Two electric dipoles, A, B with respective dipole moments $${\overrightarrow d _A} = - 4qai$$ and $${\overrightarrow d _B} = - 2qai$$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -

To get output 1 at R, for the given logic gate circuit the input values must be

In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R₁ and R₂ respectively, are -

Three Carnot engines operate in series between a heat source at a temperature T₁ and a heat sink at temperature T₄ (see figure). There are two other reservoirs at temperature T₂ and T₃, as shown, with T₁ > T₂ > T₃ > T₄. The three engines are equally efficient if -