GATE CE 1998

## GATE CE

In matrix algebra $$AS=AT$$ ($$A,S,T,$$ are matrices of appropriate order) implies $$S=T$$ only if

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If $$A$$ is a real square matrix then $$A{A^T}$$ is

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The real symmetric matrix $$C$$ corresponding to the quadratic form $$Q = 4{x_1}{x_2} - 5{x_2}{x_2}$$ is

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Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{
8 & -4 \cr
2 & { 2 } \cr
} } \ri

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A discontinuous real function can be expressed as

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The Taylor's series expansion of sin $$x$$ is ______.

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The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

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Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$

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The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as
$$\matrix{
{{u_a}\left( t \right

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$${\left( {s + 1} \right)^{ - 2}}$$ is laplace transform of

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Water distribution systems are sized to meet the

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The microbial quality of treated piped water supplies is monitored by

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The return period for the annual maximum flood of a given magnitude is 8 years. The probability that this flood magnitud

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An isolated $$T$$ beam is used as a walkway. The beam is simply supported with an effective span of $$6$$ $$m.$$ The eff

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The cross-section of a pretensioned pre-stressed concrete beam is shown in Figure. The reinforcement is placed concentri

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The cross-section of a simply supported plate girder is shown in figure. The loading on the girder is symmetrical. The b

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A cantilever beam is shown in the figure. The moment to be applied at free end for zero vertical deflection at the point

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A three hinged arch shown in Figure is quarter of a circle. If the vertical and horizontal components of reaction at $$A

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The strain energy stored in member $$'AB'$$ of the pin jointed truss shown aside when $$'E'$$ and $$'A'$$ are same for a

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The plastic modulus of a section is $$4.8 \times {10^{ - 4}}\,\,{m^3}.$$ The shape factor is $$1.2$$. The plastic moment

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The steel portal frame shown in figure is subjected to an imposed service load of $$15$$ $$kN$$. Compute the required pl

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The stiffness matrix of a beam element is given as $${{2EI} \over L}\left[ {\matrix{
2 & { + 1} \cr
{ + 1} &

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For a highway with a design speed of 100kmph, the safe OSD is assume acceleration as 0.53 $$m/sec^2$$. the road is two l

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