Given the reaction of N,N-dimethylaniline ('A') with NaNO2 and HX to form 'B', the correct statements are: (1) The electrophile involved in the reaction is NO+. (3) The reaction occurs at low temperature. (4) The product 'B' formed in the above reaction is p-nitroso compound at low temperature.
Explanation: The reaction is a diazotization reaction specific to tertiary aromatic amines. NaNO2 and HX generate the nitrosonium ion (NO+), which is the electrophile. Diazotization reactions are performed at low temperatures to prevent decomposition of intermediates. The product formed is a p-nitroso compound due to electrophilic aromatic substitution at the para position. Statement (2) is incorrect because the product is a p-nitroso compound, not an N-nitroso ammonium compound.
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 ___________.