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	$-47^{\circ }30^{\prime }$	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, $A\to 4,B\to 3,C\to 2,D\to 1$
$\therefore$ Correct answer is (b).