gate mock test-1.pdf

8/9/2019 gate mock test-1.pdf

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R ogOut

Solution Report For GATE Mock Test : 1Repres ent w hole test solution with correct and incorrect answe rs.

Q.No Question Status

Q.1

Attempt Correct Correct Ans. a Solution

Rajats house is facing east. One fine morning, after coming out of his

house, he walks a distance of 1 km and then takes a left turn but keeps

walking. He takes a left turn after having walked twice the distance in the

previous step. He keeps doing this i.e. taking left turn and walking twice

the distance of the previous step just before he is due to take a left turn a

6th time. Where is he with respect to the starting point?

a. 13 km E and 26 km Nb. 13 km W, 26 km Sc. 12 km E and 24 km Nd. 26 km E, 13 km N

Q.2


In the sentence given below, some part of the sentence needs an

improvement. Identify the option which makes a meaningful and

grammatically correct sentence:

A taller cadet rushed forward than any of his comrades.

a. A cadet, taller than any of his comrades rushed forwardb. A cadet rushed forward, taller than any of his comradesc. A cadet rushed forward than any of his taller comradesd. no need of improvement
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Q.3

Attempt Correct Correct Ans. c Solution

In this question, a sentence has been split into 4 parts labeled as a to

d. Only one of these parts has an error. Error could be in the form of a

missing word, an extra word or in grammar. Identify the part that has an

error.

a. The Indian radiob. which was previously controlled by the British rulersc. is free now from the narrow vested interestsd. No error

Q.4

Attempt Correct Correct Ans. b Solution

Choose the most appropriate word to fill in the blanks in the given

sentence:

Each occupation has its own _______; bankers, lawyers and IT

professionals, for example, all use among themselves a language which

outsiders have difficulty in assimilating.

a. problemsb. jargonc. rewards

d. compound

Q.5

Attempt Correct Correct Ans. 360 Solution

In a test given by Prof Virus during the minors, Raju gets 32% marks and

fails by 20 marks whereas Chaturbhuj gets 30 marks more than passing

marks while scoring 42% marks. The marks required to get twice the

passing marks are ____________.

Q.6

Given below are 5 statements out of which 3 are logically related to each

other. Out of the 4 options having a set of 3 statements each, identify the

set where the statements are most closely

related to each other.

i. All flowers are fragrant.

ii. All flowers are majestic.

iii. All flowers are plants.
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iv. All flowers need air.

v. All plants need air.

a. iii, v and ivb. i, iii and iic. ii, iv and iiid. iii, v and ii

Q.7

Atte mpt Corre ct Ans . a Solution

There were p pigeons and s sparrows in a cage. One fine morning m

birds escaped to freedom. If the caretaker was able to figure out by only

looking (not counting) into the cage that at least one pigeon had escaped,

based on the knowledge that m = 7, then which of the following cannot

be the value of the number of sparrows and pigeons?

a. 8 and 10b. 4 and 12c. 6 and 25d. 2 and 7

Q.8

Atte mpt Corre ct Ans . d Solution

Assume that equal number of people are born each day of the year. If the

century under consideration is the 20 th century, what is the percentage

of people who are born on 29 th February?

[Assume no deaths occur during the period under consideration].

a. 0.685b. 0.0685c. 0.684

d. 0.0684

Q.9

Two trains T1 and T2 are running at speed of 60 km per hour and 45 km

per hour respectively. T1 leaves from station A for station B and train

T2 leaves from B for A at the same time it is given that distance

between A and B is 1260 km. They cross each other at station C

between A and B. Both strains start their return journey immediately

after reaching their respective destinations. After how much time (in

hours) of T2 reaching A, will they cross each other again?


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Atte mpt Corre ct Ans . b Solution

a. 6b. 8c. 10d. 12

Q.10

Atte mpt Corre ct Ans . 5 Solution

Rajarams monthly income is distributed in 5 expense heads namely

house rent, groceries, transport expenses, electricity and water

expenses and finally under the head miscellaneous expenditure. After

meeting these expenses, the remaining amount (which is non zero) goes

towards savings which is a fixed percentage of his income every month.

