Match the LIST-I with LIST-II.
Choose the correct answer from the options given below :
Let's analyze the molecular structures: ICl\(^-\): This ion has a central iodine atom with 2 bonding pairs and 3 lone pairs, resulting in a 2 : 3 ratio (option III). H\(_2\)O:
The oxygen atom has 2 lone pairs and 2 bonding pairs, which gives the ratio 2 : 2 (option IV). SO\(_2\):
The sulfur atom has 2 bonding pairs and 1 lone pair, leading to a 4 : 1 ratio (option II).
XeF\(_4\): The xenon atom has 4 bonding pairs and 2 lone pairs, giving the ratio 4 : 2 (option I).
Therefore, the correct matching is: A-III, B-IV, C-II, D-I.
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
Let \[ I(x) = \int \frac{dx}{(x-11)^{\frac{11}{13}} (x+15)^{\frac{15}{13}}} \] If \[ I(37) - I(24) = \frac{1}{4} \left( b^{\frac{1}{13}} - c^{\frac{1}{13}} \right) \] where \( b, c \in \mathbb{N} \), then \[ 3(b + c) \] is equal to: