The equation $p cos x - q sin x = r$ admits of a solution of $x$ only if

r < m a x {p, q}

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- \sqrt{p^{2} + q^{2}} < r < \sqrt{p^{2} + q^{2}}

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r^{2} = p^{2} + q^{2}

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none of these

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Solution

The correct option is D none of these
Given, $p cos x - q sin x = r$
so the range of L.H.S is $[- \sqrt{p^{2} + q^{2}}, \sqrt{p^{2} + q^{2}}]$
therefore given equation posses solution only if,
$- \sqrt{p^{2} + q^{2}} \leq r \leq \sqrt{p^{2} + q^{2}}$

hence option D is correct choice.

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