Chromium in chromyl chloride (CrO$_2$Cl$_2$):
Oxidation state of Cr is +6.
Electronic configuration: Cr$^{6+}$ = [Ar] 3d$^0$ 4s$^0$, meaning there are zero d-electrons.
Manganese in Mn (VII):
Oxidation state of Mn is +7.
Electronic configuration: Mn$^{7+}$ = [Ar] 3d$^0$ 4s$^0$, also zero d-electrons.
Thus, the number of d-electrons is the same for Cr in CrO$_2$Cl$_2$ and Mn in Mn (VII).
Given below are the quantum numbers for 4 electrons.
A. n=3, l=2, ml=1,ms=+\(\frac{1}{2}\)
B. n=4, l=1, ml=0,ms=+\(\frac{1}{2}\)
C. n=4, l=2, ml=–2,ms=–\(\frac{1}{2}\)
D. n=3, l=1, ml=–1,ms=+\(\frac{1}{2}\)
The correct order of increasing energy is
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.