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GATE2019 ME-1: 55
A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below: ... amount of time, the maximum duration (in weeks) of the activity $S$ without delaying the completion of the project is ________

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GATE2019 ME-1: 54
Five jobs $(J1, J2, J3, J4$ and $J5)$ need to be processes in a factory. Each job can be assigned to any of the five different machines $(M1, M2, M3, M4$ and $M5)$. The time durations taken (in minutes) by the machines for each of the jobs, are given in the table. ...

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GATE2019 ME-1: 53
Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools $X$ and $Y$ are used. For tool $X$, $n=0.3$ and $C=60$ and for tool $Y$, $n=0.6$ and $C=90$. Both the tools will have the same tool life for the cutting speed (in $m/min$, round off to one decimal place) of ____________

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GATE2019 ME-1: 52
In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning is $0.1 \: mm/rev$. The center line average surface roughness (in $\mu m$, round off to one decimal place) of the generated surface is __________

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GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$

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GATE2019 ME-1: 50
A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is increased to $5$, while maintaining the same inlet conditions. Assume air as a ... the cases, the isentropic efficiency of the turbine at the pressure ratio of $5$ is ___________ (round off to two decimal places)

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GATE2019 ME-1: 49
A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater ... from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state $1$ is _______

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GATE2019 ME-1: 48
If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pressure of the contained gas (round off to two decimal places), assuming ideal gas behaviour, is _______ Pa. $(R=8.314 \: J/mol \cdot K)$

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GATE2019 ME-1: 47
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000 \: Wm^{-3}$, while the left and right slabs have no ... $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.

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GATE2019 ME-1: 46
A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of density $1000 \: kg/m^3$ is now poured into the container. The minimum height to which the liquid needs to be poured into the container for the cube to just lift up is __________$mm$.

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GATE2019 ME-1: 45
Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant ... fluid, $\mu_1$, then the velocity at the interface (round off to two decimal places) is _______ $m/s$.

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GATE2019 ME-1: 44
A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coefficient of friction is $0.25$. The value of $a$ in mm (round off to one decimal place), such that the minimum actuating force $P$ is $2000 \: N$, is ___________

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GATE2019 ME-1: 43
A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk center $A$ ... disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is _________ $rad/s$ (round off to oe decimal place).

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GATE2019 ME-1: 42
At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all other stress components are zero. The yield strength of the material is $468 \: MPa$ The factor of safety on the basis of maximum shear stress theory is ___________ (round off to one decimal place)

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GATE2019 ME-1: 41
In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{-8} \: m/N$. The strain at failure in the sample is ______$\%$

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GATE2019 ME-1: 40
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.

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GATE2019 ME-1: 39
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young's modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a ... $MPa$.

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GATE2019 ME-1: 38
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the member BC is __________

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GATE2019 ME-1: 37
Match the following sand mold casting defects with their respective causes. ... $P-3, Q-4, R-2, S-1$ $P-2, Q-4, R-1, S-3$ $P-3, Q-4, R-1, S-2$

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GATE2019 ME-1: 36
A circular shaft having diameter $65.00_{-0.05}^{+0.01} \: mm$ is manufactured by turning process. A $50 \: \mu m$ thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is $\pm 5 \mu m$. The minimum hole diameter (in mm) to just provide clearance fit is $65.01$ $65.12$ $64.95$ $65.10$

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GATE2019 ME-1: 35
In orthogonal turning of a cylindrical tube of wall thickness $5 \: mm$, the axial and the tangential cutting forces were measured as $1259 \: N$ and $1601 \:N$, respectively. The measured chip thickness after machining was found to be $0.3 \: mm$. The rake angle was ... solution, the shear strength of the material is closest to $722 \: MPa$ $920 \: MPa$ $200 \: MPa$ $875 \: MPa$

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GATE2019 ME-1: 34
A plane-strain compression (forging) of a block is shown in the figure. The strain in the $z$-direction is zero. The yield strength $(S_y)$ in uniaxial tension/compression of the material of the block is $300 \: MPa$ and it follows the Tresca (maximum shear stress) ... $340 \: MPa$ (compressive) $340 \: MPa$ (tensile) $260 \: MPa$ (compressive) $260 \: MPa$ (tensile)

