JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equations \(x+y+z=5\) ; \(x+2 y+3 z=\mu\) ; \(x+3 y+\lambda z=1\) is constructed. If \(\mathrm{p}\) is the probability that the system has a unique solution and \(\mathrm{q}\) is the probability that the system has no solution, then :
- A \(\mathrm{p}=\frac{1}{6}\) and \(\mathrm{q}=\frac{1}{36}\)
- B \(\mathrm{p}=\frac{5}{6}\) and \(\mathrm{q}=\frac{5}{36}\)
- C \(\mathrm{p}=\frac{5}{6}\) and \(\mathrm{q}=\frac{1}{36}\)
- D \(\mathrm{p}=\frac{1}{6}\) and \(\mathrm{q}=\frac{5}{36}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{p}=\frac{5}{6}\) and \(\mathrm{q}=\frac{5}{36}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{D} \neq 0 \Rightarrow\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda\end{array}\right| \neq 0 \Rightarrow \lambda \neq 5\) For no solution \(\mathrm{D}=0 \Rightarrow \lambda=5\)…
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