Chemical Engineering
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Consider the hyperbolic functions in $\textbf{Group-1}$ and their definitions in $\textbf{Group-2}$.

$\begin{array}{llll} & \textbf{Group-1} & & \textbf{Group-2} \\ \textbf{P} & \tanh x & \textbf{I} & \dfrac{e^x+e^{-x}}{e^x-e^{-x}} \\  \textbf{Q} & \coth x & \textbf{II} & \dfrac{2}{e^x+e^{-x}} \\ \textbf{R} & \text{sech } x & \textbf{III} & \dfrac{2}{e^x-e^{-x}} \\ \textbf{S} & \text{cosech } x & \textbf{IV} & \dfrac{e^x-e^{-x}}{e^x+e^{-x}} \end{array}$

  1. $P-IV, Q-I, R-III, S-II$
  2. $P-II, Q-III, R-I, S-IV$
  3. $P-IV, Q-I, R-II, S-III$
  4. $P-I, Q-II, R-IV, S-III$
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