# Recent questions tagged gateme-2014-set1

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 _______
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 $\dfrac{5}{7} \\$ $\dfrac{14}{3} \\$ $\dfrac{7}{5} \\$ $\dfrac{10}{3}$
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 _______
For the given assembly: $25 \: H7/g8$, match Group $A$ with Group $B$ ... $P-I, Q-III, R-IV, S-II$ $P-I, Q-IV, R-III, S-II$ $P-II, Q-III, R-IV, S-I$ $P-II, Q-IV, R-III, S-I$
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 _______
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 _______
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 _______
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 $0.8$ $1.0$ $1.4$ $2.0$
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 _______
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 $a$ $b$ $2c$ $(b+2c)$
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 _______
For a fully developed flow of water in a pipe having diameter $10$ $cm$, velocity $0.1$ $m/s$ and kinematic viscosity $10^{−5}$ $m^2$/$s$, the value of Darcy friction factor is _______
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 _______
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 _______
$1.5$ 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 _______
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 _______
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 _____
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 $x = 10$, $f(15) =$ _____________ .
In the following table, $x$ is a discrete random variable and $p(x)$ is the probability density. The standard deviation of $x$ is $\begin{array}{|c|c|c|c|} \hline x & 1 & 2 & 3 \\ \hline p(x) & 0.3 & 0.6 & 0.1 \\ \hline \end{array}$ $0.18$ $0.36$ $0.54$ $0.60$
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 ______
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 $\sqrt{\dfrac{k}{2m}} \\$ $\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{2k}{m} } \\$ $\sqrt{\dfrac{5k}{m}}$
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 _______
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 _____
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 _______
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 _______
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 _______
A pair of spur gears with module $5$ $mm$ and a center distance of $450$ $mm$ is used for a speed reduction of $5:1$. The number of teeth on pinion is _______
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 . $0.69$ $0.88$ $0.98$ $1.37$
The state of stress at a point is given by $\sigma _x=-6 MPa$ ,$\sigma _y=4 MPa$ and $\tau _{xy}=-8 MPa$.The maximum tensile stress in (MPa) at the point is _____
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 $0$ $\frac{-\pi }{4}$ $\frac{-\pi }{2}$ $\frac{\pi }{4}$
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
In solid-state welding, the contamination layers between the surfaces to be welded are removed by alcohol plastic deformation water jet sand blasting
The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is normalising annealing quenching tempering
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 $1000$ $2000$ $3000$ $4000$
The major difficulty during welding of aluminum is due to its high tendency of oxidation high thermal conductivity low melting point low density
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 $16$ $mm$ ... $(−8,8), (94,0), (94,44), (8,44), (−8,8)$ $(0,0), (100,0), (100,50), (50,0), (0,0)$
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
Which one of the following is a CFC refrigerant? $R744$ $R290$ $R502$ $R718$
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 $0.34$ $2.48$ $2.92$ $3.43$