To determine the correct order of adsorption of the gases A, B, C, and D on a fixed amount of charcoal based on their critical temperatures, we can follow these steps:
1. Understand the Concept of Critical Temperature:
- The critical temperature of a gas is the temperature above which it cannot be liquefied, regardless of the pressure applied. It is a measure of the intermolecular forces in the gas; higher critical temperatures indicate stronger intermolecular forces.
2. Identify the Given Critical Temperatures:
- Gas A: 5.3 K
- Gas B: 33.2 K
- Gas C: 126.0 K
- Gas D: 154.3 K
3. Relate Critical Temperature to Adsorption:
- Adsorption on a solid surface (like charcoal) is generally directly proportional to the critical temperature of the gas. This means that gases with higher critical temperatures will adsorb more strongly than those with lower critical temperatures.
4. Rank the Gases by Critical Temperature:
- From the highest to the lowest critical temperature:
- D (154.3 K)
- C (126.0 K)
- B (33.2 K)
- A (5.3 K)
5. Determine the Order of Adsorption:
- Since adsorption increases with increasing critical temperature, the order of adsorption for the gases on charcoal will be:
- D > C > B > A
6. Final Answer:
- The correct order of adsorption is: D, C, B, A.
Variation of solubility with temperature \(T\) for a gas in liquid is shown by the following graphs. The correct representation is 
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to: