
In the given reaction coordinate diagram:
- \( E_1 \) represents the activation energy of the forward reaction.
- \( E_2 \) represents the activation energy of the reverse reaction.
- The total energy for the forward reaction is \( E_1 + E_2 \), and the product is more stable than the reactant as indicated by the lower position of the product compared to the reactant on the energy scale.
Thus, the correct option is option (4).
Consider the given figure and choose the correct option:
Consider the following graph between Rate Constant (K) and \( \frac{1}{T} \): Based on the graph, determine the correct order of activation energies \( E_{a1}, E_{a2}, \) and \( E_{a3} \).



For the circuit shown above, the equivalent gate is:
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: