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 $$\mathbf{Q}$$ ?

The graph of kinetic energy against the frequency $$v$$ of incident light is as shown in the figure. The slope of the graph and intercept on $$X$$-axis respectively are

The length of solenoid is $$I$$ whose windings are made of material of density $$D$$ and resistivity $$\rho$$. The winding resistance is $$R$$. The inductance of solenoid is [$$m=$$ mass of winding wire, $$\mu_0=$$ permeability of free space]