Question

Choose the correct option, if List I denotes polar co-ordinates and List II contains cartesian co-ordinates:

LIST-I	LIST-II
A) $(2,\frac{3\pi }{4})$	1. $(0,3)$
B) $(5,\frac{\pi }{4})$	2. $(-\sqrt{2,}\sqrt{2})$
C) $(3,\frac{\pi }{2})$	3. $(2,2\sqrt{3})$
D) $(4,\frac{\pi }{3})$	4. $(\frac{5}{\sqrt{2}},\frac{5}{\sqrt{2}})$

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

Answer 1

The correct option is D $A-2,B-4,C-1,D-3$

A) $(2,\frac{3\pi }{4})$

$\Rightarrow r=2,\theta =\frac{3\pi }{4}$

We have $x=r\cos \theta ,y=r\sin \theta$
$x=2\cos \frac{3\pi }{4},y=2\sin \frac{3\pi }{4}$
$\Rightarrow x=-\sqrt{2},y=\sqrt{2}$
B) $(5,\frac{\pi }{4})$

$\Rightarrow r=5,\theta =\frac{\pi }{4}$

We have $x=r\cos \theta ,y=r\sin \theta$
$x=5\cos \frac{\pi }{4},y=5\sin \frac{\pi }{4}$
$\Rightarrow x=\frac{5}{\sqrt{2}},y=\frac{5}{\sqrt{2}}$

C) $(3,\frac{\pi }{2})$

$\Rightarrow r=3,\theta =\frac{\pi }{2}$

We have $x=r\cos \theta ,y=r\sin \theta$
$x=3\cos \frac{\pi }{2},y=3\sin \frac{\pi }{2}$
$\Rightarrow x=0,y=3$

D) $(4,\frac{\pi }{3})$

$\Rightarrow r=4,\theta =\frac{\pi }{3}$

We have $x=r\cos \theta ,y=r\sin \theta$
$x=4\cos \frac{\pi }{3},y=4\sin \frac{\pi }{3}$
$\Rightarrow x=2,y=2\sqrt{3}$