




The given reaction is a Wolff-Kishner reduction, which is used to reduce carbonyl groups (aldehydes and ketones) to alkanes.
The first step involves the formation of a hydrazone derivative: \[ \text{CH}_3 - \text{CO} - \text{CH}_2 - \text{CH}_3 \xrightarrow{\text{N}_2\text{H}_4} \text{CH}_3 - \text{C}(\text{NHNH}_2) - \text{CH}_2 - \text{CH}_3. \]
In the presence of ethylene glycol and KOH, the hydrazone undergoes decomposition to form: \[ \text{CH}_3 - \text{CH}_2 - \text{CH}_2 - \text{CH}_3. \]
Thus, the product 'A' is butane.
Step 1: Recognize the reagents and the named reaction
The sequence (i) N2H4 then (ii) ethylene glycol / KOH is the classical Wolff–Kishner reduction. This reaction converts a carbonyl group (>C=O of aldehydes/ketones) into a methylene group (–CH2–) under strongly basic, high-temperature conditions.
Step 2: Identify the starting carbonyl compound from the figure
The substrate shown is a simple ketone with two methyl groups on the carbonyl carbon (acetone / propanone): CH3–C(=O)–CH3.
Step 3: Outline the Wolff–Kishner pathway (what happens to the carbonyl)
Stage A: Hydrazone formation The ketone reacts with hydrazine to give the hydrazone: CH3–C(=O)–CH3 + N2H4 ⟶ CH3–C(=NNH2)–CH3 + H2O.
Stage B: Base-promoted elimination (high temperature, ethylene glycol/KOH) Strong base deprotonates the –NH2 group(s); subsequent steps expel N2 gas and water, reducing the carbonyl carbon: … ⟶ CH3–CH2–CH3 + N2↑ + H2O.
Step 4: Predict the product for the given substrate
Replacing the >C=O of acetone by –CH2 converts CH3–C(=O)–CH3 into the fully saturated hydrocarbon CH3–CH2–CH3 (propane).
Step 5: Why Wolff–Kishner suits this case
Step 6: Comparison note (helps avoid common mistakes)
Clemmensen reduction (Zn(Hg)/HCl) also reduces >C=O to –CH2–, but under strongly acidic conditions. Wolff–Kishner is the basic analogue — ideal if the molecule is acid-sensitive.
Final identification of ‘A’
CH3–CH2–CH3 (propane)
In the given reaction sequence, the structure of Y would be:

For \( \alpha, \beta, \gamma \in \mathbb{R} \), if \[ \lim_{x \to 0} \frac{x^2 \sin(\alpha x) + (\gamma - 1)e^{x^2}}{\sin(2x - \beta x)} = 3, \] then \( \beta + \gamma - \alpha \) is equal to:

In the first configuration (1) as shown in the figure, four identical charges \( q_0 \) are kept at the corners A, B, C and D of square of side length \( a \). In the second configuration (2), the same charges are shifted to mid points C, E, H, and F of the square. If \( K = \frac{1}{4\pi \epsilon_0} \), the difference between the potential energies of configuration (2) and (1) is given by:
If \( S \) and \( S' \) are the foci of the ellipse \[ \frac{x^2}{18} + \frac{y^2}{9} = 1 \] and \( P \) is a point on the ellipse, then \[ \min (SP \cdot S'P) + \max (SP \cdot S'P) \] is equal to: