At absolute zero temperature, pure silicon behaves as

Five capacitors each of capacity $$C$$ are connected as shown in figure. If their resultant capacity is $$2 \mu \mathrm{F}$$, then the capacity of each condenser is

The work done in blowing a soap bubble of radius $$R$$ is $$W$$. The work done in blowing a bubble of radius $$2 R$$ of the same soap solution is

The $$x, y$$ components of vector $$\mathbf{P}$$ have magnitudes 1 and 3 and $$x, y$$ components of resultant of $$\mathbf{P}$$ and $$\mathbf{Q}$$ have magnitudes 5 and 6, respectively. What is the magnitude of $$\mathbf{Q}$$ ?