At what time between 6 and 7 oclock will the hands of a clock be in the same straight line but not together?

Option 4 : \(5\frac{5}{{11}}\) Minutes past 7

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The two hands of a clock will be in the same straight line but not together between H and (H + 1) o' clock at

\(\left\{ {\begin{array}{*{20}{c}} {\left( {5H - 30} \right)\;\frac{{12}}{{11}}}\\ {Minutes\;past\;H,\;when\;H > 6\;}\\ \;\\ {\left( {5H + 30} \right)\frac{{12}}{{11}}}\\ {minutes\;past\;H.\;when\;H < 6}\\ \; \end{array}} \right.\)

Here H = 7

Hands of the clock will point in opposite directions at

= (5 × 7 - 30)12/11 minutes past 7

= 5 × 12/11 minutes past 7

= 60/11 minutes past 7

\(5\frac{5}{{11}}\) minutes past 7.

Hence, the correct answer is 5(5/11) minutes past 7.

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