The \( C-O-H \) bond angle in A is \( X \) and \( C-O-C \) bond angle in B is \( Y \). What are X and Y?
Step 1: Understanding Bond Angles in Alcohols and Ethers
- Structure A: Methanol (\( CH_3OH \))
- The central oxygen atom in methanol is sp\(^3\) hybridized with a bent geometry.
- Due to the presence of lone pairs on oxygen, the actual bond angle is slightly greater than the tetrahedral angle \( 109^\circ 28' \).
- This increase is due to repulsion between the lone pairs and bond pairs.
- Structure B: Dimethyl Ether (\( CH_3OCH_3 \))
- Oxygen is sp\(^3\) hybridized and forms two sigma bonds with carbon.
- The bond angle in ethers is approximately \( 109^\circ 28' \) due to similar electron pair repulsions.
Step 2: Evaluating the Given Options
- Option (1): Incorrect, as \( Y \) should be equal to \( 109^\circ 28' \), not greater.
- Option (2): Incorrect, as alcohols generally have bond angles slightly greater than \( 109^\circ 28' \).
- Option (3): Correct, as \( X>109^\circ 28' \) (methanol) and \( Y = 109^\circ 28' \) (ether).
- Option (4): Incorrect, as it misplaces the bond angle conditions.
Thus, the correct answer is
Option (3).
The reagent 'X' used in the following reaction to obtain a good yield of the product is:
IUPAC name of the following compound is:
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List I | List II | ||
(P) | ![]() | (1) | ![]() |
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(R) | ![]() | (3) | ![]() |
(S) | ![]() | (4) | ![]() |
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Given the vectors:
\[ \mathbf{a} = \mathbf{i} + 2\mathbf{j} + \mathbf{k} \]
\[ \mathbf{b} = 3(\mathbf{i} - \mathbf{j} + \mathbf{k}) = 3\mathbf{i} - 3\mathbf{j} + 3\mathbf{k} \]
where
\[ \mathbf{a} \times \mathbf{c} = \mathbf{b} \]
\[ \mathbf{a} \cdot \mathbf{x} = 3 \]
Find:
\[ \mathbf{a} \cdot (\mathbf{x} \times \mathbf{b} - \mathbf{c}) \]
If three numbers are randomly selected from the set \( \{1,2,3,\dots,50\} \), then the probability that they are in arithmetic progression is:
A student has to write the words ABILITY, PROBABILITY, FACILITY, MOBILITY. He wrote one word and erased all the letters in it except two consecutive letters. If 'LI' is left after erasing then the probability that the boy wrote the word PROBABILITY is: \