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 $$R$$

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

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

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

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

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

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

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

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

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

View Question 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

View Question 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

View Question 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

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

View Question A flow field which has only convective acceleration is

View Question A flow field which has only convective acceleration is

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

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

View Question As the temperature increases, the thermal conductivity of a gas

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

View Question Better surface finish is obtained with a large rake angle because

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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