If 3¹⁰ × 27² = 9² × 3ⁿ then the value of n is = ?

A. 10

B. 12

C. 15

D. 30

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {{\text{3}}^{10}} \times {\text{2}}{{\text{7}}^2}{\text{ = }}{{\text{9}}^2} \times {{\text{3}}^n} \cr & \Rightarrow {{\text{3}}^{10}} \times {\left( {{3^3}} \right)^2}{\text{ = }}{\left( {{3^2}} \right)^2} \times {{\text{3}}^n} \cr & \Rightarrow {{\text{3}}^{10 + 6}}{\text{ = }}{{\text{3}}^{4 + n}} \cr & \Rightarrow 10 + 6 = 4 + n \cr & \Rightarrow n = 12 \cr} $$