It is known that these amounts can be expressed as percentage of his

income as 6 distinctive integers. The percentage expenses under 5

heads are 5 integers such that difference between 2 consecutive

expenses is a constant. The minimum percentage of his income that he

saves per month is ____________.

Q.11


Match items from groups I, II and III : Group -I Group-II Group-III

(Structure) (Effective no. (Co-ordination No.)

of atoms)

A . Simple cubic P . 2 T . 8

B. Body centered Q . 1 U. 6

C . Face centered R . 4 W . 12

D. Hexagonal closedpacked S . 6

Codes:

A B C D

(a) (P, T) (Q, U) (S, W) (R, W)

(b) (Q, U) (P, T) (R, W) (S, W)

(c) (P, U) (Q,T ) (R, W) (S, W)

(d) (Q, U) (R, T) (S, W) (P, T)

a. ab. bc. c

d. d

Q.12


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A Carnot heat engine is operating between a source at T H and a sink at

T L. If it is desired to double the thermal efficiency of this engine, keeping

the sink temperature constant. What should be the new source

temperature ( T H ) ?

a.

b.

c.

d.

Q.13


5 m 3 of an ideal gas at 1 bar pressure is compressed isothermally in an

adiabatic piston-cylinder device to 2 m 3 . Maximum work input needed by

the compressor is

a. 250 kJb. 300 kJc. 500 kJd. Compress ion is not possible

Q.14

The time in which the mass in a damped vibrating system would settle

down to 1/50 th of its initial deflection for the given data will be ?

m = 200 kg

= 0.223

k = 40 N/mm

a. 0.221 s

b. 0.455 sc. 0.622 sd. 1.260 s
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Q.15

Atte mpt Corre ct Ans . c Solution

During the process of boiling and condensation, only a phase change

take place and one fluid remains at constant temperature throughout the

heat exchanger. In terms of number of transfer units (NTU), the

effectiveness of such an heat exchanger would be

a.b. 1 exp ( NTU )

c.d. Undefined solution

Q.16


A beam simply supported at equal distance from the ends carries equal

loads at each end. Which of the following is true ?

a. The bending moment is minimum at the mid-span

b. The bending moment is minimum at the supportc. The bending mom ent varies gradually between the supportsd. The bending moment is uniform between the supports

Q.17

The diagram below represents the shear force variation over a beam AE ,

simply supported at A and D, for a particular set of loading.

For the same set of loading, magnitude of bending moment (in kN-m) at

mid-span will be


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a. 150b. 120c. 225d. None of these

Q.18


The main purpose of chaplets is

a. to ensure directional sol idificationb. to provide efficient ventingc. for aligning the mould boxesd. to support the cores

Q.19


In MIG welding, the metal is transferred in the form of?

a. A fine spray of metalb. Molten dropsc. Weld poold. Molecules

Q.20


The cut-off ratio of a diesel cycle is 2. For equal air-standard efficiencies

of Otto and Diesel cycle, the ratio of compression ratio of diesel cycle to

that of Otto cycle would be

a. 0.5b. 1.0c. 1.5d. 2.0

Q.21

The centre of gravity of the coupler link in a 4-bar mechanism would
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experience

a. no accelerationb. only linear accelerationc. only angular accelerationd. both linear and angular acceleration

Q.22


The dia of a hole is given as mm. The upper limit on the

dimensions in mm, of the shaft for achieving maximum interfence of 50

microns is

a. 60.05 mmb. 60.15 mmc. 60.25 mmd. 60.40 mm

Q.23


The equation u xx + xu xy + yu yy xyu x = 0 is hyperbolic for

a.

b.

c.d. y = x

Q.24

The solution of the differential equation

a.


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Not Atte mpt Cor re ct Ans . a Solution

b.

c.

d.

