GATE CE 1996

## GATE CE

The directional derivative of the function $$f(x, y, z) = x + y$$ at the point $$P(1,1,0)$$ along the direction $$\over

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Solve $${{{d^4}v} \over {d{x^4}}} + 4{\lambda ^4}v = 1 + x + {x^2}$$

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Using Laplace transform, solve the initial value problem $$9{y^{11}} - 6{y^1} + y = 0$$
$$y\left( 0 \right) = 3$$ and $

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Shear stress in the Newtonian fluid is proportional to

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If, for a fluid in motion, pressure at a point is same in all directions then the fluid is

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A liquid of density $$\mathrm\rho$$ and dynamic viscosity $$\mathrm\mu$$ flows steadily down an inclined plane in a thin

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Which one of the following relations is not correct?

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The effective length of a circular electric pole of length $$L$$ and constant diameters erected on ground is,

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Reaction at support $$'B'$$ of the structure shown is

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$$M$$-$$\theta $$ relationship for a simply supported beam shown below is given by

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Rotational stiffness-coefficient, $${K_{11}}$$ for the frame having two members of equal $$EI/L$$ is given by.

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Bending moments at joint $$b$$ and $$C$$ of the portal frame are respectively,

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Horizontal stiffness coefficient, $${K_{11}}$$ of bar $$ab$$ is given by,

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