GATE CE 2009

## GATE CE

In the solution of the following set of linear equations by Gauss-elimination using partial pivoting
$$$5x+y+2z=34,$$$

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A square matrix $$B$$ is symmetric if ____

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For a scalar function $$f(x,y,z)=$$ $${x^2} + 3{y^2} + 2{z^2},\,\,$$ the gradient at the point $$P(1,2,-1)$$ is

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For a scalar function $$\,f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 2{z^2},\,\,$$ the directional derivative at the poi

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The standard normal probability function can be approximated as
$$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left(

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Solution of the differential equation $$3y{{dy} \over {dx}} + 2x = 0$$ represents a family of

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The area under the curve shown between $$x=1$$ and $$x=5$$ is to be evaluated using the trapezoidal rule. The following

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The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3}

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The analytical function has singularities at, where $$f(z) = {{z - 1} \over {{z^2} + 1}}$$

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Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is

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In quadrantal bearing system, bearing of a line varies from

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An agricultural land of 437ha is to be irrigated for a particular crop. The base
period of the crop is 90 days and the t

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For limit state of collapse, the partial safety factors recommended by
IS 456:2000 for estimating the design strength of

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A rectangular concrete beam of width $$120$$ $$mm$$ and depth $$200$$ $$mm$$ is prestressed by pretensioning to a force

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A 12 mm thick plate is connected to two 8 mm plates, on either side through a
16 mm diameter power driven field rivet as

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Consider the following statements for a compression member
$${\rm I}.\,\,\,\,$$ The elastic critical stress in compress

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The square root of the ratio of moment of inertia of the cross-section to its cross-sectional area is called

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Consider the following statements:
$$1.$$ On a principal plane, only normal stress acts
$$2.$$ On a principal plane, bot

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Match List- $${\rm I}$$ (Shear Force Diagrams) beams with List- $${\rm II}$$ (Diagram of beams with supports and loading

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The point within the cross sectional plane of a beam through which the resultant of the external loading on the beam has

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A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and a wall thickness of $$25$$ $$mm.$$ The allowable she

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A vertical rod $$PQ$$ of length $$L$$ is fixed at its top end $$P$$ and has a flange fixed to the bottom end $$Q.A$$ wei

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The degree of static indeterminacy of a rigidly jointed frame in a horizontal plane
and subjected to vertical loads only

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In the theory of plastic bending of beams, the ratio of plastic moment to yield moment is called

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The value of lateral friction or side friction used in the design of horizontal curve
as per India Roads Congress guidel

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