At a certain place,a magnet makes $30$ oscillations per minute. At another place where the magnetic field is double,its time period will be:

$(x^2+y^2) dy = xy dx$. If $y(x_0) = e$ and $y(1) = 1$,then the value of $x_0$ is equal to

Three samples of the same gas $A, B$ and $C$ $(\gamma = 3/2)$ initially have equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$,isobaric for $B$ and isothermal for $C$. If the final pressures are equal for all three samples,the ratio of their initial pressures is:

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

In a simple harmonic oscillator,at the mean position