List-I (Molecule) | List-II (Shape) |
---|---|
(A) \(NH_3\) | (I) Square pyramid |
(B) \(BrF_5\) | (II) Tetrahedral |
(C) \(PCL_5\) | (III) Trigonal pyramidal |
(D) \(CH_4\) | (IV) Trigonal bipyramidal |
NH$_3$: Trigonalpyramidal ({sp}$^3$ hybridization with one lone pair on N).
BrF$_5$: Squarepyramidal ({sp}$^3${d}$^2$ hybridization with one lone pair on Br).
PCl$_5$: Trigonalbipyramidal ({sp}$^3${d} hybridization, no lone pairs).
CH$_4$: Tetrahedral ({sp}$^3$ hybridization, no lone pairs).
Matching: A-III, B-I, C-IV, D-II.
Final Answer: A-III, B-I, C-IV, D-II.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: