GATE ME 2014 Set 3
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## GATE ME

Consider a $$3 \times 3$$ real symmetric matrix $$S$$ such that two of its eigen values are $$a \ne 0,$$ $$b\,\, \ne 0$$
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If a function is continuous at a point,
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Divergence of the vector field $${x^2}z\widehat i + xy\widehat j - y{z^2}\widehat k\,\,$$ at $$(1, -1, 1)$$ is
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A group consists of equal number of men and women. Of this group $$20$$% of the men and $$50$$% of the women are unemplo
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A machine produces $$0, 1$$ or $$2$$ defective pieces in a day with associated probability of $${1 \over 6},{2 \over 3} View Question Consider two solutions$$\,x\left( t \right)\,\,\,\, = \,\,\,{x_1}\left( t \right)\,\,$$and$$x\left( t \right)\,\,\
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The definite integral $$\,\int\limits_1^3 {{1 \over x}} dx\,\,$$ is evaluated using Trapezoidal rule with a step size of
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The real root of the equation $$5x-2cosx=0$$ (up to two decimal accuracy) is
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An analytic function of a complex variable $$z = x + iy$$ is expressed as $$f\left( z \right) = u\left( {x + y} \right) View Question A mass m1 of 100kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m2 of 1000kg View Question A body of mass (m) 10kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic f View Question A four-wheel vehicle of mass 1000kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheel View Question An annular disc has a mass m, inner radius R and outer radius$$2R$$. The disc rolls on a flat surface without slipping. View Question A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is mainta View Question A fluid of dynamic viscosity$$2 \times {10^{ - 5}}\,\,kg/m.s$$and density$$1kg/{m^3}$$flows with an average velocity View Question Consider the turbulent flow of a fluid through a circular pipe of diameter,$$D.$$Identify the correct pair of statemen View Question Consider a long cylindrical tube of inner and outer radii,$${r_i}$$and$${r_0}$$, respectively, length,$$L$$and the View Question Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness$$\left( \
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A solid sphere of radius$${r_1} = 20\,\,mm$$ is placed concentrically inside a hollow sphere of radius $${r_2} = 30\,\,m View Question A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at$$19$$liter/s is View Question A manufacturer can produce$$12000$$bearings per day. The manufacturer received an order of$$8000$$bearings per day View Question Consider the given project network, where numbers along various activities represent the normal time. The free float on View Question The actual sales of a product in different months of a particular year are given below: The forecast of the sales, usi View Question Consider an objective function$$Z\left( {{x_1},{x_2}} \right) = 3{x_1} + 9{x_2}$$and the constraints$$\eqalign{ &a
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Which one of the following is NOT correct?
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A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stre
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A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction betwee
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Match the casting defects (Group A) with the probable causes (Group B):
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The hot tearing in a metal casting is due to
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A cylindrical blind riser with diameter $$d$$ and height $$h,$$ is placed on the top of the mold cavity of a closed type
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For spot welding of two steel sheets (base metal) each of $$3$$ $$mm$$ thickness, welding current of $$10000$$ $$A$$ is
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A straight turning operation is carried out using a single point cutting tool on an $$AISI$$ $$1020$$ steel rod. The fee
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Cutting tool is much harder than the work piece. Yet the tool wears out during the tool-work interaction, because
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Which pair of following statement is correct for orthogonal cutting using a single-point cutting tool? $$P.$$ reduction
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The diameter of a recessed ring was measured by using two spherical balls of diameter $${d_2} = 60mm$$ and $${d_1} = 40m View Question The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both f View Question Consider a simply supported beam of length$$50$$h, with a rectangular cross-section of depth h, and width$$2$$h. The b View Question Two solid circular shafts of$${{R_1}}$$and$${{R_2}}$$are subjected to same torque. The maximum shear stresses develo View Question A force$$P$$is applied at a distance$$x$$from the end of the beam as shown in the figure. What would be the value of View Question Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase ang View Question The damping ratio of a single degree of freedom spring-mass-damper system with mass of$$1$$kg, stiffness$$100 N/m$$a View Question A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 View Question A certain amount of an ideal gas is initially at a pressure$${p_1}$$and temperature$${T_1}$$. First, it undergoes a c View Question Which one of the following pairs of equations describes an irreversible heat engine? View Question An amount of$$100kW$$of heat is transferred through a wall in steady state. One side of the wall is maintained at View Question A source at temperature of$$500K$$provides$$1000kJ$$of heat. The temperature of environment is$${27^ \circ }C.
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At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of absolute velocity is
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