$CsBr$ has $b.c.c.$ structure with edge length $4.3 \ \mathring{A}$. The shortest inter-ionic distance between $Cs^{+}$ and $Br^{-}$ is .............. $\mathring{A}$.

$A$ parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, V$ battery. What is the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ while remaining connected to the battery?

For $x \in \mathbb{R}$,the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is

Three rods $AB$,$BC$,and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$,$C$,and $D$ are held at temperatures of $20^{\circ}C$,$80^{\circ}C$,and $80^{\circ}C$ respectively. If each rod is of the same length,then the temperature at the junction $B$ of the three rods is: (in $^{\circ}C$)

The molar heat of formation of $NH_4NO_{3(s)}$ is $-367.54 \ kJ$ and those of $N_2O_{(g)}$ and $H_2O_{(l)}$ are $+81.46 \ kJ$ and $-285.78 \ kJ$ respectively at $25 \ ^oC$ and $1.0 \ atm$ pressure. Calculate $\Delta U$ at $25 \ ^oC$ for the reaction:
$NH_4NO_{3(s)} \to N_2O_{(g)} + 2H_2O_{(l)}$ (in $kJ$)

$A$ centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $140^{\circ}F$. What is the fall in temperature as registered by the centigrade thermometer in $^{\circ}C$?