JEE Main 202227 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002If for p≠q≠0\mathrm{p} \neq \mathrm{q} \neq 0p=q=0, the function f(x)=p(729+x)7−3729+qx3−9f(x)=\frac{\sqrt[7]{\mathrm{p}(729+x)}-3}{\sqrt[3]{729+\mathrm{q} x}-9}f(x)=3729+qx−97p(729+x)−3 is continuous at x=0x=0x=0, then :AOption A. 7pq f(0)−1=07 p q \,f(0)-1=07pqf(0)−1=0BOption B. 63q f(0)−p2=063 q \,f(0)-\mathrm{p}^{2}=063qf(0)−p2=0COption C. 21q f(0)−p2=021 q \,f(0)-\mathrm{p}^{2}=021qf(0)−p2=0DOption D. 7pq f(0)−9=07 p q \,f(0)-9=07pqf(0)−9=0CheckSkip · show solution
