JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S\) be the set of all integer solutions, \((x, y, z)\), of the system of equations \(x-2 y+5 z=0\) \(-2 x+4 y+z=0\) \(-7 x+14 y+9 z=0\) such that \(15 \leq x^{2}+y^{2}+z^{2} \leq 150 .\) Then, the number of elements in the set \(S\) is equal to
- A \(16\)
- B \(-8\)
- C \(-16\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}1 & -2 & 5 \\ -2 & 4 & 1 \\ -7 & 14 & 9\end{array}\right|=0\) Let \(\quad x=k\) \(\Rightarrow \quad\) Put in \((1)\;and\;(2)\) \(k-2 y+5 z=0\) \(-2 k+4 y+z=0\) \(z=0, y=\frac{k}{2}\) \(\therefore \quad x , y , z\) are integer…
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