JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(D _{ k }=\left|\begin{array}{ccc}1 & 2 k & 2 k -1 \\ n & n ^2+ n +2 & n ^2 \\ n & n ^2+ n & n ^2+ n +2\end{array}\right|\). If \(\sum \limits_{ k =1}^n\) \(D _{ k }=96\), then \(n\) is equal to
- A \(3\)
- B \(5\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(D _{ k }=\left|\begin{array}{ccc}1 & 2 k & 2 k -1 \\ n & n ^2+ n +2 & n ^2 \\ n & n ^2+ n & n ^2+ n +2\end{array}\right|\) \(\sum \limits_{ k =1}^{ n } D _{ k }=96 \Rightarrow\)…
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