
To identify compounds A and B from the given reactions, we need to analyze the transformations shown:

Therefore, for the given reactions, A is identified as 2–Pentyne and B as trans–2–butene, correlating with the correct option:
Step-by-step Analysis:
1. Reaction of A with Hydrogen (H$_2$) in the Presence of Pd/C:
This reaction involves the partial hydrogenation of an alkyne (2-pentyne) to an alkene (pent-2-ene) using a palladium catalyst supported on carbon (Pd/C). The product of this reaction is a cis-alkene if a Lindlar catalyst is used, but in this case, the hydrogenation results in a trans-alkene (trans-2-butene) under typical catalytic conditions.
2. Reduction of CH$_3$--C $\equiv$ C--CH$_3$ (2-Butyne) with Sodium in Liquid Ammonia:
This reaction is known as the Birch reduction, which selectively converts alkynes to trans-alkenes. Therefore, the product B formed is trans-2-butene.
Conclusion:
Compound A is 2-pentyne.
Compound B is trans-2-butene.
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 ___________.