e

inner and

ou

ter tu

bes

resp

ec tively, then

the

vi e

w factor F

2 2

is g iven

by

A) ~

B

) Zero

C)

~

~ : )

Answer: - D)

A D

Exp

:-

F

22

= 1 - F

2 1

=

1 -

1

= 1 -

_

A D2

41.

An Incompr

essible fluid fl

ows over a f l

a t p late w

ith zero pressure

gradient. Th

e

bounda

ry layer th ick

ness is

1m

m

at a location

where the R

eyn olds number

is

10

00. I f the ve

locity of the

fluid a lone

is increased by

a

fact

or

of

4

, th en the

boundary Iay

e r th ickness

at th e sa me lo

cation, in

m m

wil l be

www.examrace.com

(A ) 4

B) 2

(C ) 0.5

(

D)0.25


14/22

Answer: - (C

)

E xp :- Bound

ary lay

er

th ic k

ness

o) a

-

1

R

8

a

V

:::> S

a

JV

I f

ve locity

of fluid is in c

reased by 4 t

imes then bou

ndary layer t

hickness redu

ces

by ha l

f

42

. A ro om

conta ins 35k

g

of

dr

y

a

ir

a n

d 0.5g

of

w

ater vapour. Th

e

total

pressu

re and

temperatu

re o

f

a

ir

in the room

are 100kPa

and25

oc

res

pectively.

Gi

ve

n th

at the

saturat io n

pressure

fo r water

at 25oc is 3.17kPa, th

e re la t ive

h

umidity of the ai

r

in the r

oom is

A)

67

(B)

55 C

) 83

D)

71

Answer: - D)

43

. A fi l let-w

e lded

joint

is

subjected

to t ransverse lo

ading F as sh

own in the fi g

ure.

Bot

h legs

of

th e

f i l lets are

o

f

10m m size an

d

the

weldl

ength is 30 m m

. f

the

al lowable

shear stress

of the

weld

is

94 MP

a, considerin g

the

min

imum throa t a rea

of

th e w

eld, the

maximum al lowab l

e t ransverse l

oad In

kN

Is

(

A ) 14 .44

Answ er

: - C)

E xp :- P

= 0. 707

sl ,;a llowa

ble

(B)

17.92

P

= 0.707 x 10 x 30 x

94 = 19937.4N

P

19.934kM

(C) 19 .93

(D )

22.16

4

4. A conce

ntrated mass

m isat tached

at the

cen tr e

of

a rod

of

l

eng th 2L ass

hown

In

th

e

f igure. The

rod is kep t i

n a horizon ta

l equi l ibr ium

posi t ion by a

spring

of

st i f fness

k

F

or ve ry sm all

ampl

itudeof vibrat ion, ne

gle cting

the

w

eigh ts

of

the

rod and s

pr ing, the und

amped na tu r

a I frequen cy

of th system is:

(A)

(B )

k

C)

(D )

f

L

L

www.examrace.com

Answer: - D)


15/22

45.

The state

of stress

at

a

point under p l

ane stress con

dit ion Is

O xx = 40MPa;

O YY = 100MPa a

nd xy = 40MPa

The rad

ius of the Moh

r s circle repr

esent ing the g

iven sta te

of

s

tress in MPa i

s

(A) 40

(B)

50

(C) 60

(D)

100

Answe

r: - (B )

Exp:- O x

v = 40 MPa; O'w

= 100 MPa,

xv = 40M P

a

Radius

of

M

ohr s circle =

xx

+

,.2 = ./3o

2

+

4o2 = 50 MPa

' -0

J

2

xy

46.

The Inverse

Laplace transfo

rm of t

he

fun

ct ion F (s) =

(

1

) is give

n by

S

S + 1

A) f ( t ) =

sint

B)

f t )=e-

ts int

C)

f t

) = e-t

D)

f t)=1-e-t

A

nswer: - D )

Ex - L

1

1 J- . _

_

p.

5

5+1)

-

5

5+1

L

1 (. .-

_

1_

=

1e-t

5

S+

1

47.

