GATE CE 1997

## GATE CE

If $$A$$ and $$B$$ are two matrices and $$AB$$ exists then $$BA$$ exists,

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Inverse of matrix $$\left[ {\matrix{
0 & 1 & 0 \cr
0 & 0 & 1 \cr
1 & 0 & 0 \cr

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If the determinant of the matrix $$\left[ {\matrix{
1 & 3 & 2 \cr
0 & 5 & { - 6} \cr
2 &

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If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then

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If $$\varphi \left( x \right) = \int\limits_0^{{x^2}} {\sqrt t \,dt\,} $$ then $${{d\varphi } \over {dx}} = \_\_\_\_\_\_

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For the differential equation $$f\left( {x,y} \right){{dy} \over {dx}} + g\left( {x,y} \right) = 0\,\,$$ to be exact is

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The differential equation $${{dy} \over {dx}} + py = Q,$$ is a linear equation of first order only if,

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$${e^z}$$ is a periodic with a period of

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Alkalinity of water can be defined correctly in one of the following ways

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MPN index is measure of one of the following:

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If the porosity of a soil sample is 20%, the void ratio is

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Hyetograph is a graph representing

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Lysimeter and Tensiometer are used to measure respectively, one of the following groups of quantities:

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The permissible tensile stress in concrete made of M 25 concrete is

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The cylinder strength of the concrete is less than the cube strength because of

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A hall is covered by a beam and slab system with beams placed at $$3.0$$ $$m$$ center. The effective span of the beam is

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A simply supported beam of a beam and slab system, rests on a support of width $$450$$ $$mm.$$ The clear span of the bea

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Design a square $$R.C$$ column to resist an axial load of $$400$$ $$kN$$ due to dead load and $$240$$ $$kN$$ due to live

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A prestressed concrete rectangular beam of size $$300\,\,mm \times 900\,\,mm$$ is prestressed with an intial prestressin

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Factor of safety adopted by IS: 800-1984 while arriving at the permissible stress in axial compression is

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Maximum size of a fillet weld for a plate of square edge is

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A compound steel column consisting of $$2$$ $$ISHB$$ $$400$$ placed at $$320$$ $$mm$$ centers, carries a total axial loa

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Allowable average shear stress in an unstiffened web for beams made of steel of grade $$250\,\,N/m{m^2}$$ is

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A small element at the critical section of component is in a state of stress with the two principal stresses being $$36

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A cantilever beam of span $$'L'$$ is loaded with a concentrated load $$'P'$$ at the free end. Deflection of the beam at

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The degree of Kinematic Indeterminacy of the rigid frame with clamped ends at $$A$$ and $$D$$ shown in the fig. is

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For the frame shown in the Fig. the maximum bending moment in the column is,

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A propped cantilever beam of span $$'L'$$ is loaded with $$u.d.l$$ of intensity $$w$$/unit length, all through the span.

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The force in the member $$DE$$ of the truss shown in the fig. is,

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The order for the flexibility matrix for a structure is,

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The value of camber recommended for CC roads in area of heavy rainfall is

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