GATE ME 2014 Set 3

## 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}$

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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)

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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

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A body of mass (m) 10kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic f

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A four-wheel vehicle of mass 1000kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheel

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An annular disc has a mass m, inner radius R and outer radius $$2R$$. The disc rolls on a flat surface without slipping.

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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

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A fluid of dynamic viscosity $$2 \times {10^{ - 5}}\,\,kg/m.s$$ and density $$1kg/{m^3}$$ flows with an average velocity

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Consider the turbulent flow of a fluid through a circular pipe of diameter, $$D.$$ Identify the correct pair of statemen

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Consider a long cylindrical tube of inner and outer radii, $${r_i}$$ and $${r_0}$$ , respectively, length, $$L$$ and
the

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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

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A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at $$19$$ liter/s is

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A manufacturer can produce $$12000$$ bearings per day. The manufacturer received an order of $$8000$$ bearings per day

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Consider the given project network, where numbers along various activities represent the normal time. The free float on

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The actual sales of a product in different months of a particular year are given below:
The forecast of the sales, usi

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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

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The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both f

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Consider a simply supported beam of length $$50$$h, with a rectangular cross-section of depth h, and width $$2$$h. The b

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Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses develo

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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

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Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase ang

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The damping ratio of a single degree of freedom spring-mass-damper system with mass of $$1$$ kg, stiffness $$100 N/m$$ a

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A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10

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A certain amount of an ideal gas is initially at a pressure $${p_1}$$ and temperature $${T_1}$$. First, it undergoes a c

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Which one of the following pairs of equations describes an irreversible heat engine?

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An amount of $$100$$ $$kW$$ of heat is transferred through a wall in steady state. One side of the wall is maintained at

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A source at temperature of $$500K$$ provides $$1000$$ $$kJ$$ 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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