Three  vectors act at a point ‘O’ as shown in figure . For given value of P and $\theta$ the correct options are 

a) If $\theta =0$and $P=10\sqrt{2}N$   then  resultant  is $=\sqrt{P^2+{20}^2}=\sqrt{200+400}=10\sqrt{6}N$

b) If $\theta =90°$ and P = 10Nthe resultant  = 10N

C)

If $\theta =\frac{3\pi }{2}$and P = 10N; The resultant is $=30\widehat{i}$
d)

If P = 10 N and $\theta =30°$ ; Resultant  $\overrightarrow{R}=15\widehat{i}+5\sqrt{3}\widehat{j}$

$R=\sqrt{225+75}=\sqrt{300}=10\sqrt{3}N$