GATE CE 2005

## GATE CE

Consider the following system of equations in three real variable $${x_1},$$ $${x_2}$$ and $${x_3}:$$
$$$2{x_1} - {x_2}

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Consider a non-homogeneous system of linear equations represents mathematically an over determined system. Such a system

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Consider the matrices $$\,{X_{4x3,}}\,\,{Y_{4x3}}$$ $$\,\,{P_{2x3}}.$$ The order of $$\,{\left[ {P{{\left( {{X^T}Y} \ri

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Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda $$ is a scalar. L

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Value of the integral $$\,\,\oint {xydy - {y^2}dx,\,\,} $$ where, $$c$$ is the square cut from the first quadrant by the

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The line integral $$\int {\,\,V.dr\,\,} $$ of the vector function $$V\left( r \right) = 2xyz\widehat i + {x^2}z\widehat

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Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \righ

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The solution $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 17y = 0;$$ $$y\left( 0 \right) = 1,{\left( {{{d\,y} \ov

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Which one of the following is not true for the complex number z1 and z2 ?

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Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around t

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Given $$a>0,$$ we wish to calculate it reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0

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Given $$a>0,$$ we wish to calculate its reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=

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The Laplace transform of a function $$f(t)$$ is
$$$F\left( s \right) = {{5{s^2} + 23s + 6} \over {s\left( {{s^2} + 2s +

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Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is

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1 TCU is equivalent to color produced by

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If tomato juice is having a pH of 4.1, the hydrogen ion concentration will be

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The partial factor of safety for concrete as per IS: 456-2000 is

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The flexural strength of M30 concrete as per IS: 456-2000 is

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A rectangular column section of $$250\,\,mm \times 400\,mm$$ is reinforced with five steel bars of grade $$Fe$$ $$500,$$

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$$IS:$$ $$1343 – 1980$$ limits the minimum characteristic strength of pre-stressed concrete for post tensioned works and

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As per Indian standard code of practice for prestressed concrete $$(IS:1343-1980)$$ the minimum grades of concrete to be

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A concrete beam of rectangular cross section of $$200\,\,mm \times 400\,\,mm$$ is pre-stressed with a force $$400$$ $$kN

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A fillet-welded joint of $$6$$ $$mm$$ size is shown in the figure. The welded surfaces meet at $$60$$ - $$90$$ degree an

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The permissible stress in axial tension in steel member on the net effective area of the section shall not exceed the f

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Which of the following is NOT correct for steel sections as per $$IS:$$ $$800-1984$$?

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An unstiffened web $${\rm I}$$ section is fabricated from a $$10$$ $$mm$$ thick plate by fillet welding as shown in the

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The symmetry of stress tensor at a point in the body under equilibrium is obtained from

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The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in

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The bending Moment diagram for a beam is given below:
The shear force at sections $$aa'$$ and $$bb'$$ respectively ar

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If a beam of rectangular cross-section is subjected to a vertical shear force $$V,$$ the shear force carried by the upp

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A circular shaft shown in the figure is subject to torsion $$T$$ at two points $$A$$ and $$B.$$ The torsional rigidity o

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The maximum tensile stress at the section $$X$$ - $$X$$ shown in the figure below is

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Considering beam as axially rigid, the degree of freedom of a plane frame shown below is

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Match List - $${\rm I}$$ with List - $${\rm II}$$ and select the correct answer using the codes given below the lists :

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A truss is shown in the figure. Members are to equal cross section $$A$$ and same modulus of elasticity $$E.$$ $$A$$ ver

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A truss is shown in the figure. Members are to equal cross section $$A$$ and same modulus of elasticity $$E.$$ $$A$$ ver

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All members of the frame shown below have the same flexural rigidity $$EI$$ and length $$L.$$ If a moment $$M$$ is appli

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A cantilever beam of length $$l,$$ width $$b$$ and depth $$d$$ is loaded with a concentrated vertical load at the tip. I

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Pradhan Mantri Gram Sadak Yojana (PMGSY), launched in the year 2000 aims to provide rural connectivity with all weather

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