For the matrix

A =

~ l O N E of

the no

rmalized

eigenvectors

is g iv

en as

(A) [ l

Answer: - B)

1

5-A

.

Exp

:-

lA

A.II =

0 ::;>

1

(B)

~

C) [ ~ l

.J

10

1 = 0 ~

5 - 1 . ) 3 - A . )

= 3 = 0

3-A.

:

:;> A.

2

- 8/ ,

+

5

3 = 0 A.

2

-

SA

.+ 12 =

0 /, = 2,

A.

=

6

A -

21

x

X= 0

At, A. =2

~

www.examrace.com


16/22

Hence

the required v

ector

Is

[

~

o

mmon

Data Quest ions

48 . 4

9

Two ste

el truss m em

bers

AC

and

B

C

each h

aving cross

sectional area

of

100mm

2

are subj ect

ed

to a hor izonta l fo rce F as sho w n

in

the

figure. Al l the

j

o in ts are hin g

ed.

A

48

. The

maximum force

Fin

kN that

can

be applied

a

t

C such

that th

e

axial stres

s in

any

o

f the truss m e

mb e r s

DO

ES

NOT exceed 1

00MPa

Is

A

)

8.

17

(B) 11

.15 (C )

14 . 14

D

)22.30

An

s w er: - (B )

Exp

: - From La

me s theore m r

F FA

FB

Sin105 S

in120 S in13

5

> F

A=

0.8 9

6 SF; FB =

0.

732F

:.maximu

m

force is FA a n

d s t r e s s

= ~ = 1 M P a

Area

0

8965

F

= 100MPa

>

F

= 11154.48

N

or 11.1SKN

1 0 0

4 9.

f F = 1

kN

,

the

magn i tud e

of the

ver t ica

I react ion forc

e developed

at

the

point

B

In

KN is

A) 0.63

(B)

0.32

C)

1. 26

Answer : -

(A)

vertlcaI eact ion

at point

B is R

8

=F

cos 30 = 0.633 F

F = 1KN

:.R

=0.63

3KN

Common Data Ques

t ions 50

. 51

D

) 1.46

A refr igera to

r operates b

etween 120 k

Pa and 800

kPa in

an ideal v apour

compre

ssion cycl e

with R-134a a

s the refr ige

rant . The re f

r igerant en te r

s the

www.examrace.com

com pressor as saturated vapour and leaves the condenser as satura ted liquid.


17/22

The mass

f low ra te of t

h e refri

gerant is 0.2kgl

s. Propert ies fo r

R-134a are

as

fo ll o

ws:

Sa tu ra ted

R-134a

P

kPa

)

TOC

h

1

k

J

kg )

h

9

k

J

kg )

st

kJ

kg K)

s

9

kJ

kg

K)

1 2 0

-22. 32

22.5

237

80

0 31 .3 1

95 5

267 3

Superheate d R-134a

P

kPa )

TC

h k

J kg)

800

40

276.45

50. T

he power req

uired for th e c

ompressor in

kW is

A ) 5 94

Answ

e r: - C)

E xp :-

T

4

B) 1 83

C) 7.9

L

s

Power

required

for

c

ompressor

= mr h

2

- h

1

)

0 .09 3

0

.95

0354

0.918

s kJ

kg K

0

.95

D) 39. 5

=

0.2x

276.45 - 237)

=

7.9kW

51

. The rate

at which hea t

is ext racte d in

k is f rom th e

ref r igerated

space is

A) 28 .3

B) 42

9

C) 3

4 .4

D) 14 6

www.examrace.com

Answer: - A)

Exp: -

Rateat which


18/22

heat is

extracted=mr h

1

- h

4

=

0.2 237 -95.5)

28.3 kW

Stat

ement for Linked Ans

wer Questio

ns: 5

53

For a part icu lar project, e ig ht act i v ities are to

e

carried out. Their relationships

w it

h

o

ther acti v it i

es and expect

ed durat ions a

re me

nt

ioned

in the tab le b

elow.

