Let's analyze the trends based on periodic properties:

1. Ionization Potential (Option B): Generally, ionization enthalpy increases across a period. However, there is an anomaly between Group 2 and Group 13. Beryllium ($Z=4$) has a stable, completely filled $2s$ subshell ($1s^2 2s^2$), whereas Boron ($Z=5$) has one electron in the $2p$ subshell ($1s^2 2s^2 2p^1$). The $2p$ electron in boron is more shielded and easier to remove than the $2s$ electron in beryllium. Consequently, the first ionization enthalpy of Boron is lower than that of Beryllium ($IE_1(B) < IE_1(Be)$). The correct order is $Li < B < Be < C$. The option stating $Li < Be < B < C$ is therefore incorrect , .

2. Ionic Radius (Option D): As we move down a group, new electron shells are added, increasing the size of the ion. Thus, the trend $Li^+ < Na^+ < K^+ < Cs^+$ is correct , .

3. Basic Nature of Oxides (Option C): Metallic character increases down a group and decreases across a period. More metallic elements form more basic oxides. Potassium ($K$) is more metallic than Sodium ($Na$), which is more metallic than Magnesium ($Mg$). Aluminum ($Al$) forms amphoteric oxides. Therefore, the basic strength order $Al_2O_3 < MgO < Na_2O < K_2O$ is correct .

4. Acidic Nature of Hydrides (Option A): For Group 15 hydrides, as the size of the central atom increases ($N < P < As$), the E–H bond strength decreases, making it easier to release a proton ($H^+$). Thus, acidic character increases down the group: $NH_3 < PH_3 < AsH_3$. This is correct.