A) 7
B) 6
C) 8
D) 5
Correct Answer: A
Solution :
We have, \[{{n}_{1}},\]\[{{n}_{2}},\]\[{{n}_{3}},\]\[{{n}_{4}},\]\[{{n}_{5}}\] are positive integer and \[{{n}_{5}}>{{n}_{4}}>{{n}_{3}}>{{n}_{2}}>{{n}_{1}}\] |
\[\therefore \]\[{{n}_{1}}\ge 1,\]\[{{n}_{2}}\ge 2,\]\[{{n}_{3}}\ge 3,\]\[{{n}_{4}}\ge 4,\]\[{{n}_{5}}\ge 5\] |
Let \[{{n}_{1}}-1={{x}_{1}}\ge 0,\]\[{{n}_{2}}-2={{x}_{2}}\ge 0\] |
\[{{x}_{5}}-5={{x}_{5}};{{x}_{5}}\ge 0\] |
\[\therefore \]\[{{x}_{1}}+1+{{x}_{2}}+2+...+{{x}_{5}}+5=20\] |
\[\Rightarrow \]\[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}+{{x}_{5}}=5\] |
Now, \[{{x}_{1}}\le {{x}_{2}}\le {{x}_{3}}\le {{x}_{4}}\le {{x}_{5}}\] | ||||||||||||||||||||||||||||||||||||||||
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