Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2)

# Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2)

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## 65 Questions MCQ Test GATE Mechanical (ME) 2023 Mock Test Series | Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2)

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) for Mechanical Engineering 2023 is part of GATE Mechanical (ME) 2023 Mock Test Series preparation. The Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) MCQs are made for Mechanical Engineering 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) below.
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Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 1

### The perimeters of a circle, a square and an equilateral triangle are equal. Which one ofthe following statements is true?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 1

Let us take a circle, square and an equilateral triangle each of equal perimeter say 100m.
πD = 4a = 3s = 100
D=31.84; a=25; s=33.33;

a2 = 625

Hence circle has largest area.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 2

### The value of the expression

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 2

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 3

### Find the missing group of letters in the following series: BC, FGH, LMNO, _________

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 3

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 4

“The dress ________ her so well that they all immediately _________ her on her appearance.”The words that best fill the blanks in the above sentence are

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 4

Complement: a thing that contributes extra features to something else in such a way as to improve or emphasize its quality.
Compliment: a polite expression of praise or admiration

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 5

“The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained __________.”The word that best fills the blank in the above sentence is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 5

Even though there were false allegations, but judge’s standing remained same.
Undiminished: Not reduced.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 6

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number.
i. If the house number is a multiple of 3, then it is a number from 50 to 59.
ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.

Q. What is the house number?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 6

I. 51,54,57, but none of them is multiple of 4, hence none is valid
II. 61, 62, 63, 65, 66, 67, 69: 63, 66 and 69 are multiple of three hence not valid.
Rest 61, 62, 65, 67 are not a multiple of 6, Hence not valid
III. 70, 71, 73, 74, 75, 76, 77, 79: 75 is multiple of three, hence not valid.
Except 76 none is a multiple of 4, hence only 76 is a valid entry.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 7

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 7

Total student = 40
13 − x +16 − x +19 − x + x = 40
Students watches all three movies,
x = 4

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 8

An unbiased coin is tossed six times in a row and four different such trials areconducted. One trial implies six tosses of the coin. If H stands for head and T stands fortail, the following are the observations from the four trials:
(1) HTHTHT
(2) TTHHHT
(3) HTTHHT
(4) HHHT ___ ___.
Which statement describing the last two coin tosses of the fourth trial has the highest
probability of being correct?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 8

Since the coin is unbiased, the probability of getting heads is equal of tail.
In unbiased coin previous trials does not matter.
Probability of getting both heads =
Probability of getting a head and a tail( HT+TH)
Probability of getting both tails

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 9

A wire would enclose an area of 1936 m2 , if it is bent into a square. The wire is cut intotwo pieces. The longer piece is thrice as long as the shorter piece. The long and the shortpieces are bent into a square and a circle, respectively. Which of the following choicesis closest to the sum of the areas enclosed by the two pieces in square meters?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 9

Area = 1936 m2
a2 = 1936 m2
a = 44 m2
length of wire = 4a
= 4 x 44 = 176 m
part-1 length = 3 x 44 = 132 m
part-2 length = 1 x 44 = 44 m
Long wire is bent in square.
4a = 132
a = 33 m
Area of Square = 332 = 1089 m2
Now, small wire is bent in circle,
So,  πD = 44

D = 44
Area of circle
= 153.94m2
Total area enclosed Area of square Area of circle
= 1089 + 153.94
= 1242.97≈1243m2

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 10

A contract is to be completed in 52 days and 125 identical robots were employed, each
operational for 7 hours a day. After 39 days, five-seventh of the work was completed.
How many additional robots would be required to complete the work on time, if each
robot is now operational for 8 hours a day?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 10

Additional robots required = 131.25 − 125 = 6.25 ≈ 7

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 11

A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 11

T4 = 2000

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 12

For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy from state 1 to 2?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 12

Standard Equation for change of entropy from state 1 to 2

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 13

Select the correct statement for 50% reaction stage in a steam turbine.

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 13

In Parsons Reaction Turbine (50% reaction), α2 = β1

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 14

In a single degree of freedom underdamped spring-mass-damper system as shown in
the figure, an additional damper is added in parallel such that the system still remains
underdamped. Which one of the following statements is ALWAYS true?

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 14

Transmissibility can increase or decrease depending upon the frequency of oscillation.

