$A$ string fixed at one end and free at the other is vibrating in its second overtone. The length of the string is $10 \ cm$ and the maximum amplitude of vibration of particles of the string is $2 \ mm$. The amplitude of the particle at $9 \ cm$ from the fixed end is

$X$ being a higher category is the assemblage of families which exhibit a few $Y$ characters. The $Z$ characters are less in number as compared to different genera included in a family. Identify $X$,$Y$,and $Z$.

During an adiabatic process,the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is

Cataract and skin cancer are caused by

Two blocks of masses $1 ~kg$ and $2 ~kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 ~N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 ~m/s^2$.