Two identical parallel plate air capacitors are connected in series to a battery of emf $V$. If one of the capacitors is inserted in a liquid of dielectric constant $K$,then the potential difference of the other capacitor will become:

$A$ man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance,he takes a boat. His speed of travelling in mud,in water,and on tar road is in the ratio $3:4:5$. The ratio of the durations he requires to cross the patch of mud,stream,and tar road is

On a new scale of temperature (which is linear) called the $W$ scale,the freezing and boiling points of water are $39\,^{\circ}W$ and $239\,^{\circ}W$ respectively. What will be the temperature on the new scale,corresponding to a temperature of $39\,^{\circ}C$ on the Celsius scale? ............. $^{\circ}W$

$A$ particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

In gel electrophoresis,the separated bands of $DNA$ are cut out and extracted from the gel piece. This step is called

The product of the lengths of the perpendiculars from any point on the hyperbola $x^2 - y^2 = 8$ to its asymptotes is: