When two resistance $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ connected in series and introduced into the left gap of a meter bridge and a resistance of 10 $$\Omega$$ is introduced into the right gap, a null point is found at 60 cm from left side. When $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ are connected in parallel and introduced into the left gap, a resistance of 3 $$\Omega$$ is introduced into the right gap to get null point at 40 cm from left end. The product of $$\mathrm{R_1}$$ $$\mathrm{R_2}$$ is ____________$$\Omega^2$$

In a metre bridge experiment the balance point is obtained if the gaps are closed by 2$$\Omega$$ and 3$$\Omega$$. A shunt of X $$\Omega$$ is added to 3$$\Omega$$ resistor to shift the balancing point by 22.5 cm. The value of X is ___________.

Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3$$\Omega$$. Cell 2 has emf of 6V and internal resistance of 6$$\Omega$$. An external resistor R of 4$$\Omega$$ is connected across A and B. The current flowing through R will be ____________ A.

In the given circuit, the equivalent resistance between the terminal A and B is __________ $$\Omega$$.