A transverse wave is represented by $$y=2 \sin (\omega t-k x)\, \mathrm{cm}$$. The value of wavelength (in $$\mathrm{cm}$$) for which the wave velocity becomes equal to the maximum particle velocity, will be :

A battery of $$6 \mathrm{~V}$$ is connected to the circuit as shown below. The current I drawn from the battery is :

A source of potential difference $$V$$ is connected to the combination of two identical capacitors as shown in the figure. When key '$$K$$' is closed, the total energy stored across the combination is $$E_{1}$$. Now key '$$K$$' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now $$E_{2}$$. The ratio $$E_{1} / E_{2}$$ will be :

Two concentric circular loops of radii $$r_{1}=30 \mathrm{~cm}$$ and $$r_{2}=50 \mathrm{~cm}$$ are placed in $$\mathrm{X}-\mathrm{Y}$$ plane as shown in the figure. A current $$I=7 \mathrm{~A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :