GATE CE 2010

## GATE CE

The inverse of the matrix $$\left[ {\matrix{
{3 + 2i} & i \cr
{ - i} & {3 - 2i} \cr
} } \right]$$ is

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A parabolic cable is held between two supports at the same level. The horizontal span between the supports is $$L.$$ The

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The $$\mathop {Lim}\limits_{x \to 0} {{\sin \left( {{2 \over 3}x} \right)} \over x}\,\,\,$$ is

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Given a function $$f\left( {x,y} \right) = 4{x^2} + 6{y^2} - 8x - 4y + 8,$$ the optimal values of $$f(x,y)$$ is

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Two coins are simultaneously tossed. The probability of two heads simultaneously appearing

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The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \righ

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The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is

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The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \

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The table below gives values of a function $$f(x)$$ obtained for values of $$x$$ at intervals of $$0.25$$
The value o

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The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is

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Ion concentrations obtained for a groundwater sample (having pH=8.1) are given
below.
.tg {border-collapse:collapse;bo

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Ion concentrations obtained for a groundwater sample (having pH=8.1) are given
below.
.tg {border-collapse:collapse;bo

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The moisture holding capacity of the soil in a 100 hectare farm is 18cm/m. the field is to
be irrigated when 50 percent

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The moisture holding capacity of the soil in a 100 hectare farm is 18 cm/m. the field is to
be irrigated when 50 percent

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A doubly reinforced rectangular concrete beam has a width of $$300$$ $$mm$$ and an effective depth of $$500$$ $$mm.$$ th

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A doubly reinforced rectangular concrete beam has a width of $$300$$ $$mm$$ and an effective depth of $$500$$ $$mm.$$ th

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A double cover butt riveted joint is used to connect two flat plates of 200 mm
width and 14 mm thickness as show in the

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Two plates, subjected to direct tension, each of $$10$$ $$mm$$ thickness and having widths of $$100$$ $$mm$$ and $$175$$

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The number of independent elastic constants for a linear elastic isotropic and
homogeneous material is

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The major and minor principal stresses at a point are $$3MPa$$ and $$-3MPa$$ respectively. The maximum shear stress at t

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Two people weighing W each are sitting on a plank of length $$L$$ floating on water at $$L/4$$ from either end. Neglecti

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For the simply supported beam of length $$L,$$ subjected to a uniformly distributed moment $$(M)$$ $$kN$$-$$m$$ per unit

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A solid circular shaft of diameter d and length $$L$$ is fixed at one end and free at the other end. A torque t is appli

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In the cantilever beam $$PQR$$ shown in figure below, the segment $$PQ$$ has flexural $$EI$$ and the segment $$QR$$ has

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In the cantilever beam $$PQR$$ shown in figure below, the segment $$PQ$$ has flexural $$EI$$ and the segment $$QR$$ has

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The effective length of a column of length $$L$$ fixed against rotation and translation at one end is

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A three hinged parabolic arch having a span of $$20$$ $$m$$ and a rise of $$5$$ $$m$$ carries a point load of $$10$$ $$k

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For the truss shown in the figure, the force in the member QR is

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