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GATE2019 ME1: 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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May 24
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GATE2019 ME1: 3
For the equation $\frac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is $\frac{7}{3}e^{7/3}$ $\frac{7}{3}e^{3/7}$ $\frac{3}{7}e^{7/3}$ $\frac{3}{7}e^{3/7}$
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GATE2017 ME2: 29
If $f(z)=(x^{2}+ay^{2})+i bxy$ is a complex analytic function of $z=x+iy$, where $i=\sqrt{1}$, then $a=1, b=1$ $a=1, b=2$ $a=1, b= 2$ $a=2, b=2$
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May 24
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390
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gate2017me2
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GATE2019 ME2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
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May 18
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Shalini26
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GATE2019 ME2: 10
Sphere $1$ with a diameter of $0.1$ m is completely enclosed by another sphere $2$ of diameter $0.4$m. The view factor $F_{12}$ is $0.0625$ $0.25$ $0.5$ $1.0$
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Feb 9
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GATE2019 ME2: 15
The fluidity of molten metal of cast alloys (without any addition of fluxes) increases with increase in viscosity surface tension freezing range degree of superheat
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Feb 9
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GATE2019 ME2: 16
The cold forming process in which a hardened tool is pressed against a workpiece (when there is relative motion between the tool and the workpiece) to produce a roughened surface with a regular pattern is Roll forming Strip forming Knurling Chamfering
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GATE2019 ME2: 17
The most common limit gage used for inspecting the hole diameter is Snap gage Ring gage Plus gage Madter gage
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Feb 9
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21.2k
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GATE2019 ME2: 18
The transformation matrix for mirroring a point in $x – y$ plane about the line $y=x$ is given by $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$
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Feb 9
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gate2019me2
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GATE2019 ME2: 20
The figure shows an idealized plane truss. If a horizontal force of $300$ N is applied at point A, then the magnitude of the force produced in member CD is ____ N
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Feb 9
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21.2k
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GATE2019 ME2: 21
The state of stress at a point in a component is represented by a Mohr’s circle of radius $100$ MPa centered at $200$ MPa on the thermal stress axis. On a plane plassing through the same point, the normal stress is $260$ MPa. The magnitude of the shear stress on the same plane at the same point is _______ MPa
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GATE2019 ME2: 22
A wire of circular crosssection of diameter $1.0$ mm is bent into a circular arc of radius. $1.0$ m by application of pure bending moments at its ends. The Young’s modulus of the material of the wire is $100$ GPa. The maximum tensile stress developed in the wire is ______ MPa
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GATE2019 ME2: 23
Water enters a circular pipe of length $L=5.0$ m and diameter $D=0.20$m with Reynolds number $Re_D=500$. The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is ____
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GATE2019 ME2: 24
A thin vertical flat plate of height $L$, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatured of the plate and the surroundings by natural convection. The temperatures of the plate and the ... first plate is $h_1$ and that for the second plate is $h_2$, the value of the raio $h_1/h_2$ is ______
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GATE2019 ME2: 25
In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is $200$ V and the capacitance of the RC circuit is $50 \mu F$ The energy (in $J$) released per spark across the IEG is ______
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Feb 9
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GATE2019 ME2: 26
Given a vector $\overrightarrow{u} = \frac{1}{3} \big(y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$ ... $S$ is $ \frac{\pi}{2}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\pi$
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 27
A diffferential equation is given as $x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$ The solution of the differential equation in terms of arbitrary constants $C_1$ and $C_2$ is $y=C_1x^2 +C_2 x+2$ $y=\frac{C_1}{x^2} +C_2x+2$ $y=C_1x^2+C_2x+4$ $y=\frac{C_1}{x^2}C_2x+4$
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 28
The derivative of $f(x)= \cos x$ can be estimated using the approximation $f'(x)=\frac{f(x+h)f(xh)}{2h}$. The percentage error is calculated as $\bigg( \frac{\text{Exact value  Approximate value}}{\text{Exact value}} \bigg) \times 100$. The percentage error in the derivative of $f(x)$ ... $> 0.1 \% \text{ and } <1 \%$ $> 1 \% \text{ and } <5 \%$ $>5 \%$
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Feb 9
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21.2k
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GATE2019 ME2: 29
A ball of mass $3$ kg moving with a velocity of $4$ m/s undergoes a perfectlyelastic directcentral impact with a stationary ball of mass $m$. After the impact is over, the kinetic energy of the $3$ kg ball is $6$ J. The possible value(s) of $m$ is/are $1$ kg only $6$ kg only $1$ kg, $6$ kg $1$ kg, $9$ kg
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 30
Consider two concentric circular cylinders of different materials $M$ and $N$ in contact with each other at $r=b$, as shown below. The interface at $r=b$ is frictionless, The composite cylinder is subjected to internal presure $P$. Let $(u_r^M, u_{\theta}^M)$ ... $\sigma_{rr}^M = \sigma_{rr}^N \text{ and } \sigma_{\theta \theta}^M = \sigma_{\theta \theta}^N$
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 32
A slender uniform rigid bar of mass $m$ is hinged at $O$ and supported by two springs, with stiffness, $3k$ and $k$ and a damper with damping coefficient $c$, as shown in the figure. For the system to be critically damped, the ratio $c/\sqrt{km}$ should be $2$ $4$ $2 \sqrt{7}$ $4 \sqrt{7}$
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Feb 9
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gate2019me2
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GATE2019 ME2: 33
The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output $(W)$ of the heat engine. If temperatures, $T_1 >T_3>T_2$, then the relation between ... $\text{COP}= 1 + \eta$ $\text{COP}= \eta^{1}$ $\text{COP}= \eta^{1} 1 $
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 34
The binary phase diagram of metals $P$ and $Q$ is shown in the figure. An alloy $X$ containing $60 \% P$ and $40 \% Q$ (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at $1250^o C$, respectively, will be $77.8 \% \text{ and } 22.2 \%$ $22.2 \% \text{ and } 77.8 \%$ $68.0 \% \text{ and } 38.0 \%$ $38.0 \% \text{ and } 68.0 \%$
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Feb 9
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21.2k
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gate2019me2
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GATE2019 ME2: 35
The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship $ X<Y,Z $ means that $X$ is predecessor of activities $Y$ and $Z$ ... $17$ $21$ $23$ $25$
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 36
The crank of a slidercrank mechanism rotates counterclockwise (CCW) with a constant angular velocity $\omega$, as shown. Assume the length of the crank to be $r$. Using exact analysis, the acceleration of the slider in the $y$direction, at the instant shown, where the crank is parallel to $x$axis, is given by $ \omega ^2r$ $2 \omega ^2r$ $\omega ^2r$ $2 \omega ^2r$
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 37
A horizontal cantilever beam of circular crosssection, length $1.0$ m and flexural rigidity $EI=200 \: N \cdot m^2$ is subjected to an applied moment $M_A = 1.0 \: N \cdot m$ at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is ______ mm (round off to one decimal place).
