JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q5

MathematicsSingle correct+4 / -1Question 5 of 90

If for $p\ne q\ne0$ , the function $f(x)=\dfrac{\sqrt[7]{p(729+x)}-3}{\sqrt[3]{729+qx}-9}$ is continuous at $x=0$ , then :

7pq\,f(0)-1=0

63q\,f(0)-p^2=0

21q\,f(0)-p^2=0

7pq\,f(0)-9=0

Answer and worked solution

Official answer: B

Finite limit needs the numerator to vanish at 0: $729p=3^7$ , so $p=3$ .

Expand. The numerator is $\approx\frac{3x}{7\cdot729}$ and the denominator $\approx\frac{qx}{243}$ , so $f(0)=\frac1{7q}$ .

Check. $63q\,f(0)=9=p^2$ . (B)

Topics:Continuity Limits

JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 5