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 |
\(\textbf{(A) $N_2(g) + O_2(g) \rightarrow 2NO(g)$:}\) 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 one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
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: