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

Options

A. `4`
B. `2`
C. `6`
D. `7`

Answer

B

Explanation

`(b)` 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)):}|`
Applying `R_(1)toR_(1)-R_(2)` and `R_(2)toR_(2)-R_(3)`
`=((20)^(3))/(4xx7)|{:(0,(-3)/(10),(-1)/(3)),(0,(-3)/(40),(-1)/(9)),(1,(7)/(8),(7)/(9)):}|`
`=(50)/(21)`