Match the following complexes with their number of unpaired electrons:
List-I (Complex) | List-II (No. of unpaired electrons) | ||
---|---|---|---|
A) \([\mathrm{MnCl}_6]^{3-}\) | I) 5 | ||
B) \([\mathrm{FeF}_6]^{3-}\) | II) 2 | ||
C) \([\mathrm{Mn(CN)}_6]^{3-}\) | III) 0 | ||
D) \([\mathrm{Co(C}_2\mathrm{O}_4)_3]^{3-}\) | IV) 4 |
If \( \vec{u}, \vec{v}, \vec{w} \) are non-coplanar vectors and \( p, q \) are real numbers, then the equality:
\[ [3\vec{u} \quad p\vec{v} \quad p\vec{w}] - [p\vec{v} \quad \vec{w} \quad q\vec{u}] - [2\vec{w} \quad q\vec{v} \quad q\vec{u}] = 0 \]
holds for:
Statement-I: In the interval \( [0, 2\pi] \), the number of common solutions of the equations
\[ 2\sin^2\theta - \cos 2\theta = 0 \]
and
\[ 2\cos^2\theta - 3\sin\theta = 0 \]
is two.
Statement-II: The number of solutions of
\[ 2\cos^2\theta - 3\sin\theta = 0 \]
in \( [0, \pi] \) is two.
If \( A \) and \( B \) are acute angles satisfying
\[ 3\cos^2 A + 2\cos^2 B = 4 \]
and
\[ \frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}, \]
Then \( A + 2B = \ ? \)