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GATE2019 ME-1: 33
A gas is heated in a duct as it flows over a resistance heater. Consider a $101 \: kW$ electric heating system. The gas enters the heating section of the duct at $100 \: kPa$ and $27^{\circ} C$ with a volume flow rate of $15 m^3/s$. If heat is lost from the gas in the duct to the ... $32^{\circ} C$ $37^{\circ} C$ $53^{\circ} C$ $76^{\circ} C$

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GATE2019 ME-1: 32
The wall of a constant diameter pipe of length $1 \: m$ is heated uniformly with flux $q''$ by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and ... the location P, Q and R, the flow is thermally developed at P, Q and R P and Q only Q and R only R only

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GATE2019 ME-1: 31
The rotor of a turbojet engine of an aircraft has a mass $180 \: kg$ and polar moment of inertia $10 \: kg \cdot m^2$ about the rotor axis. The rotor rotates at a constant speed of $1100 \: rad/s$ in the clockwise direction when viewed from the front of the aircraft. The ... the nose goes down $162.9 \: N \cdot m$ and the nose goes up $162.9 \: N \cdot m$ and the nose goes down

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GATE2019 ME-1: 30
In a four bar planar mechanism shown in the figure, $AB= 5 \: cm, AD=4 \: cm $ and $DC=2 \: cm$. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of $10 \: rad/s$. The magnitude of angular velocity (in rad/s) of bar DC at this instant is $0$ $10$ $15$ $25$

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GATE2019 ME-1: 29
A car having weight $W$ is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height $h$ from the ground, midway between the front and rear wheels. The distance between front and rear wheel is $l$. The acceleration of the car is $a$, and ... $R_f=R_r = \frac{W}{2}+\frac{W}{g} \big( \frac{h}{l} \big) a$

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GATE2019 ME-1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$

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GATE2019 ME-1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is $4xy-2x^2+2y^2+ \text{constant}$ $4y^2-4xy + \text{constant}$ $2x^2-2y^2+ xy + \text{constant}$ $-4xy+2y^2-2x^2+ \text{constant}$

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GATE2019 ME-1: 26
The set of equations $x+y+z=1$ $ax-ay+3z=5$ $5x-3y+az=6$ has infinite solutions, if $a=$ $-3$ $3$ $4$ $-4$

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GATE2019 ME-1: 25
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stress-strain curve passes through initial yield point at $P$, and then ... specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.

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GATE2019 ME-1: 24
Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas constant of $0.287 \: kJ/kg.K$, the change in entropy of air (in $kJ/kg.K$, round off to two decimal places) is ______

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GATE2019 ME-1: 23
Water flows through a pipe with a velocity given by $\overrightarrow{V}= \big( \frac{4}{t}+x+y \big) \hat{j} \: m/s$, where $\hat{j}$ is the unit vector in the $y$ direction, $t(>0)$ is in seconds, and $x$ and $y$ are in meters. The magnitude of total acceleration at the point $(x,y)=(1,1)$ at $t=2\: s$ is ______$m/s^2$

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GATE2019 ME-1: 22
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)

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GATE2019 ME-1: 21
A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\circ}C$ and the bulk modulus is $200$ GPa. If the cube is constrained all around and heated uniformly to $42^{\circ}C$, then the magnitude of volumetric (mean) stress (in MPa) included due to heating is _______

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GATE2019 ME-1: 20
A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{-3}$, then $p$ is equal to ____ (round off to two decimal places).

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GATE2019 ME-1: 19
A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the block is $0.2$. A horizontal force of $10$ N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____

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GATE2019 ME-1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

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GATE2019 ME-1: 17
The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is ... $490$ $510$ $530$ $536.67$

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GATE2019 ME-1: 16
The position vector $\overrightarrow{OP}$ of point $P(20,10)$ is rotated anti-clockwise in $X-Y$ plane by an angle $\theta = 30^{\circ}$ such that point $P$ occupies position $Q$, as shown in the figure. The coordinates $(x,y)$ of $Q$ are $(13.40,22.32)$ $(22.32, 8.26)$ $(12.32, 18.66)$ $(18.66, 12.32)$

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