Match the following: List I (Ore) List II (Composition)
Step 1: - Siderite is a mineral that primarily contains iron carbonate (\( FeCO_3 \)). Thus, it corresponds to composition III.
Step 2: - Malachite is a copper carbonate mineral (\( CuCO_3 . Cu(OH)_2 \)). Hence, it matches with V.
Step 3: - Sphalerite is a zinc sulfide mineral (\( ZnS \)). Therefore, it corresponds to I.
Step 4: - Zincite is an ore of zinc and contains zinc oxide (\( ZnO \)). Therefore, it matches with II. Thus, the correct matching is: \[ A-III, B-V, C-I, D-II \]
In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl. The percentage composition of chlorine in the compound is ___________%. [Given: Molar mass in g mol\(^{-1}\) of Ag = 108, Cl = 35.5]
If \( \sqrt{5} - i\sqrt{15} = r(\cos\theta + i\sin\theta), -\pi < \theta < \pi, \) then
\[ r^2(\sec\theta + 3\csc^2\theta) = \]
For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).