GATE 1998 Civil Engineering

A discontinuous real function can be expressed as

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

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 lane with two way traffic. User other specifications as per I...

The return period for the annual maximum flood of a given magnitude is 8 years. The probability that this flood magnitude will be executed once during the next 5 years is

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

Water distribution systems are sized to meet the

The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as $$\matrix{ {{u_a}\left( t \right) = 0} & {for\,\,\,t < a\,} \cr { = 1} & {for\,\,\,t > a,} \cr }...

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

The plastic modulus of a section is $$4.8 \times {10^{ - 4}}\,\,{m^3}.$$ The shape factor is $$1.2$$. The plastic moment capacity of the section is $$120$$ $$kN$$-$$m.$$ The yield...

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

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

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

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

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

The microbial quality of treated piped water supplies is monitored by

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