$A$ uniform metallic wire has a resistance of $18\,\Omega$ and is bent into an equilateral triangle. Then,the resistance between any two vertices of the triangle is .................. $\Omega$.

$A$ man has some identical resistors,each with a resistance $R = 10 \, \Omega$ and a maximum current rating of $1 \, \text{A}$. He needs to create a circuit with an equivalent resistance of $5 \, \Omega$ that can handle a total current of $4 \, \text{A}$. What is the minimum number of such resistors required?

Two wires of same metal have the same length but their cross-sections are in the ratio $3:1$. They are joined in series. The resistance of the thicker wire is $10\,\Omega$. The total resistance of the combination will be ............. $\Omega$.

The effective resistance of two resistors in parallel is $\frac{12}{7} \ \Omega$. If one of the resistors is disconnected,the resistance becomes $4 \ \Omega$. The resistance of the other resistor is ............. $\Omega$.

$A$ wire of resistance $12 \, \Omega$ is bent to form an equilateral triangle. What is the equivalent resistance between any two corners of the triangle?

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is