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.
In the circuit shown, assuming the threshold voltage of the diode is negligibly small, then the voltage \( V_{AB} \) is correctly represented by:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: