WBJEE 2012 Math Solved Paper

Let a be the first term and r be the common ratio of a GP.
∴ Pth, Qth and Rth terms of a GP are respectively arP−1,arQ−1 and arR−1
According to question,
arp−1=64.......(i)
arQ−1=27....(ii)
arR−1=36.......(iii)
Dividing Eq. (i) by Eq. (ii), we get
rp−Q=(‌

4

3

)3...(iv)
Dividing Eq. (ii) by Eq. (iii), we get
rQ−R=‌

3

4

⇒r3Q−3R=(‌

3

4

)3...(v)
Multiplying Eq. (iv) and Eq. (v), we get
rp−Q×r3Q−3R=1
⇒rP−Q+3Q−3R=1
⇒rP+2Q−3R=r0
⇒P+2Q−3R=0
⇒P+2Q=3R