| List-I Reaction | List-II Type of redox reaction |
|---|---|
| (A) N2(g) + O2(g) → 2NO(g) | (I) Decomposition |
| (B) 2Pb (NO3)2(s) → 2PbO(s) + 4NO2(g) + O2(g) | (II) Displacement |
| (C) 2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g) | (III) Disproportionation |
| (D) 2NO2(g) + 2OH-(aq) → NO2-(aq) + NO3-(aq) + H2O(l) | (IV) Combination |
To solve the given problem, we need to match each reaction in List-I with the corresponding type of redox reaction mentioned in List-II.
Step-by-step Explanation:
Matching the reactions with the type:
| List-I Reaction | List-II Type of Redox Reaction |
|---|---|
| (A) N2(g) + O2(g) → 2NO(g) | (IV) Combination |
| (B) 2Pb(NO3)2(s) → 2PbO(s) + 4NO2(g) + O2(g) | (I) Decomposition |
| (C) 2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g) | (II) Displacement |
| (D) 2NO2(g) + 2OH-(aq) → NO2-(aq) + NO3-(aq) + H2O(l) | (III) Disproportionation |
Therefore, the correct answer is (A)-(IV), (B)-(I), (C)-(II), (D)-(III).
\(\textbf{(A) $N_2(g) + O_2(g) \rightarrow 2NO(g)$:}\) This reaction is a combination reaction because two reactants combine to form a single product. Thus, $A \rightarrow (IV)$.
\(\textbf{(B) $2Pb(NO_3)_2(s) \rightarrow 2PbO(s) + 4NO_2(g) + O_2(g)$:} \\\) This is a decomposition reaction because a single compound breaks down into multiple products. Thus, $B \rightarrow (I)$.
\(\textbf{(C) $2Na(s) + 2H_2O \rightarrow 2NaOH(aq) + H_2(g)$:} \\\) This is a displacement reaction as sodium displaces hydrogen from water. Thus, $C \rightarrow (II)$.
\(\textbf{(D) $2NO_2(g) + 2OH^-(aq) \rightarrow NO^-_2(aq) + NO^-_3(aq) + H_2O(l)$:} \\\) This reaction involves disproportionation because the same species ($NO_2$) is oxidized and reduced simultaneously. Thus, $D \rightarrow (III)$.
Let \( C_{t-1} = 28, C_t = 56 \) and \( C_{t+1} = 70 \). Let \( A(4 \cos t, 4 \sin t), B(2 \sin t, -2 \cos t) \text{ and } C(3r - n_1, r^2 - n - 1) \) be the vertices of a triangle ABC, where \( t \) is a parameter. If \( (3x - 1)^2 + (3y)^2 = \alpha \) is the locus of the centroid of triangle ABC, then \( \alpha \) equals: