A vector field is defined as

$$\vec f\left( {x,y,z} \right) = \frac{x}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat i + \frac{y}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat j + \frac{z}{{{{\left[ {{x^2} + {y^2} + {z^2}} \right]}^{\frac{3}{2}}}}}\hat k$$

where î, ĵ, k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system. The surface integral $$\smallint \smallint \vec f.d\vec S$$ (Where $$d\vec S$$ is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the centre, and internal and external radii of 1 and 2, respectively, is

Which of the following function f(z), of the complex variable z, is NOT analytic at all the points of the complex plane?

The base of a brass bracket needs rough grinding. For this purpose, the most suitable grinding wheel grade specification is

Jofra Archer, the England fast bowler, is _____ than accurate.