GATE CE 1999

## GATE CE

If $$A$$ is any $$nxn$$ matrix and $$k$$ is a scalar then $$\left| {kA} \right| = \alpha \left| A \right|$$ where $$\alp

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The equation $$\left[ {\matrix{
2 & 1 & 1 \cr
1 & 1 & { - 1} \cr
y & {{x^2}} & x \

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The number of terms in the expansion of general determinant of order $$n$$ is

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The function $$f\left( x \right) = {e^x}$$ is _________.

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Number of inflection points for the curve $$\,\,\,y = x + 2{x^4}\,\,\,\,$$ is_______.

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Limit of the function, $$\mathop {Lim}\limits_{n \to \infty } {n \over {\sqrt {{n^2} + n} }}$$ is _______.

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For the function $$\phi = a{x^2}y - {y^3}$$ to represent the velocity potential of an ideal fluid, $${\nabla ^2}\,\,\p

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If $$c$$ is a constant, then the solution of $${{dy} \over {dx}} = 1 + {y^2}$$ is

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The Laplace transform of the function
$$\eqalign{
& f\left( t \right) = k,\,0 < t < c \cr
& \,\,\,\

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Temporary hardness in water is caused by the presence of

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Principle involved in the relationship between submerged unit weight and saturated weight of a soil is based on

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The minimum area of tension reinforcement in a beam shall be greater than

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Maximum strain at the level of compression steel for a rectangular section having effective cover to compression steel

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The width and effective depth of a reinforced concrete beam is $$250$$ $$mm$$ and $$440$$ $$mm$$ respectively. The beam

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In reinforced concrete, pedestal is defined as compression member, whose effective length does not exceed its dimension

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A beam with a rectangular cross section of size $$250$$ $$mm$$ wide and $$350$$ $$mm$$ deep is prestressed by a force of

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In section, shear centre is a point through which, if the resultant load passes, the section will not be subjected to an

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Two steel plates each of width $$150$$ $$mm$$ and thickness $$10$$ $$mm$$ are connected with three $$20$$ $$mm$$ diamete

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The problem of lateral buckling can arise only in those steel beams which have

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A steel beam supporting loads from the floors slab as well as from wall is termed as

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Two wheels, placed at a distance of $$2.5$$ $$m$$ apart, with a load of $$200\,\,kN$$ on each of them are moving on a si

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In a section, shear center is a point through which, if the resultant load passes, the section will not be subjected to

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For a fixed beam with span $$L,$$ having plastic moment capacity of $${{M_p}}$$, the ultimate central concentrated load

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The shape factor of the section shown in fig. is

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The total length (in km) of the existing National Highways in India is in the range of

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The reaction time for calculating stopping sight distance may be assumed as

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