JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \( n \) be the number obtained on rolling a fair die. If the probability that the system
\( x-ny+z=6 \)
\( x+(n-2)y+(n+1)z=8 \)
\( (n-1)y+z=1 \)
Has a unique solution is \( \frac{k}{6} \), then the sum of \( k \) and all possible values of \( n \) is:
- A 21
- B 24
- C 20
- D 22
Answer & Solution
Correct Answer
(D) 22
Step-by-step Solution
Detailed explanation
\(x-n y+z=6\) \(x+(n-2) y+(n+1) z=8\) \((n-1) y+z=1\) \(\left|\begin{array}{ccc}1 & - n & 1 \\ 1 & ( n -2) & n +1 \\ 0 & n -1 & 1\end{array}\right| \neq 0\) \(\Rightarrow n^2-3 n+2 \neq 0\) \(n \neq 1,2\) for unique solution \(n =3,4,5,6\) Now \(P\) (probability when system of…
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