GATE CE 1998

## GATE CE

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

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

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

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

View Question A discontinuous real function can be expressed as

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

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

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

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

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

View Question Water distribution systems are sized to meet the

View Question The microbial quality of treated piped water supplies is monitored by

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

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

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

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

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

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

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

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

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

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

View Question 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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