Write the reactions involved when D-glucose is treated with the following reagents: (a) HCN (b) Br\(_2\) water
When D-glucose is treated with hydrogen cyanide (HCN), it undergoes cyanohydrin formation. The reaction occurs at the aldehyde group, resulting in the formation of D-glucose cyanohydrin.
\[ \text{D-glucose} + HCN \rightarrow \text{D-glucose cyanohydrin} \]
When D-glucose is treated with bromine water (a mild oxidizing agent), it specifically oxidizes the aldehyde group at C-1 to a carboxylic acid, producing gluconic acid.
\[ \text{D-glucose} + Br_2\text{(water)} \rightarrow \text{Gluconic acid} \]
These reactions demonstrate the aldehydic nature of glucose and its ability to undergo addition and oxidation reactions.
Consider the following compounds: K$_2$O$_2$, H$_2$O$_2$, and H$_2$SO$_4$
The oxidation states of the underlined elements in them are, respectively:
Write the structures of A, B, and C in the following sequence of reactions:

A ladder of fixed length \( h \) is to be placed along the wall such that it is free to move along the height of the wall.
Based upon the above information, answer the following questions:
(iii) (b) If the foot of the ladder, whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance \( y \) is \( 2 \, \text{m/s} \), then at what rate is the height on the wall \( x \) increasing when the foot of the ladder is 3 m away from the wall?