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Mathematics

Statement I: From 8:00 PM to 8:50 PM, the minute hand of a clock covers an angle of 300°.

Statement II: 56×360∘=300∘\dfrac{5}{6} \times 360^\circ = 300^\circ.

  1. Statement I is true but statement II is false.

  2. Statement I is false but statement II is true.

  3. Both Statement I and statement II are true.

  4. Both Statement I and statement II are false.

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Answer

Statement I:

From 8:00 PM to 8:50 PM, the minute hand moves through 50 minutes.

In 60 minutes (1 full revolution), the minute hand covers 360°.

In 50 minutes, the minute hand covers = 5060×360∘\dfrac{50}{60} \times 360^\circ = 56×360∘\dfrac{5}{6} \times 360^\circ = 300°.

∴ Statement I is true.

Statement II:

56×360∘\dfrac{5}{6} \times 360^\circ = 5×360∘6\dfrac{5 \times 360^\circ}{6} = 1800∘6\dfrac{1800^\circ}{6} = 300°.

∴ Statement II is true.

Both statements are true.

Hence, option 3 is the correct option.

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