Question

The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\frac{D}{90}=\frac{G}{100}=\frac{2C}{\pi }$ but $1^{\circ }={\left(\frac{180}{\pi }\right)}^{\circ }\simeq {57}^{\circ },{17}^{\prime },44.8^{\prime \prime }$ and sum of interior angles of a $n$-sided regular polygon is $(2n-4)\frac{\pi }{2}$. 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 -

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{5\pi }{12}$
• D. $\frac{7\pi }{12}$

Answer 1

The correct option is C $\frac{5\pi }{12}$

At half past three , the minutes hand will make an angle $\frac{\pi }{2}$ with the horizontal axis

The hours hand will make an angle $\frac{\pi }{12}$ with the horizontal axis

So the angle between hours hand and minutes hand is $\frac{\pi }{2}-\frac{\pi }{12}=\frac{5\pi }{12}$

Therefore the correct option is $C$