Question

Match the terms of Column I with the terms of Column II and choose the correct options from the codes given below.

Column I (Degree Measure)		Column II (Radian Measure)
A	$25^{\circ}$	1	$\frac{26\pi}{9}$
B	$-47^{\circ} \, 30'$	2	$\frac{4\pi}{3}$
C	$240^{\circ}$	3	$\frac{-19\pi}{72}$
D	$520^{\circ}$	4	$\frac{5\pi}{36}$

• A. A - (4), B -(1), C -(2), D -(3)
• B. A - (4), B -(3), C -(2), D -(1)
• C. A - (1), B -(3), C -(2), D -(4)
• D. A - (1), B -(4), C -(3), D -(2)

Answer 1

Answer: (B)

We know that,
Radian measure $=\frac{\pi}{180} \times$ Degree measure
A. Radian measure of $25^{\circ}=\frac{\pi}{180} \times 25^{\circ}=\frac{5 \pi}{36}$
B. We know that, $30^{\prime}=\left(\frac{1}{2}\right)^{\circ} \left(\because 60^{\prime}=1^{\circ}\right)$
$\therefore-47^{\circ} 30^{\prime}=-\left(47 \frac{1}{2}\right)^{\circ}=\left(\frac{-95}{2}\right)^{\circ}$
$\therefore$ Radian measure of $\left(-47^{\circ} 30^{\prime}\right)=\frac{\pi}{180} \times\left(\frac{-95}{2}\right)$ $=\frac{-19 \pi}{72}$
C. Radian measure of $240^{\circ}=\frac{\pi}{180} \times 240=\frac{4 \pi}{3}$
D. Radian measure of $520^{\circ}=\frac{\pi}{180} \times 520=\frac{26 \pi}{9}$
So, $A \rightarrow 4, B \rightarrow 3, C \rightarrow 2, D \rightarrow 1$
$\therefore$ Correct answer is (b).