Self inductance of solenoid is

The capacitance of a parallel plate capacitor is $$2.5 ~\mu \mathrm{F}$$. When it is half filled with a dielectric as shown in figure, its capacitance becomes $$5 ~\mu \mathrm{F}$$. The dielectric constant of the dielectric is

Equation of simple harmonic progressive wave is given by $$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$$ then the resultant amplitude of the wave is $$\left(\cos 90^{\circ}=0\right)$$

Two uniform brass rods $$A$$ and $$B$$ of length '$$l$$' and '$$2 l$$' and their radii '$$2 r$$' and '$$r$$' respectively are heated to same temperature. The ratio of the increase in the volume of $$\operatorname{rod} \mathrm{A}$$ to that of $$\operatorname{rod} \mathrm{B}$$ is