But due to under-damping, frequencydecreases, hence time period of free oscillations will increase.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 15

The divergence of the vector fieldis

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 15

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 16

Fatigue life of a material for a fully reversed loading condition is estimated from
σ = 1100 N-0.15,
Where, σa is the stress amplitude in MPa and is the failure life in cycles. The maximum
allowable stress amplitude (in MPa) for a life of 1 x 10cycles under the same loading
condition is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 16

σ = 1100 × (105)−0.15
σ = 195.61 MPa

*Multiple options can be correct
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 17

Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 17

A and D both
Option A represents cooling, while option D represents heating.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 18

Metal removal in electric discharge machining takes place through​

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 18

Metal removal in electric discharge machining takes place through melting and vaporization.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 19

Match the following products with the suitable manufacturing process

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 19

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 20

Pre-tensioning of a bolted joint is used to

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 20

Pre-tensioning of bolt increases the stiffness of bolted joint.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 21

The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 um. If the peak wavelength of emitted radiation changes to 2.90 um, then the temperature (in K) of the black body is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 21

λmT = constant
2000 × 1.45 = 2.9 × T
T=1000

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 22

A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 22

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 23

The Fourier cosine series for an even function is given by

The value of the coefficient a2 for the function

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 23

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 24
1. If y is the solution of the differential equation the value of y (−1)
is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 24

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 25

If A = then det (A-10 is _________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 25

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 26

Consider a function u which depends on position x and time t. The partial differential equation

is known as the

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 26

The above equation is known as heat equation.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 27

The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is  . When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to ) is (correct to two
decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 27

Percentage change=

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 28

Feed rate in slab milling operation is equal to

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 28

Feed rate in slab milling= ftZN
Where, ft=feed/tooth
Z= number of teeth
N= rpm

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 29

The minimum axial compressive load, P, required to initiate buckling for a pinnedpinned
slender column with bending stiffness EI and length L is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 29

Pinned-pinned column means hinged on both sides. And the minimum load required to buckle is given by

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 30

During solidification of a pure molten metal, the grains in the casting near the mouldwall are

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 30

Grain orientation is random at time of solidification because of many different
nucleation sites. Coarse grain structure is obtained after solidification at slower rates.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 31

A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in m) by the ball is ___________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 31

Since the tube is frictionless, the ball will travel to and fro, up-down motion without being stopped, hence the total distance travelled by ball is infinite.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 32

An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in kJ/cycle) is _________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 32

Work Output from cycle= Area under PV curve.

=62.5

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 33

The preferred option for holding an odd-shaped workpiece in a centre lathe is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 33

A four jaw chuck is preferred to handle odd-shaped work piece in centre lathe, because the motion of 4 different jaws are not dependent on each other, hence most of the odd shapes can be fit in.

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 34

A local tyre distributor expects to sell approximately 9600 steel belted radial tyres nextyear. Annual carrying cost in Rs. 16 per tyre and ordering cost is Rs. 75. The economicorder quantity of the tyres is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 34

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 35

The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrivals is between 1 and 3 minutes is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 35

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Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 36

A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between -10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the material is600 MPa. The bar cross-section is square with side a. If the factor of safety is 2, the value
of a (in mm), according to the modified Goodman’s criterion, is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 36

Solution by Goodman Equation,

Solution by Langar euation,

Hence final answer by modified Goodman’s Griterion is 31.62 mm.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 37

A thin-walled cylindrical can with rigid end caps has a mean radius R = 100 mm and a wall thickness of t = 5 mm. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and
circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 37

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 38

The true stress (in MPa) versus true strain relationship for a metal is given byThe cross-sectional area at the start of test (when the stress and strain values are equal to zero) is 100 mm2 . The cross-sectional area at the time of necking (in mm2) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 38

At necking, true strain equals the strain hardening exponent.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 39

Air is held inside a non-insulated cylinder using a piston (mass M=25 kg and area A=100 cm2) and stoppers (of negligible area), as shown in the figure. The initial pressure i P and temperature Ti of air inside the cylinder are 200 kPa and 400°C, respectively. The ambient pressure P and temperature T are 100 kPa and 27°C, respectively. The temperature of the air inside the cylinder (°C) at which the piston will begin to move is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 39

Using pressure balance, Pressure at which the piston will start to move,

Since volume and mass remains constant.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 40

A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s2) of the centre of the disc is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 40

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 41

Steam in the condenser of a thermal power plant is to be condensed at a temperature of 30°C with cooling water which enters the tubes of the condenser at 14°C and exits at 22°C.Overall heat transfer coefficient is 2000W/m2K and the total surface area of the tubes is 50 m2. Net heat transfer (in MW) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 41

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 42

A steel wire is drawn from an initial diameter (di ) of 10 mm to a final diameter (df) of 7.5 mm. The half cone angle (α) of the die is 5° and the coefficient of friction (μ ) between the die and the wire is 0.1. The average of the initial and final yield stress  is 350 MPa. The equation for drawing stress σf , (in MPa) is given as:

The drawing stress (in MPa) required to carry out this operation is _________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 42

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 43

A bimetallic cylindrical bar of cross sectional area 1 m2 is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude  10−6 in Steel bar and compressive axial strain of magnitude10−6 in Aluminum bar, the magnitude of the
required force P (in kN.) along the indicated direction is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 43

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 44

Let z be a complex variable. For a counter-clockwise integration around a unit circle C,
centred at origin,

the value of A is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 44

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 45

In a rigid body in plane motion, the point R is accelerating with respect to point P at  m/s . o is zero If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2) of point R is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 45

Since acceleration of point Q is zero, so body PQR is hinged at Q.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 46

Given the ordinary differential equation

the value of y (1) is _________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 46

