GATE 2009 Civil Engineering

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

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

A rectangular concrete beam of width $$120$$ $$mm$$ and depth $$200$$ $$mm$$ is prestressed by pretensioning to a force of $$150$$ $$kN$$ at an eccentricity of $$20$$ $$mm.$$ The c...

Consider the following statements for a compression member $${\rm I}.\,\,\,\,$$ The elastic critical stress in compression increases with decrease in slenderness ratio $${\rm II}.\...

For limit state of collapse, the partial safety factors recommended by IS 456:2000 for estimating the design strength of concrete and reinforcing steel are respectively

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

In the solution of the following set of linear equations by Gauss-elimination using partial pivoting $$$5x+y+2z=34,$$$ $$$4y-3z=12$$$ and $$$10x-2y+z=-4.$$$ The pivots for eliminat...

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

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

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

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

The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}} \right|}^{0.12}}} \right)}}\,...

The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} \right)}}} dz$$ where C is a closed curve given by |z| = 1 i...

For a scalar function $$\,f\left( {x,y,z} \right) = {x^2} + 3{y^2} + 2{z^2},\,\,$$ the directional derivative at the point $$P(1,2,-1)$$ in the direction of a vector $$\widehat i -...

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

In quadrantal bearing system, bearing of a line varies from

The point within the cross sectional plane of a beam through which the resultant of the external loading on the beam has to pass through to ensure pure bending without twisting of...

A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and a wall thickness of $$25$$ $$mm.$$ The allowable shear stress in the shaft is $$125$$ $$MPa.$$ The maximum torqu...

A vertical rod $$PQ$$ of length $$L$$ is fixed at its top end $$P$$ and has a flange fixed to the bottom end $$Q.A$$ weight $$W$$ is dropped vertically from a height $$h\left( { <...

Consider the following statements: $$1.$$ On a principal plane, only normal stress acts $$2.$$ On a principal plane, both normal and shear stresses act $$3.$$ On a principal plane,...

An agricultural land of 437ha is to be irrigated for a particular crop. The base period of the crop is 90 days and the total depth of water required by the crop is 105cm. If a rain...