$BX_3 + NH_3 \xrightarrow{R.T} BX_3 \cdot NH_3 + \text{Heat of adduct formation } (\Delta H)$. The numerical value of $\Delta H$ is found to be maximum for:

$1\, kg$ of a diatomic gas is at a pressure of $8 \times 10^4\, N/m^2$. The density of the gas is $4\, kg/m^3$. What is the energy of the gas due to its thermal motion?

$A$ diode having a potential difference of $0.5\,V$ across its junction,which does not depend on the current,is connected in series with a resistance of $20\,\Omega$ across a source. If $0.1\,A$ current passes through the resistance,what is the voltage of the source (in $,V$)?

If the curves $x^2 - 6x + y^2 + 8 = 0$ and $x^2 - 8y + y^2 + 16 - k = 0$ $(k > 0)$ touch each other at a point,then the largest value of $k$ is

An electron in a Hydrogen atom first jumps from the third excited state to the second excited state and then from the second excited state to the first excited state. The ratio of the wavelengths $\lambda_{1} : \lambda_{2}$ emitted in the two cases respectively is:

Which is the most widely cultivated fiber-yielding crop in India?