GATE ME 2004
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## GATE ME

For what value of $$x$$ will the matrix given below become singular? $$\left[ {\matrix{ 8 &amp; x &amp; 0 \cr 4 View Question The sum of the eigen values of the matrix$$\left[ {\matrix{ 1 &amp; 1 &amp; 3 \cr 1 &amp; 5 &amp; 1 \cr 3
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The volume of an object expressed in spherical co-ordinates is given by $$V = \int\limits_0^{2\pi } {\int\limits_0^{{\r View Question If$$\,\,\,x = a\left( {\theta + Sin\theta } \right)$$and$$y = a\left( {1 - Cos\theta } \right)$$then$$\,\,{{dy} \o
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From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kin
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The following data about the flow of liquid was observed in a continuous chemical process plant Mean flow rate of th
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The figure shows a pin-jointed plane truss loaded at the point M by hanging a mass of 100 kg. The member LN of the truss
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The figure below shown a pair of pin jointed gripper tongs holding an object weighing $$2000N$$. The coefficient of fric
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A rigid body shown in the fig.(a) has a mass of 10kg. It rotates with a uniform angular velocity $$'\omega '$$ A balan
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An ejector mechanism consists of a helical compression spring having a spring constant of k = 981 × 103 N/m. It is pre-c
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An incompressible fluid (kinematic viscosity $$= 7.4 \times {10^{ - 7}}\,\,{m^2}/s,$$ specific gravity, $$0.88$$) is he
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A fluid flow is represented by the velocity field $$\overrightarrow V = ax\,\overrightarrow i + ay\,\overrightarrow j View Question A closed cylinder having a radius$$R$$and height$$H$$is filled with oil of density$$\rho .$$If the cylinder is rot View Question For a fluid flow through a divergent pipe of length$$L$$having inlet and outlet radii of$${R_1}$$and$${R_2}$$respe View Question The pressure gauges$${G_1}$$and$${G_2}$$installed on the system shown pressures of$${P_{G1}} = 5.00$$bar and$${P_
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The pressure gauges $${G_1}$$ and $${G_2}$$ installed on the system show pressures of $${P_{G1}} = 5.00$$ bar and $${P_{ View Question For air flow over a flat plate, velocity$$(U)$$and boundary layer thickness$$\left( \delta \right)$$can be expresse View Question One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate$$'{q_g}',$$can be View Question A spherical thermocouple junction of diameter$$0.706 mm$$is to be used for the measurement of temperature of a gas str View Question In a condenser, water enters at$${30^ \circ }C$$and flows at the rate$$1500Kg/hr.$$The condensing steam is at a View Question There are two products P and Q with the following characteristics The economic order quantity (EOQ) of products P and Q View Question A company has an annual demand of$$1000$$units, ordering cost of Rs.$$100$$/order and carrying cost of Rs.$$100$$/unit View Question In$$PERT$$analysis a critical activity has View Question For a product, the forecast and the actual sales for December$$2002$$were$$25$$and$$20$$respectively. If the expon View Question An electronic equipment manufacturer has decided to add a component sub-assembly operation that can produce$$80$$units View Question A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a ‘first com View Question A company produces two types of toys:$$P$$and$$Q.$$Production time of$$Q$$is twice that of$$P$$and the company h View Question Two mating spur gears have$$40$$and$$120$$teeth respectively. The pinion rotates at$$1200rpm$$and transmits a View Question A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arran View Question A compacting machine shown in the figure below is used to create a desired thrust force by using a rack and pinion arran View Question Misrun is a casting defect which occurs due to View Question Gray cast iron blocks$$200 \times 100 \times 10\,\,mm$$are to be cast in sand moulds. Shrinkage allowance for pattern View Question In a rolling process, sheet of$$25mm$$thickness is rolled to$$20mm$$thickness. Roll is of diameter$$600$$View Question Two 1 mm thick steel sheets are to be spot welded at a current of$$5000A.$$Assuming effective resistance to be  View Question In a machining operation, doubling the cutting speed reduces the tool life to$$1/{8^{th}}$$of the original value. The View Question A standard machine tool and an automatic machine tool are being compared for the production of a component. Following da View Question In an orthogonal cutting test on mild steel, the following data were obtained Cutting speed:$$40m/min,$$Depth of View Question Through holes of$$10mm$$diameter are to be drilled in steel plate of$$20mm$$thickness. Drill spindle speed View Question$$10mm$$diameter holes are to be punched in a steel sheet of$$3mm$$thickness. Shear strength of the materia View Question A hole of diameter$${25.00^{ + 0.01}}\,\,mm$$is to be inspected by using GO / NO GO gages. The size of the GO plug gag View Question During the execution of a CNC part program block$$NO20\,\,\,\,GO2\,\,\,\,X45.0\,\,\,\,Y25.0\,\,\,\,R5.0.$$The type of View Question In a$$2-DCAD$$package, clockwise circular arc of radius,$$5,$$specified from$${P_1}\left( {15,10} \right)$$t View Question A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surf View Question In terms of Poisson's ratio$$\left( \mu \right)$$the ratio of Young's Modulus$$(E)$$to Shear Modulus$$(G)$$of ela View Question The figure below shows a steel rod of$$25$$mm2 cross sectional area. It is loaded at four points, K, L, M and N. Assum View Question The figure shows the state of stress at a certain point in a stressed body. The magnitudes of normal stresses in the$$x
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The Mohr's circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum s
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A torque of $$10$$ $$N-m$$ is transmitted through a stepped shaft as shown in figure. The torsional stiffnesses of indiv
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A solid circular shaft of $$60$$ mm diameter transmits a torque of $$1600$$ N - m. The value of maximum shear developed
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A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 G
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A steel beam of breadth 120 mm and height 750 mm is loaded as shown in the figure. Assume modulus of elasticity as 200 G
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For a mechanism shown below, the mechanical advantage for the given configuration is
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Match the following Type of Mechanism $$P.$$ Scott - Russel mechanism $$Q.$$ Geneva mechanism $$R.$$ Off-set slider- cr
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In the figure shown, the relative velocity of link $$1$$ with respect to link $$2$$ is $$12$$ m/sec. Link $$2$$ rotates
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Match the following with respect to spatial mechanism. Type of Joint $$P.$$ Revolute $$Q.$$ Cylindrical $$R.$$ Spherical
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The figure below shows a planar mechanism with single degree of freedom. The instant center $${{\rm I}_{24}}$$ for the g
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A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machi
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A uniform stiff rod of length $$300$$ $$mm$$ and having a weight of $$300$$ $$N$$ is pivoted at one end and connected to
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A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25
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A gas contained in a cylinder is compressed, the work required for compression being $$5000$$ $$kJ.$$ During the process
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A heat engine having an efficiency of $$70\%$$ is used to drive a refrigerator having a coefficient of performance of \$
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A solar collector receiving solar radiation at the rate of $$0.6$$$$kW/{m^2}$$ transforms it to the internal energy of a
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A steel billet of $$2000$$ $$kg$$ mass is to be cooled from $$1250$$ $$K$$ to $$450$$ $$K.$$ The heat released during th
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Consider a steam power plant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at $$4$$ $$MP View Question Consider a steam power plant using a reheat cycle as shown. Steam leaves the boiler and enters the turbine at$$4MP
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A centrifugal pump is required to pump water to an open water tank situated $$4$$ $$km$$ away from the location of the p
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At a hydro electric power plant site, available head and flow rate are $$24.5$$ $$m$$ and $$10.1{m^3}/s$$ respectively.
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