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

The foci of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the hyperbola $\frac{x^{2}}{144}-\frac{y^{2}}{81}=\frac{1}{25}$ coincide. Then the value of $b^{2}$ is:

Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is

At any instant,two elements $X_1$ and $X_2$ have the same number of radioactive atoms. If the decay constants of $X_1$ and $X_2$ are $10 \lambda$ and $\lambda$ respectively,then the time when the ratio of their atoms becomes $\frac{1}{e}$ will be:

Two identical flutes produce fundamental notes of frequency $300\,Hz$ at $27\,^{\circ}C.$ If the temperature of air in one flute is increased to $31\,^{\circ}C,$ the number of beats heard per second will be

If $A+B+C=270^{\circ}$,then $\cos 2A+\cos 2B+\cos 2C$ is equal to: