Let m be a positive integer and $\Delta_r=\left|\begin{array}{ccc}2 r-1 & m C_r & 1 \\ m^2-1 & 2^m & m+1 \\ \sin ^2\left(m^2\right) & \sin ^2(m) & \sin \left(m^2\right)\end{array}\right|$. Then the value of $\sum\limits_{r=0}^m \Delta_r$ is given by
Answer & explanation
Correct answer: option 1
Using concept of summation of determinant.
We get R1, R2 are identical so $\sum\limits_{r=0}^m \Delta_r$ is zero.
Hence (1) is the correct answer.