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## GATE CE 2002

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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## GATE CE

Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} &amp; 4 \... The following function has local minima at which value of$$x,f\left( x \ri...
Limit of the following sequence as $$n \to \infty$$ $$\,\,\,$$ is $$\,\,\,$$ $... The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,... The value of the following definite integral in$$\int\limits_{{\raise0.5ex\hbox... The directional derivative of the following function at $$(1, 2)$$ in the direc... The Laplace transform of the following function is $$f\left( t \right) = \left... Using Laplace transforms, solve$${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{... In natural water, hardness is mainly caused by During a 6-hour storm the rainfall intensity was 0.8 cm/hr on a catchment of are... Modulus of elasticity of M25 grade concrete in MPa is Read the following two statements <p>$${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Maximu... As per provision of $$IS$$ $$456$$-$$2000$$, in the limit state method for desig... A $$10m$$ long prestressing bed is used to cast $$4$$ (pretensioned) prestressed... $$ISA$$ $$100 \times 100 \times 10\,\,mm$$ (Cross sectional area $$= 1903\,\,m{...$$ISA100 \times 100 \times 10mm$$(cross sectional area$$ = 1903\,\,m{m^2}... Given reason for the following is not more than $$20$$ words <p>(a) A maximum pe... When designing steel structures, one must ensure that local buckling in webs doe... An $$ISMB$$ $$500$$ is used as a beam in a multi-storey construction. From the v... The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio ($$\mu... For the loading given in the figure below, two statements ($${\rm I}$$and$${\... In the propped cantilever beam carrying a uniformly distributed load of $$w$$-$$... A propped cantilever beam of span$$'L'$$is loaded with$$u.d.l$$of intensity ... A steel beam (with a constant$$EI,$$and span$$L$$) is fixed at both ends and ... Calculate the shape factor for the$$T$\$-section shown in the following figure m...
SSD and Friction coefficients are

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