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Feb 9
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21.2k
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gate2019me2
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GATE2019 ME2: 38
Two masses $A$ and $B$ having mass $m_a$ and $m_b$, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses $m_a$ and ... $200$ mm is ____ kg (round off to two decimal places).
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 40
The probability that a part manufactured by a company will be defective if $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).
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Feb 9
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21.2k
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gate2019me2
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GATE2019 ME2: 41
A uniform disc with radius $r$ and a mass $m$ kg is mounted centrally on a horizontal axle of negligible mass and length $1.5r$. The disc spins counterclockwise about the axle with angular speed $\omega$, when viewed from the righthand side bearing, Q ... $g=10 m/s^2$, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is ______
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 42
A short shoe external drum brake is shown in the figure. The diameter of the brake drum is $500 \: mm$. The dimensions $a=1000 \: mm, \: b=500 \: mm$ and $c=200 \: mm$. The coefficient of friction between the drum and the shoe is $0.35$. ... in the figure. The drum is rotating anticlockwise. The braking torque on the drum is ______ $N \cdot m$ (round off to two decimal places).
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Feb 9
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Arjun
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21.2k
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gate2019me2
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GATE2019 ME2: 43
Water flows through two different pipes A and B of the same circular crosssection but at different flow rates. The length of pipe A is $1.0 \: m$ and that of pipe B is $2.0 \: m$. The flow in both the pipes is laminar and fully developed. If ... head loss across the length of the pipes is same, the ratio of volume flow rates $Q_B/Q_A$ is _____ (round off to two decimal places).
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Feb 9
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Arjun
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gate2019me2
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GATE2019 ME2: 44
The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of $0.1$ with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes $0.8$. The car travels at $44$ km/h with the windows ... (round off to two decimal places), is ____ km/h (The density of air and the frontal area may be assumed to be constant).
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Feb 9
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Arjun
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21.2k
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GATE2019 ME2: 45
Three sets parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor $F_{IJ}$ is defined as the fraction of radiation leaving plate $I$ that is intercepted by plate $J$. Assume that the values of $F_{LM}$ and $F_{NR}$ are $0.8$ and $0.4$, respectively. The value of $F_{PQ}$ (round off to two decimal place) is _______
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GATE2019 ME2: 46
Hot cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and fluids are $C_h=2000 \: W/K$ and $C_c =1200 \: W/K$, respectively. If the outlet temperature of ... $45^{\circ} C$, the log mean temperature difference (LMTD) of the heat exchanger is _______ $K$ (round off to two decimal places).
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GATE2019 ME2: 47
Water flowing at the rate of $1$ kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by $2.50 \: kJ/kg$ and the specific entropy increases by $0.007 \: kJ/kg \cdot K$. The power input ... Assuming an ambient temperature of $300 \: K$, the irreversibility rate of the system is ______ $kW$ (round off to two decimal places).
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GATE2019 ME2: 48
An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kQ$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. The losses are neglected, then the mass flow rate of the liquid through the pump is _______ $kg/s$ (round off to two decimal places)
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GATE2019 ME2: 49
An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$ and specific gas constant $R=0.287 \: kJ/kg \cdot K$. If the pressure and ... $300 \: K$, respectively, then the specific net work output of the cycle is _____ $kJ/kg $ (round off to two decimal places).
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GATE2019 ME2: 50
The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is $9.81 \: m/s^2$ .The time (in $s$, round off to two decimal places) to fill up the mold cavity (of size $40 \: cm \times 30 \: cm \times 15 \: cm) is _____
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GATE2019 ME2: 51
A gas tungsten arc welding operation is performed using a current of $250 \: A$ and an arc voltage if $20 \: V$ at a welding speed of $5 \: mm/s$. Assuming that the arc efficiency is $70 \%$, the net heat input per unit length of the weld will be ____$kJ/mm$ (round off to one decimal place)
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Feb 9
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GATE2019 ME2: 52
The thickness of a sheet is reduced by rolling (without any change in width) using $600 \: mm$ diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the rollworkpiece interface is $0.05$. The sheet enters the ... final thickness that can be produced by this process in a single pass is ______ $mm$ (round off to two decimal places).
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