A) \[\max (p,q)<\max (p,q,r)\]
B) \[\min (p,q)=\frac{1}{2}(p+q-\left| p-q \right|)\]
C) \[\max (p,q)<\min (p,q,r)\]
D) None of these
Correct Answer: B
Solution :
| if \[p=5,q=3,r=2\] |
| \[\max (p,q)=5;\,\,\,\,\,\max (p,q,r)=5\] |
| \[\Rightarrow \]\[\max (p,q)=\,\,\,max(p,q,r)\] |
| \[\therefore \] [a] is not true. Similarly we can show that [c] is not true. |
| Also \[\min (p,q)=\frac{1}{2}(p+q-\left| p-q \right|)\,\] |
| Let \[q<p\]then \[LHS=p\] |
| and \[R.H.S=\frac{1}{2}(p+q-q+p)=p\] |
| Similarly, we can prove that [b] is true for \[q>p\]too. |
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