Multiple choice

The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\displaystyle \frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $\displaystyle 1^{\circ}=\left ( \frac{180}{\pi } \right )^{\circ}:\simeq 57^{\circ},17',44.{8}''$ and sum of interior angles of a $n$-sided regular polygon is $\displaystyle \left ( 2n-4 \right )\dfrac {\pi }2$. On the basis of above information, answer the following questions : The angles between the hour hand and minute hand of a clock at half past three is -

  1. $\displaystyle \frac{\pi }{3}$
  2. $\displaystyle \frac{\pi }{4}$
  3. $\displaystyle \frac{5\pi }{12}$
  4. $\displaystyle \frac{7\pi }{12}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 3:30, the minute hand is at 180 degrees and the hour hand is at 105 degrees. Their smaller angle is 75 degrees, which equals 75 × pi/180 = 5pi/12 radians. Therefore, option C is correct.

AI explanation

Using the clock angle formula, the minute hand at 30 minutes is at 180 degrees, while the hour hand is at 90 degrees plus 0.5 multiplied by 30, which equals 105 degrees. The difference between the two hands is 180 minus 105, resulting in 75 degrees. Converting this angle to radians, 75 multiplied by pi divided by 180 simplifies to 5pi divided by 12.

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