UPSC NDA 2 2021 Mathematics Solved Paper

(a) Given that x,y,z are in GP.
⇒‌‌y2=xz
(1) If log(3x),log(3y),log(3z) are in AP
Then, 2‌log(3y)=log(3x)+log(3z)
9y2=(9xz)
9y2=(9xz)
y2=xz
Hence, statement (1) is correct.
Hence, we can say if x,y,z are in GP.
∴log‌x,log‌y,log‌z are in AP.
⇒xyz+log‌x,xyz+log‌y,xyz+log‌z are in AP.
Hence, Statement (2) is wrong.
∴ Option (a) is correct.