Under isothermal conditions, two soap bubbles of radii '$$r_1$$' and '$$r_2$$' combine to form a single soap bubble of radius '$$R$$'. The surface tension of soap solution is ( $$P=$$ outside pressure)

Two identical parallel plate air capacitors are connected in series to a battery of emf '$$\mathrm{V}$$'. If one of the capacitor is inserted in liquid of dielectric constant '$$\mathrm{K}$$' then, potential difference of the other capacitor will become

In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are

Two coherent sources of wavelength '$$\lambda$$' produce steady interference pattern. The path difference corresponding to 10$$^{th}$$ order maximum will be