GATE CE 2000

## GATE CE

Consider the following two statements.
$$(I)$$ The maximum number of linearly independent column vectors of a matrix $$

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If $$A,B,C$$ are square matrices of the same order then $${\left( {ABC} \right)^{ - 1}}$$ is equal be

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The Taylor series expansion of sin $$x$$ about $$x = {\pi \over 6}$$ is given by

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Limit of the function
$$f\left( x \right) = {{1 - {a^4}} \over {{x^4}}}\,\,as\,\,x \to \infty $$ is given by

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If $$f\left( {x,y,z} \right) = $$
$${\left( {{x^2} + {y^2} + {z^2}} \right)^{{\raise0.5ex\hbox{$\scriptstyle { - 1}$}
\

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Consider the following integral $$\mathop {Lim}\limits_{x \to 0} \int\limits_1^a {{x^{ - 4}}} dx$$ ________.

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Let $$F\left( s \right) = L\left[ {f\left( t \right)} \right]$$ denote the Laplace transform of the function $$f(t)$$. W

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Two Samples of Water A and B have pH values of a 4.4 and 6.4 respectively. How many times more acidic sample A is than s

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Cavitation is caused by

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A soil sample has a void ratio of 0.5 and its porosity will be closed to

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A borrow pit soil has a dry density of 17 kN/m3. How many cubic meters of this soils will be required to construct an em

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If duty (D) is 1428 hectares/cumec and base period (B) is 120 days for an irrigated crop, then delta ($$\Delta$$) in met

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A tube well having a capacity of 4 $$m^3 /hour$$ operates for 20 hours each day during the irrigation season. How much a

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The working stress method of design specifies the value of modular ratio, $$m = 280/\left( {3{\sigma _{cbc}}} \right),$$

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The following two statements are made with reference to a simply supported under - reinforced $$RCC$$ beam:
$${\rm I}.\

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Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safet

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Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safet

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A continuous beam $$250\,mm \times 450\,mm$$ carries $$6$$ numbers of $$12$$ $$mm$$ diameter longitudinal bars as shown.

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A simply supported rectangular prestressed concrete beam $$200$$ $$mm$$ wide and $$400$$ $$mm$$ deep has an effective s

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A $$12$$ $$mm$$ bracket plate is connected to a column flange as shown in the figure below. The bracket transmits a load

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The stress-strain diagram for two materials A and B is shown below:
The following statements are made based on this dia

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Pick the incorrect statement from the following four statements:

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A frame $$ABCD$$ is supported by a roller at $$A$$ and is on a hinge at $$C$$ as shown below:
The reaction at the roll

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A two span beam with an internal hinge is shown below.
Conjugate beam corresponding to this beam is

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For the structure shown below, the vertical deflection at point $$A$$ is given by

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Four column of the same material having identical geometric properties are supported in different ways as shown below

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The following two statements are made with reference to the planar truss shown below :
$${\rm I}.$$ The truss is stat

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Identify the FALSE statement from the following, pertaining to the methods of structural analysis.

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A simply supported beam with an overhang is traversed by a unit concentrated moment from left to the right as shown belo

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For the structure shown below, the vertical deflection at point $$A$$ is given by

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A frame $$ABCD$$ is supported by a roller at $$A$$ and is on a hinge at $$C$$ as shown below. The reaction at the roller

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Identify the correct deflection diagram corresponding to the loading in the plane frame shown below :

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A cantilever beam of length $$L$$ and a cross section with shape factor $$'f'$$ supports a concentrated load $$P$$ as sh

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The four cross sections shown below are required to be ordered in the increasing order of their respective shape factors

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Width of carriage way for a single lane is recommended to be

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The ruling minimum radius of horizontal curve of a national highway in plain terrain for a ruling design speed of 100 km

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Design rate of super elevation for horizontal highway curve of radius 450 m for a mixed traffic condition, having a spee

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