let \(\lambda\neq 0\) be in r.If \(\alpha\) and \(\beta\) are the roots of the equation, then x2-x+2\(\lambda\)=0 and \(\alpha\) and \(\gamma\) are the roots of the equation, 3x2-10x+27\(\lambda\)=0,then \(\frac{\beta\gamma}{\lambda}=?\)
36
27
9
18
The correct answer is option (D) : 18
Match the following List-I with List-II and choose the correct option: List-I (Compounds) | List-II (Shape and Hybridisation) (A) PF\(_{3}\) (I) Tetrahedral and sp\(^3\) (B) SF\(_{6}\) (III) Octahedral and sp\(^3\)d\(^2\) (C) Ni(CO)\(_{4}\) (I) Tetrahedral and sp\(^3\) (D) [PtCl\(_{4}\)]\(^{2-}\) (II) Square planar and dsp\(^2\)
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to: