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Recent questions tagged gateme-2014-set1

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If the Taylor’s tool life exponent $n$ is $0.2$, and the tool changing time is $1.5$ $min$, then the tool life (in $min$) for maximum production rate is _______
asked Feb 19, 2017 in Mechanics of Materials Arjun 24.6k points
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Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be $\dfrac{5}{7} \\$ $\dfrac{14}{3} \\$ $\dfrac{7}{5} \\$ $\dfrac{10}{3}$
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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An aluminium alloy (density $2600$ $kg$/$m^3$) casting is to be produced. A cylindrical hole of $100$ $mm$ diameter and $100$ $mm$ length is made in the casting using sand core (density $1600$ $kg$/$m^3$). The net buoyancy force (in newton) acting on the core is _______
asked Feb 19, 2017 in Mechanics of Materials Arjun 24.6k points
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For the given assembly: $25 \: H7/g8$, match Group $A$ with Group $B$ ... $P-I, Q-III, R-IV, S-II$ $P-I, Q-IV, R-III, S-II$ $P-II, Q-III, R-IV, S-I$ $P-II, Q-IV, R-III, S-I$
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produced is $0.5$ $mm$. The feed given to the zero degree rake angle tool is $0.2$ $mm/rev$. The shear strain produced during the operation is _______
asked Feb 19, 2017 in Mechanics of Materials Arjun 24.6k points
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A metal rod of initial length $L_0$ is subjected to a drawing process. The length of the rod at any instant is given by the expression, $L(t)=L_0(1+t^2)$ , where $t$ is the time in minutes. The true strain rate (in $min^{−1}$) at the end of one minute is _______
asked Feb 19, 2017 in Engineering Materials Arjun 24.6k points
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An ideal reheat Rankine cycle operates between the pressure limits of $10 \: kPa$ and $8 \: MPa$, with reheat being done at $4 \: MPa$. The temperature of steam at the inlets of both turbines is $500^ \circ C$ and the enthalpy of steam is $3185 \: kJ/kg$ at the ... Disregarding the pump work, the cycle efficiency (in percentage) is _______
asked Feb 19, 2017 in Applications Arjun 24.6k points
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A reversible heat engine receives $2$ $kJ$ of heat from a reservoir at $1000$ $K$ and a certain amount of heat from a reservoir at $800$ $K$. It rejects $1$ $kJ$ of heat to a reservoir at $400$ $K$. The net work output (in $kJ$) of the cycle is $0.8$ $1.0$ $1.4$ $2.0$
asked Feb 19, 2017 in Heat Transfer Arjun 24.6k points
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In an air-standard Otto cycle, air is supplied at $0.1$ $MPa$ and $308$ $K$. The ratio of the specific heats $(γ)$ and the specific gas constant $(R)$ of air are $1.4$ and $288.8$ $J/kg.K$, respectively. If the compression ratio is $8$ and the maximum temperature in the cycle is $2660$ $K$, the heat (in $kJ/kg$) supplied to the engine is _______
asked Feb 19, 2017 in Heat Transfer Arjun 24.6k points
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The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $\dfrac{T_W-T}{T_W-T_\infty }=a+b\dfrac{y}{L}+c \left (\dfrac{y}{L} \right)^2$ , where $y$ is measured perpendicular to the plate, $L$ is the plate length, and $a$, $b$ and $c$ ... $Nu=\dfrac{{q}''}{T_W-T_\infty }\dfrac{L}{k}$ is equal to $a$ $b$ $2c$ $(b+2c)$
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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In a simple concentric shaft-bearing arrangement, the lubricant flows in the $2$ $mm$ gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is $100$ $mm$ ... lubricant is $0.1$ $kg/m.s$. The frictional resisting force (in newton) per $100$ $mm$ length of the bearing is _______
asked Feb 19, 2017 in Machine Design Arjun 24.6k points
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Water flows through a pipe having an inner radius of $10 mm$ at the rate of $36 \: kg/hr$ at $25^ \circ C$. The viscosity of water at $25^ \circ C$ is $0.001 \: kg/m.s$. The Reynolds number of the flow is _______
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $30$ $mm$ and thermal conductivity $15$ $W/m.K$. At $x$ = $0$, a constant heat flux, ${q}''$ = $1 105$ $W$/$m^2$ is applied. On the other side of the wall, heat is ... a fluid at $25^0C$ and heat transfer coefficient of $250$ $W$/$m^2.K$. The temperature (in $°C$), at $x$ = $0$ is _______
asked Feb 19, 2017 in Heat Transfer Arjun 24.6k points
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$1.5$ kg of water is in saturated liquid state at $2$ bar $(vf = 0.001061 \: m^3/kg, uf = 504.0 \: kJ/kg,$ $hf = 505 kJ/kg$). Heat is added in a constant pressure process till the temperature of water reaches $400^ \circ C (v = 1.5493 \: m^3/kg, u = 2967.0 kJ/kg,$ $h = 3277.0 \: kJ/kg)$. The heat added (in $kJ$) in the process is _______
asked Feb 19, 2017 in Heat Transfer Arjun 24.6k points
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A $200$ mm long, stress free rod at room temperature is held between two immovable rigid walls. The temperature of the rod is uniformly raised by $250^\circ C$. If the Young’s modulus and coefficient of thermal expansion are $200$ GPa and $1 \times 10^{−5} / _{}^{\circ}\textrm{C}$ , respectively, the magnitude of the longitudinal stress (in MPa) developed in the rod is _______
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
asked Feb 19, 2017 in Numerical Methods Arjun 24.6k points
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If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .
