LIST-I | LIST-II | ||
---|---|---|---|
I | \(\text{[Cr(CN)}_6\text{]}^{4-}\) | P | t2g orbitals contain 4 electrons |
II | \(\text{[RuCl}_6\text{]}^{2-}\) | Q | \(\mu\)(spin-only) = 4.9 BM |
III | \(\text{[Cr(H}_2\text{O)}_6\text{]}^{2+}\) | R | low spin complex ion |
IV | \(\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}\) | S | metal ion in 4+ oxidation state |
T | d4 species |
I → R, T; II → P, S; III → Q, T; IV → P, Q
I → R, S; II → P, T; III → P, Q; IV → Q, T
I → P, R; II → R, S; III → R, T; IV → P, T
I → Q, T; II → S, T; III → P, T; IV → Q, R
(I) \(\text{[Cr(CN)}_6\text{]}^{4-}\)
The Cr2+ ion, with the electron configuration [Ar] 3d4 4s0, undergoes d2sp3 hybridization due to the strong field ligand CN–.
(II) \(\text{[RuCl}_6\text{]}^{2-}\):
The Ru4+ ion, with the electron configuration [Kr] 4d4 5s0, has a t2g set that contains four electrons.
(III) \(\text{[Cr(H}_2\text{O)}_6\text{]}^{2+}\):
The Cr2+ ion, with the electron configuration [Ar] 3d4 4s0, exhibits four unpaired electrons due to the weak field ligand H2O, resulting in a magnetic moment of 4.9 B.M.
(IV) \(\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}\)
The Fe2+ ion, with the electron configuration [Ar] 3d6 4s0, also possesses four unpaired electrons, resulting in a magnetic moment of 4.9 B.M.
Hence option A is Correct
In the following species, how many species have the same magnetic moment?
(i) Cr\(^{2+}\)
(ii) Mn\(^{3+}\)
(iii) Ni\(^{2+}\)
(iv) Sc\(^{2+}\)
(v) Zn\(^{2+}\)
(vi) V\(^{3+}\)
(vii) Ti\(^{4+}\)
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.