Q.25

Not Atte mpt Cor re ct Ans . c Solution

The value of , where C is the left half of the unit circle, is

a. 0b. 2i c. -2i d. None of these

Q.26

Atte mpt Corre ct Ans . 3.75 (3.25-4.25) Solution

A full journal bearing with a journal of 75 mm diameter and a bearing of

100 mm length is subjected to a radial load 3000 N at 500 rpm. If the

viscosity of oil is 18 centipoise then the bearing modulus is __________

10 7 .

Q.27

Atte mpt Corre ct Ans . 648 (647-649) Solution

Two carnot heat engines are operating in series. The first engine

receives heat from the reservoir at 1400 K and rejects the waste heat to

another reservoir at temperature T . The second engine receives this

energy rejected by the first one, converts some of it to work; and rejects

the rest to a reservoir at 300 K. If thermal efficiencies of both engines

are the same, then the temperature T is ____________ K.

Q.28

Dry saturated steam at a pressure of 10 bar enters a convergent -

divergent nozzle and leaves at a pressure of 2 bar. If the flow is adiabatic

and frictionless, pressure at the throat of the nozzle is ________ bar.


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Not Atte mpt Cor re ct Ans . 5.77 (5.5-6.0) Solution

(For saturated steam take, n = 1.135)

Q.29

Not Atte mpt Cor re ct Ans . -36 Solution

The circulation around a rectangle defined by x = 1, y = 1, x = 5 and y = 4

for the velocity field u = 2 x + 3 y , v = 2 y will be ______ units.

Q.30


A mild steel plate has to be rolled in one pass such that the final plate

thickness is of the initial thickness, with the entrance speed of 10

m/min and roll diameter of 500 mm. If the plate widens by 2% during

rolling, the exit velocity (in m/min) is______ .

Q.31


In a whitworth quick return motion mechanism, the distance between

the fixed centres is 50 mm and the length of the driving crank is 75 mm.

The length of slotted lever is 150 mm and length of the connecting rod is

135 mm. The ratio of the time of cutting stroke to the time of return

stroke is _________ .


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Q.32


A orange consists of 12 ear-shaped pieces. Two piece diametrically

opposite to it are removed and eaten. If initially the mass moment of

Inertia about an axis passing through the centre of the orange, is I i and

after the pieces are eaten is I f , then the value of is ____________.

Q.33

Atte mpt Corre ct Ans . 8 (7.9-8.1) Solution

A cylindrical pin fin of diameter 5 cm and length 20 cm with negligible

heat loss from the tip has an efficiency of 0.5. The effectiveness of this

fin is ___________.

Q.34

Atte mpt Corre ct Ans . 0.35 Solution

The probability that A speaks truth is 4/5, while this probability for B is

3/4. The probability that they contradict each other when asked to speak

on a fact is ___________.

Q.35


is ____________.

Q.36

Saturated ammonia at 0.2365 MPa enters a single acting compressor

and liquid ammonia at 21C enters the expansion valve of a refrigerating

plant.

If head pressure is 1.1638 MPa, then the COP of the refrigerating cycleis:

Given: C P (Liquid NH 3 ) = 4.6 kJ/kgK ; C P (Vapour NH 3 ) = 2.75 kJ/kgK


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Q.39

Not Atte mpt Cor re ct Ans . b Solution

A freezing plant requires 50 tons of refrigeration. The freezing

temperature is 33C and ambient temperature is 27C. If the

performance of the plant is one-third of the theoretical reversed carnot

cycle working between the same temperature limits, the power input (in

kW) required for the plant is

a. 90.25b. 131.25c. 80.15d. 151.15

Q.40

Not Atte mpt Cor re ct Ans . b Solution

Two component of a machine are connected by a bolt. The stiffness of

bolt is one-third of the combined stiffness of two components. Pre

loading of bolt is 5 kN due to initial tightening of bolt. The bolt material

has yt = 400 MPa and FOS = 2. To sustain the external force of 15 kN,

diameter of the bolt should be

a. 5 mmb. 8 mmc. 2 mmd. 4 mm

Q.41

For an assignment problem, Initial basic feasible solution is given below.

