If y = f(x) represents a straight line passing through origin and not passing through any of the points with integral Co-ordinates in the co-ordinate plane. Then the number of such continuous functions on ‘R’ is ( it is known that straight line represents a function)

Finite

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Infinite

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At most one

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Solution

The correct option is B Infinite
$\exists$ infinitely many continuous functions of the form f(x) = mx. When m is Irrational, and when slope is irrational the line obviously will not pass through any of the pts in the Co-ordinate plane with integral Co-ordinates. We know a straight line is always continuous.

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