asked Feb 19, 2017 in Calculus Arjun 24.6k points
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In the following table, $x$ is a discrete random variable and $p(x)$ is the probability density. The standard deviation of $x$ is $\begin{array}{|c|c|c|c|} \hline x & 1 & 2 & 3 \\ \hline p(x) & 0.3 & 0.6 & 0.1 \\ \hline \end{array}$ $0.18$ $0.36$ $0.54$ $0.60$
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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A hydrodynamic journal bearing is subject to $2000$ N load at a rotational speed of $2000$ rpm. Both bearing bore diameter and length are $40$ mm. If radial clearance is µm and bearing is lubricated with an oil having viscosity $0.03$ $P_{a.s}$, the Sommerfeld number of the bearing is ______
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A rigid uniform rod $AB$ of length $L$ and mass $m$ is hinged at $C$ such that $AC = L/3$, $CB = 2L/3$. Ends $A$ and $B$ are supported by springs of spring constant k. The natural frequency of the system is given by $\sqrt{\dfrac{k}{2m}} \\$ $\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{2k}{m} } \\$ $\sqrt{\dfrac{5k}{m}}$
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A slider crank mechanism has slider mass of $10$ kg, stroke of $0.2$ m and rotates with a uniform angular velocity of $10$ rad/s. The primary inertia forces of the slider are partially balanced by a revolving mass of $6$ kg at the crank, placed at a distance ... When the crank angle (with respect to slider axis) is $30^\circ$, the unbalanced force (in newton) normal to the slider axis is _____
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A block weighing $200 N$ is in contact with a level plane whose coefficients of static and kinetic friction are $0.4$ and $0.2$, respectively. The block is acted upon by a horizontal force (in newton) $P=10t$, where $t$ denotes the time in seconds. The velocity (in $m/s$) of the block attained after $10$ seconds is _______
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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An ideal water jet with volume flow rate of $0.05$ $m^3$/$s$ strikes a flat plate placed normal to its path and exerts a force of $1000$ $N$. Considering the density of water as $1000kg$/$m^3$,the diameter(in $mm$) of the water jet is _______
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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Consider a cantilever beam, having negligible mass and uniform flexural rigidity, with length $0.01$ $m$. The frequency of vibration of the beam, with a $0.5$ $kg$ mass attached at the free tip, is $100$ $Hz$. The flexural rigidity (in $N$.$m^2$) of the beam is _______
asked Feb 19, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A block R of mass $100$ kg is placed on a block S of mass $150$ kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ .If the coefficient of static friction for all surfaces is $0.4$, the minimum force F (in $kN$) needed to move the block S is . $0.69$ $0.88$ $0.98$ $1.37$
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
asked Feb 19, 2017 in Calculus Arjun 24.6k points
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The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is Normal Poisson Erlang Beta
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is $400$ $N$. The turning was performed using $2$ $mm$ depth of cut and $0.1$ $mm/rev$ feed rate. The specific cutting pressure (in $N$/$mm^2$) is $1000$ $2000$ $3000$ $4000$
asked Feb 19, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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For machining a rectangular island represented by coordinates $P(0,0), Q(100,0), R(100,50)$ and $S(0,50)$ on a casting using CNC milling machine, an end mill with a diameter of $16$ $mm$ ... $(−8,8), (94,0), (94,44), (8,44), (−8,8)$ $(0,0), (100,0), (100,50), (50,0), (0,0)$
asked Feb 19, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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In exponential smoothening method, which one of the following is true? $0 \leq \alpha \leq 1$ and high value of $\alpha$ is used for stable demand $0 \leq \alpha \leq 1$ and high value of $α$ is used for unstable demand $\alpha \geq 1$ and high value of $\alpha$ is used for stable demand $\alpha \geq 0$ and high value of $\alpha$ is used for unstable demand
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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In a power plant, water (density = $1000$ $kg$/$m^3$) is pumped from $80$ $kPa$ to $3$ $MPa$. The pump has an isentropic efficiency of $0.85$. Assuming that the temperature of the water remains the same, the specific work (in $kJ$/$kg$) supplied to the pump is $0.34$ $2.48$ $2.92$ $3.43$
asked Feb 19, 2017 in Fluid Mechanics Arjun 24.6k points
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