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GATE2019 ME1: 4
The lengths of a large stock of titanium rods follow a normal distribution with a mean $(\mu)$ of $440$ mm and a standard deviation $(\sigma)$ of $1$ mm.What is the percentage of rods whose lengths lie between $438$ mm and $441$ mm? $81.85 \%$ $68.4 \%$ $99.75 \%$ $86.64 \%$
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GATE2019 ME1: 5
A flatfaced follower is driven using a circular eccentric cam rotating at a constant angular velocity $\omega$. At time $t=0$, the vertical position of the follower is $y(0)=0$, and the system is in the configuration shown below: The vertical position of the follower face, $(y(t)$ is given by $e \sin \omega t$ $e(1+ \cos 2 \omega t)$ $e(1 \cos \omega t)$ $e \sin 2 \omega t$
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GATE2019 ME1: 6
The natural frequencies corresponding tot he springmass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. Tha ratio $\frac{\omega_I}{\omega_{II}}$ is $\frac{1}{4}$ $\frac{1}{2}$ $2$ $4$
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GATE2019 ME1: 7
A spur gear with $20^{\circ}$ full depth teeth is transmitting $20 \: kW$ at $200 \: rad/s$. The pitch circle diameter of the gear is $100 \: mm$. The magnitude of the force applied on the gear in the radial direction is $0.36 \: kN$ $0.36 \: kN$ $1.39 \: kN$ $2.78 \: kN$
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GATE2019 ME1: 8
During a nonflow thermodynamic process $(12)$ executed by a perfect gas, the heat interaction is equal to the work interaction $(Q_{12} = W_{12})$ when the process is Isentropic Polytropic Isothermal Adiabatic
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GATE2019 ME1: 9
For a hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant crosssection, the Nusselt number at constant wall heat flux $(Nu_q)$ and that at constant wall temperature $(Nu_T)$ are related as $Nu_q > Nu_r$ $Nu_q < Nu_r$ $Nu_q = Nu_r$ $Nu_q = (Nu_r)^2$
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GATE2019 ME1: 10
As per common design practice, the three types of hydraulic turbines, in descending order of flow rate, are Kaplan, Francis, Pelton Pelton, Francis, Kaplan Francis, Kaplan, Pelton Pelton, Kaplan, Francis
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GATE2019 ME1: 11
A slender rod of length $L$, diameter $d$ $(L d)$ and thermal conductivity $k_1$ is joined with another rod of identical dimensions, but of thermal conductivity $k_2$, to form a composite cylinderical rod of length $2L$. The heat transfer in radial direction and ... conductivity of the composite rod is $k_1+k_2$ $\sqrt{k_1k_2}$ $\frac{k_1k_2}{k_1+k_2}$ $\frac{2k_1k_2}{k_1+k_2}$
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GATE2019 ME1: 12
Consider an ideal vapor compression refrigeration cycle. If the throttling process is replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle? Coefficient of ... of performance is same as that of the original cycle Refrigerating effect is lower than that of the original cycle
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GATE2019 ME1: 13
In a casting process, a vertical channel through which molten metal flows downward from pouring basin to runner for reaching the mold cavity is called blister sprue riser pin hole
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GATE2019 ME1: 14
Which one of the following welding methods provides the highest heat flux $(W/mm^2)$? Oxyacetylene gas welding Tungsten inert gas welding Plasma arc welding Laser beam welding
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GATE2019 ME1: 15
The length, width and thickness of a steel sample are $400$ mm, $40$ mm and $20$ mm, respectively. Its thickness needs to be uniformly reduced by $2$ mm in a single pass by using horizontal slab milling. The milling cutter (diameter: $100$ mm, width: $50$ mm) has $20$ ... task are $14$ mm, $18.4$ s $21$ mm, $28.9$ s $21$ mm, $39.4$ s $14$ mm, $21.4$ s
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GATE2019 ME1: 16
The position vector $\overrightarrow{OP}$ of point $P(20,10)$ is rotated anticlockwise in XY 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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GATE2019 ME1: 17
The table presents the demand of a product. By simple threemonths moving average method, the demandforecast of the product for the month of September is ... $490$ $510$ $530$ $536.67$
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GATE2019 ME1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$equalsegment trapezoidal rule gives a value of _______
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GATE2019 ME1: 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 ME1: 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 ME1: 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 ME1: 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 $R$ration (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)
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GATE2019 ME1: 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 teh 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 ME1: 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 ME1: 25
Consider the stressstrain curve for an ideal elasticplastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stressstrain 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 ME1: 26
The set of equations $x+y+z=1$ $axay+3z=5$ $5x3y+az=6$ has infinite solutions, if $a=$ $3$ $3$ $4$ $4$
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GATE2019 ME1: 27
A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^22y^2+4xy$ is a harmonic function, then it is conjugate harmonic function $v(x,y)$ is $4xy2x^2+2y^2+ \text{constant}$ $4y^24xy + \text{constant}$ $2x^22y^2+ xy + \text{constant}$ $4xy+2x^22y^2+ \text{constant}$
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GATE2019 ME1: 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 ME1: 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 real and front 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 ME1: 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 ME1: 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 ME1: 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 ME1: 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 $27^{\circ}$ with a volume flow rate of $51 \: kW$, the exit temperature of the gas is (Assume constant pressure ... $32^{\circ} C$ $37^{\circ} C$ $53^{\circ} C$ $76^{\circ} C$
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GATE2019 ME1: 34
A planestrain compression (forgoing) 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 ME1: 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 ME1: 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 ME1: 37
Match the following sand mold casting defects with their respective causes. ... $P3, Q4, R2, S1$ $P2, Q4, R1, S3$ $P3, Q4, R1, S2$
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GATE2019 ME1: 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 ME1: 39
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square crosssection 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 ME1: 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 crosssection of side $p=6 \: mm$. The Youngâ€™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 ME1: 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 crosshead 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 ME1: 42
At a critial 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 cmponents 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 ME1: 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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