Let the function $ f(x) $ be defined as follows: $$ f(x) = \begin{cases} (1 + | \sin x |)^{\frac{a}{|\sin x|}}, & -\frac{\pi}{6}<x<0 \\b, & x = 0 \\ \frac{\tan 2x}{\tan 3x}, & 0<x<\frac{\pi}{6} \end{cases} $$ Then the values of $ a $ and $ b $ are:
| LIST I | LIST II | ||
| A. | \(\lim\limits_{x\rightarrow0}(1+sinx)^{2\cot x}\) | I. | e-1/6 |
| B. | \(\lim\limits_{x\rightarrow0}e^x-(1+x)/x^2\) | II. | e |
| C. | \(\lim\limits_{x\rightarrow0}(\frac{sinx}{x})^{1/x^2}\) | III. | e2 |
| D. | \(\lim\limits_{x\rightarrow\infty}(\frac{x+2}{x+1})^{x+3}\) | IV. | ½ |
Match List-I with List-II 
Match List-I with List-II\[\begin{array}{|c|c|} \hline \textbf{Provision} & \textbf{Case Law} \\ \hline \text{(A) Strict Liability} & \text{(1) Ryland v. Fletcher} \\ \hline \text{(B) Absolute Liability} & \text{(II) M.C. Mehta v. Union of India} \\ \hline \text{(C) Negligence} & \text{(III) Nicholas v. Marsland} \\ \hline \text{(D) Act of God} & \text{(IV) MCD v. Subhagwanti} \\ \hline \end{array}\]