JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(N\) denote the number that turns up when a fair die is rolled. If the probability that the system of equations \(x+y+z=1\) ; \(2 x+N y+2 z=2\) ; \(3 x+3 y+N z=3\) has unique solution is \(\frac{k}{6}\), then the sum of value of \(k\) and all possible values of \(N\) is
- A \(18\)
- B \(19\)
- C \(20\)
- D \(21\)
Answer & Solution
Correct Answer
(C) \(20\)
Step-by-step Solution
Detailed explanation
\(x+y+z=1\) \(2 x+N y+2 z=2\) \(3 x+3 y+N z=3\) \(\Delta=\left|\begin{array}{ccc}1 & 1 & 1 \\2 & N & 2 \\3 & 3 & N\end{array}\right| =( N -2)( N -3)\)For unique solution \(\Delta \neq 0\) So \(N \neq 2,3\) \(\Rightarrow P (\) system has unique solution \()=\frac{4}{6}\) So…
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