The area (in sq. units) bounded by the parabolae y = x² – 1, the tangent at the point (2, 3) to it and the y-axis is :

If $$\theta $$ denotes the acute angle between the curves, y = 10 – x² and y = 2 + x² at a point of their intersection, the |tan $$\theta $$| is equal to :

A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d < < a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is :

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 10¹⁹ m^$$-$$3 and their mobility is 1.6 m²/(V.s) then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to :