GATE CE 2007

## GATE CE

The inverse of $$2 \times 2$$ matrix $$\left[ {\matrix{
1 & 2 \cr
5 & 7 \cr
} } \right]$$ is

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The minimum and maximum eigen values of matrix $$\left[ {\matrix{
1 & 1 & 3 \cr
1 & 5 & 1 \cr

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For what values of $$\alpha $$ and $$\beta $$ the following simultaneous equations have an infinite number of solutions

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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

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If the standard deviation of the speed of vehicles in a highway is $$8.8$$ kmph and the mean speed of the vehicles is $$

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The solution for the differential equation $$\,{{d\,y} \over {d\,x}} = {x^2}\,y$$ with the condition that $$y=1$$ at $$x

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The degree of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{x^3} = 0\,\,$$ is

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A body originally at $${60^ \circ }$$ cools down to $$40$$ in $$15$$ minutes when kept in air at a temperature of $${25^

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Potential function $$\phi $$ is given as $$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function $$\psi $$ w

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Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are

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The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$

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The presence of hardness in excess of permissible limit causes

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The alkalinity and the hardness of a water sample are 250 mg/L and 350 mg/L as
$$CaCo_3$$, respectively. The water has

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The plan of a map was photo copied to a reduced size such that a line originally
100mm, measures 90mm. The original scal

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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 meas

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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

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The water content of a saturated soil and the specific gravity of soil solids were
found to be 30% and 2.70, respectivel

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The consumptive use of water for a crop during a particular stage of growth is
2.0mm / day. The maximum depth of availab

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The culturable command area for a distributary channel is 20,000 hectares. Wheat
grown in the entire area and the intens

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Consider the following statements:
1. The compressive strength of concrete decreases with increase in water-cement
ratio

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Consider the following statements:
I. Modulus of elasticity concrete increases with increase in compressive
strength of

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A singly reinforced rectangular concrete beam has a width of $$150$$ $$mm$$ and an effective depth of $$330$$ $$mm.$$ Th

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A singly reinforced rectangular concrete beam has a width of $$150$$ $$mm$$ and an effective depth of $$330$$ $$mm.$$ Th

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A concrete beam of rectangular cross-section of size $$120$$ $$mm$$ (width) and $$200$$ $$mm$$ (depth) is prestressed by

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A bracket connection is made with four bolts of $$10$$ $$mm$$ diameter and supports a load of $$10$$ $$kN$$ a an eccentr

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A steel flat of rectangular section of size $$70 \times 6\,\,mm$$ is connected to a gusset plate by three bolts each hav

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For an isotropic material, the relationship between the young’s modulus (E),
shear modulus (G) and Poisson’s ratio (μ) i

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A metal bar of length 100mm is inserted between two rigid supports and its
temperature is increased by $$10^o$$C. If the

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An axially loaded bar is subjected to a normal stress of $$173$$ $$MPa.$$ The maximum shear stress in the bar is

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The shear stress at the neutral axis in a beam of triangular section with a base of $$40$$ $$mm$$ and height $$20$$ $$mm

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The maximum and minimum shear stresses in a hollow circular shaft of outer diameter $$20$$ $$mm$$ and thickness $$2$$ $$

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A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega

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A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$\omega

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A steel column, pinned at both ends, has a buckling load of $$200$$ $$kN.$$ If the column is restrained against lateral

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The influence line diagram $$(ILD)$$ shown is for the member

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The right triangular truss is made of members having equal cross sectional area of $$1550$$ $$m{m^2}$$ and Young's Modul

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A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$w$$ pe

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A two span continuous beam having equal spans each of length $$L$$ is subjected to a uniformly distributed load $$w$$ pe

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The plastic collapse load $${{W_P}}$$ for the propped cantilever supporting two point loads as shown in the figure in te

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The stiffness coefficient $${k_{ij}}$$ indicates

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While designing a hill road with a ruling gradient of 6%, if a sharp horizontal
curve of 50m radius is encountered, the

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