question_answer

P (m, n) (Where m, n are natural numbers) is an point in the interior of the quadrilateral formed by the pair of lines xy=0 and the two lines \[2x+y-2=0\] and \[4x+5y=20.\] The possible number of positions of the point P is

A) Six

B) Five

C) Four     

D) Eleven  

Correct Answer: A

Solution :

[a] It is clear from the figure m<5 and n<4 so, \[1\le m<5\] and \[2\le n\le 4\] Also \[2m+n-2>0\] and \[4m+5n-20<0.\] under these condition possible coordinates are \[(1,1),(1,2),(1,3),(2,1),(2,2),(3,2)\]