2-Methyl propyl bromide, also known as isobutyl bromide (\(\text{CH}_3\text{CH}_2\text{CH}(\text{CH}_3)\text{Br}\)), reacts differently with \( \text{C}_2\text{H}_5\text{O}^- \) and \( \text{C}_2\text{H}_5\text{OH} \) due to their differing nucleophilicity and basicity.
Reaction with \( \text{C}_2\text{H}_5\text{O}^- \) (Ethoxide Ion):
Ethoxide ion is a strong, bulky nucleophile.
The reaction proceeds via an SN2 mechanism due to the strong nucleophilic nature of \( \text{C}_2\text{H}_5\text{O}^- \).
The substitution occurs at the less hindered primary carbon, leading to the formation of iso-butyl ethyl ether (\(\text{CH}_3\text{CH}_2\text{CH}(\text{CH}_3)\text{O}\text{C}_2\text{H}_5\)).
Reaction with \( \text{C}_2\text{H}_5\text{OH} \) (Ethanol):
Ethanol is a weak nucleophile and cannot effectively participate in SN2 reactions.
The reaction proceeds via an SN1 mechanism, which involves the formation of a carbocation intermediate.
Upon ionization, the secondary carbocation formed can rearrange to a more stable tertiary carbocation.
This leads to the formation of tert-butyl ethyl ether (\(\text{(CH}_3)_3\text{C}\text{O}\text{C}_2\text{H}_5\)).
Therefore, the correct mechanism and products are:
A = iso-butyl ethyl ether via SN2 mechanism.
B = tert-butyl ethyl ether via SN1 mechanism.
This corresponds to option (3).
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 equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\). 
Method used for separation of mixture of products (B and C) obtained in the following reaction is: 
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.