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.

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.

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. the difference in wavelengths of red and violet light is ................ nm.