$A$ motor is used to deliver water at a certain rate through a given horizontal pipe. To deliver $n$-times the water through the same pipe in the same time,the power of the motor must be increased as follows:

$A$ hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_1$ or $L_2$ having refractive indices $n_1$ and $n_2$ respectively $(n_2 > n_1 > 1)$. The lens will diverge a parallel beam of light if it is filled with

$A$ meter bridge is set up as shown to determine end corrections at $A$ and $B$. When a resistance of $15 \ \Omega$ is used in the left gap and $20 \ \Omega$ in the right gap,the null point is obtained at a distance of $42 \ cm$ from $A$. When these resistances are interchanged,the null point is obtained at a distance of $57 \ cm$ from $A$. The values of the end corrections are:

Identify the blank spaces $a, b, c$ and $d$ given in the following table and select the correct answer.
| Organism | Type | Product |
| :--- | :--- | :--- |
| $a$ | $b$ | Cyclosporin-$A$ |
| $c$ | Bacterium | Butyric acid |
| $d$ | Bacterium | Lactic acid |

Two spherical conductors each of capacity $C$ are charged to potentials $V$ and $-V$. These are then connected by means of a fine conducting wire. The loss of energy will be

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):