question_answer

If  \[{{\text{ }\!\!\Delta\!\!\text{ }}_{\text{r}}}\text{=}\left| \begin{matrix}    \text{2r-1} & ^{\text{m}}{{\text{C}}_{\text{r}}} & \text{1}  \\    {{\text{m}}^{\text{2}}}\text{-1} & {{\text{2}}^{\text{m}}} & \text{m+1}  \\    \text{si}{{\text{n}}^{\text{2}}}\left( {{\text{m}}^{\text{2}}} \right) & \text{si}{{\text{n}}^{\text{2}}}\left( \text{m} \right) & \text{si}{{\text{n}}^{\text{2}}}\left( \text{m+1} \right)  \\ \end{matrix} \right|\text{,}\] then value of \[\sum\limits_{r=0}^{m}{{{\Delta }_{r}}}\] is

A) 1                                             

B)  0

C)  2                                            

D) None of these