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GATE CE 1998

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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GATE CE

In matrix algebra $$AS=AT$$ ($$A,S,T,$$ are matrices of appropriate order) impli...
If $$A$$ is a real square matrix then $$A{A^T}$$ is
The real symmetric matrix $$C$$ corresponding to the quadratic form $$Q = 4{x_1}...
Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -...
A discontinuous real function can be expressed as
The Taylor's series expansion of sin $$x$$ is ______.
The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ i...
Solve $${{{d^4}y} \over {d{x^4}}} - y = 15\,\cos \,\,2x$$
The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined...
$${\left( {s + 1} \right)^{ - 2}}$$ is laplace transform of
Water distribution systems are sized to meet the
The microbial quality of treated piped water supplies is monitored by
The return period for the annual maximum flood of a given magnitude is 8 years. ...
An isolated $$T$$ beam is used as a walkway. The beam is simply supported with a...
The cross-section of a pretensioned pre-stressed concrete beam is shown in Figur...
The cross-section of a simply supported plate girder is shown in figure. The loa...
A cantilever beam is shown in the figure. The moment to be applied at free end f...
A three hinged arch shown in Figure is quarter of a circle. If the vertical and ...
The strain energy stored in member $$'AB'$$ of the pin jointed truss shown aside...
The plastic modulus of a section is $$4.8 \times {10^{ - 4}}\,\,{m^3}.$$ The sha...
The steel portal frame shown in figure is subjected to an imposed service load o...
The stiffness matrix of a beam element is given as $${{2EI} \over L}\left[ {\mat...
For a highway with a design speed of 100kmph, the safe OSD is assume acceleratio...

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