The uncertainties in the velocities of two particles $A$ and $B$ are $0.05 \ m/s$ and $0.02 \ m/s$ respectively. The mass of $B$ is five times that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

The solution of $\frac{dx}{dy} + \frac{x}{y} = x^2$ is:

The number of points at which the function $f(x) = |x - 0.5| + |x - 1| + \tan x$ does not have a derivative in the interval $(0, 2)$ is:

If force $F$ is increasing with time and at $t=0, F=0$,where will slipping first start?

The polymer having an amide linkage is

$A$ deflection magnetometer is adjusted and a magnet of magnetic moment $M$ is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needle before settling of the deflection is $T$. When the magnet is removed,the period of oscillation of the needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's horizontal magnetic field is $B_H$,the relation between $T$ and $T_0$ is