Discussion

Explanation:

Hands should be in straight line but not together ⇒ hands should be opposite each other.

Angle between the two hands at h : m = |$\left|30h-\frac{11}{2}m\right|$| = 180°.

Between 7 and 8, h = 7.

∴ |$\left|30\times 7-\frac{11}{2}m\right|$| = 180°

⇒ |$\left|210-\frac{11}{2}m\right|$| = 180°

⇒  210 - $\frac{11}{2}$m = ± 180°

Case 1: 210 - $\frac{11}{2}$m = 180°

⇒ $\frac{11}{2}$m = 30°

⇒ m = 60/11 minutes = 5$\frac{5}{11}$  minutes

∴ Hands will be opposite at 5$\frac{5}{11}$ minutes past 7.

Case 2: 210 - $\frac{11}{2}$m = - 180°

⇒ $\frac{11}{2}$m = 370°

⇒ m = $\frac{740}{11}$ (not possible since m should be ≤ 60).

Hence, option (d).

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