A) \[\frac{1}{2}\]
B) \[\frac{2}{3}\]
C) \[\frac{3}{4}\]
D) \[\frac{\pi }{2}\]
Correct Answer: C
Solution :
Let the length of circumference in \[2l.\]Let \[x\] denotes the clockwise are length of \[PQ\] and let \[y\] denotes the clockwise are length of \[PR.\] then \[0<x<2l\,\operatorname{and}\,<y<2l\] |
Thus, sample space is the set of points inside a square of edge length \[2l.\] |
Now \[P,Q,R\]lie on a semicircle under following conditions: |
(1) \[x<l,y<l\] |
(2) \[x<l\,\operatorname{and}\,y-x>l\] |
(3) \[x>l,y>l\] |
(4) \[y<l,\,and\,x-y>l\] |
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