Write the reaction of D-Glucose with the following:
$\text{HCN}$
$\text{Br}_2 \text{water} $
$\text{(CH}_3\text{COO)}_2 \text{O}$
(a) When D-glucose reacts with HCN, it forms cyanohydrin, as the nucleophilic cyanide attacks the electrophilic carbonyl carbon in glucose. \[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{HCN} \longrightarrow \text{C}_6\text{H}_{11}\text{O}_6\text{CN} \]
(b) When D-glucose reacts with $Br_2\text{water, it undergoes oxidation to form gluconic acid}$ \[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{Br}_2 \longrightarrow \text{C}_6\text{H}_{12}\text{O}_7 \]
(c) When D-glucose reacts with acetic anhydride (\( \text{(CH}_3\text{COO)}_2 \text{O} \)), it forms glucose pentaacetate.} \[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{(CH}_3\text{COO)}_2 \text{O} \longrightarrow \text{C}_6\text{H}_{9}(\text{COOCH}_3)_5 \]
Two batteries of emf's \(3V \& 6V\) and internal resistances 0.2 Ω \(\&\) 0.4 Ω are connected in parallel. This combination is connected to a 4 Ω resistor. Find:
(i) the equivalent emf of the combination
(ii) the equivalent internal resistance of the combination
(iii) the current drawn from the combination
Four students of class XII are given a problem to solve independently. Their respective chances of solving the problem are: \[ \frac{1}{2},\quad \frac{1}{3},\quad \frac{2}{3},\quad \frac{1}{5} \] Find the probability that at most one of them will solve the problem.