The condition for the coaxial system $x^2+y^2+2\lambda x+c=0$,where $\lambda$ is a parameter and $c$ is a constant,to have distinct limiting points,is

If $0 < y < 2^{1/3}$ and $x(y^3 - 1) = 1$,then $\frac{2}{x} + \frac{2}{3x^3} + \frac{2}{5x^5} + \dots$ is equal to:

During the electrolysis of cryolite,aluminium and fluorine are formed in ........ molar ratio :

The time period of a vibration magnetometer is $T_0$. Its magnet is replaced by another magnet whose moment of inertia is $3$ times and magnetic moment is $1/3$ of the initial magnet. The new time period will be:

Two wires $A$ and $B$ are of the same material. Their lengths are in the ratio $1:2$ and their diameters are in the ratio $2:1$. When stretched by forces $F_A$ and $F_B$ respectively,they experience an equal increase in their lengths. Then the ratio $F_A/F_B$ is:

In the equation $\log S = \log C + Z \log A$,what does $S$ represent?