Two ideal electric dipoles A and B, having their dipole moment p₁ and p₂ respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$$^\circ$$ with the axis. The ratio of the dipole moment of A and B, $${{{p_1}} \over {{p_2}}}$$ is : (take $$\sin 37^\circ = {3 \over 5}$$)

Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

The force is given in terms of time t and displacement x by the equation

F = A cos Bx + C sin Dt

The dimensional formula of $${{AD} \over B}$$ is :

The given potentiometer has its wire of resistance 10$$\Omega$$. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2$$\Omega$$ resistor is :