In the given circuit,the galvanometer shows zero deflection. What is the value of $R$ in $\Omega$?

In the given circuit diagram,the currents $I_1 = -0.3\,A$,$I_4 = 0.8\,A$ and $I_5 = 0.4\,A$ are flowing as shown. The currents $I_2, I_3$ and $I_6$ respectively are

What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate $R_{\text{unknown}}$ by any other method?

Two resistances $R_1 = X \Omega$ and $R_2 = 1 \Omega$ are connected to a wire $AB$ of uniform resistivity,as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \text{ mm}$ at $A$ to $1 \text{ mm}$ at $B$. $A$ galvanometer $(G)$ connected to the center of the wire,$50 \text{ cm}$ from each end along its axis,shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is:

The equivalent resistance of the following circuit when no current flows in the resistance of $5 \Omega$ is nearly (in $\Omega$)

The resultant resistance between points $B$ and $D$ in the given figure is: (in $\Omega$)