





→ P may be → H2/Pd, ethanol; Sn/HCl
→ R may be → NaNO2/HCl; HNO2
→ U may be → (i) H3PO2, (ii) KMnO4 – KOH, Δ or (i) CH3 – CH2 – OH, (ii) KMnO4 – KOH, Δ
So the correct options are A,B and C.
The first step involves the reduction of nitrobenzene (\( \text{C}_6\text{H}_5\text{NO}_2 \)) to an amine derivative.
The reagent for reducing the nitro group to an amine group is \( \text{H}_2/\text{Pd} \), ethanol, which matches with option A and B for P → H₂/Pd, ethanol.
The next step involves the conversion of the amine group to a diazonium salt using \( \text{NaNO}_2/\text{HCl} \).
This corresponds to option A and option B for R → NaNO₂/HCl.
The reaction involves the substitution of the diazonium group with a chlorine atom to form a chlorobenzene derivative.
This step is facilitated by CuCl, as shown in option C for S → \( \text{C}_6\text{H}_4\text{Cl} \) (Chlorobenzene).
The next step involves the oxidation of the chlorobenzene derivative into a carboxyl group, forming benzoic acid.
The reducing agent for this reaction is KMnO₄ - KOH, heat, which corresponds to U in option A and option C.
The final product, benzoic acid, is formed by the reaction of the compound under oxidation conditions.
This matches with the final step T: \( \text{C}_6\text{H}_5\text{COOH} \) in option A and option C.
The correct matches are:
The correct options are A, B, C.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).

The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Alcohols, phenols, and ethers are organic compounds that have distinct chemical properties.
Alcohols are characterized by the presence of the hydroxyl (-OH) functional group, which makes them polar and capable of forming hydrogen bonds. They are typically classified as primary, secondary, or tertiary, depending on the number of alkyl groups attached to the carbon atom bearing the hydroxyl group. Alcohols undergo various chemical reactions, including oxidation, dehydration, and esterification.
Phenols are organic compounds that contain an -OH group attached to an aromatic ring. They are weaker acids than carboxylic acids but stronger acids than alcohols due to the resonance stabilization of the phenoxide ion. Phenols undergo various chemical reactions, including electrophilic substitution and oxidation.
Read More: Classification of Alcohol, Phenols and Ethers
Ethers are organic compounds that contain an oxygen atom bonded to two alkyl or aryl groups. They are characterized by their low boiling points and are often used as solvents. Ethers undergo various chemical reactions, including cleavage of the C-O bond and oxidation.
In summary, alcohols, phenols, and ethers have distinct chemical properties due to the presence of the hydroxyl or ether functional group. Understanding these properties is important for understanding their reactivity and potential applications in various fields, including chemistry, biology, and industry.