A sealed flask with a capacity of $2\, dm ^3$ contains $11 \, g$ of propane gas The flask is so weak that it will burst if the pressure becomes $2\, MPa$ The minimum temperature at which the flask will burst is ______${ }^{\circ} C$ [Nearest integer]
(Given: $R =8.3 \,J \,K ^{-1} mol ^{-1}$ Atomic masses of $C$ and $H$ are $12\, u$ and $1 \,u$ respectively) (Assume that propane behaves as an ideal gas)
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
The three states of matter are as follows: