| List-I (Molecule / Species) | List-II (Property / Shape) |
|---|---|
| (A) \(SO_2Cl_2\) | (I) Paramagnetic |
| (B) NO | (II) Diamagnetic |
| (C) \(NO^{-}_{2}\) | (III) Tetrahedral |
| (D) \(I^{-}_{3}\) | (IV) Linear |
(A) SO$_2$Cl$_2$: Hybridization is sp$^3$, Tetrahedral shape.
(B) NO: Unpaired electron, hence Paramagnetic.
(C) NO$_2^-$: Paired electrons, hence Diamagnetic.
(D) I$_3^-$: Linear shape with sp$^3$d hybridization.
To solve the problem of matching molecules/species with their properties or shapes, let's systematically analyze each molecule listed under List-I and match them with the appropriate category from List-II.
After analyzing each molecule/species, the correct matches are established as follows:
Therefore, the correct match-answer is: A-III, B-I, C-II, D-IV.
Temperature of a body \( \theta \) is slightly more than the temperature of the surroundings \( \theta_0 \). Its rate of cooling \( R \) versus temperature \( \theta \) graph should be 
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}