The optimal assignment is

a. P V , Q I,R IV,S - III, T IIb. P V, Q I, R III,S - IV,T II


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Not Atte mpt Cor re ct Ans . a Solution

c. P V, Q II,R III,S - IV,T Id. P I, Q II,R III,S - IV,T V

Q.42


A bush manufacturing company has a contract to supply 5000 bushes toan automobile factory per day. The company has capacity to

manufacture 8, 000 bushes and holding cost of 1000 bushes is 8 paise.

Set up cost is Rs 20. The frequency of production run is approximately

a. 11 daysb. 16 daysc. 20 daysd. 23 days

Q.43


The copper thermocouple, spherical in shape, initially at 25C, which

when placed in a gas stream at 200C measures a temperature of 198C

in 5 seconds. For copper, = 8940 kg/m 3 , C = 384 J/kg-K, k = 390 W/m-K

and the convective heat transfer coefficient = 400 W/m 2 -K. The diameter of the thermocouple is

a. 0.58 mmb. 0.78 mmc. 1.23 mmd. 1.68 mm

Q.44

For a maximization problem, after some simplex iteration the following

table is obtained


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From this, one can conclude that

a. The LPP has a unique optimal solutionb. The LPP is infeasiblec. The LPP is unboundedd. The LPP has multiple optimal solution

Q.45


A solid shaft of diameter d and length L is fixed at both the ends. A

torque, T 0 is applied at a distance, L/4 from the left end as shown in the

figure given below.

The difference of magnitude of maximum and minimum shear stress in

the shaft is

a.

b.

c.

d.


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Q.46


The power absorbed by fluid friction in a thrust bearing consisting of a

flat disc 10 cm in diameter placed at the lower end of a vertical shaft is

223.93 W. The oil film is 0.25 mm thick and the viscosity of the oil is 1.3

poise. The angular speed of shaft will be

a. 1000 rpmb. 1500 rpmc. 2000 rpmd. 2500 rpm

Q.47


A cylindrical vessel of 1 m diameter has water in it to a height of 2 m. Oil

of relative density 0.75 is kept over the water column for another 1 m.

Above the oil, a dead weight of 5 kN, base diameter 1 m is placed. The

total hydrostatic force and the centre of pressure on a gate 30 cm in

diameter placed along the vertical surface of the vessel such that the

lowest point of the gate is on the base of the vessel will be?

a. f = 1030 N,z p = 1.25 m

b. f = 2000 N,z p = 2 m

c. f = 2427 N,z p = 3.50 m

d. f = 3000 N,z p = 4 m

Q.48

A body of mass 1 kg is acted on by a force as shown in the diagram. If the velocity of the bodyis zero at t =0, the velocity and distance traversed

to t = 1 min will be?

[The force acts for only 45 sec]


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a. V = 435 m/s, S = 4.3 kmb. V = 235 m/s, S = 8.9 kmc. V = 435 m/s, S = 16.3 kmd. V = 235 m/s, S = 29.8 km

Q.49


The voltage current characteristics of a dc generator for arc welding is a

straight line between an open-circuit voltage of 80 V and short circuit

current of 300 Ampere. The generator settings for the maximum arc

power will be

a. 80 V and 150 Ab. 40 V and 300 Ac. 40 V and 150 Ad. 80 V and 300 A

Q.50

Match Group-I with Group-II and select the correct answer using the

codes given below the lists:

Group-I Group-II

P. G09 1. Linear Interpolation

Q. G41 2. Retardation

R. G01 3. Circular interpolation

S. G03 4. Cutter radius compensation

Codes:

P Q R S

(a) 3 1 4 2

(b) 4 1 3 2

(c) 3 4 1 2


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Not Atte mpt Cor re ct Ans . d Solution

(d) 2 4 1 3

a. ab. bc. cd. d

Q.51


A pinion of 20 involute teeth and 125 mm pitch circle diameter drives a

rack. The addendum of both pinion and rack is 6.25 mm. The length of

arc of contact corresponding to the least pressure which can be used to

avoid interference is

a. 36.68 cmb. 36.68 mmc. 72.44 cmd. 72.44 mm

Q.52


Consider the following statements relating to forecasting.

