GATE CE 2010

## GATE CE

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

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

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

View Question 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

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

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

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

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

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

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

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

View Question Ion concentrations obtained for a groundwater sample (having pH=8.1) are given
below.
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View Question The moisture holding capacity of the soil in a 100 hectare farm is 18cm/m. the field is to
be irrigated when 50 percent

View Question 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

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

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

View Question 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

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

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

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

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

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

View Question 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

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

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

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

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

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

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