GATE CE 2002

## GATE CE

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

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

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

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

View Question The value of the following definite integral in $$\int\limits_{{\raise0.5ex\hbox{$\scriptstyle { - \pi }$}
\kern-0.1em/\

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

View Question The Laplace transform of the following function is
$$$f\left( t \right) = \left\{ {\matrix{
{\sin t} & {for\,\,0

View Question Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$
given th

View Question In natural water, hardness is mainly caused by

View Question During a 6-hour storm the rainfall intensity was 0.8 cm/hr on a catchment of area 8.6 km2. The measured runoff volume du

View Question Modulus of elasticity of M25 grade concrete in MPa is

View Question Read the following two statements
$${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Maximum strain in concrete at the outermost compr

View Question As per provision of $$IS$$ $$456$$-$$2000$$, in the limit state method for design of beams, the limiting value of the de

View Question A $$10m$$ long prestressing bed is used to cast $$4$$ (pretensioned) prestressed concrete beams of $$2.3$$ $$m$$ each. A

View Question $$ISA$$ $$100 \times 100 \times 10\,\,mm$$ (Cross sectional area $$ = 1903\,\,m{m^2})$$ serves as tensile member. This a

View Question $$ISA$$ $$100 \times 100 \times 10mm$$ (cross sectional area $$ = 1903\,\,m{m^2}$$) is welded along $$A$$ and $$B$$ (Ref

View Question Given reason for the following is not more than $$20$$ words
(a) A maximum permissible distance between lacing and batte

View Question When designing steel structures, one must ensure that local buckling in webs does not take place. This check may not be

View Question An $$ISMB$$ $$500$$ is used as a beam in a multi-storey construction. From the view point of structural design, it can b

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

View Question For the loading given in the figure below, two statements ( $${\rm I}$$ and $${\rm II}$$ ) are made.
$${\rm I}.$$ $$\,

View Question In the propped cantilever beam carrying a uniformly distributed load of $$w$$-$$kN/m,$$ shown in the following figure, t

View Question A propped cantilever beam of span $$'L'$$ is loaded with $$u.d.l$$ of intensity $$w$$/unit length, all through the span.

View Question A steel beam (with a constant $$EI,$$ and span $$L$$) is fixed at both ends and carries a uniformly distributed load ($$

View Question Calculate the shape factor for the $$T$$-section shown in the following figure made up of two plates $$100\,\,mm \times

View Question SSD and Friction coefficients are

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