GATE 2005 Civil Engineering
29 questions across 1 session
Consider likely applicability of Cauchy's Integral theorem to evaluate the following integral counterclockwise around the unit circle C. $$I\, = \,\oint\limits_C {\sec z\,dz} $$, z...
A rectangular column section of $$250\,\,mm \times 400\,mm$$ is reinforced with five steel bars of grade $$Fe$$ $$500,$$ each of $$20$$ $$mm$$ diameters. Concrete mix is $$M30.$$ A...
The partial factor of safety for concrete as per IS: 456-2000 is
The flexural strength of M30 concrete as per IS: 456-2000 is
Pradhan Mantri Gram Sadak Yojana (PMGSY), launched in the year 2000 aims to provide rural connectivity with all weather roads. It is proposed to connect the habitations and plain a...
As per Indian standard code of practice for prestressed concrete $$(IS:1343-1980)$$ the minimum grades of concrete to be used for post-tensioned and pre-tensioned structural elemen...
A concrete beam of rectangular cross section of $$200\,\,mm \times 400\,\,mm$$ is pre-stressed with a force $$400$$ $$kN$$ at eccentricity $$100$$ $$mm.$$ the maximum compressive s...
Which of the following is NOT correct for steel sections as per $$IS:$$ $$800-1984$$?
The line integral $$\int {\,\,V.dr\,\,} $$ of the vector function $$V\left( r \right) = 2xyz\widehat i + {x^2}z\widehat j + {x^2}y\widehat k\,\,$$ from the origin to the point $$P(...
Laplace transform of $$f\left( t \right) = \cos \left( {pt + q} \right)$$ is
Given $$a>0,$$ we wish to calculate its reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ For $$a=7$$ and starting with $${x_0} = 0.2\,\,$$ the firs...
A cantilever beam of length $$l,$$ width $$b$$ and depth $$d$$ is loaded with a concentrated vertical load at the tip. If yielding starts at a load $$P,$$ the collapse load shall b...
Consider the following system of equations in three real variable $${x_1},$$ $${x_2}$$ and $${x_3}:$$ $$$2{x_1} - {x_2} + 3{x_3} = 1$$$ $$$3{x_1} + 2{x_2} + 5{x_3} = 2$$$ $$$ - {x_...
Given $$a>0,$$ we wish to calculate it reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ The Newton - Raphson algorithm for the function will be
Consider a non-homogeneous system of linear equations represents mathematically an over determined system. Such a system will be
Consider the system of equations, $${A_{nxn}}\,\,{X_{nx1}}\,\, = \lambda \,{X_{nx1}}$$ where $$\lambda $$ is a scalar. Let $$\left( {{\lambda _i},\,\,{X_i}} \right)$$ be an eigen v...
The Laplace transform of a function $$f(t)$$ is $$$F\left( s \right) = {{5{s^2} + 23s + 6} \over {s\left( {{s^2} + 2s + 2} \right)}}$$$ As $$t \to \propto ,\,\,f\left( t \right)$$...
The solution $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 17y = 0;$$ $$y\left( 0 \right) = 1,{\left( {{{d\,y} \over {d\,x}}} \right)_{x = {\raise0.5ex\hbox{$\scriptstyle \pi...
Value of the integral $$\,\,\oint {xydy - {y^2}dx,\,\,} $$ where, $$c$$ is the square cut from the first quadrant by the line $$x=1$$ and $$y=1$$ will be (Use Green's theorem to ch...
Transformation to linear form by substituting $$v = {y^{1 - n}}$$ of the equation $${{dy} \over {dt}} + p\left( t \right)y = q\left( t \right){y^n},\,\,n > 0$$ will be
Consider the matrices $$\,{X_{4x3,}}\,\,{Y_{4x3}}$$ $$\,\,{P_{2x3}}.$$ The order of $$\,{\left[ {P{{\left( {{X^T}Y} \right)}^{ - 1}}{P^T}} \right]^T}$$ will be
1 TCU is equivalent to color produced by
If tomato juice is having a pH of 4.1, the hydrogen ion concentration will be
$$IS:$$ $$1343 – 1980$$ limits the minimum characteristic strength of pre-stressed concrete for post tensioned works and pretension work as
The permissible stress in axial tension in steel member on the net effective area of the section shall not exceed the following value ($${{f_y}}$$ is the yield stress)
Which one of the following is not true for the complex number z 1 and z 2 ?
If a beam of rectangular cross-section is subjected to a vertical shear force $$V,$$ the shear force carried by the upper one-third of the cross-section is
The symmetry of stress tensor at a point in the body under equilibrium is obtained from
The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions.