When is the '$DUB$' sound heard during the cardiac cycle?

Let $z = \cos \theta + i \sin \theta$. Then the value of $\sum_{m=1}^{15} \operatorname{Im}(z^{2m-1})$ at $\theta = 2^{\circ}$ is

An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is (in $/T$)

Data Entry - Physics

$A$ parallel plate capacitor of capacity $100 \mu F$ is charged by a battery of $50 \text{ V}$. The battery remains connected,and if the plates of the capacitor are separated so that the distance between them becomes double the original distance,the additional energy supplied by the battery to the capacitor in joules is:

Consider a reaction $A+R \rightarrow$ Product. The rate of this reaction is measured to be $k[A][R]$. At the start of the reaction, the concentration of $R,[R]_0$, is $10-$times the concentration of $A,[A]_0$. The reaction can be considered to be a pseudo first order reaction with assumption that $k[R]=k^{\prime}$ is constant. Due to this assumption, the relative error $(in \%)$ in the rate when this reaction is $40 \%$ complete, is $....$
$[ k$ and $k^{\prime}$ represent corresponding rate constants$]$