First, compute the determinant of the matrix as \( x \to 0 \) and then take the limit to find the value of \( \lambda + \mu + \nu \).
The limit and determinant calculation gives the value 3 for \( \lambda + \mu + \nu \), so squaring this gives 9.
Final Answer: \( (\lambda + \mu + \nu)^2 = 9 \).
Given below are two statements:
Statement (I): The first ionization energy of Pb is greater than that of Sn.
Statement (II): The first ionization energy of Ge is greater than that of Si.
In light of the above statements, choose the correct answer from the options given below:
The compound with molecular formula C\(_6\)H\(_6\), which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ___ \(\pi\) electrons.