If $\bar{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\bar{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$,then the value of $(2 \bar{a}-\bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a}+2 \bar{b})) = $

Determine the correct configuration of the following molecule:

$A$ compound $X$ with molecular formula $C_3H_8O$ can be oxidised to a compound $Y$ with the molecular formula $C_3H_6O_2$. $X$ is most likely to be

Find the value of the current through the $2\,\Omega$ resistance for the given circuit. (in $,A$)

$A$ ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$. The total distance covered before it comes to rest is

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and a pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. The correct values of $a, b$ and $c$ are