question_answer

The number of real solutions of\[(x,\,\,y),\] where \[y=\,|\], \[\sin \,x\,|,\,\,y={{\cos }^{-1}}(\cos \,x),\]\[-2\pi \le \,x\le 2\pi ,\] is

A)  2                                

B)  1                 

C)  3                                

D)  4

Correct Answer: C

Solution :

 for \[{{m}_{1}}=\frac{M}{4},\,{{x}_{1}}=\frac{R}{2}\] For \[{{m}_{2}}=\frac{3M}{4}\] \[{{x}_{2}}=-\frac{M/4}{3M/4}\cdot \frac{R}{2}=\frac{-R}{6}\] For \[\frac{R}{6}\], \[{{d}_{w}}\] For \[{{d}_{o}}\] \[h{{d}_{w}}g={{h}_{w}}{{d}_{w}}g+{{h}_{o}}{{d}_{o}}g\] On plotting the graphs we have