
\(\text{CH}_3(\text{CH}_2)_5\text{COOC}_2\text{H}_5 \xrightarrow{\text{DIBAL-H, H}_2\text{O}} \text{CH}_3(\text{CH}_2)_5\text{CHO}\)
\(\text{C}_6\text{H}_5\text{COC}_6\text{H}_5 \xrightarrow{\text{Zn(Hg) \& conc. HCl}} \text{C}_6\text{H}_5\text{CH}_2\text{C}_6\text{H}_5\)
\(\text{C}_6\text{H}_5 \xrightarrow{\text{CH}_3\text{MgBr, H}_2\text{O}} \text{C}_6\text{H}_5\text{CH(OH)CH}_3\)
\(\text{CH}_3\text{COCH}_2\text{COOC}_2\text{H}_5 \xrightarrow{\text{NaBH}_4, \text{H}^+} \text{CH}_3\text{CH(OH)CH}_2\text{COOC}_2\text{H}_5\)
To solve this problem, we need to match the reactions in List I with the appropriate reagents in List II. Let's analyze each reaction:
Thus, by matching our understanding with our provided options, the correct answer should be:
A - (III), B - (IV), C - (I), D - (II)
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 ___________.