The value of k for which the function

$$f\left( x \right) = \left\{ {\matrix{ {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \cr {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \cr } } \right.$$

is continuous at x = $${\pi \over 2},$$ is :

If three positive numbers a, b and c are in A.P. such that abc = 8, then the minimum possible value of b is :

A combination of parallel plate capacitors is maintained at a certain potential difference.



When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.

The electric field component of a monochromatic radiation is given by

$$\overrightarrow E $$ = 2 E₀ $$\widehat i$$ cos kz cos $$\omega $$t

Its magnetic field $$\overrightarrow B $$ is then given by :