If `a ,b ,c ,d ,e ,a n df` are in G.P. then the value of `|a^2d^2x b^2e^2y c^2f^2z|` depends on `xa n dy` b. `xa n dz` c. `ya n dz` d. independent of `x ,y ,a n dz`

Options

A. x and y
B. x and z
C. y and z
D. independent of x,y and z

Answer

D

Explanation

since a,b,c ,d,e, f are in G.P. and if r is the common ration of the G.P. then
`b=ar`
`c-ar^(2)`
`d=ar^(3)`
`e=ar^(4)`
`r=ar^(5)`
Therefore given determinant is
` |{:(a_(1),,a_(2)r^(2),,x),(a_(2)r^(2),,a_(2)r^(8),,y),(a_(2)r^(4),,a_(2)r^(10),,z):}|=a^(2)a^(2)r^(7) |{:(1,,1,,x),(r_(2),,r_(2),,y),(r_(4),,r_(4),,z):}|`
`=a^(4) r^(6) (0)+0`
`[ :' C_(1) ,C_(2) " are identical ] "`