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 47

A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The material removal rate (in mm3/min) is expressed as

where I = 300 A and the melting point of the material .T =1600°C The time (in minutes) for machining this hole is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 47

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 48

In a cam-follower, the follower rises by h as the cam rotates by (radians) at constant angular velocity ω (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period.
Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 48

Since the cam is having uniform velocity, first half of rise will be accelerating, other half will be decelerating. Hence velocity will be maximum at height=h/2

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 49

Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then  is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 49

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 50

A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment T = 150 Nm is applied at a distance of 100 mm from end P. The torsional reactions (TP,TQ) in Nm at the ends P and Q respectively are

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 50

Since, G and are constant for bar,
T1L1=T2L2
T1.100=T2.200
T1=2T2
And, T1 + T2 = T
Hence, T1 = 100nm T2 = 50Nm

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 51

Air flows at the rate of 1.5 m3 /s through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of 400 mm and 200 mm. Take the air density as 1.2kg/m3 and assume inviscid incompressible flow. The change in pressure (p2 - p1) (in kPa) between sections 1 and 2 is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 51

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 52

The problem of maximizing z= x1 - x2  subject to constraints and x2 ≤ 5 has

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 52

The problem has one solution

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 53

A standard vapor compression refrigeration cycle operating with a condensing temperature of 35oC and an evaporating temperature of -10oC develops 15 kW of cooling. The p-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is 0.75, the magnitude of compressor power (in kW) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 53

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 54

A 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is 350 K. The value of Stefan-Boltzmann constant, σ, is 5.67 x 10-8 W/mK4 . Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in w/m2) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 54

Since there is steady state, the heat transfer between plate and surface is equal to heat transfer between the two surfaces, which is equal to heat transferred through the plate.

Heat flux  between  plate and surface, q" =

1=∈2= 1, Surface are black

q" = 391.612 W/m2

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 55

Following data correspond to an orthogonal turning of a 100 mm diameter rod on a lathe. Rake angle: +15o; Uncut chip thickness: 0.5 mm; nominal chip thickness after the cut: 1.25 mm. The shear angle (in degrees) for this process is _________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 55

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 56

Taylor’s tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in 20 mm thick mild steel plates. In test 1, a drill lasted 300 holes at 150 rpm while in test 2, another drill lasted 200 holes at 300 rpm. The maximum number of holes that can be made by another drill from the above batch at 200 rpm is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 56

Here tool life is represented by number of holes (H) and speed is represented by rpm (N)
Taylors Tool life equation:
Since all the conditions are same for different batches, except rpm and number of holes,

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 57

A rigid rod of length 1 m is resting at an angle θ = 450 as shown in the figure. The end P is dragged with a velocity of U = 5 m/s to the right. At the instant shown, the magnitude of the velocity V (in m/s) of point Q as it moves along the wall without losing contact is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 57

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 58

A frictionless circular piston of area 10-2 m and mass 100 kg sinks into a cylindrical container of the same area filled with water of density 3 1000 kg/m as shown in the figure. The container has a hole of area 10-3 m2 at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 58

Total gauge pressure at top
Total gauge pressure at bottom = 0

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 59

A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m3 /s at 450 rpm. Take the water density and the acceleration due to gravity as 103 kg/m3 and 10 m/s2 , respectively. Assume no losses both in model and prototype turbines. The power (in MW) of a full sized turbine while working under a head of 30 m is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 59

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 60

A welding operation is being performed with voltage = 30 V and current = 100 A. The cross-sectional area of the weld bead is 20 mm2 . The work-piece and filler are of titanium for which the specific energy of melting is 14 J/mm3. Assuming a thermal efficiency of the welding process 70%, the welding speed (in mm/s) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 60

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 61

The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is ____________.

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 61

There was ambiguity in question. In some textbooks it is mentioned that critical path is the shortest path. But the question intended to ask the shortest time taking path. The shortest time taking path is of 7 days and critical path is of 11 days.

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 62

Ambient air is at a pressure of 100 kPa, dry bulb temperature of 30oC and 60% relative humidity. The saturation pressure of water at 30oC is 4.24 kPa. The specific humidity of air (in g/kg of dry air) is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 62

Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 63

For a position vector  the norm of the vector can be defined as Given a function its gradient  is

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 63

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 64

A vehicle powered by a spark ignition engine follows air standard Otto cycle (γ = 1.4 .) The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is __________ (correct to two decimal places). Answer: 7.61

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 64

Amount of heat supplied per second= 10.3×44000/3600 kJ/s
=125.88kW

*Answer can only contain numeric values
Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 65

For sand-casting a steel rectangular plate with dimensions 80mm x 120mm x 20mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov’s law for the estimation of the total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal places).

Detailed Solution for Past Year Paper - Mechanical Engineering GATE : 2018 (Session - 2) - Question 65

## GATE Mechanical (ME) 2023 Mock Test Series

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## GATE Mechanical (ME) 2023 Mock Test Series

27 docs|243 tests