Act iv i ty

P ed ece s

sors Du

ration da ys)

A

-

3

B

a

4

c

a

5

D

a

4

E

b

2

F

d

9

c.e

6

H

f,g

2

52. T

he crit ical path

for the projec

t is

A)

a-b-e-g-h

B) a-c-g-h

Answer: - C

)

C) a-d - f- h

D) a-b

-c- f -h

Exp :-

4

Varies

pathare

A B E G

H -17 days

A C G H

- 16 days

A D F H

-18 days ;

:

A D F H is c

ritica l path

2

4

6

F

9

6

53

. f the dur

at ion of act iv i

ty f a lone is ch

anged f rom 9

to 10 days, th

en the

A) Crit ical

path remains

the same and

the to ta l dura

t ion to comp l

ete the project

ch a

nges to 19da

ys

B) Crit i

cal path and th

e to ta l durat i

o n to complet

e the project

remain the sa

me

C) Critlca

I path chang

es but the

tota durat ion to

com plete the

p roject rema

ins

th

e same

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D) Critica l path changes and th e total dura t ion

to

co mple te the p ro je c t changes

to 17days


19/22

Answer: -

A )

Exp : - I

f

d

ura t ion

of activity F has ch

anged to

10 days, cri t ica l

path remains

the same

and proj

ect

d

urat ion wi l l in c

rease

to

1 9d

ays.

State

ment forLinked

Ans

wer

Ques

tions: 54

55

Ai r

e nte rs an ad iabatic nozz le at 300kPa,

SOOK

w ith a veloc it y of

1Dm

ls

I t

l

ea

ves

th

e

nozzle

at 100kPa w

ith a veloc i ty

o

f

18Dmls. T

h

e

in le t area is

80cm

2

The

specif ic he

a t

of

air Cp is

1008J ikg .

K

54. T

he

exit

te

mperature

of

the a

i r is

A) 5 1 6 K

B) 53 2K

A ns we r: - C)

E xp :- h

1

v/ 2

=

h

2

v

2

v 2

_v

2

2 2 t

=

h

t - hz

= P

Tt -

Tz)

55.

180

2

2

-

102

= 1008X S OD - T

2

)

T

2

=

4

8 4 K

The exi t area

of

the nozzle

in

cm

2

is

C ) 484K

A)

90.1

B)

56.3

C) 4 .

4

A

n sw er : - D )

E xp

:- From con ti

nu i ty equa tio n

we get,

Vl = P

2A2V2

P

P

PT V

-

1

x V

= -

2

- x AzV

= _ _

RTt

t 1 RT2

2 PzTt

Vz

A = 300 x 48

4

x

10 x 80=12 9c

m2

2

50 0

x

100 180

Q.

No 56 - 60

CarryOne M

ark Each

D

) 468K

D) 12 .9

56.

The cos t fu

nct ion

for

a

product in a

firm is given b

y Sq

2

, w here

q is the

amou

nt

of

productio

n. The f irm c

an sell

the

produc t

at

a market price

of

RsSO

per un it.

The

number

of units to be pr

oduced by t

he f i rm such

tha

t

the

profit is

ma

x imized is

A) 5

Answer: A )

E xp :-

P

=

SOq -

Sq

2

B) 10

C)15

D) 25

www.examrace.com

dp

d

2

p

dq =

SO

-

1Oq dq

2

0


20/22

: p Is m ximum

at

50

10

q 0 o

r, q 5

Else

check w it

h options

57. Ch

oose the m

ost appropria

te a l ternat ive

from the o

ptions given

below to

complete the

following se n

tence:

Suresh s dog is the one was hurt

in

the stampede.

(

A)

th t

(B) which

(C)

who

(D) whom

Answer: (A

)

58. Choos

e

the

gramma

tical ly

INC

ORRECT

senten

ce:

(A) The

y gave us the

money bac

k less the se

rvice charges

of

Three Hu

ndred

r

upees.

(B ) This country s expenditure is not less than

th t

of

Ban gladesh.

(C) Th

e commit tee

in i t ia l ly asked

for

a fundin g

of

Fifty Lak

h rupees, bu

t la ter

s

ett led fo

r

a

lesser sum.

