Consider a gas phase reaction which occurs in a closed vessel: $2A \rightarrow 4B + C$. The concentration of $B$ is found to be increased by $5 \times 10^{-3} \ mol \ L^{-1}$ in $10 \ s$. The rate of disappearance of $A$ (in $mol \ L^{-1} \ s^{-1}$) is:

Heating an aqueous solution of aluminium chloride to dryness will give:

Different conformations of the same molecule are called

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

The system of equations $3x + 2y + z = 6$,$3x + 4y + 3z = 14$ and $6x + 10y + 8z = a$ has an infinite number of solutions if $a$ is equal to

The point of intersection of the lines $l_1: r(t)=(i-6j+2k)+t(i+2j+k)$ and $l_2: R(u)=(4j+k)+u(2i+j+2k)$ is