Consider sets $A=\{z\in C:z^{27}-1=0\}$ and $B=\{z\in C:z^{36}-1=0\}.$ Now, much the following lists.

	List – I		List – II
A	Number of elements in A which have negative imaginary part is	P	18
B	Number of elements in B which have positive real part is	Q	17
C	Number of elements in $A\cap B$ is	R	13
D	If number of elements in $A\cup B$ is p then p is  divisible by	S	9

We have  $z^{27}-1=0$
The roots of the equation are  $\cos \frac{2k\pi }{27}+i\sin \frac{2k\pi }{27};k=0,1,2,3\mathrm{.....},26.$
This equation has one real root ‘1’. The other 26 roots are in the form of 13 conjugate pairs.
Of these, 13 roots lie above real-axis and the other 13 are lie below real axis.
So, there are 13 roots having negative imaginary part.
The other equation is $z^{36}-1=0.$ 
This equation has two real roots, $\pm 1$ and two purely imaginary roots,  $\pm i$.
Of remaining 32 roots, 16 lie to the right of imaginary axis.
So, there are 17 roots having positive real part.
The roots of the equation are  $\cos \frac{2k\pi }{36}+i\sin \frac{2k\pi }{36};k=0,1,2,3,\mathrm{...},35.$
Number of common roots $\text{=\hspace{0.17em}HCF}\left(\text{27,\hspace{0.17em}36}\right)\text{\hspace{0.17em}=\hspace{0.17em}9}$

$$\begin{gathered} \therefore n(A\cap B)=9 \\ \therefore n(A\cup B)=27+36-9=54 \end{gathered}$$