$A$ small square loop of wire of side $l$ is placed inside a large square loop of side $L$ $(L \gg l)$. If the loops are coplanar and their centres coincide,the mutual inductance of the system is directly proportional to :

$A$ coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current through it is changing) so that their centers coincide. $(R \gg r)$. If both are coplanar,then the mutual inductance between them is proportional to

The specific resistance (resistivity) of material $B$ is twice that of material $A$. The diameter of a circular wire made of $B$ is twice that of a wire made of $A$. If the resistances of both wires are equal,then the ratio of their lengths $l_B/l_A$ will be .......

Which one of the following sets of ions represents the collection of isoelectronic species?

There is an error of $\pm 0.04 \text{ cm}$ in the measurement of the diameter of a sphere. When the radius is $10 \text{ cm}$,the percentage error in the volume of the sphere is

Two polaroids are placed in the path of an unpolarized beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid,whose polarization axis makes an angle $\theta$ with the polarization axis of the first polaroid,is placed between these polaroids,then the intensity of light emerging from the last polaroid will be: