Analyze Each Reaction:
Reaction (A): The reaction conditions suggest Friedel-Crafts acylation using anhydrous \( \text{AlCl}_3 \) and a carboxylic acid chloride. This reaction should proceed correctly, forming the expected acylated aromatic product.
Reaction (B): In this reaction, \( \text{Pd/BaSO}_4 \) (Rosenmund reduction conditions) is used to reduce an acyl chloride to an aldehyde. This reaction is incorrect.
Reaction (C): This reaction involves a carboxylic acid reacting with CO and HCl under anhydrous conditions with \( \text{AlCl}_3 \) or CuCl. However, this is not a standard reaction for carboxylic acid conversion to an acyl chloride under these conditions, so this reaction is incorrect.
Reaction (D): The conditions involve the reaction of a benzene derivative with \( \text{CONH}_2 \) and HCl. However, these reagents are not compatible with producing an expected product under the given conditions, making this reaction incorrect.
Conclusion:
Only Reaction (A) is correct among the given reactions. Therefore, the number of correct reactions is 1, corresponding to Option (1).
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 ___________.