GATE 2007 Civil Engineering
36 questions across 1 session
The culturable command area for a distributary channel is 20,000 hectares. Wheat grown in the entire area and the intensity of irrigation is 50%. The kor period for wheat is 30 day...
The minimum and maximum eigen values of matrix $$\left[ {\matrix{ 1 & 1 & 3 \cr 1 & 5 & 1 \cr 3 & 1 & 1 \cr } } \right]$$ are $$-2$$ and $$6$$ respectively. What is the other eigen...
While designing a hill road with a ruling gradient of 6%, if a sharp horizontal curve of 50m radius is encountered, the compensated gradient at the curve as per the Indian Roads Co...
Consider the following statements: 1. The compressive strength of concrete decreases with increase in water-cement ratio of the concrete mix. 2. Water is added to the concrete mix...
A concrete beam of rectangular cross-section of size $$120$$ $$mm$$ (width) and $$200$$ $$mm$$ (depth) is prestressed by a straight tendon to an effective force of $$150$$ $$kN$$ a...
A singly reinforced rectangular concrete beam has a width of $$150$$ $$mm$$ and an effective depth of $$330$$ $$mm.$$ The characteristic compressive strength of concrete is $$20$$...
The water content of a saturated soil and the specific gravity of soil solids were found to be 30% and 2.70, respectively. Assuming the unit weight of water to be 10 $$kN /m^3$$, t...
Consider the following statements: I. Modulus of elasticity concrete increases with increase in compressive strength of concrete. II. Brittleness of concrete increases with decreas...
A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$w$$ per unit length. The beam has constant flexural rigidity. The...
A singly reinforced rectangular concrete beam has a width of $$150$$ $$mm$$ and an effective depth of $$330$$ $$mm.$$ The characteristic compressive strength of concrete is $$20$$...
The alkalinity and the hardness of a water sample are 250 mg/L and 350 mg/L as $$CaCo_3$$, respectively. The water has
The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ The iterative equation for this purpose is ($$k$$ indicates...
Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are
The stiffness coefficient $${k_{ij}}$$ indicates
A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$w$$ per unit length. The beam has constant flexural rigidity. The...
The inverse of $$2 \times 2$$ matrix $$\left[ {\matrix{ 1 & 2 \cr 5 & 7 \cr } } \right]$$ is
A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^ \circ }$$c. What will be the temperature of the body at the...
Potential function $$\phi $$ is given as $$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function $$\psi $$ with the condition $$\psi \, = \,0$$ at x = 0, y = 0?
The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x=0$$ is
If the standard deviation of the speed of vehicles in a highway is $$8.8$$ kmph and the mean speed of the vehicles is $$33$$ kmph, the coefficient of variation in speed is
The degree of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{x^3} = 0\,\,$$ is
The velocity vector is given as $${\mkern 1mu} \vec V = 5xy\widehat i + 2{y^2}\widehat j + 3y{z^2}\widehat k.{\mkern 1mu} {\mkern 1mu} $$ The divergence of this velocity vector at...
The presence of hardness in excess of permissible limit causes
For what values of $$\alpha $$ and $$\beta $$ the following simultaneous equations have an infinite number of solutions $$$x+y+z=5,$$$ $$$x+3y+3z=9,$$$ $$$x + 2y + \alpha z = \beta...
The magnetic bearing of a line AB is S 45° E and the declination is 5° west. The true bearing of the line AB is
The plan of a survey plotted to a scale of 10m to 1cm is reduced in such a way that a line originally 10cm long now measures 9cm. the area of the reduced plan is measured as 81cm2....
The plan of a map was photo copied to a reduced size such that a line originally 100mm, measures 90mm. The original scale of the plan was 1:1000. The revised scale is
For an isotropic material, the relationship between the young’s modulus (E), shear modulus (G) and Poisson’s ratio (μ) is given by
A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by $$10^o$$C. If the coefficient of thermal expansion is 12 x$$10^{-6}$$ per $$^...
A steel column, pinned at both ends, has a buckling load of $$200$$ $$kN.$$ If the column is restrained against lateral movement at its mid-height, its buckling load will be
A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam has constant flexural rigidity...
The maximum and minimum shear stresses in a hollow circular shaft of outer diameter $$20$$ $$mm$$ and thickness $$2$$ $$mm,$$ subjected to a torque of $$92.7$$ $$N.m$$ will be
An axially loaded bar is subjected to a normal stress of $$173$$ $$MPa.$$ The maximum shear stress in the bar is
A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega $$ per unit length. The beam has constant flexural rigidity...
The shear stress at the neutral axis in a beam of triangular section with a base of $$40$$ $$mm$$ and height $$20$$ $$mm,$$ subjected to a shear force of $$3$$ $$kN$$ is
The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of available water is the root zone is 60mm. Irrigation is required wh...