The following question consist of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answer. Assertion (A) : `1//8, log_(a^(2))ato" exponent should be to the base, "log_aa^(2)" are in GP but not in AP."` Reason :(R) :x,y,z are in GP but not in AP.

Options

A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation A
C. A is true but R is false
D. A is false but R is true

Answer

A

Explanation

If x, y, z are in GP then `x.z=y^(2)`
Here `x=(1)/(8),z=log_(a)a^(2),y=(log_(a)^(2)a)`
`(1)/(8)xxlog_(a)a^(2)=(1)/(8).2=(1)/(4)`
and `(log_(a^(2))a)^(2)=((1)/(2))^(2)=(1)/(4)`
Hence, `(1)/(8),log_(a^(2))a,log_(a)a^(2)` are in GP.
Thus, both A and R are individually true and R is correct explanation of A.