GATE CE 2004

## GATE CE

Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\

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The eigen values of the matrix $$\left[ {\matrix{
4 & { - 2} \cr
{ - 2} & 1 \cr
} } \right]$$ are

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The function $$f\left( x \right) = 2{x^3} - 3{x^2} - 36x + 2\,\,\,$$ has its maxima at

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The value of the function, $$f\left( x \right) = \mathop {Lim}\limits_{x \to 0} {{{x^3} + {x^2}} \over {2{x^3} - 7{x^2}}

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A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Gi

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Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equ

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A delayed unit step function is defined as
$$$u\left( {t - a} \right) = \left\{ {\matrix{
{0,} & {t < a} \cr

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The present population of a community is 28000 with an average water consumption of 4200 $$m^3/d$$. The existing water t

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Most of the turbidity meters work on the scattering principle. The turbidity value obtained is expressed in

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The ratio of saturated unit weight to dry unit weight of a soil is 1.25. If the specific gravity of solids (Gs) is 2.65,

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A sprinkler irrigation system is suitable when

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In the limit state design method of concrete structures, the recommended partial material safety factor $$\left( {{\gamm

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At the limit state of collapse, an $$RC$$ beam is subjected to flexural moment $$200$$ $$kN$$-$$m$$, shear force $$20$$

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At the limit state of collapse, an $$RC$$ beam is subjected to flexural moment $$200$$ $$kN$$-$$m$$, shear force $$20$$

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An $$RC$$ short column with $$300\,\,mm \times 300\,mm$$ square cross-section is made of $$M20$$ grade concrete and has

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An $$RC$$ square footing of side length $$2$$ $$m$$ and uniform effective depth $$200$$ $$mm$$ is provided for a $$300$$

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A simply supported prestressed concrete beam is $$6$$ $$m$$ long and $$300$$ $$mm$$ wide. Its gross depth is $$600$$ $$

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Rivet value is defined as

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Two equal angles $$ISA$$ $$100\,\,mm \times 100\,\,mm$$ of thickness $$10$$ $$mm$$ are placed back-to-back and connected

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A moment $$M$$ of magnitude $$50$$ $$kN$$-$$m$$ is transmitted to a column flange through a bracket by using four $$20$$

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A strut in a steel truss is composed of two equal angles $$ISA$$ $$150mm \times 150mm$$ of thickness $$100$$ $$mm$$ conn

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In a plate girder, the web plate is connected to the flange plates by fillet welding. The size of the fillet welds is de

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If principle stresses in two-dimensional case are $$\left( - \right)\,\,10\,MPa$$ and $$20$$ $$MPa$$ respectively, t

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In a two dimensional analysis, the state of stress at a point is shown below.
If $$\sigma = 120\,\,MPa$$ and $${\tau

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A three-span continuous beam has an internal hinge at $$B.$$ Section $$B$$ is at the mid-span of $$A.C.$$ Section $$E$$

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A three-span continuous beam has an internal hinge at $$B.$$ Section $$B$$ is at the mid-span of $$A.C.$$ Section $$E$$

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A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated

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A circular solid shaft of span $$L=5m$$ is fixed at one end and free at the other end. A twisting moment $$T=100$$ $$kN$

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$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P

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For the linear elastic beam shown in the figure, the flexural rigidity, $$EI$$ is $$781250\,\,kN$$ - $${m^2}.$$ When $$w

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For the plane frame with an overhang as shown below, assuming negligible axial deformation, the degree of static indeter

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A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated

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A three hinged parabolic arch $$ABC$$ has a span of $$20$$ $$m$$ and a central rise of $$4$$ $$m.$$ The arch has hinges

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The unit load method used in Structural analysis is

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For a linear elastic structural system, minimization of potential energy yields

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The plane frame below is analyzed by neglecting axial deformations. Following statements are made with respect to the an

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For the plane truss shown in the figure, the number of zero force members for the given loading is

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For linear elastic frame, if stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection o

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The star and grid pattern of road networks are adopted in

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