



Step 1. Identify Aromatic Stability: The most stable species among the options will be the one that is aromatic as aromatic compounds exhibit additional stability due to delocalized π-electrons.
Step 2. Analyze Each Structure: Option (1): This structure satisfies Huckel’s rule (4n + 2) for aromaticity and has a planar conjugated ring structure, making it aromatic and stable. Other Options: Do not satisfy Huckel’s rule or are non-aromatic.
Step 3. Conclusion: Option (3) is the most stable due to its aromaticity.
Consider the following reaction sequence.

In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 
Let $\alpha,\beta\in\mathbb{R}$ be such that the function \[ f(x)= \begin{cases} 2\alpha(x^2-2)+2\beta x, & x<1 \\ (\alpha+3)x+(\alpha-\beta), & x\ge1 \end{cases} \] is differentiable at all $x\in\mathbb{R}$. Then $34(\alpha+\beta)$ is equal to}
