GATE CE 2001
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GATE CE

The eigen values of the matrix $$\left[ {\matrix{ 5 & 3 \cr 2 & 9 \cr } } \right]$$ are
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The product $$\left[ P \right]\,\,{\left[ Q \right]^T}$$ of the following two matrices $$\left[ P \right]\,$$ and $$\lef
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The determinant of the following matrix $$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 &a
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Limit of the following series as $$x$$ approaches $${\pi \over 2}$$ is $$f\left( x \right) = x - {{{x^3}} \over {3!}}
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The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \righ
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The number of boundary conditions required to solve the differential equation $$\,\,{{{\partial ^2}\phi } \over {\parti
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The inverse Laplace transform of $$1/\left( {{s^2} + 2s} \right)$$ is
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A 15 cm length of steel rod with relative density of 7.4 is submerged in a two layer fluid. The bottom layer is mercury
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Identify the FALSE statement from the following, pertaining to the design of concrete structures.
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Consider the following two statements related to reinforced concrete design, and identify whether they are TRUE/FALSE:
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The effective spans for a simple one-way slab system, with an overhang are indicated in the figure below. The specified
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Identify the most efficient butt joint (with double cover plates) for a plate in tension from the patterns (plan views)
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Consider the following two statements related to structural steel design, and identify whether they are True or FALSE. $
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The relevant cross-sectional details of a compound beam comprising a symmetric $${\rm I}$$-section and a channel section
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The bending moment (in $$kN$$-$$m$$ units) at the mid-span location $$X$$ in the beam with overhangs shown below is equ
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The degree of static indeterminacy, $${N_s}$$ and the degree of kinematic indeterminacy, $${N_k}$$ for the plane frame s
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Identify, from the following, the correct value of the bending moment $${M_A}\,\,$$ (in $$kNm$$ units) at the fixed end
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Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise $$\Delta T$$ of the
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The frame below shows three beam elements $$OA, OB$$ and $$OC$$, with identical length $$L$$ and flexural rigidity $$EI$
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The two-span continuous beam shown below is subject to a clockwise rotational slip $${\theta _A} = 0.004$$ radian at the
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The design value of lateral friction coefficient on highway is
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