GATE CE 2007
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## GATE CE

The inverse of $$2 \times 2$$ matrix $$\left[ {\matrix{ 1 &amp; 2 \cr 5 &amp; 7 \cr } } \right]$$ is
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The minimum and maximum eigen values of matrix $$\left[ {\matrix{ 1 &amp; 1 &amp; 3 \cr 1 &amp; 5 &amp; 1 \cr View Question For what values of$$\alpha $$and$$\beta $$the following simultaneous equations have an infinite number of solutions View Question The velocity vector is given as$${\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 $$View Question The solution for the differential equation$$\,{{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 $${25^ View Question Potential function$$\phi $$is given as$$\phi \, = \,{x^2}\, - \,{y^2}$$. What will be the stream function$$\psi $$w View Question Given that one root of the equation$$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$is$$5$$then other roots are View Question The following equation needs to be numerically solved using the Newton$$-$$Raphson method$${x^3} + 4x - 9 = 0.\,\,$$View Question The presence of hardness in excess of permissible limit causes View Question The alkalinity and the hardness of a water sample are 250 mg/L and 350 mg/L as$$CaCo_3$$, respectively. The water has View Question The plan of a map was photo copied to a reduced size such that a line originally 100mm, measures 90mm. The original scal View Question The plan of a survey plotted to a scale of 10m to 1cm is reduced in such a way that a line originally 10cm long now meas View Question The magnetic bearing of a line AB is S 45° E and the declination is 5° west. The true bearing of the line AB is View Question The water content of a saturated soil and the specific gravity of soil solids were found to be 30% and 2.70, respectivel View Question The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of availab View Question The culturable command area for a distributary channel is 20,000 hectares. Wheat grown in the entire area and the intens View Question Consider the following statements: 1. The compressive strength of concrete decreases with increase in water-cement ratio View Question Consider the following statements: I. Modulus of elasticity concrete increases with increase in compressive strength of View Question A singly reinforced rectangular concrete beam has a width of$$150mm$$and an effective depth of$$330mm.$$Th View Question A singly reinforced rectangular concrete beam has a width of$$150mm$$and an effective depth of$$330mm.$$Th View Question A concrete beam of rectangular cross-section of size$$120mm$$(width) and$$200mm$$(depth) is prestressed by View Question A bracket connection is made with four bolts of$$10mm$$diameter and supports a load of$$10kN$$a an eccentr View Question A steel flat of rectangular section of size$$70 \times 6\,\,mm$$is connected to a gusset plate by three bolts each hav View Question For an isotropic material, the relationship between the young’s modulus (E), shear modulus (G) and Poisson’s ratio (μ) i View Question A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by$$10^o$$C. If the View Question An axially loaded bar is subjected to a normal stress of$$173MPa.$$The maximum shear stress in the bar is View Question The shear stress at the neutral axis in a beam of triangular section with a base of$$40mm$$and height$$20mm
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The maximum and minimum shear stresses in a hollow circular shaft of outer diameter $$20$$ $$mm$$ and thickness $$2$$ $$View Question A two span continuous beam having equal spans each of length$$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 $$\omega View Question A steel column, pinned at both ends, has a buckling load of$$200kN.$$If the column is restrained against lateral View Question The influence line diagram$$(ILD)$$shown is for the member View Question The right triangular truss is made of members having equal cross sectional area of$$1550m{m^2}$$and Young's Modul View Question A two span continuous beam having equal spans each of length$$L$$is subjected to a uniformly distributed load$$w$$pe View Question A two span continuous beam having equal spans each of length$$L$$is subjected to a uniformly distributed load$$w$$pe View Question The plastic collapse load$${{W_P}}$$for the propped cantilever supporting two point loads as shown in the figure in te View Question The stiffness coefficient$${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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