JEE (Advanced) 2019 Paper-2 Question 45

Question 45

Suppose
$$det\begin{bmatrix} \sum_{k = 0}^nk & \sum_{k = 0}^n {^nC_k k^2} \\\sum_{k = 0}^n {^n C_k k} & \sum_{k = 0}^n {^n C_k 3^k} \end{bmatrix} = 0$$
holds for somepositive integer n. Then $$\sum_{k = 0}^n \frac {^nC_k}{k + 1}$$ Equals __________


Correct Answer: e



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