If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$,then the radius of a nucleus with mass number $64$ is: (in $\text{ fermi}$)

Consider the following reactions:
$C_2H_2 \xrightarrow[500^{\circ}C]{\text{red hot iron tube}} A$
$A \xrightarrow[70^{\circ}C]{\text{conc. } HNO_3, \text{conc. } H_2SO_4} B$
$B \xrightarrow{LiAlH_4} C_6H_5-N=N-C_6H_5$
$A$ and $B$ are:

The minimum value of $2x^2+x-1$ is:

If two glass plates have water between them and are separated by a very small distance (see figure),it is very difficult to pull them apart. This is because the water in between forms a cylindrical surface on the side that gives rise to a lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is $R$ and the surface tension of water is $T$,then the pressure in the water between the plates is lower by:

Consider two reactions:
$I.$ $Zn +$ conc. $HNO_3$ (hot) $\rightarrow Zn(NO_3)_2 + X + H_2O$
$II.$ $Zn +$ dil. $HNO_3$ (cold) $\rightarrow Zn(NO_3)_2 + Y + H_2O$
Compounds $X$ and $Y$ are respectively:

$A$ body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body from the surface of the earth is