Question

Assertion :If $\int \frac{1}{f\left(x\right)}dx=2\ln \left|f\right(x\left)\right|+C$, then $f\left(x\right)=\frac{x}{2}$ Reason: When $f\left(x\right)=\frac{x}{2}$ then $\int \frac{1}{f\left(x\right)}dx=\int \frac{2}{x}dx=2\ln \left|x\right|+C$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion is incorrect but Reason are correct

Answer 1

The correct option is D Both Assertion is incorrect but Reason are correct

Solving Assertion

$\int \frac{1}{f\left(x\right)}dx=2\ln x+c$

Differentitate R.H.S w.r.t x we get

$\int \frac{1}{f\left(x\right)}dx=\int \frac{2{f\left(x\right)}^{{}^{\prime }}}{f\left(x\right)}dx1=2{f\left(x\right)}^{{}^{\prime }}$

Integrating both side w.r.t x we get

$f\left(x\right)=\frac{x}{2}+c$

Hence Assertion is wrong

Reason statement is correct but not right explanation