The mirror image of the point $(1, 2, 3)$ in a plane is $\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$. Which of the following points lies on this plane?

Liquids $A$ and $B$ form an ideal solution. If $X_A$ and $Y_A$ are the mole fractions of $A$ in the solution and in vapour phase in equilibrium,respectively,then (Given $P_A^o > P_B^o$):

$A$ lead bullet at $27\,^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^{\circ}C$,specific heat of lead $= 0.03\,cal/g\,^{\circ}C$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

Considering the gases to be ideal,the value of $\gamma = \frac{C_p}{C_v}$ for a gaseous mixture consisting of $3 \ moles$ of carbon dioxide $(CO_2)$ and $2 \ moles$ of oxygen $(O_2)$ will be $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.

$A$ cylindrical vessel open at the top is $20 \ cm$ high and $10 \ cm$ in diameter. $A$ circular hole whose cross-sectional area is $1 \ cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate of $100 \ cm^3 s^{-1}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g = 1000 \ cm s^{-2}$)

$A$ $DC$ source with internal resistance $R_0$ is connected to three identical resistors,each of resistance $R$,as shown in the figure. If the thermal power generated in the circuit is highest,then