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

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

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

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 $$(a, b)$$ if

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 as $$\matrix{ {{u_a}\left( t \right

$${\left( {s + 1} \right)^{ - 2}}$$ 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. The probability that this flood magnitud

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

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

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

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

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

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

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

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

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

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