If $$\mathrm{g}$$ is the inverse of $$\mathrm{f}$$ and $$\mathrm{f}^{\prime}(x)=\frac{1}{1+x^3}$$, then $$\mathrm{g}^{\prime}(x)$$ is

A problem in statistics is given to three students A, B and C. Their probabilities of solving the problem are $$\frac{1}{2}, \frac{1}{3}$$ and $$\frac{1}{4}$$ respectively. If all of them try independently, then the probability, that problem is solved, is

Let $$A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right], B=\left[\begin{array}{c}6 \\ 11 \\ 0\end{array}\right]$$ and $$X=\left[\begin{array}{l}a \\ b \\ c\end{array}\right]$$, if $$\mathrm{AX}=\mathrm{B}$$, then the value of $$2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}$$ is

$$f(x)=\left\{\begin{array}{ll} \frac{1-\cos k x}{x^2}, & \text { if } x \leq 0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & \text { if } x>0 \end{array}\right. \text { is continuous at }$$ $$x=0$$, then the value of $$\mathrm{k}$$ is