Which one of the following reactions occurs at the anode in the Castner process of extracting sodium metal?

Assertion $(A)$: Optical fibres are widely used in communication networks. Reason $(R)$: Optical fibres are small in size,light in weight,flexible,and there is no scope for interference in them.

If $f: R \rightarrow R$ is defined by $f(x) = x - [x]$,where $[x]$ is the greatest integer not exceeding $x$,then the set of points of discontinuity of $f$ is

$A$ lead bullet at $27\,^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^{\circ}C$,specific heat of lead $= 0.03\,cal/g\,^{\circ}C$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

Cultivation of $Bt$ cotton has been much in the news. The prefix $Bt$ means

$A$ Van de Graaff generator has a spherical metal shell as an electrode which is at a potential $15 \times 10^6 \ V$. If the dielectric strength of the surrounding medium is $5 \times 10^7 \ V \ m^{-1}$,then the diameter of the shell is: (in $cm$)