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

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

Using Laplace transform, solve the initial value problem $$9{y^{11}} - 6{y^1} + y = 0$$
$$y\left( 0 \right) = 3$$ and $${y^1}\left( 0 \right) = 1,$$ where prime denotes derivative with respect to $$t.$$

Shear stress in the Newtonian fluid is proportional to

A liquid of density $$\mathrm\rho$$ and dynamic viscosity $$\mathrm\mu$$ flows steadily down an inclined plane in a thin sheet of constant thickness t. Neglecting air friction the shear stress on the bottom surface due to the liquid flow is (where θ is the angle, the plane makes with horizontal)

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

Which one of the following relations is not correct?

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

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

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

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

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

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