The correct match of the group reagents in List-I for precipitating the metal ion given in List-II from solutions is:
| List-I | List-II |
|---|---|
| (P) Passing H2S in the presence of NH4OH | (1) Cu2+ |
| (Q) (NH4)2CO3 in the presence of NH4OH | (2) Al3+ |
| (R) NH4OH in the presence of NH4Cl | (3) Mn2+ |
| (S) Passing H2S in the presence of dilute HCl | (4) Ba2+ (5) Mg2+ |
P → 5; Q → 3; R → 2; S → 4
(P) H\(_2\)S + NH\(_4\)OH → Precipitates Group IV cations
Group IV cations include Mn\(^{2+}\), Zn\(^{2+}\), Co\(^{2+}\), etc., which precipitate as sulfides in basic medium. \[ \Rightarrow \text{P} \rightarrow \boxed{3} \quad \text{(Mn}^{2+}\text{)} \] (Q) (NH\(_4\))\(_2\)CO\(_3\) + NH\(_4\)OH → Precipitates Group V cations
This group includes alkaline earth metals like Ba\(^{2+}\), Ca\(^{2+}\), Sr\(^{2+}\), which form carbonates. \[ \Rightarrow \text{Q} \rightarrow \boxed{4} \quad \text{(Ba}^{2+}\text{)} \] (R) NH\(_4\)OH + NH\(_4\)Cl → Precipitates Group III cations
Group III cations like Al\(^{3+}\), Cr\(^{3+}\), Fe\(^{3+}\) form hydroxides in weakly basic conditions. \[ \Rightarrow \text{R} \rightarrow \boxed{2} \quad \text{(Al}^{3+}\text{)} \] (S) H\(_2\)S + dilute HCl → Precipitates Group II cations
Group II includes Cu\(^{2+}\), Pb\(^{2+}\), Hg\(^{2+}\) which form sulfides in acidic medium. \[ \Rightarrow \text{S} \rightarrow \boxed{1} \quad \text{(Cu}^{2+}\text{)} \]
Final Answer: \( \boxed{\text{A}} \)
In the group analysis of cations, Ba$^{2+}$ & Ca$^{2+}$ are precipitated respectively as
Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?