A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ................ cm.

An amplitude modulated wave is represented by
C_m(t) = 10(1 + 0.2 cos 12560t) sin(111 $$\times$$ 10⁴t) volts. The modulating frequency in kHz will be ................. .

Two short magnetic dipoles m₁ and m₂ each having magnetic moment of 1 Am² are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole m₂ due to the presence of m₁ is ........... $$\times$$ 10^$$-$$7 Nm.

Two travelling waves produces a standing wave represented by equation,

y = 1.0 mm cos(1.57 cm^$$-$$1) x sin(78.5 s^$$-$$1)t.

The node closest to the origin in the region x > 0 will be at x = .............. cm.