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TS EAMCET · Maths · Determinants

\(\begin{aligned} & \text { If }\left|\begin{array}{ccc}n^2 & (n+1)^2 & (n+2)^2 \\ (n+1)^2 & (n+2)^2 & (n+3)^2 \\ (n+2)^2 & (n+3)^2 & (n+4)^2\end{array}\right|=\Delta \text { and } \\ & \left|\begin{array}{ccc}1 & -4 & 7 \\ -2 & 3 & -5 \\ 3 & x & -3\end{array}\right|=2 \Delta+1, \text { then } x=\end{aligned}\)

  1. A \(3\)
  2. B \(4\)
  3. C \(5\)
  4. D \(6\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(3\)

Step-by-step Solution

Detailed explanation

Given determinant \(\Delta=\left|\begin{array}{ccc}n^2 & (n+1)^2 & (n+2)^2 \\ (n+1)^2 & (n+2)^2 & (n+3)^2 \\ (n+2)^2 & (n+3)^2 & (n+4)^2\end{array}\right|\) On applying \(R_2 \rightarrow R_2-R_1\) and \(R_3 \rightarrow R_3-R_1\), we get…