Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.
| List-I | List-II |
|---|---|
| (P) XeF$_2$ | (1) Trigonal bipyramidal and two lone pair of electrons |
| (Q) XeF$_4$ | (2) Tetrahedral and one lone pair of electrons |
| (R) XeO$_3$ | (3) Octahedral and two lone pair of electrons |
| (S) XeO$_3$F$_2$ | (4) Trigonal bipyramidal and no lone pair of electrons |
| (5) Trigonal bipyramidal and three lone pair of electrons |
List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.
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List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.
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Let $f(x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f(1)=2$ and
$$ \lim\limits_{t \rightarrow x} \frac{t^{10} f(x)-x^{10} f(t)}{t^9-x^9}=1 $$
for each $x>0$. Then, for all $x>0, f(x)$ is equal to :