Among the given elements, Cr has the least metallic radii. The CrO$_4^{2-}$ ion has Cr$^{6+}$, which has a $d^0$ configuration (diamagnetic).
The spin-only magnetic moment:
\[\mu = \sqrt{n(n+2)} \, \text{BM},\]
where $n = 0$.
Final Answer:
\[0 \, \text{BM}.\]
Match List - I with List - II:
List - I:
(A) \([ \text{MnBr}_4]^{2-}\)
(B) \([ \text{FeF}_6]^{3-}\)
(C) \([ \text{Co(C}_2\text{O}_4)_3]^{3-}\)
(D) \([ \text{Ni(CO)}_4]\)
List - II:
(I) d²sp³ diamagnetic
(II) sp²d² paramagnetic
(III) sp³ diamagnetic
(IV) sp³ paramagnetic
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: