A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is place symmetrically with respect to the plates. If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio $$\varepsilon_1\;:\;\varepsilon_2$$ is

The magnitude of magnetic flux density ($$\overrightarrow B$$) at a point having normal distance d meters from an infinitely extended wire carrying current of I A is $$\frac{\mu_0I}{2\mathrm{πd}}$$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. μ₀ is permeability of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. Assuming right handed coordinate system, magnetic field intensity, $$\overrightarrow H$$ at coordinate (2,1,0) will be

Which one of the following statements is true for all real symmetric matrices?

Minimum of the real valued function $$f\left( x \right) = {\left( {x - 1} \right)^{2/3}}$$ occurs at $$x$$ equal to