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1

Numerical
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 Your Input ________ ## Answer Correct Answer is 7 2 ### IIT-JEE 2009 Numerical The smallest value of $$k$$, for which both the roots of the equation $${x^2} - 8kx + 16\left( {{k^2} - k + 1} \right) = 0$$$ are real, distinct and have values at least 4, is
Your Input ________

## Answer

Correct Answer is 2

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