GATE ME 1999
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GATE ME

Value of the function $$\mathop {Lim}\limits_{x \to a} \,{\left( {x - a} \right)^{x - a}}$$ is _______.
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Four arbitrary points $$\,\,\,\left( {{x_1},{y_1}} \right),\,\,\left( {{x_2},{y_2}} \right),\,\,\left( {{x_3},{y_3}} \ri
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The equation $$\,\,\,{{{d^2}u} \over {d{x^2}}} + \left( {{x^2} + 4x} \right){{dy} \over {dx}} + y = {x^8} - 8\,\,{u \ove
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Laplace transform of $${\left( {a + bt} \right)^2}$$ where $$'a'$$ and $$'b'$$ are constants is given by:
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A shown in Figure, a person A is standing at he centre of a rotating platform facing person B who is riding a bicycle, h
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If $$'P'$$ is the gauge pressure within a spherical droplet, then gauge pressure within a bubble of the same fluid and o
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Kinematic viscosity of air at $${20^0}C$$ is given to be $$1.6 \times {10^{ - 5}}\,\,\,{m^2}s.$$ Its kinematic viscosity
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Water flows through a vertical contraction from a pipe of diameter $$d$$ to another of diameter $$d/2$$ (see Figure). T
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It is proposed to coat a $$1mm$$ diameter wire with enamel paint $$\left( {k\,\,\,\, = 0.1W/m} \right.$$ - $$\left. K \r
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Two fluids, $$A$$ and $$B$$ exchange heat in a counter-current heat exchanger. Fluid $$A$$ enters at $${420^ \circ }C$$
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In computing Wilson’s economic lot size for an item, by mistake the demand rate estimate used was $$40\% $$ higher than
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At a production machine, parts arrive according to a Poisson process at the rate of $$0.35$$ parts per minute. Processin
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Which of the following materials requires the largest shrinkage allowance, while making a pattern for casting?
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In a particular mold design, the down sprue has an area of Cross section of $$6.45\,\,c{m^2}$$ where the pouring basin l
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For butt welding $$40mm$$ thick steel plates, when the expected quantity of such jobs is $$5000$$ per month over a perio
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In butt welding operation on plates, the heat input necessary is given by $$Q = 8\,K\,{T_c}\,t\,\,\,\left[ {0.2 + {{Vb
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What is the approximate $$\% $$ change in the life, $$t,$$ of the tool with zero rake angle used in orthogonal cutting w
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In an orthogonal cutting experiment with a tool of rake angle $$7$$$$deg$$, the chip thickness was found to be $$2.5mm$$
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The lives of two tools $$A$$ & $$B$$, governed by the equation $$V{T^{0.125}} = 2.5$$ and $$V{T^{0.25}} = 7$$ respec
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Identify the stress strain in the flange portion of a partially drawn cylindrical cup when deep drawing without a blank
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For the planar mechanism shown in Fig. select the most appropriate choice for the motion of link 2 when link 4 is moved
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For the audio Cassette mechanism shown in Figure given below where is the instantaneous center of rotation (point) of th
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A planetary gear train is shown in Figure. Internal gear (1) has 104 teeth and is held fixed and planet gear (2) has 96
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Consider the system of two wagons shown in Figure. The natural frequencies of this system are
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An isolated thermodynamic system executes a process. Choose the correct statement $$(s)$$ from the following:
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A steel ball of mass $$1$$ $$kg$$ and specific heat $$0.4$$ $$kJ/kg$$ is at temperature of $${60^ \circ }C.$$ It is drop
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An adiabatic steam turbine receives dry saturated steam at $$1.0\,\,\,MN/{m^2}$$ and discharges it $$0.1\,\,\,MN/{m^2}.$
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