GATE CE 2011

## GATE CE

What is the value of the definite integral? $$\,\,\int\limits_0^a {{{\sqrt x } \over {\sqrt x + \sqrt {a - x} }}dx\,\,}

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What should be the value of $$\lambda $$ such that the function defined below is continuous at $$x = {\pi \over 2}$$?
$

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If $$\overrightarrow a $$ and $$\overrightarrow b $$ are two arbitrary vectors with magnitudes $$a$$ and $$b$$ respectiv

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There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls a

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The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$

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The square root of a number $$N$$ is to be obtained by applying the Newton $$-$$ Raphson iteration to the equation $$\,{

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Given two continuous time signals $$x\left( t \right) = {e^{ - t}}$$ and $$y\left( t \right) = {e^{ - 2t}}$$ which exist

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If $$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ th

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For an analytic function $$f\left( {x + i\,y} \right) = u\left( {x,y} \right) + i\,v\left( {x,y} \right),\,u$$ is given

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For a body completely submerged in a fluid, the centre of gravity (G) and centre of Buoyancy
(O) are known. The body is

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The cross-section of a thermo-mechanically treated (TMT) reinforcing bar has

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Consider a reinforcing bar embedded in concrete. In a marine environment this bar undergoes
uniform corrosion, which lea

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Consider two $$RCC$$ beams, $$P$$ and $$Q$$, each having the section $$400$$ $$mm$$ $$ \times \,\,750\,\,mm$$ (effective

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Consider a bar of diameter $$'D'$$ embedded in a large concrete block as shown in the adjoining figure, with a pull out

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For the fillet weld of size $$'S'$$ shown in the adjoining figure the effective throat thickness is

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The adjoining figure shows a schematic representation of a steel plate girder to be used as a simply supported beam wit

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For the cantilever bracket, $$PQRS,$$ loaded as shown in the adjoining figure $$(PQ=RS=L,$$ and $$QR=2L),$$ which of th

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Consider a simply supported beam with a uniformly distributed load having a neutral axis $$(NA)$$ as shown. For points $

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A disc of radius $$'r'$$ has a hole of radius $$'r/2'$$ cut-out as shown. The centroid of the remaining disc (shaded por

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The value of $$W$$ that results in the collapses of the beam shown in the adjoining figure and having a plastic moment c

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