What is the equivalent resistance across $A$ and $B$ in the figure shown,if $R = 3\,\Omega$?

Consider two circuits, $(A)$ and $(B)$, each having two resistors. One of them has a positive temperature coefficient of resistance, $+\alpha$, while the other one has a negative temperature coefficient of resistance, $-\alpha$. The current through these circuits are denoted by $I_A$ and $I_B$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits is:

Three resistances of $1\, \Omega$ each are connected in parallel. Such a connection is then connected in series with a $\frac{2}{3}\, \Omega$ resistor. The resultant resistance will be ........... $\Omega$.

The figure shows a tetrahedron where each edge has a resistance $r$. If a battery is connected between any two vertices of the tetrahedron,identify the correct statement$(s)$.

Net resistance of the given circuit between $X$ and $Y$ is ............... $\Omega$.

The equivalent resistance between $A$ and $B$ is $6 \Omega$. The value of $R_1$ is (in $\Omega$)