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IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
Let $$\left( {x,\,y,\,z} \right)$$ be points with integer coordinates satisfying the system of homogeneous equation: $$$\matrix{ {3x - y - z = 0} \cr { - 3x + z = 0} \cr { - 3x + 2y + z = 0} \cr } $$$

Then the number of such points for which $$^2 + {y^2} + {z^2} \le 100$$ is

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