Hey!
See, as given in question no quantity is dimensionless, but ln(BD) is a dimension less quantity as natural log has no dimensions.
Which means [A] [D] =[C]
And after checking a the options, we can conclude that c option that is (A-C) /D is not a meaningful quantity as A and C has different dimensions, thus can't be subtracted from each other.
Hope it helped to clear your delimma.
Thank you
Question : In $\Delta ABC,\angle BAC=90^{\circ}$ and D is the mid-point of BC. Then which of the following relations is true?
Option 1: $AD=BD=CD$
Option 2: $AD=BD=2CD$
Option 3: $AD=2BD=CD$
Option 4: $2AD=BD=CD$
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