If `a_1, a_2, a_3,54,a_6,a_7, a_8, a_9` are in H.P., and `D=|a_1a_2a_3 5 4a_6a_7a_8a_9|` , then the value of `[D]i sw h e r e[dot]` represents the greatest integer function

Answer

2

Explanation

We have `D=|{:(a_(1),,a_(2),,a_(3)),(5,,4,,a_(6)),(a_(7),,a_(8),,a_(9)):}|`
Since `a_(n)=(20)/(n): d=(1)/(20)`
`" Hence " D= |{:(20,,(20)/(2),,(20)/(3)),((20)/(4),,(20)/(5),,(20)/(6)),((20)/(7),,(20)/(8),,(20)/(9)):}|=((20)^(3))/(4xx7) |{:(1,,(1)/(2),,(1)/(3)),(1,,(4)/(5),,(2)/(3)),(1,,(7)/(8),,(7)/(9)):}|`
`R_(1) to R_(1)-R_(2) " and " R_(2) to R_(2)-R_(3)`
`=((20)^(3))/(4xx7) |{:(0,,(-3)/(10),,(-1)/(3)),(0,,(-3)/(40),,(-1)/(9)),(1,,(7)/(8),,(7)/(9)):}|=(50)/(21)`
`rArr [D] =2`