If $\mathrm{f}(x)=\frac{x^2-x}{x^2+2 x}$ then $\frac{\mathrm{d}}{\mathrm{d} x}\left(\mathrm{f}^{-1}(x)\right)$ at $x=2$ is

For the triangle ABC , with usual notations, if the angles $A, B, C$ are in A.P. and $\mathrm{m} \angle \mathrm{A}=30^{\circ}, \mathrm{c}=3$, then the values of a and b are respectively

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively

Let k be a non-zero real number. If $f(x)=\left\{\begin{array}{cl}\frac{\left(\mathrm{e}^x-1\right)^2}{\sin \left(\frac{x}{k}\right) \log \left(1+\frac{x}{4}\right)} & , x \neq 0 \\ 12 & , x=0\end{array}\right.$ is a continuous function, then the value of $k$ is