1. The time horizon to forecast depends upon where the product

currently lies in its life cycle.

2. Opinion and Judgemental forecasting method sometimes incorporate

statistical analysis.

3. In exponential smoothing, low values of smoothing constant, alpha

result in more smoothing than higher value of alpha.

Which of these statements are correct?

a. 1, 2 and 3b. 1 and 2 onlyc. 1 and 3 onlyd. 2 and 3 only

Q.53


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An eigen vector of the matrix, is

a.

b.

c.

d.

Q.54

Not Atte mpt Cor re ct Ans . d Solution

The value of is

a. 22

b.

c.

d.

Q.55

Consider the following equations


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x + y + w = 0

y + z = 0

x + y + z + w = 0

x + y + 2 z = 0

The system of equations will be

a. consistent having a unique solution but not trivialb. consistent having many solutionsc. consistent having a trivial solutiond. inconsis tent having no solution

Q.56


Air at 27 and 1 bar is heated at constant volume until the pressure is 5bar and then cooled at constant pressure back to original temperature.

Net decrease in entropy of the process is __________ kJ/kgK.

Q.57


A 20 full depth involute system have a pinion of diameter 300 mm and

number of teeth on pinion is 60. If the length of line of action is 20 mm,

then the contact ratio is _______.

Q.58

Not Atte mpt Cor re ct Ans . 1852.76 (1850-1855) Solution

Air (1 atm; 5 C) with free stream velocity of 2 m/s flowing over a

stationary thin 1 m 1 m flat plate.The flat plate has a uniform surface temperature of 35 C. If the friction

force asserted on the flat plate is 0.1 N, the rate of heat transfer from the

plate is ________ W.

Properties of air (1 atm; 5 C) is

= 1.269 kg/m 3

Cp = 1006 J/kg-K

= 1.729 10 5 kg/m-s

Pr = 0.7350


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Q.59


A flat steel plate is of trapezoidal form. The thickness of the plate is 15

mm and it tapers uniformly from a width of 60 mm to a width of 10 mm in

a length of 300 mm. The elongation of the plate under an axial force of

120 kN is __________ mm.

[Take E = 2.04 105

N/mm2

]

Q.60

Atte mpt Corre ct Ans . 71.12 (70-73) Solution

A symmetric I -section (with width of each flange = 50 mm, thickness of

web = 10 mm) of steel is subjected to a shear force of 100 kN. Find the

magnitude of the shear stress in the web at its junction with the top

flange is ___________ N/mm 2 .

Q.61

A slender rod weighing 140 N is held by a frictionless pin at A and by aspring having a spring constant of 8.80 N/mm at B. The natural frequency

of oscillation for small vibrations will be ___________ Hz.


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Q.62


During pure orthogonal turning operation of a hollow cylindrical pipe, it is

found that the thickness of the chip produced is 0.5 m. The feed given to

the zero degree rake angle tool is 0.25 mm/rev. The shear strain

produced during the operation is________ .

Q.63


A liquid of specific gravity 1.5 is discharged from a tank through a siphon

whose summit point is 1.2 m above the liquid level in tank. The siphon

pipe has a diameter of 0.1 m and it discharges the liquid into atmosphere

at 100 kPa. If liquid vapour pressure is 28 kPa, the safe location of outlet

is ____________ m below the liquid level in the tank.

Q.64

Atte mpt Corre ct Ans . 41 Solution

If x is real, the maximum value of is ____________.

Q.65

Atte mpt Corre ct Ans . 78

In an experiment with 15 observations on x , the following results we

available

x 2 = 2830, x = 170

One observation that was 20 was found to be wrong and was replacedby the correct value 30. Then the corrected variance is _____________.


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