For a sample of a perfect gas,when its pressure is changed isothermally from $p_i$ to $p_f$,the entropy change is given by:

An ideal coil of $10 \, H$ is connected in series with a resistance of $5 \, \Omega$ and a battery of $5 \, V$. $2 \, s$ after the connection is made,the current flowing (in ampere) in the circuit is:

Which one of the following population interactions is widely used in medical science for the production of antibiotics?

Assertion $(A)$: The aqueous solution of $CH_3COONa$ is alkaline in nature. Reason $(R)$: Acetate ion undergoes anionic hydrolysis. The correct answer is

Choose the incorrect statement from the following:
$S1:$ The efficiency of a heat engine can be $1$,but the coefficient of performance of a refrigerator can never be infinity.
$S2:$ The first law of thermodynamics is basically the principle of conservation of energy.
$S3:$ The second law of thermodynamics does not allow several phenomena consistent with the first law.
$S4:$ $A$ process,whose only result is to transfer heat from a colder to a hotter object,is impossible.

$A$ bullet of mass $10 \ g$ pierces through a plate $A$ of mass $500 \ g$ and then gets embedded into a second plate $B$ of mass $1.49 \ kg$ as shown in the figure. Initially,the two plates $A$ and $B$ are at rest and move with the same velocity after the collision. The percentage loss in the initial kinetic energy of the bullet,when it is between the plates $A$ and $B$,is . . . . . .
(Neglect any loss of material of the plates during the collision)