(D

) This country

s expenditu re

on education

a I reforms Is

very less

Answer: (D

)

5

9. Which o

ne

o

f the fo l

lowing option

s is the close

st In meaning

to

the word

given

bel

ow?

M

it igate

(A) Dim

inish

A

nswer: (A)

(B) Divulge

(C) Ded

icate (D

) Denote

60.

Choose th

e most appr

opr iate ltern

tive from

the options gi

v

en

below

to

comple

te

the

follow in

g sentence:

Despite se

veral

the m

ission succeed

ed in i ts atte

mpt to resolve

the

co nfl let.

(A ) ttem

pts

Answer: (B )

(B) setbacks

C) m e

etings

(D) delegation

s

Q No

6

6 Carry Tw

o Ma

rks

E

ach

61.

Wanted Tem

porary, Part-

t ime persons

for

th

e post of

Field Inter

viewer to condu

ct

personal interv iews

to

collect and collate economic data. Requirements: High

Sc

hool-pass, must

be ava

ilable for D

ay, Evening

and Saturd

ay work.

Transportatio

n paid, expens

es reimbursed

.

W

hich one of t

he fo l lowing is

the

best in fe

rence from th

e above adver

t isement?

(

A) Gender-d is

cr iminatory

(B )

Xenophobic

(C) N

ot designed t

o

rna

ke the po

st attract ive

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(D ) No t gender-d is cr iminatory

Answer: (C)


21/22

E xp:- G ender

Is not m entio

ned in the ad

ver t isementan

d (B) clearly

eliminated

62

. Given the

sequence of

termsr AD CG

FK JP, the ne

xt term is

(A)

OV

B)

OW

(C)

PV

(D)

PW

Answ

er: (A)

Exp:-

+2 +3

+4

+5

AD

I CG

I

FK

I JP

I v

. .

. . . . _ _ ~

~

-

+3

4 +5 Y

63.

Which of th e

following asse

rtions are CO R

RECl?

P: Adding 7 to

each entry in

a list adds7

to

the meanof

the list

Q:

Adding7

to

each

entry

in

a

l ist

adds7

to

the standard deviation of the list

R:

Doubling each

entry in a

list

doublesth

e mean of the

l ist

5: Doubling each

entry in a

I st

leaves the

standard devi

ation of the

I

s t

unchanged

(A) P, Q

B) Q, R

(C

) P, R

(D) Rr S

Answer

:

C)

Exp:- P

and R always

holds

true

Else

conside r

a sample se t

{1,

1 1

4} an

d check acco

rdingly

64 . An

automobilep

lant contracte d

to buy shock

absorbers fro

m two supplie

rs X andY.

X supplies

60

andY

su

pplies 40 of

the shock abs

orbers. All sho

ck absorbers a

re

subjec

ted to a qualit

y test. The one

s t hat pass the

quality testare

considered

reliable

O

f

X s

shock ab

sorbers, 96 a

re reliable. O f

Y s

shock abs

orbers, 72 a

re reliable.

Th

e probabil ity t

hat a randomly

chosen shock

absorber, whi

ch is found to

be rel ia

b

ler

Is

made byY

is

A)

0.288 B

) 0

.334 C )

0.667

(D) 0 .7

20

Answ

er:

B)

Exp:-

Supply

X

60

Reliable

96

Overa II

0. 576

: P(x ) =

0

288

=0.3

34

0.57

6 0 .288

y

40

72

0

.288

65. A

politicalparty

orders

an

arc

h

for

the entr

ance

to

the gr

ound

In

which

the annual

c

onvention isb

eing held. The

profileof the

arch follows t

he equation y

=

2x-

0.1x

2

w

here y is the

height of the

arch in meter

s . The ma xi m

um possibleh

eight

of

the

arch Is

(A) 8 m ete

rs (B )10

meters

(C) 12 mete

rs (D) 14

meters

Answ

er: (B)

Exp:-

y = 2x - 0.1x

2

www.examrace.com

y

2 0.2x

x


22/22

< 0 : ma

ximises

at 20

.2x

= 0

x

1

: y = 2 1

0 =1

0m

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gate mechanical engineering 2012

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