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Given below are two statements:
Statement I: Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in water to a very small extent.
Statement II: Sodium metal can be used to dry diethyl ether and not ethyl alcohol.
In the light of the given statements, choose the correct answer from the options given below:
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 ________.
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is
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): 
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.