GATE 2002 Civil Engineering

The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.$$

Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right]$$

Given reason for the following is not more than $$20$$ words (a) A maximum permissible distance between lacing and battens in steel columns is $$\,\,\,\,\,\,\,$$ usually specified....

As per provision of $$IS$$ $$456$$-$$2000$$, in the limit state method for design of beams, the limiting value of the depth of neutral axis in a reinforced concrete beam of effecti...

Modulus of elasticity of M25 grade concrete in MPa is

SSD and Friction coefficients are

A propped cantilever beam of span $$'L'$$ is loaded with $$u.d.l$$ of intensity $$w$$/unit length, all through the span. Bending Moment at the fixed end is

An $$ISMB$$ $$500$$ is used as a beam in a multi-storey construction. From the view point of structural design, it can be considered to be 'laterally restrained' when,

When designing steel structures, one must ensure that local buckling in webs does not take place. This check may not be very critical when using rolled steel sections because

Read the following two statements $${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Maximum strain in concrete at the outermost compression fibre is taken to be $$0.0035$$ in bending $${\rm II}...

The Laplace transform of the following function is $$$f\left( t \right) = \left\{ {\matrix{ {\sin t} & {for\,\,0 \le t \le \pi } \cr 0 & {for\,\,t > \pi } \cr } } \right.$$$

The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio ($$\mu$$) of a material are related as

The following function has local minima at which value of $$x,$$ $$f\left( x \right) = x\sqrt {5 - {x^2}} $$

The value of the following definite integral in $$\int\limits_{{\raise0.5ex\hbox{$\scriptstyle { - \pi }$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}^{{\raise0....

The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y} \right) = {x^2} + {y^2}$$

In natural water, hardness is mainly caused by

Limit of the following sequence as $$n \to \infty $$ $$\,\,\,$$ is $$\,\,\,$$ $${x_n} = {n^{{1 \over n}}}$$

Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$ given that $$y=0$$ and $$dy/dt=9$$ at $$t=0$$

During a 6-hour storm the rainfall intensity was 0.8 cm/hr on a catchment of area 8.6 km 2 . The measured runoff volume during this period was 2,56,000 m 3 . The total rainfall was...