$A$ solution of sodium sulphate contains $92 \ g$ of $Na^{+}$ ions per kilogram of water. The molality of $Na^{+}$ ions in that solution in $mol \ kg^{-1}$ is:

$A$ proton of mass $1.67 \times 10^{-27} \, kg$ and charge $1.6 \times 10^{-19} \, C$ is projected with a speed of $2 \times 10^6 \, m/s$ at an angle of $60^{\circ}$ to the $X$-axis. If a uniform magnetic field of $0.104 \, T$ is applied along the $Y$-axis,the path of the proton is:

Two particles $A$ and $B$ of masses $m$ and $2m$ are suspended from massless springs of force constants $K_1$ and $K_2$. During their oscillation,if their maximum velocities are equal,then the ratio of amplitudes of $A$ and $B$ is

If $Alpha$,$Beta$,and $Gamma$ rays carry the same momentum,which has the longest wavelength?

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \, s$,after starting from rest,it travels a distance $a$,and in the next $\tau \, s$,it travels $2a$ in the same direction. Then:

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to