The correct increasing order for bond angles among \( \text{BF}_3, \, \text{PF}_3, \, \text{and} \, \text{CF}_3 \) is:
\( \text{PF}_3 \, < \, \text{BF}_3 \, < \, \text{CF}_3 \)
\( \text{BF}_3 \, < \, \text{PF}_3 \, < \, \text{CF}_3 \)
\( \text{CF}_3 \, < \, \text{PF}_3 \, < \, \text{BF}_3 \)
\( \text{BF}_3 \, = \, \text{PF}_3 \, < \, \text{CF}_3 \)
BF$_3$: Planar structure with 120$^\circ$ bond angles ($sp^2$ hybridization).
PF$_3$: Tetrahedral geometry distorted by lone pair on phosphorus, bond angle $<$ 109.5$^\circ$.
CF$_3$: Tetrahedral geometry with strong electron-withdrawing fluorine atoms, bond angle $\sim$ 104$^\circ$.
The order of bond angles is CF$_3$ $<$ PF$_3$ $<$ BF$_3$.
In the circuit shown, assuming the threshold voltage of the diode is negligibly small, then the voltage \( V_{AB} \) is correctly represented by:
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: