Oil is extracted from mustard seeds having 20 wt% oil and 80 wt% solids, using hexane as a solvent. After extraction, the hexane-free residual cake contains 1 wt% oil. Assuming negligible dissolution of cake in hexane, the percentage oil recovery in hexane is ___________ % (rounded off to the nearest integer).
Step 1: Calculate Initial and Remaining Oil Content. Initial oil content = 20% of 100 kg = 20 kg.
Oil remaining in cake = 1% of 100 kg = 1 kg.
Step 2: Calculate the Oil Extracted and Percentage Recovery. Oil extracted = Initial oil - Remaining oil = 20 kg - 1 kg = 19 kg.
Percentage recovery = \(\left(\frac{19 { kg}}{20 { kg}}\right) \times 100% = 95%\).

Choose the option that correctly matches the items in Group 1 with those in Group 2.

The residence-time distribution (RTD) function of a reactor (in min−1) is:
\[ E(t) = \begin{cases} 1 - 2t, & \text{if } t \leq 0.5\ \text{min} \\ 0, & \text{if } t > 0.5\ \text{min} \end{cases} \]
The mean residence time of the reactor is _____ min (rounded off to 2 decimal places).