The pitch of a screw gauge is $0.5 \mathrm{mm}$ and there are $100$ divisions on its circular scale. The instrument reads $+2$ divisions when nothing is put in between its jaws. In measuring the diameter of a wire, there are $8$ divisions on the main scale and ${83}^{\mathrm{rd}}$ divisions coincide with the reference line. Then the diameter of the wire is:

Consider the $MB$ shown in the diagram, let the resistance $X$ have temperature coefficient ${\alpha }_1$ and the resistance from the $RB$ have the temperature coefficient ${\alpha }_2.$ Let the reading of the meter scale be $10 \mathrm{cm}$ from the $\mathrm{LHS}$. If the temperature of the two resistance increase by small temperature $\mathrm{\Delta }$$T$ then what is the shift in the position of the null point? Neglect all the other changes in the bridge due to temperature rise.

A metre bridge is set up as shown, to determine an unknown resistance $X$ using a standard $10 \mathrm{\Omega }$ resistor. The galvanometer shows null point when the tapping key is at $52 \mathrm{cm}$ mark. The end-corrections are $1 \mathrm{cm}$ and $2 \mathrm{cm}$ respectively for the ends $\mathrm{A}$ and $\mathrm{B}$. The determined value of $X$ is 

$1 \mathrm{cm}$ of the main scale of vernier calipers is divided into $10 \mathrm{divisions}$. The vernier scale had $n \mathrm{divisions}$, so that least count of the calipers is $0.005 \mathrm{cm}$. The value of $n$ is