The correct increasing order for bond angles among \( \text{BF}_3, \, \text{PF}_3, \, \text{and} \, \text{CF}_3 \) is:
\( \text{PF}_3 \, < \, \text{BF}_3 \, < \, \text{CF}_3 \)
\( \text{BF}_3 \, < \, \text{PF}_3 \, < \, \text{CF}_3 \)
\( \text{CF}_3 \, < \, \text{PF}_3 \, < \, \text{BF}_3 \)
\( \text{BF}_3 \, = \, \text{PF}_3 \, < \, \text{CF}_3 \)
To determine the increasing order of bond angles among \( \text{BF}_3, \, \text{PF}_3, \text{and} \, \text{CF}_3 \), we need to understand the molecular geometry and electronic effects influencing these compounds:
Based on these observations, we conclude:
Thus, the increasing order of bond angles is:
\(\text{CF}_3 \, < \, \text{PF}_3 \, < \, \text{BF}_3\)
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$_3$.
Which of the following is the correct statement for an ideal gas (constant =\( \textit{energy}\) )?
The given circuit works as: 
Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4\hat k)$, $\lambda \in \mathbb{R}$ and $L_2 : \vec r = (4\hat i + \hat j) + \mu(5\hat i + + 2\hat j + \hat k)$, $\mu \in \mathbb{R}$ intersect at the point $R$. Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$, respectively, such that $|PR|=\sqrt{29}$ and $|PQ|=\sqrt{\frac{47}{3}}$. If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to}