Question

Which among the following statement is incorrect?
I. The angle between two consecutive digits in a clock is $30^{\circ }$.
II. The minute hand rotates through an angle of $6^{\circ }$ in a minute.
III. The hour hand rotates through an angle of $30^{\circ }$ in one hour i.e., $(1/2{)}^{\circ }$ in a minute.
IV. The second hand rotates through an angle of $180^{\circ }$ in a minute.

• A. I is incorrect
• B. II is incorrect
• C. III is incorrect
• D. IV is incorrect

Answer 1

Answer: (D)

The number of digits in a clock is 12 .
So, the angle between two consecutive digits in a clock is
$=\frac{360^{\circ }}{12}=30^{\circ }$
or $\frac{\pi }{6}$ radian.
The minute hand rotates through $360^{\circ }$ in $60\min$.
So, in $1\min$ it rotates through $\frac{360^{\circ }}{60}=6^{\circ }$.
The hour hand rotates through $360^{\circ }$ in $12h$.
So, in one hour it rotates through $\frac{360^{\circ }}{12}=30^{\circ }$ and in one minute it rotates through $\frac{30^{\circ }}{60}={\left(\frac{1}{2}\right)}^{\circ }$. The second hand rotates through $360^{\circ }$ in a minute.
Thus, we see that option (d) is incorrect.