GATE CE 2012
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## GATE CE

The eigen values of matrix $$\left[ {\matrix{ 9 &amp; 5 \cr 5 &amp; 8 \cr } } \right]$$ are
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The infinite series $$1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + {{{x^4}} \over {4!}} + ........$$ correspond
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For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\o View Question Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one neg View Question The annual precipitation data of a city is normally distributed with mean and standard deviation as$$1000$$mm and$$200
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The solution of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at
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The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point functio
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A water sample has a pH of 9.25. The concentration of hydroxyl ions in the water sample is
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If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cu
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The ratio of actual evapo-transpiration to potential evapo-transpiration is in the range
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Wheat crop requires 55 cm of water during 120 days of base period. The total rainfall during this period is 100 mm. Assu
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As per $$IS$$ $$456:2000,$$ in the Limit State Design of a flexural member, the strain in reinforcing bars under tension
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The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. $$A$$ portion of the slab is consi
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The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. $$A$$ portion of the slab is consi
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Which one of the following is categorized as a long-term loss of prestress in a prestressed concrete member?
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A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured f
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In a steel plate with bolted connections, the rupture of the net section is a mode of failure under
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Two plates are connected by fillet welds of size $$10$$ $$mm$$ and subjected to tension, as shown in the sketch. The thi
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If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cu
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The following statements are related to bending of beams: $${\rm I}.$$ The slope of the bending moment diagram is equal
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The Poisson's ratio is defined as
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A simply supported beam is subjected to a uniformly distributed load of intensity $$w$$ per unit length. On half of the
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The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same
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The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force $$P$$ and a m
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A symmetric frame $$PQR$$ consists of two inclined members $$PQ$$ and $$QR$$, connected at $$‘Q’$$ with a rigid joint, a
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