GATE ME 2014 Set 4

## GATE ME

Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$

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The value of the integral $$\int\limits_0^2 {{{{{\left( {x - 1} \right)}^2}\sin \left( {x - 1} \right)} \over {{{\left(

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The value of the integral $$\,\int\limits_0^2 {\int\limits_0^x {{e^{x + y}}\,\,dy} } $$ $$dx$$ is

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The number of accidents occurring in a plant in a month follows Poisson distribution with mean as $$5.2.$$ The probabil

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A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution wit

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The solution of the initial value problem $$\,\,{{dy} \over {dx}} = - 2xy;y\left( 0 \right) = 2\,\,\,$$ is

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Consider an ordinary differential equation $${{dx} \over {dt}} = 4t + 4.\,\,$$ If $$x = {x_0}$$ at $$t=0,$$ the increme

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If $$z$$ is a complex variable, the value of $$\int\limits_5^{3i} {{{dz} \over z}} $$ is

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Laplace transform of $$\cos \,\left( {\omega t} \right)$$ is $${s \over {{s^2} + {\omega ^2}.}}$$. The Laplace transfor

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In a statically determinate plane truss, the number of joints $$(j)$$ and the number of members $$(m)$$ are related by

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For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The force (in kN) in the member

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A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis 1m from its end as

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A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands on a rough level floor

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A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B)

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A flow field which has only convective acceleration is

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A flow field which has only convective acceleration is

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Consider the following statements regarding streamline(s):
(i) It is a continuous line such that the tangent at any poin

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Consider a velocity field $$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$ where $$K$$ is a constan

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As the temperature increases, the thermal conductivity of a gas

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A plane wall has a thermal conductivity of $$1.15$$ $$W/m.K.$$ If the inner surface is at $${1100^ \circ }C$$ and the ou

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Match Group $$A$$ with Group $$B$$
Group-A
$$P:$$$$\,\,\,\,\,\,\,$$ Biot number
$$Q:$$$$\,\,\,\,\,\,\,$$ Grashof numbe

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Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between th

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Demand during lead time with associated probabilities is shown below:
Expected demand during lead time is ___________

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The precedence relations and duration (in days) of activities of a project network are given in the table. The total flo

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At a work station, $$5$$ jobs arrive every minute. The mean time spent on each job in the work station is $$1/8$$ minute

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A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The y

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A bolt of major diameter $$12$$ $$mm$$ is required to clamp two steel plates. Cross sectional area of the threaded porti

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Ball bearings are rated by a manufacturer for a life of $${10^6}$$ revolutions. The catalogue rating of a particular b

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A cylindrical riser of $$6$$ $$cm$$ diameter and $$6$$ $$cm$$ height has to be designed for a sand casting mould for pro

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In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness

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Within the Heat Affected Zone (HAZ) in a fusion welding process, the work material undergoes

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A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $$500$$ $$MPa$$ and $$700$$

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Better surface finish is obtained with a large rake angle because

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A cast iron block of $$200$$ $$mm$$ length is being shaped in a shaping machine with a depth of cut of $$4$$ $$mm,$$ fee

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Two separate slab milling operations, $$1$$ and $$2,$$ are performed with identical milling cutters. The depth of cut in

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A $$GO-No$$ $$GO$$ plug gauge is to be designed for measuring a hole of nominal diameter $$25$$ $$mm$$ with a hole toler

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If the Poisson's ratio of an elastic material is $$0.4$$, the ratio of modulus of rigidity to Young's modulus is _____ .

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The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic s

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A frame is subjected to a load $$P$$ as shown in the figure. The frame has a constant flexural rigidity $$EI$$. The effe

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A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissi

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Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of ine

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A point mass is executing simple harmonic motion with an amplitude of $$10$$ mm and frequency of $$4$$ Hz. The maximum a

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A single degree of freedom system has a mass of 2kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnifi

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A reversed Carnot cycle refrigerator maintains a temperature of $$ - {5^ \circ }C.$$ The ambient air temperature is $${3

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A closed system contains $$10$$ $$kg$$ of saturated liquid ammonia at $${10^ \circ }C.$$ Heat addition required to conve

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Two identical metal blocks $$L$$ and $$M$$ (specific heat $$=0.4$$ $$kJ/kg.K$$), each having a mass of $$5$$ $$kg,$$ are

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Steam with specific enthalpy $$\left( h \right)\,\,3214\,\,kJ/kg$$ enters an adiabatic turbine operating at steady state

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Kaplan water turbine is commonly used when the flow through its runner is

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