The centroid of the triangle formed by the lines $6x^2 + xy - y^2 = 0$ and $x + 3y - 10 = 0$ is

The only cations present in a slightly acidic solution are $Fe^{3+}$,$Zn^{2+}$,and $Cu^{2+}$. The reagent that,when added in excess to this solution,would identify and separate $Fe^{3+}$ in one step is

The lanthanide contraction is responsible for the fact that

One mole of an ideal gas having initial volume $V$,pressure $2P$ and temperature $T$ undergoes a cyclic process $ABCDA$ as shown in the figure. The net work done in the complete cycle is:

Consider a block of conducting material of resistivity ' $\rho$ ' shown in the figure. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$.
(iv) Repeat $(i)$,$(ii)$ and $(iii)$ for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is

Secondary sewage treatment is mainly a