In a medium, the phase difference between two particles separated by a distance '$$x$$' is $$\left(\frac{\pi}{5}\right)^{\text {c }}$$. If the frequency of the oscillation of particles is $$25 \mathrm{~Hz}$$ and the velocity of propagation of the waves is $$75 \mathrm{~m} / \mathrm{s}$$, then the value of $$x$$ is

The work done in blowing a soap bubble of radius $$\mathrm{R}$$ is '$$\mathrm{W}_1$$' at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius $$2 \mathrm{R}$$ is blown and the work done is '$$\mathrm{W}_2$$'. Then

A capacitor of capacitance $$50 \mu \mathrm{F}$$ is connected to a.c. source $$\mathrm{e}=220 \sin 50 \mathrm{t}$$ ($$\mathrm{e}$$ in volt, $$\mathrm{t}$$ in second). The value of peak current is

Two waves are superimposed whose ratio of intensities is $$9: 1$$. The ratio of maximum and minimum intensity is