$XY$ is the membrane / partition between two chambers 1 and 2 containing sugar solutions of concentration $\mathrm{c}_{1}$ and $\mathrm{c}_{2}\left(\mathrm{c}_{1}>\mathrm{c}_{2}\right) \mathrm{mol} \mathrm{L}^{-1}$. For the reverse osmosis to take place identify the correct condition} (Here $\mathrm{p}_{1}$ and $\mathrm{p}_{2}$ are pressures applied on chamber 1 and 2 )
1. Normal osmosis occurs from chamber 2 to chamber 1.
2. For reverse osmosis from chamber 1 to chamber 2, the pressure $\mathrm{p}_{1}$ must be greater than the osmotic pressure $\pi$.
3. Therefore, the correct conditions are A and C.
Therefore, the correct answer is (3) A and C only.
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: